Centralizers of semisimple elements in E8(q) -------------------------------------------- |G(q)| = q^120 phi1^8 phi2^8 phi3^4 phi4^4 phi5^2 phi6^4 phi7 phi8^2 phi9 phi1\ 0^2 phi12^2 phi14 phi15 phi18 phi20 phi24 phi30 Semisimple class types: i = 1: Pi = [ 1, 2, 3, 4, 5, 6, 7, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [1,1,1] Dynkin type is E_8(q) Order of center |Z^F|: 1 Numbers of classes in class type: q congruent 1 modulo 60: 1 q congruent 2 modulo 60: 1 q congruent 3 modulo 60: 1 q congruent 4 modulo 60: 1 q congruent 5 modulo 60: 1 q congruent 7 modulo 60: 1 q congruent 8 modulo 60: 1 q congruent 9 modulo 60: 1 q congruent 11 modulo 60: 1 q congruent 13 modulo 60: 1 q congruent 16 modulo 60: 1 q congruent 17 modulo 60: 1 q congruent 19 modulo 60: 1 q congruent 21 modulo 60: 1 q congruent 23 modulo 60: 1 q congruent 25 modulo 60: 1 q congruent 27 modulo 60: 1 q congruent 29 modulo 60: 1 q congruent 31 modulo 60: 1 q congruent 32 modulo 60: 1 q congruent 37 modulo 60: 1 q congruent 41 modulo 60: 1 q congruent 43 modulo 60: 1 q congruent 47 modulo 60: 1 q congruent 49 modulo 60: 1 q congruent 53 modulo 60: 1 q congruent 59 modulo 60: 1 Fusion of maximal tori of C^F in those of G^F: [ 1 .. 112 ] elements of other class types in center: [ ] i = 2: Pi = [ 1, 2, 3, 4, 5, 6, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [2,1,1] Dynkin type is E_7(q) + A_1(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1 q congruent 7 modulo 60: 1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1 q congruent 11 modulo 60: 1 q congruent 13 modulo 60: 1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1 q congruent 19 modulo 60: 1 q congruent 21 modulo 60: 1 q congruent 23 modulo 60: 1 q congruent 25 modulo 60: 1 q congruent 27 modulo 60: 1 q congruent 29 modulo 60: 1 q congruent 31 modulo 60: 1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1 q congruent 41 modulo 60: 1 q congruent 43 modulo 60: 1 q congruent 47 modulo 60: 1 q congruent 49 modulo 60: 1 q congruent 53 modulo 60: 1 q congruent 59 modulo 60: 1 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 5, 67, 3, 69, 4, 68, 7, 69, 8, 77, 12, 79, 14, 83, 16, 73, 19, 72, 20, 71, 18, 74, 19, 76, 23, 93, 31, 78, 28, 82, 33, 86, 30, 81, 38, 84, 35, 88, 40, 88, 41, 103, 43, 90, 44, 91, 46, 105, 51, 94, 59, 95, 60, 98, 57, 101, 62, 111, 67, 2, 66, 4, 68, 3, 69, 5, 68, 7, 78, 9, 80, 13, 84, 15, 74, 17, 72, 20, 70, 19, 73, 18, 76, 20, 94, 24, 77, 30, 81, 27, 85, 34, 82, 31, 83, 37, 87, 35, 87, 40, 104, 42, 89, 43, 91, 45, 106, 47, 93, 50, 96, 60, 97, 59, 102, 58, 112, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 3: Pi = [ 1, 2, 3, 4, 5, 6, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [3,1,1] Dynkin type is E_6(q) + A_2(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1 q congruent 16 modulo 60: 1 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 8, 3, 69, 27, 4, 68, 30, 12, 79, 10, 8, 77, 14, 14, 83, 12, 16, 73, 53, 19, 76, 59, 23, 93, 62, 33, 86, 29, 28, 82, 36, 35, 88, 34, 30, 81, 37, 46, 105, 48, 57, 101, 55, 66, 4, 77, 68, 7, 81, 72, 20, 95, 70, 19, 97, 77, 30, 83, 83, 37, 79, 87, 40, 85, 89, 43, 109, 93, 50, 111, 96, 60, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 1, 6)( 3, 5)( 8,240) [3,1,2] Dynkin type is ^2E_6(q) + ^2A_2(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1 q congruent 59 modulo 60: 1 Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 9, 3, 68, 28, 5, 69, 31, 13, 80, 11, 9, 78, 15, 15, 84, 13, 17, 74, 54, 20, 76, 60, 24, 94, 63, 34, 85, 29, 27, 81, 36, 35, 87, 33, 31, 82, 38, 47, 106, 49, 58, 102, 56, 67, 5, 78, 69, 7, 82, 72, 19, 96, 71, 20, 98, 78, 31, 84, 84, 38, 80, 88, 40, 86, 90, 43, 110, 94, 51, 112, 95, 59, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 4: Pi = [ 1, 2, 3, 4, 5, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [4,1,1] Dynkin type is D_5(q) + A_3(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 4 4, q congruent 1 modulo 4 1, q congruent 2 modulo 4 2, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 1 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1 q congruent 41 modulo 60: 1 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1 q congruent 53 modulo 60: 1 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 8, 70, 4, 68, 3, 30, 72, 3, 69, 5, 27, 71, 66, 4, 68, 77, 19, 70, 19, 72, 97, 18, 68, 7, 69, 81, 20, 72, 20, 71, 95, 17, 4, 68, 7, 30, 76, 16, 73, 18, 53, 75, 19, 76, 20, 59, 74, 8, 77, 30, 14, 97, 28, 82, 31, 36, 98, 30, 81, 27, 37, 95, 77, 30, 81, 83, 59, 96, 60, 98, 99, 54, 70, 19, 76, 97, 22, 89, 43, 90, 109, 45, 23, 93, 50, 62, 107 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 2, 5)( 7,240) [4,1,2] Dynkin type is ^2D_5(q) + ^2A_3(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 4 2, q congruent 1 modulo 4 1, q congruent 2 modulo 4 4, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 1 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1 q congruent 47 modulo 60: 1 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 1 Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 4, 28, 70, 5, 69, 3, 31, 72, 2, 67, 5, 9, 71, 72, 19, 70, 96, 16, 69, 7, 68, 82, 19, 71, 20, 72, 98, 18, 67, 5, 69, 78, 20, 20, 76, 19, 60, 73, 5, 69, 7, 31, 76, 17, 74, 18, 54, 75, 31, 82, 28, 38, 96, 27, 81, 30, 36, 97, 9, 78, 31, 15, 98, 78, 31, 82, 84, 60, 95, 59, 97, 99, 53, 90, 43, 89, 110, 44, 71, 20, 76, 98, 22, 24, 94, 51, 63, 108 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ] i = 5: Pi = [ 1, 2, 3, 4, 6, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [5,1,1] Dynkin type is A_4(q) + A_4(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 5 5, q congruent 1 modulo 5 1, q congruent 2 modulo 5 1, q congruent 3 modulo 5 1, q congruent 4 modulo 5 Numbers of classes in class type: q congruent 1 modulo 60: 1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 1 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 1 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 8, 77, 70, 23, 66, 4, 68, 77, 30, 19, 93, 4, 68, 7, 30, 81, 76, 50, 8, 77, 30, 14, 83, 97, 62, 77, 30, 81, 83, 37, 59, 111, 70, 19, 76, 97, 59, 22, 107, 23, 93, 50, 62, 111, 107, 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 1, 2)( 3, 4)( 6,240)( 7, 8) [5,1,2] Dynkin type is ^2A_4(q) + ^2A_4(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 5 1, q congruent 1 modulo 5 1, q congruent 2 modulo 5 1, q congruent 3 modulo 5 5, q congruent 4 modulo 5 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 1 Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 9, 78, 71, 24, 67, 5, 69, 78, 31, 20, 94, 5, 69, 7, 31, 82, 76, 51, 9, 78, 31, 15, 84, 98, 63, 78, 31, 82, 84, 38, 60, 112, 71, 20, 76, 98, 60, 22, 108, 24, 94, 51, 63, 112, 108, 26 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 3: F-action on Pi is ( 1, 6, 2,240)( 3, 7, 4, 8) [5,1,3] Dynkin type is ^2A_4(q^2) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 5 1, q congruent 1 modulo 5 5, q congruent 2 modulo 5 1, q congruent 3 modulo 5 1, q congruent 4 modulo 5 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 1 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1 q congruent 37 modulo 60: 1 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 6, 75, 22, 39, 100, 92, 52 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 4: F-action on Pi is ( 1,240, 2, 6)( 3, 8, 4, 7) [5,1,4] Dynkin type is ^2A_4(q^2) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 5 1, q congruent 1 modulo 5 1, q congruent 2 modulo 5 5, q congruent 3 modulo 5 1, q congruent 4 modulo 5 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 6, 75, 22, 39, 100, 92, 52 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 6: Pi = [ 1, 2, 3, 5, 6, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [6,1,1] Dynkin type is A_5(q) + A_2(q) + A_1(q) Order of center |Z^F|: 1 times 6, q congruent 1 modulo 6 1, q congruent 2 modulo 6 2, q congruent 3 modulo 6 3, q congruent 4 modulo 6 2, q congruent 5 modulo 6 Numbers of classes in class type: q congruent 1 modulo 60: 1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 68, 3, 7, 69, 81, 27, 8, 77, 77, 30, 14, 83, 77, 30, 30, 81, 83, 37, 14, 83, 83, 37, 12, 79, 70, 19, 19, 76, 97, 59, 19, 72, 76, 20, 59, 95, 23, 93, 93, 50, 62, 111, 87, 35, 40, 88, 85, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 1, 3)( 5,240)( 6, 8) [6,1,2] Dynkin type is ^2A_5(q) + ^2A_2(q) + A_1(q) Order of center |Z^F|: 1 times 2, q congruent 1 modulo 6 3, q congruent 2 modulo 6 2, q congruent 3 modulo 6 1, q congruent 4 modulo 6 6, q congruent 5 modulo 6 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1 q congruent 59 modulo 60: 1 Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 3, 69, 68, 7, 28, 82, 78, 9, 31, 78, 84, 15, 31, 78, 82, 31, 38, 84, 84, 15, 38, 84, 80, 13, 20, 71, 76, 20, 60, 98, 72, 20, 19, 76, 96, 60, 94, 24, 51, 94, 112, 63, 35, 88, 87, 40, 33, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ] ] i = 7: Pi = [ 1, 2, 4, 5, 6, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [7,1,1] Dynkin type is A_7(q) + A_1(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 4 4, q congruent 1 modulo 4 1, q congruent 2 modulo 4 2, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 1 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1 q congruent 41 modulo 60: 1 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1 q congruent 53 modulo 60: 1 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 4, 68, 68, 7, 3, 69, 8, 77, 77, 30, 30, 81, 14, 83, 83, 37, 70, 19, 19, 76, 72, 20, 97, 59, 18, 74, 23, 93, 93, 50, 62, 111, 87, 40, 35, 88, 41, 103, 91, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 2,240)( 4, 8)( 5, 7) [7,1,2] Dynkin type is ^2A_7(q) + A_1(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 4 2, q congruent 1 modulo 4 1, q congruent 2 modulo 4 4, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 1 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1 q congruent 47 modulo 60: 1 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 1 Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 69, 5, 7, 69, 68, 3, 78, 9, 31, 78, 82, 31, 84, 15, 38, 84, 20, 71, 76, 20, 19, 72, 60, 98, 73, 18, 94, 24, 51, 94, 112, 63, 40, 88, 87, 35, 104, 42, 44, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 8: Pi = [ 1, 3, 4, 5, 6, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [8,1,1] Dynkin type is A_8(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1 q congruent 16 modulo 60: 1 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 68, 7, 8, 77, 30, 81, 14, 83, 12, 70, 19, 76, 97, 59, 22, 23, 93, 50, 62, 107, 87, 40, 85, 41, 103, 92, 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 1,240)( 3, 8)( 4, 7)( 5, 6) [8,1,2] Dynkin type is ^2A_8(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1 q congruent 59 modulo 60: 1 Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 69, 7, 9, 78, 31, 82, 15, 84, 13, 71, 20, 76, 98, 60, 22, 24, 94, 51, 63, 108, 88, 40, 86, 42, 104, 92, 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 9: Pi = [ 2, 3, 4, 5, 6, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [9,1,1] Dynkin type is D_8(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1 q congruent 7 modulo 60: 1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1 q congruent 11 modulo 60: 1 q congruent 13 modulo 60: 1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1 q congruent 19 modulo 60: 1 q congruent 21 modulo 60: 1 q congruent 23 modulo 60: 1 q congruent 25 modulo 60: 1 q congruent 27 modulo 60: 1 q congruent 29 modulo 60: 1 q congruent 31 modulo 60: 1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1 q congruent 41 modulo 60: 1 q congruent 43 modulo 60: 1 q congruent 47 modulo 60: 1 q congruent 49 modulo 60: 1 q congruent 53 modulo 60: 1 q congruent 59 modulo 60: 1 Fusion of maximal tori of C^F in those of G^F: [ 1, 4, 3, 5, 2, 66, 70, 68, 72, 69, 71, 67, 4, 16, 19, 7, 18, 20, 5, 17, 68, 73, 76, 75, 69, 74, 3, 7, 18, 6, 8, 28, 30, 31, 27, 9, 77, 96, 82, 97, 81, 98, 78, 95, 30, 60, 53, 31, 59, 54, 14, 38, 36, 37, 15, 83, 84, 99, 70, 89, 76, 90, 71, 19, 44, 43, 22, 20, 45, 72, 76, 91, 75, 97, 110, 109, 98, 18, 22, 21, 23, 51, 50, 24, 93, 108, 94, 107, 62, 63, 87, 100, 88, 35, 40, 39, 41, 42, 91, 92 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 10: Pi = [ 1, 2, 3, 4, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [10,1,1] Dynkin type is E_7(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-3 ) q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-2 ) q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 ( q-3 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-3 ) q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 ( q-3 ) q congruent 16 modulo 60: 1/2 ( q-2 ) q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 ( q-3 ) q congruent 21 modulo 60: 1/2 ( q-3 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-3 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 ( q-3 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 ( q-3 ) q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 ( q-3 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-3 ) q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 5, 3, 4, 7, 8, 12, 14, 16, 19, 20, 18, 19, 23, 31, 28, 33, 30, 38, 35, 40, 41, 43, 44, 46, 51, 59, 60, 57, 62, 67, 66, 68, 69, 68, 78, 80, 84, 74, 72, 70, 73, 76, 94, 77, 81, 85, 82, 83, 87, 87, 104, 89, 91, 106, 93, 96, 97, 102, 112 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 2: F-action on Pi is () [10,1,2] Dynkin type is E_7(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 1/2 q q congruent 3 modulo 60: 1/2 phi1 q congruent 4 modulo 60: 1/2 q q congruent 5 modulo 60: 1/2 phi1 q congruent 7 modulo 60: 1/2 phi1 q congruent 8 modulo 60: 1/2 q q congruent 9 modulo 60: 1/2 phi1 q congruent 11 modulo 60: 1/2 phi1 q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 1/2 phi1 q congruent 19 modulo 60: 1/2 phi1 q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 phi1 q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 phi1 q congruent 29 modulo 60: 1/2 phi1 q congruent 31 modulo 60: 1/2 phi1 q congruent 32 modulo 60: 1/2 q q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 phi1 q congruent 43 modulo 60: 1/2 phi1 q congruent 47 modulo 60: 1/2 phi1 q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 1/2 phi1 q congruent 59 modulo 60: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 66, 67, 69, 68, 69, 77, 79, 83, 73, 72, 71, 74, 76, 93, 78, 82, 86, 81, 84, 88, 88, 103, 90, 91, 105, 94, 95, 98, 101, 111, 2, 4, 3, 5, 7, 9, 13, 15, 17, 20, 19, 18, 20, 24, 30, 27, 34, 31, 37, 35, 40, 42, 43, 45, 47, 50, 60, 59, 58, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 11: Pi = [ 1, 2, 3, 4, 5, 6, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [11,1,1] Dynkin type is E_6(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-5 ) q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-4 ) q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 ( q-5 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-3 ) q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 ( q-5 ) q congruent 16 modulo 60: 1/2 ( q-4 ) q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 ( q-5 ) q congruent 21 modulo 60: 1/2 ( q-3 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-5 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 ( q-5 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 ( q-5 ) q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 ( q-5 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-5 ) q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 3, 69, 4, 68, 12, 79, 8, 77, 14, 83, 16, 73, 19, 76, 23, 93, 33, 86, 28, 82, 35, 88, 30, 81, 46, 105, 57, 101, 66, 4, 68, 7, 72, 20, 70, 19, 77, 30, 83, 37, 87, 40, 89, 43, 93, 50, 96, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ] ] k = 2: F-action on Pi is (1,6)(3,5) [11,1,2] Dynkin type is ^2E_6(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 phi1 q congruent 4 modulo 60: 1/2 q q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 phi1 q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 phi1 q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 phi1 q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 phi1 q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 phi1 q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 phi1 q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 68, 3, 69, 5, 80, 13, 78, 9, 84, 15, 74, 17, 76, 20, 94, 24, 85, 34, 81, 27, 87, 35, 82, 31, 106, 47, 102, 58, 5, 67, 7, 69, 19, 72, 20, 71, 31, 78, 38, 84, 40, 88, 43, 90, 51, 94, 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ] ] i = 12: Pi = [ 1, 2, 3, 4, 5, 7, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [12,1,1] Dynkin type is D_5(q) + A_2(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-7 ) q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-4 ) q congruent 5 modulo 60: 1/2 ( q-5 ) q congruent 7 modulo 60: 1/2 ( q-5 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-5 ) q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 ( q-7 ) q congruent 16 modulo 60: 1/2 ( q-4 ) q congruent 17 modulo 60: 1/2 ( q-5 ) q congruent 19 modulo 60: 1/2 ( q-5 ) q congruent 21 modulo 60: 1/2 ( q-5 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-7 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-5 ) q congruent 31 modulo 60: 1/2 ( q-5 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 ( q-7 ) q congruent 41 modulo 60: 1/2 ( q-5 ) q congruent 43 modulo 60: 1/2 ( q-5 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-7 ) q congruent 53 modulo 60: 1/2 ( q-5 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 8, 4, 68, 30, 3, 69, 27, 66, 4, 77, 70, 19, 97, 68, 7, 81, 72, 20, 95, 4, 68, 30, 16, 73, 53, 19, 76, 59, 8, 77, 14, 28, 82, 36, 30, 81, 37, 77, 30, 83, 96, 60, 99, 70, 19, 97, 89, 43, 109, 23, 93, 62 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ] ] k = 2: F-action on Pi is (2,5)(7,8) [12,1,2] Dynkin type is ^2D_5(q) + ^2A_2(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 q q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 ( q-3 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 phi1 q congruent 11 modulo 60: 1/2 ( q-5 ) q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 ( q-3 ) q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 ( q-5 ) q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 ( q-3 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 ( q-3 ) q congruent 47 modulo 60: 1/2 ( q-5 ) q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 28, 5, 69, 31, 2, 67, 9, 72, 19, 96, 69, 7, 82, 71, 20, 98, 67, 5, 78, 20, 76, 60, 5, 69, 31, 17, 74, 54, 31, 82, 38, 27, 81, 36, 9, 78, 15, 78, 31, 84, 95, 59, 99, 90, 43, 110, 71, 20, 98, 24, 94, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ] ] i = 13: Pi = [ 1, 2, 3, 4, 5, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [13,1,1] Dynkin type is D_5(q) + A_1(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 ( q-5 ) q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 ( q-5 ) q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 ( q-5 ) q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 ( q-5 ) q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 ( q-5 ) q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 ( q-5 ) q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 ( q-5 ) q congruent 41 modulo 60: 1/4 ( q-5 ) q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 ( q-5 ) q congruent 53 modulo 60: 1/4 ( q-5 ) q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 4, 68, 68, 3, 3, 69, 69, 5, 66, 4, 4, 68, 70, 19, 19, 72, 68, 7, 7, 69, 72, 20, 20, 71, 4, 68, 68, 7, 16, 73, 73, 18, 19, 76, 76, 20, 8, 77, 77, 30, 28, 82, 82, 31, 30, 81, 81, 27, 77, 30, 30, 81, 96, 60, 60, 98, 70, 19, 19, 76, 89, 43, 43, 90, 23, 93, 93, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 7,240) [13,1,2] Dynkin type is D_5(q) + A_1(q^2) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 phi2 q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 phi2 q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 phi2 q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 phi2 q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 phi2 q congruent 47 modulo 60: 1/4 phi2 q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 3, 72, 5, 71, 68, 19, 72, 18, 69, 20, 71, 17, 7, 76, 18, 75, 20, 74, 30, 97, 31, 98, 27, 95, 81, 59, 98, 54, 76, 22, 90, 45, 50, 107 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 2, 2 ] ] k = 3: F-action on Pi is ( 2, 5)( 7,240) [13,1,3] Dynkin type is ^2D_5(q) + A_1(q^2) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 3, 72, 5, 71, 70, 16, 68, 19, 72, 18, 69, 20, 19, 73, 7, 76, 18, 75, 28, 96, 30, 97, 31, 98, 82, 60, 97, 53, 89, 44, 76, 22, 51, 108 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ] ] k = 4: F-action on Pi is (2,5) [13,1,4] Dynkin type is ^2D_5(q) + A_1(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 3, 3, 69, 69, 5, 5, 67, 67, 2, 70, 19, 19, 72, 68, 7, 7, 69, 72, 20, 20, 71, 69, 5, 5, 67, 19, 76, 76, 20, 7, 69, 69, 5, 18, 74, 74, 17, 28, 82, 82, 31, 30, 81, 81, 27, 31, 78, 78, 9, 82, 31, 31, 78, 97, 59, 59, 95, 89, 43, 43, 90, 76, 20, 20, 71, 51, 94, 94, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 2, 2 ] ] i = 14: Pi = [ 1, 2, 3, 4, 6, 7, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [14,1,1] Dynkin type is A_4(q) + A_3(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-11 ) q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-4 ) q congruent 5 modulo 60: 1/2 ( q-5 ) q congruent 7 modulo 60: 1/2 ( q-5 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-5 ) q congruent 11 modulo 60: 1/2 ( q-7 ) q congruent 13 modulo 60: 1/2 ( q-7 ) q congruent 16 modulo 60: 1/2 ( q-8 ) q congruent 17 modulo 60: 1/2 ( q-5 ) q congruent 19 modulo 60: 1/2 ( q-5 ) q congruent 21 modulo 60: 1/2 ( q-9 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-7 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-5 ) q congruent 31 modulo 60: 1/2 ( q-9 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 ( q-7 ) q congruent 41 modulo 60: 1/2 ( q-9 ) q congruent 43 modulo 60: 1/2 ( q-5 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-7 ) q congruent 53 modulo 60: 1/2 ( q-5 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 8, 70, 66, 4, 68, 77, 19, 4, 68, 7, 30, 76, 8, 77, 30, 14, 97, 77, 30, 81, 83, 59, 70, 19, 76, 97, 22, 23, 93, 50, 62, 107 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ] ] k = 2: F-action on Pi is (1,2)(3,4)(6,8) [14,1,2] Dynkin type is ^2A_4(q) + ^2A_3(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-4 ) q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 ( q-3 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-5 ) q congruent 11 modulo 60: 1/2 ( q-5 ) q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 ( q-7 ) q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 ( q-5 ) q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-7 ) q congruent 31 modulo 60: 1/2 ( q-3 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 ( q-3 ) q congruent 47 modulo 60: 1/2 ( q-5 ) q congruent 49 modulo 60: 1/2 ( q-5 ) q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 9, 71, 67, 5, 69, 78, 20, 5, 69, 7, 31, 76, 9, 78, 31, 15, 98, 78, 31, 82, 84, 60, 71, 20, 76, 98, 22, 24, 94, 51, 63, 108 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ] ] i = 15: Pi = [ 1, 2, 3, 5, 6, 7, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [15,1,1] Dynkin type is A_4(q) + A_2(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-13 ) q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-4 ) q congruent 5 modulo 60: 1/2 ( q-5 ) q congruent 7 modulo 60: 1/2 ( q-7 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-5 ) q congruent 11 modulo 60: 1/2 ( q-7 ) q congruent 13 modulo 60: 1/2 ( q-9 ) q congruent 16 modulo 60: 1/2 ( q-8 ) q congruent 17 modulo 60: 1/2 ( q-5 ) q congruent 19 modulo 60: 1/2 ( q-7 ) q congruent 21 modulo 60: 1/2 ( q-9 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-9 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-5 ) q congruent 31 modulo 60: 1/2 ( q-11 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 ( q-9 ) q congruent 41 modulo 60: 1/2 ( q-9 ) q congruent 43 modulo 60: 1/2 ( q-7 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-9 ) q congruent 53 modulo 60: 1/2 ( q-5 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 8, 77, 77, 30, 14, 83, 77, 30, 30, 81, 83, 37, 70, 19, 19, 76, 97, 59, 23, 93, 93, 50, 62, 111 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ] ] k = 2: F-action on Pi is (1,3)(5,8)(6,7) [15,1,2] Dynkin type is ^2A_4(q) + ^2A_2(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-4 ) q congruent 5 modulo 60: 1/2 ( q-5 ) q congruent 7 modulo 60: 1/2 ( q-3 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-5 ) q congruent 11 modulo 60: 1/2 ( q-7 ) q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 1/2 ( q-5 ) q congruent 19 modulo 60: 1/2 ( q-7 ) q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 ( q-7 ) q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-9 ) q congruent 31 modulo 60: 1/2 ( q-3 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 ( q-5 ) q congruent 43 modulo 60: 1/2 ( q-3 ) q congruent 47 modulo 60: 1/2 ( q-7 ) q congruent 49 modulo 60: 1/2 ( q-5 ) q congruent 53 modulo 60: 1/2 ( q-5 ) q congruent 59 modulo 60: 1/2 ( q-11 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 78, 9, 31, 78, 84, 15, 31, 78, 82, 31, 38, 84, 20, 71, 76, 20, 60, 98, 94, 24, 51, 94, 112, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ] ] i = 16: Pi = [ 1, 2, 3, 5, 6, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [16,1,1] Dynkin type is A_3(q) + A_2(q) + A_1(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q-9 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 ( q-5 ) q congruent 7 modulo 60: 1/4 ( q-7 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 ( q-5 ) q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 ( q-9 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 ( q-5 ) q congruent 19 modulo 60: 1/4 ( q-7 ) q congruent 21 modulo 60: 1/4 ( q-5 ) q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 ( q-9 ) q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 ( q-5 ) q congruent 31 modulo 60: 1/4 ( q-7 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 ( q-9 ) q congruent 41 modulo 60: 1/4 ( q-5 ) q congruent 43 modulo 60: 1/4 ( q-7 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 ( q-9 ) q congruent 53 modulo 60: 1/4 ( q-5 ) q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 8, 77, 77, 30, 66, 4, 4, 68, 4, 68, 68, 7, 77, 30, 30, 81, 4, 68, 68, 3, 68, 7, 7, 69, 30, 81, 81, 27, 8, 77, 77, 30, 77, 30, 30, 81, 14, 83, 83, 37, 70, 19, 19, 72, 19, 76, 76, 20, 97, 59, 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 2,240)( 5, 7) [16,1,2] Dynkin type is ^2A_3(q) + A_2(q) + A_1(q^2) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 69, 20, 27, 95, 68, 19, 7, 76, 81, 59, 4, 70, 68, 19, 30, 97, 28, 96, 82, 60, 36, 99, 70, 16, 19, 73, 97, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ] ] k = 3: F-action on Pi is (1,3)(5,7) [16,1,3] Dynkin type is ^2A_3(q) + ^2A_2(q) + A_1(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 ( q-5 ) q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 ( q-7 ) q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 ( q-5 ) q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 ( q-7 ) q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 ( q-5 ) q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 ( q-5 ) q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-7 ) q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 ( q-5 ) q congruent 59 modulo 60: 1/4 ( q-7 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 67, 2, 69, 5, 5, 67, 31, 78, 78, 9, 69, 5, 5, 67, 7, 69, 69, 5, 82, 31, 31, 78, 3, 69, 69, 5, 68, 7, 7, 69, 28, 82, 82, 31, 31, 78, 78, 9, 82, 31, 31, 78, 38, 84, 84, 15, 72, 20, 20, 71, 19, 76, 76, 20, 96, 60, 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ] ] k = 4: F-action on Pi is ( 1, 3)( 2,240) [16,1,4] Dynkin type is A_3(q) + ^2A_2(q) + A_1(q^2) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 phi2 q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 phi2 q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 phi2 q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 phi2 q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 phi2 q congruent 47 modulo 60: 1/4 phi2 q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 68, 19, 28, 96, 69, 20, 7, 76, 82, 60, 5, 71, 69, 20, 31, 98, 27, 95, 81, 59, 36, 99, 71, 17, 20, 74, 98, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ] ] i = 17: Pi = [ 1, 2, 3, 5, 6, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [17,1,1] Dynkin type is A_2(q) + A_2(q) + A_2(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 ( q-7 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/6 ( q-4 ) q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/6 ( q-7 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/6 ( q-7 ) q congruent 16 modulo 60: 1/6 ( q-4 ) q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/6 ( q-7 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/6 ( q-7 ) q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/6 ( q-7 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/6 ( q-7 ) q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/6 ( q-7 ) q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/6 ( q-7 ) q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 8, 77, 77, 30, 14, 83, 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 77, 30, 30, 81, 83, 37, 8, 77, 77, 30, 14, 83, 77, 30, 30, 81, 83, 37, 14, 83, 83, 37, 12, 79 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], [ 11, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 5, 8)( 6,240) [17,1,2] Dynkin type is A_2(q) + A_2(q^2) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/2 q q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/2 phi1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/2 phi1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/2 phi1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/2 phi1 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 68, 3, 19, 72, 87, 35, 7, 69, 76, 20, 40, 88, 81, 27, 59, 95, 85, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 11, 1, 2, 2 ] ] k = 3: F-action on Pi is ( 1, 3)( 5,240)( 6, 8) [17,1,3] Dynkin type is ^2A_2(q) + A_2(q^2) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 72, 20, 35, 88, 68, 7, 19, 76, 87, 40, 28, 82, 96, 60, 33, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 11, 1, 1, 2 ] ] k = 4: F-action on Pi is ( 1, 3)( 5, 6)( 8,240) [17,1,4] Dynkin type is ^2A_2(q) + ^2A_2(q) + ^2A_2(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/6 ( q-2 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/6 ( q-5 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/6 ( q-2 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/6 ( q-5 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/6 ( q-5 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/6 ( q-5 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/6 ( q-5 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/6 ( q-2 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/6 ( q-5 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/6 ( q-5 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/6 ( q-5 ) q congruent 59 modulo 60: 1/6 ( q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 78, 9, 31, 78, 84, 15, 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 31, 78, 82, 31, 38, 84, 78, 9, 31, 78, 84, 15, 31, 78, 82, 31, 38, 84, 84, 15, 38, 84, 80, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], [ 11, 1, 2, 2 ] ] k = 5: F-action on Pi is ( 1, 5, 8)( 3, 6,240) [17,1,5] Dynkin type is A_2(q^3) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/3 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/3 phi1 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/3 phi1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/3 phi1 q congruent 16 modulo 60: 1/3 phi1 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/3 phi1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/3 phi1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/3 phi1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/3 phi1 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/3 phi1 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/3 phi1 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 14, 83, 87, 40, 46, 105 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 2 ] ] k = 6: F-action on Pi is ( 1, 6, 8, 3, 5,240) [17,1,6] Dynkin type is ^2A_2(q^3) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/3 phi2 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/3 phi2 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/3 phi2 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/3 phi2 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/3 phi2 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/3 phi2 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/3 phi2 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/3 phi2 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/3 phi2 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/3 phi2 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/3 phi2 q congruent 59 modulo 60: 1/3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 84, 15, 40, 88, 106, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 2 ] ] i = 18: Pi = [ 1, 2, 4, 5, 6, 7, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [18,1,1] Dynkin type is A_6(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-7 ) q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-4 ) q congruent 5 modulo 60: 1/2 ( q-5 ) q congruent 7 modulo 60: 1/2 ( q-5 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-5 ) q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 ( q-7 ) q congruent 16 modulo 60: 1/2 ( q-4 ) q congruent 17 modulo 60: 1/2 ( q-5 ) q congruent 19 modulo 60: 1/2 ( q-5 ) q congruent 21 modulo 60: 1/2 ( q-5 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-7 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-5 ) q congruent 31 modulo 60: 1/2 ( q-5 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 ( q-7 ) q congruent 41 modulo 60: 1/2 ( q-5 ) q congruent 43 modulo 60: 1/2 ( q-5 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-7 ) q congruent 53 modulo 60: 1/2 ( q-5 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 4, 68, 68, 7, 8, 77, 77, 30, 30, 81, 14, 83, 70, 19, 19, 76, 97, 59, 23, 93, 93, 50, 87, 40, 41, 103 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ] ] k = 2: F-action on Pi is (2,8)(4,7)(5,6) [18,1,2] Dynkin type is ^2A_6(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 q q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 ( q-3 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 phi1 q congruent 11 modulo 60: 1/2 ( q-5 ) q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 ( q-3 ) q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 ( q-5 ) q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 ( q-3 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 ( q-3 ) q congruent 47 modulo 60: 1/2 ( q-5 ) q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 69, 5, 7, 69, 78, 9, 31, 78, 82, 31, 84, 15, 20, 71, 76, 20, 60, 98, 94, 24, 51, 94, 40, 88, 104, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ] ] i = 19: Pi = [ 1, 2, 4, 5, 6, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [19,1,1] Dynkin type is A_5(q) + A_1(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-7 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/2 ( q-5 ) q congruent 7 modulo 60: 1/2 ( q-5 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/2 ( q-5 ) q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 ( q-7 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/2 ( q-5 ) q congruent 19 modulo 60: 1/2 ( q-5 ) q congruent 21 modulo 60: 1/2 ( q-5 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-7 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-5 ) q congruent 31 modulo 60: 1/2 ( q-5 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/2 ( q-7 ) q congruent 41 modulo 60: 1/2 ( q-5 ) q congruent 43 modulo 60: 1/2 ( q-5 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-7 ) q congruent 53 modulo 60: 1/2 ( q-5 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 4, 68, 68, 7, 68, 3, 7, 69, 8, 77, 77, 30, 77, 30, 30, 81, 14, 83, 83, 37, 70, 19, 19, 76, 19, 72, 76, 20, 23, 93, 93, 50, 87, 35, 40, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 2 ] ] k = 2: F-action on Pi is (2,7)(4,6) [19,1,2] Dynkin type is ^2A_5(q) + A_1(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/2 phi1 q congruent 11 modulo 60: 1/2 ( q-5 ) q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 ( q-3 ) q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 ( q-5 ) q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 ( q-3 ) q congruent 47 modulo 60: 1/2 ( q-5 ) q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 67, 2, 69, 5, 5, 67, 7, 69, 69, 5, 68, 7, 3, 69, 31, 78, 78, 9, 82, 31, 31, 78, 38, 84, 84, 15, 76, 20, 20, 71, 19, 76, 72, 20, 51, 94, 94, 24, 87, 40, 35, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 2, 2 ] ] i = 20: Pi = [ 1, 2, 4, 5, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [20,1,1] Dynkin type is A_3(q) + A_3(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 4 4, q congruent 1 modulo 4 1, q congruent 2 modulo 4 2, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 ( q-5 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 ( q-5 ) q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/4 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 ( q-5 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 1/4 ( q-5 ) q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/4 ( q-5 ) q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/4 ( q-5 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 ( q-5 ) q congruent 41 modulo 60: 1/4 ( q-5 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/4 ( q-5 ) q congruent 53 modulo 60: 1/4 ( q-5 ) q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 4, 68, 8, 77, 70, 19, 66, 4, 4, 68, 68, 7, 77, 30, 19, 76, 4, 68, 68, 7, 3, 69, 30, 81, 72, 20, 8, 77, 77, 30, 30, 81, 14, 83, 97, 59, 70, 19, 19, 76, 72, 20, 97, 59, 18, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 24, 1, 1, 2 ] ] k = 2: F-action on Pi is () [20,1,2] Dynkin type is A_3(q) + A_3(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 4 4, q congruent 1 modulo 4 1, q congruent 2 modulo 4 2, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 68, 3, 77, 30, 19, 72, 4, 68, 68, 7, 7, 69, 30, 81, 76, 20, 68, 3, 7, 69, 69, 5, 81, 27, 20, 71, 77, 30, 30, 81, 81, 27, 83, 37, 59, 95, 19, 72, 76, 20, 20, 71, 59, 95, 74, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 24, 1, 2, 2 ] ] k = 3: F-action on Pi is ( 2, 5)( 7,240) [20,1,3] Dynkin type is ^2A_3(q) + ^2A_3(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 4 2, q congruent 1 modulo 4 1, q congruent 2 modulo 4 4, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 69, 5, 3, 69, 31, 78, 72, 20, 69, 5, 7, 69, 68, 7, 82, 31, 19, 76, 3, 69, 68, 7, 4, 68, 28, 82, 70, 19, 31, 78, 82, 31, 28, 82, 38, 84, 96, 60, 72, 20, 19, 76, 70, 19, 96, 60, 16, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 24, 1, 1, 2 ] ] k = 4: F-action on Pi is ( 2, 5)( 7,240) [20,1,4] Dynkin type is ^2A_3(q) + ^2A_3(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 4 2, q congruent 1 modulo 4 1, q congruent 2 modulo 4 4, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 69, 5, 78, 9, 20, 71, 5, 67, 69, 5, 7, 69, 31, 78, 76, 20, 69, 5, 7, 69, 68, 3, 82, 31, 19, 72, 78, 9, 31, 78, 82, 31, 84, 15, 60, 98, 20, 71, 76, 20, 19, 72, 60, 98, 73, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 24, 1, 2, 2 ] ] k = 5: F-action on Pi is ( 2, 7)( 4, 8)( 5,240) [20,1,5] Dynkin type is A_3(q^2) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 4 4, q congruent 1 modulo 4 1, q congruent 2 modulo 4 2, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 72, 20, 18, 74, 35, 88, 91, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 24, 1, 2, 2 ] ] k = 6: F-action on Pi is ( 2, 7)( 4, 8)( 5,240) [20,1,6] Dynkin type is A_3(q^2) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 4 4, q congruent 1 modulo 4 1, q congruent 2 modulo 4 2, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 19, 76, 73, 18, 87, 40, 44, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 24, 1, 1, 2 ] ] k = 7: F-action on Pi is ( 2,240)( 4, 8)( 5, 7) [20,1,7] Dynkin type is A_3(q^2) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 4 2, q congruent 1 modulo 4 1, q congruent 2 modulo 4 4, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/4 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/4 phi2 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/4 phi2 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/4 phi2 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 1/4 phi2 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/4 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/4 phi2 q congruent 47 modulo 60: 1/4 phi2 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 1/4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 7, 69, 76, 20, 18, 74, 40, 88, 91, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 24, 1, 2, 2 ] ] k = 8: F-action on Pi is ( 2,240)( 4, 8)( 5, 7) [20,1,8] Dynkin type is A_3(q^2) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 4 2, q congruent 1 modulo 4 1, q congruent 2 modulo 4 4, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 3, 19, 72, 73, 18, 87, 35, 44, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 24, 1, 1, 2 ] ] i = 21: Pi = [ 1, 3, 4, 5, 6, 7, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [21,1,1] Dynkin type is A_7(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-5 ) q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-4 ) q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 ( q-5 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-3 ) q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 ( q-5 ) q congruent 16 modulo 60: 1/2 ( q-4 ) q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 ( q-5 ) q congruent 21 modulo 60: 1/2 ( q-3 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-5 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 ( q-5 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 ( q-5 ) q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 ( q-5 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-5 ) q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 68, 7, 8, 77, 30, 14, 83, 70, 19, 76, 97, 22, 23, 93, 62, 87, 40, 41, 92 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ] ] k = 2: F-action on Pi is (1,8)(3,7)(4,6) [21,1,2] Dynkin type is ^2A_7(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 phi1 q congruent 4 modulo 60: 1/2 q q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 phi1 q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 phi1 q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 phi1 q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 phi1 q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 phi1 q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 phi1 q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 69, 7, 9, 78, 31, 15, 84, 71, 20, 76, 98, 22, 24, 94, 63, 88, 40, 42, 92 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ] ] i = 22: Pi = [ 1, 3, 4, 5, 6, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [22,1,1] Dynkin type is A_5(q) + A_2(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/2 ( q-4 ) q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/2 ( q-5 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/2 ( q-5 ) q congruent 16 modulo 60: 1/2 ( q-4 ) q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/2 ( q-5 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/2 ( q-5 ) q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/2 ( q-5 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/2 ( q-5 ) q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/2 ( q-5 ) q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/2 ( q-5 ) q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 8, 66, 4, 77, 4, 68, 30, 68, 7, 81, 8, 77, 14, 77, 30, 83, 14, 83, 12, 70, 19, 97, 19, 76, 59, 23, 93, 62, 87, 40, 85 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ] ] k = 2: F-action on Pi is () [22,1,2] Dynkin type is A_5(q) + A_2(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/2 q q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/2 phi1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/2 phi1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/2 phi1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/2 phi1 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 77, 4, 68, 30, 68, 7, 81, 3, 69, 27, 77, 30, 83, 30, 81, 37, 83, 37, 79, 19, 76, 59, 72, 20, 95, 93, 50, 111, 35, 88, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 10, 1, 2, 2 ] ] k = 3: F-action on Pi is ( 1, 6)( 3, 5)( 8,240) [22,1,3] Dynkin type is ^2A_5(q) + ^2A_2(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 78, 5, 69, 31, 69, 7, 82, 3, 68, 28, 78, 31, 84, 31, 82, 38, 84, 38, 80, 20, 76, 60, 72, 19, 96, 94, 51, 112, 35, 87, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 10, 1, 1, 2 ] ] k = 4: F-action on Pi is ( 1, 6)( 3, 5)( 8,240) [22,1,4] Dynkin type is ^2A_5(q) + ^2A_2(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 9, 67, 5, 78, 5, 69, 31, 69, 7, 82, 9, 78, 15, 78, 31, 84, 15, 84, 13, 71, 20, 98, 20, 76, 60, 24, 94, 63, 88, 40, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ] ] i = 23: Pi = [ 2, 3, 4, 5, 6, 7, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [23,1,1] Dynkin type is D_7(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-3 ) q congruent 2 modulo 60: 1/2 ( q-2 ) q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 1/2 ( q-2 ) q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 ( q-3 ) q congruent 8 modulo 60: 1/2 ( q-2 ) q congruent 9 modulo 60: 1/2 ( q-3 ) q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 ( q-3 ) q congruent 16 modulo 60: 1/2 ( q-2 ) q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 ( q-3 ) q congruent 21 modulo 60: 1/2 ( q-3 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-3 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 ( q-3 ) q congruent 32 modulo 60: 1/2 ( q-2 ) q congruent 37 modulo 60: 1/2 ( q-3 ) q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 ( q-3 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-3 ) q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 4, 3, 5, 66, 70, 68, 72, 69, 71, 4, 16, 19, 7, 18, 20, 68, 73, 76, 75, 8, 28, 30, 31, 27, 77, 96, 82, 97, 81, 98, 30, 60, 53, 14, 38, 36, 70, 89, 76, 90, 19, 44, 43, 22, 97, 110, 23, 51, 50, 93, 108, 87, 100, 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ] k = 2: F-action on Pi is (2,3) [23,1,2] Dynkin type is ^2D_7(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 1/2 q q congruent 3 modulo 60: 1/2 phi1 q congruent 4 modulo 60: 1/2 q q congruent 5 modulo 60: 1/2 phi1 q congruent 7 modulo 60: 1/2 phi1 q congruent 8 modulo 60: 1/2 q q congruent 9 modulo 60: 1/2 phi1 q congruent 11 modulo 60: 1/2 phi1 q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 1/2 q q congruent 17 modulo 60: 1/2 phi1 q congruent 19 modulo 60: 1/2 phi1 q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 phi1 q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 phi1 q congruent 29 modulo 60: 1/2 phi1 q congruent 31 modulo 60: 1/2 phi1 q congruent 32 modulo 60: 1/2 q q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 phi1 q congruent 43 modulo 60: 1/2 phi1 q congruent 47 modulo 60: 1/2 phi1 q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 1/2 phi1 q congruent 59 modulo 60: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 4, 3, 5, 2, 70, 68, 72, 69, 71, 67, 19, 7, 18, 20, 5, 17, 76, 75, 69, 74, 28, 30, 31, 27, 9, 82, 97, 81, 98, 78, 95, 31, 59, 54, 36, 37, 15, 89, 76, 90, 71, 43, 22, 20, 45, 109, 98, 51, 50, 24, 94, 107, 100, 88, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ] i = 24: Pi = [ 2, 3, 4, 5, 6, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [24,1,1] Dynkin type is D_6(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/2 ( q-3 ) q congruent 7 modulo 60: 1/2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/2 ( q-3 ) q congruent 11 modulo 60: 1/2 ( q-3 ) q congruent 13 modulo 60: 1/2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/2 ( q-3 ) q congruent 19 modulo 60: 1/2 ( q-3 ) q congruent 21 modulo 60: 1/2 ( q-3 ) q congruent 23 modulo 60: 1/2 ( q-3 ) q congruent 25 modulo 60: 1/2 ( q-3 ) q congruent 27 modulo 60: 1/2 ( q-3 ) q congruent 29 modulo 60: 1/2 ( q-3 ) q congruent 31 modulo 60: 1/2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/2 ( q-3 ) q congruent 41 modulo 60: 1/2 ( q-3 ) q congruent 43 modulo 60: 1/2 ( q-3 ) q congruent 47 modulo 60: 1/2 ( q-3 ) q congruent 49 modulo 60: 1/2 ( q-3 ) q congruent 53 modulo 60: 1/2 ( q-3 ) q congruent 59 modulo 60: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 68, 3, 69, 5, 67, 66, 4, 70, 19, 68, 7, 72, 20, 69, 5, 4, 68, 16, 73, 19, 76, 7, 69, 18, 74, 68, 3, 68, 7, 73, 18, 8, 77, 28, 82, 30, 81, 31, 78, 77, 30, 96, 60, 82, 31, 97, 59, 14, 83, 38, 84, 70, 19, 89, 43, 76, 20, 19, 72, 19, 76, 44, 91, 23, 93, 51, 94, 87, 35, 87, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ] ] k = 2: F-action on Pi is () [24,1,2] Dynkin type is D_6(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/2 phi1 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/2 phi1 q congruent 7 modulo 60: 1/2 phi1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/2 phi1 q congruent 11 modulo 60: 1/2 phi1 q congruent 13 modulo 60: 1/2 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/2 phi1 q congruent 19 modulo 60: 1/2 phi1 q congruent 21 modulo 60: 1/2 phi1 q congruent 23 modulo 60: 1/2 phi1 q congruent 25 modulo 60: 1/2 phi1 q congruent 27 modulo 60: 1/2 phi1 q congruent 29 modulo 60: 1/2 phi1 q congruent 31 modulo 60: 1/2 phi1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/2 phi1 q congruent 41 modulo 60: 1/2 phi1 q congruent 43 modulo 60: 1/2 phi1 q congruent 47 modulo 60: 1/2 phi1 q congruent 49 modulo 60: 1/2 phi1 q congruent 53 modulo 60: 1/2 phi1 q congruent 59 modulo 60: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 3, 69, 5, 67, 2, 4, 68, 19, 72, 7, 69, 20, 71, 5, 67, 68, 7, 73, 18, 76, 20, 69, 5, 74, 17, 7, 69, 3, 69, 18, 74, 77, 30, 82, 31, 81, 27, 78, 9, 30, 81, 60, 98, 31, 78, 59, 95, 83, 37, 84, 15, 19, 76, 43, 90, 20, 71, 76, 20, 72, 20, 91, 45, 93, 50, 94, 24, 40, 88, 35, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ] ] i = 25: Pi = [ 2, 3, 4, 5, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [25,1,1] Dynkin type is D_4(q) + A_3(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 ( q-5 ) q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 ( q-5 ) q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 ( q-5 ) q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 ( q-5 ) q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 ( q-5 ) q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 ( q-5 ) q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 ( q-5 ) q congruent 41 modulo 60: 1/4 ( q-5 ) q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 ( q-5 ) q congruent 53 modulo 60: 1/4 ( q-5 ) q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 8, 70, 4, 68, 7, 30, 76, 3, 69, 5, 27, 71, 66, 4, 68, 77, 19, 70, 19, 76, 97, 22, 68, 7, 69, 81, 20, 4, 68, 3, 30, 72, 4, 68, 7, 30, 76, 16, 73, 18, 53, 75, 8, 77, 30, 14, 97, 28, 82, 31, 36, 98, 70, 19, 72, 97, 18, 70, 19, 76, 97, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 2, 5)( 7,240) [25,1,2] Dynkin type is ^2D_4(q) + ^2A_3(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 4, 28, 70, 5, 69, 3, 31, 72, 72, 19, 70, 96, 16, 69, 7, 68, 82, 19, 71, 20, 72, 98, 18, 20, 76, 19, 60, 73, 31, 82, 28, 38, 96, 27, 81, 30, 36, 97, 90, 43, 89, 110, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ] ] k = 3: F-action on Pi is ( 7,240) [25,1,3] Dynkin type is D_4(q) + ^2A_3(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 4, 28, 70, 5, 69, 7, 31, 76, 2, 67, 5, 9, 71, 69, 7, 68, 82, 19, 71, 20, 76, 98, 22, 67, 5, 69, 78, 20, 5, 69, 3, 31, 72, 5, 69, 7, 31, 76, 17, 74, 18, 54, 75, 27, 81, 30, 36, 97, 9, 78, 31, 15, 98, 71, 20, 72, 98, 18, 71, 20, 76, 98, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 2, 2 ] ] k = 4: F-action on Pi is (2,5) [25,1,4] Dynkin type is ^2D_4(q) + A_3(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 phi2 q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 phi2 q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 phi2 q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 phi2 q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 phi2 q congruent 47 modulo 60: 1/4 phi2 q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 3, 30, 72, 3, 69, 5, 27, 71, 70, 19, 72, 97, 18, 68, 7, 69, 81, 20, 72, 20, 71, 95, 17, 19, 76, 20, 59, 74, 28, 82, 31, 36, 98, 30, 81, 27, 37, 95, 89, 43, 90, 109, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 2, 2 ] ] i = 26: Pi = [ 2, 4, 5, 6, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [26,1,1] Dynkin type is A_7(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 ( q-5 ) q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 ( q-5 ) q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 ( q-5 ) q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 ( q-5 ) q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 ( q-5 ) q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 ( q-5 ) q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 ( q-5 ) q congruent 41 modulo 60: 1/4 ( q-5 ) q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 ( q-5 ) q congruent 53 modulo 60: 1/4 ( q-5 ) q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 68, 3, 8, 77, 30, 14, 83, 70, 19, 72, 97, 18, 23, 93, 62, 87, 35, 41, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 2,240)( 4, 8)( 5, 7) [26,1,2] Dynkin type is ^2A_7(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 69, 7, 68, 78, 31, 82, 84, 38, 20, 76, 19, 60, 73, 94, 51, 112, 40, 87, 104, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 2 ] ] k = 3: F-action on Pi is () [26,1,3] Dynkin type is A_7(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 phi2 q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 phi2 q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 phi2 q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 phi2 q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 phi2 q congruent 47 modulo 60: 1/4 phi2 q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 7, 69, 77, 30, 81, 83, 37, 19, 76, 20, 59, 74, 93, 50, 111, 40, 88, 103, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 10, 1, 2, 2 ] ] k = 4: F-action on Pi is ( 2,240)( 4, 8)( 5, 7) [26,1,4] Dynkin type is ^2A_7(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 q congruent 7 modulo 60: 1/4 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 q congruent 11 modulo 60: 1/4 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 q congruent 19 modulo 60: 1/4 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 q congruent 23 modulo 60: 1/4 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 q congruent 27 modulo 60: 1/4 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 q congruent 31 modulo 60: 1/4 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 q congruent 41 modulo 60: 1/4 phi1 q congruent 43 modulo 60: 1/4 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 q congruent 53 modulo 60: 1/4 phi1 q congruent 59 modulo 60: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 69, 3, 9, 78, 31, 15, 84, 71, 20, 72, 98, 18, 24, 94, 63, 88, 35, 42, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ] ] i = 27: Pi = [ 1, 2, 3, 4, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [27,1,1] Dynkin type is E_6(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 ( q^2-8*q+19 ) q congruent 2 modulo 60: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/12 ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/12 ( q^2-8*q+19 ) q congruent 8 modulo 60: 1/12 ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/12 ( q^2-8*q+19 ) q congruent 16 modulo 60: 1/12 ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/12 ( q^2-8*q+19 ) q congruent 21 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/12 ( q^2-8*q+19 ) q congruent 27 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/12 ( q^2-8*q+19 ) q congruent 32 modulo 60: 1/12 ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/12 ( q^2-8*q+19 ) q congruent 41 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/12 ( q^2-8*q+19 ) q congruent 47 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/12 ( q^2-8*q+19 ) q congruent 53 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/12 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 3, 4, 12, 8, 14, 16, 19, 23, 33, 28, 35, 30, 46, 57, 66, 68, 72, 70, 77, 83, 87, 89, 93, 96 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ] ] k = 2: F-action on Pi is () [27,1,2] Dynkin type is E_6(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1^2 q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1^2 q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1^2 q congruent 7 modulo 60: 1/4 phi1^2 q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1^2 q congruent 11 modulo 60: 1/4 phi1^2 q congruent 13 modulo 60: 1/4 phi1^2 q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1^2 q congruent 19 modulo 60: 1/4 phi1^2 q congruent 21 modulo 60: 1/4 phi1^2 q congruent 23 modulo 60: 1/4 phi1^2 q congruent 25 modulo 60: 1/4 phi1^2 q congruent 27 modulo 60: 1/4 phi1^2 q congruent 29 modulo 60: 1/4 phi1^2 q congruent 31 modulo 60: 1/4 phi1^2 q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1^2 q congruent 41 modulo 60: 1/4 phi1^2 q congruent 43 modulo 60: 1/4 phi1^2 q congruent 47 modulo 60: 1/4 phi1^2 q congruent 49 modulo 60: 1/4 phi1^2 q congruent 53 modulo 60: 1/4 phi1^2 q congruent 59 modulo 60: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 66, 69, 68, 79, 77, 83, 73, 76, 93, 86, 82, 88, 81, 105, 101, 4, 7, 20, 19, 30, 37, 40, 43, 50, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ] ] k = 3: F-action on Pi is (1,6)(3,5) [27,1,3] Dynkin type is ^2E_6(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1^2 q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1^2 q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1^2 q congruent 7 modulo 60: 1/4 phi1^2 q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1^2 q congruent 11 modulo 60: 1/4 phi1^2 q congruent 13 modulo 60: 1/4 phi1^2 q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1^2 q congruent 19 modulo 60: 1/4 phi1^2 q congruent 21 modulo 60: 1/4 phi1^2 q congruent 23 modulo 60: 1/4 phi1^2 q congruent 25 modulo 60: 1/4 phi1^2 q congruent 27 modulo 60: 1/4 phi1^2 q congruent 29 modulo 60: 1/4 phi1^2 q congruent 31 modulo 60: 1/4 phi1^2 q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1^2 q congruent 41 modulo 60: 1/4 phi1^2 q congruent 43 modulo 60: 1/4 phi1^2 q congruent 47 modulo 60: 1/4 phi1^2 q congruent 49 modulo 60: 1/4 phi1^2 q congruent 53 modulo 60: 1/4 phi1^2 q congruent 59 modulo 60: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 67, 68, 69, 80, 78, 84, 74, 76, 94, 85, 81, 87, 82, 106, 102, 5, 7, 19, 20, 31, 38, 40, 43, 51, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ] ] k = 4: F-action on Pi is (1,6)(3,5) [27,1,4] Dynkin type is ^2E_6(q) + T(phi6) Order of center |Z^F|: phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q phi1 q congruent 2 modulo 60: 1/6 phi2 ( q-2 ) q congruent 3 modulo 60: 1/6 q phi1 q congruent 4 modulo 60: 1/6 q phi1 q congruent 5 modulo 60: 1/6 phi2 ( q-2 ) q congruent 7 modulo 60: 1/6 q phi1 q congruent 8 modulo 60: 1/6 phi2 ( q-2 ) q congruent 9 modulo 60: 1/6 q phi1 q congruent 11 modulo 60: 1/6 phi2 ( q-2 ) q congruent 13 modulo 60: 1/6 q phi1 q congruent 16 modulo 60: 1/6 q phi1 q congruent 17 modulo 60: 1/6 phi2 ( q-2 ) q congruent 19 modulo 60: 1/6 q phi1 q congruent 21 modulo 60: 1/6 q phi1 q congruent 23 modulo 60: 1/6 phi2 ( q-2 ) q congruent 25 modulo 60: 1/6 q phi1 q congruent 27 modulo 60: 1/6 q phi1 q congruent 29 modulo 60: 1/6 phi2 ( q-2 ) q congruent 31 modulo 60: 1/6 q phi1 q congruent 32 modulo 60: 1/6 phi2 ( q-2 ) q congruent 37 modulo 60: 1/6 q phi1 q congruent 41 modulo 60: 1/6 phi2 ( q-2 ) q congruent 43 modulo 60: 1/6 q phi1 q congruent 47 modulo 60: 1/6 phi2 ( q-2 ) q congruent 49 modulo 60: 1/6 q phi1 q congruent 53 modulo 60: 1/6 phi2 ( q-2 ) q congruent 59 modulo 60: 1/6 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 28, 31, 11, 15, 13, 54, 60, 63, 29, 36, 33, 38, 49, 56, 78, 82, 96, 98, 84, 80, 86, 110, 112, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ] ] k = 5: F-action on Pi is () [27,1,5] Dynkin type is E_6(q) + T(phi3) Order of center |Z^F|: phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 phi1 ( q+2 ) q congruent 2 modulo 60: 1/6 q phi2 q congruent 3 modulo 60: 1/6 q phi2 q congruent 4 modulo 60: 1/6 phi1 ( q+2 ) q congruent 5 modulo 60: 1/6 q phi2 q congruent 7 modulo 60: 1/6 phi1 ( q+2 ) q congruent 8 modulo 60: 1/6 q phi2 q congruent 9 modulo 60: 1/6 q phi2 q congruent 11 modulo 60: 1/6 q phi2 q congruent 13 modulo 60: 1/6 phi1 ( q+2 ) q congruent 16 modulo 60: 1/6 phi1 ( q+2 ) q congruent 17 modulo 60: 1/6 q phi2 q congruent 19 modulo 60: 1/6 phi1 ( q+2 ) q congruent 21 modulo 60: 1/6 q phi2 q congruent 23 modulo 60: 1/6 q phi2 q congruent 25 modulo 60: 1/6 phi1 ( q+2 ) q congruent 27 modulo 60: 1/6 q phi2 q congruent 29 modulo 60: 1/6 q phi2 q congruent 31 modulo 60: 1/6 phi1 ( q+2 ) q congruent 32 modulo 60: 1/6 q phi2 q congruent 37 modulo 60: 1/6 phi1 ( q+2 ) q congruent 41 modulo 60: 1/6 q phi2 q congruent 43 modulo 60: 1/6 phi1 ( q+2 ) q congruent 47 modulo 60: 1/6 q phi2 q congruent 49 modulo 60: 1/6 phi1 ( q+2 ) q congruent 53 modulo 60: 1/6 q phi2 q congruent 59 modulo 60: 1/6 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 8, 27, 30, 10, 14, 12, 53, 59, 62, 29, 36, 34, 37, 48, 55, 77, 81, 95, 97, 83, 79, 85, 109, 111, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ] ] k = 6: F-action on Pi is (1,6)(3,5) [27,1,6] Dynkin type is ^2E_6(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q-3 ) q congruent 2 modulo 60: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/12 phi1 ( q-3 ) q congruent 4 modulo 60: 1/12 q ( q-4 ) q congruent 5 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 7 modulo 60: 1/12 phi1 ( q-3 ) q congruent 8 modulo 60: 1/12 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/12 phi1 ( q-3 ) q congruent 11 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 13 modulo 60: 1/12 phi1 ( q-3 ) q congruent 16 modulo 60: 1/12 q ( q-4 ) q congruent 17 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 19 modulo 60: 1/12 phi1 ( q-3 ) q congruent 21 modulo 60: 1/12 phi1 ( q-3 ) q congruent 23 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 25 modulo 60: 1/12 phi1 ( q-3 ) q congruent 27 modulo 60: 1/12 phi1 ( q-3 ) q congruent 29 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 31 modulo 60: 1/12 phi1 ( q-3 ) q congruent 32 modulo 60: 1/12 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/12 phi1 ( q-3 ) q congruent 41 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 43 modulo 60: 1/12 phi1 ( q-3 ) q congruent 47 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 49 modulo 60: 1/12 phi1 ( q-3 ) q congruent 53 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 59 modulo 60: 1/12 ( q^2-4*q+7 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 3, 5, 13, 9, 15, 17, 20, 24, 34, 27, 35, 31, 47, 58, 67, 69, 72, 71, 78, 84, 88, 90, 94, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ] ] i = 28: Pi = [ 1, 2, 3, 4, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [28,1,1] Dynkin type is D_5(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q^2-10*q+29 ) q congruent 2 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 4 modulo 60: 1/4 ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 7 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 8 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 11 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 13 modulo 60: 1/4 ( q^2-10*q+29 ) q congruent 16 modulo 60: 1/4 ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 19 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 21 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 23 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 25 modulo 60: 1/4 ( q^2-10*q+29 ) q congruent 27 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 31 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 32 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/4 ( q^2-10*q+29 ) q congruent 41 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 43 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 47 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 49 modulo 60: 1/4 ( q^2-10*q+29 ) q congruent 53 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 59 modulo 60: 1/4 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 68, 3, 69, 66, 4, 70, 19, 68, 7, 72, 20, 4, 68, 16, 73, 19, 76, 8, 77, 28, 82, 30, 81, 77, 30, 96, 60, 70, 19, 89, 43, 23, 93 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ] ] k = 2: F-action on Pi is () [28,1,2] Dynkin type is D_5(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-3 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1 ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-3 ) q congruent 7 modulo 60: 1/4 phi1 ( q-3 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-3 ) q congruent 11 modulo 60: 1/4 phi1 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-3 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-3 ) q congruent 19 modulo 60: 1/4 phi1 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-3 ) q congruent 23 modulo 60: 1/4 phi1 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-3 ) q congruent 27 modulo 60: 1/4 phi1 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-3 ) q congruent 31 modulo 60: 1/4 phi1 ( q-3 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-3 ) q congruent 41 modulo 60: 1/4 phi1 ( q-3 ) q congruent 43 modulo 60: 1/4 phi1 ( q-3 ) q congruent 47 modulo 60: 1/4 phi1 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-3 ) q congruent 53 modulo 60: 1/4 phi1 ( q-3 ) q congruent 59 modulo 60: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 3, 69, 5, 4, 68, 19, 72, 7, 69, 20, 71, 68, 7, 73, 18, 76, 20, 77, 30, 82, 31, 81, 27, 30, 81, 60, 98, 19, 76, 43, 90, 93, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ] ] k = 3: F-action on Pi is (2,5) [28,1,3] Dynkin type is ^2D_5(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-3 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1 ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-3 ) q congruent 7 modulo 60: 1/4 phi1 ( q-3 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-3 ) q congruent 11 modulo 60: 1/4 phi1 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-3 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-3 ) q congruent 19 modulo 60: 1/4 phi1 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-3 ) q congruent 23 modulo 60: 1/4 phi1 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-3 ) q congruent 27 modulo 60: 1/4 phi1 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-3 ) q congruent 31 modulo 60: 1/4 phi1 ( q-3 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-3 ) q congruent 41 modulo 60: 1/4 phi1 ( q-3 ) q congruent 43 modulo 60: 1/4 phi1 ( q-3 ) q congruent 47 modulo 60: 1/4 phi1 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-3 ) q congruent 53 modulo 60: 1/4 phi1 ( q-3 ) q congruent 59 modulo 60: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 3, 69, 5, 67, 70, 19, 68, 7, 72, 20, 69, 5, 19, 76, 7, 69, 18, 74, 28, 82, 30, 81, 31, 78, 82, 31, 97, 59, 89, 43, 76, 20, 51, 94 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 13, 1, 4, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ] ] k = 4: F-action on Pi is (2,5) [28,1,4] Dynkin type is ^2D_5(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-5 ) q congruent 2 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/4 q ( q-4 ) q congruent 5 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/4 phi1 ( q-5 ) q congruent 11 modulo 60: 1/4 ( q^2-6*q+13 ) q congruent 13 modulo 60: 1/4 phi1 ( q-5 ) q congruent 16 modulo 60: 1/4 q ( q-4 ) q congruent 17 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/4 phi1 ( q-5 ) q congruent 23 modulo 60: 1/4 ( q^2-6*q+13 ) q congruent 25 modulo 60: 1/4 phi1 ( q-5 ) q congruent 27 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/4 phi1 ( q-5 ) q congruent 41 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/4 ( q^2-6*q+13 ) q congruent 49 modulo 60: 1/4 phi1 ( q-5 ) q congruent 53 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/4 ( q^2-6*q+13 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 3, 69, 5, 67, 2, 19, 72, 7, 69, 20, 71, 5, 67, 76, 20, 69, 5, 74, 17, 82, 31, 81, 27, 78, 9, 31, 78, 59, 95, 43, 90, 20, 71, 94, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ] ] i = 29: Pi = [ 1, 2, 3, 4, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [29,1,1] Dynkin type is A_4(q) + A_2(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q^2-13*q+56 ) q congruent 2 modulo 60: 1/4 ( q^2-10*q+16 ) q congruent 3 modulo 60: 1/4 ( q^2-11*q+24 ) q congruent 4 modulo 60: 1/4 ( q^2-12*q+32 ) q congruent 5 modulo 60: 1/4 ( q^2-11*q+30 ) q congruent 7 modulo 60: 1/4 ( q^2-13*q+42 ) q congruent 8 modulo 60: 1/4 ( q^2-10*q+16 ) q congruent 9 modulo 60: 1/4 ( q^2-11*q+30 ) q congruent 11 modulo 60: 1/4 ( q^2-11*q+32 ) q congruent 13 modulo 60: 1/4 ( q^2-13*q+48 ) q congruent 16 modulo 60: 1/4 ( q^2-12*q+40 ) q congruent 17 modulo 60: 1/4 ( q^2-11*q+30 ) q congruent 19 modulo 60: 1/4 ( q^2-13*q+42 ) q congruent 21 modulo 60: 1/4 ( q^2-11*q+38 ) q congruent 23 modulo 60: 1/4 ( q^2-11*q+24 ) q congruent 25 modulo 60: 1/4 ( q^2-13*q+48 ) q congruent 27 modulo 60: 1/4 ( q^2-11*q+24 ) q congruent 29 modulo 60: 1/4 ( q^2-11*q+30 ) q congruent 31 modulo 60: 1/4 ( q^2-13*q+50 ) q congruent 32 modulo 60: 1/4 ( q^2-10*q+16 ) q congruent 37 modulo 60: 1/4 ( q^2-13*q+48 ) q congruent 41 modulo 60: 1/4 ( q^2-11*q+38 ) q congruent 43 modulo 60: 1/4 ( q^2-13*q+42 ) q congruent 47 modulo 60: 1/4 ( q^2-11*q+24 ) q congruent 49 modulo 60: 1/4 ( q^2-13*q+48 ) q congruent 53 modulo 60: 1/4 ( q^2-11*q+30 ) q congruent 59 modulo 60: 1/4 ( q^2-11*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 8, 66, 4, 77, 4, 68, 30, 8, 77, 14, 77, 30, 83, 70, 19, 97, 23, 93, 62 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 26, 1, 1, 4 ] ] k = 2: F-action on Pi is () [29,1,2] Dynkin type is A_4(q) + A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-4 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 q ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-4 ) q congruent 5 modulo 60: 1/4 phi1 ( q-2 ) q congruent 7 modulo 60: 1/4 ( q^2-5*q+2 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 q ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-4 ) q congruent 16 modulo 60: 1/4 q ( q-4 ) q congruent 17 modulo 60: 1/4 phi1 ( q-2 ) q congruent 19 modulo 60: 1/4 ( q^2-5*q+2 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 q ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-4 ) q congruent 27 modulo 60: 1/4 q ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-2 ) q congruent 31 modulo 60: 1/4 ( q^2-5*q+2 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-4 ) q congruent 41 modulo 60: 1/4 phi1 ( q-2 ) q congruent 43 modulo 60: 1/4 ( q^2-5*q+2 ) q congruent 47 modulo 60: 1/4 q ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-4 ) q congruent 53 modulo 60: 1/4 phi1 ( q-2 ) q congruent 59 modulo 60: 1/4 q ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 77, 4, 68, 30, 68, 7, 81, 77, 30, 83, 30, 81, 37, 19, 76, 59, 93, 50, 111 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 15, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 26, 1, 3, 4 ] ] k = 3: F-action on Pi is (1,2)(3,4)(6,7) [29,1,3] Dynkin type is ^2A_4(q) + ^2A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-2 ) q congruent 2 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 7 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 ( q^2-5*q+10 ) q congruent 13 modulo 60: 1/4 phi1 ( q-2 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 19 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 ( q^2-5*q+10 ) q congruent 25 modulo 60: 1/4 phi1 ( q-2 ) q congruent 27 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 29 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 31 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 32 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/4 phi1 ( q-2 ) q congruent 41 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 43 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 47 modulo 60: 1/4 ( q^2-5*q+10 ) q congruent 49 modulo 60: 1/4 phi1 ( q-2 ) q congruent 53 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 59 modulo 60: 1/4 ( q^2-5*q+10 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 78, 5, 69, 31, 69, 7, 82, 78, 31, 84, 31, 82, 38, 20, 76, 60, 94, 51, 112 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 15, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 26, 1, 2, 4 ] ] k = 4: F-action on Pi is (1,2)(3,4)(6,7) [29,1,4] Dynkin type is ^2A_4(q) + ^2A_2(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-6 ) q congruent 2 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/4 ( q^2-7*q+12 ) q congruent 4 modulo 60: 1/4 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 7 modulo 60: 1/4 ( q^2-7*q+12 ) q congruent 8 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/4 ( q^2-7*q+14 ) q congruent 11 modulo 60: 1/4 ( q^2-9*q+26 ) q congruent 13 modulo 60: 1/4 phi1 ( q-6 ) q congruent 16 modulo 60: 1/4 q ( q-6 ) q congruent 17 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 19 modulo 60: 1/4 ( q^2-7*q+20 ) q congruent 21 modulo 60: 1/4 phi1 ( q-6 ) q congruent 23 modulo 60: 1/4 ( q^2-9*q+26 ) q congruent 25 modulo 60: 1/4 phi1 ( q-6 ) q congruent 27 modulo 60: 1/4 ( q^2-7*q+12 ) q congruent 29 modulo 60: 1/4 ( q^2-9*q+28 ) q congruent 31 modulo 60: 1/4 ( q^2-7*q+12 ) q congruent 32 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/4 phi1 ( q-6 ) q congruent 41 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 43 modulo 60: 1/4 ( q^2-7*q+12 ) q congruent 47 modulo 60: 1/4 ( q^2-9*q+26 ) q congruent 49 modulo 60: 1/4 ( q^2-7*q+14 ) q congruent 53 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 59 modulo 60: 1/4 ( q^2-9*q+34 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 9, 67, 5, 78, 5, 69, 31, 9, 78, 15, 78, 31, 84, 71, 20, 98, 24, 94, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ] ] i = 30: Pi = [ 1, 2, 3, 4, 6, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [30,1,1] Dynkin type is A_4(q) + A_1(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q^2-13*q+60 ) q congruent 2 modulo 60: 1/4 ( q^2-10*q+16 ) q congruent 3 modulo 60: 1/4 ( q^2-13*q+30 ) q congruent 4 modulo 60: 1/4 ( q^2-10*q+24 ) q congruent 5 modulo 60: 1/4 ( q^2-13*q+40 ) q congruent 7 modulo 60: 1/4 ( q^2-13*q+42 ) q congruent 8 modulo 60: 1/4 ( q^2-10*q+16 ) q congruent 9 modulo 60: 1/4 ( q^2-13*q+40 ) q congruent 11 modulo 60: 1/4 ( q^2-13*q+38 ) q congruent 13 modulo 60: 1/4 ( q^2-13*q+52 ) q congruent 16 modulo 60: 1/4 ( q^2-10*q+32 ) q congruent 17 modulo 60: 1/4 ( q^2-13*q+40 ) q congruent 19 modulo 60: 1/4 ( q^2-13*q+42 ) q congruent 21 modulo 60: 1/4 ( q^2-13*q+48 ) q congruent 23 modulo 60: 1/4 ( q^2-13*q+30 ) q congruent 25 modulo 60: 1/4 ( q^2-13*q+52 ) q congruent 27 modulo 60: 1/4 ( q^2-13*q+30 ) q congruent 29 modulo 60: 1/4 ( q^2-13*q+40 ) q congruent 31 modulo 60: 1/4 ( q^2-13*q+50 ) q congruent 32 modulo 60: 1/4 ( q^2-10*q+16 ) q congruent 37 modulo 60: 1/4 ( q^2-13*q+52 ) q congruent 41 modulo 60: 1/4 ( q^2-13*q+48 ) q congruent 43 modulo 60: 1/4 ( q^2-13*q+42 ) q congruent 47 modulo 60: 1/4 ( q^2-13*q+30 ) q congruent 49 modulo 60: 1/4 ( q^2-13*q+52 ) q congruent 53 modulo 60: 1/4 ( q^2-13*q+40 ) q congruent 59 modulo 60: 1/4 ( q^2-13*q+30 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 4, 68, 68, 7, 8, 77, 77, 30, 77, 30, 30, 81, 70, 19, 19, 76, 23, 93, 93, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 15, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 4 ], [ 23, 1, 1, 2 ] ] k = 2: F-action on Pi is (6,8) [30,1,2] Dynkin type is A_4(q) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-2 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 q ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-2 ) q congruent 7 modulo 60: 1/4 q ( q-3 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 q ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-2 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-2 ) q congruent 19 modulo 60: 1/4 q ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 q ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-2 ) q congruent 27 modulo 60: 1/4 q ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-2 ) q congruent 31 modulo 60: 1/4 q ( q-3 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-2 ) q congruent 41 modulo 60: 1/4 phi1 ( q-2 ) q congruent 43 modulo 60: 1/4 q ( q-3 ) q congruent 47 modulo 60: 1/4 q ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-2 ) q congruent 53 modulo 60: 1/4 phi1 ( q-2 ) q congruent 59 modulo 60: 1/4 q ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19, 7, 76, 30, 97, 81, 59, 76, 22, 50, 107 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], [ 14, 1, 1, 2 ], [ 23, 1, 2, 2 ] ] k = 3: F-action on Pi is (1,2)(3,4) [30,1,3] Dynkin type is ^2A_4(q) + A_1(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-8 ) q congruent 2 modulo 60: 1/4 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 4 modulo 60: 1/4 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 7 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 8 modulo 60: 1/4 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/4 ( q^2-9*q+16 ) q congruent 11 modulo 60: 1/4 ( q^2-9*q+30 ) q congruent 13 modulo 60: 1/4 phi1 ( q-8 ) q congruent 16 modulo 60: 1/4 q ( q-6 ) q congruent 17 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 19 modulo 60: 1/4 ( q^2-9*q+26 ) q congruent 21 modulo 60: 1/4 phi1 ( q-8 ) q congruent 23 modulo 60: 1/4 ( q^2-9*q+30 ) q congruent 25 modulo 60: 1/4 phi1 ( q-8 ) q congruent 27 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 29 modulo 60: 1/4 ( q^2-9*q+28 ) q congruent 31 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 32 modulo 60: 1/4 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/4 phi1 ( q-8 ) q congruent 41 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 43 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 47 modulo 60: 1/4 ( q^2-9*q+30 ) q congruent 49 modulo 60: 1/4 ( q^2-9*q+16 ) q congruent 53 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 59 modulo 60: 1/4 ( q^2-9*q+38 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 67, 2, 69, 5, 5, 67, 7, 69, 69, 5, 31, 78, 78, 9, 82, 31, 31, 78, 76, 20, 20, 71, 51, 94, 94, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 4 ], [ 23, 1, 2, 2 ] ] k = 4: F-action on Pi is (1,2)(3,4)(6,8) [30,1,4] Dynkin type is ^2A_4(q) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-2 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-2 ) q congruent 7 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 13 modulo 60: 1/4 phi1 ( q-2 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-2 ) q congruent 19 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 25 modulo 60: 1/4 phi1 ( q-2 ) q congruent 27 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 29 modulo 60: 1/4 phi1 ( q-2 ) q congruent 31 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-2 ) q congruent 41 modulo 60: 1/4 phi1 ( q-2 ) q congruent 43 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 47 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 49 modulo 60: 1/4 phi1 ( q-2 ) q congruent 53 modulo 60: 1/4 phi1 ( q-2 ) q congruent 59 modulo 60: 1/4 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 71, 69, 20, 7, 76, 31, 98, 82, 60, 76, 22, 51, 108 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 2 ], [ 23, 1, 1, 2 ] ] i = 31: Pi = [ 1, 2, 3, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [31,1,1] Dynkin type is A_3(q) + A_2(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q^2-16*q+75 ) q congruent 2 modulo 60: 1/4 ( q^2-10*q+16 ) q congruent 3 modulo 60: 1/4 ( q^2-12*q+27 ) q congruent 4 modulo 60: 1/4 ( q^2-12*q+32 ) q congruent 5 modulo 60: 1/4 ( q^2-14*q+45 ) q congruent 7 modulo 60: 1/4 ( q^2-14*q+49 ) q congruent 8 modulo 60: 1/4 ( q^2-10*q+16 ) q congruent 9 modulo 60: 1/4 ( q^2-14*q+45 ) q congruent 11 modulo 60: 1/4 ( q^2-12*q+35 ) q congruent 13 modulo 60: 1/4 ( q^2-16*q+67 ) q congruent 16 modulo 60: 1/4 ( q^2-12*q+40 ) q congruent 17 modulo 60: 1/4 ( q^2-14*q+45 ) q congruent 19 modulo 60: 1/4 ( q^2-14*q+49 ) q congruent 21 modulo 60: 1/4 ( q^2-14*q+53 ) q congruent 23 modulo 60: 1/4 ( q^2-12*q+27 ) q congruent 25 modulo 60: 1/4 ( q^2-16*q+67 ) q congruent 27 modulo 60: 1/4 ( q^2-12*q+27 ) q congruent 29 modulo 60: 1/4 ( q^2-14*q+45 ) q congruent 31 modulo 60: 1/4 ( q^2-14*q+57 ) q congruent 32 modulo 60: 1/4 ( q^2-10*q+16 ) q congruent 37 modulo 60: 1/4 ( q^2-16*q+67 ) q congruent 41 modulo 60: 1/4 ( q^2-14*q+53 ) q congruent 43 modulo 60: 1/4 ( q^2-14*q+49 ) q congruent 47 modulo 60: 1/4 ( q^2-12*q+27 ) q congruent 49 modulo 60: 1/4 ( q^2-16*q+67 ) q congruent 53 modulo 60: 1/4 ( q^2-14*q+45 ) q congruent 59 modulo 60: 1/4 ( q^2-12*q+27 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 8, 77, 77, 30, 14, 83, 70, 19, 19, 76, 97, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 2 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ] ] k = 2: F-action on Pi is () [31,1,2] Dynkin type is A_3(q) + A_2(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-7 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1 ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-4 ) q congruent 5 modulo 60: 1/4 phi1 ( q-5 ) q congruent 7 modulo 60: 1/4 phi1 ( q-5 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-5 ) q congruent 11 modulo 60: 1/4 phi1 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-7 ) q congruent 16 modulo 60: 1/4 q ( q-4 ) q congruent 17 modulo 60: 1/4 phi1 ( q-5 ) q congruent 19 modulo 60: 1/4 phi1 ( q-5 ) q congruent 21 modulo 60: 1/4 phi1 ( q-5 ) q congruent 23 modulo 60: 1/4 phi1 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-7 ) q congruent 27 modulo 60: 1/4 phi1 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-5 ) q congruent 31 modulo 60: 1/4 phi1 ( q-5 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-7 ) q congruent 41 modulo 60: 1/4 phi1 ( q-5 ) q congruent 43 modulo 60: 1/4 phi1 ( q-5 ) q congruent 47 modulo 60: 1/4 phi1 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-7 ) q congruent 53 modulo 60: 1/4 phi1 ( q-5 ) q congruent 59 modulo 60: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 68, 3, 7, 69, 81, 27, 77, 30, 30, 81, 83, 37, 19, 72, 76, 20, 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 2 ], [ 16, 1, 1, 4 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 2 ] ] k = 3: F-action on Pi is (1,3)(5,7) [31,1,3] Dynkin type is ^2A_3(q) + ^2A_2(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-3 ) q congruent 2 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/4 phi1 ( q-3 ) q congruent 11 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/4 phi1 ( q-3 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/4 phi1 ( q-3 ) q congruent 23 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/4 phi1 ( q-3 ) q congruent 27 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/4 phi1 ( q-3 ) q congruent 41 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/4 phi1 ( q-3 ) q congruent 53 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/4 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 3, 69, 68, 7, 28, 82, 31, 78, 82, 31, 38, 84, 72, 20, 19, 76, 96, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 3, 4 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 2 ] ] k = 4: F-action on Pi is (1,3)(5,7) [31,1,4] Dynkin type is ^2A_3(q) + ^2A_2(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-7 ) q congruent 2 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 4 modulo 60: 1/4 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 7 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 8 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/4 ( q^2-12*q+39 ) q congruent 13 modulo 60: 1/4 phi1 ( q-7 ) q congruent 16 modulo 60: 1/4 q ( q-6 ) q congruent 17 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 19 modulo 60: 1/4 ( q^2-10*q+29 ) q congruent 21 modulo 60: 1/4 phi1 ( q-7 ) q congruent 23 modulo 60: 1/4 ( q^2-12*q+39 ) q congruent 25 modulo 60: 1/4 phi1 ( q-7 ) q congruent 27 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/4 ( q^2-10*q+33 ) q congruent 31 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 32 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/4 phi1 ( q-7 ) q congruent 41 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 43 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/4 ( q^2-12*q+39 ) q congruent 49 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 59 modulo 60: 1/4 ( q^2-12*q+47 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 78, 9, 31, 78, 84, 15, 20, 71, 76, 20, 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 4, 8 ], [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ] ] i = 32: Pi = [ 1, 2, 3, 5, 6, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [32,1,1] Dynkin type is A_2(q) + A_2(q) + A_1(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 ( q^2-18*q+97 ) q congruent 2 modulo 60: 1/8 ( q^2-10*q+16 ) q congruent 3 modulo 60: 1/8 ( q^2-14*q+33 ) q congruent 4 modulo 60: 1/8 ( q^2-14*q+40 ) q congruent 5 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 7 modulo 60: 1/8 ( q^2-18*q+77 ) q congruent 8 modulo 60: 1/8 ( q^2-10*q+16 ) q congruent 9 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 11 modulo 60: 1/8 ( q^2-14*q+41 ) q congruent 13 modulo 60: 1/8 ( q^2-18*q+89 ) q congruent 16 modulo 60: 1/8 ( q^2-14*q+48 ) q congruent 17 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 19 modulo 60: 1/8 ( q^2-18*q+77 ) q congruent 21 modulo 60: 1/8 ( q^2-14*q+53 ) q congruent 23 modulo 60: 1/8 ( q^2-14*q+33 ) q congruent 25 modulo 60: 1/8 ( q^2-18*q+89 ) q congruent 27 modulo 60: 1/8 ( q^2-14*q+33 ) q congruent 29 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 31 modulo 60: 1/8 ( q^2-18*q+85 ) q congruent 32 modulo 60: 1/8 ( q^2-10*q+16 ) q congruent 37 modulo 60: 1/8 ( q^2-18*q+89 ) q congruent 41 modulo 60: 1/8 ( q^2-14*q+53 ) q congruent 43 modulo 60: 1/8 ( q^2-18*q+77 ) q congruent 47 modulo 60: 1/8 ( q^2-14*q+33 ) q congruent 49 modulo 60: 1/8 ( q^2-18*q+89 ) q congruent 53 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 59 modulo 60: 1/8 ( q^2-14*q+33 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 8, 77, 77, 30, 66, 4, 4, 68, 4, 68, 68, 7, 77, 30, 30, 81, 8, 77, 77, 30, 77, 30, 30, 81, 14, 83, 83, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ] ] k = 2: F-action on Pi is (2,8)(5,6) [32,1,2] Dynkin type is A_2(q) + ^2A_2(q) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-3 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1 ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-3 ) q congruent 7 modulo 60: 1/4 phi1 ( q-3 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-3 ) q congruent 11 modulo 60: 1/4 phi1 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-3 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-3 ) q congruent 19 modulo 60: 1/4 phi1 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-3 ) q congruent 23 modulo 60: 1/4 phi1 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-3 ) q congruent 27 modulo 60: 1/4 phi1 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-3 ) q congruent 31 modulo 60: 1/4 phi1 ( q-3 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-3 ) q congruent 41 modulo 60: 1/4 phi1 ( q-3 ) q congruent 43 modulo 60: 1/4 phi1 ( q-3 ) q congruent 47 modulo 60: 1/4 phi1 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-3 ) q congruent 53 modulo 60: 1/4 phi1 ( q-3 ) q congruent 59 modulo 60: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 68, 19, 28, 96, 69, 20, 7, 76, 82, 60, 27, 95, 81, 59, 36, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ] ] k = 3: F-action on Pi is (1,3)(5,6) [32,1,3] Dynkin type is ^2A_2(q) + ^2A_2(q) + A_1(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-9 ) q congruent 2 modulo 60: 1/8 ( q^2-10*q+16 ) q congruent 3 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 4 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 7 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 8 modulo 60: 1/8 ( q^2-10*q+16 ) q congruent 9 modulo 60: 1/8 ( q^2-10*q+17 ) q congruent 11 modulo 60: 1/8 ( q^2-14*q+57 ) q congruent 13 modulo 60: 1/8 phi1 ( q-9 ) q congruent 16 modulo 60: 1/8 q ( q-6 ) q congruent 17 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 19 modulo 60: 1/8 ( q^2-10*q+29 ) q congruent 21 modulo 60: 1/8 phi1 ( q-9 ) q congruent 23 modulo 60: 1/8 ( q^2-14*q+57 ) q congruent 25 modulo 60: 1/8 phi1 ( q-9 ) q congruent 27 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/8 ( q^2-14*q+53 ) q congruent 31 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 32 modulo 60: 1/8 ( q^2-10*q+16 ) q congruent 37 modulo 60: 1/8 phi1 ( q-9 ) q congruent 41 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 43 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/8 ( q^2-14*q+57 ) q congruent 49 modulo 60: 1/8 ( q^2-10*q+17 ) q congruent 53 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 59 modulo 60: 1/8 ( q^2-14*q+65 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 67, 2, 69, 5, 5, 67, 31, 78, 78, 9, 69, 5, 5, 67, 7, 69, 69, 5, 82, 31, 31, 78, 31, 78, 78, 9, 82, 31, 31, 78, 38, 84, 84, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ] ] k = 4: F-action on Pi is (1,5)(3,6) [32,1,4] Dynkin type is A_2(q^2) + A_1(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-5 ) q congruent 2 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/4 phi1 ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-4 ) q congruent 5 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/4 phi1 ( q-5 ) q congruent 8 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/4 phi1 ( q-3 ) q congruent 11 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/4 phi1 ( q-5 ) q congruent 16 modulo 60: 1/4 q ( q-4 ) q congruent 17 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/4 phi1 ( q-5 ) q congruent 21 modulo 60: 1/4 phi1 ( q-3 ) q congruent 23 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/4 phi1 ( q-5 ) q congruent 27 modulo 60: 1/4 phi1 ( q-3 ) q congruent 29 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/4 phi1 ( q-5 ) q congruent 32 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/4 phi1 ( q-5 ) q congruent 41 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/4 phi1 ( q-5 ) q congruent 47 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/4 phi1 ( q-5 ) q congruent 53 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/4 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 3, 69, 19, 76, 72, 20, 87, 40, 35, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ] ] k = 5: F-action on Pi is (1,5,3,6)(2,8) [32,1,5] Dynkin type is ^2A_2(q^2) + A_1(q^2) + T(phi4) Order of center |Z^F|: phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 phi2 q congruent 2 modulo 60: 1/4 ( q^2-4 ) q congruent 3 modulo 60: 1/4 ( q^2-5 ) q congruent 4 modulo 60: 1/4 q^2 q congruent 5 modulo 60: 1/4 phi1 phi2 q congruent 7 modulo 60: 1/4 ( q^2-5 ) q congruent 8 modulo 60: 1/4 ( q^2-4 ) q congruent 9 modulo 60: 1/4 phi1 phi2 q congruent 11 modulo 60: 1/4 phi1 phi2 q congruent 13 modulo 60: 1/4 ( q^2-5 ) q congruent 16 modulo 60: 1/4 q^2 q congruent 17 modulo 60: 1/4 ( q^2-5 ) q congruent 19 modulo 60: 1/4 phi1 phi2 q congruent 21 modulo 60: 1/4 phi1 phi2 q congruent 23 modulo 60: 1/4 ( q^2-5 ) q congruent 25 modulo 60: 1/4 phi1 phi2 q congruent 27 modulo 60: 1/4 ( q^2-5 ) q congruent 29 modulo 60: 1/4 phi1 phi2 q congruent 31 modulo 60: 1/4 phi1 phi2 q congruent 32 modulo 60: 1/4 ( q^2-4 ) q congruent 37 modulo 60: 1/4 ( q^2-5 ) q congruent 41 modulo 60: 1/4 phi1 phi2 q congruent 43 modulo 60: 1/4 ( q^2-5 ) q congruent 47 modulo 60: 1/4 ( q^2-5 ) q congruent 49 modulo 60: 1/4 phi1 phi2 q congruent 53 modulo 60: 1/4 ( q^2-5 ) q congruent 59 modulo 60: 1/4 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 75, 6, 22, 75, 100, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 9, 1, 1, 1 ] ] i = 33: Pi = [ 1, 2, 3, 5, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [33,1,1] Dynkin type is A_2(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 ( q^2-14*q+61 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/48 ( q^2-14*q+33 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/48 ( q^2-14*q+45 ) q congruent 7 modulo 60: 1/48 ( q^2-14*q+49 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/48 ( q^2-14*q+45 ) q congruent 11 modulo 60: 1/48 ( q^2-14*q+33 ) q congruent 13 modulo 60: 1/48 ( q^2-14*q+61 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/48 ( q^2-14*q+45 ) q congruent 19 modulo 60: 1/48 ( q^2-14*q+49 ) q congruent 21 modulo 60: 1/48 ( q^2-14*q+45 ) q congruent 23 modulo 60: 1/48 ( q^2-14*q+33 ) q congruent 25 modulo 60: 1/48 ( q^2-14*q+61 ) q congruent 27 modulo 60: 1/48 ( q^2-14*q+33 ) q congruent 29 modulo 60: 1/48 ( q^2-14*q+45 ) q congruent 31 modulo 60: 1/48 ( q^2-14*q+49 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/48 ( q^2-14*q+61 ) q congruent 41 modulo 60: 1/48 ( q^2-14*q+45 ) q congruent 43 modulo 60: 1/48 ( q^2-14*q+49 ) q congruent 47 modulo 60: 1/48 ( q^2-14*q+33 ) q congruent 49 modulo 60: 1/48 ( q^2-14*q+61 ) q congruent 53 modulo 60: 1/48 ( q^2-14*q+45 ) q congruent 59 modulo 60: 1/48 ( q^2-14*q+33 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 3, 66, 4, 4, 68, 4, 68, 68, 7, 4, 68, 68, 7, 68, 7, 7, 69, 8, 77, 77, 30, 77, 30, 30, 81, 77, 30, 30, 81, 30, 81, 81, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 40, 1, 1, 12 ] ] k = 2: F-action on Pi is ( 7,240) [33,1,2] Dynkin type is A_2(q) + A_1(q) + A_1(q) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19, 68, 19, 3, 72, 68, 19, 7, 76, 7, 76, 69, 20, 30, 97, 81, 59, 81, 59, 27, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 40, 1, 3, 4 ] ] k = 3: F-action on Pi is ( 5, 7,240) [33,1,3] Dynkin type is A_2(q) + A_1(q) + A_1(q^3) + T(phi3) Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 phi1 ( q+2 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/6 q phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/6 q phi2 q congruent 7 modulo 60: 1/6 phi1 ( q+2 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/6 q phi2 q congruent 11 modulo 60: 1/6 q phi2 q congruent 13 modulo 60: 1/6 phi1 ( q+2 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/6 q phi2 q congruent 19 modulo 60: 1/6 phi1 ( q+2 ) q congruent 21 modulo 60: 1/6 q phi2 q congruent 23 modulo 60: 1/6 q phi2 q congruent 25 modulo 60: 1/6 phi1 ( q+2 ) q congruent 27 modulo 60: 1/6 q phi2 q congruent 29 modulo 60: 1/6 q phi2 q congruent 31 modulo 60: 1/6 phi1 ( q+2 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/6 phi1 ( q+2 ) q congruent 41 modulo 60: 1/6 q phi2 q congruent 43 modulo 60: 1/6 phi1 ( q+2 ) q congruent 47 modulo 60: 1/6 q phi2 q congruent 49 modulo 60: 1/6 phi1 ( q+2 ) q congruent 53 modulo 60: 1/6 q phi2 q congruent 59 modulo 60: 1/6 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 14, 87, 83, 35, 83, 40, 37, 88, 12, 85, 79, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 40, 1, 5, 6 ] ] k = 4: F-action on Pi is ( 2, 5)( 7,240) [33,1,4] Dynkin type is A_2(q) + A_1(q^2) + A_1(q^2) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q-5 ) q congruent 7 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q-5 ) q congruent 11 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q-5 ) q congruent 19 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1 ( q-5 ) q congruent 23 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1 ( q-5 ) q congruent 27 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1 ( q-5 ) q congruent 31 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q-5 ) q congruent 41 modulo 60: 1/16 phi1 ( q-5 ) q congruent 43 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1 ( q-5 ) q congruent 53 modulo 60: 1/16 phi1 ( q-5 ) q congruent 59 modulo 60: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 70, 16, 68, 19, 19, 73, 30, 97, 97, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 3, 8 ], [ 16, 1, 2, 8 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 40, 1, 1, 12 ] ] k = 5: F-action on Pi is ( 2, 5,240, 7) [33,1,5] Dynkin type is A_2(q) + A_1(q^4) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 phi2 q congruent 7 modulo 60: 1/8 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 phi2 q congruent 11 modulo 60: 1/8 phi1 phi2 q congruent 13 modulo 60: 1/8 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 phi2 q congruent 19 modulo 60: 1/8 phi1 phi2 q congruent 21 modulo 60: 1/8 phi1 phi2 q congruent 23 modulo 60: 1/8 phi1 phi2 q congruent 25 modulo 60: 1/8 phi1 phi2 q congruent 27 modulo 60: 1/8 phi1 phi2 q congruent 29 modulo 60: 1/8 phi1 phi2 q congruent 31 modulo 60: 1/8 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 phi2 q congruent 41 modulo 60: 1/8 phi1 phi2 q congruent 43 modulo 60: 1/8 phi1 phi2 q congruent 47 modulo 60: 1/8 phi1 phi2 q congruent 49 modulo 60: 1/8 phi1 phi2 q congruent 53 modulo 60: 1/8 phi1 phi2 q congruent 59 modulo 60: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 19, 89, 76, 43, 59, 109 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 40, 1, 3, 4 ] ] k = 6: F-action on Pi is ( 1, 3)( 5,240) [33,1,6] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 72, 20, 69, 5, 20, 71, 68, 7, 19, 76, 7, 69, 76, 20, 28, 82, 96, 60, 82, 31, 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 40, 1, 2, 4 ] ] k = 7: F-action on Pi is ( 1, 3)( 5,240, 7) [33,1,7] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q^3) + T(phi6) Order of center |Z^F|: phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/6 q phi1 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/6 phi2 ( q-2 ) q congruent 7 modulo 60: 1/6 q phi1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/6 q phi1 q congruent 11 modulo 60: 1/6 phi2 ( q-2 ) q congruent 13 modulo 60: 1/6 q phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/6 phi2 ( q-2 ) q congruent 19 modulo 60: 1/6 q phi1 q congruent 21 modulo 60: 1/6 q phi1 q congruent 23 modulo 60: 1/6 phi2 ( q-2 ) q congruent 25 modulo 60: 1/6 q phi1 q congruent 27 modulo 60: 1/6 q phi1 q congruent 29 modulo 60: 1/6 phi2 ( q-2 ) q congruent 31 modulo 60: 1/6 q phi1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/6 q phi1 q congruent 41 modulo 60: 1/6 phi2 ( q-2 ) q congruent 43 modulo 60: 1/6 q phi1 q congruent 47 modulo 60: 1/6 phi2 ( q-2 ) q congruent 49 modulo 60: 1/6 q phi1 q congruent 53 modulo 60: 1/6 phi2 ( q-2 ) q congruent 59 modulo 60: 1/6 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 84, 88, 15, 87, 38, 40, 84, 33, 80, 86, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 40, 1, 4, 6 ] ] k = 8: F-action on Pi is (1,3) [33,1,8] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 phi1 ( q-9 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/48 ( q^2-10*q+21 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/48 ( q^2-10*q+25 ) q congruent 7 modulo 60: 1/48 ( q^2-10*q+21 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/48 phi1 ( q-9 ) q congruent 11 modulo 60: 1/48 ( q^2-10*q+37 ) q congruent 13 modulo 60: 1/48 phi1 ( q-9 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/48 ( q^2-10*q+25 ) q congruent 19 modulo 60: 1/48 ( q^2-10*q+21 ) q congruent 21 modulo 60: 1/48 phi1 ( q-9 ) q congruent 23 modulo 60: 1/48 ( q^2-10*q+37 ) q congruent 25 modulo 60: 1/48 phi1 ( q-9 ) q congruent 27 modulo 60: 1/48 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/48 ( q^2-10*q+25 ) q congruent 31 modulo 60: 1/48 ( q^2-10*q+21 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/48 phi1 ( q-9 ) q congruent 41 modulo 60: 1/48 ( q^2-10*q+25 ) q congruent 43 modulo 60: 1/48 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/48 ( q^2-10*q+37 ) q congruent 49 modulo 60: 1/48 phi1 ( q-9 ) q congruent 53 modulo 60: 1/48 ( q^2-10*q+25 ) q congruent 59 modulo 60: 1/48 ( q^2-10*q+37 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 69, 5, 69, 5, 5, 67, 69, 5, 5, 67, 5, 67, 67, 2, 68, 7, 7, 69, 7, 69, 69, 5, 7, 69, 69, 5, 69, 5, 5, 67, 28, 82, 82, 31, 82, 31, 31, 78, 82, 31, 31, 78, 31, 78, 78, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 18 ], [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 24 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 40, 1, 6, 12 ] ] k = 9: F-action on Pi is ( 1, 3)( 2, 5, 7,240) [33,1,9] Dynkin type is ^2A_2(q) + A_1(q^4) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 phi2 q congruent 7 modulo 60: 1/8 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 phi2 q congruent 11 modulo 60: 1/8 phi1 phi2 q congruent 13 modulo 60: 1/8 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 phi2 q congruent 19 modulo 60: 1/8 phi1 phi2 q congruent 21 modulo 60: 1/8 phi1 phi2 q congruent 23 modulo 60: 1/8 phi1 phi2 q congruent 25 modulo 60: 1/8 phi1 phi2 q congruent 27 modulo 60: 1/8 phi1 phi2 q congruent 29 modulo 60: 1/8 phi1 phi2 q congruent 31 modulo 60: 1/8 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 phi2 q congruent 41 modulo 60: 1/8 phi1 phi2 q congruent 43 modulo 60: 1/8 phi1 phi2 q congruent 47 modulo 60: 1/8 phi1 phi2 q congruent 49 modulo 60: 1/8 phi1 phi2 q congruent 53 modulo 60: 1/8 phi1 phi2 q congruent 59 modulo 60: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 20, 90, 76, 43, 60, 110 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 40, 1, 2, 4 ] ] k = 10: F-action on Pi is ( 1, 3)( 2, 5)( 7,240) [33,1,10] Dynkin type is ^2A_2(q) + A_1(q^2) + A_1(q^2) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 q congruent 7 modulo 60: 1/16 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 q congruent 11 modulo 60: 1/16 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 q congruent 19 modulo 60: 1/16 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1^2 q congruent 23 modulo 60: 1/16 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1^2 q congruent 27 modulo 60: 1/16 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1^2 q congruent 31 modulo 60: 1/16 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 q congruent 41 modulo 60: 1/16 phi1^2 q congruent 43 modulo 60: 1/16 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1^2 q congruent 53 modulo 60: 1/16 phi1^2 q congruent 59 modulo 60: 1/16 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 71, 71, 17, 69, 20, 20, 74, 31, 98, 98, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 2, 8 ], [ 16, 1, 4, 8 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 40, 1, 6, 12 ] ] i = 34: Pi = [ 1, 2, 4, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [34,1,1] Dynkin type is A_5(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q^2-12*q+39 ) q congruent 2 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 4 modulo 60: 1/4 ( q^2-10*q+24 ) q congruent 5 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 7 modulo 60: 1/4 ( q^2-12*q+35 ) q congruent 8 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 11 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 13 modulo 60: 1/4 ( q^2-12*q+39 ) q congruent 16 modulo 60: 1/4 ( q^2-10*q+24 ) q congruent 17 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 19 modulo 60: 1/4 ( q^2-12*q+35 ) q congruent 21 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 23 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 25 modulo 60: 1/4 ( q^2-12*q+39 ) q congruent 27 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 31 modulo 60: 1/4 ( q^2-12*q+35 ) q congruent 32 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/4 ( q^2-12*q+39 ) q congruent 41 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 43 modulo 60: 1/4 ( q^2-12*q+35 ) q congruent 47 modulo 60: 1/4 ( q^2-10*q+21 ) q congruent 49 modulo 60: 1/4 ( q^2-12*q+39 ) q congruent 53 modulo 60: 1/4 ( q^2-10*q+25 ) q congruent 59 modulo 60: 1/4 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 4, 68, 68, 7, 8, 77, 77, 30, 14, 83, 70, 19, 19, 76, 23, 93, 87, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ] ] k = 2: F-action on Pi is () [34,1,2] Dynkin type is A_5(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-5 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1 ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-4 ) q congruent 5 modulo 60: 1/4 phi1 ( q-3 ) q congruent 7 modulo 60: 1/4 phi1 ( q-5 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-3 ) q congruent 11 modulo 60: 1/4 phi1 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-5 ) q congruent 16 modulo 60: 1/4 q ( q-4 ) q congruent 17 modulo 60: 1/4 phi1 ( q-3 ) q congruent 19 modulo 60: 1/4 phi1 ( q-5 ) q congruent 21 modulo 60: 1/4 phi1 ( q-3 ) q congruent 23 modulo 60: 1/4 phi1 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-5 ) q congruent 27 modulo 60: 1/4 phi1 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-3 ) q congruent 31 modulo 60: 1/4 phi1 ( q-5 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-5 ) q congruent 41 modulo 60: 1/4 phi1 ( q-3 ) q congruent 43 modulo 60: 1/4 phi1 ( q-5 ) q congruent 47 modulo 60: 1/4 phi1 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-5 ) q congruent 53 modulo 60: 1/4 phi1 ( q-3 ) q congruent 59 modulo 60: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 68, 7, 3, 69, 77, 30, 30, 81, 83, 37, 19, 76, 72, 20, 93, 50, 35, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 19, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 2 ] ] k = 3: F-action on Pi is (2,7)(4,6) [34,1,3] Dynkin type is ^2A_5(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-3 ) q congruent 2 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/4 phi1 ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/4 phi1 ( q-3 ) q congruent 8 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/4 phi1 ( q-3 ) q congruent 11 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/4 phi1 ( q-3 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/4 phi1 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-3 ) q congruent 23 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/4 phi1 ( q-3 ) q congruent 27 modulo 60: 1/4 phi1 ( q-3 ) q congruent 29 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/4 phi1 ( q-3 ) q congruent 32 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/4 phi1 ( q-3 ) q congruent 41 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/4 phi1 ( q-3 ) q congruent 47 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/4 phi1 ( q-3 ) q congruent 53 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/4 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 69, 5, 7, 69, 68, 3, 31, 78, 82, 31, 38, 84, 76, 20, 19, 72, 51, 94, 87, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 19, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 2 ] ] k = 4: F-action on Pi is (2,7)(4,6) [34,1,4] Dynkin type is ^2A_5(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-5 ) q congruent 2 modulo 60: 1/4 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/4 q ( q-4 ) q congruent 5 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/4 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/4 phi1 ( q-5 ) q congruent 11 modulo 60: 1/4 ( q^2-8*q+19 ) q congruent 13 modulo 60: 1/4 phi1 ( q-5 ) q congruent 16 modulo 60: 1/4 q ( q-4 ) q congruent 17 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/4 phi1 ( q-5 ) q congruent 23 modulo 60: 1/4 ( q^2-8*q+19 ) q congruent 25 modulo 60: 1/4 phi1 ( q-5 ) q congruent 27 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/4 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/4 phi1 ( q-5 ) q congruent 41 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/4 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/4 ( q^2-8*q+19 ) q congruent 49 modulo 60: 1/4 phi1 ( q-5 ) q congruent 53 modulo 60: 1/4 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/4 ( q^2-8*q+19 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 69, 5, 7, 69, 78, 9, 31, 78, 84, 15, 20, 71, 76, 20, 94, 24, 40, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ] ] i = 35: Pi = [ 1, 2, 4, 5, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [35,1,1] Dynkin type is A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 ( q^2-14*q+53 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 ( q^2-12*q+27 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 7 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 11 modulo 60: 1/8 ( q^2-12*q+27 ) q congruent 13 modulo 60: 1/8 ( q^2-14*q+53 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 19 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 21 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 23 modulo 60: 1/8 ( q^2-12*q+27 ) q congruent 25 modulo 60: 1/8 ( q^2-14*q+53 ) q congruent 27 modulo 60: 1/8 ( q^2-12*q+27 ) q congruent 29 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 31 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 ( q^2-14*q+53 ) q congruent 41 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 43 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 47 modulo 60: 1/8 ( q^2-12*q+27 ) q congruent 49 modulo 60: 1/8 ( q^2-14*q+53 ) q congruent 53 modulo 60: 1/8 ( q^2-14*q+45 ) q congruent 59 modulo 60: 1/8 ( q^2-12*q+27 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 7, 4, 68, 68, 3, 68, 7, 7, 69, 8, 77, 77, 30, 77, 30, 30, 81, 70, 19, 19, 72, 19, 76, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 6 ], [ 25, 1, 1, 4 ], [ 28, 1, 1, 4 ] ] k = 2: F-action on Pi is ( 7,240) [35,1,2] Dynkin type is A_3(q) + A_1(q) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 phi2 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 phi2 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 phi2 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 phi2 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 phi2 ( q-3 ) q congruent 47 modulo 60: 1/8 phi2 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19, 68, 19, 7, 76, 3, 72, 69, 20, 30, 97, 81, 59, 72, 18, 20, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 20, 1, 1, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 4, 4 ], [ 28, 1, 3, 4 ] ] k = 3: F-action on Pi is () [35,1,3] Dynkin type is A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-5 ) q congruent 7 modulo 60: 1/8 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-5 ) q congruent 11 modulo 60: 1/8 phi1 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-5 ) q congruent 19 modulo 60: 1/8 phi1 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-5 ) q congruent 23 modulo 60: 1/8 phi1 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-5 ) q congruent 27 modulo 60: 1/8 phi1 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-5 ) q congruent 31 modulo 60: 1/8 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-5 ) q congruent 41 modulo 60: 1/8 phi1 ( q-5 ) q congruent 43 modulo 60: 1/8 phi1 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-5 ) q congruent 53 modulo 60: 1/8 phi1 ( q-5 ) q congruent 59 modulo 60: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 3, 4, 68, 68, 7, 68, 7, 7, 69, 68, 7, 7, 69, 3, 69, 69, 5, 77, 30, 30, 81, 30, 81, 81, 27, 19, 76, 76, 20, 72, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 28, 1, 2, 4 ] ] k = 4: F-action on Pi is ( 7,240) [35,1,4] Dynkin type is A_3(q) + A_1(q) + A_1(q^2) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 phi2 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 phi2 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 phi2 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 phi2 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 phi2 ( q-3 ) q congruent 47 modulo 60: 1/8 phi2 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 3, 72, 7, 76, 69, 20, 69, 20, 5, 71, 81, 59, 27, 95, 20, 74, 71, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 4, 8 ], [ 20, 1, 2, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 28, 1, 4, 4 ] ] k = 5: F-action on Pi is ( 2, 5)( 7,240) [35,1,5] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q^2) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-5 ) q congruent 7 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-5 ) q congruent 11 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/8 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-5 ) q congruent 19 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/8 phi1 ( q-5 ) q congruent 23 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/8 phi1 ( q-5 ) q congruent 27 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/8 phi1 ( q-5 ) q congruent 31 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-5 ) q congruent 41 modulo 60: 1/8 phi1 ( q-5 ) q congruent 43 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/8 phi1 ( q-5 ) q congruent 53 modulo 60: 1/8 phi1 ( q-5 ) q congruent 59 modulo 60: 1/8 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 69, 20, 68, 19, 7, 76, 4, 70, 68, 19, 28, 96, 82, 60, 70, 16, 19, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 28, 1, 1, 4 ] ] k = 6: F-action on Pi is (2,5) [35,1,6] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/8 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 69, 5, 69, 5, 5, 67, 68, 7, 7, 69, 7, 69, 69, 5, 4, 68, 68, 3, 68, 7, 7, 69, 28, 82, 82, 31, 82, 31, 31, 78, 70, 19, 19, 72, 19, 76, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 13, 1, 4, 8 ], [ 20, 1, 3, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 25, 1, 3, 4 ], [ 28, 1, 3, 4 ] ] k = 7: F-action on Pi is ( 2, 5)( 7,240) [35,1,7] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1^2 q congruent 7 modulo 60: 1/8 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1^2 q congruent 11 modulo 60: 1/8 phi1 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1^2 q congruent 19 modulo 60: 1/8 phi1 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1^2 q congruent 23 modulo 60: 1/8 phi1 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1^2 q congruent 27 modulo 60: 1/8 phi1 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1^2 q congruent 31 modulo 60: 1/8 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1^2 q congruent 41 modulo 60: 1/8 phi1^2 q congruent 43 modulo 60: 1/8 phi1 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1^2 q congruent 53 modulo 60: 1/8 phi1^2 q congruent 59 modulo 60: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 5, 71, 7, 76, 69, 20, 68, 19, 3, 72, 82, 60, 31, 98, 19, 73, 72, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 28, 1, 2, 4 ] ] k = 8: F-action on Pi is (2,5) [35,1,8] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-7 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-7 ) q congruent 11 modulo 60: 1/8 ( q^2-10*q+29 ) q congruent 13 modulo 60: 1/8 phi1 ( q-7 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 21 modulo 60: 1/8 phi1 ( q-7 ) q congruent 23 modulo 60: 1/8 ( q^2-10*q+29 ) q congruent 25 modulo 60: 1/8 phi1 ( q-7 ) q congruent 27 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-7 ) q congruent 41 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/8 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/8 ( q^2-10*q+29 ) q congruent 49 modulo 60: 1/8 phi1 ( q-7 ) q congruent 53 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/8 ( q^2-10*q+29 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 5, 67, 5, 67, 67, 2, 7, 69, 69, 5, 69, 5, 5, 67, 68, 7, 7, 69, 3, 69, 69, 5, 82, 31, 31, 78, 31, 78, 78, 9, 19, 76, 76, 20, 72, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 4, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 4 ], [ 28, 1, 4, 4 ] ] i = 36: Pi = [ 1, 3, 4, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [36,1,1] Dynkin type is A_6(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 ( q^2-9*q+24 ) q congruent 2 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 4 modulo 60: 1/4 ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 7 modulo 60: 1/4 ( q^2-9*q+22 ) q congruent 8 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 11 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 13 modulo 60: 1/4 ( q^2-9*q+24 ) q congruent 16 modulo 60: 1/4 ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 19 modulo 60: 1/4 ( q^2-9*q+22 ) q congruent 21 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 23 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 25 modulo 60: 1/4 ( q^2-9*q+24 ) q congruent 27 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 29 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 31 modulo 60: 1/4 ( q^2-9*q+22 ) q congruent 32 modulo 60: 1/4 ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/4 ( q^2-9*q+24 ) q congruent 41 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 43 modulo 60: 1/4 ( q^2-9*q+22 ) q congruent 47 modulo 60: 1/4 ( q^2-9*q+18 ) q congruent 49 modulo 60: 1/4 ( q^2-9*q+24 ) q congruent 53 modulo 60: 1/4 ( q^2-9*q+20 ) q congruent 59 modulo 60: 1/4 ( q^2-9*q+18 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 68, 8, 77, 30, 14, 70, 19, 97, 23, 93, 87, 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 18, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 23, 1, 1, 4 ], [ 26, 1, 1, 4 ] ] k = 2: F-action on Pi is () [36,1,2] Dynkin type is A_6(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-2 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 q ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-2 ) q congruent 7 modulo 60: 1/4 q ( q-3 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 q ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-2 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-2 ) q congruent 19 modulo 60: 1/4 q ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 q ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-2 ) q congruent 27 modulo 60: 1/4 q ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-2 ) q congruent 31 modulo 60: 1/4 q ( q-3 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-2 ) q congruent 41 modulo 60: 1/4 phi1 ( q-2 ) q congruent 43 modulo 60: 1/4 q ( q-3 ) q congruent 47 modulo 60: 1/4 q ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-2 ) q congruent 53 modulo 60: 1/4 phi1 ( q-2 ) q congruent 59 modulo 60: 1/4 q ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 7, 77, 30, 81, 83, 19, 76, 59, 93, 50, 40, 103 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 18, 1, 1, 2 ], [ 26, 1, 3, 4 ] ] k = 3: F-action on Pi is (1,7)(3,6)(4,5) [36,1,3] Dynkin type is ^2A_6(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-2 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-2 ) q congruent 7 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 13 modulo 60: 1/4 phi1 ( q-2 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-2 ) q congruent 19 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 25 modulo 60: 1/4 phi1 ( q-2 ) q congruent 27 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 29 modulo 60: 1/4 phi1 ( q-2 ) q congruent 31 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-2 ) q congruent 41 modulo 60: 1/4 phi1 ( q-2 ) q congruent 43 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 47 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 49 modulo 60: 1/4 phi1 ( q-2 ) q congruent 53 modulo 60: 1/4 phi1 ( q-2 ) q congruent 59 modulo 60: 1/4 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 69, 7, 78, 31, 82, 84, 20, 76, 60, 94, 51, 40, 104 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 18, 1, 2, 2 ], [ 26, 1, 2, 4 ] ] k = 4: F-action on Pi is (1,7)(3,6)(4,5) [36,1,4] Dynkin type is ^2A_6(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-4 ) q congruent 2 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/4 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/4 q ( q-4 ) q congruent 5 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 7 modulo 60: 1/4 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/4 phi1 ( q-4 ) q congruent 11 modulo 60: 1/4 ( q^2-5*q+10 ) q congruent 13 modulo 60: 1/4 phi1 ( q-4 ) q congruent 16 modulo 60: 1/4 q ( q-4 ) q congruent 17 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 19 modulo 60: 1/4 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/4 phi1 ( q-4 ) q congruent 23 modulo 60: 1/4 ( q^2-5*q+10 ) q congruent 25 modulo 60: 1/4 phi1 ( q-4 ) q congruent 27 modulo 60: 1/4 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 31 modulo 60: 1/4 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/4 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/4 phi1 ( q-4 ) q congruent 41 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 43 modulo 60: 1/4 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/4 ( q^2-5*q+10 ) q congruent 49 modulo 60: 1/4 phi1 ( q-4 ) q congruent 53 modulo 60: 1/4 ( q^2-5*q+8 ) q congruent 59 modulo 60: 1/4 ( q^2-5*q+10 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 69, 9, 78, 31, 15, 71, 20, 98, 24, 94, 88, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 18, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 23, 1, 2, 4 ], [ 26, 1, 4, 4 ] ] i = 37: Pi = [ 1, 3, 4, 6, 7, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [37,1,1] Dynkin type is A_3(q) + A_3(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 ( q^2-12*q+51 ) q congruent 2 modulo 60: 1/8 ( q^2-10*q+16 ) q congruent 3 modulo 60: 1/8 ( q^2-12*q+27 ) q congruent 4 modulo 60: 1/8 ( q^2-10*q+24 ) q congruent 5 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 7 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 8 modulo 60: 1/8 ( q^2-10*q+16 ) q congruent 9 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 11 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 13 modulo 60: 1/8 ( q^2-12*q+43 ) q congruent 16 modulo 60: 1/8 ( q^2-10*q+32 ) q congruent 17 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 19 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 21 modulo 60: 1/8 ( q^2-12*q+43 ) q congruent 23 modulo 60: 1/8 ( q^2-12*q+27 ) q congruent 25 modulo 60: 1/8 ( q^2-12*q+43 ) q congruent 27 modulo 60: 1/8 ( q^2-12*q+27 ) q congruent 29 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 31 modulo 60: 1/8 ( q^2-12*q+43 ) q congruent 32 modulo 60: 1/8 ( q^2-10*q+16 ) q congruent 37 modulo 60: 1/8 ( q^2-12*q+43 ) q congruent 41 modulo 60: 1/8 ( q^2-12*q+43 ) q congruent 43 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 47 modulo 60: 1/8 ( q^2-12*q+27 ) q congruent 49 modulo 60: 1/8 ( q^2-12*q+43 ) q congruent 53 modulo 60: 1/8 ( q^2-12*q+35 ) q congruent 59 modulo 60: 1/8 ( q^2-12*q+27 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 8, 70, 66, 4, 68, 77, 19, 4, 68, 7, 30, 76, 8, 77, 30, 14, 97, 70, 19, 76, 97, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 14, 1, 1, 8 ], [ 21, 1, 1, 4 ], [ 23, 1, 1, 4 ], [ 25, 1, 1, 8 ] ] k = 2: F-action on Pi is (6,8) [37,1,2] Dynkin type is A_3(q) + ^2A_3(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-3 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1 ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-3 ) q congruent 7 modulo 60: 1/4 phi1 ( q-3 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-3 ) q congruent 11 modulo 60: 1/4 phi1 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-3 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-3 ) q congruent 19 modulo 60: 1/4 phi1 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-3 ) q congruent 23 modulo 60: 1/4 phi1 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-3 ) q congruent 27 modulo 60: 1/4 phi1 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-3 ) q congruent 31 modulo 60: 1/4 phi1 ( q-3 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-3 ) q congruent 41 modulo 60: 1/4 phi1 ( q-3 ) q congruent 43 modulo 60: 1/4 phi1 ( q-3 ) q congruent 47 modulo 60: 1/4 phi1 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-3 ) q congruent 53 modulo 60: 1/4 phi1 ( q-3 ) q congruent 59 modulo 60: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 4, 28, 70, 69, 7, 68, 82, 19, 5, 69, 7, 31, 76, 27, 81, 30, 36, 97, 71, 20, 76, 98, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ] ] k = 3: F-action on Pi is (1,4)(6,8) [37,1,3] Dynkin type is ^2A_3(q) + ^2A_3(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-7 ) q congruent 2 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 8 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/8 ( q^2-8*q+23 ) q congruent 13 modulo 60: 1/8 phi1 ( q-7 ) q congruent 16 modulo 60: 1/8 q ( q-6 ) q congruent 17 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/8 ( q^2-8*q+23 ) q congruent 21 modulo 60: 1/8 phi1 ( q-7 ) q congruent 23 modulo 60: 1/8 ( q^2-8*q+23 ) q congruent 25 modulo 60: 1/8 phi1 ( q-7 ) q congruent 27 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/8 ( q^2-8*q+23 ) q congruent 31 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 32 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/8 phi1 ( q-7 ) q congruent 41 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/8 ( q^2-8*q+23 ) q congruent 49 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/8 ( q^2-8*q+31 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 9, 71, 67, 5, 69, 78, 20, 5, 69, 7, 31, 76, 9, 78, 31, 15, 98, 71, 20, 76, 98, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 14, 1, 2, 8 ], [ 21, 1, 2, 4 ], [ 23, 1, 2, 4 ], [ 25, 1, 3, 8 ] ] k = 4: F-action on Pi is (1,6)(3,7)(4,8) [37,1,4] Dynkin type is A_3(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1^2 q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1^2 q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1^2 q congruent 7 modulo 60: 1/4 phi1^2 q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1^2 q congruent 11 modulo 60: 1/4 phi1^2 q congruent 13 modulo 60: 1/4 phi1^2 q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1^2 q congruent 19 modulo 60: 1/4 phi1^2 q congruent 21 modulo 60: 1/4 phi1^2 q congruent 23 modulo 60: 1/4 phi1^2 q congruent 25 modulo 60: 1/4 phi1^2 q congruent 27 modulo 60: 1/4 phi1^2 q congruent 29 modulo 60: 1/4 phi1^2 q congruent 31 modulo 60: 1/4 phi1^2 q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1^2 q congruent 41 modulo 60: 1/4 phi1^2 q congruent 43 modulo 60: 1/4 phi1^2 q congruent 47 modulo 60: 1/4 phi1^2 q congruent 49 modulo 60: 1/4 phi1^2 q congruent 53 modulo 60: 1/4 phi1^2 q congruent 59 modulo 60: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 7, 76, 22, 40, 92 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 21, 1, 1, 2 ], [ 21, 1, 2, 2 ] ] k = 5: F-action on Pi is (1,6,4,8)(3,7) [37,1,5] Dynkin type is ^2A_3(q^2) + T(phi4) Order of center |Z^F|: phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 phi2 q congruent 2 modulo 60: 1/4 ( q^2-4 ) q congruent 3 modulo 60: 1/4 ( q^2-5 ) q congruent 4 modulo 60: 1/4 q^2 q congruent 5 modulo 60: 1/4 phi1 phi2 q congruent 7 modulo 60: 1/4 ( q^2-5 ) q congruent 8 modulo 60: 1/4 ( q^2-4 ) q congruent 9 modulo 60: 1/4 phi1 phi2 q congruent 11 modulo 60: 1/4 phi1 phi2 q congruent 13 modulo 60: 1/4 ( q^2-5 ) q congruent 16 modulo 60: 1/4 q^2 q congruent 17 modulo 60: 1/4 ( q^2-5 ) q congruent 19 modulo 60: 1/4 phi1 phi2 q congruent 21 modulo 60: 1/4 phi1 phi2 q congruent 23 modulo 60: 1/4 ( q^2-5 ) q congruent 25 modulo 60: 1/4 phi1 phi2 q congruent 27 modulo 60: 1/4 ( q^2-5 ) q congruent 29 modulo 60: 1/4 phi1 phi2 q congruent 31 modulo 60: 1/4 phi1 phi2 q congruent 32 modulo 60: 1/4 ( q^2-4 ) q congruent 37 modulo 60: 1/4 ( q^2-5 ) q congruent 41 modulo 60: 1/4 phi1 phi2 q congruent 43 modulo 60: 1/4 ( q^2-5 ) q congruent 47 modulo 60: 1/4 ( q^2-5 ) q congruent 49 modulo 60: 1/4 phi1 phi2 q congruent 53 modulo 60: 1/4 ( q^2-5 ) q congruent 59 modulo 60: 1/4 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 6, 75, 22, 39, 92 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 9, 1, 1, 1 ] ] i = 38: Pi = [ 1, 3, 5, 6, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [38,1,1] Dynkin type is A_2(q) + A_2(q) + A_2(q) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 ( q^2-14*q+49 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/36 ( q^2-14*q+40 ) q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/36 ( q^2-14*q+49 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/36 ( q^2-14*q+49 ) q congruent 16 modulo 60: 1/36 ( q^2-14*q+40 ) q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/36 ( q^2-14*q+49 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/36 ( q^2-14*q+49 ) q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/36 ( q^2-14*q+49 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/36 ( q^2-14*q+49 ) q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/36 ( q^2-14*q+49 ) q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/36 ( q^2-14*q+49 ) q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 8, 66, 4, 77, 8, 77, 14, 66, 4, 77, 4, 68, 30, 77, 30, 83, 8, 77, 14, 77, 30, 83, 14, 83, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 18 ], [ 8, 1, 1, 12 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 22, 1, 1, 36 ], [ 27, 1, 1, 12 ] ] k = 2: F-action on Pi is ( 5, 8)( 6,240) [38,1,2] Dynkin type is A_2(q) + A_2(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/4 phi1^2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/4 phi1^2 q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/4 phi1^2 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/4 phi1^2 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/4 phi1^2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1^2 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/4 phi1^2 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/4 phi1^2 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 87, 7, 76, 40, 81, 59, 85 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 22, 1, 1, 4 ], [ 27, 1, 3, 4 ] ] k = 3: F-action on Pi is () [38,1,3] Dynkin type is A_2(q) + A_2(q) + A_2(q) + T(phi3) Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/18 phi1 ( q+2 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/18 phi1 ( q+2 ) q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/18 phi1 ( q+2 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/18 phi1 ( q+2 ) q congruent 16 modulo 60: 1/18 phi1 ( q+2 ) q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/18 phi1 ( q+2 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/18 phi1 ( q+2 ) q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/18 phi1 ( q+2 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/18 phi1 ( q+2 ) q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/18 phi1 ( q+2 ) q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/18 phi1 ( q+2 ) q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 14, 77, 30, 83, 14, 83, 12, 77, 30, 83, 30, 81, 37, 83, 37, 79, 14, 83, 12, 83, 37, 79, 12, 79, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 27, 1, 5, 6 ] ] k = 4: F-action on Pi is ( 5, 8)( 6,240) [38,1,4] Dynkin type is A_2(q) + A_2(q^2) + T(phi6) Order of center |Z^F|: phi6 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/6 q phi1 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/6 q phi1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/6 q phi1 q congruent 16 modulo 60: 1/6 q phi1 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/6 q phi1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/6 q phi1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/6 q phi1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/6 q phi1 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/6 q phi1 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/6 q phi1 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 28, 96, 33, 82, 60, 86, 36, 99, 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 27, 1, 4, 6 ] ] k = 5: F-action on Pi is () [38,1,5] Dynkin type is A_2(q) + A_2(q) + A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/12 q ( q-4 ) q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/12 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/12 phi1 ( q-3 ) q congruent 16 modulo 60: 1/12 q ( q-4 ) q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/12 phi1 ( q-3 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/12 phi1 ( q-3 ) q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/12 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 phi1 ( q-3 ) q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/12 phi1 ( q-3 ) q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/12 phi1 ( q-3 ) q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 77, 4, 68, 30, 77, 30, 83, 4, 68, 30, 68, 7, 81, 30, 81, 37, 77, 30, 83, 30, 81, 37, 83, 37, 79 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 1, 12 ], [ 22, 1, 2, 12 ], [ 27, 1, 2, 4 ] ] k = 6: F-action on Pi is ( 5, 8)( 6,240) [38,1,6] Dynkin type is A_2(q) + A_2(q^2) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/12 q ( q-4 ) q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/12 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/12 phi1 ( q-3 ) q congruent 16 modulo 60: 1/12 q ( q-4 ) q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/12 phi1 ( q-3 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/12 phi1 ( q-3 ) q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/12 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 phi1 ( q-3 ) q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/12 phi1 ( q-3 ) q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/12 phi1 ( q-3 ) q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 35, 69, 20, 88, 27, 95, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 22, 1, 2, 12 ], [ 27, 1, 6, 12 ] ] k = 7: F-action on Pi is ( 1, 3)( 5,240)( 6, 8) [38,1,7] Dynkin type is ^2A_2(q) + A_2(q^2) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/12 ( q^2-8*q+12 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/12 ( q^2-8*q+12 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/12 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/12 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 35, 68, 19, 87, 28, 96, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 6 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 3, 12 ], [ 22, 1, 3, 12 ], [ 27, 1, 1, 12 ] ] k = 8: F-action on Pi is ( 1, 3)( 5, 6)( 8,240) [38,1,8] Dynkin type is ^2A_2(q) + ^2A_2(q) + ^2A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/12 ( q^2-4*q+4 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/12 ( q^2-4*q+4 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/12 ( q^2-4*q+7 ) q congruent 59 modulo 60: 1/12 ( q^2-4*q+7 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 78, 5, 69, 31, 78, 31, 84, 5, 69, 31, 69, 7, 82, 31, 82, 38, 78, 31, 84, 31, 82, 38, 84, 38, 80 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 4, 12 ], [ 22, 1, 3, 12 ], [ 27, 1, 3, 4 ] ] k = 9: F-action on Pi is ( 1, 3)( 5,240)( 6, 8) [38,1,9] Dynkin type is ^2A_2(q) + A_2(q^2) + T(phi3) Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/6 q phi2 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/6 q phi2 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/6 q phi2 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/6 q phi2 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/6 q phi2 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/6 q phi2 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/6 q phi2 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/6 q phi2 q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/6 q phi2 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/6 q phi2 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/6 q phi2 q congruent 59 modulo 60: 1/6 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 27, 95, 34, 81, 59, 85, 36, 99, 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 27, 1, 5, 6 ] ] k = 10: F-action on Pi is ( 1, 3)( 5,240)( 6, 8) [38,1,10] Dynkin type is ^2A_2(q) + A_2(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1^2 q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/4 phi1^2 q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1^2 q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/4 phi1^2 q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/4 phi1^2 q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/4 phi1^2 q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/4 phi1^2 q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/4 phi1^2 q congruent 59 modulo 60: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 88, 7, 76, 40, 82, 60, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 27, 1, 2, 4 ] ] k = 11: F-action on Pi is ( 1, 3)( 5, 6)( 8,240) [38,1,11] Dynkin type is ^2A_2(q) + ^2A_2(q) + ^2A_2(q) + T(phi6) Order of center |Z^F|: phi6 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/18 phi2 ( q-2 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/18 phi2 ( q-2 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/18 phi2 ( q-2 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/18 phi2 ( q-2 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/18 phi2 ( q-2 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/18 phi2 ( q-2 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/18 phi2 ( q-2 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/18 phi2 ( q-2 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/18 phi2 ( q-2 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/18 phi2 ( q-2 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/18 phi2 ( q-2 ) q congruent 59 modulo 60: 1/18 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 78, 15, 78, 31, 84, 15, 84, 13, 78, 31, 84, 31, 82, 38, 84, 38, 80, 15, 84, 13, 84, 38, 80, 13, 80, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 27, 1, 4, 6 ] ] k = 12: F-action on Pi is ( 1, 3)( 5, 6)( 8,240) [38,1,12] Dynkin type is ^2A_2(q) + ^2A_2(q) + ^2A_2(q) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/36 ( q^2-10*q+16 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/36 ( q^2-10*q+25 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/36 ( q^2-10*q+16 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/36 ( q^2-10*q+25 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/36 ( q^2-10*q+25 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/36 ( q^2-10*q+25 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/36 ( q^2-10*q+25 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/36 ( q^2-10*q+16 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/36 ( q^2-10*q+25 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/36 ( q^2-10*q+25 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/36 ( q^2-10*q+25 ) q congruent 59 modulo 60: 1/36 ( q^2-10*q+25 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 9, 67, 5, 78, 9, 78, 15, 67, 5, 78, 5, 69, 31, 78, 31, 84, 9, 78, 15, 78, 31, 84, 15, 84, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 18 ], [ 8, 1, 2, 12 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 4, 36 ], [ 22, 1, 4, 36 ], [ 27, 1, 6, 12 ] ] k = 13: F-action on Pi is ( 1, 5, 8)( 3, 6,240) [38,1,13] Dynkin type is A_2(q^3) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/18 phi1 ( q-4 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/18 phi1 ( q-4 ) q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/18 phi1 ( q-4 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/18 phi1 ( q-4 ) q congruent 16 modulo 60: 1/18 phi1 ( q-4 ) q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/18 phi1 ( q-4 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/18 phi1 ( q-4 ) q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/18 phi1 ( q-4 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/18 phi1 ( q-4 ) q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/18 phi1 ( q-4 ) q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/18 phi1 ( q-4 ) q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 14, 87, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 5, 18 ], [ 27, 1, 1, 12 ] ] k = 14: F-action on Pi is ( 1, 5, 8)( 3, 6,240) [38,1,14] Dynkin type is A_2(q^3) + T(phi3) Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/9 phi1 ( q+2 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/9 phi1 ( q+2 ) q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/9 phi1 ( q+2 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/9 phi1 ( q+2 ) q congruent 16 modulo 60: 1/9 phi1 ( q+2 ) q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/9 phi1 ( q+2 ) q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/9 phi1 ( q+2 ) q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/9 phi1 ( q+2 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/9 phi1 ( q+2 ) q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/9 phi1 ( q+2 ) q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/9 phi1 ( q+2 ) q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 12, 85, 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 8, 1, 1, 6 ], [ 27, 1, 5, 6 ] ] k = 15: F-action on Pi is ( 1, 5, 8)( 3, 6,240) [38,1,15] Dynkin type is A_2(q^3) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 1/6 q phi1 q congruent 5 modulo 60: 0 q congruent 7 modulo 60: 1/6 q phi1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 0 q congruent 13 modulo 60: 1/6 q phi1 q congruent 16 modulo 60: 1/6 q phi1 q congruent 17 modulo 60: 0 q congruent 19 modulo 60: 1/6 q phi1 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 0 q congruent 25 modulo 60: 1/6 q phi1 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 0 q congruent 31 modulo 60: 1/6 q phi1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/6 q phi1 q congruent 41 modulo 60: 0 q congruent 43 modulo 60: 1/6 q phi1 q congruent 47 modulo 60: 0 q congruent 49 modulo 60: 1/6 q phi1 q congruent 53 modulo 60: 0 q congruent 59 modulo 60: 0 Fusion of maximal tori of C^F in those of G^F: [ 83, 40, 105 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 5, 6 ], [ 27, 1, 2, 4 ] ] k = 16: F-action on Pi is ( 1, 6, 8, 3, 5,240) [38,1,16] Dynkin type is ^2A_2(q^3) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/6 phi2 ( q-2 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/6 phi2 ( q-2 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/6 phi2 ( q-2 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/6 phi2 ( q-2 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/6 phi2 ( q-2 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/6 phi2 ( q-2 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/6 phi2 ( q-2 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/6 phi2 ( q-2 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/6 phi2 ( q-2 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/6 phi2 ( q-2 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/6 phi2 ( q-2 ) q congruent 59 modulo 60: 1/6 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 84, 40, 106 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 6, 6 ], [ 27, 1, 3, 4 ] ] k = 17: F-action on Pi is ( 1, 6, 8, 3, 5,240) [38,1,17] Dynkin type is ^2A_2(q^3) + T(phi6) Order of center |Z^F|: phi6 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/9 phi2 ( q-2 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/9 phi2 ( q-2 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/9 phi2 ( q-2 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/9 phi2 ( q-2 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/9 phi2 ( q-2 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/9 phi2 ( q-2 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/9 phi2 ( q-2 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/9 phi2 ( q-2 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/9 phi2 ( q-2 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/9 phi2 ( q-2 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/9 phi2 ( q-2 ) q congruent 59 modulo 60: 1/9 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 13, 86, 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 8, 1, 2, 6 ], [ 27, 1, 4, 6 ] ] k = 18: F-action on Pi is ( 1, 6, 8, 3, 5,240) [38,1,18] Dynkin type is ^2A_2(q^3) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 60: 0 q congruent 2 modulo 60: 1/18 phi2 ( q-2 ) q congruent 3 modulo 60: 0 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/18 phi2 ( q-2 ) q congruent 7 modulo 60: 0 q congruent 8 modulo 60: 1/18 phi2 ( q-2 ) q congruent 9 modulo 60: 0 q congruent 11 modulo 60: 1/18 phi2 ( q-2 ) q congruent 13 modulo 60: 0 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/18 phi2 ( q-2 ) q congruent 19 modulo 60: 0 q congruent 21 modulo 60: 0 q congruent 23 modulo 60: 1/18 phi2 ( q-2 ) q congruent 25 modulo 60: 0 q congruent 27 modulo 60: 0 q congruent 29 modulo 60: 1/18 phi2 ( q-2 ) q congruent 31 modulo 60: 0 q congruent 32 modulo 60: 1/18 phi2 ( q-2 ) q congruent 37 modulo 60: 0 q congruent 41 modulo 60: 1/18 phi2 ( q-2 ) q congruent 43 modulo 60: 0 q congruent 47 modulo 60: 1/18 phi2 ( q-2 ) q congruent 49 modulo 60: 0 q congruent 53 modulo 60: 1/18 phi2 ( q-2 ) q congruent 59 modulo 60: 1/18 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 15, 88, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 6, 18 ], [ 27, 1, 6, 12 ] ] i = 39: Pi = [ 2, 3, 4, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [39,1,1] Dynkin type is D_6(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 2 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 8 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 16 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 32 modulo 60: 1/8 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/8 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/8 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 4, 3, 5, 66, 70, 68, 72, 69, 4, 16, 19, 7, 18, 68, 68, 73, 8, 28, 30, 31, 77, 96, 82, 97, 14, 38, 70, 89, 76, 19, 19, 44, 23, 51, 87, 87 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ] ] k = 2: F-action on Pi is (2,3) [39,1,2] Dynkin type is ^2D_6(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1^2 q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1^2 q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1^2 q congruent 7 modulo 60: 1/4 phi1^2 q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1^2 q congruent 11 modulo 60: 1/4 phi1^2 q congruent 13 modulo 60: 1/4 phi1^2 q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1^2 q congruent 19 modulo 60: 1/4 phi1^2 q congruent 21 modulo 60: 1/4 phi1^2 q congruent 23 modulo 60: 1/4 phi1^2 q congruent 25 modulo 60: 1/4 phi1^2 q congruent 27 modulo 60: 1/4 phi1^2 q congruent 29 modulo 60: 1/4 phi1^2 q congruent 31 modulo 60: 1/4 phi1^2 q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1^2 q congruent 41 modulo 60: 1/4 phi1^2 q congruent 43 modulo 60: 1/4 phi1^2 q congruent 47 modulo 60: 1/4 phi1^2 q congruent 49 modulo 60: 1/4 phi1^2 q congruent 53 modulo 60: 1/4 phi1^2 q congruent 59 modulo 60: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 4, 3, 5, 70, 68, 72, 69, 71, 19, 7, 18, 20, 76, 75, 28, 30, 31, 27, 82, 97, 81, 98, 36, 89, 76, 90, 43, 22, 51, 50, 100 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ] ] k = 3: F-action on Pi is () [39,1,3] Dynkin type is D_6(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 1/8 q ( q-2 ) q congruent 3 modulo 60: 1/8 phi1 ( q-3 ) q congruent 4 modulo 60: 1/8 q ( q-2 ) q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 ( q-3 ) q congruent 8 modulo 60: 1/8 q ( q-2 ) q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 1/8 q ( q-2 ) q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 ( q-3 ) q congruent 32 modulo 60: 1/8 q ( q-2 ) q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 3, 5, 2, 68, 72, 69, 71, 67, 7, 18, 20, 5, 17, 69, 69, 74, 30, 31, 27, 9, 81, 98, 78, 95, 37, 15, 76, 90, 71, 20, 20, 45, 50, 24, 88, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ] ] k = 4: F-action on Pi is () [39,1,4] Dynkin type is D_6(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-3 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 phi1 ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-3 ) q congruent 7 modulo 60: 1/4 phi1 ( q-3 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-3 ) q congruent 11 modulo 60: 1/4 phi1 ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-3 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-3 ) q congruent 19 modulo 60: 1/4 phi1 ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-3 ) q congruent 23 modulo 60: 1/4 phi1 ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-3 ) q congruent 27 modulo 60: 1/4 phi1 ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-3 ) q congruent 31 modulo 60: 1/4 phi1 ( q-3 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-3 ) q congruent 41 modulo 60: 1/4 phi1 ( q-3 ) q congruent 43 modulo 60: 1/4 phi1 ( q-3 ) q congruent 47 modulo 60: 1/4 phi1 ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-3 ) q congruent 53 modulo 60: 1/4 phi1 ( q-3 ) q congruent 59 modulo 60: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 68, 69, 67, 4, 19, 7, 20, 5, 68, 73, 76, 69, 74, 7, 3, 18, 77, 82, 81, 78, 30, 60, 31, 59, 83, 84, 19, 43, 20, 76, 72, 91, 93, 94, 40, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ] ] k = 5: F-action on Pi is (2,3) [39,1,5] Dynkin type is ^2D_6(q) + T(phi4) Order of center |Z^F|: phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 phi2 q congruent 2 modulo 60: 1/4 q^2 q congruent 3 modulo 60: 1/4 phi1 phi2 q congruent 4 modulo 60: 1/4 q^2 q congruent 5 modulo 60: 1/4 phi1 phi2 q congruent 7 modulo 60: 1/4 phi1 phi2 q congruent 8 modulo 60: 1/4 q^2 q congruent 9 modulo 60: 1/4 phi1 phi2 q congruent 11 modulo 60: 1/4 phi1 phi2 q congruent 13 modulo 60: 1/4 phi1 phi2 q congruent 16 modulo 60: 1/4 q^2 q congruent 17 modulo 60: 1/4 phi1 phi2 q congruent 19 modulo 60: 1/4 phi1 phi2 q congruent 21 modulo 60: 1/4 phi1 phi2 q congruent 23 modulo 60: 1/4 phi1 phi2 q congruent 25 modulo 60: 1/4 phi1 phi2 q congruent 27 modulo 60: 1/4 phi1 phi2 q congruent 29 modulo 60: 1/4 phi1 phi2 q congruent 31 modulo 60: 1/4 phi1 phi2 q congruent 32 modulo 60: 1/4 q^2 q congruent 37 modulo 60: 1/4 phi1 phi2 q congruent 41 modulo 60: 1/4 phi1 phi2 q congruent 43 modulo 60: 1/4 phi1 phi2 q congruent 47 modulo 60: 1/4 phi1 phi2 q congruent 49 modulo 60: 1/4 phi1 phi2 q congruent 53 modulo 60: 1/4 phi1 phi2 q congruent 59 modulo 60: 1/4 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 70, 72, 71, 16, 19, 18, 20, 17, 73, 76, 75, 74, 18, 6, 96, 97, 98, 95, 60, 53, 59, 54, 99, 44, 22, 45, 91, 75, 108, 107, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ] i = 40: Pi = [ 2, 3, 4, 5, 7, 8 ] j = 1: Omega trivial k = 1: F-action on Pi is () [40,1,1] Dynkin type is D_4(q) + A_2(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 2 modulo 60: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 4 modulo 60: 1/12 ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 7 modulo 60: 1/12 ( q^2-11*q+28 ) q congruent 8 modulo 60: 1/12 ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 11 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 13 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 16 modulo 60: 1/12 ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 19 modulo 60: 1/12 ( q^2-11*q+28 ) q congruent 21 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 23 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 25 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 27 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 29 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 31 modulo 60: 1/12 ( q^2-11*q+28 ) q congruent 32 modulo 60: 1/12 ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 41 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 43 modulo 60: 1/12 ( q^2-11*q+28 ) q congruent 47 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 49 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 53 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 59 modulo 60: 1/12 ( q^2-11*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 8, 4, 68, 30, 3, 69, 27, 66, 4, 77, 70, 19, 97, 68, 7, 81, 4, 68, 30, 4, 68, 30, 16, 73, 53, 8, 77, 14, 28, 82, 36, 70, 19, 97, 70, 19, 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ] ] k = 2: F-action on Pi is (2,3)(7,8) [40,1,2] Dynkin type is ^2D_4(q) + ^2A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-2 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-2 ) q congruent 7 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 13 modulo 60: 1/4 phi1 ( q-2 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-2 ) q congruent 19 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 25 modulo 60: 1/4 phi1 ( q-2 ) q congruent 27 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 29 modulo 60: 1/4 phi1 ( q-2 ) q congruent 31 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-2 ) q congruent 41 modulo 60: 1/4 phi1 ( q-2 ) q congruent 43 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 47 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 49 modulo 60: 1/4 phi1 ( q-2 ) q congruent 53 modulo 60: 1/4 phi1 ( q-2 ) q congruent 59 modulo 60: 1/4 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 28, 5, 69, 31, 72, 19, 96, 69, 7, 82, 71, 20, 98, 20, 76, 60, 31, 82, 38, 27, 81, 36, 90, 43, 110 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ] ] k = 3: F-action on Pi is (2,5) [40,1,3] Dynkin type is ^2D_4(q) + A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-2 ) q congruent 2 modulo 60: 1/4 q ( q-2 ) q congruent 3 modulo 60: 1/4 q ( q-3 ) q congruent 4 modulo 60: 1/4 q ( q-2 ) q congruent 5 modulo 60: 1/4 phi1 ( q-2 ) q congruent 7 modulo 60: 1/4 q ( q-3 ) q congruent 8 modulo 60: 1/4 q ( q-2 ) q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 q ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-2 ) q congruent 16 modulo 60: 1/4 q ( q-2 ) q congruent 17 modulo 60: 1/4 phi1 ( q-2 ) q congruent 19 modulo 60: 1/4 q ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 q ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-2 ) q congruent 27 modulo 60: 1/4 q ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-2 ) q congruent 31 modulo 60: 1/4 q ( q-3 ) q congruent 32 modulo 60: 1/4 q ( q-2 ) q congruent 37 modulo 60: 1/4 phi1 ( q-2 ) q congruent 41 modulo 60: 1/4 phi1 ( q-2 ) q congruent 43 modulo 60: 1/4 q ( q-3 ) q congruent 47 modulo 60: 1/4 q ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-2 ) q congruent 53 modulo 60: 1/4 phi1 ( q-2 ) q congruent 59 modulo 60: 1/4 q ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 30, 3, 69, 27, 70, 19, 97, 68, 7, 81, 72, 20, 95, 19, 76, 59, 28, 82, 36, 30, 81, 37, 89, 43, 109 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ] ] k = 4: F-action on Pi is (2,3,5)(7,8) [40,1,4] Dynkin type is ^3D_4(q) + ^2A_2(q) + T(phi6) Order of center |Z^F|: phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q phi1 q congruent 2 modulo 60: 1/6 phi2 ( q-2 ) q congruent 3 modulo 60: 1/6 q phi1 q congruent 4 modulo 60: 1/6 q phi1 q congruent 5 modulo 60: 1/6 phi2 ( q-2 ) q congruent 7 modulo 60: 1/6 q phi1 q congruent 8 modulo 60: 1/6 phi2 ( q-2 ) q congruent 9 modulo 60: 1/6 q phi1 q congruent 11 modulo 60: 1/6 phi2 ( q-2 ) q congruent 13 modulo 60: 1/6 q phi1 q congruent 16 modulo 60: 1/6 q phi1 q congruent 17 modulo 60: 1/6 phi2 ( q-2 ) q congruent 19 modulo 60: 1/6 q phi1 q congruent 21 modulo 60: 1/6 q phi1 q congruent 23 modulo 60: 1/6 phi2 ( q-2 ) q congruent 25 modulo 60: 1/6 q phi1 q congruent 27 modulo 60: 1/6 q phi1 q congruent 29 modulo 60: 1/6 phi2 ( q-2 ) q congruent 31 modulo 60: 1/6 q phi1 q congruent 32 modulo 60: 1/6 phi2 ( q-2 ) q congruent 37 modulo 60: 1/6 q phi1 q congruent 41 modulo 60: 1/6 phi2 ( q-2 ) q congruent 43 modulo 60: 1/6 q phi1 q congruent 47 modulo 60: 1/6 phi2 ( q-2 ) q congruent 49 modulo 60: 1/6 q phi1 q congruent 53 modulo 60: 1/6 phi2 ( q-2 ) q congruent 59 modulo 60: 1/6 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 87, 33, 84, 38, 80, 88, 40, 86, 15, 84, 13, 34, 85, 29, 58, 102, 56, 13, 80, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ] ] k = 5: F-action on Pi is (2,5,3) [40,1,5] Dynkin type is ^3D_4(q) + A_2(q) + T(phi3) Order of center |Z^F|: phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 phi1 ( q+2 ) q congruent 2 modulo 60: 1/6 q phi2 q congruent 3 modulo 60: 1/6 q phi2 q congruent 4 modulo 60: 1/6 phi1 ( q+2 ) q congruent 5 modulo 60: 1/6 q phi2 q congruent 7 modulo 60: 1/6 phi1 ( q+2 ) q congruent 8 modulo 60: 1/6 q phi2 q congruent 9 modulo 60: 1/6 q phi2 q congruent 11 modulo 60: 1/6 q phi2 q congruent 13 modulo 60: 1/6 phi1 ( q+2 ) q congruent 16 modulo 60: 1/6 phi1 ( q+2 ) q congruent 17 modulo 60: 1/6 q phi2 q congruent 19 modulo 60: 1/6 phi1 ( q+2 ) q congruent 21 modulo 60: 1/6 q phi2 q congruent 23 modulo 60: 1/6 q phi2 q congruent 25 modulo 60: 1/6 phi1 ( q+2 ) q congruent 27 modulo 60: 1/6 q phi2 q congruent 29 modulo 60: 1/6 q phi2 q congruent 31 modulo 60: 1/6 phi1 ( q+2 ) q congruent 32 modulo 60: 1/6 q phi2 q congruent 37 modulo 60: 1/6 phi1 ( q+2 ) q congruent 41 modulo 60: 1/6 q phi2 q congruent 43 modulo 60: 1/6 phi1 ( q+2 ) q congruent 47 modulo 60: 1/6 q phi2 q congruent 49 modulo 60: 1/6 phi1 ( q+2 ) q congruent 53 modulo 60: 1/6 q phi2 q congruent 59 modulo 60: 1/6 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 14, 83, 12, 87, 40, 85, 83, 37, 79, 35, 88, 34, 12, 79, 10, 57, 101, 55, 33, 86, 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ] ] k = 6: F-action on Pi is (7,8) [40,1,6] Dynkin type is D_4(q) + ^2A_2(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q-6 ) q congruent 2 modulo 60: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 4 modulo 60: 1/12 q ( q-4 ) q congruent 5 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 7 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 8 modulo 60: 1/12 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/12 phi1 ( q-6 ) q congruent 11 modulo 60: 1/12 ( q^2-7*q+16 ) q congruent 13 modulo 60: 1/12 phi1 ( q-6 ) q congruent 16 modulo 60: 1/12 q ( q-4 ) q congruent 17 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 19 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 21 modulo 60: 1/12 phi1 ( q-6 ) q congruent 23 modulo 60: 1/12 ( q^2-7*q+16 ) q congruent 25 modulo 60: 1/12 phi1 ( q-6 ) q congruent 27 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 29 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 31 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 32 modulo 60: 1/12 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/12 phi1 ( q-6 ) q congruent 41 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 43 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 47 modulo 60: 1/12 ( q^2-7*q+16 ) q congruent 49 modulo 60: 1/12 phi1 ( q-6 ) q congruent 53 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 59 modulo 60: 1/12 ( q^2-7*q+16 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 28, 5, 69, 31, 2, 67, 9, 69, 7, 82, 71, 20, 98, 67, 5, 78, 5, 69, 31, 5, 69, 31, 17, 74, 54, 27, 81, 36, 9, 78, 15, 71, 20, 98, 71, 20, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ] ] i = 41: Pi = [ 2, 3, 4, 5, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [41,1,1] Dynkin type is D_4(q) + A_1(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 ( q^2-10*q+21 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 7 modulo 60: 1/16 ( q^2-10*q+21 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 11 modulo 60: 1/16 ( q^2-10*q+21 ) q congruent 13 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 19 modulo 60: 1/16 ( q^2-10*q+21 ) q congruent 21 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 23 modulo 60: 1/16 ( q^2-10*q+21 ) q congruent 25 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 27 modulo 60: 1/16 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 31 modulo 60: 1/16 ( q^2-10*q+21 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 41 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 43 modulo 60: 1/16 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/16 ( q^2-10*q+21 ) q congruent 49 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 53 modulo 60: 1/16 ( q^2-10*q+25 ) q congruent 59 modulo 60: 1/16 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 4, 68, 68, 7, 3, 69, 69, 5, 66, 4, 4, 68, 70, 19, 19, 76, 68, 7, 7, 69, 4, 68, 68, 3, 4, 68, 68, 7, 16, 73, 73, 18, 8, 77, 77, 30, 28, 82, 82, 31, 70, 19, 19, 72, 70, 19, 19, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 39, 1, 1, 8 ] ] k = 2: F-action on Pi is ( 7,240) [41,1,2] Dynkin type is D_4(q) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 7, 76, 5, 71, 68, 19, 76, 22, 69, 20, 3, 72, 7, 76, 18, 75, 30, 97, 31, 98, 72, 18, 76, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ], [ 39, 1, 2, 4 ] ] k = 3: F-action on Pi is ( 2, 5)( 7,240) [41,1,3] Dynkin type is ^2D_4(q) + A_1(q^2) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q-5 ) q congruent 7 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q-5 ) q congruent 11 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q-5 ) q congruent 19 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1 ( q-5 ) q congruent 23 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1 ( q-5 ) q congruent 27 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1 ( q-5 ) q congruent 31 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q-5 ) q congruent 41 modulo 60: 1/16 phi1 ( q-5 ) q congruent 43 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1 ( q-5 ) q congruent 53 modulo 60: 1/16 phi1 ( q-5 ) q congruent 59 modulo 60: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 3, 72, 70, 16, 68, 19, 72, 18, 19, 73, 28, 96, 30, 97, 89, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 39, 1, 1, 8 ] ] k = 4: F-action on Pi is (2,5) [41,1,4] Dynkin type is ^2D_4(q) + A_1(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 3, 3, 69, 69, 5, 70, 19, 19, 72, 68, 7, 7, 69, 72, 20, 20, 71, 19, 76, 76, 20, 28, 82, 82, 31, 30, 81, 81, 27, 89, 43, 43, 90 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 39, 1, 2, 4 ] ] k = 5: F-action on Pi is ( 7,240) [41,1,5] Dynkin type is D_4(q) + A_1(q^2) + T(phi4) Order of center |Z^F|: phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 phi2 q congruent 7 modulo 60: 1/8 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 phi2 q congruent 11 modulo 60: 1/8 phi1 phi2 q congruent 13 modulo 60: 1/8 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 phi2 q congruent 19 modulo 60: 1/8 phi1 phi2 q congruent 21 modulo 60: 1/8 phi1 phi2 q congruent 23 modulo 60: 1/8 phi1 phi2 q congruent 25 modulo 60: 1/8 phi1 phi2 q congruent 27 modulo 60: 1/8 phi1 phi2 q congruent 29 modulo 60: 1/8 phi1 phi2 q congruent 31 modulo 60: 1/8 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 phi2 q congruent 41 modulo 60: 1/8 phi1 phi2 q congruent 43 modulo 60: 1/8 phi1 phi2 q congruent 47 modulo 60: 1/8 phi1 phi2 q congruent 49 modulo 60: 1/8 phi1 phi2 q congruent 53 modulo 60: 1/8 phi1 phi2 q congruent 59 modulo 60: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 70, 16, 76, 18, 71, 17, 19, 73, 22, 75, 20, 74, 72, 18, 76, 18, 75, 6, 97, 53, 98, 54, 18, 75, 22, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 3 ], [ 39, 1, 5, 4 ] ] k = 6: F-action on Pi is () [41,1,6] Dynkin type is D_4(q) + A_1(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 68, 7, 3, 69, 69, 5, 5, 67, 4, 68, 68, 7, 19, 76, 72, 20, 7, 69, 69, 5, 68, 7, 7, 69, 68, 3, 7, 69, 73, 18, 18, 74, 77, 30, 30, 81, 82, 31, 31, 78, 19, 76, 76, 20, 19, 72, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 39, 1, 4, 4 ] ] k = 7: F-action on Pi is ( 2, 5)( 7,240) [41,1,7] Dynkin type is ^2D_4(q) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 phi2 q congruent 7 modulo 60: 1/8 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 phi2 q congruent 11 modulo 60: 1/8 phi1 phi2 q congruent 13 modulo 60: 1/8 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 phi2 q congruent 19 modulo 60: 1/8 phi1 phi2 q congruent 21 modulo 60: 1/8 phi1 phi2 q congruent 23 modulo 60: 1/8 phi1 phi2 q congruent 25 modulo 60: 1/8 phi1 phi2 q congruent 27 modulo 60: 1/8 phi1 phi2 q congruent 29 modulo 60: 1/8 phi1 phi2 q congruent 31 modulo 60: 1/8 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 phi2 q congruent 41 modulo 60: 1/8 phi1 phi2 q congruent 43 modulo 60: 1/8 phi1 phi2 q congruent 47 modulo 60: 1/8 phi1 phi2 q congruent 49 modulo 60: 1/8 phi1 phi2 q congruent 53 modulo 60: 1/8 phi1 phi2 q congruent 59 modulo 60: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 69, 20, 19, 73, 7, 76, 20, 74, 76, 18, 82, 60, 81, 59, 43, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 39, 1, 4, 4 ] ] k = 8: F-action on Pi is (2,5) [41,1,8] Dynkin type is ^2D_4(q) + A_1(q) + A_1(q) + T(phi4) Order of center |Z^F|: phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 phi2 q congruent 7 modulo 60: 1/8 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 phi2 q congruent 11 modulo 60: 1/8 phi1 phi2 q congruent 13 modulo 60: 1/8 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 phi2 q congruent 19 modulo 60: 1/8 phi1 phi2 q congruent 21 modulo 60: 1/8 phi1 phi2 q congruent 23 modulo 60: 1/8 phi1 phi2 q congruent 25 modulo 60: 1/8 phi1 phi2 q congruent 27 modulo 60: 1/8 phi1 phi2 q congruent 29 modulo 60: 1/8 phi1 phi2 q congruent 31 modulo 60: 1/8 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 phi2 q congruent 41 modulo 60: 1/8 phi1 phi2 q congruent 43 modulo 60: 1/8 phi1 phi2 q congruent 47 modulo 60: 1/8 phi1 phi2 q congruent 49 modulo 60: 1/8 phi1 phi2 q congruent 53 modulo 60: 1/8 phi1 phi2 q congruent 59 modulo 60: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 19, 72, 72, 20, 20, 71, 16, 73, 73, 18, 19, 76, 76, 20, 18, 74, 74, 17, 73, 18, 18, 74, 96, 60, 60, 98, 97, 59, 59, 95, 44, 91, 91, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 39, 1, 5, 4 ] ] k = 9: F-action on Pi is () [41,1,9] Dynkin type is D_4(q) + A_1(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q-5 ) q congruent 7 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q-5 ) q congruent 11 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q-5 ) q congruent 19 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1 ( q-5 ) q congruent 23 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1 ( q-5 ) q congruent 27 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1 ( q-5 ) q congruent 31 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q-5 ) q congruent 41 modulo 60: 1/16 phi1 ( q-5 ) q congruent 43 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1 ( q-5 ) q congruent 53 modulo 60: 1/16 phi1 ( q-5 ) q congruent 59 modulo 60: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 3, 7, 69, 69, 5, 5, 67, 67, 2, 68, 7, 7, 69, 76, 20, 20, 71, 69, 5, 5, 67, 3, 69, 69, 5, 7, 69, 69, 5, 18, 74, 74, 17, 30, 81, 81, 27, 31, 78, 78, 9, 72, 20, 20, 71, 76, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 39, 1, 3, 8 ] ] k = 10: F-action on Pi is ( 2, 5)( 7,240) [41,1,10] Dynkin type is ^2D_4(q) + A_1(q^2) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 q congruent 7 modulo 60: 1/16 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 q congruent 11 modulo 60: 1/16 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 q congruent 19 modulo 60: 1/16 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1^2 q congruent 23 modulo 60: 1/16 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1^2 q congruent 27 modulo 60: 1/16 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1^2 q congruent 31 modulo 60: 1/16 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 q congruent 41 modulo 60: 1/16 phi1^2 q congruent 43 modulo 60: 1/16 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1^2 q congruent 53 modulo 60: 1/16 phi1^2 q congruent 59 modulo 60: 1/16 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 5, 71, 72, 18, 69, 20, 71, 17, 20, 74, 31, 98, 27, 95, 90, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 8 ], [ 39, 1, 3, 8 ] ] i = 42: Pi = [ 2, 4, 5, 6, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [42,1,1] Dynkin type is A_5(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 7 modulo 60: 1/12 ( q^2-11*q+28 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 11 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 13 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 19 modulo 60: 1/12 ( q^2-11*q+28 ) q congruent 21 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 23 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 25 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 27 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 29 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 31 modulo 60: 1/12 ( q^2-11*q+28 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 41 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 43 modulo 60: 1/12 ( q^2-11*q+28 ) q congruent 47 modulo 60: 1/12 ( q^2-11*q+24 ) q congruent 49 modulo 60: 1/12 ( q^2-11*q+34 ) q congruent 53 modulo 60: 1/12 ( q^2-11*q+30 ) q congruent 59 modulo 60: 1/12 ( q^2-11*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 4, 68, 68, 3, 8, 77, 77, 30, 14, 83, 70, 19, 19, 72, 23, 93, 87, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 19, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ] ] k = 2: F-action on Pi is (2,7)(4,6) [42,1,2] Dynkin type is ^2A_5(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-2 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 ( q-2 ) q congruent 7 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 13 modulo 60: 1/4 phi1 ( q-2 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 ( q-2 ) q congruent 19 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 25 modulo 60: 1/4 phi1 ( q-2 ) q congruent 27 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 29 modulo 60: 1/4 phi1 ( q-2 ) q congruent 31 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 ( q-2 ) q congruent 41 modulo 60: 1/4 phi1 ( q-2 ) q congruent 43 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 47 modulo 60: 1/4 ( q^2-3*q+4 ) q congruent 49 modulo 60: 1/4 phi1 ( q-2 ) q congruent 53 modulo 60: 1/4 phi1 ( q-2 ) q congruent 59 modulo 60: 1/4 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 69, 5, 7, 69, 68, 7, 31, 78, 82, 31, 38, 84, 76, 20, 19, 76, 51, 94, 87, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 19, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ] ] k = 3: F-action on Pi is () [42,1,3] Dynkin type is A_5(q) + A_1(q) + T(phi3) Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 phi1 ( q+2 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/6 q phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/6 q phi2 q congruent 7 modulo 60: 1/6 phi1 ( q+2 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/6 q phi2 q congruent 11 modulo 60: 1/6 q phi2 q congruent 13 modulo 60: 1/6 phi1 ( q+2 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/6 q phi2 q congruent 19 modulo 60: 1/6 phi1 ( q+2 ) q congruent 21 modulo 60: 1/6 q phi2 q congruent 23 modulo 60: 1/6 q phi2 q congruent 25 modulo 60: 1/6 phi1 ( q+2 ) q congruent 27 modulo 60: 1/6 q phi2 q congruent 29 modulo 60: 1/6 q phi2 q congruent 31 modulo 60: 1/6 phi1 ( q+2 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/6 phi1 ( q+2 ) q congruent 41 modulo 60: 1/6 q phi2 q congruent 43 modulo 60: 1/6 phi1 ( q+2 ) q congruent 47 modulo 60: 1/6 q phi2 q congruent 49 modulo 60: 1/6 phi1 ( q+2 ) q congruent 53 modulo 60: 1/6 q phi2 q congruent 59 modulo 60: 1/6 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30, 30, 81, 81, 27, 14, 83, 83, 37, 12, 79, 97, 59, 59, 95, 62, 111, 85, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 27, 1, 5, 6 ] ] k = 4: F-action on Pi is () [42,1,4] Dynkin type is A_5(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q-2 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4 q ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4 phi1 ( q-2 ) q congruent 7 modulo 60: 1/4 q ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4 phi1 ( q-2 ) q congruent 11 modulo 60: 1/4 q ( q-3 ) q congruent 13 modulo 60: 1/4 phi1 ( q-2 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4 phi1 ( q-2 ) q congruent 19 modulo 60: 1/4 q ( q-3 ) q congruent 21 modulo 60: 1/4 phi1 ( q-2 ) q congruent 23 modulo 60: 1/4 q ( q-3 ) q congruent 25 modulo 60: 1/4 phi1 ( q-2 ) q congruent 27 modulo 60: 1/4 q ( q-3 ) q congruent 29 modulo 60: 1/4 phi1 ( q-2 ) q congruent 31 modulo 60: 1/4 q ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4 phi1 ( q-2 ) q congruent 41 modulo 60: 1/4 phi1 ( q-2 ) q congruent 43 modulo 60: 1/4 q ( q-3 ) q congruent 47 modulo 60: 1/4 q ( q-3 ) q congruent 49 modulo 60: 1/4 phi1 ( q-2 ) q congruent 53 modulo 60: 1/4 phi1 ( q-2 ) q congruent 59 modulo 60: 1/4 q ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 68, 7, 7, 69, 77, 30, 30, 81, 83, 37, 19, 76, 76, 20, 93, 50, 40, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 19, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ] ] k = 5: F-action on Pi is (2,7)(4,6) [42,1,5] Dynkin type is ^2A_5(q) + A_1(q) + T(phi6) Order of center |Z^F|: phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/6 q phi1 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/6 phi2 ( q-2 ) q congruent 7 modulo 60: 1/6 q phi1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/6 q phi1 q congruent 11 modulo 60: 1/6 phi2 ( q-2 ) q congruent 13 modulo 60: 1/6 q phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/6 phi2 ( q-2 ) q congruent 19 modulo 60: 1/6 q phi1 q congruent 21 modulo 60: 1/6 q phi1 q congruent 23 modulo 60: 1/6 phi2 ( q-2 ) q congruent 25 modulo 60: 1/6 q phi1 q congruent 27 modulo 60: 1/6 q phi1 q congruent 29 modulo 60: 1/6 phi2 ( q-2 ) q congruent 31 modulo 60: 1/6 q phi1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/6 q phi1 q congruent 41 modulo 60: 1/6 phi2 ( q-2 ) q congruent 43 modulo 60: 1/6 q phi1 q congruent 47 modulo 60: 1/6 phi2 ( q-2 ) q congruent 49 modulo 60: 1/6 q phi1 q congruent 53 modulo 60: 1/6 phi2 ( q-2 ) q congruent 59 modulo 60: 1/6 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 9, 31, 78, 82, 31, 28, 82, 84, 15, 38, 84, 80, 13, 60, 98, 96, 60, 112, 63, 33, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 27, 1, 4, 6 ] ] k = 6: F-action on Pi is (2,7)(4,6) [42,1,6] Dynkin type is ^2A_5(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q-6 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 7 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/12 phi1 ( q-6 ) q congruent 11 modulo 60: 1/12 ( q^2-7*q+16 ) q congruent 13 modulo 60: 1/12 phi1 ( q-6 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 19 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 21 modulo 60: 1/12 phi1 ( q-6 ) q congruent 23 modulo 60: 1/12 ( q^2-7*q+16 ) q congruent 25 modulo 60: 1/12 phi1 ( q-6 ) q congruent 27 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 29 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 31 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 phi1 ( q-6 ) q congruent 41 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 43 modulo 60: 1/12 ( q^2-7*q+12 ) q congruent 47 modulo 60: 1/12 ( q^2-7*q+16 ) q congruent 49 modulo 60: 1/12 phi1 ( q-6 ) q congruent 53 modulo 60: 1/12 ( q^2-7*q+10 ) q congruent 59 modulo 60: 1/12 ( q^2-7*q+16 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 69, 5, 3, 69, 78, 9, 31, 78, 84, 15, 20, 71, 72, 20, 94, 24, 35, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 19, 1, 2, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ] ] i = 43: Pi = [ 2, 4, 5, 7, 8, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [43,1,1] Dynkin type is A_3(q) + A_3(q) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 7 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 11 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 13 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 19 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 21 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 23 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 25 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 27 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 31 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 41 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 43 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 49 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 53 modulo 60: 1/32 ( q^2-14*q+45 ) q congruent 59 modulo 60: 1/32 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 8, 70, 66, 4, 68, 77, 19, 4, 68, 3, 30, 72, 8, 77, 30, 14, 97, 70, 19, 72, 97, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 20, 1, 1, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 16 ], [ 26, 1, 1, 16 ], [ 39, 1, 1, 8 ] ] k = 2: F-action on Pi is () [43,1,2] Dynkin type is A_3(q) + A_3(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q-5 ) q congruent 7 modulo 60: 1/16 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q-5 ) q congruent 11 modulo 60: 1/16 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q-5 ) q congruent 19 modulo 60: 1/16 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1 ( q-5 ) q congruent 23 modulo 60: 1/16 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1 ( q-5 ) q congruent 27 modulo 60: 1/16 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 ( q-5 ) q congruent 31 modulo 60: 1/16 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q-5 ) q congruent 41 modulo 60: 1/16 phi1 ( q-5 ) q congruent 43 modulo 60: 1/16 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1 ( q-5 ) q congruent 53 modulo 60: 1/16 phi1 ( q-5 ) q congruent 59 modulo 60: 1/16 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 77, 19, 4, 68, 7, 30, 76, 68, 7, 69, 81, 20, 77, 30, 81, 83, 59, 19, 76, 20, 59, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 8 ], [ 39, 1, 4, 4 ] ] k = 3: F-action on Pi is ( 2, 5)( 7,240) [43,1,3] Dynkin type is ^2A_3(q) + ^2A_3(q) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1 ( q-5 ) q congruent 7 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1 ( q-5 ) q congruent 11 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 13 modulo 60: 1/32 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1 ( q-5 ) q congruent 19 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 21 modulo 60: 1/32 phi1 ( q-5 ) q congruent 23 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 25 modulo 60: 1/32 phi1 ( q-5 ) q congruent 27 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/32 phi1 ( q-5 ) q congruent 31 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1 ( q-5 ) q congruent 41 modulo 60: 1/32 phi1 ( q-5 ) q congruent 43 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 49 modulo 60: 1/32 phi1 ( q-5 ) q congruent 53 modulo 60: 1/32 phi1 ( q-5 ) q congruent 59 modulo 60: 1/32 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 69, 3, 31, 72, 69, 7, 68, 82, 19, 3, 68, 4, 28, 70, 31, 82, 28, 38, 96, 72, 19, 70, 96, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 20, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 16 ], [ 39, 1, 1, 8 ] ] k = 4: F-action on Pi is ( 2, 5)( 7,240) [43,1,4] Dynkin type is ^2A_3(q) + ^2A_3(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 q congruent 7 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 q congruent 11 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 q congruent 19 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1^2 q congruent 23 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1^2 q congruent 27 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1^2 q congruent 31 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 q congruent 41 modulo 60: 1/16 phi1^2 q congruent 43 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1^2 q congruent 53 modulo 60: 1/16 phi1^2 q congruent 59 modulo 60: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 69, 78, 20, 5, 69, 7, 31, 76, 69, 7, 68, 82, 19, 78, 31, 82, 84, 60, 20, 76, 19, 60, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 2, 8 ], [ 39, 1, 4, 4 ] ] k = 5: F-action on Pi is ( 2, 7)( 4, 8)( 5,240) [43,1,5] Dynkin type is A_3(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q-5 ) q congruent 7 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q-5 ) q congruent 11 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q-5 ) q congruent 19 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1 ( q-5 ) q congruent 23 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1 ( q-5 ) q congruent 27 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1 ( q-5 ) q congruent 31 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q-5 ) q congruent 41 modulo 60: 1/16 phi1 ( q-5 ) q congruent 43 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1 ( q-5 ) q congruent 53 modulo 60: 1/16 phi1 ( q-5 ) q congruent 59 modulo 60: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 18, 35, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 5, 8 ], [ 20, 1, 8, 8 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 39, 1, 4, 4 ] ] k = 6: F-action on Pi is ( 2, 7)( 4, 8)( 5,240) [43,1,6] Dynkin type is A_3(q^2) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q-5 ) q congruent 7 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q-5 ) q congruent 11 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q-5 ) q congruent 19 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1 ( q-5 ) q congruent 23 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1 ( q-5 ) q congruent 27 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1 ( q-5 ) q congruent 31 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q-5 ) q congruent 41 modulo 60: 1/16 phi1 ( q-5 ) q congruent 43 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1 ( q-5 ) q congruent 53 modulo 60: 1/16 phi1 ( q-5 ) q congruent 59 modulo 60: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 73, 87, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 20, 1, 6, 8 ], [ 20, 1, 8, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 26, 1, 2, 8 ], [ 39, 1, 1, 8 ] ] k = 7: F-action on Pi is ( 2,240)( 4, 8)( 5, 7) [43,1,7] Dynkin type is A_3(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 q congruent 7 modulo 60: 1/16 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 q congruent 11 modulo 60: 1/16 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 q congruent 19 modulo 60: 1/16 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1^2 q congruent 23 modulo 60: 1/16 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1^2 q congruent 27 modulo 60: 1/16 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1^2 q congruent 31 modulo 60: 1/16 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 q congruent 41 modulo 60: 1/16 phi1^2 q congruent 43 modulo 60: 1/16 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1^2 q congruent 53 modulo 60: 1/16 phi1^2 q congruent 59 modulo 60: 1/16 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 76, 18, 40, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 6, 8 ], [ 20, 1, 7, 8 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 39, 1, 4, 4 ] ] k = 8: F-action on Pi is ( 7,240) [43,1,8] Dynkin type is A_3(q) + ^2A_3(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 4, 28, 70, 69, 7, 68, 82, 19, 5, 69, 3, 31, 72, 27, 81, 30, 36, 97, 71, 20, 72, 98, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 4 ], [ 39, 1, 2, 4 ] ] k = 9: F-action on Pi is ( 7,240) [43,1,9] Dynkin type is A_3(q) + ^2A_3(q) + T(phi4) Order of center |Z^F|: phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 phi2 q congruent 7 modulo 60: 1/8 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 phi2 q congruent 11 modulo 60: 1/8 phi1 phi2 q congruent 13 modulo 60: 1/8 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 phi2 q congruent 19 modulo 60: 1/8 phi1 phi2 q congruent 21 modulo 60: 1/8 phi1 phi2 q congruent 23 modulo 60: 1/8 phi1 phi2 q congruent 25 modulo 60: 1/8 phi1 phi2 q congruent 27 modulo 60: 1/8 phi1 phi2 q congruent 29 modulo 60: 1/8 phi1 phi2 q congruent 31 modulo 60: 1/8 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 phi2 q congruent 41 modulo 60: 1/8 phi1 phi2 q congruent 43 modulo 60: 1/8 phi1 phi2 q congruent 47 modulo 60: 1/8 phi1 phi2 q congruent 49 modulo 60: 1/8 phi1 phi2 q congruent 53 modulo 60: 1/8 phi1 phi2 q congruent 59 modulo 60: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 72, 19, 70, 96, 16, 20, 76, 19, 60, 73, 71, 20, 72, 98, 18, 95, 59, 97, 99, 53, 17, 74, 18, 54, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 39, 1, 5, 4 ] ] k = 10: F-action on Pi is ( 2, 7, 5,240)( 4, 8) [43,1,10] Dynkin type is ^2A_3(q^2) + T(phi4) Order of center |Z^F|: phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 phi2 q congruent 7 modulo 60: 1/8 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 phi2 q congruent 11 modulo 60: 1/8 phi1 phi2 q congruent 13 modulo 60: 1/8 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 phi2 q congruent 19 modulo 60: 1/8 phi1 phi2 q congruent 21 modulo 60: 1/8 phi1 phi2 q congruent 23 modulo 60: 1/8 phi1 phi2 q congruent 25 modulo 60: 1/8 phi1 phi2 q congruent 27 modulo 60: 1/8 phi1 phi2 q congruent 29 modulo 60: 1/8 phi1 phi2 q congruent 31 modulo 60: 1/8 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 phi2 q congruent 41 modulo 60: 1/8 phi1 phi2 q congruent 43 modulo 60: 1/8 phi1 phi2 q congruent 47 modulo 60: 1/8 phi1 phi2 q congruent 49 modulo 60: 1/8 phi1 phi2 q congruent 53 modulo 60: 1/8 phi1 phi2 q congruent 59 modulo 60: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 6, 75, 18, 39, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 3 ], [ 39, 1, 5, 4 ] ] k = 11: F-action on Pi is ( 2, 7, 5,240)( 4, 8) [43,1,11] Dynkin type is ^2A_3(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/8 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/8 phi1 phi2 q congruent 7 modulo 60: 1/8 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/8 phi1 phi2 q congruent 11 modulo 60: 1/8 phi1 phi2 q congruent 13 modulo 60: 1/8 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/8 phi1 phi2 q congruent 19 modulo 60: 1/8 phi1 phi2 q congruent 21 modulo 60: 1/8 phi1 phi2 q congruent 23 modulo 60: 1/8 phi1 phi2 q congruent 25 modulo 60: 1/8 phi1 phi2 q congruent 27 modulo 60: 1/8 phi1 phi2 q congruent 29 modulo 60: 1/8 phi1 phi2 q congruent 31 modulo 60: 1/8 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/8 phi1 phi2 q congruent 41 modulo 60: 1/8 phi1 phi2 q congruent 43 modulo 60: 1/8 phi1 phi2 q congruent 47 modulo 60: 1/8 phi1 phi2 q congruent 49 modulo 60: 1/8 phi1 phi2 q congruent 53 modulo 60: 1/8 phi1 phi2 q congruent 59 modulo 60: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 75, 22, 76, 100, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 39, 1, 2, 4 ] ] k = 12: F-action on Pi is () [43,1,12] Dynkin type is A_3(q) + A_3(q) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1 ( q-5 ) q congruent 7 modulo 60: 1/32 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1 ( q-5 ) q congruent 11 modulo 60: 1/32 phi2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1 ( q-5 ) q congruent 19 modulo 60: 1/32 phi2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1 ( q-5 ) q congruent 23 modulo 60: 1/32 phi2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1 ( q-5 ) q congruent 27 modulo 60: 1/32 phi2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1 ( q-5 ) q congruent 31 modulo 60: 1/32 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1 ( q-5 ) q congruent 41 modulo 60: 1/32 phi1 ( q-5 ) q congruent 43 modulo 60: 1/32 phi2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1 ( q-5 ) q congruent 53 modulo 60: 1/32 phi1 ( q-5 ) q congruent 59 modulo 60: 1/32 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 3, 30, 72, 68, 7, 69, 81, 20, 3, 69, 5, 27, 71, 30, 81, 27, 37, 95, 72, 20, 71, 95, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 20, 1, 2, 16 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 16 ], [ 39, 1, 3, 8 ] ] k = 13: F-action on Pi is ( 2, 5)( 7,240) [43,1,13] Dynkin type is ^2A_3(q) + ^2A_3(q) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1 ( q-5 ) q congruent 7 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1 ( q-5 ) q congruent 11 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 13 modulo 60: 1/32 phi1 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1 ( q-5 ) q congruent 19 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 21 modulo 60: 1/32 phi1 ( q-5 ) q congruent 23 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 25 modulo 60: 1/32 phi1 ( q-5 ) q congruent 27 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/32 phi1 ( q-5 ) q congruent 31 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1 ( q-5 ) q congruent 41 modulo 60: 1/32 phi1 ( q-5 ) q congruent 43 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/32 ( q^2-10*q+21 ) q congruent 49 modulo 60: 1/32 phi1 ( q-5 ) q congruent 53 modulo 60: 1/32 phi1 ( q-5 ) q congruent 59 modulo 60: 1/32 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 9, 71, 67, 5, 69, 78, 20, 5, 69, 3, 31, 72, 9, 78, 31, 15, 98, 71, 20, 72, 98, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 20, 1, 4, 16 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 3, 16 ], [ 26, 1, 4, 16 ], [ 39, 1, 3, 8 ] ] k = 14: F-action on Pi is ( 2, 7)( 4, 8)( 5,240) [43,1,14] Dynkin type is A_3(q^2) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 q congruent 7 modulo 60: 1/16 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 q congruent 11 modulo 60: 1/16 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 q congruent 19 modulo 60: 1/16 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1^2 q congruent 23 modulo 60: 1/16 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1^2 q congruent 27 modulo 60: 1/16 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1^2 q congruent 31 modulo 60: 1/16 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 q congruent 41 modulo 60: 1/16 phi1^2 q congruent 43 modulo 60: 1/16 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1^2 q congruent 53 modulo 60: 1/16 phi1^2 q congruent 59 modulo 60: 1/16 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 74, 88, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 20, 1, 5, 8 ], [ 20, 1, 7, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 26, 1, 3, 8 ], [ 39, 1, 3, 8 ] ] i = 44: Pi = [ 1, 2, 3, 4, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [44,1,1] Dynkin type is D_5(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 ( q^3-16*q^2+85*q-166 ) q congruent 2 modulo 60: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 60: 1/48 ( q^3-16*q^2+85*q-138 ) q congruent 4 modulo 60: 1/48 ( q^3-16*q^2+76*q-112 ) q congruent 5 modulo 60: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 7 modulo 60: 1/48 ( q^3-16*q^2+85*q-154 ) q congruent 8 modulo 60: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 60: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 11 modulo 60: 1/48 ( q^3-16*q^2+85*q-138 ) q congruent 13 modulo 60: 1/48 ( q^3-16*q^2+85*q-166 ) q congruent 16 modulo 60: 1/48 ( q^3-16*q^2+76*q-112 ) q congruent 17 modulo 60: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 19 modulo 60: 1/48 ( q^3-16*q^2+85*q-154 ) q congruent 21 modulo 60: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 23 modulo 60: 1/48 ( q^3-16*q^2+85*q-138 ) q congruent 25 modulo 60: 1/48 ( q^3-16*q^2+85*q-166 ) q congruent 27 modulo 60: 1/48 ( q^3-16*q^2+85*q-138 ) q congruent 29 modulo 60: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 31 modulo 60: 1/48 ( q^3-16*q^2+85*q-154 ) q congruent 32 modulo 60: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 37 modulo 60: 1/48 ( q^3-16*q^2+85*q-166 ) q congruent 41 modulo 60: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 43 modulo 60: 1/48 ( q^3-16*q^2+85*q-154 ) q congruent 47 modulo 60: 1/48 ( q^3-16*q^2+85*q-138 ) q congruent 49 modulo 60: 1/48 ( q^3-16*q^2+85*q-166 ) q congruent 53 modulo 60: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 59 modulo 60: 1/48 ( q^3-16*q^2+85*q-138 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 4, 3, 66, 70, 68, 72, 4, 16, 19, 8, 28, 30, 77, 96, 70, 89, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 12 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 39, 1, 1, 24 ] ] k = 2: F-action on Pi is () [44,1,2] Dynkin type is D_5(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 2 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 68, 69, 4, 19, 7, 20, 68, 73, 76, 77, 82, 81, 30, 60, 19, 43, 93 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 39, 1, 4, 4 ] ] k = 3: F-action on Pi is () [44,1,3] Dynkin type is D_5(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 2 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 13 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 16 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 17 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 19 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 21 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 23 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 25 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 27 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 29 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 31 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 32 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 37 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 41 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 43 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 47 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 49 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 53 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 59 modulo 60: 1/6 q phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 30, 27, 77, 97, 81, 95, 30, 53, 59, 14, 36, 37, 83, 99, 97, 109, 62 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 27, 1, 5, 6 ] ] k = 4: F-action on Pi is () [44,1,4] Dynkin type is D_5(q) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 q phi1 phi2 q congruent 2 modulo 60: 1/8 q^3 q congruent 3 modulo 60: 1/8 q phi1 phi2 q congruent 4 modulo 60: 1/8 q^3 q congruent 5 modulo 60: 1/8 q phi1 phi2 q congruent 7 modulo 60: 1/8 q phi1 phi2 q congruent 8 modulo 60: 1/8 q^3 q congruent 9 modulo 60: 1/8 q phi1 phi2 q congruent 11 modulo 60: 1/8 q phi1 phi2 q congruent 13 modulo 60: 1/8 q phi1 phi2 q congruent 16 modulo 60: 1/8 q^3 q congruent 17 modulo 60: 1/8 q phi1 phi2 q congruent 19 modulo 60: 1/8 q phi1 phi2 q congruent 21 modulo 60: 1/8 q phi1 phi2 q congruent 23 modulo 60: 1/8 q phi1 phi2 q congruent 25 modulo 60: 1/8 q phi1 phi2 q congruent 27 modulo 60: 1/8 q phi1 phi2 q congruent 29 modulo 60: 1/8 q phi1 phi2 q congruent 31 modulo 60: 1/8 q phi1 phi2 q congruent 32 modulo 60: 1/8 q^3 q congruent 37 modulo 60: 1/8 q phi1 phi2 q congruent 41 modulo 60: 1/8 q phi1 phi2 q congruent 43 modulo 60: 1/8 q phi1 phi2 q congruent 47 modulo 60: 1/8 q phi1 phi2 q congruent 49 modulo 60: 1/8 q phi1 phi2 q congruent 53 modulo 60: 1/8 q phi1 phi2 q congruent 59 modulo 60: 1/8 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 70, 72, 71, 19, 18, 20, 17, 76, 75, 74, 97, 98, 95, 59, 54, 22, 45, 107 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 39, 1, 5, 4 ] ] k = 5: F-action on Pi is () [44,1,5] Dynkin type is D_5(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 2 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 4 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 7 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 8 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 11 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 13 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 16 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 19 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 21 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 23 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 25 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 27 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 29 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 31 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 32 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 41 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 43 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 47 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 49 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 53 modulo 60: 1/16 phi1^2 ( q-2 ) q congruent 59 modulo 60: 1/16 ( q^3-4*q^2+5*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 3, 5, 68, 72, 69, 71, 7, 18, 20, 30, 31, 27, 81, 98, 76, 90, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 28, 1, 2, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ] ] k = 6: F-action on Pi is (2,5) [44,1,6] Dynkin type is ^2D_5(q) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 2 modulo 60: 1/8 q^2 ( q-2 ) q congruent 3 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 4 modulo 60: 1/8 q^2 ( q-2 ) q congruent 5 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 7 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 8 modulo 60: 1/8 q^2 ( q-2 ) q congruent 9 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 11 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 13 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 16 modulo 60: 1/8 q^2 ( q-2 ) q congruent 17 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 19 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 21 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 23 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 25 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 27 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 29 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 31 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 32 modulo 60: 1/8 q^2 ( q-2 ) q congruent 37 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 41 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 43 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 47 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 49 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 53 modulo 60: 1/8 phi1 phi2 ( q-2 ) q congruent 59 modulo 60: 1/8 phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 72, 71, 16, 19, 18, 20, 73, 76, 75, 96, 97, 98, 60, 53, 44, 22, 108 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 39, 1, 5, 4 ] ] k = 7: F-action on Pi is (2,5) [44,1,7] Dynkin type is ^2D_5(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q^2 phi1 q congruent 2 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 60: 1/6 q^2 phi1 q congruent 4 modulo 60: 1/6 q^2 phi1 q congruent 5 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 60: 1/6 q^2 phi1 q congruent 8 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 60: 1/6 q^2 phi1 q congruent 11 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 13 modulo 60: 1/6 q^2 phi1 q congruent 16 modulo 60: 1/6 q^2 phi1 q congruent 17 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 19 modulo 60: 1/6 q^2 phi1 q congruent 21 modulo 60: 1/6 q^2 phi1 q congruent 23 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 25 modulo 60: 1/6 q^2 phi1 q congruent 27 modulo 60: 1/6 q^2 phi1 q congruent 29 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 31 modulo 60: 1/6 q^2 phi1 q congruent 32 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 37 modulo 60: 1/6 q^2 phi1 q congruent 41 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 43 modulo 60: 1/6 q^2 phi1 q congruent 47 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 49 modulo 60: 1/6 q^2 phi1 q congruent 53 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 59 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 31, 9, 96, 82, 98, 78, 60, 31, 54, 38, 36, 15, 84, 99, 110, 98, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 27, 1, 4, 6 ] ] k = 8: F-action on Pi is (2,5) [44,1,8] Dynkin type is ^2D_5(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 4 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 7 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 11 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 16 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 19 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 23 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 27 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 31 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 43 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 47 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) q congruent 59 modulo 60: 1/8 phi1 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 69, 67, 19, 7, 20, 5, 76, 69, 74, 82, 81, 78, 31, 59, 43, 20, 94 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 39, 1, 4, 4 ] ] k = 9: F-action on Pi is (2,5) [44,1,9] Dynkin type is ^2D_5(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 2 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/16 q ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 7 modulo 60: 1/16 q ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 11 modulo 60: 1/16 q ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 16 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 19 modulo 60: 1/16 q ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 23 modulo 60: 1/16 q ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 27 modulo 60: 1/16 q ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 31 modulo 60: 1/16 q ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 41 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 43 modulo 60: 1/16 q ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 q ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 53 modulo 60: 1/16 phi1^2 ( q-4 ) q congruent 59 modulo 60: 1/16 q ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 3, 5, 70, 68, 72, 69, 19, 7, 18, 28, 30, 31, 82, 97, 89, 76, 51 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 28, 1, 3, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ] ] k = 10: F-action on Pi is (2,5) [44,1,10] Dynkin type is ^2D_5(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 phi1 ( q^2-9*q+24 ) q congruent 2 modulo 60: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 3 modulo 60: 1/48 ( q^3-10*q^2+33*q-36 ) q congruent 4 modulo 60: 1/48 q ( q^2-10*q+24 ) q congruent 5 modulo 60: 1/48 ( q^3-10*q^2+33*q-40 ) q congruent 7 modulo 60: 1/48 ( q^3-10*q^2+33*q-36 ) q congruent 8 modulo 60: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 9 modulo 60: 1/48 phi1 ( q^2-9*q+24 ) q congruent 11 modulo 60: 1/48 ( q^3-10*q^2+33*q-52 ) q congruent 13 modulo 60: 1/48 phi1 ( q^2-9*q+24 ) q congruent 16 modulo 60: 1/48 q ( q^2-10*q+24 ) q congruent 17 modulo 60: 1/48 ( q^3-10*q^2+33*q-40 ) q congruent 19 modulo 60: 1/48 ( q^3-10*q^2+33*q-36 ) q congruent 21 modulo 60: 1/48 phi1 ( q^2-9*q+24 ) q congruent 23 modulo 60: 1/48 ( q^3-10*q^2+33*q-52 ) q congruent 25 modulo 60: 1/48 phi1 ( q^2-9*q+24 ) q congruent 27 modulo 60: 1/48 ( q^3-10*q^2+33*q-36 ) q congruent 29 modulo 60: 1/48 ( q^3-10*q^2+33*q-40 ) q congruent 31 modulo 60: 1/48 ( q^3-10*q^2+33*q-36 ) q congruent 32 modulo 60: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 37 modulo 60: 1/48 phi1 ( q^2-9*q+24 ) q congruent 41 modulo 60: 1/48 ( q^3-10*q^2+33*q-40 ) q congruent 43 modulo 60: 1/48 ( q^3-10*q^2+33*q-36 ) q congruent 47 modulo 60: 1/48 ( q^3-10*q^2+33*q-52 ) q congruent 49 modulo 60: 1/48 phi1 ( q^2-9*q+24 ) q congruent 53 modulo 60: 1/48 ( q^3-10*q^2+33*q-40 ) q congruent 59 modulo 60: 1/48 ( q^3-10*q^2+33*q-52 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 5, 2, 72, 69, 71, 67, 20, 5, 17, 31, 27, 9, 78, 95, 90, 71, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 4, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], [ 39, 1, 3, 24 ] ] i = 45: Pi = [ 1, 2, 3, 4, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [45,1,1] Dynkin type is A_4(q) + A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 ( q^3-20*q^2+135*q-368 ) q congruent 2 modulo 60: 1/12 ( q^3-19*q^2+106*q-144 ) q congruent 3 modulo 60: 1/12 ( q^3-20*q^2+129*q-234 ) q congruent 4 modulo 60: 1/12 ( q^3-19*q^2+112*q-208 ) q congruent 5 modulo 60: 1/12 ( q^3-20*q^2+129*q-270 ) q congruent 7 modulo 60: 1/12 ( q^3-20*q^2+135*q-308 ) q congruent 8 modulo 60: 1/12 ( q^3-19*q^2+106*q-144 ) q congruent 9 modulo 60: 1/12 ( q^3-20*q^2+129*q-270 ) q congruent 11 modulo 60: 1/12 ( q^3-20*q^2+129*q-258 ) q congruent 13 modulo 60: 1/12 ( q^3-20*q^2+135*q-344 ) q congruent 16 modulo 60: 1/12 ( q^3-19*q^2+112*q-232 ) q congruent 17 modulo 60: 1/12 ( q^3-20*q^2+129*q-270 ) q congruent 19 modulo 60: 1/12 ( q^3-20*q^2+135*q-308 ) q congruent 21 modulo 60: 1/12 ( q^3-20*q^2+129*q-294 ) q congruent 23 modulo 60: 1/12 ( q^3-20*q^2+129*q-234 ) q congruent 25 modulo 60: 1/12 ( q^3-20*q^2+135*q-344 ) q congruent 27 modulo 60: 1/12 ( q^3-20*q^2+129*q-234 ) q congruent 29 modulo 60: 1/12 ( q^3-20*q^2+129*q-270 ) q congruent 31 modulo 60: 1/12 ( q^3-20*q^2+135*q-332 ) q congruent 32 modulo 60: 1/12 ( q^3-19*q^2+106*q-144 ) q congruent 37 modulo 60: 1/12 ( q^3-20*q^2+135*q-344 ) q congruent 41 modulo 60: 1/12 ( q^3-20*q^2+129*q-294 ) q congruent 43 modulo 60: 1/12 ( q^3-20*q^2+135*q-308 ) q congruent 47 modulo 60: 1/12 ( q^3-20*q^2+129*q-234 ) q congruent 49 modulo 60: 1/12 ( q^3-20*q^2+135*q-344 ) q congruent 53 modulo 60: 1/12 ( q^3-20*q^2+129*q-270 ) q congruent 59 modulo 60: 1/12 ( q^3-20*q^2+129*q-234 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 4, 68, 8, 77, 77, 30, 70, 19, 23, 93 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 6 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 12 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 15, 1, 1, 8 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 12 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 28, 1, 1, 12 ], [ 29, 1, 1, 12 ], [ 30, 1, 1, 12 ], [ 34, 1, 1, 12 ], [ 36, 1, 1, 12 ], [ 42, 1, 1, 12 ] ] k = 2: F-action on Pi is () [45,1,2] Dynkin type is A_4(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q^2-7*q+12 ) q congruent 2 modulo 60: 1/4 q ( q^2-7*q+10 ) q congruent 3 modulo 60: 1/4 ( q^3-8*q^2+17*q-6 ) q congruent 4 modulo 60: 1/4 q ( q^2-7*q+12 ) q congruent 5 modulo 60: 1/4 phi1 ( q^2-7*q+10 ) q congruent 7 modulo 60: 1/4 ( q^3-8*q^2+19*q-8 ) q congruent 8 modulo 60: 1/4 q ( q^2-7*q+10 ) q congruent 9 modulo 60: 1/4 phi1 ( q^2-7*q+10 ) q congruent 11 modulo 60: 1/4 ( q^3-8*q^2+17*q-6 ) q congruent 13 modulo 60: 1/4 phi1 ( q^2-7*q+12 ) q congruent 16 modulo 60: 1/4 q ( q^2-7*q+12 ) q congruent 17 modulo 60: 1/4 phi1 ( q^2-7*q+10 ) q congruent 19 modulo 60: 1/4 ( q^3-8*q^2+19*q-8 ) q congruent 21 modulo 60: 1/4 phi1 ( q^2-7*q+10 ) q congruent 23 modulo 60: 1/4 ( q^3-8*q^2+17*q-6 ) q congruent 25 modulo 60: 1/4 phi1 ( q^2-7*q+12 ) q congruent 27 modulo 60: 1/4 ( q^3-8*q^2+17*q-6 ) q congruent 29 modulo 60: 1/4 phi1 ( q^2-7*q+10 ) q congruent 31 modulo 60: 1/4 ( q^3-8*q^2+19*q-8 ) q congruent 32 modulo 60: 1/4 q ( q^2-7*q+10 ) q congruent 37 modulo 60: 1/4 phi1 ( q^2-7*q+12 ) q congruent 41 modulo 60: 1/4 phi1 ( q^2-7*q+10 ) q congruent 43 modulo 60: 1/4 ( q^3-8*q^2+19*q-8 ) q congruent 47 modulo 60: 1/4 ( q^3-8*q^2+17*q-6 ) q congruent 49 modulo 60: 1/4 phi1 ( q^2-7*q+12 ) q congruent 53 modulo 60: 1/4 phi1 ( q^2-7*q+10 ) q congruent 59 modulo 60: 1/4 ( q^3-8*q^2+17*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 68, 7, 77, 30, 30, 81, 19, 76, 93, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 15, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 28, 1, 2, 4 ], [ 29, 1, 2, 4 ], [ 30, 1, 1, 4 ], [ 34, 1, 2, 4 ], [ 36, 1, 2, 4 ], [ 42, 1, 4, 4 ] ] k = 3: F-action on Pi is () [45,1,3] Dynkin type is A_4(q) + A_1(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 phi1 ( q^2-q-4 ) q congruent 2 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 4 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 7 modulo 60: 1/6 phi1 ( q^2-q-4 ) q congruent 8 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 11 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 13 modulo 60: 1/6 phi1 ( q^2-q-4 ) q congruent 16 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 17 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 19 modulo 60: 1/6 phi1 ( q^2-q-4 ) q congruent 21 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 23 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 25 modulo 60: 1/6 phi1 ( q^2-q-4 ) q congruent 27 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 29 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 31 modulo 60: 1/6 phi1 ( q^2-q-4 ) q congruent 32 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 37 modulo 60: 1/6 phi1 ( q^2-q-4 ) q congruent 41 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 43 modulo 60: 1/6 phi1 ( q^2-q-4 ) q congruent 47 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 49 modulo 60: 1/6 phi1 ( q^2-q-4 ) q congruent 53 modulo 60: 1/6 q phi2 ( q-3 ) q congruent 59 modulo 60: 1/6 q phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30, 30, 81, 14, 83, 83, 37, 97, 59, 62, 111 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 15, 1, 1, 2 ], [ 27, 1, 5, 6 ], [ 42, 1, 3, 6 ] ] k = 4: F-action on Pi is (1,2)(3,4) [45,1,4] Dynkin type is ^2A_4(q) + A_1(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q phi1^2 q congruent 2 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 60: 1/6 q phi1^2 q congruent 4 modulo 60: 1/6 q^2 phi1 q congruent 5 modulo 60: 1/6 phi2 ( q^2-3*q+4 ) q congruent 7 modulo 60: 1/6 q phi1^2 q congruent 8 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 60: 1/6 q phi1^2 q congruent 11 modulo 60: 1/6 phi2 ( q^2-3*q+4 ) q congruent 13 modulo 60: 1/6 q phi1^2 q congruent 16 modulo 60: 1/6 q^2 phi1 q congruent 17 modulo 60: 1/6 phi2 ( q^2-3*q+4 ) q congruent 19 modulo 60: 1/6 q phi1^2 q congruent 21 modulo 60: 1/6 q phi1^2 q congruent 23 modulo 60: 1/6 phi2 ( q^2-3*q+4 ) q congruent 25 modulo 60: 1/6 q phi1^2 q congruent 27 modulo 60: 1/6 q phi1^2 q congruent 29 modulo 60: 1/6 phi2 ( q^2-3*q+4 ) q congruent 31 modulo 60: 1/6 q phi1^2 q congruent 32 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 37 modulo 60: 1/6 q phi1^2 q congruent 41 modulo 60: 1/6 phi2 ( q^2-3*q+4 ) q congruent 43 modulo 60: 1/6 q phi1^2 q congruent 47 modulo 60: 1/6 phi2 ( q^2-3*q+4 ) q congruent 49 modulo 60: 1/6 q phi1^2 q congruent 53 modulo 60: 1/6 phi2 ( q^2-3*q+4 ) q congruent 59 modulo 60: 1/6 phi2 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 9, 31, 78, 82, 31, 84, 15, 38, 84, 60, 98, 112, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 15, 1, 2, 2 ], [ 27, 1, 4, 6 ], [ 42, 1, 5, 6 ] ] k = 5: F-action on Pi is (1,2)(3,4) [45,1,5] Dynkin type is ^2A_4(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4 phi1 ( q^2-5*q+8 ) q congruent 2 modulo 60: 1/4 phi1 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/4 ( q^3-6*q^2+13*q-12 ) q congruent 4 modulo 60: 1/4 q ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/4 ( q^3-6*q^2+15*q-14 ) q congruent 7 modulo 60: 1/4 ( q^3-6*q^2+13*q-12 ) q congruent 8 modulo 60: 1/4 phi1 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/4 phi1 ( q^2-5*q+8 ) q congruent 11 modulo 60: 1/4 ( q^3-6*q^2+15*q-18 ) q congruent 13 modulo 60: 1/4 phi1 ( q^2-5*q+8 ) q congruent 16 modulo 60: 1/4 q ( q^2-5*q+6 ) q congruent 17 modulo 60: 1/4 ( q^3-6*q^2+15*q-14 ) q congruent 19 modulo 60: 1/4 ( q^3-6*q^2+13*q-12 ) q congruent 21 modulo 60: 1/4 phi1 ( q^2-5*q+8 ) q congruent 23 modulo 60: 1/4 ( q^3-6*q^2+15*q-18 ) q congruent 25 modulo 60: 1/4 phi1 ( q^2-5*q+8 ) q congruent 27 modulo 60: 1/4 ( q^3-6*q^2+13*q-12 ) q congruent 29 modulo 60: 1/4 ( q^3-6*q^2+15*q-14 ) q congruent 31 modulo 60: 1/4 ( q^3-6*q^2+13*q-12 ) q congruent 32 modulo 60: 1/4 phi1 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/4 phi1 ( q^2-5*q+8 ) q congruent 41 modulo 60: 1/4 ( q^3-6*q^2+15*q-14 ) q congruent 43 modulo 60: 1/4 ( q^3-6*q^2+13*q-12 ) q congruent 47 modulo 60: 1/4 ( q^3-6*q^2+15*q-18 ) q congruent 49 modulo 60: 1/4 phi1 ( q^2-5*q+8 ) q congruent 53 modulo 60: 1/4 ( q^3-6*q^2+15*q-14 ) q congruent 59 modulo 60: 1/4 ( q^3-6*q^2+15*q-18 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 69, 5, 7, 69, 31, 78, 82, 31, 76, 20, 51, 94 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 28, 1, 3, 4 ], [ 29, 1, 3, 4 ], [ 30, 1, 3, 4 ], [ 34, 1, 3, 4 ], [ 36, 1, 3, 4 ], [ 42, 1, 2, 4 ] ] k = 6: F-action on Pi is (1,2)(3,4) [45,1,6] Dynkin type is ^2A_4(q) + A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^2-13*q+48 ) q congruent 2 modulo 60: 1/12 ( q^3-13*q^2+48*q-52 ) q congruent 3 modulo 60: 1/12 ( q^3-14*q^2+61*q-84 ) q congruent 4 modulo 60: 1/12 ( q^3-13*q^2+42*q-24 ) q congruent 5 modulo 60: 1/12 ( q^3-14*q^2+67*q-110 ) q congruent 7 modulo 60: 1/12 ( q^3-14*q^2+61*q-84 ) q congruent 8 modulo 60: 1/12 ( q^3-13*q^2+48*q-52 ) q congruent 9 modulo 60: 1/12 ( q^3-14*q^2+61*q-72 ) q congruent 11 modulo 60: 1/12 ( q^3-14*q^2+67*q-146 ) q congruent 13 modulo 60: 1/12 phi1 ( q^2-13*q+48 ) q congruent 16 modulo 60: 1/12 q ( q^2-13*q+42 ) q congruent 17 modulo 60: 1/12 ( q^3-14*q^2+67*q-110 ) q congruent 19 modulo 60: 1/12 ( q^3-14*q^2+61*q-108 ) q congruent 21 modulo 60: 1/12 phi1 ( q^2-13*q+48 ) q congruent 23 modulo 60: 1/12 ( q^3-14*q^2+67*q-146 ) q congruent 25 modulo 60: 1/12 phi1 ( q^2-13*q+48 ) q congruent 27 modulo 60: 1/12 ( q^3-14*q^2+61*q-84 ) q congruent 29 modulo 60: 1/12 ( q^3-14*q^2+67*q-134 ) q congruent 31 modulo 60: 1/12 ( q^3-14*q^2+61*q-84 ) q congruent 32 modulo 60: 1/12 ( q^3-13*q^2+48*q-52 ) q congruent 37 modulo 60: 1/12 phi1 ( q^2-13*q+48 ) q congruent 41 modulo 60: 1/12 ( q^3-14*q^2+67*q-110 ) q congruent 43 modulo 60: 1/12 ( q^3-14*q^2+61*q-84 ) q congruent 47 modulo 60: 1/12 ( q^3-14*q^2+67*q-146 ) q congruent 49 modulo 60: 1/12 ( q^3-14*q^2+61*q-72 ) q congruent 53 modulo 60: 1/12 ( q^3-14*q^2+67*q-110 ) q congruent 59 modulo 60: 1/12 ( q^3-14*q^2+67*q-170 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 69, 5, 78, 9, 31, 78, 20, 71, 94, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 6 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 14, 1, 2, 6 ], [ 15, 1, 2, 8 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 21, 1, 2, 12 ], [ 22, 1, 4, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 28, 1, 4, 12 ], [ 29, 1, 4, 12 ], [ 30, 1, 3, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 4, 12 ], [ 42, 1, 6, 12 ] ] i = 46: Pi = [ 1, 2, 3, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [46,1,1] Dynkin type is A_2(q) + A_2(q) + A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 ( q^3-25*q^2+215*q-719 ) q congruent 2 modulo 60: 1/24 ( q^3-22*q^2+136*q-192 ) q congruent 3 modulo 60: 1/24 ( q^3-23*q^2+165*q-315 ) q congruent 4 modulo 60: 1/24 ( q^3-24*q^2+180*q-400 ) q congruent 5 modulo 60: 1/24 ( q^3-23*q^2+171*q-405 ) q congruent 7 modulo 60: 1/24 ( q^3-25*q^2+209*q-581 ) q congruent 8 modulo 60: 1/24 ( q^3-22*q^2+136*q-192 ) q congruent 9 modulo 60: 1/24 ( q^3-23*q^2+171*q-405 ) q congruent 11 modulo 60: 1/24 ( q^3-23*q^2+165*q-363 ) q congruent 13 modulo 60: 1/24 ( q^3-25*q^2+215*q-671 ) q congruent 16 modulo 60: 1/24 ( q^3-24*q^2+180*q-448 ) q congruent 17 modulo 60: 1/24 ( q^3-23*q^2+171*q-405 ) q congruent 19 modulo 60: 1/24 ( q^3-25*q^2+209*q-581 ) q congruent 21 modulo 60: 1/24 ( q^3-23*q^2+171*q-453 ) q congruent 23 modulo 60: 1/24 ( q^3-23*q^2+165*q-315 ) q congruent 25 modulo 60: 1/24 ( q^3-25*q^2+215*q-671 ) q congruent 27 modulo 60: 1/24 ( q^3-23*q^2+165*q-315 ) q congruent 29 modulo 60: 1/24 ( q^3-23*q^2+171*q-405 ) q congruent 31 modulo 60: 1/24 ( q^3-25*q^2+209*q-629 ) q congruent 32 modulo 60: 1/24 ( q^3-22*q^2+136*q-192 ) q congruent 37 modulo 60: 1/24 ( q^3-25*q^2+215*q-671 ) q congruent 41 modulo 60: 1/24 ( q^3-23*q^2+171*q-453 ) q congruent 43 modulo 60: 1/24 ( q^3-25*q^2+209*q-581 ) q congruent 47 modulo 60: 1/24 ( q^3-23*q^2+165*q-315 ) q congruent 49 modulo 60: 1/24 ( q^3-25*q^2+215*q-671 ) q congruent 53 modulo 60: 1/24 ( q^3-23*q^2+171*q-405 ) q congruent 59 modulo 60: 1/24 ( q^3-23*q^2+165*q-315 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 8, 77, 77, 30, 14, 83 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 48 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 20, 1, 1, 24 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 36 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 29, 1, 1, 24 ], [ 31, 1, 1, 24 ], [ 32, 1, 1, 24 ], [ 34, 1, 1, 12 ], [ 38, 1, 1, 72 ], [ 42, 1, 1, 12 ] ] k = 2: F-action on Pi is () [46,1,2] Dynkin type is A_2(q) + A_2(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 2 modulo 60: 1/8 q ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/8 ( q^3-9*q^2+21*q-9 ) q congruent 4 modulo 60: 1/8 q ( q^2-10*q+24 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/8 ( q^3-11*q^2+33*q-19 ) q congruent 8 modulo 60: 1/8 q ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/8 ( q^3-9*q^2+21*q-9 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 16 modulo 60: 1/8 q ( q^2-10*q+24 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/8 ( q^3-11*q^2+33*q-19 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/8 ( q^3-9*q^2+21*q-9 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 27 modulo 60: 1/8 ( q^3-9*q^2+21*q-9 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/8 ( q^3-11*q^2+33*q-19 ) q congruent 32 modulo 60: 1/8 q ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/8 ( q^3-11*q^2+33*q-19 ) q congruent 47 modulo 60: 1/8 ( q^3-9*q^2+21*q-9 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/8 ( q^3-9*q^2+21*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 77, 30, 30, 81, 83, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 12 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 29, 1, 2, 8 ], [ 31, 1, 2, 8 ], [ 32, 1, 1, 8 ], [ 34, 1, 2, 4 ], [ 38, 1, 5, 24 ], [ 42, 1, 4, 4 ] ] k = 3: F-action on Pi is () [46,1,3] Dynkin type is A_2(q) + A_2(q) + A_1(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^2-3*q-10 ) q congruent 2 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 4 modulo 60: 1/12 phi1 ( q^2-2*q-8 ) q congruent 5 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 7 modulo 60: 1/12 phi1 ( q^2-3*q-10 ) q congruent 8 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 11 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 13 modulo 60: 1/12 phi1 ( q^2-3*q-10 ) q congruent 16 modulo 60: 1/12 phi1 ( q^2-2*q-8 ) q congruent 17 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 19 modulo 60: 1/12 phi1 ( q^2-3*q-10 ) q congruent 21 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 23 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 25 modulo 60: 1/12 phi1 ( q^2-3*q-10 ) q congruent 27 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 29 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 31 modulo 60: 1/12 phi1 ( q^2-3*q-10 ) q congruent 32 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 phi1 ( q^2-3*q-10 ) q congruent 41 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 43 modulo 60: 1/12 phi1 ( q^2-3*q-10 ) q congruent 47 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 49 modulo 60: 1/12 phi1 ( q^2-3*q-10 ) q congruent 53 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 59 modulo 60: 1/12 q phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30, 14, 83, 77, 30, 30, 81, 83, 37, 14, 83, 83, 37, 12, 79 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], [ 11, 1, 1, 2 ], [ 17, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 38, 1, 3, 36 ], [ 42, 1, 3, 6 ] ] k = 4: F-action on Pi is (1,3)(5,6) [46,1,4] Dynkin type is ^2A_2(q) + ^2A_2(q) + A_1(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^2 q congruent 2 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/12 q phi1^2 q congruent 4 modulo 60: 1/12 q^2 phi1 q congruent 5 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/12 q phi1^2 q congruent 8 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/12 q phi1^2 q congruent 11 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/12 q phi1^2 q congruent 16 modulo 60: 1/12 q^2 phi1 q congruent 17 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/12 q phi1^2 q congruent 21 modulo 60: 1/12 q phi1^2 q congruent 23 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/12 q phi1^2 q congruent 27 modulo 60: 1/12 q phi1^2 q congruent 29 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/12 q phi1^2 q congruent 32 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/12 q phi1^2 q congruent 41 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/12 q phi1^2 q congruent 47 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/12 q phi1^2 q congruent 53 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 9, 31, 78, 84, 15, 31, 78, 82, 31, 38, 84, 84, 15, 38, 84, 80, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], [ 11, 1, 2, 2 ], [ 17, 1, 4, 12 ], [ 27, 1, 4, 6 ], [ 38, 1, 11, 36 ], [ 42, 1, 5, 6 ] ] k = 5: F-action on Pi is (1,3)(5,6) [46,1,5] Dynkin type is ^2A_2(q) + ^2A_2(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-6*q+11 ) q congruent 2 modulo 60: 1/8 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 ( q^3-9*q^2+29*q-37 ) q congruent 7 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 8 modulo 60: 1/8 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-6*q+11 ) q congruent 11 modulo 60: 1/8 ( q^3-9*q^2+31*q-47 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-6*q+11 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 ( q^3-9*q^2+29*q-37 ) q congruent 19 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-6*q+11 ) q congruent 23 modulo 60: 1/8 ( q^3-9*q^2+31*q-47 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-6*q+11 ) q congruent 27 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 29 modulo 60: 1/8 ( q^3-9*q^2+29*q-37 ) q congruent 31 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 32 modulo 60: 1/8 ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-6*q+11 ) q congruent 41 modulo 60: 1/8 ( q^3-9*q^2+29*q-37 ) q congruent 43 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 47 modulo 60: 1/8 ( q^3-9*q^2+31*q-47 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-6*q+11 ) q congruent 53 modulo 60: 1/8 ( q^3-9*q^2+29*q-37 ) q congruent 59 modulo 60: 1/8 ( q^3-9*q^2+31*q-47 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 31, 78, 82, 31, 38, 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 12 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 29, 1, 3, 8 ], [ 31, 1, 3, 8 ], [ 32, 1, 3, 8 ], [ 34, 1, 3, 4 ], [ 38, 1, 8, 24 ], [ 42, 1, 2, 4 ] ] k = 6: F-action on Pi is (1,3)(5,6) [46,1,6] Dynkin type is ^2A_2(q) + ^2A_2(q) + A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^2-16*q+69 ) q congruent 2 modulo 60: 1/24 ( q^3-18*q^2+96*q-128 ) q congruent 3 modulo 60: 1/24 ( q^3-17*q^2+91*q-147 ) q congruent 4 modulo 60: 1/24 ( q^3-16*q^2+60*q-48 ) q congruent 5 modulo 60: 1/24 ( q^3-19*q^2+121*q-255 ) q congruent 7 modulo 60: 1/24 ( q^3-17*q^2+91*q-147 ) q congruent 8 modulo 60: 1/24 ( q^3-18*q^2+96*q-128 ) q congruent 9 modulo 60: 1/24 ( q^3-17*q^2+85*q-117 ) q congruent 11 modulo 60: 1/24 ( q^3-19*q^2+127*q-333 ) q congruent 13 modulo 60: 1/24 phi1 ( q^2-16*q+69 ) q congruent 16 modulo 60: 1/24 q ( q^2-16*q+60 ) q congruent 17 modulo 60: 1/24 ( q^3-19*q^2+121*q-255 ) q congruent 19 modulo 60: 1/24 ( q^3-17*q^2+91*q-195 ) q congruent 21 modulo 60: 1/24 phi1 ( q^2-16*q+69 ) q congruent 23 modulo 60: 1/24 ( q^3-19*q^2+127*q-333 ) q congruent 25 modulo 60: 1/24 phi1 ( q^2-16*q+69 ) q congruent 27 modulo 60: 1/24 ( q^3-17*q^2+91*q-147 ) q congruent 29 modulo 60: 1/24 ( q^3-19*q^2+121*q-303 ) q congruent 31 modulo 60: 1/24 ( q^3-17*q^2+91*q-147 ) q congruent 32 modulo 60: 1/24 ( q^3-18*q^2+96*q-128 ) q congruent 37 modulo 60: 1/24 phi1 ( q^2-16*q+69 ) q congruent 41 modulo 60: 1/24 ( q^3-19*q^2+121*q-255 ) q congruent 43 modulo 60: 1/24 ( q^3-17*q^2+91*q-147 ) q congruent 47 modulo 60: 1/24 ( q^3-19*q^2+127*q-333 ) q congruent 49 modulo 60: 1/24 ( q^3-17*q^2+85*q-117 ) q congruent 53 modulo 60: 1/24 ( q^3-19*q^2+121*q-255 ) q congruent 59 modulo 60: 1/24 ( q^3-19*q^2+127*q-381 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 78, 9, 31, 78, 84, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 12 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 24 ], [ 16, 1, 3, 24 ], [ 17, 1, 4, 48 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 20, 1, 4, 24 ], [ 21, 1, 2, 12 ], [ 22, 1, 4, 36 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 29, 1, 4, 24 ], [ 31, 1, 4, 24 ], [ 32, 1, 3, 24 ], [ 34, 1, 4, 12 ], [ 38, 1, 12, 72 ], [ 42, 1, 6, 12 ] ] k = 7: F-action on Pi is (1,5)(3,6) [46,1,7] Dynkin type is A_2(q^2) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 2 modulo 60: 1/24 ( q^3-10*q^2+28*q-24 ) q congruent 3 modulo 60: 1/24 ( q^3-9*q^2+17*q+3 ) q congruent 4 modulo 60: 1/24 q ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/24 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 60: 1/24 ( q^3-9*q^2+21*q-1 ) q congruent 8 modulo 60: 1/24 ( q^3-10*q^2+28*q-24 ) q congruent 9 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/24 ( q^3-11*q^2+33*q-27 ) q congruent 13 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 16 modulo 60: 1/24 q ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/24 ( q^3-11*q^2+39*q-45 ) q congruent 19 modulo 60: 1/24 ( q^3-9*q^2+21*q-1 ) q congruent 21 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/24 ( q^3-11*q^2+33*q-27 ) q congruent 25 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 27 modulo 60: 1/24 ( q^3-9*q^2+17*q+3 ) q congruent 29 modulo 60: 1/24 ( q^3-11*q^2+39*q-45 ) q congruent 31 modulo 60: 1/24 ( q^3-9*q^2+21*q-1 ) q congruent 32 modulo 60: 1/24 ( q^3-10*q^2+28*q-24 ) q congruent 37 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 41 modulo 60: 1/24 ( q^3-11*q^2+39*q-45 ) q congruent 43 modulo 60: 1/24 ( q^3-9*q^2+21*q-1 ) q congruent 47 modulo 60: 1/24 ( q^3-11*q^2+33*q-27 ) q congruent 49 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 53 modulo 60: 1/24 ( q^3-11*q^2+39*q-45 ) q congruent 59 modulo 60: 1/24 ( q^3-11*q^2+33*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 3, 19, 72, 87, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 12 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 8, 24 ], [ 22, 1, 3, 12 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 32, 1, 4, 12 ], [ 34, 1, 3, 12 ], [ 38, 1, 7, 24 ], [ 42, 1, 1, 12 ] ] k = 8: F-action on Pi is (1,5)(3,6) [46,1,8] Dynkin type is A_2(q^2) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1^3 q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 phi4 ( q-3 ) q congruent 4 modulo 60: 1/8 q^2 ( q-2 ) q congruent 5 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 7 modulo 60: 1/8 phi4 ( q-3 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1^3 q congruent 11 modulo 60: 1/8 ( q^3-5*q^2+5*q-5 ) q congruent 13 modulo 60: 1/8 phi1^3 q congruent 16 modulo 60: 1/8 q^2 ( q-2 ) q congruent 17 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 19 modulo 60: 1/8 phi4 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1^3 q congruent 23 modulo 60: 1/8 ( q^3-5*q^2+5*q-5 ) q congruent 25 modulo 60: 1/8 phi1^3 q congruent 27 modulo 60: 1/8 phi4 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 31 modulo 60: 1/8 phi4 ( q-3 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1^3 q congruent 41 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 43 modulo 60: 1/8 phi4 ( q-3 ) q congruent 47 modulo 60: 1/8 ( q^3-5*q^2+5*q-5 ) q congruent 49 modulo 60: 1/8 phi1^3 q congruent 53 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 59 modulo 60: 1/8 ( q^3-5*q^2+5*q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 69, 76, 20, 40, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ], [ 20, 1, 7, 8 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 32, 1, 4, 4 ], [ 34, 1, 4, 4 ], [ 38, 1, 10, 8 ], [ 42, 1, 4, 4 ] ] k = 9: F-action on Pi is (1,5)(3,6) [46,1,9] Dynkin type is A_2(q^2) + A_1(q) + T(phi2 phi3) Order of center |Z^F|: phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 2 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1 phi2 q congruent 4 modulo 60: 1/12 q phi1 ( q+2 ) q congruent 5 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 7 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 8 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1 phi2 q congruent 11 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 13 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 16 modulo 60: 1/12 q phi1 ( q+2 ) q congruent 17 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 19 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 q congruent 23 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 25 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 q congruent 29 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 31 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 32 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 41 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 43 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 47 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 49 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 53 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 59 modulo 60: 1/12 q phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 81, 27, 59, 95, 85, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 27, 1, 5, 6 ], [ 38, 1, 9, 12 ], [ 42, 1, 3, 6 ] ] k = 10: F-action on Pi is (1,6)(3,5) [46,1,10] Dynkin type is A_2(q^2) + A_1(q) + T(phi1 phi6) Order of center |Z^F|: phi1 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 ( q-5 ) q congruent 2 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 4 modulo 60: 1/12 q phi1 ( q-4 ) q congruent 5 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/12 q phi1 ( q-5 ) q congruent 8 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 11 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/12 q phi1 ( q-5 ) q congruent 16 modulo 60: 1/12 q phi1 ( q-4 ) q congruent 17 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/12 q phi1 ( q-5 ) q congruent 21 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 23 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/12 q phi1 ( q-5 ) q congruent 27 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 29 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/12 q phi1 ( q-5 ) q congruent 32 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/12 q phi1 ( q-5 ) q congruent 41 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/12 q phi1 ( q-5 ) q congruent 47 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/12 q phi1 ( q-5 ) q congruent 53 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 82, 96, 60, 33, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 3, 4 ], [ 27, 1, 4, 6 ], [ 38, 1, 4, 12 ], [ 42, 1, 5, 6 ] ] k = 11: F-action on Pi is (1,6)(3,5) [46,1,11] Dynkin type is A_2(q^2) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-6*q+3 ) q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-4*q+1 ) q congruent 7 modulo 60: 1/8 phi1^2 ( q-5 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-4*q+1 ) q congruent 11 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-6*q+3 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-4*q+1 ) q congruent 19 modulo 60: 1/8 phi1^2 ( q-5 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-4*q+1 ) q congruent 23 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-6*q+3 ) q congruent 27 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-4*q+1 ) q congruent 31 modulo 60: 1/8 phi1^2 ( q-5 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-6*q+3 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-4*q+1 ) q congruent 43 modulo 60: 1/8 phi1^2 ( q-5 ) q congruent 47 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-6*q+3 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-4*q+1 ) q congruent 59 modulo 60: 1/8 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 19, 76, 87, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ], [ 20, 1, 6, 8 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 32, 1, 4, 4 ], [ 34, 1, 1, 4 ], [ 38, 1, 2, 8 ], [ 42, 1, 2, 4 ] ] k = 12: F-action on Pi is (1,6)(3,5) [46,1,12] Dynkin type is A_2(q^2) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^2-8*q+9 ) q congruent 2 modulo 60: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/24 q ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/24 ( q^3-7*q^2+13*q-15 ) q congruent 7 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 60: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/24 phi1 ( q^2-6*q+3 ) q congruent 11 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 13 modulo 60: 1/24 phi1 ( q^2-8*q+9 ) q congruent 16 modulo 60: 1/24 q ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/24 ( q^3-7*q^2+13*q-15 ) q congruent 19 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/24 phi1 ( q^2-6*q+3 ) q congruent 23 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 25 modulo 60: 1/24 phi1 ( q^2-8*q+9 ) q congruent 27 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/24 ( q^3-7*q^2+13*q-15 ) q congruent 31 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 32 modulo 60: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/24 phi1 ( q^2-8*q+9 ) q congruent 41 modulo 60: 1/24 ( q^3-7*q^2+13*q-15 ) q congruent 43 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 49 modulo 60: 1/24 phi1 ( q^2-8*q+9 ) q congruent 53 modulo 60: 1/24 ( q^3-7*q^2+13*q-15 ) q congruent 59 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 72, 20, 35, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 6 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 17, 1, 3, 4 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 5, 24 ], [ 22, 1, 2, 12 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 32, 1, 4, 12 ], [ 34, 1, 2, 12 ], [ 38, 1, 6, 24 ], [ 42, 1, 6, 12 ] ] i = 47: Pi = [ 1, 2, 3, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [47,1,1] Dynkin type is A_2(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 ( q^3-26*q^2+229*q-804 ) q congruent 2 modulo 60: 1/24 ( q^3-22*q^2+136*q-192 ) q congruent 3 modulo 60: 1/24 ( q^3-26*q^2+207*q-414 ) q congruent 4 modulo 60: 1/24 ( q^3-22*q^2+152*q-320 ) q congruent 5 modulo 60: 1/24 ( q^3-26*q^2+213*q-540 ) q congruent 7 modulo 60: 1/24 ( q^3-26*q^2+223*q-630 ) q congruent 8 modulo 60: 1/24 ( q^3-22*q^2+136*q-192 ) q congruent 9 modulo 60: 1/24 ( q^3-26*q^2+213*q-540 ) q congruent 11 modulo 60: 1/24 ( q^3-26*q^2+207*q-462 ) q congruent 13 modulo 60: 1/24 ( q^3-26*q^2+229*q-756 ) q congruent 16 modulo 60: 1/24 ( q^3-22*q^2+152*q-368 ) q congruent 17 modulo 60: 1/24 ( q^3-26*q^2+213*q-540 ) q congruent 19 modulo 60: 1/24 ( q^3-26*q^2+223*q-630 ) q congruent 21 modulo 60: 1/24 ( q^3-26*q^2+213*q-588 ) q congruent 23 modulo 60: 1/24 ( q^3-26*q^2+207*q-414 ) q congruent 25 modulo 60: 1/24 ( q^3-26*q^2+229*q-756 ) q congruent 27 modulo 60: 1/24 ( q^3-26*q^2+207*q-414 ) q congruent 29 modulo 60: 1/24 ( q^3-26*q^2+213*q-540 ) q congruent 31 modulo 60: 1/24 ( q^3-26*q^2+223*q-678 ) q congruent 32 modulo 60: 1/24 ( q^3-22*q^2+136*q-192 ) q congruent 37 modulo 60: 1/24 ( q^3-26*q^2+229*q-756 ) q congruent 41 modulo 60: 1/24 ( q^3-26*q^2+213*q-588 ) q congruent 43 modulo 60: 1/24 ( q^3-26*q^2+223*q-630 ) q congruent 47 modulo 60: 1/24 ( q^3-26*q^2+207*q-414 ) q congruent 49 modulo 60: 1/24 ( q^3-26*q^2+229*q-756 ) q congruent 53 modulo 60: 1/24 ( q^3-26*q^2+213*q-540 ) q congruent 59 modulo 60: 1/24 ( q^3-26*q^2+207*q-414 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 7, 8, 77, 77, 30, 77, 30, 30, 81 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 4, 1, 1, 18 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 18 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], [ 16, 1, 1, 48 ], [ 17, 1, 1, 72 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], [ 20, 1, 1, 24 ], [ 22, 1, 1, 4 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 28, 1, 1, 12 ], [ 30, 1, 1, 24 ], [ 31, 1, 1, 12 ], [ 32, 1, 1, 48 ], [ 33, 1, 1, 48 ], [ 35, 1, 1, 24 ], [ 40, 1, 1, 12 ] ] k = 2: F-action on Pi is () [47,1,2] Dynkin type is A_2(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^2-11*q+34 ) q congruent 2 modulo 60: 1/24 q ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/24 phi1 ( q^2-11*q+24 ) q congruent 4 modulo 60: 1/24 q ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/24 phi1 ( q^2-11*q+30 ) q congruent 7 modulo 60: 1/24 phi1 ( q^2-11*q+28 ) q congruent 8 modulo 60: 1/24 q ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/24 phi1 ( q^2-11*q+30 ) q congruent 11 modulo 60: 1/24 phi1 ( q^2-11*q+24 ) q congruent 13 modulo 60: 1/24 phi1 ( q^2-11*q+34 ) q congruent 16 modulo 60: 1/24 q ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/24 phi1 ( q^2-11*q+30 ) q congruent 19 modulo 60: 1/24 phi1 ( q^2-11*q+28 ) q congruent 21 modulo 60: 1/24 phi1 ( q^2-11*q+30 ) q congruent 23 modulo 60: 1/24 phi1 ( q^2-11*q+24 ) q congruent 25 modulo 60: 1/24 phi1 ( q^2-11*q+34 ) q congruent 27 modulo 60: 1/24 phi1 ( q^2-11*q+24 ) q congruent 29 modulo 60: 1/24 phi1 ( q^2-11*q+30 ) q congruent 31 modulo 60: 1/24 phi1 ( q^2-11*q+28 ) q congruent 32 modulo 60: 1/24 q ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/24 phi1 ( q^2-11*q+34 ) q congruent 41 modulo 60: 1/24 phi1 ( q^2-11*q+30 ) q congruent 43 modulo 60: 1/24 phi1 ( q^2-11*q+28 ) q congruent 47 modulo 60: 1/24 phi1 ( q^2-11*q+24 ) q congruent 49 modulo 60: 1/24 phi1 ( q^2-11*q+34 ) q congruent 53 modulo 60: 1/24 phi1 ( q^2-11*q+30 ) q congruent 59 modulo 60: 1/24 phi1 ( q^2-11*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 3, 4, 68, 68, 7, 68, 7, 7, 69, 77, 30, 30, 81, 30, 81, 81, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 6 ], [ 13, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 20, 1, 2, 24 ], [ 22, 1, 2, 4 ], [ 23, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 28, 1, 2, 12 ], [ 31, 1, 2, 12 ], [ 33, 1, 1, 48 ], [ 35, 1, 3, 24 ], [ 40, 1, 1, 12 ] ] k = 3: F-action on Pi is (5,7) [47,1,3] Dynkin type is A_2(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 2 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 7 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 8 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 11 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 19 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 23 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 27 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 31 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 32 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 43 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-7*q+10 ) q congruent 59 modulo 60: 1/8 q ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19, 68, 19, 7, 76, 30, 97, 81, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 4, 4 ], [ 28, 1, 3, 4 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 33, 1, 2, 8 ], [ 35, 1, 2, 8 ], [ 40, 1, 3, 4 ] ] k = 4: F-action on Pi is (5,7) [47,1,4] Dynkin type is A_2(q) + A_1(q) + A_1(q^2) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1^2 ( q-4 ) q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/8 q^2 ( q-4 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-5*q+8 ) q congruent 7 modulo 60: 1/8 phi1 ( q^2-5*q+2 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-5*q+8 ) q congruent 11 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/8 phi1^2 ( q-4 ) q congruent 16 modulo 60: 1/8 q^2 ( q-4 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-5*q+8 ) q congruent 19 modulo 60: 1/8 phi1 ( q^2-5*q+2 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-5*q+8 ) q congruent 23 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/8 phi1^2 ( q-4 ) q congruent 27 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-5*q+8 ) q congruent 31 modulo 60: 1/8 phi1 ( q^2-5*q+2 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1^2 ( q-4 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-5*q+8 ) q congruent 43 modulo 60: 1/8 phi1 ( q^2-5*q+2 ) q congruent 47 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/8 phi1^2 ( q-4 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-5*q+8 ) q congruent 59 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 3, 72, 7, 76, 69, 20, 81, 59, 27, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 28, 1, 4, 4 ], [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 40, 1, 3, 4 ] ] k = 5: F-action on Pi is (2,5,7) [47,1,5] Dynkin type is A_2(q) + A_1(q^3) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 2 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 4 modulo 60: 1/12 phi1 ( q^2-4 ) q congruent 5 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 7 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 8 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 11 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 13 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 16 modulo 60: 1/12 phi1 ( q^2-4 ) q congruent 17 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 19 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 21 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 23 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 25 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 27 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 29 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 31 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 32 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 41 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 43 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 47 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 49 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 53 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 59 modulo 60: 1/12 q phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 87, 83, 40, 12, 85 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 22, 1, 1, 4 ], [ 33, 1, 3, 6 ], [ 40, 1, 5, 6 ] ] k = 6: F-action on Pi is (2,5,7) [47,1,6] Dynkin type is A_2(q) + A_1(q^3) + T(phi2 phi3) Order of center |Z^F|: phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 2 modulo 60: 1/12 q^2 phi2 q congruent 3 modulo 60: 1/12 q phi1 phi2 q congruent 4 modulo 60: 1/12 q phi1 ( q+2 ) q congruent 5 modulo 60: 1/12 q phi1 phi2 q congruent 7 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 8 modulo 60: 1/12 q^2 phi2 q congruent 9 modulo 60: 1/12 q phi1 phi2 q congruent 11 modulo 60: 1/12 q phi1 phi2 q congruent 13 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 16 modulo 60: 1/12 q phi1 ( q+2 ) q congruent 17 modulo 60: 1/12 q phi1 phi2 q congruent 19 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 q congruent 23 modulo 60: 1/12 q phi1 phi2 q congruent 25 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 q congruent 29 modulo 60: 1/12 q phi1 phi2 q congruent 31 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 32 modulo 60: 1/12 q^2 phi2 q congruent 37 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 41 modulo 60: 1/12 q phi1 phi2 q congruent 43 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 47 modulo 60: 1/12 q phi1 phi2 q congruent 49 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 53 modulo 60: 1/12 q phi1 phi2 q congruent 59 modulo 60: 1/12 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 83, 35, 37, 88, 79, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 22, 1, 2, 4 ], [ 33, 1, 3, 6 ], [ 40, 1, 5, 6 ] ] k = 7: F-action on Pi is (1,3) [47,1,7] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^2-9*q+18 ) q congruent 2 modulo 60: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/24 ( q^3-10*q^2+33*q-36 ) q congruent 4 modulo 60: 1/24 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/24 ( q^3-10*q^2+31*q-30 ) q congruent 7 modulo 60: 1/24 ( q^3-10*q^2+33*q-36 ) q congruent 8 modulo 60: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/24 phi1 ( q^2-9*q+18 ) q congruent 11 modulo 60: 1/24 ( q^3-10*q^2+37*q-48 ) q congruent 13 modulo 60: 1/24 phi1 ( q^2-9*q+18 ) q congruent 16 modulo 60: 1/24 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/24 ( q^3-10*q^2+31*q-30 ) q congruent 19 modulo 60: 1/24 ( q^3-10*q^2+33*q-36 ) q congruent 21 modulo 60: 1/24 phi1 ( q^2-9*q+18 ) q congruent 23 modulo 60: 1/24 ( q^3-10*q^2+37*q-48 ) q congruent 25 modulo 60: 1/24 phi1 ( q^2-9*q+18 ) q congruent 27 modulo 60: 1/24 ( q^3-10*q^2+33*q-36 ) q congruent 29 modulo 60: 1/24 ( q^3-10*q^2+31*q-30 ) q congruent 31 modulo 60: 1/24 ( q^3-10*q^2+33*q-36 ) q congruent 32 modulo 60: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/24 phi1 ( q^2-9*q+18 ) q congruent 41 modulo 60: 1/24 ( q^3-10*q^2+31*q-30 ) q congruent 43 modulo 60: 1/24 ( q^3-10*q^2+33*q-36 ) q congruent 47 modulo 60: 1/24 ( q^3-10*q^2+37*q-48 ) q congruent 49 modulo 60: 1/24 phi1 ( q^2-9*q+18 ) q congruent 53 modulo 60: 1/24 ( q^3-10*q^2+31*q-30 ) q congruent 59 modulo 60: 1/24 ( q^3-10*q^2+37*q-48 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 69, 5, 69, 5, 5, 67, 68, 7, 7, 69, 7, 69, 69, 5, 28, 82, 82, 31, 82, 31, 31, 78 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 18 ], [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 12, 1, 2, 6 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 24 ], [ 20, 1, 3, 24 ], [ 22, 1, 3, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 25, 1, 3, 12 ], [ 28, 1, 3, 12 ], [ 31, 1, 3, 12 ], [ 33, 1, 8, 48 ], [ 35, 1, 6, 24 ], [ 40, 1, 6, 12 ] ] k = 8: F-action on Pi is (1,3) [47,1,8] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^2-19*q+96 ) q congruent 2 modulo 60: 1/24 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 60: 1/24 ( q^3-20*q^2+121*q-210 ) q congruent 4 modulo 60: 1/24 ( q^3-16*q^2+60*q-48 ) q congruent 5 modulo 60: 1/24 ( q^3-20*q^2+131*q-280 ) q congruent 7 modulo 60: 1/24 ( q^3-20*q^2+121*q-210 ) q congruent 8 modulo 60: 1/24 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 60: 1/24 ( q^3-20*q^2+115*q-144 ) q congruent 11 modulo 60: 1/24 ( q^3-20*q^2+137*q-394 ) q congruent 13 modulo 60: 1/24 phi1 ( q^2-19*q+96 ) q congruent 16 modulo 60: 1/24 q ( q^2-16*q+60 ) q congruent 17 modulo 60: 1/24 ( q^3-20*q^2+131*q-280 ) q congruent 19 modulo 60: 1/24 ( q^3-20*q^2+121*q-258 ) q congruent 21 modulo 60: 1/24 phi1 ( q^2-19*q+96 ) q congruent 23 modulo 60: 1/24 ( q^3-20*q^2+137*q-394 ) q congruent 25 modulo 60: 1/24 phi1 ( q^2-19*q+96 ) q congruent 27 modulo 60: 1/24 ( q^3-20*q^2+121*q-210 ) q congruent 29 modulo 60: 1/24 ( q^3-20*q^2+131*q-328 ) q congruent 31 modulo 60: 1/24 ( q^3-20*q^2+121*q-210 ) q congruent 32 modulo 60: 1/24 ( q^3-16*q^2+76*q-96 ) q congruent 37 modulo 60: 1/24 phi1 ( q^2-19*q+96 ) q congruent 41 modulo 60: 1/24 ( q^3-20*q^2+131*q-280 ) q congruent 43 modulo 60: 1/24 ( q^3-20*q^2+121*q-210 ) q congruent 47 modulo 60: 1/24 ( q^3-20*q^2+137*q-394 ) q congruent 49 modulo 60: 1/24 ( q^3-20*q^2+115*q-144 ) q congruent 53 modulo 60: 1/24 ( q^3-20*q^2+131*q-280 ) q congruent 59 modulo 60: 1/24 ( q^3-20*q^2+137*q-442 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 5, 67, 5, 67, 67, 2, 7, 69, 69, 5, 69, 5, 5, 67, 82, 31, 31, 78, 31, 78, 78, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 14 ], [ 4, 1, 2, 18 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 18 ], [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], [ 16, 1, 3, 48 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], [ 20, 1, 4, 24 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 28, 1, 4, 12 ], [ 30, 1, 3, 24 ], [ 31, 1, 4, 12 ], [ 32, 1, 3, 48 ], [ 33, 1, 8, 48 ], [ 35, 1, 8, 24 ], [ 40, 1, 6, 12 ] ] k = 9: F-action on Pi is (1,3)(5,7) [47,1,9] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-7*q+12 ) q congruent 2 modulo 60: 1/8 ( q^3-6*q^2+4*q+8 ) q congruent 3 modulo 60: 1/8 ( q^3-8*q^2+21*q-18 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/8 ( q^3-8*q^2+21*q-18 ) q congruent 8 modulo 60: 1/8 ( q^3-6*q^2+4*q+8 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-7*q+12 ) q congruent 11 modulo 60: 1/8 ( q^3-8*q^2+17*q-6 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-7*q+12 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/8 ( q^3-8*q^2+21*q-18 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-7*q+12 ) q congruent 23 modulo 60: 1/8 ( q^3-8*q^2+17*q-6 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-7*q+12 ) q congruent 27 modulo 60: 1/8 ( q^3-8*q^2+21*q-18 ) q congruent 29 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/8 ( q^3-8*q^2+21*q-18 ) q congruent 32 modulo 60: 1/8 ( q^3-6*q^2+4*q+8 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-7*q+12 ) q congruent 41 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/8 ( q^3-8*q^2+21*q-18 ) q congruent 47 modulo 60: 1/8 ( q^3-8*q^2+17*q-6 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-7*q+12 ) q congruent 53 modulo 60: 1/8 q ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/8 ( q^3-8*q^2+17*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 69, 20, 68, 19, 7, 76, 28, 96, 82, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 28, 1, 1, 4 ], [ 31, 1, 3, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 35, 1, 5, 8 ], [ 40, 1, 2, 4 ] ] k = 10: F-action on Pi is (1,3)(5,7) [47,1,10] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q^2) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 4 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 47 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/8 ( q^3-6*q^2+13*q-12 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 5, 71, 7, 76, 69, 20, 82, 60, 31, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 4, 8 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 28, 1, 2, 4 ], [ 30, 1, 4, 8 ], [ 31, 1, 4, 4 ], [ 33, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 40, 1, 2, 4 ] ] k = 11: F-action on Pi is (1,3)(2,5,7) [47,1,11] Dynkin type is ^2A_2(q) + A_1(q^3) + T(phi1 phi6) Order of center |Z^F|: phi1 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 2 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 4 modulo 60: 1/12 q phi1 ( q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 8 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 11 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 16 modulo 60: 1/12 q phi1 ( q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 21 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 23 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 27 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 29 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 32 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 41 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 47 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 53 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 84, 87, 38, 33, 80 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 22, 1, 3, 4 ], [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ] ] k = 12: F-action on Pi is (1,3)(2,5,7) [47,1,12] Dynkin type is ^2A_2(q) + A_1(q^3) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^2 q congruent 2 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1^2 q congruent 4 modulo 60: 1/12 q^2 phi1 q congruent 5 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 7 modulo 60: 1/12 q phi1^2 q congruent 8 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1^2 q congruent 11 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 13 modulo 60: 1/12 q phi1^2 q congruent 16 modulo 60: 1/12 q^2 phi1 q congruent 17 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 19 modulo 60: 1/12 q phi1^2 q congruent 21 modulo 60: 1/12 q phi1^2 q congruent 23 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 25 modulo 60: 1/12 q phi1^2 q congruent 27 modulo 60: 1/12 q phi1^2 q congruent 29 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 31 modulo 60: 1/12 q phi1^2 q congruent 32 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 q phi1^2 q congruent 41 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 43 modulo 60: 1/12 q phi1^2 q congruent 47 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 49 modulo 60: 1/12 q phi1^2 q congruent 53 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 59 modulo 60: 1/12 phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 88, 15, 40, 84, 86, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 22, 1, 4, 4 ], [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ] ] i = 48: Pi = [ 1, 2, 4, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [48,1,1] Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 ( q^3-23*q^2+179*q-541 ) q congruent 2 modulo 60: 1/16 ( q^3-20*q^2+116*q-160 ) q congruent 3 modulo 60: 1/16 ( q^3-23*q^2+163*q-309 ) q congruent 4 modulo 60: 1/16 ( q^3-20*q^2+124*q-240 ) q congruent 5 modulo 60: 1/16 ( q^3-23*q^2+171*q-405 ) q congruent 7 modulo 60: 1/16 ( q^3-23*q^2+171*q-413 ) q congruent 8 modulo 60: 1/16 ( q^3-20*q^2+116*q-160 ) q congruent 9 modulo 60: 1/16 ( q^3-23*q^2+171*q-405 ) q congruent 11 modulo 60: 1/16 ( q^3-23*q^2+163*q-341 ) q congruent 13 modulo 60: 1/16 ( q^3-23*q^2+179*q-509 ) q congruent 16 modulo 60: 1/16 ( q^3-20*q^2+124*q-272 ) q congruent 17 modulo 60: 1/16 ( q^3-23*q^2+171*q-405 ) q congruent 19 modulo 60: 1/16 ( q^3-23*q^2+171*q-413 ) q congruent 21 modulo 60: 1/16 ( q^3-23*q^2+171*q-437 ) q congruent 23 modulo 60: 1/16 ( q^3-23*q^2+163*q-309 ) q congruent 25 modulo 60: 1/16 ( q^3-23*q^2+179*q-509 ) q congruent 27 modulo 60: 1/16 ( q^3-23*q^2+163*q-309 ) q congruent 29 modulo 60: 1/16 ( q^3-23*q^2+171*q-405 ) q congruent 31 modulo 60: 1/16 ( q^3-23*q^2+171*q-445 ) q congruent 32 modulo 60: 1/16 ( q^3-20*q^2+116*q-160 ) q congruent 37 modulo 60: 1/16 ( q^3-23*q^2+179*q-509 ) q congruent 41 modulo 60: 1/16 ( q^3-23*q^2+171*q-437 ) q congruent 43 modulo 60: 1/16 ( q^3-23*q^2+171*q-413 ) q congruent 47 modulo 60: 1/16 ( q^3-23*q^2+163*q-309 ) q congruent 49 modulo 60: 1/16 ( q^3-23*q^2+179*q-509 ) q congruent 53 modulo 60: 1/16 ( q^3-23*q^2+171*q-405 ) q congruent 59 modulo 60: 1/16 ( q^3-23*q^2+163*q-309 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 4, 68, 68, 7, 8, 77, 77, 30, 70, 19, 19, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 16 ], [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 8 ], [ 22, 1, 1, 16 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 12 ], [ 28, 1, 1, 8 ], [ 30, 1, 1, 16 ], [ 31, 1, 1, 16 ], [ 34, 1, 1, 16 ], [ 35, 1, 1, 16 ], [ 37, 1, 1, 16 ], [ 39, 1, 1, 8 ], [ 41, 1, 1, 16 ] ] k = 2: F-action on Pi is () [48,1,2] Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-10*q+29 ) q congruent 2 modulo 60: 1/8 q ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/8 phi1 ( q^2-10*q+21 ) q congruent 4 modulo 60: 1/8 q ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 7 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 8 modulo 60: 1/8 q ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 11 modulo 60: 1/8 phi1 ( q^2-10*q+21 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-10*q+29 ) q congruent 16 modulo 60: 1/8 q ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 19 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 23 modulo 60: 1/8 phi1 ( q^2-10*q+21 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-10*q+29 ) q congruent 27 modulo 60: 1/8 phi1 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 31 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 32 modulo 60: 1/8 q ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-10*q+29 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 43 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 47 modulo 60: 1/8 phi1 ( q^2-10*q+21 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-10*q+29 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-10*q+25 ) q congruent 59 modulo 60: 1/8 phi1 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 7, 68, 3, 7, 69, 77, 30, 30, 81, 19, 72, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 31, 1, 2, 8 ], [ 34, 1, 2, 8 ], [ 35, 1, 1, 8 ], [ 35, 1, 3, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 6, 8 ] ] k = 3: F-action on Pi is () [48,1,3] Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 3, 68, 7, 7, 69, 7, 69, 69, 5, 30, 81, 81, 27, 76, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 4, 8 ], [ 20, 1, 2, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 8 ], [ 28, 1, 2, 8 ], [ 35, 1, 3, 16 ], [ 37, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 41, 1, 9, 16 ] ] k = 4: F-action on Pi is (2,5) [48,1,4] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 16 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 32 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 69, 5, 68, 7, 7, 69, 4, 68, 68, 7, 28, 82, 82, 31, 70, 19, 19, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 4, 8 ], [ 20, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 4 ], [ 28, 1, 3, 8 ], [ 35, 1, 6, 16 ], [ 37, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 41, 1, 1, 16 ] ] k = 5: F-action on Pi is (2,5) [48,1,5] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 60: 1/8 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 7 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 60: 1/8 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/8 ( q^3-9*q^2+31*q-39 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 19 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/8 ( q^3-9*q^2+31*q-39 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 29 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 31 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 32 modulo 60: 1/8 ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 43 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 47 modulo 60: 1/8 ( q^3-9*q^2+31*q-39 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/8 ( q^3-9*q^2+27*q-27 ) q congruent 59 modulo 60: 1/8 ( q^3-9*q^2+31*q-39 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 5, 67, 7, 69, 69, 5, 68, 3, 7, 69, 82, 31, 31, 78, 19, 72, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 31, 1, 3, 8 ], [ 34, 1, 3, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 6, 8 ] ] k = 6: F-action on Pi is (2,5) [48,1,6] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-16*q+67 ) q congruent 2 modulo 60: 1/16 ( q^3-14*q^2+56*q-64 ) q congruent 3 modulo 60: 1/16 ( q^3-17*q^2+91*q-147 ) q congruent 4 modulo 60: 1/16 ( q^3-14*q^2+48*q-32 ) q congruent 5 modulo 60: 1/16 ( q^3-17*q^2+91*q-155 ) q congruent 7 modulo 60: 1/16 ( q^3-17*q^2+91*q-147 ) q congruent 8 modulo 60: 1/16 ( q^3-14*q^2+56*q-64 ) q congruent 9 modulo 60: 1/16 ( q^3-17*q^2+83*q-99 ) q congruent 11 modulo 60: 1/16 ( q^3-17*q^2+99*q-235 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-16*q+67 ) q congruent 16 modulo 60: 1/16 q ( q^2-14*q+48 ) q congruent 17 modulo 60: 1/16 ( q^3-17*q^2+91*q-155 ) q congruent 19 modulo 60: 1/16 ( q^3-17*q^2+91*q-179 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-16*q+67 ) q congruent 23 modulo 60: 1/16 ( q^3-17*q^2+99*q-235 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-16*q+67 ) q congruent 27 modulo 60: 1/16 ( q^3-17*q^2+91*q-147 ) q congruent 29 modulo 60: 1/16 ( q^3-17*q^2+91*q-187 ) q congruent 31 modulo 60: 1/16 ( q^3-17*q^2+91*q-147 ) q congruent 32 modulo 60: 1/16 ( q^3-14*q^2+56*q-64 ) q congruent 37 modulo 60: 1/16 phi1 ( q^2-16*q+67 ) q congruent 41 modulo 60: 1/16 ( q^3-17*q^2+91*q-155 ) q congruent 43 modulo 60: 1/16 ( q^3-17*q^2+91*q-147 ) q congruent 47 modulo 60: 1/16 ( q^3-17*q^2+99*q-235 ) q congruent 49 modulo 60: 1/16 ( q^3-17*q^2+83*q-99 ) q congruent 53 modulo 60: 1/16 ( q^3-17*q^2+91*q-155 ) q congruent 59 modulo 60: 1/16 ( q^3-17*q^2+99*q-267 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 67, 2, 69, 5, 5, 67, 7, 69, 69, 5, 31, 78, 78, 9, 76, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 10 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 8 ], [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 3, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 4, 16 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 12 ], [ 28, 1, 4, 8 ], [ 30, 1, 3, 16 ], [ 31, 1, 4, 16 ], [ 34, 1, 4, 16 ], [ 35, 1, 8, 16 ], [ 37, 1, 3, 16 ], [ 39, 1, 3, 8 ], [ 41, 1, 9, 16 ] ] k = 7: F-action on Pi is (1,7) [48,1,7] Dynkin type is A_3(q) + A_1(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 2 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 8 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 19 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 23 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 27 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 31 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 32 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 43 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 47 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 59 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19, 7, 76, 30, 97, 76, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 1, 8 ], [ 21, 1, 1, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 4 ], [ 30, 1, 2, 8 ], [ 37, 1, 1, 8 ], [ 37, 1, 2, 4 ], [ 39, 1, 2, 4 ], [ 41, 1, 2, 8 ] ] k = 8: F-action on Pi is (1,7) [48,1,8] Dynkin type is A_3(q) + A_1(q^2) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 1/8 q^2 ( q-2 ) q congruent 3 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/8 q^2 ( q-2 ) q congruent 5 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 1/8 q^2 ( q-2 ) q congruent 9 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 1/8 q^2 ( q-2 ) q congruent 17 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 1/8 q^2 ( q-2 ) q congruent 37 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 16, 19, 73, 76, 18, 97, 53, 22, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 1, 2 ], [ 25, 1, 1, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ] ] k = 9: F-action on Pi is (1,7)(2,5) [48,1,9] Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1^2 phi2 q congruent 2 modulo 60: 1/8 q^3 q congruent 3 modulo 60: 1/8 phi1^2 phi2 q congruent 4 modulo 60: 1/8 q^3 q congruent 5 modulo 60: 1/8 phi1^2 phi2 q congruent 7 modulo 60: 1/8 phi1^2 phi2 q congruent 8 modulo 60: 1/8 q^3 q congruent 9 modulo 60: 1/8 phi1^2 phi2 q congruent 11 modulo 60: 1/8 phi1^2 phi2 q congruent 13 modulo 60: 1/8 phi1^2 phi2 q congruent 16 modulo 60: 1/8 q^3 q congruent 17 modulo 60: 1/8 phi1^2 phi2 q congruent 19 modulo 60: 1/8 phi1^2 phi2 q congruent 21 modulo 60: 1/8 phi1^2 phi2 q congruent 23 modulo 60: 1/8 phi1^2 phi2 q congruent 25 modulo 60: 1/8 phi1^2 phi2 q congruent 27 modulo 60: 1/8 phi1^2 phi2 q congruent 29 modulo 60: 1/8 phi1^2 phi2 q congruent 31 modulo 60: 1/8 phi1^2 phi2 q congruent 32 modulo 60: 1/8 q^3 q congruent 37 modulo 60: 1/8 phi1^2 phi2 q congruent 41 modulo 60: 1/8 phi1^2 phi2 q congruent 43 modulo 60: 1/8 phi1^2 phi2 q congruent 47 modulo 60: 1/8 phi1^2 phi2 q congruent 49 modulo 60: 1/8 phi1^2 phi2 q congruent 53 modulo 60: 1/8 phi1^2 phi2 q congruent 59 modulo 60: 1/8 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 71, 17, 20, 74, 76, 18, 98, 54, 22, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 2, 2 ], [ 25, 1, 3, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ] ] k = 10: F-action on Pi is (1,7)(2,5) [48,1,10] Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 4 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 16 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 19 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 23 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 27 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 31 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 43 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 47 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 59 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 71, 69, 20, 7, 76, 31, 98, 76, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 8 ], [ 21, 1, 2, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 8 ], [ 30, 1, 4, 8 ], [ 37, 1, 2, 4 ], [ 37, 1, 3, 8 ], [ 39, 1, 2, 4 ], [ 41, 1, 2, 8 ] ] i = 49: Pi = [ 1, 2, 5, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [49,1,1] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 ( q^3-25*q^2+199*q-559 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/192 ( q^3-25*q^2+187*q-363 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 7 modulo 60: 1/192 ( q^3-25*q^2+187*q-427 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 11 modulo 60: 1/192 ( q^3-25*q^2+187*q-363 ) q congruent 13 modulo 60: 1/192 ( q^3-25*q^2+199*q-559 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 19 modulo 60: 1/192 ( q^3-25*q^2+187*q-427 ) q congruent 21 modulo 60: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 23 modulo 60: 1/192 ( q^3-25*q^2+187*q-363 ) q congruent 25 modulo 60: 1/192 ( q^3-25*q^2+199*q-559 ) q congruent 27 modulo 60: 1/192 ( q^3-25*q^2+187*q-363 ) q congruent 29 modulo 60: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 31 modulo 60: 1/192 ( q^3-25*q^2+187*q-427 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/192 ( q^3-25*q^2+199*q-559 ) q congruent 41 modulo 60: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 43 modulo 60: 1/192 ( q^3-25*q^2+187*q-427 ) q congruent 47 modulo 60: 1/192 ( q^3-25*q^2+187*q-363 ) q congruent 49 modulo 60: 1/192 ( q^3-25*q^2+199*q-559 ) q congruent 53 modulo 60: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 59 modulo 60: 1/192 ( q^3-25*q^2+187*q-363 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 3, 66, 4, 4, 68, 4, 68, 68, 7, 4, 68, 68, 7, 68, 7, 7, 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 72 ], [ 16, 1, 1, 96 ], [ 19, 1, 1, 32 ], [ 20, 1, 1, 48 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 42 ], [ 25, 1, 1, 72 ], [ 28, 1, 1, 24 ], [ 33, 1, 1, 192 ], [ 35, 1, 1, 96 ], [ 39, 1, 1, 24 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 144 ], [ 52, 1, 1, 48 ] ] k = 2: F-action on Pi is ( 7,240) [49,1,2] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19, 68, 19, 3, 72, 68, 19, 7, 76, 7, 76, 69, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 3, 4 ], [ 33, 1, 2, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 3, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 52, 1, 3, 8 ] ] k = 3: F-action on Pi is ( 5, 7,240) [49,1,3] Dynkin type is A_1(q) + A_1(q) + A_1(q^3) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 13 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 19 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 21 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 23 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 25 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 27 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 29 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 31 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 41 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 43 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 47 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 49 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 53 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 59 modulo 60: 1/6 q phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 87, 83, 35, 83, 40, 37, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 2 ], [ 19, 1, 1, 2 ], [ 33, 1, 3, 6 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 6 ] ] k = 4: F-action on Pi is ( 5,240) [49,1,4] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + A_1(q) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1^2 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 phi2 q congruent 7 modulo 60: 1/16 phi1^2 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 phi2 q congruent 11 modulo 60: 1/16 phi1^2 phi2 q congruent 13 modulo 60: 1/16 phi1^2 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 phi2 q congruent 19 modulo 60: 1/16 phi1^2 phi2 q congruent 21 modulo 60: 1/16 phi1^2 phi2 q congruent 23 modulo 60: 1/16 phi1^2 phi2 q congruent 25 modulo 60: 1/16 phi1^2 phi2 q congruent 27 modulo 60: 1/16 phi1^2 phi2 q congruent 29 modulo 60: 1/16 phi1^2 phi2 q congruent 31 modulo 60: 1/16 phi1^2 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 phi2 q congruent 41 modulo 60: 1/16 phi1^2 phi2 q congruent 43 modulo 60: 1/16 phi1^2 phi2 q congruent 47 modulo 60: 1/16 phi1^2 phi2 q congruent 49 modulo 60: 1/16 phi1^2 phi2 q congruent 53 modulo 60: 1/16 phi1^2 phi2 q congruent 59 modulo 60: 1/16 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 19, 76, 73, 18, 76, 20, 18, 74, 72, 20, 18, 74, 20, 71, 74, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 24, 1, 2, 6 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 52, 1, 5, 8 ] ] k = 5: F-action on Pi is () [49,1,5] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 13 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 21 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 25 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 29 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 47 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 49 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/64 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/64 ( q^3-9*q^2+27*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 3, 68, 7, 7, 69, 68, 7, 7, 69, 3, 69, 69, 5, 68, 7, 7, 69, 7, 69, 69, 5, 7, 69, 69, 5, 69, 5, 5, 67 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 4, 24 ], [ 20, 1, 3, 16 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 28 ], [ 25, 1, 3, 24 ], [ 28, 1, 3, 8 ], [ 35, 1, 6, 32 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 6, 48 ], [ 41, 1, 9, 48 ], [ 52, 1, 9, 16 ] ] k = 6: F-action on Pi is ( 5,240, 7) [49,1,6] Dynkin type is A_1(q) + A_1(q) + A_1(q^3) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q^2 phi1 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/6 q^2 phi1 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 60: 1/6 q^2 phi1 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/6 q^2 phi1 q congruent 11 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 13 modulo 60: 1/6 q^2 phi1 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 19 modulo 60: 1/6 q^2 phi1 q congruent 21 modulo 60: 1/6 q^2 phi1 q congruent 23 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 25 modulo 60: 1/6 q^2 phi1 q congruent 27 modulo 60: 1/6 q^2 phi1 q congruent 29 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 31 modulo 60: 1/6 q^2 phi1 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/6 q^2 phi1 q congruent 41 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 43 modulo 60: 1/6 q^2 phi1 q congruent 47 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 49 modulo 60: 1/6 q^2 phi1 q congruent 53 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 59 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 38, 40, 84, 35, 84, 88, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 2, 2 ], [ 19, 1, 2, 2 ], [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ], [ 52, 1, 7, 6 ] ] k = 7: F-action on Pi is ( 5,240) [49,1,7] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/16 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 16, 73, 19, 72, 73, 18, 19, 76, 73, 18, 76, 20, 18, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 24, 1, 1, 6 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 52, 1, 8, 8 ] ] k = 8: F-action on Pi is (5,7) [49,1,8] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 19, 76, 7, 69, 76, 20, 3, 69, 72, 20, 69, 5, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], [ 16, 1, 4, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 8 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 2, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 6, 16 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 2, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 52, 1, 4, 8 ] ] k = 9: F-action on Pi is () [49,1,9] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 7 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 11 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) q congruent 13 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 19 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) q congruent 21 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 23 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) q congruent 25 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 27 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 31 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 41 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 43 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) q congruent 49 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 53 modulo 60: 1/64 phi1 ( q^2-10*q+25 ) q congruent 59 modulo 60: 1/64 phi1 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 7, 4, 68, 68, 7, 68, 7, 7, 69, 4, 68, 68, 7, 68, 7, 3, 69, 68, 3, 7, 69, 7, 69, 69, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 24 ], [ 20, 1, 2, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 24 ], [ 28, 1, 2, 8 ], [ 35, 1, 3, 32 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 1, 48 ], [ 41, 1, 6, 48 ], [ 52, 1, 2, 16 ] ] k = 10: F-action on Pi is () [49,1,10] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^2-18*q+81 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/192 ( q^3-19*q^2+99*q-145 ) q congruent 7 modulo 60: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/192 phi1 ( q^2-18*q+81 ) q congruent 11 modulo 60: 1/192 ( q^3-19*q^2+111*q-253 ) q congruent 13 modulo 60: 1/192 phi1 ( q^2-18*q+81 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/192 ( q^3-19*q^2+99*q-145 ) q congruent 19 modulo 60: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 21 modulo 60: 1/192 phi1 ( q^2-18*q+81 ) q congruent 23 modulo 60: 1/192 ( q^3-19*q^2+111*q-253 ) q congruent 25 modulo 60: 1/192 phi1 ( q^2-18*q+81 ) q congruent 27 modulo 60: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 29 modulo 60: 1/192 ( q^3-19*q^2+99*q-145 ) q congruent 31 modulo 60: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/192 phi1 ( q^2-18*q+81 ) q congruent 41 modulo 60: 1/192 ( q^3-19*q^2+99*q-145 ) q congruent 43 modulo 60: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 47 modulo 60: 1/192 ( q^3-19*q^2+111*q-253 ) q congruent 49 modulo 60: 1/192 phi1 ( q^2-18*q+81 ) q congruent 53 modulo 60: 1/192 ( q^3-19*q^2+99*q-145 ) q congruent 59 modulo 60: 1/192 ( q^3-19*q^2+111*q-253 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 7, 69, 7, 69, 69, 5, 7, 69, 69, 5, 69, 5, 5, 67, 3, 69, 69, 5, 69, 5, 5, 67, 69, 5, 5, 67, 5, 67, 67, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 36 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 4, 72 ], [ 16, 1, 3, 96 ], [ 19, 1, 2, 32 ], [ 20, 1, 4, 48 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 42 ], [ 25, 1, 3, 72 ], [ 28, 1, 4, 24 ], [ 33, 1, 8, 192 ], [ 35, 1, 8, 96 ], [ 39, 1, 3, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 9, 144 ], [ 52, 1, 10, 48 ] ] k = 11: F-action on Pi is ( 2, 5)( 7,240) [49,1,11] Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1^3) Order of center |Z^F|: phi1^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 7 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 11 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 13 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 19 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 21 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 23 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 25 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 27 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 29 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 31 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 41 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 43 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 47 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 49 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 53 modulo 60: 1/64 phi1 ( q^2-12*q+35 ) q congruent 59 modulo 60: 1/64 ( q^3-13*q^2+51*q-63 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 70, 16, 68, 19, 19, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 16 ], [ 16, 1, 2, 32 ], [ 20, 1, 3, 16 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 33, 1, 4, 64 ], [ 35, 1, 5, 32 ], [ 39, 1, 1, 24 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 3, 32 ], [ 52, 1, 1, 48 ] ] k = 12: F-action on Pi is ( 2, 5,240, 7) [49,1,12] Dynkin type is A_1(q) + A_1(q^4) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/16 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 89, 76, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 28, 1, 1, 4 ], [ 28, 1, 3, 4 ], [ 33, 1, 5, 16 ], [ 39, 1, 2, 4 ], [ 40, 1, 3, 8 ], [ 41, 1, 4, 8 ], [ 52, 1, 3, 8 ] ] k = 13: F-action on Pi is ( 2, 5, 7,240) [49,1,13] Dynkin type is A_1(q) + A_1(q^4) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 phi2^2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 phi2^2 q congruent 7 modulo 60: 1/16 phi1 phi2^2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 phi2^2 q congruent 11 modulo 60: 1/16 phi1 phi2^2 q congruent 13 modulo 60: 1/16 phi1 phi2^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 phi2^2 q congruent 19 modulo 60: 1/16 phi1 phi2^2 q congruent 21 modulo 60: 1/16 phi1 phi2^2 q congruent 23 modulo 60: 1/16 phi1 phi2^2 q congruent 25 modulo 60: 1/16 phi1 phi2^2 q congruent 27 modulo 60: 1/16 phi1 phi2^2 q congruent 29 modulo 60: 1/16 phi1 phi2^2 q congruent 31 modulo 60: 1/16 phi1 phi2^2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 phi2^2 q congruent 41 modulo 60: 1/16 phi1 phi2^2 q congruent 43 modulo 60: 1/16 phi1 phi2^2 q congruent 47 modulo 60: 1/16 phi1 phi2^2 q congruent 49 modulo 60: 1/16 phi1 phi2^2 q congruent 53 modulo 60: 1/16 phi1 phi2^2 q congruent 59 modulo 60: 1/16 phi1 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 18, 91, 74, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 20, 1, 5, 8 ], [ 20, 1, 7, 8 ], [ 24, 1, 2, 2 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 52, 1, 5, 8 ] ] k = 14: F-action on Pi is ( 2, 5)( 7,240) [49,1,14] Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 7 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 11 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 19 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 23 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 27 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 31 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 41 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 43 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 53 modulo 60: 1/64 phi1 phi2 ( q-5 ) q congruent 59 modulo 60: 1/64 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 72, 18, 69, 20, 20, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 8 ], [ 20, 1, 1, 16 ], [ 20, 1, 5, 32 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 28, 1, 3, 8 ], [ 35, 1, 2, 32 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], [ 52, 1, 9, 16 ] ] k = 15: F-action on Pi is ( 2, 5)( 7,240) [49,1,15] Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi2^2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1^2 phi2 q congruent 7 modulo 60: 1/32 phi2^2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1^2 phi2 q congruent 11 modulo 60: 1/32 phi2^2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1^2 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1^2 phi2 q congruent 19 modulo 60: 1/32 phi2^2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1^2 phi2 q congruent 23 modulo 60: 1/32 phi2^2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1^2 phi2 q congruent 27 modulo 60: 1/32 phi2^2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1^2 phi2 q congruent 31 modulo 60: 1/32 phi2^2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1^2 phi2 q congruent 41 modulo 60: 1/32 phi1^2 phi2 q congruent 43 modulo 60: 1/32 phi2^2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi2^2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1^2 phi2 q congruent 53 modulo 60: 1/32 phi1^2 phi2 q congruent 59 modulo 60: 1/32 phi2^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 76, 76, 18, 69, 20, 20, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 20, 1, 7, 16 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 28, 1, 3, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 16 ], [ 41, 1, 9, 16 ], [ 52, 1, 9, 16 ] ] k = 16: F-action on Pi is ( 2, 5,240, 7) [49,1,16] Dynkin type is A_1(q) + A_1(q^4) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1^2 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 phi2 q congruent 7 modulo 60: 1/16 phi1^2 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 phi2 q congruent 11 modulo 60: 1/16 phi1^2 phi2 q congruent 13 modulo 60: 1/16 phi1^2 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 phi2 q congruent 19 modulo 60: 1/16 phi1^2 phi2 q congruent 21 modulo 60: 1/16 phi1^2 phi2 q congruent 23 modulo 60: 1/16 phi1^2 phi2 q congruent 25 modulo 60: 1/16 phi1^2 phi2 q congruent 27 modulo 60: 1/16 phi1^2 phi2 q congruent 29 modulo 60: 1/16 phi1^2 phi2 q congruent 31 modulo 60: 1/16 phi1^2 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 phi2 q congruent 41 modulo 60: 1/16 phi1^2 phi2 q congruent 43 modulo 60: 1/16 phi1^2 phi2 q congruent 47 modulo 60: 1/16 phi1^2 phi2 q congruent 49 modulo 60: 1/16 phi1^2 phi2 q congruent 53 modulo 60: 1/16 phi1^2 phi2 q congruent 59 modulo 60: 1/16 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 76, 43, 20, 90 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 9, 16 ], [ 39, 1, 2, 4 ], [ 40, 1, 2, 8 ], [ 41, 1, 4, 8 ], [ 52, 1, 4, 8 ] ] k = 17: F-action on Pi is ( 2, 5, 7,240) [49,1,17] Dynkin type is A_1(q) + A_1(q^4) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1^2 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 phi2 q congruent 7 modulo 60: 1/16 phi1^2 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 phi2 q congruent 11 modulo 60: 1/16 phi1^2 phi2 q congruent 13 modulo 60: 1/16 phi1^2 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 phi2 q congruent 19 modulo 60: 1/16 phi1^2 phi2 q congruent 21 modulo 60: 1/16 phi1^2 phi2 q congruent 23 modulo 60: 1/16 phi1^2 phi2 q congruent 25 modulo 60: 1/16 phi1^2 phi2 q congruent 27 modulo 60: 1/16 phi1^2 phi2 q congruent 29 modulo 60: 1/16 phi1^2 phi2 q congruent 31 modulo 60: 1/16 phi1^2 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 phi2 q congruent 41 modulo 60: 1/16 phi1^2 phi2 q congruent 43 modulo 60: 1/16 phi1^2 phi2 q congruent 47 modulo 60: 1/16 phi1^2 phi2 q congruent 49 modulo 60: 1/16 phi1^2 phi2 q congruent 53 modulo 60: 1/16 phi1^2 phi2 q congruent 59 modulo 60: 1/16 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 73, 44, 18, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 20, 1, 6, 8 ], [ 20, 1, 8, 8 ], [ 24, 1, 1, 2 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 52, 1, 8, 8 ] ] k = 18: F-action on Pi is ( 2, 5)( 7,240) [49,1,18] Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 7 modulo 60: 1/32 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 11 modulo 60: 1/32 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 19 modulo 60: 1/32 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 23 modulo 60: 1/32 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 27 modulo 60: 1/32 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 31 modulo 60: 1/32 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 41 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 43 modulo 60: 1/32 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 53 modulo 60: 1/32 phi1 ( q^2-2*q-7 ) q congruent 59 modulo 60: 1/32 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 19, 73, 7, 76, 76, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 20, 1, 6, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 28, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 16 ], [ 52, 1, 2, 16 ] ] k = 19: F-action on Pi is ( 2, 5)( 7,240) [49,1,19] Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi2^3) Order of center |Z^F|: phi2^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 7 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 11 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 19 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 23 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 27 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 31 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 41 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 43 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 53 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 59 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 20, 74, 5, 71, 71, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 24 ], [ 16, 1, 4, 32 ], [ 20, 1, 2, 16 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 28, 1, 4, 24 ], [ 33, 1, 10, 64 ], [ 35, 1, 4, 32 ], [ 39, 1, 3, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 32 ], [ 52, 1, 10, 48 ] ] k = 20: F-action on Pi is ( 2, 5)( 7,240) [49,1,20] Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 7 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 11 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 19 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 23 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 27 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 31 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 41 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 43 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 53 modulo 60: 1/64 phi1^2 ( q-5 ) q congruent 59 modulo 60: 1/64 phi2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 19, 73, 3, 72, 72, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 16 ], [ 20, 1, 4, 16 ], [ 20, 1, 8, 32 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 28, 1, 2, 8 ], [ 35, 1, 7, 32 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 3, 32 ], [ 41, 1, 6, 16 ], [ 52, 1, 2, 16 ] ] i = 50: Pi = [ 1, 3, 4, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [50,1,1] Dynkin type is A_5(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 ( q^3-17*q^2+97*q-201 ) q congruent 2 modulo 60: 1/24 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 60: 1/24 ( q^3-17*q^2+93*q-153 ) q congruent 4 modulo 60: 1/24 ( q^3-16*q^2+80*q-128 ) q congruent 5 modulo 60: 1/24 ( q^3-17*q^2+93*q-165 ) q congruent 7 modulo 60: 1/24 ( q^3-17*q^2+97*q-189 ) q congruent 8 modulo 60: 1/24 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 60: 1/24 ( q^3-17*q^2+93*q-165 ) q congruent 11 modulo 60: 1/24 ( q^3-17*q^2+93*q-153 ) q congruent 13 modulo 60: 1/24 ( q^3-17*q^2+97*q-201 ) q congruent 16 modulo 60: 1/24 ( q^3-16*q^2+80*q-128 ) q congruent 17 modulo 60: 1/24 ( q^3-17*q^2+93*q-165 ) q congruent 19 modulo 60: 1/24 ( q^3-17*q^2+97*q-189 ) q congruent 21 modulo 60: 1/24 ( q^3-17*q^2+93*q-165 ) q congruent 23 modulo 60: 1/24 ( q^3-17*q^2+93*q-153 ) q congruent 25 modulo 60: 1/24 ( q^3-17*q^2+97*q-201 ) q congruent 27 modulo 60: 1/24 ( q^3-17*q^2+93*q-153 ) q congruent 29 modulo 60: 1/24 ( q^3-17*q^2+93*q-165 ) q congruent 31 modulo 60: 1/24 ( q^3-17*q^2+97*q-189 ) q congruent 32 modulo 60: 1/24 ( q^3-16*q^2+76*q-96 ) q congruent 37 modulo 60: 1/24 ( q^3-17*q^2+97*q-201 ) q congruent 41 modulo 60: 1/24 ( q^3-17*q^2+93*q-165 ) q congruent 43 modulo 60: 1/24 ( q^3-17*q^2+97*q-189 ) q congruent 47 modulo 60: 1/24 ( q^3-17*q^2+93*q-153 ) q congruent 49 modulo 60: 1/24 ( q^3-17*q^2+97*q-201 ) q congruent 53 modulo 60: 1/24 ( q^3-17*q^2+93*q-165 ) q congruent 59 modulo 60: 1/24 ( q^3-17*q^2+93*q-153 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 68, 8, 77, 14, 70, 19, 23, 87 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 8 ], [ 11, 1, 1, 6 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 6 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 4 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 12 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 34, 1, 1, 12 ], [ 36, 1, 1, 24 ], [ 39, 1, 1, 24 ], [ 42, 1, 1, 12 ] ] k = 2: F-action on Pi is () [50,1,2] Dynkin type is A_5(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 2 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 8 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 19 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 23 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 27 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 31 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 32 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 43 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 47 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 59 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 7, 77, 30, 83, 19, 76, 93, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 34, 1, 1, 4 ], [ 36, 1, 2, 8 ], [ 39, 1, 4, 4 ], [ 42, 1, 4, 4 ] ] k = 3: F-action on Pi is () [50,1,3] Dynkin type is A_5(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 2 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 4 modulo 60: 1/12 phi1 ( q^2-4 ) q congruent 5 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 7 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 8 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 11 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 13 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 16 modulo 60: 1/12 phi1 ( q^2-4 ) q congruent 17 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 19 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 21 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 23 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 25 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 27 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 29 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 31 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 32 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 41 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 43 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 47 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 49 modulo 60: 1/12 phi1 ( q^2-q-6 ) q congruent 53 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 59 modulo 60: 1/12 q phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 30, 81, 14, 83, 12, 97, 59, 62, 85 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 22, 1, 1, 4 ], [ 27, 1, 5, 6 ], [ 42, 1, 3, 6 ] ] k = 4: F-action on Pi is () [50,1,4] Dynkin type is A_5(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 2 modulo 60: 1/24 q ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/24 q ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 8 modulo 60: 1/24 q ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 16 modulo 60: 1/24 q ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 21 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 27 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 32 modulo 60: 1/24 q ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 41 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 47 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/24 phi1 ( q^2-8*q+19 ) q congruent 53 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/24 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 3, 77, 30, 83, 19, 72, 93, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 6 ], [ 19, 1, 1, 6 ], [ 22, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 34, 1, 2, 12 ], [ 39, 1, 4, 12 ], [ 42, 1, 1, 12 ] ] k = 5: F-action on Pi is () [50,1,5] Dynkin type is A_5(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1^3 q congruent 2 modulo 60: 1/8 q^2 ( q-2 ) q congruent 3 modulo 60: 1/8 phi1^3 q congruent 4 modulo 60: 1/8 q^2 ( q-2 ) q congruent 5 modulo 60: 1/8 phi1^3 q congruent 7 modulo 60: 1/8 phi1^3 q congruent 8 modulo 60: 1/8 q^2 ( q-2 ) q congruent 9 modulo 60: 1/8 phi1^3 q congruent 11 modulo 60: 1/8 phi1^3 q congruent 13 modulo 60: 1/8 phi1^3 q congruent 16 modulo 60: 1/8 q^2 ( q-2 ) q congruent 17 modulo 60: 1/8 phi1^3 q congruent 19 modulo 60: 1/8 phi1^3 q congruent 21 modulo 60: 1/8 phi1^3 q congruent 23 modulo 60: 1/8 phi1^3 q congruent 25 modulo 60: 1/8 phi1^3 q congruent 27 modulo 60: 1/8 phi1^3 q congruent 29 modulo 60: 1/8 phi1^3 q congruent 31 modulo 60: 1/8 phi1^3 q congruent 32 modulo 60: 1/8 q^2 ( q-2 ) q congruent 37 modulo 60: 1/8 phi1^3 q congruent 41 modulo 60: 1/8 phi1^3 q congruent 43 modulo 60: 1/8 phi1^3 q congruent 47 modulo 60: 1/8 phi1^3 q congruent 49 modulo 60: 1/8 phi1^3 q congruent 53 modulo 60: 1/8 phi1^3 q congruent 59 modulo 60: 1/8 phi1^3 Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 7, 69, 30, 81, 37, 76, 20, 50, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 2 ], [ 19, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 34, 1, 2, 4 ], [ 39, 1, 3, 8 ], [ 42, 1, 4, 4 ] ] k = 6: F-action on Pi is () [50,1,6] Dynkin type is A_5(q) + T(phi2 phi3) Order of center |Z^F|: phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 2 modulo 60: 1/12 q^2 phi2 q congruent 3 modulo 60: 1/12 q phi1 phi2 q congruent 4 modulo 60: 1/12 q phi1 ( q+2 ) q congruent 5 modulo 60: 1/12 q phi1 phi2 q congruent 7 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 8 modulo 60: 1/12 q^2 phi2 q congruent 9 modulo 60: 1/12 q phi1 phi2 q congruent 11 modulo 60: 1/12 q phi1 phi2 q congruent 13 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 16 modulo 60: 1/12 q phi1 ( q+2 ) q congruent 17 modulo 60: 1/12 q phi1 phi2 q congruent 19 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 q congruent 23 modulo 60: 1/12 q phi1 phi2 q congruent 25 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 q congruent 29 modulo 60: 1/12 q phi1 phi2 q congruent 31 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 32 modulo 60: 1/12 q^2 phi2 q congruent 37 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 41 modulo 60: 1/12 q phi1 phi2 q congruent 43 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 47 modulo 60: 1/12 q phi1 phi2 q congruent 49 modulo 60: 1/12 phi1^2 ( q+2 ) q congruent 53 modulo 60: 1/12 q phi1 phi2 q congruent 59 modulo 60: 1/12 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 77, 30, 81, 27, 83, 37, 79, 59, 95, 111, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 22, 1, 2, 4 ], [ 27, 1, 5, 6 ], [ 42, 1, 3, 6 ] ] k = 7: F-action on Pi is (1,6)(3,5) [50,1,7] Dynkin type is ^2A_5(q) + T(phi1 phi6) Order of center |Z^F|: phi1 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 2 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 4 modulo 60: 1/12 q phi1 ( q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 8 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 11 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 16 modulo 60: 1/12 q phi1 ( q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 21 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 23 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 27 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 29 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 32 modulo 60: 1/12 phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 41 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 47 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/12 q phi1 ( q-3 ) q congruent 53 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 31, 82, 28, 84, 38, 80, 60, 96, 112, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 22, 1, 3, 4 ], [ 27, 1, 4, 6 ], [ 42, 1, 5, 6 ] ] k = 8: F-action on Pi is (1,6)(3,5) [50,1,8] Dynkin type is ^2A_5(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 4 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 16 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1^2 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 69, 7, 68, 31, 82, 38, 76, 19, 51, 87 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 11, 1, 2, 2 ], [ 19, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 34, 1, 3, 4 ], [ 39, 1, 1, 8 ], [ 42, 1, 2, 4 ] ] k = 9: F-action on Pi is (1,6)(3,5) [50,1,9] Dynkin type is ^2A_5(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/24 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 7 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 13 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/24 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 19 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 25 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 31 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 43 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 49 modulo 60: 1/24 phi1 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) q congruent 59 modulo 60: 1/24 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 69, 3, 78, 31, 84, 20, 72, 94, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 19, 1, 2, 6 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 34, 1, 3, 12 ], [ 39, 1, 4, 12 ], [ 42, 1, 6, 12 ] ] k = 10: F-action on Pi is (1,6)(3,5) [50,1,10] Dynkin type is ^2A_5(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^2 q congruent 2 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1^2 q congruent 4 modulo 60: 1/12 q^2 phi1 q congruent 5 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 7 modulo 60: 1/12 q phi1^2 q congruent 8 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1^2 q congruent 11 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 13 modulo 60: 1/12 q phi1^2 q congruent 16 modulo 60: 1/12 q^2 phi1 q congruent 17 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 19 modulo 60: 1/12 q phi1^2 q congruent 21 modulo 60: 1/12 q phi1^2 q congruent 23 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 25 modulo 60: 1/12 q phi1^2 q congruent 27 modulo 60: 1/12 q phi1^2 q congruent 29 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 31 modulo 60: 1/12 q phi1^2 q congruent 32 modulo 60: 1/12 q phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 q phi1^2 q congruent 41 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 43 modulo 60: 1/12 q phi1^2 q congruent 47 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 49 modulo 60: 1/12 q phi1^2 q congruent 53 modulo 60: 1/12 phi1 phi2 ( q-2 ) q congruent 59 modulo 60: 1/12 phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 78, 31, 82, 15, 84, 13, 98, 60, 63, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 22, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 42, 1, 5, 6 ] ] k = 11: F-action on Pi is (1,6)(3,5) [50,1,11] Dynkin type is ^2A_5(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 4 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 16 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 19 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 23 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 27 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 31 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 43 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 47 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 59 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 69, 7, 78, 31, 84, 20, 76, 94, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 34, 1, 4, 4 ], [ 36, 1, 3, 8 ], [ 39, 1, 4, 4 ], [ 42, 1, 2, 4 ] ] k = 12: F-action on Pi is (1,6)(3,5) [50,1,12] Dynkin type is ^2A_5(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^2-10*q+27 ) q congruent 2 modulo 60: 1/24 ( q^3-10*q^2+28*q-24 ) q congruent 3 modulo 60: 1/24 ( q^3-11*q^2+37*q-39 ) q congruent 4 modulo 60: 1/24 q ( q^2-10*q+24 ) q congruent 5 modulo 60: 1/24 ( q^3-11*q^2+41*q-55 ) q congruent 7 modulo 60: 1/24 ( q^3-11*q^2+37*q-39 ) q congruent 8 modulo 60: 1/24 ( q^3-10*q^2+28*q-24 ) q congruent 9 modulo 60: 1/24 phi1 ( q^2-10*q+27 ) q congruent 11 modulo 60: 1/24 ( q^3-11*q^2+41*q-67 ) q congruent 13 modulo 60: 1/24 phi1 ( q^2-10*q+27 ) q congruent 16 modulo 60: 1/24 q ( q^2-10*q+24 ) q congruent 17 modulo 60: 1/24 ( q^3-11*q^2+41*q-55 ) q congruent 19 modulo 60: 1/24 ( q^3-11*q^2+37*q-39 ) q congruent 21 modulo 60: 1/24 phi1 ( q^2-10*q+27 ) q congruent 23 modulo 60: 1/24 ( q^3-11*q^2+41*q-67 ) q congruent 25 modulo 60: 1/24 phi1 ( q^2-10*q+27 ) q congruent 27 modulo 60: 1/24 ( q^3-11*q^2+37*q-39 ) q congruent 29 modulo 60: 1/24 ( q^3-11*q^2+41*q-55 ) q congruent 31 modulo 60: 1/24 ( q^3-11*q^2+37*q-39 ) q congruent 32 modulo 60: 1/24 ( q^3-10*q^2+28*q-24 ) q congruent 37 modulo 60: 1/24 phi1 ( q^2-10*q+27 ) q congruent 41 modulo 60: 1/24 ( q^3-11*q^2+41*q-55 ) q congruent 43 modulo 60: 1/24 ( q^3-11*q^2+37*q-39 ) q congruent 47 modulo 60: 1/24 ( q^3-11*q^2+41*q-67 ) q congruent 49 modulo 60: 1/24 phi1 ( q^2-10*q+27 ) q congruent 53 modulo 60: 1/24 ( q^3-11*q^2+41*q-55 ) q congruent 59 modulo 60: 1/24 ( q^3-11*q^2+41*q-67 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 69, 9, 78, 15, 71, 20, 24, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 8 ], [ 11, 1, 2, 6 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 6 ], [ 21, 1, 2, 12 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 12 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 4, 24 ], [ 39, 1, 3, 24 ], [ 42, 1, 6, 12 ] ] i = 51: Pi = [ 1, 3, 4, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [51,1,1] Dynkin type is A_3(q) + A_2(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 ( q^3-21*q^2+151*q-435 ) q congruent 2 modulo 60: 1/16 ( q^3-20*q^2+116*q-160 ) q congruent 3 modulo 60: 1/16 ( q^3-21*q^2+139*q-255 ) q congruent 4 modulo 60: 1/16 ( q^3-20*q^2+124*q-240 ) q congruent 5 modulo 60: 1/16 ( q^3-21*q^2+143*q-315 ) q congruent 7 modulo 60: 1/16 ( q^3-21*q^2+147*q-343 ) q congruent 8 modulo 60: 1/16 ( q^3-20*q^2+116*q-160 ) q congruent 9 modulo 60: 1/16 ( q^3-21*q^2+143*q-315 ) q congruent 11 modulo 60: 1/16 ( q^3-21*q^2+139*q-287 ) q congruent 13 modulo 60: 1/16 ( q^3-21*q^2+151*q-403 ) q congruent 16 modulo 60: 1/16 ( q^3-20*q^2+124*q-272 ) q congruent 17 modulo 60: 1/16 ( q^3-21*q^2+143*q-315 ) q congruent 19 modulo 60: 1/16 ( q^3-21*q^2+147*q-343 ) q congruent 21 modulo 60: 1/16 ( q^3-21*q^2+143*q-347 ) q congruent 23 modulo 60: 1/16 ( q^3-21*q^2+139*q-255 ) q congruent 25 modulo 60: 1/16 ( q^3-21*q^2+151*q-403 ) q congruent 27 modulo 60: 1/16 ( q^3-21*q^2+139*q-255 ) q congruent 29 modulo 60: 1/16 ( q^3-21*q^2+143*q-315 ) q congruent 31 modulo 60: 1/16 ( q^3-21*q^2+147*q-375 ) q congruent 32 modulo 60: 1/16 ( q^3-20*q^2+116*q-160 ) q congruent 37 modulo 60: 1/16 ( q^3-21*q^2+151*q-403 ) q congruent 41 modulo 60: 1/16 ( q^3-21*q^2+143*q-347 ) q congruent 43 modulo 60: 1/16 ( q^3-21*q^2+147*q-343 ) q congruent 47 modulo 60: 1/16 ( q^3-21*q^2+139*q-255 ) q congruent 49 modulo 60: 1/16 ( q^3-21*q^2+151*q-403 ) q congruent 53 modulo 60: 1/16 ( q^3-21*q^2+143*q-315 ) q congruent 59 modulo 60: 1/16 ( q^3-21*q^2+139*q-255 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 8, 66, 4, 77, 4, 68, 30, 8, 77, 14, 70, 19, 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 12, 1, 1, 10 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 8 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 32 ], [ 26, 1, 1, 16 ], [ 29, 1, 1, 16 ], [ 31, 1, 1, 8 ], [ 36, 1, 1, 16 ], [ 37, 1, 1, 32 ], [ 39, 1, 1, 8 ], [ 40, 1, 1, 24 ], [ 43, 1, 1, 32 ] ] k = 2: F-action on Pi is () [51,1,2] Dynkin type is A_3(q) + A_2(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-8*q+19 ) q congruent 2 modulo 60: 1/8 q ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/8 ( q^3-9*q^2+19*q-3 ) q congruent 4 modulo 60: 1/8 q ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/8 ( q^3-9*q^2+23*q-7 ) q congruent 8 modulo 60: 1/8 q ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/8 ( q^3-9*q^2+19*q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-8*q+19 ) q congruent 16 modulo 60: 1/8 q ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/8 ( q^3-9*q^2+23*q-7 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/8 ( q^3-9*q^2+19*q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-8*q+19 ) q congruent 27 modulo 60: 1/8 ( q^3-9*q^2+19*q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/8 ( q^3-9*q^2+23*q-7 ) q congruent 32 modulo 60: 1/8 q ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-8*q+19 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/8 ( q^3-9*q^2+23*q-7 ) q congruent 47 modulo 60: 1/8 ( q^3-9*q^2+19*q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-8*q+19 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/8 ( q^3-9*q^2+19*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 77, 4, 68, 30, 68, 7, 81, 77, 30, 83, 19, 76, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 2 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 8 ], [ 29, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 31, 1, 2, 4 ], [ 36, 1, 2, 8 ], [ 39, 1, 4, 4 ], [ 43, 1, 2, 16 ] ] k = 3: F-action on Pi is (6,7) [51,1,3] Dynkin type is A_3(q) + ^2A_2(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 4 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 16 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 19 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 23 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 27 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 31 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 43 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 47 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 59 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 28, 69, 7, 82, 5, 69, 31, 27, 81, 36, 71, 20, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 16, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 4 ], [ 37, 1, 2, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 2, 4 ], [ 40, 1, 6, 12 ], [ 43, 1, 8, 8 ] ] k = 4: F-action on Pi is (6,7) [51,1,4] Dynkin type is A_3(q) + ^2A_2(q) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1^2 phi2 q congruent 2 modulo 60: 1/8 q^3 q congruent 3 modulo 60: 1/8 phi1^2 phi2 q congruent 4 modulo 60: 1/8 q^3 q congruent 5 modulo 60: 1/8 phi1^2 phi2 q congruent 7 modulo 60: 1/8 phi1^2 phi2 q congruent 8 modulo 60: 1/8 q^3 q congruent 9 modulo 60: 1/8 phi1^2 phi2 q congruent 11 modulo 60: 1/8 phi1^2 phi2 q congruent 13 modulo 60: 1/8 phi1^2 phi2 q congruent 16 modulo 60: 1/8 q^3 q congruent 17 modulo 60: 1/8 phi1^2 phi2 q congruent 19 modulo 60: 1/8 phi1^2 phi2 q congruent 21 modulo 60: 1/8 phi1^2 phi2 q congruent 23 modulo 60: 1/8 phi1^2 phi2 q congruent 25 modulo 60: 1/8 phi1^2 phi2 q congruent 27 modulo 60: 1/8 phi1^2 phi2 q congruent 29 modulo 60: 1/8 phi1^2 phi2 q congruent 31 modulo 60: 1/8 phi1^2 phi2 q congruent 32 modulo 60: 1/8 q^3 q congruent 37 modulo 60: 1/8 phi1^2 phi2 q congruent 41 modulo 60: 1/8 phi1^2 phi2 q congruent 43 modulo 60: 1/8 phi1^2 phi2 q congruent 47 modulo 60: 1/8 phi1^2 phi2 q congruent 49 modulo 60: 1/8 phi1^2 phi2 q congruent 53 modulo 60: 1/8 phi1^2 phi2 q congruent 59 modulo 60: 1/8 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 72, 19, 96, 20, 76, 60, 71, 20, 98, 95, 59, 99, 17, 74, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 16, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 43, 1, 9, 8 ] ] k = 5: F-action on Pi is () [51,1,5] Dynkin type is A_3(q) + A_2(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 2 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 4 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 7 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 8 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 11 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 16 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 19 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 23 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 27 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 31 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 32 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 43 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-4*q+7 ) q congruent 59 modulo 60: 1/16 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 30, 68, 7, 81, 3, 69, 27, 30, 81, 37, 72, 20, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 16, 1, 1, 4 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 16 ], [ 31, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 40, 1, 3, 8 ], [ 43, 1, 12, 32 ] ] k = 6: F-action on Pi is (1,4) [51,1,6] Dynkin type is ^2A_3(q) + A_2(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 2 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 8 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 19 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 23 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 27 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 31 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 32 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 43 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 47 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 59 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 27, 68, 7, 81, 4, 68, 30, 28, 82, 36, 70, 19, 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 16, 1, 2, 4 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 4 ], [ 37, 1, 2, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 1, 12 ], [ 40, 1, 3, 4 ], [ 43, 1, 8, 8 ] ] k = 7: F-action on Pi is (1,4) [51,1,7] Dynkin type is ^2A_3(q) + A_2(q) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 1/8 q^2 ( q-2 ) q congruent 3 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/8 q^2 ( q-2 ) q congruent 5 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 1/8 q^2 ( q-2 ) q congruent 9 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 1/8 q^2 ( q-2 ) q congruent 17 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 1/8 q^2 ( q-2 ) q congruent 37 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20, 95, 19, 76, 59, 70, 19, 97, 96, 60, 99, 16, 73, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 43, 1, 9, 8 ] ] k = 8: F-action on Pi is (1,4)(6,7) [51,1,8] Dynkin type is ^2A_3(q) + ^2A_2(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/8 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 7 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 8 modulo 60: 1/8 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/8 ( q^3-7*q^2+23*q-33 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 19 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/8 ( q^3-7*q^2+23*q-33 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 29 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 31 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 32 modulo 60: 1/8 ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 43 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 47 modulo 60: 1/8 ( q^3-7*q^2+23*q-33 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 59 modulo 60: 1/8 ( q^3-7*q^2+23*q-33 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 78, 5, 69, 31, 69, 7, 82, 78, 31, 84, 20, 76, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 2, 8 ], [ 29, 1, 3, 8 ], [ 31, 1, 3, 4 ], [ 31, 1, 4, 4 ], [ 36, 1, 3, 8 ], [ 39, 1, 4, 4 ], [ 43, 1, 4, 16 ] ] k = 9: F-action on Pi is (1,4)(6,7) [51,1,9] Dynkin type is ^2A_3(q) + ^2A_2(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-14*q+53 ) q congruent 2 modulo 60: 1/16 ( q^3-14*q^2+56*q-64 ) q congruent 3 modulo 60: 1/16 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 60: 1/16 ( q^3-14*q^2+48*q-32 ) q congruent 5 modulo 60: 1/16 ( q^3-15*q^2+75*q-125 ) q congruent 7 modulo 60: 1/16 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 60: 1/16 ( q^3-14*q^2+56*q-64 ) q congruent 9 modulo 60: 1/16 ( q^3-15*q^2+67*q-85 ) q congruent 11 modulo 60: 1/16 ( q^3-15*q^2+79*q-177 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-14*q+53 ) q congruent 16 modulo 60: 1/16 q ( q^2-14*q+48 ) q congruent 17 modulo 60: 1/16 ( q^3-15*q^2+75*q-125 ) q congruent 19 modulo 60: 1/16 ( q^3-15*q^2+71*q-137 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-14*q+53 ) q congruent 23 modulo 60: 1/16 ( q^3-15*q^2+79*q-177 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-14*q+53 ) q congruent 27 modulo 60: 1/16 ( q^3-15*q^2+71*q-105 ) q congruent 29 modulo 60: 1/16 ( q^3-15*q^2+75*q-157 ) q congruent 31 modulo 60: 1/16 ( q^3-15*q^2+71*q-105 ) q congruent 32 modulo 60: 1/16 ( q^3-14*q^2+56*q-64 ) q congruent 37 modulo 60: 1/16 phi1 ( q^2-14*q+53 ) q congruent 41 modulo 60: 1/16 ( q^3-15*q^2+75*q-125 ) q congruent 43 modulo 60: 1/16 ( q^3-15*q^2+71*q-105 ) q congruent 47 modulo 60: 1/16 ( q^3-15*q^2+79*q-177 ) q congruent 49 modulo 60: 1/16 ( q^3-15*q^2+67*q-85 ) q congruent 53 modulo 60: 1/16 ( q^3-15*q^2+75*q-125 ) q congruent 59 modulo 60: 1/16 ( q^3-15*q^2+79*q-209 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 9, 67, 5, 78, 5, 69, 31, 9, 78, 15, 71, 20, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 10 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 4 ], [ 25, 1, 3, 32 ], [ 26, 1, 4, 16 ], [ 29, 1, 4, 16 ], [ 31, 1, 4, 8 ], [ 36, 1, 4, 16 ], [ 37, 1, 3, 32 ], [ 39, 1, 3, 8 ], [ 40, 1, 6, 24 ], [ 43, 1, 13, 32 ] ] k = 10: F-action on Pi is (1,4)(6,7) [51,1,10] Dynkin type is ^2A_3(q) + ^2A_2(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 4 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 8 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 32 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 47 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 69, 31, 69, 7, 82, 3, 68, 28, 31, 82, 38, 72, 19, 96 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 16, 1, 3, 4 ], [ 20, 1, 3, 16 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 16 ], [ 31, 1, 3, 8 ], [ 39, 1, 1, 8 ], [ 40, 1, 2, 8 ], [ 43, 1, 3, 32 ] ] i = 52: Pi = [ 2, 3, 4, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [52,1,1] Dynkin type is D_4(q) + A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 ( q^3-19*q^2+115*q-241 ) q congruent 2 modulo 60: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 60: 1/48 ( q^3-19*q^2+115*q-201 ) q congruent 4 modulo 60: 1/48 ( q^3-16*q^2+76*q-112 ) q congruent 5 modulo 60: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 7 modulo 60: 1/48 ( q^3-19*q^2+115*q-217 ) q congruent 8 modulo 60: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 60: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 11 modulo 60: 1/48 ( q^3-19*q^2+115*q-201 ) q congruent 13 modulo 60: 1/48 ( q^3-19*q^2+115*q-241 ) q congruent 16 modulo 60: 1/48 ( q^3-16*q^2+76*q-112 ) q congruent 17 modulo 60: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 19 modulo 60: 1/48 ( q^3-19*q^2+115*q-217 ) q congruent 21 modulo 60: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 23 modulo 60: 1/48 ( q^3-19*q^2+115*q-201 ) q congruent 25 modulo 60: 1/48 ( q^3-19*q^2+115*q-241 ) q congruent 27 modulo 60: 1/48 ( q^3-19*q^2+115*q-201 ) q congruent 29 modulo 60: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 31 modulo 60: 1/48 ( q^3-19*q^2+115*q-217 ) q congruent 32 modulo 60: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 37 modulo 60: 1/48 ( q^3-19*q^2+115*q-241 ) q congruent 41 modulo 60: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 43 modulo 60: 1/48 ( q^3-19*q^2+115*q-217 ) q congruent 47 modulo 60: 1/48 ( q^3-19*q^2+115*q-201 ) q congruent 49 modulo 60: 1/48 ( q^3-19*q^2+115*q-241 ) q congruent 53 modulo 60: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 59 modulo 60: 1/48 ( q^3-19*q^2+115*q-201 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 68, 3, 69, 66, 4, 70, 19, 68, 7, 4, 68, 4, 68, 16, 73, 8, 77, 28, 82, 70, 19, 70, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], [ 28, 1, 1, 24 ], [ 39, 1, 1, 24 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ] ] k = 2: F-action on Pi is () [52,1,2] Dynkin type is D_4(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 16 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 32 modulo 60: 1/16 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 7, 69, 5, 4, 68, 19, 76, 7, 69, 68, 3, 68, 7, 73, 18, 77, 30, 82, 31, 19, 72, 19, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 28, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 6, 16 ] ] k = 3: F-action on Pi is (2,5) [52,1,3] Dynkin type is ^2D_4(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 2 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 4 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 8 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 16 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 19 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 23 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 27 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 31 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 32 modulo 60: 1/8 q ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 43 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 47 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-6*q+7 ) q congruent 59 modulo 60: 1/8 ( q^3-7*q^2+13*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 3, 69, 70, 19, 68, 7, 72, 20, 19, 76, 28, 82, 30, 81, 89, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 28, 1, 1, 4 ], [ 28, 1, 3, 4 ], [ 39, 1, 2, 4 ], [ 40, 1, 3, 8 ], [ 41, 1, 4, 8 ] ] k = 4: F-action on Pi is (2,5) [52,1,4] Dynkin type is ^2D_4(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 2 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 4 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 8 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 13 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 16 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 19 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 21 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 23 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 25 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 27 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 29 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 31 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 32 modulo 60: 1/8 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 41 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 43 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 47 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 49 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 53 modulo 60: 1/8 phi1 ( q^2-4*q+5 ) q congruent 59 modulo 60: 1/8 ( q^3-5*q^2+9*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 3, 69, 5, 19, 72, 7, 69, 20, 71, 76, 20, 82, 31, 81, 27, 43, 90 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 4, 4 ], [ 39, 1, 2, 4 ], [ 40, 1, 2, 8 ], [ 41, 1, 4, 8 ] ] k = 5: F-action on Pi is (3,5) [52,1,5] Dynkin type is ^2D_4(q) + A_1(q) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1^2 phi2 q congruent 2 modulo 60: 1/8 q^3 q congruent 3 modulo 60: 1/8 phi1^2 phi2 q congruent 4 modulo 60: 1/8 q^3 q congruent 5 modulo 60: 1/8 phi1^2 phi2 q congruent 7 modulo 60: 1/8 phi1^2 phi2 q congruent 8 modulo 60: 1/8 q^3 q congruent 9 modulo 60: 1/8 phi1^2 phi2 q congruent 11 modulo 60: 1/8 phi1^2 phi2 q congruent 13 modulo 60: 1/8 phi1^2 phi2 q congruent 16 modulo 60: 1/8 q^3 q congruent 17 modulo 60: 1/8 phi1^2 phi2 q congruent 19 modulo 60: 1/8 phi1^2 phi2 q congruent 21 modulo 60: 1/8 phi1^2 phi2 q congruent 23 modulo 60: 1/8 phi1^2 phi2 q congruent 25 modulo 60: 1/8 phi1^2 phi2 q congruent 27 modulo 60: 1/8 phi1^2 phi2 q congruent 29 modulo 60: 1/8 phi1^2 phi2 q congruent 31 modulo 60: 1/8 phi1^2 phi2 q congruent 32 modulo 60: 1/8 q^3 q congruent 37 modulo 60: 1/8 phi1^2 phi2 q congruent 41 modulo 60: 1/8 phi1^2 phi2 q congruent 43 modulo 60: 1/8 phi1^2 phi2 q congruent 47 modulo 60: 1/8 phi1^2 phi2 q congruent 49 modulo 60: 1/8 phi1^2 phi2 q congruent 53 modulo 60: 1/8 phi1^2 phi2 q congruent 59 modulo 60: 1/8 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 19, 72, 20, 71, 73, 18, 76, 20, 74, 17, 18, 74, 60, 98, 59, 95, 91, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ] ] k = 6: F-action on Pi is (2,3,5) [52,1,6] Dynkin type is ^3D_4(q) + A_1(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 2 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 13 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 16 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 17 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 19 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 21 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 23 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 25 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 27 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 29 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 31 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 32 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 37 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 41 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 43 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 47 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 49 modulo 60: 1/6 phi1 ( q^2-2 ) q congruent 53 modulo 60: 1/6 q phi2 ( q-2 ) q congruent 59 modulo 60: 1/6 q phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 83, 87, 40, 83, 37, 35, 88, 12, 79, 57, 101, 33, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 40, 1, 5, 6 ] ] k = 7: F-action on Pi is (2,3,5) [52,1,7] Dynkin type is ^3D_4(q) + A_1(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/6 q^2 phi1 q congruent 2 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 60: 1/6 q^2 phi1 q congruent 4 modulo 60: 1/6 q^2 phi1 q congruent 5 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 60: 1/6 q^2 phi1 q congruent 8 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 60: 1/6 q^2 phi1 q congruent 11 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 13 modulo 60: 1/6 q^2 phi1 q congruent 16 modulo 60: 1/6 q^2 phi1 q congruent 17 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 19 modulo 60: 1/6 q^2 phi1 q congruent 21 modulo 60: 1/6 q^2 phi1 q congruent 23 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 25 modulo 60: 1/6 q^2 phi1 q congruent 27 modulo 60: 1/6 q^2 phi1 q congruent 29 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 31 modulo 60: 1/6 q^2 phi1 q congruent 32 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 37 modulo 60: 1/6 q^2 phi1 q congruent 41 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 43 modulo 60: 1/6 q^2 phi1 q congruent 47 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 49 modulo 60: 1/6 q^2 phi1 q congruent 53 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) q congruent 59 modulo 60: 1/6 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 35, 38, 84, 40, 88, 84, 15, 85, 34, 102, 58, 80, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 40, 1, 4, 6 ] ] k = 8: F-action on Pi is (2,3) [52,1,8] Dynkin type is ^2D_4(q) + A_1(q) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 1/8 q^2 ( q-2 ) q congruent 3 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/8 q^2 ( q-2 ) q congruent 5 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 1/8 q^2 ( q-2 ) q congruent 9 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 1/8 q^2 ( q-2 ) q congruent 17 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 1/8 q^2 ( q-2 ) q congruent 37 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/8 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/8 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 72, 20, 16, 73, 19, 76, 18, 74, 73, 18, 96, 60, 97, 59, 44, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ] ] k = 9: F-action on Pi is () [52,1,9] Dynkin type is D_4(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/16 q ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 7, 69, 5, 67, 68, 7, 76, 20, 69, 5, 7, 69, 3, 69, 18, 74, 30, 81, 31, 78, 76, 20, 72, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 28, 1, 3, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ] ] k = 10: F-action on Pi is () [52,1,10] Dynkin type is D_4(q) + A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 phi1 ( q^2-12*q+39 ) q congruent 2 modulo 60: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 3 modulo 60: 1/48 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 60: 1/48 q ( q^2-10*q+24 ) q congruent 5 modulo 60: 1/48 ( q^3-13*q^2+51*q-55 ) q congruent 7 modulo 60: 1/48 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 60: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 9 modulo 60: 1/48 phi1 ( q^2-12*q+39 ) q congruent 11 modulo 60: 1/48 ( q^3-13*q^2+51*q-79 ) q congruent 13 modulo 60: 1/48 phi1 ( q^2-12*q+39 ) q congruent 16 modulo 60: 1/48 q ( q^2-10*q+24 ) q congruent 17 modulo 60: 1/48 ( q^3-13*q^2+51*q-55 ) q congruent 19 modulo 60: 1/48 ( q^3-13*q^2+51*q-63 ) q congruent 21 modulo 60: 1/48 phi1 ( q^2-12*q+39 ) q congruent 23 modulo 60: 1/48 ( q^3-13*q^2+51*q-79 ) q congruent 25 modulo 60: 1/48 phi1 ( q^2-12*q+39 ) q congruent 27 modulo 60: 1/48 ( q^3-13*q^2+51*q-63 ) q congruent 29 modulo 60: 1/48 ( q^3-13*q^2+51*q-55 ) q congruent 31 modulo 60: 1/48 ( q^3-13*q^2+51*q-63 ) q congruent 32 modulo 60: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 37 modulo 60: 1/48 phi1 ( q^2-12*q+39 ) q congruent 41 modulo 60: 1/48 ( q^3-13*q^2+51*q-55 ) q congruent 43 modulo 60: 1/48 ( q^3-13*q^2+51*q-63 ) q congruent 47 modulo 60: 1/48 ( q^3-13*q^2+51*q-79 ) q congruent 49 modulo 60: 1/48 phi1 ( q^2-12*q+39 ) q congruent 53 modulo 60: 1/48 ( q^3-13*q^2+51*q-55 ) q congruent 59 modulo 60: 1/48 ( q^3-13*q^2+51*q-79 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 3, 69, 5, 67, 2, 7, 69, 20, 71, 5, 67, 69, 5, 69, 5, 74, 17, 81, 27, 78, 9, 20, 71, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 4, 24 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 39, 1, 3, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 9, 48 ] ] i = 53: Pi = [ 2, 4, 5, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [53,1,1] Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 ( q^3-23*q^2+171*q-437 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/96 ( q^3-23*q^2+159*q-297 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 7 modulo 60: 1/96 ( q^3-23*q^2+159*q-329 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 11 modulo 60: 1/96 ( q^3-23*q^2+159*q-297 ) q congruent 13 modulo 60: 1/96 ( q^3-23*q^2+171*q-437 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 19 modulo 60: 1/96 ( q^3-23*q^2+159*q-329 ) q congruent 21 modulo 60: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 23 modulo 60: 1/96 ( q^3-23*q^2+159*q-297 ) q congruent 25 modulo 60: 1/96 ( q^3-23*q^2+171*q-437 ) q congruent 27 modulo 60: 1/96 ( q^3-23*q^2+159*q-297 ) q congruent 29 modulo 60: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 31 modulo 60: 1/96 ( q^3-23*q^2+159*q-329 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/96 ( q^3-23*q^2+171*q-437 ) q congruent 41 modulo 60: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 43 modulo 60: 1/96 ( q^3-23*q^2+159*q-329 ) q congruent 47 modulo 60: 1/96 ( q^3-23*q^2+159*q-297 ) q congruent 49 modulo 60: 1/96 ( q^3-23*q^2+171*q-437 ) q congruent 53 modulo 60: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 59 modulo 60: 1/96 ( q^3-23*q^2+159*q-297 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 4, 68, 68, 3, 8, 77, 77, 30, 70, 19, 19, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 24 ], [ 16, 1, 1, 16 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 48 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 36 ], [ 25, 1, 1, 36 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 35, 1, 1, 48 ], [ 39, 1, 1, 24 ], [ 41, 1, 1, 48 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 44, 1, 1, 48 ] ] k = 2: F-action on Pi is ( 7,240) [53,1,2] Dynkin type is A_3(q) + A_1(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 13 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 21 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 25 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 29 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 47 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 49 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/32 ( q^3-9*q^2+19*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19, 3, 72, 30, 97, 72, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 4 ], [ 20, 1, 1, 16 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 16 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 4 ], [ 26, 1, 1, 16 ], [ 28, 1, 3, 8 ], [ 35, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 41, 1, 2, 16 ], [ 41, 1, 3, 16 ], [ 43, 1, 1, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ] ] k = 3: F-action on Pi is () [53,1,3] Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 47 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/16 ( q^3-9*q^2+19*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 7, 68, 7, 7, 69, 77, 30, 30, 81, 19, 76, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 35, 1, 1, 8 ], [ 35, 1, 3, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 6, 8 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 44, 1, 2, 8 ] ] k = 4: F-action on Pi is ( 7,240) [53,1,4] Dynkin type is A_3(q) + A_1(q^2) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^3 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^3 q congruent 7 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^3 q congruent 11 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1^3 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^3 q congruent 19 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1^3 q congruent 23 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1^3 q congruent 27 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1^3 q congruent 31 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^3 q congruent 41 modulo 60: 1/16 phi1^3 q congruent 43 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1^3 q congruent 53 modulo 60: 1/16 phi1^3 q congruent 59 modulo 60: 1/16 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 7, 76, 69, 20, 81, 59, 20, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 4, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 7, 8 ], [ 43, 1, 2, 16 ], [ 44, 1, 8, 8 ] ] k = 5: F-action on Pi is ( 2, 5)( 7,240) [53,1,5] Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1^3) Order of center |Z^F|: phi1^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 7 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 11 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 13 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 19 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 21 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 23 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 25 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 27 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 29 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 31 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 41 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 43 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 47 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 49 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 53 modulo 60: 1/96 phi1 ( q^2-14*q+45 ) q congruent 59 modulo 60: 1/96 ( q^3-15*q^2+71*q-105 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 68, 19, 4, 70, 28, 96, 70, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 8 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 12 ], [ 16, 1, 2, 16 ], [ 20, 1, 3, 48 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 36 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 35, 1, 5, 48 ], [ 39, 1, 1, 24 ], [ 41, 1, 3, 48 ], [ 43, 1, 3, 96 ], [ 44, 1, 1, 48 ] ] k = 6: F-action on Pi is (2,5) [53,1,6] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 13 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 21 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 25 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 29 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 47 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 49 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/32 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/32 ( q^3-9*q^2+27*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 69, 5, 68, 7, 7, 69, 4, 68, 68, 3, 28, 82, 82, 31, 70, 19, 19, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], [ 20, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 3, 8 ], [ 35, 1, 6, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 4, 16 ], [ 43, 1, 3, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ] ] k = 7: F-action on Pi is ( 2, 5)( 7,240) [53,1,7] Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 7 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 11 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 19 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 23 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 27 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 31 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 43 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1^2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-4*q-1 ) q congruent 59 modulo 60: 1/16 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 7, 76, 68, 19, 82, 60, 19, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 35, 1, 5, 8 ], [ 35, 1, 7, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 7, 8 ], [ 43, 1, 4, 16 ], [ 44, 1, 2, 8 ] ] k = 8: F-action on Pi is (2,5) [53,1,8] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 13 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 21 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 25 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 29 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 47 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) q congruent 49 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/16 phi1 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/16 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 5, 67, 7, 69, 69, 5, 68, 7, 7, 69, 82, 31, 31, 78, 19, 76, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 6, 8 ], [ 42, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 44, 1, 8, 8 ] ] k = 9: F-action on Pi is () [53,1,9] Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 7 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 11 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 19 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 23 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 27 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 31 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 41 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 43 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 53 modulo 60: 1/32 phi1 ( q^2-6*q+13 ) q congruent 59 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 3, 68, 7, 7, 69, 3, 69, 69, 5, 30, 81, 81, 27, 72, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 8 ], [ 20, 1, 2, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 28, 1, 2, 8 ], [ 35, 1, 3, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 43, 1, 8, 16 ], [ 43, 1, 12, 32 ], [ 44, 1, 5, 16 ] ] k = 10: F-action on Pi is ( 7,240) [53,1,10] Dynkin type is A_3(q) + A_1(q^2) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/16 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 16, 19, 73, 72, 18, 97, 53, 18, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 25, 1, 1, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ] ] k = 11: F-action on Pi is () [53,1,11] Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1^2 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 phi2 q congruent 7 modulo 60: 1/16 phi1^2 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 phi2 q congruent 11 modulo 60: 1/16 phi1^2 phi2 q congruent 13 modulo 60: 1/16 phi1^2 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 phi2 q congruent 19 modulo 60: 1/16 phi1^2 phi2 q congruent 21 modulo 60: 1/16 phi1^2 phi2 q congruent 23 modulo 60: 1/16 phi1^2 phi2 q congruent 25 modulo 60: 1/16 phi1^2 phi2 q congruent 27 modulo 60: 1/16 phi1^2 phi2 q congruent 29 modulo 60: 1/16 phi1^2 phi2 q congruent 31 modulo 60: 1/16 phi1^2 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 phi2 q congruent 41 modulo 60: 1/16 phi1^2 phi2 q congruent 43 modulo 60: 1/16 phi1^2 phi2 q congruent 47 modulo 60: 1/16 phi1^2 phi2 q congruent 49 modulo 60: 1/16 phi1^2 phi2 q congruent 53 modulo 60: 1/16 phi1^2 phi2 q congruent 59 modulo 60: 1/16 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 19, 72, 19, 76, 76, 20, 72, 20, 20, 71, 97, 59, 59, 95, 18, 74, 74, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ] ] k = 12: F-action on Pi is ( 2, 5)( 7,240) [53,1,12] Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 7 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 11 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 19 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 23 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 27 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 31 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 41 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 43 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 53 modulo 60: 1/32 phi1^2 ( q-5 ) q congruent 59 modulo 60: 1/32 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 71, 69, 20, 3, 72, 31, 98, 72, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 4 ], [ 20, 1, 4, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 16 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 16 ], [ 28, 1, 2, 8 ], [ 35, 1, 7, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 41, 1, 2, 16 ], [ 41, 1, 10, 16 ], [ 43, 1, 8, 16 ], [ 43, 1, 13, 32 ], [ 44, 1, 5, 16 ] ] k = 13: F-action on Pi is (2,5) [53,1,13] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/16 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/16 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20, 20, 71, 19, 76, 76, 20, 70, 19, 19, 72, 96, 60, 60, 98, 16, 73, 73, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ] ] k = 14: F-action on Pi is ( 2, 5)( 7,240) [53,1,14] Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1^2 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1^2 phi2 q congruent 7 modulo 60: 1/16 phi1^2 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1^2 phi2 q congruent 11 modulo 60: 1/16 phi1^2 phi2 q congruent 13 modulo 60: 1/16 phi1^2 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1^2 phi2 q congruent 19 modulo 60: 1/16 phi1^2 phi2 q congruent 21 modulo 60: 1/16 phi1^2 phi2 q congruent 23 modulo 60: 1/16 phi1^2 phi2 q congruent 25 modulo 60: 1/16 phi1^2 phi2 q congruent 27 modulo 60: 1/16 phi1^2 phi2 q congruent 29 modulo 60: 1/16 phi1^2 phi2 q congruent 31 modulo 60: 1/16 phi1^2 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1^2 phi2 q congruent 41 modulo 60: 1/16 phi1^2 phi2 q congruent 43 modulo 60: 1/16 phi1^2 phi2 q congruent 47 modulo 60: 1/16 phi1^2 phi2 q congruent 49 modulo 60: 1/16 phi1^2 phi2 q congruent 53 modulo 60: 1/16 phi1^2 phi2 q congruent 59 modulo 60: 1/16 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 71, 17, 20, 74, 72, 18, 98, 54, 18, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 8 ], [ 23, 1, 2, 2 ], [ 25, 1, 3, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ] ] k = 15: F-action on Pi is ( 7,240) [53,1,15] Dynkin type is A_3(q) + A_1(q^2) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/12 q phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 q phi1 phi2 q congruent 7 modulo 60: 1/12 q phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/12 q phi1 phi2 q congruent 11 modulo 60: 1/12 q phi1 phi2 q congruent 13 modulo 60: 1/12 q phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 q phi1 phi2 q congruent 19 modulo 60: 1/12 q phi1 phi2 q congruent 21 modulo 60: 1/12 q phi1 phi2 q congruent 23 modulo 60: 1/12 q phi1 phi2 q congruent 25 modulo 60: 1/12 q phi1 phi2 q congruent 27 modulo 60: 1/12 q phi1 phi2 q congruent 29 modulo 60: 1/12 q phi1 phi2 q congruent 31 modulo 60: 1/12 q phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 q phi1 phi2 q congruent 41 modulo 60: 1/12 q phi1 phi2 q congruent 43 modulo 60: 1/12 q phi1 phi2 q congruent 47 modulo 60: 1/12 q phi1 phi2 q congruent 49 modulo 60: 1/12 q phi1 phi2 q congruent 53 modulo 60: 1/12 q phi1 phi2 q congruent 59 modulo 60: 1/12 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 28, 96, 82, 60, 31, 98, 36, 99, 98, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 16, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 44, 1, 7, 6 ] ] k = 16: F-action on Pi is () [53,1,16] Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^2-q-4 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 7 modulo 60: 1/12 phi1 ( q^2-q-4 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 11 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 13 modulo 60: 1/12 phi1 ( q^2-q-4 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 19 modulo 60: 1/12 phi1 ( q^2-q-4 ) q congruent 21 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 23 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 25 modulo 60: 1/12 phi1 ( q^2-q-4 ) q congruent 27 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 29 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 31 modulo 60: 1/12 phi1 ( q^2-q-4 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 phi1 ( q^2-q-4 ) q congruent 41 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 43 modulo 60: 1/12 phi1 ( q^2-q-4 ) q congruent 47 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 49 modulo 60: 1/12 phi1 ( q^2-q-4 ) q congruent 53 modulo 60: 1/12 q phi2 ( q-3 ) q congruent 59 modulo 60: 1/12 q phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30, 77, 30, 30, 81, 30, 81, 81, 27, 14, 83, 83, 37, 97, 59, 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 16, 1, 1, 4 ], [ 27, 1, 5, 6 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ] ] k = 17: F-action on Pi is ( 2, 5)( 7,240) [53,1,17] Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/12 q phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 q phi1 phi2 q congruent 7 modulo 60: 1/12 q phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/12 q phi1 phi2 q congruent 11 modulo 60: 1/12 q phi1 phi2 q congruent 13 modulo 60: 1/12 q phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 q phi1 phi2 q congruent 19 modulo 60: 1/12 q phi1 phi2 q congruent 21 modulo 60: 1/12 q phi1 phi2 q congruent 23 modulo 60: 1/12 q phi1 phi2 q congruent 25 modulo 60: 1/12 q phi1 phi2 q congruent 27 modulo 60: 1/12 q phi1 phi2 q congruent 29 modulo 60: 1/12 q phi1 phi2 q congruent 31 modulo 60: 1/12 q phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 q phi1 phi2 q congruent 41 modulo 60: 1/12 q phi1 phi2 q congruent 43 modulo 60: 1/12 q phi1 phi2 q congruent 47 modulo 60: 1/12 q phi1 phi2 q congruent 49 modulo 60: 1/12 q phi1 phi2 q congruent 53 modulo 60: 1/12 q phi1 phi2 q congruent 59 modulo 60: 1/12 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 27, 95, 81, 59, 30, 97, 36, 99, 97, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 27, 1, 5, 6 ], [ 44, 1, 3, 6 ] ] k = 18: F-action on Pi is (2,5) [53,1,18] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/12 q phi1^2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 phi2 ( q^2-3*q+4 ) q congruent 7 modulo 60: 1/12 q phi1^2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/12 q phi1^2 q congruent 11 modulo 60: 1/12 phi2 ( q^2-3*q+4 ) q congruent 13 modulo 60: 1/12 q phi1^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 phi2 ( q^2-3*q+4 ) q congruent 19 modulo 60: 1/12 q phi1^2 q congruent 21 modulo 60: 1/12 q phi1^2 q congruent 23 modulo 60: 1/12 phi2 ( q^2-3*q+4 ) q congruent 25 modulo 60: 1/12 q phi1^2 q congruent 27 modulo 60: 1/12 q phi1^2 q congruent 29 modulo 60: 1/12 phi2 ( q^2-3*q+4 ) q congruent 31 modulo 60: 1/12 q phi1^2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 q phi1^2 q congruent 41 modulo 60: 1/12 phi2 ( q^2-3*q+4 ) q congruent 43 modulo 60: 1/12 q phi1^2 q congruent 47 modulo 60: 1/12 phi2 ( q^2-3*q+4 ) q congruent 49 modulo 60: 1/12 q phi1^2 q congruent 53 modulo 60: 1/12 phi2 ( q^2-3*q+4 ) q congruent 59 modulo 60: 1/12 phi2 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 78, 78, 9, 82, 31, 31, 78, 28, 82, 82, 31, 38, 84, 84, 15, 96, 60, 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 16, 1, 3, 4 ], [ 27, 1, 4, 6 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ] ] k = 19: F-action on Pi is ( 7,240) [53,1,19] Dynkin type is A_3(q) + A_1(q^2) + T(phi2^3) Order of center |Z^F|: phi2^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) q congruent 13 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) q congruent 21 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) q congruent 25 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) q congruent 29 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) q congruent 47 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) q congruent 49 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/96 phi1 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/96 phi2 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 69, 20, 5, 71, 27, 95, 71, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 16, 1, 4, 16 ], [ 20, 1, 2, 48 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 4, 36 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], [ 35, 1, 4, 48 ], [ 39, 1, 3, 24 ], [ 41, 1, 10, 48 ], [ 43, 1, 12, 96 ], [ 44, 1, 10, 48 ] ] k = 20: F-action on Pi is (2,5) [53,1,20] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^2-16*q+63 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/96 ( q^3-17*q^2+79*q-95 ) q congruent 7 modulo 60: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/96 phi1 ( q^2-16*q+63 ) q congruent 11 modulo 60: 1/96 ( q^3-17*q^2+91*q-179 ) q congruent 13 modulo 60: 1/96 phi1 ( q^2-16*q+63 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/96 ( q^3-17*q^2+79*q-95 ) q congruent 19 modulo 60: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 21 modulo 60: 1/96 phi1 ( q^2-16*q+63 ) q congruent 23 modulo 60: 1/96 ( q^3-17*q^2+91*q-179 ) q congruent 25 modulo 60: 1/96 phi1 ( q^2-16*q+63 ) q congruent 27 modulo 60: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 29 modulo 60: 1/96 ( q^3-17*q^2+79*q-95 ) q congruent 31 modulo 60: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/96 phi1 ( q^2-16*q+63 ) q congruent 41 modulo 60: 1/96 ( q^3-17*q^2+79*q-95 ) q congruent 43 modulo 60: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 47 modulo 60: 1/96 ( q^3-17*q^2+91*q-179 ) q congruent 49 modulo 60: 1/96 phi1 ( q^2-16*q+63 ) q congruent 53 modulo 60: 1/96 ( q^3-17*q^2+79*q-95 ) q congruent 59 modulo 60: 1/96 ( q^3-17*q^2+91*q-179 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 67, 2, 69, 5, 5, 67, 3, 69, 69, 5, 31, 78, 78, 9, 72, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 10 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 16 ], [ 19, 1, 2, 48 ], [ 20, 1, 4, 48 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 36 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], [ 35, 1, 8, 48 ], [ 39, 1, 3, 24 ], [ 41, 1, 9, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 10, 48 ] ] i = 54: Pi = [ 1, 2, 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [54,1,1] Dynkin type is A_4(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1429*q+2831 ) q congruent 2 modulo 60: 1/240 ( q^4-29*q^3+296*q^2-1204*q+1440 ) q congruent 3 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 ) q congruent 4 modulo 60: 1/240 ( q^4-29*q^3+296*q^2-1244*q+1840 ) q congruent 5 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 ) q congruent 7 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1429*q+2555 ) q congruent 8 modulo 60: 1/240 ( q^4-29*q^3+296*q^2-1204*q+1440 ) q congruent 9 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 ) q congruent 11 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2211 ) q congruent 13 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1429*q+2735 ) q congruent 16 modulo 60: 1/240 ( q^4-29*q^3+296*q^2-1244*q+1936 ) q congruent 17 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 ) q congruent 19 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1429*q+2555 ) q congruent 21 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2391 ) q congruent 23 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 ) q congruent 25 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1429*q+2735 ) q congruent 27 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 ) q congruent 29 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 ) q congruent 31 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1429*q+2651 ) q congruent 32 modulo 60: 1/240 ( q^4-29*q^3+296*q^2-1204*q+1440 ) q congruent 37 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1429*q+2735 ) q congruent 41 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2391 ) q congruent 43 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1429*q+2555 ) q congruent 47 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 ) q congruent 49 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1429*q+2735 ) q congruent 53 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 ) q congruent 59 modulo 60: 1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 8, 77, 70, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 10 ], [ 3, 1, 1, 20 ], [ 4, 1, 1, 10 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 20 ], [ 7, 1, 1, 20 ], [ 8, 1, 1, 10 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 20 ], [ 11, 1, 1, 60 ], [ 12, 1, 1, 40 ], [ 13, 1, 1, 60 ], [ 14, 1, 1, 10 ], [ 15, 1, 1, 20 ], [ 18, 1, 1, 60 ], [ 19, 1, 1, 60 ], [ 21, 1, 1, 40 ], [ 22, 1, 1, 40 ], [ 23, 1, 1, 30 ], [ 24, 1, 1, 60 ], [ 26, 1, 1, 40 ], [ 27, 1, 1, 120 ], [ 28, 1, 1, 120 ], [ 29, 1, 1, 40 ], [ 30, 1, 1, 60 ], [ 34, 1, 1, 120 ], [ 36, 1, 1, 120 ], [ 39, 1, 1, 120 ], [ 42, 1, 1, 120 ], [ 44, 1, 1, 240 ], [ 45, 1, 1, 120 ], [ 50, 1, 1, 240 ] ] k = 2: F-action on Pi is () [54,1,2] Dynkin type is A_4(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-49 ) q congruent 2 modulo 60: 1/24 q ( q^3-13*q^2+52*q-60 ) q congruent 3 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-89*q+33 ) q congruent 4 modulo 60: 1/24 q ( q^3-13*q^2+52*q-64 ) q congruent 5 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-45 ) q congruent 7 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-93*q+37 ) q congruent 8 modulo 60: 1/24 q ( q^3-13*q^2+52*q-60 ) q congruent 9 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-45 ) q congruent 11 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-89*q+33 ) q congruent 13 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-49 ) q congruent 16 modulo 60: 1/24 q ( q^3-13*q^2+52*q-64 ) q congruent 17 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-45 ) q congruent 19 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-93*q+37 ) q congruent 21 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-45 ) q congruent 23 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-89*q+33 ) q congruent 25 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-49 ) q congruent 27 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-89*q+33 ) q congruent 29 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-45 ) q congruent 31 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-93*q+37 ) q congruent 32 modulo 60: 1/24 q ( q^3-13*q^2+52*q-60 ) q congruent 37 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-49 ) q congruent 41 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-45 ) q congruent 43 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-93*q+37 ) q congruent 47 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-89*q+33 ) q congruent 49 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-49 ) q congruent 53 modulo 60: 1/24 phi1 ( q^3-12*q^2+44*q-45 ) q congruent 59 modulo 60: 1/24 ( q^4-13*q^3+56*q^2-89*q+33 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 77, 30, 19, 93 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 6 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 12 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 15, 1, 1, 8 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 12 ], [ 22, 1, 2, 4 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 1, 12 ], [ 26, 1, 3, 4 ], [ 27, 1, 1, 12 ], [ 27, 1, 2, 12 ], [ 28, 1, 1, 12 ], [ 28, 1, 2, 12 ], [ 29, 1, 1, 12 ], [ 29, 1, 2, 4 ], [ 30, 1, 1, 12 ], [ 34, 1, 1, 12 ], [ 34, 1, 2, 12 ], [ 36, 1, 1, 12 ], [ 36, 1, 2, 12 ], [ 39, 1, 4, 12 ], [ 42, 1, 1, 12 ], [ 42, 1, 4, 12 ], [ 44, 1, 2, 24 ], [ 45, 1, 1, 12 ], [ 45, 1, 2, 12 ], [ 50, 1, 2, 24 ], [ 50, 1, 4, 24 ] ] k = 3: F-action on Pi is () [54,1,3] Dynkin type is A_4(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^3-4*q^2-q+10 ) q congruent 2 modulo 60: 1/12 q phi2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/12 phi1 ( q^3-4*q^2-2*q+8 ) q congruent 5 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/12 phi1 ( q^3-4*q^2-q+10 ) q congruent 8 modulo 60: 1/12 q phi2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/12 phi1 ( q^3-4*q^2-q+10 ) q congruent 16 modulo 60: 1/12 phi1 ( q^3-4*q^2-2*q+8 ) q congruent 17 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/12 phi1 ( q^3-4*q^2-q+10 ) q congruent 21 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/12 phi1 ( q^3-4*q^2-q+10 ) q congruent 27 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/12 phi1 ( q^3-4*q^2-q+10 ) q congruent 32 modulo 60: 1/12 q phi2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/12 phi1 ( q^3-4*q^2-q+10 ) q congruent 41 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/12 phi1 ( q^3-4*q^2-q+10 ) q congruent 47 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/12 phi1 ( q^3-4*q^2-q+10 ) q congruent 53 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/12 q phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 30, 14, 83, 97, 62 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 26, 1, 1, 4 ], [ 27, 1, 5, 6 ], [ 29, 1, 1, 4 ], [ 42, 1, 3, 6 ], [ 44, 1, 3, 12 ], [ 45, 1, 3, 6 ], [ 50, 1, 3, 12 ] ] k = 4: F-action on Pi is () [54,1,4] Dynkin type is A_4(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 2 modulo 60: 1/8 q^2 phi2 ( q-2 ) q congruent 3 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 4 modulo 60: 1/8 q^2 phi2 ( q-2 ) q congruent 5 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 7 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 8 modulo 60: 1/8 q^2 phi2 ( q-2 ) q congruent 9 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 11 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 13 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 16 modulo 60: 1/8 q^2 phi2 ( q-2 ) q congruent 17 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 19 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 21 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 23 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 25 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 27 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 29 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 31 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 32 modulo 60: 1/8 q^2 phi2 ( q-2 ) q congruent 37 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 41 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 43 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 47 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 49 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 53 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 59 modulo 60: 1/8 phi1 phi2 ( q^2-q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 76, 97, 59, 22, 107 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], [ 14, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 30, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 44, 1, 4, 8 ] ] k = 5: F-action on Pi is () [54,1,5] Dynkin type is A_4(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 2 modulo 60: 1/16 q ( q^3-5*q^2+4*q+4 ) q congruent 3 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) q congruent 4 modulo 60: 1/16 q ( q^3-5*q^2+4*q+4 ) q congruent 5 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 7 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) q congruent 8 modulo 60: 1/16 q ( q^3-5*q^2+4*q+4 ) q congruent 9 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 11 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) q congruent 13 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 16 modulo 60: 1/16 q ( q^3-5*q^2+4*q+4 ) q congruent 17 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 19 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) q congruent 21 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 23 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) q congruent 25 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 27 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) q congruent 29 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 31 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) q congruent 32 modulo 60: 1/16 q ( q^3-5*q^2+4*q+4 ) q congruent 37 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 41 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 43 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) q congruent 47 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) q congruent 49 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 53 modulo 60: 1/16 phi1^2 ( q^2-3*q-1 ) q congruent 59 modulo 60: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 7, 30, 81, 76, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 8 ], [ 14, 1, 1, 2 ], [ 15, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 4 ], [ 22, 1, 2, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 2, 8 ], [ 29, 1, 2, 8 ], [ 30, 1, 1, 4 ], [ 30, 1, 2, 8 ], [ 34, 1, 2, 8 ], [ 36, 1, 2, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 42, 1, 4, 8 ], [ 44, 1, 5, 16 ], [ 45, 1, 2, 8 ], [ 50, 1, 5, 16 ] ] k = 6: F-action on Pi is () [54,1,6] Dynkin type is A_4(q) + T(phi5) Order of center |Z^F|: phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/10 phi1 ( q^3+2*q^2+3*q+4 ) q congruent 2 modulo 60: 1/10 q phi2 phi4 q congruent 3 modulo 60: 1/10 q phi2 phi4 q congruent 4 modulo 60: 1/10 q phi2 phi4 q congruent 5 modulo 60: 1/10 q phi2 phi4 q congruent 7 modulo 60: 1/10 q phi2 phi4 q congruent 8 modulo 60: 1/10 q phi2 phi4 q congruent 9 modulo 60: 1/10 q phi2 phi4 q congruent 11 modulo 60: 1/10 phi1 ( q^3+2*q^2+3*q+4 ) q congruent 13 modulo 60: 1/10 q phi2 phi4 q congruent 16 modulo 60: 1/10 phi1 ( q^3+2*q^2+3*q+4 ) q congruent 17 modulo 60: 1/10 q phi2 phi4 q congruent 19 modulo 60: 1/10 q phi2 phi4 q congruent 21 modulo 60: 1/10 phi1 ( q^3+2*q^2+3*q+4 ) q congruent 23 modulo 60: 1/10 q phi2 phi4 q congruent 25 modulo 60: 1/10 q phi2 phi4 q congruent 27 modulo 60: 1/10 q phi2 phi4 q congruent 29 modulo 60: 1/10 q phi2 phi4 q congruent 31 modulo 60: 1/10 phi1 ( q^3+2*q^2+3*q+4 ) q congruent 32 modulo 60: 1/10 q phi2 phi4 q congruent 37 modulo 60: 1/10 q phi2 phi4 q congruent 41 modulo 60: 1/10 phi1 ( q^3+2*q^2+3*q+4 ) q congruent 43 modulo 60: 1/10 q phi2 phi4 q congruent 47 modulo 60: 1/10 q phi2 phi4 q congruent 49 modulo 60: 1/10 q phi2 phi4 q congruent 53 modulo 60: 1/10 q phi2 phi4 q congruent 59 modulo 60: 1/10 q phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 23, 93, 50, 62, 111, 107, 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 1, 4 ] ] k = 7: F-action on Pi is () [54,1,7] Dynkin type is A_4(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^3-q+2 ) q congruent 2 modulo 60: 1/12 q^2 phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1^2 phi2 q congruent 4 modulo 60: 1/12 q phi1 ( q^2-2 ) q congruent 5 modulo 60: 1/12 q phi1^2 phi2 q congruent 7 modulo 60: 1/12 phi1 ( q^3-q+2 ) q congruent 8 modulo 60: 1/12 q^2 phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1^2 phi2 q congruent 11 modulo 60: 1/12 q phi1^2 phi2 q congruent 13 modulo 60: 1/12 phi1 ( q^3-q+2 ) q congruent 16 modulo 60: 1/12 q phi1 ( q^2-2 ) q congruent 17 modulo 60: 1/12 q phi1^2 phi2 q congruent 19 modulo 60: 1/12 phi1 ( q^3-q+2 ) q congruent 21 modulo 60: 1/12 q phi1^2 phi2 q congruent 23 modulo 60: 1/12 q phi1^2 phi2 q congruent 25 modulo 60: 1/12 phi1 ( q^3-q+2 ) q congruent 27 modulo 60: 1/12 q phi1^2 phi2 q congruent 29 modulo 60: 1/12 q phi1^2 phi2 q congruent 31 modulo 60: 1/12 phi1 ( q^3-q+2 ) q congruent 32 modulo 60: 1/12 q^2 phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 phi1 ( q^3-q+2 ) q congruent 41 modulo 60: 1/12 q phi1^2 phi2 q congruent 43 modulo 60: 1/12 phi1 ( q^3-q+2 ) q congruent 47 modulo 60: 1/12 q phi1^2 phi2 q congruent 49 modulo 60: 1/12 phi1 ( q^3-q+2 ) q congruent 53 modulo 60: 1/12 q phi1^2 phi2 q congruent 59 modulo 60: 1/12 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 77, 30, 81, 83, 37, 59, 111 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 15, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 26, 1, 3, 4 ], [ 27, 1, 5, 6 ], [ 29, 1, 2, 4 ], [ 42, 1, 3, 6 ], [ 45, 1, 3, 6 ], [ 50, 1, 6, 12 ] ] k = 8: F-action on Pi is (1,2)(3,4) [54,1,8] Dynkin type is ^2A_4(q) + T(phi10) Order of center |Z^F|: phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/10 q phi1 phi4 q congruent 2 modulo 60: 1/10 q phi1 phi4 q congruent 3 modulo 60: 1/10 q phi1 phi4 q congruent 4 modulo 60: 1/10 phi2 ( q^3-2*q^2+3*q-4 ) q congruent 5 modulo 60: 1/10 q phi1 phi4 q congruent 7 modulo 60: 1/10 q phi1 phi4 q congruent 8 modulo 60: 1/10 q phi1 phi4 q congruent 9 modulo 60: 1/10 phi2 ( q^3-2*q^2+3*q-4 ) q congruent 11 modulo 60: 1/10 q phi1 phi4 q congruent 13 modulo 60: 1/10 q phi1 phi4 q congruent 16 modulo 60: 1/10 q phi1 phi4 q congruent 17 modulo 60: 1/10 q phi1 phi4 q congruent 19 modulo 60: 1/10 phi2 ( q^3-2*q^2+3*q-4 ) q congruent 21 modulo 60: 1/10 q phi1 phi4 q congruent 23 modulo 60: 1/10 q phi1 phi4 q congruent 25 modulo 60: 1/10 q phi1 phi4 q congruent 27 modulo 60: 1/10 q phi1 phi4 q congruent 29 modulo 60: 1/10 phi2 ( q^3-2*q^2+3*q-4 ) q congruent 31 modulo 60: 1/10 q phi1 phi4 q congruent 32 modulo 60: 1/10 q phi1 phi4 q congruent 37 modulo 60: 1/10 q phi1 phi4 q congruent 41 modulo 60: 1/10 q phi1 phi4 q congruent 43 modulo 60: 1/10 q phi1 phi4 q congruent 47 modulo 60: 1/10 q phi1 phi4 q congruent 49 modulo 60: 1/10 phi2 ( q^3-2*q^2+3*q-4 ) q congruent 53 modulo 60: 1/10 q phi1 phi4 q congruent 59 modulo 60: 1/10 phi2 ( q^3-2*q^2+3*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 24, 94, 51, 63, 112, 108, 26 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 2, 4 ] ] k = 9: F-action on Pi is (1,2)(3,4) [54,1,9] Dynkin type is ^2A_4(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 phi6 q congruent 2 modulo 60: 1/8 q^3 phi1 q congruent 3 modulo 60: 1/8 phi1 phi2 phi6 q congruent 4 modulo 60: 1/8 q^3 phi1 q congruent 5 modulo 60: 1/8 phi1 phi2 phi6 q congruent 7 modulo 60: 1/8 phi1 phi2 phi6 q congruent 8 modulo 60: 1/8 q^3 phi1 q congruent 9 modulo 60: 1/8 phi1 phi2 phi6 q congruent 11 modulo 60: 1/8 phi1 phi2 phi6 q congruent 13 modulo 60: 1/8 phi1 phi2 phi6 q congruent 16 modulo 60: 1/8 q^3 phi1 q congruent 17 modulo 60: 1/8 phi1 phi2 phi6 q congruent 19 modulo 60: 1/8 phi1 phi2 phi6 q congruent 21 modulo 60: 1/8 phi1 phi2 phi6 q congruent 23 modulo 60: 1/8 phi1 phi2 phi6 q congruent 25 modulo 60: 1/8 phi1 phi2 phi6 q congruent 27 modulo 60: 1/8 phi1 phi2 phi6 q congruent 29 modulo 60: 1/8 phi1 phi2 phi6 q congruent 31 modulo 60: 1/8 phi1 phi2 phi6 q congruent 32 modulo 60: 1/8 q^3 phi1 q congruent 37 modulo 60: 1/8 phi1 phi2 phi6 q congruent 41 modulo 60: 1/8 phi1 phi2 phi6 q congruent 43 modulo 60: 1/8 phi1 phi2 phi6 q congruent 47 modulo 60: 1/8 phi1 phi2 phi6 q congruent 49 modulo 60: 1/8 phi1 phi2 phi6 q congruent 53 modulo 60: 1/8 phi1 phi2 phi6 q congruent 59 modulo 60: 1/8 phi1 phi2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 71, 20, 76, 98, 60, 22, 108 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 30, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 44, 1, 6, 8 ] ] k = 10: F-action on Pi is (1,2)(3,4) [54,1,10] Dynkin type is ^2A_4(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^3 q congruent 2 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 3 modulo 60: 1/12 q phi1^3 q congruent 4 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 7 modulo 60: 1/12 q phi1^3 q congruent 8 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 9 modulo 60: 1/12 q phi1^3 q congruent 11 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 13 modulo 60: 1/12 q phi1^3 q congruent 16 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 19 modulo 60: 1/12 q phi1^3 q congruent 21 modulo 60: 1/12 q phi1^3 q congruent 23 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 25 modulo 60: 1/12 q phi1^3 q congruent 27 modulo 60: 1/12 q phi1^3 q congruent 29 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 31 modulo 60: 1/12 q phi1^3 q congruent 32 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 37 modulo 60: 1/12 q phi1^3 q congruent 41 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 43 modulo 60: 1/12 q phi1^3 q congruent 47 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 49 modulo 60: 1/12 q phi1^3 q congruent 53 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 78, 31, 15, 84, 98, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 29, 1, 4, 4 ], [ 42, 1, 5, 6 ], [ 44, 1, 7, 12 ], [ 45, 1, 4, 6 ], [ 50, 1, 10, 12 ] ] k = 11: F-action on Pi is (1,2)(3,4) [54,1,11] Dynkin type is ^2A_4(q) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^3 q congruent 2 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 3 modulo 60: 1/12 q phi1^3 q congruent 4 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 7 modulo 60: 1/12 q phi1^3 q congruent 8 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 9 modulo 60: 1/12 q phi1^3 q congruent 11 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 13 modulo 60: 1/12 q phi1^3 q congruent 16 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 19 modulo 60: 1/12 q phi1^3 q congruent 21 modulo 60: 1/12 q phi1^3 q congruent 23 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 25 modulo 60: 1/12 q phi1^3 q congruent 27 modulo 60: 1/12 q phi1^3 q congruent 29 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 31 modulo 60: 1/12 q phi1^3 q congruent 32 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 37 modulo 60: 1/12 q phi1^3 q congruent 41 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 43 modulo 60: 1/12 q phi1^3 q congruent 47 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 49 modulo 60: 1/12 q phi1^3 q congruent 53 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^3-4*q^2+7*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 31, 82, 84, 38, 60, 112 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 15, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 26, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 29, 1, 3, 4 ], [ 42, 1, 5, 6 ], [ 45, 1, 4, 6 ], [ 50, 1, 7, 12 ] ] k = 12: F-action on Pi is (1,2)(3,4) [54,1,12] Dynkin type is ^2A_4(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^3-8*q^2+22*q-27 ) q congruent 2 modulo 60: 1/24 ( q^4-9*q^3+26*q^2-28*q+8 ) q congruent 3 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-49*q+39 ) q congruent 4 modulo 60: 1/24 q ( q^3-9*q^2+26*q-24 ) q congruent 5 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-53*q+39 ) q congruent 7 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-49*q+39 ) q congruent 8 modulo 60: 1/24 ( q^4-9*q^3+26*q^2-28*q+8 ) q congruent 9 modulo 60: 1/24 phi1 ( q^3-8*q^2+22*q-27 ) q congruent 11 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-53*q+51 ) q congruent 13 modulo 60: 1/24 phi1 ( q^3-8*q^2+22*q-27 ) q congruent 16 modulo 60: 1/24 q ( q^3-9*q^2+26*q-24 ) q congruent 17 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-53*q+39 ) q congruent 19 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-49*q+39 ) q congruent 21 modulo 60: 1/24 phi1 ( q^3-8*q^2+22*q-27 ) q congruent 23 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-53*q+51 ) q congruent 25 modulo 60: 1/24 phi1 ( q^3-8*q^2+22*q-27 ) q congruent 27 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-49*q+39 ) q congruent 29 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-53*q+39 ) q congruent 31 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-49*q+39 ) q congruent 32 modulo 60: 1/24 ( q^4-9*q^3+26*q^2-28*q+8 ) q congruent 37 modulo 60: 1/24 phi1 ( q^3-8*q^2+22*q-27 ) q congruent 41 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-53*q+39 ) q congruent 43 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-49*q+39 ) q congruent 47 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-53*q+51 ) q congruent 49 modulo 60: 1/24 phi1 ( q^3-8*q^2+22*q-27 ) q congruent 53 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-53*q+39 ) q congruent 59 modulo 60: 1/24 ( q^4-9*q^3+30*q^2-53*q+51 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 69, 78, 31, 20, 94 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 6 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 14, 1, 2, 6 ], [ 15, 1, 2, 8 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 21, 1, 2, 12 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 12 ], [ 27, 1, 3, 12 ], [ 27, 1, 6, 12 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 12 ], [ 29, 1, 3, 4 ], [ 29, 1, 4, 12 ], [ 30, 1, 3, 12 ], [ 34, 1, 3, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 3, 12 ], [ 36, 1, 4, 12 ], [ 39, 1, 4, 12 ], [ 42, 1, 2, 12 ], [ 42, 1, 6, 12 ], [ 44, 1, 8, 24 ], [ 45, 1, 5, 12 ], [ 45, 1, 6, 12 ], [ 50, 1, 9, 24 ], [ 50, 1, 11, 24 ] ] k = 13: F-action on Pi is (1,2)(3,4) [54,1,13] Dynkin type is ^2A_4(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 2 modulo 60: 1/16 q^2 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) q congruent 4 modulo 60: 1/16 q^2 ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 7 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) q congruent 8 modulo 60: 1/16 q^2 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 11 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) q congruent 13 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 16 modulo 60: 1/16 q^2 ( q^2-5*q+6 ) q congruent 17 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 19 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) q congruent 21 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 23 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) q congruent 25 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 27 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) q congruent 29 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 31 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) q congruent 32 modulo 60: 1/16 q^2 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 41 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 43 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) q congruent 47 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) q congruent 49 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 53 modulo 60: 1/16 phi1^2 ( q^2-3*q+1 ) q congruent 59 modulo 60: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 69, 7, 31, 82, 76, 51 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 4 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 4 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 8 ], [ 29, 1, 3, 8 ], [ 30, 1, 3, 4 ], [ 30, 1, 4, 8 ], [ 34, 1, 3, 8 ], [ 36, 1, 3, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 42, 1, 2, 8 ], [ 44, 1, 9, 16 ], [ 45, 1, 5, 8 ], [ 50, 1, 8, 16 ] ] k = 14: F-action on Pi is (1,2)(3,4) [54,1,14] Dynkin type is ^2A_4(q) + T(phi2^4) Order of center |Z^F|: phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/240 phi1 ( q^3-20*q^2+136*q-345 ) q congruent 2 modulo 60: 1/240 ( q^4-21*q^3+146*q^2-376*q+320 ) q congruent 3 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-481*q+525 ) q congruent 4 modulo 60: 1/240 ( q^4-21*q^3+146*q^2-336*q+96 ) q congruent 5 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-521*q+705 ) q congruent 7 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-481*q+525 ) q congruent 8 modulo 60: 1/240 ( q^4-21*q^3+146*q^2-376*q+320 ) q congruent 9 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-481*q+441 ) q congruent 11 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-521*q+885 ) q congruent 13 modulo 60: 1/240 phi1 ( q^3-20*q^2+136*q-345 ) q congruent 16 modulo 60: 1/240 q ( q^3-21*q^2+146*q-336 ) q congruent 17 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-521*q+705 ) q congruent 19 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-481*q+621 ) q congruent 21 modulo 60: 1/240 phi1 ( q^3-20*q^2+136*q-345 ) q congruent 23 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-521*q+885 ) q congruent 25 modulo 60: 1/240 phi1 ( q^3-20*q^2+136*q-345 ) q congruent 27 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-481*q+525 ) q congruent 29 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-521*q+801 ) q congruent 31 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-481*q+525 ) q congruent 32 modulo 60: 1/240 ( q^4-21*q^3+146*q^2-376*q+320 ) q congruent 37 modulo 60: 1/240 phi1 ( q^3-20*q^2+136*q-345 ) q congruent 41 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-521*q+705 ) q congruent 43 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-481*q+525 ) q congruent 47 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-521*q+885 ) q congruent 49 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-481*q+441 ) q congruent 53 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-521*q+705 ) q congruent 59 modulo 60: 1/240 ( q^4-21*q^3+156*q^2-521*q+981 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 9, 78, 71, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 10 ], [ 3, 1, 2, 20 ], [ 4, 1, 2, 10 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 20 ], [ 7, 1, 2, 20 ], [ 8, 1, 2, 10 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 20 ], [ 11, 1, 2, 60 ], [ 12, 1, 2, 40 ], [ 13, 1, 4, 60 ], [ 14, 1, 2, 10 ], [ 15, 1, 2, 20 ], [ 18, 1, 2, 60 ], [ 19, 1, 2, 60 ], [ 21, 1, 2, 40 ], [ 22, 1, 4, 40 ], [ 23, 1, 2, 30 ], [ 24, 1, 2, 60 ], [ 26, 1, 4, 40 ], [ 27, 1, 6, 120 ], [ 28, 1, 4, 120 ], [ 29, 1, 4, 40 ], [ 30, 1, 3, 60 ], [ 34, 1, 4, 120 ], [ 36, 1, 4, 120 ], [ 39, 1, 3, 120 ], [ 42, 1, 6, 120 ], [ 44, 1, 10, 240 ], [ 45, 1, 6, 120 ], [ 50, 1, 12, 240 ] ] i = 55: Pi = [ 1, 2, 3, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [55,1,1] Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 ( q^4-37*q^3+501*q^2-3039*q+7950 ) q congruent 2 modulo 60: 1/96 ( q^4-36*q^3+444*q^2-2096*q+2688 ) q congruent 3 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 ) q congruent 4 modulo 60: 1/96 ( q^4-36*q^3+452*q^2-2336*q+4160 ) q congruent 5 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 ) q congruent 7 modulo 60: 1/96 ( q^4-37*q^3+501*q^2-2979*q+6594 ) q congruent 8 modulo 60: 1/96 ( q^4-36*q^3+444*q^2-2096*q+2688 ) q congruent 9 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 ) q congruent 11 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2739*q+5082 ) q congruent 13 modulo 60: 1/96 ( q^4-37*q^3+501*q^2-3039*q+7566 ) q congruent 16 modulo 60: 1/96 ( q^4-36*q^3+452*q^2-2336*q+4544 ) q congruent 17 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 ) q congruent 19 modulo 60: 1/96 ( q^4-37*q^3+501*q^2-2979*q+6594 ) q congruent 21 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2799*q+6054 ) q congruent 23 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 ) q congruent 25 modulo 60: 1/96 ( q^4-37*q^3+501*q^2-3039*q+7566 ) q congruent 27 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 ) q congruent 29 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 ) q congruent 31 modulo 60: 1/96 ( q^4-37*q^3+501*q^2-2979*q+6978 ) q congruent 32 modulo 60: 1/96 ( q^4-36*q^3+444*q^2-2096*q+2688 ) q congruent 37 modulo 60: 1/96 ( q^4-37*q^3+501*q^2-3039*q+7566 ) q congruent 41 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2799*q+6054 ) q congruent 43 modulo 60: 1/96 ( q^4-37*q^3+501*q^2-2979*q+6594 ) q congruent 47 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 ) q congruent 49 modulo 60: 1/96 ( q^4-37*q^3+501*q^2-3039*q+7566 ) q congruent 53 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 ) q congruent 59 modulo 60: 1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 8, 77, 77, 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 26 ], [ 4, 1, 1, 46 ], [ 5, 1, 1, 80 ], [ 6, 1, 1, 96 ], [ 7, 1, 1, 40 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 40 ], [ 12, 1, 1, 70 ], [ 13, 1, 1, 72 ], [ 14, 1, 1, 120 ], [ 15, 1, 1, 152 ], [ 16, 1, 1, 176 ], [ 17, 1, 1, 240 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 112 ], [ 20, 1, 1, 144 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 120 ], [ 23, 1, 1, 18 ], [ 24, 1, 1, 36 ], [ 25, 1, 1, 60 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 72 ], [ 29, 1, 1, 144 ], [ 30, 1, 1, 144 ], [ 31, 1, 1, 168 ], [ 32, 1, 1, 224 ], [ 33, 1, 1, 144 ], [ 34, 1, 1, 96 ], [ 35, 1, 1, 144 ], [ 36, 1, 1, 48 ], [ 37, 1, 1, 96 ], [ 38, 1, 1, 288 ], [ 39, 1, 1, 24 ], [ 40, 1, 1, 36 ], [ 41, 1, 1, 48 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 44, 1, 1, 48 ], [ 45, 1, 1, 96 ], [ 46, 1, 1, 192 ], [ 47, 1, 1, 144 ], [ 48, 1, 1, 96 ], [ 51, 1, 1, 48 ], [ 53, 1, 1, 96 ] ] k = 2: F-action on Pi is () [55,1,2] Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^3-16*q^2+83*q-148 ) q congruent 2 modulo 60: 1/16 q ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 60: 1/16 ( q^4-17*q^3+95*q^2-187*q+84 ) q congruent 4 modulo 60: 1/16 q ( q^3-16*q^2+80*q-128 ) q congruent 5 modulo 60: 1/16 phi1 ( q^3-16*q^2+79*q-120 ) q congruent 7 modulo 60: 1/16 ( q^4-17*q^3+99*q^2-219*q+112 ) q congruent 8 modulo 60: 1/16 q ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 60: 1/16 phi1 ( q^3-16*q^2+79*q-120 ) q congruent 11 modulo 60: 1/16 ( q^4-17*q^3+95*q^2-187*q+84 ) q congruent 13 modulo 60: 1/16 phi1 ( q^3-16*q^2+83*q-148 ) q congruent 16 modulo 60: 1/16 q ( q^3-16*q^2+80*q-128 ) q congruent 17 modulo 60: 1/16 phi1 ( q^3-16*q^2+79*q-120 ) q congruent 19 modulo 60: 1/16 ( q^4-17*q^3+99*q^2-219*q+112 ) q congruent 21 modulo 60: 1/16 phi1 ( q^3-16*q^2+79*q-120 ) q congruent 23 modulo 60: 1/16 ( q^4-17*q^3+95*q^2-187*q+84 ) q congruent 25 modulo 60: 1/16 phi1 ( q^3-16*q^2+83*q-148 ) q congruent 27 modulo 60: 1/16 ( q^4-17*q^3+95*q^2-187*q+84 ) q congruent 29 modulo 60: 1/16 phi1 ( q^3-16*q^2+79*q-120 ) q congruent 31 modulo 60: 1/16 ( q^4-17*q^3+99*q^2-219*q+112 ) q congruent 32 modulo 60: 1/16 q ( q^3-16*q^2+76*q-96 ) q congruent 37 modulo 60: 1/16 phi1 ( q^3-16*q^2+83*q-148 ) q congruent 41 modulo 60: 1/16 phi1 ( q^3-16*q^2+79*q-120 ) q congruent 43 modulo 60: 1/16 ( q^4-17*q^3+99*q^2-219*q+112 ) q congruent 47 modulo 60: 1/16 ( q^4-17*q^3+95*q^2-187*q+84 ) q congruent 49 modulo 60: 1/16 phi1 ( q^3-16*q^2+83*q-148 ) q congruent 53 modulo 60: 1/16 phi1 ( q^3-16*q^2+79*q-120 ) q congruent 59 modulo 60: 1/16 ( q^4-17*q^3+95*q^2-187*q+84 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 7, 77, 30, 30, 81 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 4, 1, 1, 18 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 18 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], [ 16, 1, 1, 48 ], [ 17, 1, 1, 72 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 24 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 20 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 12 ], [ 28, 1, 2, 12 ], [ 29, 1, 2, 24 ], [ 30, 1, 1, 24 ], [ 31, 1, 1, 12 ], [ 31, 1, 2, 28 ], [ 32, 1, 1, 48 ], [ 33, 1, 1, 48 ], [ 34, 1, 2, 16 ], [ 35, 1, 1, 24 ], [ 35, 1, 3, 24 ], [ 36, 1, 2, 8 ], [ 38, 1, 5, 48 ], [ 39, 1, 4, 4 ], [ 40, 1, 1, 12 ], [ 41, 1, 6, 8 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 44, 1, 2, 8 ], [ 45, 1, 2, 16 ], [ 46, 1, 2, 32 ], [ 47, 1, 1, 24 ], [ 47, 1, 2, 24 ], [ 48, 1, 2, 16 ], [ 51, 1, 2, 8 ], [ 53, 1, 3, 16 ] ] k = 3: F-action on Pi is () [55,1,3] Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^3-6*q^2+3*q+24 ) q congruent 2 modulo 60: 1/12 q phi2 ( q^2-7*q+10 ) q congruent 3 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/12 phi1 ( q^3-5*q^2+16 ) q congruent 5 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/12 phi1 ( q^3-6*q^2+3*q+24 ) q congruent 8 modulo 60: 1/12 q phi2 ( q^2-7*q+10 ) q congruent 9 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/12 phi1 ( q^3-6*q^2+3*q+24 ) q congruent 16 modulo 60: 1/12 phi1 ( q^3-5*q^2+16 ) q congruent 17 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/12 phi1 ( q^3-6*q^2+3*q+24 ) q congruent 21 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/12 phi1 ( q^3-6*q^2+3*q+24 ) q congruent 27 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/12 phi1 ( q^3-6*q^2+3*q+24 ) q congruent 32 modulo 60: 1/12 q phi2 ( q^2-7*q+10 ) q congruent 37 modulo 60: 1/12 phi1 ( q^3-6*q^2+3*q+24 ) q congruent 41 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/12 phi1 ( q^3-6*q^2+3*q+24 ) q congruent 47 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/12 phi1 ( q^3-6*q^2+3*q+24 ) q congruent 53 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/12 q phi2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30, 77, 30, 30, 81, 14, 83, 83, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 27, 1, 5, 6 ], [ 32, 1, 1, 8 ], [ 38, 1, 3, 36 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], [ 45, 1, 3, 12 ], [ 46, 1, 3, 24 ], [ 53, 1, 16, 12 ] ] k = 4: F-action on Pi is () [55,1,4] Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/16 q phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 19, 72, 19, 76, 76, 20, 97, 59, 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 33, 1, 2, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 51, 1, 7, 8 ], [ 53, 1, 11, 16 ] ] k = 5: F-action on Pi is () [55,1,5] Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 2 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 4 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 7 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 8 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 11 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 16 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 19 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 23 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 27 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 31 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 32 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 43 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 47 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 59 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-18 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 3, 68, 7, 7, 69, 30, 81, 81, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 12, 1, 1, 6 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 8 ], [ 20, 1, 2, 48 ], [ 22, 1, 2, 8 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 28, 1, 2, 24 ], [ 31, 1, 2, 24 ], [ 33, 1, 1, 48 ], [ 33, 1, 2, 16 ], [ 35, 1, 3, 48 ], [ 37, 1, 2, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 40, 1, 1, 12 ], [ 40, 1, 3, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 43, 1, 8, 16 ], [ 43, 1, 12, 32 ], [ 44, 1, 5, 16 ], [ 47, 1, 2, 48 ], [ 48, 1, 3, 32 ], [ 51, 1, 5, 16 ], [ 51, 1, 6, 16 ], [ 53, 1, 9, 32 ] ] k = 6: F-action on Pi is (2,5) [55,1,6] Dynkin type is A_2(q) + A_1(q^2) + T(phi1^2 phi4) Order of center |Z^F|: phi1^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 2 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 4 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 7 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 8 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 11 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 13 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 16 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 19 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 21 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 23 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 25 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 27 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 29 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 31 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 32 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 41 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 43 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 49 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 53 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 59 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 16, 19, 73, 97, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 3, 8 ], [ 16, 1, 2, 8 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 33, 1, 4, 16 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 12 ], [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 48, 1, 8, 16 ], [ 51, 1, 7, 8 ], [ 53, 1, 10, 16 ] ] k = 7: F-action on Pi is (2,5) [55,1,7] Dynkin type is A_2(q) + A_1(q^2) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 ( q^2-2*q-5 ) q congruent 2 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/12 q phi1 ( q^2-q-4 ) q congruent 5 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/12 q phi1 ( q^2-2*q-5 ) q congruent 8 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/12 q phi1 ( q^2-2*q-5 ) q congruent 16 modulo 60: 1/12 q phi1 ( q^2-q-4 ) q congruent 17 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/12 q phi1 ( q^2-2*q-5 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/12 q phi1 ( q^2-2*q-5 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/12 q phi1 ( q^2-2*q-5 ) q congruent 32 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 q phi1 ( q^2-2*q-5 ) q congruent 41 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/12 q phi1 ( q^2-2*q-5 ) q congruent 47 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/12 q phi1 ( q^2-2*q-5 ) q congruent 53 modulo 60: 1/12 q phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/12 q phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 96, 82, 60, 36, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 32, 1, 2, 4 ], [ 38, 1, 4, 12 ], [ 44, 1, 7, 6 ], [ 53, 1, 15, 12 ] ] k = 8: F-action on Pi is (2,5) [55,1,8] Dynkin type is A_2(q) + A_1(q^2) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 q phi1 ( q^2-4*q-1 ) q congruent 2 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/16 q phi1^2 ( q-3 ) q congruent 4 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 5 modulo 60: 1/16 phi1 ( q^3-4*q^2+3*q-4 ) q congruent 7 modulo 60: 1/16 phi1^2 phi2 ( q-4 ) q congruent 8 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/16 phi1 ( q^3-4*q^2+3*q-4 ) q congruent 11 modulo 60: 1/16 q phi1^2 ( q-3 ) q congruent 13 modulo 60: 1/16 q phi1 ( q^2-4*q-1 ) q congruent 16 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 17 modulo 60: 1/16 phi1 ( q^3-4*q^2+3*q-4 ) q congruent 19 modulo 60: 1/16 phi1^2 phi2 ( q-4 ) q congruent 21 modulo 60: 1/16 phi1 ( q^3-4*q^2+3*q-4 ) q congruent 23 modulo 60: 1/16 q phi1^2 ( q-3 ) q congruent 25 modulo 60: 1/16 q phi1 ( q^2-4*q-1 ) q congruent 27 modulo 60: 1/16 q phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 ( q^3-4*q^2+3*q-4 ) q congruent 31 modulo 60: 1/16 phi1^2 phi2 ( q-4 ) q congruent 32 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/16 q phi1 ( q^2-4*q-1 ) q congruent 41 modulo 60: 1/16 phi1 ( q^3-4*q^2+3*q-4 ) q congruent 43 modulo 60: 1/16 phi1^2 phi2 ( q-4 ) q congruent 47 modulo 60: 1/16 q phi1^2 ( q-3 ) q congruent 49 modulo 60: 1/16 q phi1 ( q^2-4*q-1 ) q congruent 53 modulo 60: 1/16 phi1 ( q^3-4*q^2+3*q-4 ) q congruent 59 modulo 60: 1/16 q phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 7, 76, 81, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 29, 1, 2, 8 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 36, 1, 2, 8 ], [ 38, 1, 2, 16 ], [ 39, 1, 4, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 7, 8 ], [ 43, 1, 2, 16 ], [ 44, 1, 8, 8 ], [ 47, 1, 3, 8 ], [ 47, 1, 4, 8 ], [ 51, 1, 2, 8 ], [ 53, 1, 4, 16 ] ] k = 9: F-action on Pi is (2,5) [55,1,9] Dynkin type is A_2(q) + A_1(q^2) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 2 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) q congruent 4 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 7 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) q congruent 8 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 11 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) q congruent 13 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 16 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 19 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) q congruent 21 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 23 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) q congruent 25 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 27 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) q congruent 29 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 31 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) q congruent 32 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 41 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 43 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) q congruent 47 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) q congruent 49 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 53 modulo 60: 1/32 phi1^2 ( q^2-11*q+30 ) q congruent 59 modulo 60: 1/32 ( q^4-13*q^3+53*q^2-67*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19, 30, 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 12, 1, 1, 10 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 12 ], [ 18, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 8 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 32 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 4 ], [ 26, 1, 1, 16 ], [ 28, 1, 3, 8 ], [ 29, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 8 ], [ 33, 1, 2, 8 ], [ 33, 1, 4, 32 ], [ 35, 1, 2, 16 ], [ 36, 1, 1, 16 ], [ 37, 1, 1, 32 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 40, 1, 1, 24 ], [ 40, 1, 3, 4 ], [ 41, 1, 2, 16 ], [ 41, 1, 3, 16 ], [ 43, 1, 1, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 47, 1, 3, 16 ], [ 48, 1, 7, 32 ], [ 51, 1, 1, 16 ], [ 51, 1, 6, 16 ], [ 53, 1, 2, 32 ] ] k = 10: F-action on Pi is (2,5) [55,1,10] Dynkin type is A_2(q) + A_1(q^2) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1^3 ( q-6 ) q congruent 2 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 4 modulo 60: 1/96 q ( q^3-8*q^2+12*q+16 ) q congruent 5 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-30 ) q congruent 7 modulo 60: 1/96 phi1 ( q^3-8*q^2+13*q+6 ) q congruent 8 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-30 ) q congruent 11 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 13 modulo 60: 1/96 phi1^3 ( q-6 ) q congruent 16 modulo 60: 1/96 q ( q^3-8*q^2+12*q+16 ) q congruent 17 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-30 ) q congruent 19 modulo 60: 1/96 phi1 ( q^3-8*q^2+13*q+6 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-30 ) q congruent 23 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 25 modulo 60: 1/96 phi1^3 ( q-6 ) q congruent 27 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 29 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-30 ) q congruent 31 modulo 60: 1/96 phi1 ( q^3-8*q^2+13*q+6 ) q congruent 32 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/96 phi1^3 ( q-6 ) q congruent 41 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-30 ) q congruent 43 modulo 60: 1/96 phi1 ( q^3-8*q^2+13*q+6 ) q congruent 47 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-18 ) q congruent 49 modulo 60: 1/96 phi1^3 ( q-6 ) q congruent 53 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-30 ) q congruent 59 modulo 60: 1/96 phi1 ( q^3-8*q^2+21*q-18 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 69, 20, 27, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 12 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 8 ], [ 13, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 48 ], [ 20, 1, 2, 48 ], [ 22, 1, 2, 24 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 4, 36 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 2, 24 ], [ 35, 1, 4, 48 ], [ 38, 1, 6, 96 ], [ 39, 1, 3, 24 ], [ 40, 1, 3, 12 ], [ 41, 1, 10, 48 ], [ 43, 1, 12, 96 ], [ 44, 1, 10, 48 ], [ 47, 1, 4, 48 ], [ 51, 1, 5, 48 ], [ 53, 1, 19, 96 ] ] k = 11: F-action on Pi is (1,3) [55,1,11] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 7 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 11 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 13 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 19 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 21 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 23 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 25 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 27 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 29 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 31 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 41 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 43 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 47 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 49 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 53 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 59 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20, 20, 71, 19, 76, 76, 20, 96, 60, 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 33, 1, 6, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 51, 1, 4, 8 ], [ 53, 1, 13, 16 ] ] k = 12: F-action on Pi is (1,3) [55,1,12] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 2 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-8 ) q congruent 3 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 4 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 5 modulo 60: 1/12 phi2 ( q^3-6*q^2+15*q-16 ) q congruent 7 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 8 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-8 ) q congruent 9 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 11 modulo 60: 1/12 phi2 ( q^3-6*q^2+15*q-16 ) q congruent 13 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 16 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 17 modulo 60: 1/12 phi2 ( q^3-6*q^2+15*q-16 ) q congruent 19 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 21 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 23 modulo 60: 1/12 phi2 ( q^3-6*q^2+15*q-16 ) q congruent 25 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 27 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/12 phi2 ( q^3-6*q^2+15*q-16 ) q congruent 31 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 32 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-8 ) q congruent 37 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 41 modulo 60: 1/12 phi2 ( q^3-6*q^2+15*q-16 ) q congruent 43 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 47 modulo 60: 1/12 phi2 ( q^3-6*q^2+15*q-16 ) q congruent 49 modulo 60: 1/12 q phi1^2 ( q-3 ) q congruent 53 modulo 60: 1/12 phi2 ( q^3-6*q^2+15*q-16 ) q congruent 59 modulo 60: 1/12 phi2 ( q^3-6*q^2+15*q-16 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 78, 78, 9, 82, 31, 31, 78, 38, 84, 84, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 32, 1, 3, 8 ], [ 38, 1, 11, 36 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 46, 1, 4, 24 ], [ 53, 1, 18, 12 ] ] k = 13: F-action on Pi is (1,3) [55,1,13] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^3-12*q^2+49*q-74 ) q congruent 2 modulo 60: 1/16 ( q^4-12*q^3+48*q^2-80*q+48 ) q congruent 3 modulo 60: 1/16 ( q^4-13*q^3+61*q^2-135*q+126 ) q congruent 4 modulo 60: 1/16 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/16 ( q^4-13*q^3+65*q^2-155*q+150 ) q congruent 7 modulo 60: 1/16 ( q^4-13*q^3+61*q^2-135*q+126 ) q congruent 8 modulo 60: 1/16 ( q^4-12*q^3+48*q^2-80*q+48 ) q congruent 9 modulo 60: 1/16 phi1 ( q^3-12*q^2+49*q-74 ) q congruent 11 modulo 60: 1/16 ( q^4-13*q^3+65*q^2-167*q+202 ) q congruent 13 modulo 60: 1/16 phi1 ( q^3-12*q^2+49*q-74 ) q congruent 16 modulo 60: 1/16 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/16 ( q^4-13*q^3+65*q^2-155*q+150 ) q congruent 19 modulo 60: 1/16 ( q^4-13*q^3+61*q^2-135*q+126 ) q congruent 21 modulo 60: 1/16 phi1 ( q^3-12*q^2+49*q-74 ) q congruent 23 modulo 60: 1/16 ( q^4-13*q^3+65*q^2-167*q+202 ) q congruent 25 modulo 60: 1/16 phi1 ( q^3-12*q^2+49*q-74 ) q congruent 27 modulo 60: 1/16 ( q^4-13*q^3+61*q^2-135*q+126 ) q congruent 29 modulo 60: 1/16 ( q^4-13*q^3+65*q^2-155*q+150 ) q congruent 31 modulo 60: 1/16 ( q^4-13*q^3+61*q^2-135*q+126 ) q congruent 32 modulo 60: 1/16 ( q^4-12*q^3+48*q^2-80*q+48 ) q congruent 37 modulo 60: 1/16 phi1 ( q^3-12*q^2+49*q-74 ) q congruent 41 modulo 60: 1/16 ( q^4-13*q^3+65*q^2-155*q+150 ) q congruent 43 modulo 60: 1/16 ( q^4-13*q^3+61*q^2-135*q+126 ) q congruent 47 modulo 60: 1/16 ( q^4-13*q^3+65*q^2-167*q+202 ) q congruent 49 modulo 60: 1/16 phi1 ( q^3-12*q^2+49*q-74 ) q congruent 53 modulo 60: 1/16 ( q^4-13*q^3+65*q^2-155*q+150 ) q congruent 59 modulo 60: 1/16 ( q^4-13*q^3+65*q^2-167*q+202 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 5, 67, 7, 69, 69, 5, 82, 31, 31, 78 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 14 ], [ 4, 1, 2, 18 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 18 ], [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], [ 16, 1, 3, 48 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], [ 20, 1, 3, 24 ], [ 20, 1, 4, 24 ], [ 22, 1, 3, 20 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 12 ], [ 29, 1, 3, 24 ], [ 30, 1, 3, 24 ], [ 31, 1, 3, 28 ], [ 31, 1, 4, 12 ], [ 32, 1, 3, 48 ], [ 33, 1, 8, 48 ], [ 34, 1, 3, 16 ], [ 35, 1, 6, 24 ], [ 35, 1, 8, 24 ], [ 36, 1, 3, 8 ], [ 38, 1, 8, 48 ], [ 39, 1, 4, 4 ], [ 40, 1, 6, 12 ], [ 41, 1, 6, 8 ], [ 42, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 44, 1, 8, 8 ], [ 45, 1, 5, 16 ], [ 46, 1, 5, 32 ], [ 47, 1, 7, 24 ], [ 47, 1, 8, 24 ], [ 48, 1, 5, 16 ], [ 51, 1, 8, 8 ], [ 53, 1, 8, 16 ] ] k = 14: F-action on Pi is (1,3) [55,1,14] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 2 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) q congruent 4 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 7 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) q congruent 8 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 11 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 16 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 19 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 23 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 27 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 31 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) q congruent 32 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 43 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) q congruent 47 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-8*q^2+23*q-24 ) q congruent 59 modulo 60: 1/32 ( q^4-9*q^3+31*q^2-51*q+36 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 69, 5, 68, 7, 7, 69, 28, 82, 82, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 18 ], [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 12, 1, 2, 6 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 24 ], [ 16, 1, 4, 8 ], [ 20, 1, 3, 48 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 28, 1, 3, 24 ], [ 31, 1, 3, 24 ], [ 33, 1, 6, 16 ], [ 33, 1, 8, 48 ], [ 35, 1, 6, 48 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 40, 1, 2, 8 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 16 ], [ 41, 1, 4, 16 ], [ 43, 1, 3, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 47, 1, 7, 48 ], [ 48, 1, 4, 32 ], [ 51, 1, 3, 16 ], [ 51, 1, 10, 16 ], [ 53, 1, 6, 32 ] ] k = 15: F-action on Pi is (1,3) [55,1,15] Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi2^4) Order of center |Z^F|: phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-28*q^2+267*q-912 ) q congruent 2 modulo 60: 1/96 ( q^4-28*q^3+260*q^2-928*q+1024 ) q congruent 3 modulo 60: 1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 ) q congruent 4 modulo 60: 1/96 ( q^4-28*q^3+252*q^2-720*q+384 ) q congruent 5 modulo 60: 1/96 ( q^4-29*q^3+303*q^2-1387*q+2360 ) q congruent 7 modulo 60: 1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 ) q congruent 8 modulo 60: 1/96 ( q^4-28*q^3+260*q^2-928*q+1024 ) q congruent 9 modulo 60: 1/96 ( q^4-29*q^3+295*q^2-1179*q+1296 ) q congruent 11 modulo 60: 1/96 ( q^4-29*q^3+303*q^2-1447*q+3212 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-28*q^2+267*q-912 ) q congruent 16 modulo 60: 1/96 q ( q^3-28*q^2+252*q-720 ) q congruent 17 modulo 60: 1/96 ( q^4-29*q^3+303*q^2-1387*q+2360 ) q congruent 19 modulo 60: 1/96 ( q^4-29*q^3+295*q^2-1239*q+2148 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-28*q^2+267*q-912 ) q congruent 23 modulo 60: 1/96 ( q^4-29*q^3+303*q^2-1447*q+3212 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-28*q^2+267*q-912 ) q congruent 27 modulo 60: 1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 ) q congruent 29 modulo 60: 1/96 ( q^4-29*q^3+303*q^2-1387*q+2744 ) q congruent 31 modulo 60: 1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 ) q congruent 32 modulo 60: 1/96 ( q^4-28*q^3+260*q^2-928*q+1024 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-28*q^2+267*q-912 ) q congruent 41 modulo 60: 1/96 ( q^4-29*q^3+303*q^2-1387*q+2360 ) q congruent 43 modulo 60: 1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 ) q congruent 47 modulo 60: 1/96 ( q^4-29*q^3+303*q^2-1447*q+3212 ) q congruent 49 modulo 60: 1/96 ( q^4-29*q^3+295*q^2-1179*q+1296 ) q congruent 53 modulo 60: 1/96 ( q^4-29*q^3+303*q^2-1387*q+2360 ) q congruent 59 modulo 60: 1/96 ( q^4-29*q^3+303*q^2-1447*q+3596 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 67, 2, 69, 5, 5, 67, 31, 78, 78, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 26 ], [ 4, 1, 2, 46 ], [ 5, 1, 2, 80 ], [ 6, 1, 2, 96 ], [ 7, 1, 2, 40 ], [ 8, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 40 ], [ 12, 1, 2, 70 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 120 ], [ 15, 1, 2, 152 ], [ 16, 1, 3, 176 ], [ 17, 1, 4, 240 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 112 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 48 ], [ 22, 1, 4, 120 ], [ 23, 1, 2, 18 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 60 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 72 ], [ 29, 1, 4, 144 ], [ 30, 1, 3, 144 ], [ 31, 1, 4, 168 ], [ 32, 1, 3, 224 ], [ 33, 1, 8, 144 ], [ 34, 1, 4, 96 ], [ 35, 1, 8, 144 ], [ 36, 1, 4, 48 ], [ 37, 1, 3, 96 ], [ 38, 1, 12, 288 ], [ 39, 1, 3, 24 ], [ 40, 1, 6, 36 ], [ 41, 1, 9, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 10, 48 ], [ 45, 1, 6, 96 ], [ 46, 1, 6, 192 ], [ 47, 1, 8, 144 ], [ 48, 1, 6, 96 ], [ 51, 1, 9, 48 ], [ 53, 1, 20, 96 ] ] k = 16: F-action on Pi is (1,3)(2,5) [55,1,16] Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-12*q^2+47*q-60 ) q congruent 2 modulo 60: 1/96 ( q^4-12*q^3+36*q^2+16*q-96 ) q congruent 3 modulo 60: 1/96 ( q^4-13*q^3+59*q^2-119*q+96 ) q congruent 4 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/96 ( q^4-13*q^3+51*q^2-43*q-60 ) q congruent 7 modulo 60: 1/96 ( q^4-13*q^3+59*q^2-119*q+96 ) q congruent 8 modulo 60: 1/96 ( q^4-12*q^3+36*q^2+16*q-96 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-12*q^2+47*q-60 ) q congruent 11 modulo 60: 1/96 ( q^4-13*q^3+51*q^2-55*q-24 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-12*q^2+47*q-60 ) q congruent 16 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/96 ( q^4-13*q^3+51*q^2-43*q-60 ) q congruent 19 modulo 60: 1/96 ( q^4-13*q^3+59*q^2-119*q+96 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-12*q^2+47*q-60 ) q congruent 23 modulo 60: 1/96 ( q^4-13*q^3+51*q^2-55*q-24 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-12*q^2+47*q-60 ) q congruent 27 modulo 60: 1/96 ( q^4-13*q^3+59*q^2-119*q+96 ) q congruent 29 modulo 60: 1/96 ( q^4-13*q^3+51*q^2-43*q-60 ) q congruent 31 modulo 60: 1/96 ( q^4-13*q^3+59*q^2-119*q+96 ) q congruent 32 modulo 60: 1/96 ( q^4-12*q^3+36*q^2+16*q-96 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-12*q^2+47*q-60 ) q congruent 41 modulo 60: 1/96 ( q^4-13*q^3+51*q^2-43*q-60 ) q congruent 43 modulo 60: 1/96 ( q^4-13*q^3+59*q^2-119*q+96 ) q congruent 47 modulo 60: 1/96 ( q^4-13*q^3+51*q^2-55*q-24 ) q congruent 49 modulo 60: 1/96 phi1 ( q^3-12*q^2+47*q-60 ) q congruent 53 modulo 60: 1/96 ( q^4-13*q^3+51*q^2-43*q-60 ) q congruent 59 modulo 60: 1/96 ( q^4-13*q^3+51*q^2-55*q-24 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 68, 19, 28, 96 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 12 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 12 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 48 ], [ 20, 1, 3, 48 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 36 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 31, 1, 3, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 6, 24 ], [ 35, 1, 5, 48 ], [ 38, 1, 7, 96 ], [ 39, 1, 1, 24 ], [ 40, 1, 2, 12 ], [ 41, 1, 3, 48 ], [ 43, 1, 3, 96 ], [ 44, 1, 1, 48 ], [ 47, 1, 9, 48 ], [ 51, 1, 10, 48 ], [ 53, 1, 5, 96 ] ] k = 17: F-action on Pi is (1,3)(2,5) [55,1,17] Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^3 ( q-2 ) q congruent 2 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 3 modulo 60: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 4 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/16 phi1^2 ( q^2-3*q-2 ) q congruent 7 modulo 60: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 8 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 9 modulo 60: 1/16 phi1^3 ( q-2 ) q congruent 11 modulo 60: 1/16 phi1 ( q^3-4*q^2+q-2 ) q congruent 13 modulo 60: 1/16 phi1^3 ( q-2 ) q congruent 16 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/16 phi1^2 ( q^2-3*q-2 ) q congruent 19 modulo 60: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 21 modulo 60: 1/16 phi1^3 ( q-2 ) q congruent 23 modulo 60: 1/16 phi1 ( q^3-4*q^2+q-2 ) q congruent 25 modulo 60: 1/16 phi1^3 ( q-2 ) q congruent 27 modulo 60: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 29 modulo 60: 1/16 phi1^2 ( q^2-3*q-2 ) q congruent 31 modulo 60: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 32 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 37 modulo 60: 1/16 phi1^3 ( q-2 ) q congruent 41 modulo 60: 1/16 phi1^2 ( q^2-3*q-2 ) q congruent 43 modulo 60: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 47 modulo 60: 1/16 phi1 ( q^3-4*q^2+q-2 ) q congruent 49 modulo 60: 1/16 phi1^3 ( q-2 ) q congruent 53 modulo 60: 1/16 phi1^2 ( q^2-3*q-2 ) q congruent 59 modulo 60: 1/16 phi1 ( q^3-4*q^2+q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 7, 76, 82, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 29, 1, 3, 8 ], [ 30, 1, 4, 8 ], [ 31, 1, 3, 4 ], [ 31, 1, 4, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 35, 1, 5, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 3, 8 ], [ 38, 1, 10, 16 ], [ 39, 1, 4, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 7, 8 ], [ 43, 1, 4, 16 ], [ 44, 1, 2, 8 ], [ 47, 1, 9, 8 ], [ 47, 1, 10, 8 ], [ 51, 1, 8, 8 ], [ 53, 1, 7, 16 ] ] k = 18: F-action on Pi is (1,3)(2,5) [55,1,18] Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^2 phi2 q congruent 2 modulo 60: 1/12 q phi2^2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1^2 phi2 q congruent 4 modulo 60: 1/12 q^2 phi1 phi2 q congruent 5 modulo 60: 1/12 q phi2 ( q^2-2*q-1 ) q congruent 7 modulo 60: 1/12 q phi1^2 phi2 q congruent 8 modulo 60: 1/12 q phi2^2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1^2 phi2 q congruent 11 modulo 60: 1/12 q phi2 ( q^2-2*q-1 ) q congruent 13 modulo 60: 1/12 q phi1^2 phi2 q congruent 16 modulo 60: 1/12 q^2 phi1 phi2 q congruent 17 modulo 60: 1/12 q phi2 ( q^2-2*q-1 ) q congruent 19 modulo 60: 1/12 q phi1^2 phi2 q congruent 21 modulo 60: 1/12 q phi1^2 phi2 q congruent 23 modulo 60: 1/12 q phi2 ( q^2-2*q-1 ) q congruent 25 modulo 60: 1/12 q phi1^2 phi2 q congruent 27 modulo 60: 1/12 q phi1^2 phi2 q congruent 29 modulo 60: 1/12 q phi2 ( q^2-2*q-1 ) q congruent 31 modulo 60: 1/12 q phi1^2 phi2 q congruent 32 modulo 60: 1/12 q phi2^2 ( q-2 ) q congruent 37 modulo 60: 1/12 q phi1^2 phi2 q congruent 41 modulo 60: 1/12 q phi2 ( q^2-2*q-1 ) q congruent 43 modulo 60: 1/12 q phi1^2 phi2 q congruent 47 modulo 60: 1/12 q phi2 ( q^2-2*q-1 ) q congruent 49 modulo 60: 1/12 q phi1^2 phi2 q congruent 53 modulo 60: 1/12 q phi2 ( q^2-2*q-1 ) q congruent 59 modulo 60: 1/12 q phi2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 27, 95, 81, 59, 36, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 32, 1, 2, 4 ], [ 38, 1, 9, 12 ], [ 44, 1, 3, 6 ], [ 53, 1, 17, 12 ] ] k = 19: F-action on Pi is (1,3)(2,5) [55,1,19] Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi2^2 phi4) Order of center |Z^F|: phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 7 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 11 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 13 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 19 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 21 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 23 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 25 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 27 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 29 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 31 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 41 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 43 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 47 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 49 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 53 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 59 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 71, 17, 20, 74, 98, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 2, 8 ], [ 16, 1, 4, 8 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 33, 1, 10, 16 ], [ 39, 1, 5, 4 ], [ 40, 1, 6, 12 ], [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 48, 1, 9, 16 ], [ 51, 1, 4, 8 ], [ 53, 1, 14, 16 ] ] k = 20: F-action on Pi is (1,3)(2,5) [55,1,20] Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 2 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) q congruent 4 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 7 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) q congruent 8 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 11 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 16 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 19 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 23 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 27 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 31 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) q congruent 32 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 43 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) q congruent 47 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 59 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-43*q+48 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 71, 69, 20, 31, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 10 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 12 ], [ 18, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 32 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 16 ], [ 28, 1, 2, 8 ], [ 29, 1, 4, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 4, 8 ], [ 33, 1, 6, 8 ], [ 33, 1, 10, 32 ], [ 35, 1, 7, 16 ], [ 36, 1, 4, 16 ], [ 37, 1, 2, 16 ], [ 37, 1, 3, 32 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 40, 1, 2, 4 ], [ 40, 1, 6, 24 ], [ 41, 1, 2, 16 ], [ 41, 1, 10, 16 ], [ 43, 1, 8, 16 ], [ 43, 1, 13, 32 ], [ 44, 1, 5, 16 ], [ 47, 1, 10, 16 ], [ 48, 1, 10, 32 ], [ 51, 1, 3, 16 ], [ 51, 1, 9, 16 ], [ 53, 1, 12, 32 ] ] i = 56: Pi = [ 1, 2, 4, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [56,1,1] Dynkin type is A_3(q) + A_1(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2095*q+4708 ) q congruent 2 modulo 60: 1/96 ( q^4-32*q^3+356*q^2-1552*q+1920 ) q congruent 3 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 ) q congruent 4 modulo 60: 1/96 ( q^4-32*q^3+356*q^2-1616*q+2560 ) q congruent 5 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 ) q congruent 7 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2059*q+3976 ) q congruent 8 modulo 60: 1/96 ( q^4-32*q^3+356*q^2-1552*q+1920 ) q congruent 9 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 ) q congruent 11 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-1995*q+3432 ) q congruent 13 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2095*q+4516 ) q congruent 16 modulo 60: 1/96 ( q^4-32*q^3+356*q^2-1616*q+2752 ) q congruent 17 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 ) q congruent 19 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2059*q+3976 ) q congruent 21 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2031*q+3972 ) q congruent 23 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 ) q congruent 25 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2095*q+4516 ) q congruent 27 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 ) q congruent 29 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 ) q congruent 31 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2059*q+4168 ) q congruent 32 modulo 60: 1/96 ( q^4-32*q^3+356*q^2-1552*q+1920 ) q congruent 37 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2095*q+4516 ) q congruent 41 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2031*q+3972 ) q congruent 43 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2059*q+3976 ) q congruent 47 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 ) q congruent 49 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2095*q+4516 ) q congruent 53 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 ) q congruent 59 modulo 60: 1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 4, 68, 8, 77, 70, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 20 ], [ 4, 1, 1, 34 ], [ 5, 1, 1, 32 ], [ 6, 1, 1, 40 ], [ 7, 1, 1, 28 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 14 ], [ 11, 1, 1, 36 ], [ 12, 1, 1, 68 ], [ 13, 1, 1, 72 ], [ 14, 1, 1, 64 ], [ 15, 1, 1, 64 ], [ 16, 1, 1, 40 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 72 ], [ 20, 1, 1, 56 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 64 ], [ 23, 1, 1, 30 ], [ 24, 1, 1, 50 ], [ 25, 1, 1, 84 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 84 ], [ 29, 1, 1, 96 ], [ 30, 1, 1, 96 ], [ 31, 1, 1, 64 ], [ 34, 1, 1, 96 ], [ 35, 1, 1, 72 ], [ 36, 1, 1, 96 ], [ 37, 1, 1, 96 ], [ 39, 1, 1, 72 ], [ 40, 1, 1, 144 ], [ 41, 1, 1, 144 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 44, 1, 1, 48 ], [ 45, 1, 1, 96 ], [ 48, 1, 1, 96 ], [ 50, 1, 1, 96 ], [ 51, 1, 1, 96 ], [ 52, 1, 1, 144 ], [ 53, 1, 1, 96 ] ] k = 2: F-action on Pi is () [56,1,2] Dynkin type is A_3(q) + A_1(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-88 ) q congruent 2 modulo 60: 1/16 q ( q^3-14*q^2+60*q-72 ) q congruent 3 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-133*q+48 ) q congruent 4 modulo 60: 1/16 q ( q^3-14*q^2+60*q-80 ) q congruent 5 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-80 ) q congruent 7 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-141*q+56 ) q congruent 8 modulo 60: 1/16 q ( q^3-14*q^2+60*q-72 ) q congruent 9 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-80 ) q congruent 11 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-133*q+48 ) q congruent 13 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-88 ) q congruent 16 modulo 60: 1/16 q ( q^3-14*q^2+60*q-80 ) q congruent 17 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-80 ) q congruent 19 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-141*q+56 ) q congruent 21 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-80 ) q congruent 23 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-133*q+48 ) q congruent 25 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-88 ) q congruent 27 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-133*q+48 ) q congruent 29 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-80 ) q congruent 31 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-141*q+56 ) q congruent 32 modulo 60: 1/16 q ( q^3-14*q^2+60*q-72 ) q congruent 37 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-88 ) q congruent 41 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-80 ) q congruent 43 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-141*q+56 ) q congruent 47 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-133*q+48 ) q congruent 49 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-88 ) q congruent 53 modulo 60: 1/16 phi1 ( q^3-14*q^2+61*q-80 ) q congruent 59 modulo 60: 1/16 ( q^4-15*q^3+75*q^2-133*q+48 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 68, 7, 77, 30, 19, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 16 ], [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 20, 1, 1, 16 ], [ 20, 1, 2, 8 ], [ 21, 1, 1, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 8 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 8 ], [ 28, 1, 2, 12 ], [ 29, 1, 2, 16 ], [ 30, 1, 1, 16 ], [ 31, 1, 1, 16 ], [ 31, 1, 2, 8 ], [ 34, 1, 1, 16 ], [ 34, 1, 2, 8 ], [ 35, 1, 1, 16 ], [ 35, 1, 3, 8 ], [ 36, 1, 2, 16 ], [ 37, 1, 1, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 6, 16 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 44, 1, 2, 8 ], [ 45, 1, 2, 16 ], [ 48, 1, 1, 16 ], [ 48, 1, 2, 8 ], [ 50, 1, 2, 16 ], [ 51, 1, 2, 16 ], [ 52, 1, 2, 16 ], [ 53, 1, 3, 16 ] ] k = 3: F-action on Pi is () [56,1,3] Dynkin type is A_3(q) + A_1(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^3-5*q^2+14 ) q congruent 2 modulo 60: 1/12 q phi2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 4 modulo 60: 1/12 phi1 ( q^3-4*q^2-2*q+8 ) q congruent 5 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 7 modulo 60: 1/12 phi1 ( q^3-5*q^2+14 ) q congruent 8 modulo 60: 1/12 q phi2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 11 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 13 modulo 60: 1/12 phi1 ( q^3-5*q^2+14 ) q congruent 16 modulo 60: 1/12 phi1 ( q^3-4*q^2-2*q+8 ) q congruent 17 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 19 modulo 60: 1/12 phi1 ( q^3-5*q^2+14 ) q congruent 21 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 23 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 25 modulo 60: 1/12 phi1 ( q^3-5*q^2+14 ) q congruent 27 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 29 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 31 modulo 60: 1/12 phi1 ( q^3-5*q^2+14 ) q congruent 32 modulo 60: 1/12 q phi2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/12 phi1 ( q^3-5*q^2+14 ) q congruent 41 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 43 modulo 60: 1/12 phi1 ( q^3-5*q^2+14 ) q congruent 47 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 49 modulo 60: 1/12 phi1 ( q^3-5*q^2+14 ) q congruent 53 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) q congruent 59 modulo 60: 1/12 q phi2 ( q^2-7*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30, 30, 81, 14, 83, 97, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 2 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 27, 1, 5, 6 ], [ 31, 1, 1, 4 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], [ 45, 1, 3, 12 ], [ 50, 1, 3, 12 ], [ 53, 1, 16, 12 ] ] k = 4: F-action on Pi is () [56,1,4] Dynkin type is A_3(q) + A_1(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/16 q phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/16 q phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 19, 76, 72, 20, 97, 59, 18, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 20, 1, 1, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 4, 4 ], [ 28, 1, 3, 4 ], [ 35, 1, 2, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 11, 16 ] ] k = 5: F-action on Pi is () [56,1,5] Dynkin type is A_3(q) + A_1(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 2 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 4 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 7 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 8 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 11 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 16 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 19 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 23 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 27 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 31 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 32 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 43 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 47 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-8*q^2+19*q-20 ) q congruent 59 modulo 60: 1/32 ( q^4-9*q^3+27*q^2-35*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 7, 3, 69, 30, 81, 72, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 31, 1, 2, 16 ], [ 34, 1, 2, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 16 ], [ 35, 1, 3, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 40, 1, 3, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 43, 1, 8, 16 ], [ 43, 1, 12, 32 ], [ 44, 1, 5, 16 ], [ 48, 1, 2, 16 ], [ 51, 1, 5, 32 ], [ 52, 1, 3, 16 ], [ 52, 1, 9, 16 ], [ 53, 1, 9, 32 ] ] k = 6: F-action on Pi is () [56,1,6] Dynkin type is A_3(q) + A_1(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-166 ) q congruent 2 modulo 60: 1/96 q ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-138 ) q congruent 4 modulo 60: 1/96 q ( q^3-16*q^2+76*q-112 ) q congruent 5 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-150 ) q congruent 7 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-154 ) q congruent 8 modulo 60: 1/96 q ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-150 ) q congruent 11 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-138 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-166 ) q congruent 16 modulo 60: 1/96 q ( q^3-16*q^2+76*q-112 ) q congruent 17 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-150 ) q congruent 19 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-154 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-150 ) q congruent 23 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-138 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-166 ) q congruent 27 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-138 ) q congruent 29 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-150 ) q congruent 31 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-154 ) q congruent 32 modulo 60: 1/96 q ( q^3-16*q^2+76*q-96 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-166 ) q congruent 41 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-150 ) q congruent 43 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-154 ) q congruent 47 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-138 ) q congruent 49 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-166 ) q congruent 53 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-150 ) q congruent 59 modulo 60: 1/96 phi1 ( q^3-16*q^2+85*q-138 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 68, 3, 77, 30, 19, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 24 ], [ 16, 1, 1, 16 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 16 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 36 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 36 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 12 ], [ 31, 1, 2, 16 ], [ 34, 1, 2, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 24 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 24 ], [ 41, 1, 1, 48 ], [ 41, 1, 6, 48 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 44, 1, 1, 48 ], [ 48, 1, 2, 48 ], [ 50, 1, 4, 96 ], [ 52, 1, 2, 48 ], [ 53, 1, 1, 96 ] ] k = 7: F-action on Pi is () [56,1,7] Dynkin type is A_3(q) + A_1(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 2 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/16 phi1^2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 7, 7, 69, 30, 81, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 31, 1, 2, 8 ], [ 34, 1, 2, 8 ], [ 35, 1, 1, 8 ], [ 35, 1, 3, 16 ], [ 37, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 44, 1, 2, 8 ], [ 48, 1, 2, 8 ], [ 48, 1, 3, 16 ], [ 50, 1, 5, 16 ], [ 52, 1, 9, 16 ], [ 53, 1, 3, 16 ] ] k = 8: F-action on Pi is () [56,1,8] Dynkin type is A_3(q) + A_1(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 2 modulo 60: 1/12 q^2 phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 60: 1/12 q phi1 ( q^2-2 ) q congruent 5 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 8 modulo 60: 1/12 q^2 phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 13 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 16 modulo 60: 1/12 q phi1 ( q^2-2 ) q congruent 17 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 19 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 23 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 25 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 29 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 31 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 32 modulo 60: 1/12 q^2 phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 41 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 43 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 47 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 49 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 53 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 59 modulo 60: 1/12 q phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 77, 30, 30, 81, 81, 27, 83, 37, 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 2 ], [ 16, 1, 1, 4 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 2 ], [ 27, 1, 5, 6 ], [ 31, 1, 2, 4 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], [ 50, 1, 6, 12 ], [ 53, 1, 16, 12 ] ] k = 9: F-action on Pi is () [56,1,9] Dynkin type is A_3(q) + A_1(q) + T(phi2^2 phi4) Order of center |Z^F|: phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 7 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 11 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 13 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 19 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 21 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 23 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 25 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 27 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 29 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 31 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 41 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 43 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 47 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 49 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 53 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 59 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 72, 76, 20, 20, 71, 59, 95, 74, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 4, 8 ], [ 20, 1, 2, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 28, 1, 4, 4 ], [ 35, 1, 4, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 51, 1, 4, 16 ], [ 52, 1, 5, 8 ], [ 53, 1, 11, 16 ] ] k = 10: F-action on Pi is () [56,1,10] Dynkin type is A_3(q) + A_1(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 2 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 4 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 7 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 8 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 11 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 16 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 19 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 23 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 27 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 31 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 32 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 43 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 47 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 59 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 3, 7, 69, 69, 5, 81, 27, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 24 ], [ 16, 1, 4, 16 ], [ 20, 1, 2, 24 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 18 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 28, 1, 2, 12 ], [ 28, 1, 4, 24 ], [ 35, 1, 3, 24 ], [ 35, 1, 4, 16 ], [ 37, 1, 2, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 24 ], [ 40, 1, 2, 16 ], [ 40, 1, 6, 48 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 48 ], [ 43, 1, 8, 16 ], [ 43, 1, 12, 32 ], [ 44, 1, 5, 16 ], [ 48, 1, 3, 32 ], [ 51, 1, 3, 32 ], [ 52, 1, 4, 16 ], [ 52, 1, 10, 48 ], [ 53, 1, 9, 32 ] ] k = 11: F-action on Pi is (2,5) [56,1,11] Dynkin type is ^2A_3(q) + A_1(q) + T(phi1^2 phi4) Order of center |Z^F|: phi1^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 2 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 4 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 7 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 8 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 11 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 13 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 16 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 19 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 21 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 23 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 25 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 27 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 29 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 31 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 32 modulo 60: 1/16 q^2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 41 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 43 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 49 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 53 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) q congruent 59 modulo 60: 1/16 phi1 phi2 ( q^2-7*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20, 19, 76, 70, 19, 96, 60, 16, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 28, 1, 1, 4 ], [ 35, 1, 5, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 51, 1, 7, 16 ], [ 52, 1, 8, 8 ], [ 53, 1, 13, 16 ] ] k = 12: F-action on Pi is (2,5) [56,1,12] Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 2 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 3 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 4 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 7 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 8 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 9 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 11 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 13 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 16 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 19 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 21 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 23 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 25 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 27 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 29 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 31 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 32 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 37 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 41 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 43 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 47 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 49 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 53 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 78, 82, 31, 28, 82, 38, 84, 96, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 3, 4 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 2 ], [ 27, 1, 4, 6 ], [ 31, 1, 3, 4 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 50, 1, 7, 12 ], [ 53, 1, 18, 12 ] ] k = 13: F-action on Pi is (2,5) [56,1,13] Dynkin type is ^2A_3(q) + A_1(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 2 modulo 60: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 4 modulo 60: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 5 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 7 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 8 modulo 60: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 11 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 13 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 16 modulo 60: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 17 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 19 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 21 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 23 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 25 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 27 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 29 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 31 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 32 modulo 60: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 41 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 43 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 47 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 49 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 53 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) q congruent 59 modulo 60: 1/16 phi1 ( q^3-6*q^2+13*q-12 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 7, 69, 68, 7, 82, 31, 19, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 1, 4, 4 ], [ 31, 1, 3, 8 ], [ 34, 1, 3, 8 ], [ 35, 1, 6, 16 ], [ 35, 1, 8, 8 ], [ 37, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 6, 16 ], [ 42, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 44, 1, 8, 8 ], [ 48, 1, 4, 16 ], [ 48, 1, 5, 8 ], [ 50, 1, 8, 16 ], [ 52, 1, 2, 16 ], [ 53, 1, 8, 16 ] ] k = 14: F-action on Pi is (2,5) [56,1,14] Dynkin type is ^2A_3(q) + A_1(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 2 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) q congruent 4 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 7 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) q congruent 8 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 11 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 16 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 19 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 23 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 27 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 31 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) q congruent 32 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 43 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) q congruent 47 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-12*q^2+43*q-40 ) q congruent 59 modulo 60: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 68, 7, 4, 68, 28, 82, 70, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 2, 16 ], [ 20, 1, 3, 24 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 12 ], [ 35, 1, 5, 16 ], [ 35, 1, 6, 24 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 8 ], [ 40, 1, 1, 48 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 4, 16 ], [ 43, 1, 3, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 48, 1, 4, 32 ], [ 51, 1, 6, 32 ], [ 52, 1, 1, 48 ], [ 52, 1, 3, 16 ], [ 53, 1, 6, 32 ] ] k = 15: F-action on Pi is (2,5) [56,1,15] Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-12*q^2+51*q-72 ) q congruent 2 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-64*q+32 ) q congruent 3 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-135*q+108 ) q congruent 4 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-139*q+120 ) q congruent 7 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-135*q+108 ) q congruent 8 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-64*q+32 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-12*q^2+51*q-72 ) q congruent 11 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-151*q+156 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-12*q^2+51*q-72 ) q congruent 16 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-139*q+120 ) q congruent 19 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-135*q+108 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-12*q^2+51*q-72 ) q congruent 23 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-151*q+156 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-12*q^2+51*q-72 ) q congruent 27 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-135*q+108 ) q congruent 29 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-139*q+120 ) q congruent 31 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-135*q+108 ) q congruent 32 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-64*q+32 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-12*q^2+51*q-72 ) q congruent 41 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-139*q+120 ) q congruent 43 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-135*q+108 ) q congruent 47 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-151*q+156 ) q congruent 49 modulo 60: 1/96 phi1 ( q^3-12*q^2+51*q-72 ) q congruent 53 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-139*q+120 ) q congruent 59 modulo 60: 1/96 ( q^4-13*q^3+63*q^2-151*q+156 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 69, 5, 3, 69, 31, 78, 72, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 10 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 16 ], [ 19, 1, 2, 48 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 48 ], [ 22, 1, 3, 16 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 36 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 24 ], [ 31, 1, 3, 16 ], [ 34, 1, 3, 48 ], [ 35, 1, 6, 24 ], [ 35, 1, 8, 48 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 24 ], [ 41, 1, 6, 48 ], [ 41, 1, 9, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 10, 48 ], [ 48, 1, 5, 48 ], [ 50, 1, 9, 96 ], [ 52, 1, 9, 48 ], [ 53, 1, 20, 96 ] ] k = 16: F-action on Pi is (2,5) [56,1,16] Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 7 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 11 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 13 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 19 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 21 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 23 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 25 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 27 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 29 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 31 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 41 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 43 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 47 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 49 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 53 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) q congruent 59 modulo 60: 1/16 phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 71, 76, 20, 19, 72, 60, 98, 73, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 28, 1, 2, 4 ], [ 35, 1, 7, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 52, 1, 5, 8 ], [ 53, 1, 13, 16 ] ] k = 17: F-action on Pi is (2,5) [56,1,17] Dynkin type is ^2A_3(q) + A_1(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 2 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 3 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 4 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-10 ) q congruent 7 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 8 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 9 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 11 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-10 ) q congruent 13 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 16 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-10 ) q congruent 19 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 21 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 23 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-10 ) q congruent 25 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 27 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 29 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-10 ) q congruent 31 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 32 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 37 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 41 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-10 ) q congruent 43 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 47 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-10 ) q congruent 49 modulo 60: 1/12 q phi1^2 ( q-2 ) q congruent 53 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-10 ) q congruent 59 modulo 60: 1/12 phi2 ( q^3-5*q^2+10*q-10 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 9, 31, 78, 82, 31, 84, 15, 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 4, 8 ], [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ], [ 27, 1, 4, 6 ], [ 31, 1, 4, 4 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 50, 1, 10, 12 ], [ 53, 1, 18, 12 ] ] k = 18: F-action on Pi is (2,5) [56,1,18] Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^3-10*q^2+35*q-46 ) q congruent 2 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-40*q+16 ) q congruent 3 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+78 ) q congruent 4 modulo 60: 1/16 q ( q^3-10*q^2+32*q-32 ) q congruent 5 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+70 ) q congruent 7 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+78 ) q congruent 8 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-40*q+16 ) q congruent 9 modulo 60: 1/16 phi1 ( q^3-10*q^2+35*q-46 ) q congruent 11 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-97*q+102 ) q congruent 13 modulo 60: 1/16 phi1 ( q^3-10*q^2+35*q-46 ) q congruent 16 modulo 60: 1/16 q ( q^3-10*q^2+32*q-32 ) q congruent 17 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+70 ) q congruent 19 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+78 ) q congruent 21 modulo 60: 1/16 phi1 ( q^3-10*q^2+35*q-46 ) q congruent 23 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-97*q+102 ) q congruent 25 modulo 60: 1/16 phi1 ( q^3-10*q^2+35*q-46 ) q congruent 27 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+78 ) q congruent 29 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+70 ) q congruent 31 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+78 ) q congruent 32 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-40*q+16 ) q congruent 37 modulo 60: 1/16 phi1 ( q^3-10*q^2+35*q-46 ) q congruent 41 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+70 ) q congruent 43 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+78 ) q congruent 47 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-97*q+102 ) q congruent 49 modulo 60: 1/16 phi1 ( q^3-10*q^2+35*q-46 ) q congruent 53 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-89*q+70 ) q congruent 59 modulo 60: 1/16 ( q^4-11*q^3+45*q^2-97*q+102 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 69, 5, 7, 69, 31, 78, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 10 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 8 ], [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 3, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 3, 8 ], [ 22, 1, 4, 16 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 12 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 8 ], [ 29, 1, 3, 16 ], [ 30, 1, 3, 16 ], [ 31, 1, 3, 8 ], [ 31, 1, 4, 16 ], [ 34, 1, 3, 8 ], [ 34, 1, 4, 16 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 16 ], [ 36, 1, 3, 16 ], [ 37, 1, 3, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 44, 1, 8, 8 ], [ 45, 1, 5, 16 ], [ 48, 1, 5, 8 ], [ 48, 1, 6, 16 ], [ 50, 1, 11, 16 ], [ 51, 1, 8, 16 ], [ 52, 1, 9, 16 ], [ 53, 1, 8, 16 ] ] k = 19: F-action on Pi is (2,5) [56,1,19] Dynkin type is ^2A_3(q) + A_1(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 2 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 4 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 7 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 8 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 11 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 16 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 19 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 23 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 27 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 31 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 32 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 43 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 47 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-8*q^2+21*q-22 ) q congruent 59 modulo 60: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 7, 69, 68, 3, 82, 31, 19, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 1, 4, 4 ], [ 31, 1, 3, 16 ], [ 34, 1, 3, 16 ], [ 35, 1, 6, 16 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 4, 8 ], [ 40, 1, 2, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 43, 1, 3, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 48, 1, 5, 16 ], [ 51, 1, 10, 32 ], [ 52, 1, 2, 16 ], [ 52, 1, 4, 16 ], [ 53, 1, 6, 32 ] ] k = 20: F-action on Pi is (2,5) [56,1,20] Dynkin type is ^2A_3(q) + A_1(q) + T(phi2^4) Order of center |Z^F|: phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-24*q^2+197*q-582 ) q congruent 2 modulo 60: 1/96 ( q^4-24*q^3+188*q^2-544*q+512 ) q congruent 3 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-815*q+1050 ) q congruent 4 modulo 60: 1/96 ( q^4-24*q^3+188*q^2-480*q+192 ) q congruent 5 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-843*q+1190 ) q congruent 7 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-815*q+1050 ) q congruent 8 modulo 60: 1/96 ( q^4-24*q^3+188*q^2-544*q+512 ) q congruent 9 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-779*q+774 ) q congruent 11 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-879*q+1658 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-24*q^2+197*q-582 ) q congruent 16 modulo 60: 1/96 q ( q^3-24*q^2+188*q-480 ) q congruent 17 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-843*q+1190 ) q congruent 19 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-815*q+1242 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-24*q^2+197*q-582 ) q congruent 23 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-879*q+1658 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-24*q^2+197*q-582 ) q congruent 27 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-815*q+1050 ) q congruent 29 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-843*q+1382 ) q congruent 31 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-815*q+1050 ) q congruent 32 modulo 60: 1/96 ( q^4-24*q^3+188*q^2-544*q+512 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-24*q^2+197*q-582 ) q congruent 41 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-843*q+1190 ) q congruent 43 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-815*q+1050 ) q congruent 47 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-879*q+1658 ) q congruent 49 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-779*q+774 ) q congruent 53 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-843*q+1190 ) q congruent 59 modulo 60: 1/96 ( q^4-25*q^3+221*q^2-879*q+1850 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 69, 5, 78, 9, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 20 ], [ 4, 1, 2, 34 ], [ 5, 1, 2, 32 ], [ 6, 1, 2, 40 ], [ 7, 1, 2, 28 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 14 ], [ 11, 1, 2, 36 ], [ 12, 1, 2, 68 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 64 ], [ 15, 1, 2, 64 ], [ 16, 1, 3, 40 ], [ 18, 1, 2, 64 ], [ 19, 1, 2, 72 ], [ 20, 1, 4, 56 ], [ 21, 1, 2, 48 ], [ 22, 1, 4, 64 ], [ 23, 1, 2, 30 ], [ 24, 1, 2, 50 ], [ 25, 1, 3, 84 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 84 ], [ 29, 1, 4, 96 ], [ 30, 1, 3, 96 ], [ 31, 1, 4, 64 ], [ 34, 1, 4, 96 ], [ 35, 1, 8, 72 ], [ 36, 1, 4, 96 ], [ 37, 1, 3, 96 ], [ 39, 1, 3, 72 ], [ 40, 1, 6, 144 ], [ 41, 1, 9, 144 ], [ 42, 1, 6, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 10, 48 ], [ 45, 1, 6, 96 ], [ 48, 1, 6, 96 ], [ 50, 1, 12, 96 ], [ 51, 1, 9, 96 ], [ 52, 1, 10, 144 ], [ 53, 1, 20, 96 ] ] i = 57: Pi = [ 1, 2, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [57,1,1] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3608*q+9601 ) q congruent 2 modulo 60: 1/384 ( q^4-36*q^3+444*q^2-2096*q+2688 ) q congruent 3 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 ) q congruent 4 modulo 60: 1/384 ( q^4-36*q^3+444*q^2-2224*q+3840 ) q congruent 5 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 ) q congruent 7 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3512*q+7777 ) q congruent 8 modulo 60: 1/384 ( q^4-36*q^3+444*q^2-2096*q+2688 ) q congruent 9 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 ) q congruent 11 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3384*q+6369 ) q congruent 13 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3608*q+9217 ) q congruent 16 modulo 60: 1/384 ( q^4-36*q^3+444*q^2-2224*q+4224 ) q congruent 17 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 ) q congruent 19 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3512*q+7777 ) q congruent 21 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3480*q+7809 ) q congruent 23 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 ) q congruent 25 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3608*q+9217 ) q congruent 27 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 ) q congruent 29 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 ) q congruent 31 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3512*q+8161 ) q congruent 32 modulo 60: 1/384 ( q^4-36*q^3+444*q^2-2096*q+2688 ) q congruent 37 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3608*q+9217 ) q congruent 41 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3480*q+7809 ) q congruent 43 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3512*q+7777 ) q congruent 47 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 ) q congruent 49 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3608*q+9217 ) q congruent 53 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 ) q congruent 59 modulo 60: 1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 72 ], [ 5, 1, 1, 96 ], [ 6, 1, 1, 128 ], [ 7, 1, 1, 32 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 8 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 144 ], [ 14, 1, 1, 96 ], [ 15, 1, 1, 192 ], [ 16, 1, 1, 384 ], [ 17, 1, 1, 384 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 128 ], [ 20, 1, 1, 192 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 64 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 56 ], [ 25, 1, 1, 144 ], [ 28, 1, 1, 96 ], [ 30, 1, 1, 192 ], [ 31, 1, 1, 192 ], [ 32, 1, 1, 384 ], [ 33, 1, 1, 768 ], [ 34, 1, 1, 64 ], [ 35, 1, 1, 384 ], [ 37, 1, 1, 96 ], [ 39, 1, 1, 48 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 288 ], [ 47, 1, 1, 384 ], [ 48, 1, 1, 192 ], [ 49, 1, 1, 768 ], [ 52, 1, 1, 192 ] ] k = 2: F-action on Pi is () [57,1,2] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-241 ) q congruent 2 modulo 60: 1/96 q ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-201 ) q congruent 4 modulo 60: 1/96 q ( q^3-16*q^2+76*q-112 ) q congruent 5 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-225 ) q congruent 7 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-217 ) q congruent 8 modulo 60: 1/96 q ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-225 ) q congruent 11 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-201 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-241 ) q congruent 16 modulo 60: 1/96 q ( q^3-16*q^2+76*q-112 ) q congruent 17 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-225 ) q congruent 19 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-217 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-225 ) q congruent 23 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-201 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-241 ) q congruent 27 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-201 ) q congruent 29 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-225 ) q congruent 31 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-217 ) q congruent 32 modulo 60: 1/96 q ( q^3-16*q^2+76*q-96 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-241 ) q congruent 41 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-225 ) q congruent 43 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-217 ) q congruent 47 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-201 ) q congruent 49 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-241 ) q congruent 53 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-225 ) q congruent 59 modulo 60: 1/96 phi1 ( q^3-19*q^2+115*q-201 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 3, 4, 68, 68, 7, 68, 7, 7, 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 72 ], [ 16, 1, 1, 96 ], [ 19, 1, 1, 32 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 48 ], [ 22, 1, 2, 16 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 42 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 72 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 31, 1, 2, 48 ], [ 33, 1, 1, 192 ], [ 34, 1, 2, 16 ], [ 35, 1, 1, 96 ], [ 35, 1, 3, 96 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 144 ], [ 41, 1, 6, 72 ], [ 47, 1, 2, 96 ], [ 48, 1, 2, 48 ], [ 49, 1, 1, 192 ], [ 49, 1, 9, 192 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ] ] k = 3: F-action on Pi is (5,7) [57,1,3] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 2 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) q congruent 4 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 7 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) q congruent 8 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 11 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 16 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 19 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 23 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 27 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 31 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) q congruent 32 modulo 60: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 43 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) q congruent 47 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-13*q^2+51*q-55 ) q congruent 59 modulo 60: 1/32 ( q^4-14*q^3+64*q^2-98*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19, 68, 19, 7, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 20, 1, 1, 16 ], [ 20, 1, 3, 16 ], [ 21, 1, 1, 8 ], [ 22, 1, 1, 16 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 8 ], [ 28, 1, 3, 8 ], [ 30, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 16 ], [ 33, 1, 2, 32 ], [ 34, 1, 1, 16 ], [ 35, 1, 1, 16 ], [ 35, 1, 2, 16 ], [ 35, 1, 5, 16 ], [ 35, 1, 6, 16 ], [ 37, 1, 1, 16 ], [ 37, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 47, 1, 3, 32 ], [ 48, 1, 1, 16 ], [ 48, 1, 4, 16 ], [ 48, 1, 7, 16 ], [ 49, 1, 2, 32 ], [ 52, 1, 3, 16 ] ] k = 4: F-action on Pi is (5,7) [57,1,4] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 ( q^3-9*q^2+23*q-11 ) q congruent 2 modulo 60: 1/16 ( q^4-8*q^3+16*q^2-16 ) q congruent 3 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-42*q+27 ) q congruent 4 modulo 60: 1/16 q^2 ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q-5 ) q congruent 7 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q+19 ) q congruent 8 modulo 60: 1/16 ( q^4-8*q^3+16*q^2-16 ) q congruent 9 modulo 60: 1/16 phi1 ( q^3-9*q^2+23*q-19 ) q congruent 11 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q+3 ) q congruent 13 modulo 60: 1/16 phi1 ( q^3-9*q^2+23*q-11 ) q congruent 16 modulo 60: 1/16 q^2 ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q-5 ) q congruent 19 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q+19 ) q congruent 21 modulo 60: 1/16 phi1 ( q^3-9*q^2+23*q-19 ) q congruent 23 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q+3 ) q congruent 25 modulo 60: 1/16 phi1 ( q^3-9*q^2+23*q-11 ) q congruent 27 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-42*q+27 ) q congruent 29 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q-5 ) q congruent 31 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q+19 ) q congruent 32 modulo 60: 1/16 ( q^4-8*q^3+16*q^2-16 ) q congruent 37 modulo 60: 1/16 phi1 ( q^3-9*q^2+23*q-11 ) q congruent 41 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q-5 ) q congruent 43 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q+19 ) q congruent 47 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q+3 ) q congruent 49 modulo 60: 1/16 phi1 ( q^3-9*q^2+23*q-11 ) q congruent 53 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q-5 ) q congruent 59 modulo 60: 1/16 ( q^4-10*q^3+32*q^2-34*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 3, 72, 7, 76, 69, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 6, 1, 1, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 16 ], [ 19, 1, 1, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 32, 1, 2, 16 ], [ 32, 1, 4, 16 ], [ 33, 1, 2, 16 ], [ 33, 1, 6, 16 ], [ 34, 1, 2, 8 ], [ 34, 1, 3, 8 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 8 ], [ 47, 1, 4, 16 ], [ 47, 1, 9, 16 ], [ 48, 1, 2, 8 ], [ 48, 1, 5, 8 ], [ 49, 1, 2, 16 ], [ 49, 1, 8, 16 ], [ 52, 1, 3, 8 ], [ 52, 1, 4, 8 ] ] k = 5: F-action on Pi is () [57,1,5] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 13 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 16 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 19 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 21 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 23 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 25 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 27 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 29 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 31 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 32 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 41 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 43 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 47 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 49 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 53 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 59 modulo 60: 1/64 phi1 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 7, 68, 7, 3, 69, 68, 7, 7, 69, 7, 69, 69, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 24 ], [ 13, 1, 4, 24 ], [ 20, 1, 2, 32 ], [ 20, 1, 3, 32 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 28 ], [ 25, 1, 1, 24 ], [ 25, 1, 3, 24 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 35, 1, 3, 64 ], [ 35, 1, 6, 64 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], [ 48, 1, 3, 32 ], [ 48, 1, 4, 32 ], [ 49, 1, 5, 128 ], [ 49, 1, 9, 128 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ] ] k = 6: F-action on Pi is () [57,1,6] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-15*q^2+75*q-117 ) q congruent 2 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-64*q+32 ) q congruent 3 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-216*q+189 ) q congruent 4 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-208*q+165 ) q congruent 7 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-216*q+189 ) q congruent 8 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-64*q+32 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-15*q^2+75*q-117 ) q congruent 11 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-232*q+237 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-15*q^2+75*q-117 ) q congruent 16 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-208*q+165 ) q congruent 19 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-216*q+189 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-15*q^2+75*q-117 ) q congruent 23 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-232*q+237 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-15*q^2+75*q-117 ) q congruent 27 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-216*q+189 ) q congruent 29 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-208*q+165 ) q congruent 31 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-216*q+189 ) q congruent 32 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-64*q+32 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-15*q^2+75*q-117 ) q congruent 41 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-208*q+165 ) q congruent 43 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-216*q+189 ) q congruent 47 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-232*q+237 ) q congruent 49 modulo 60: 1/96 phi1 ( q^3-15*q^2+75*q-117 ) q congruent 53 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-208*q+165 ) q congruent 59 modulo 60: 1/96 ( q^4-16*q^3+90*q^2-232*q+237 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 3, 7, 69, 7, 69, 69, 5, 7, 69, 69, 5, 69, 5, 5, 67 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 36 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 4, 72 ], [ 16, 1, 3, 96 ], [ 19, 1, 2, 32 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 48 ], [ 22, 1, 3, 16 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 42 ], [ 25, 1, 3, 72 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 31, 1, 3, 48 ], [ 33, 1, 8, 192 ], [ 34, 1, 3, 16 ], [ 35, 1, 6, 96 ], [ 35, 1, 8, 96 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 6, 48 ], [ 41, 1, 6, 72 ], [ 41, 1, 9, 144 ], [ 47, 1, 7, 96 ], [ 48, 1, 5, 48 ], [ 49, 1, 5, 192 ], [ 49, 1, 10, 192 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ] ] k = 7: F-action on Pi is (5,7) [57,1,7] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/16 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 73, 76, 18, 72, 18, 20, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 8 ], [ 41, 1, 8, 16 ], [ 49, 1, 4, 16 ], [ 49, 1, 7, 16 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ] ] k = 8: F-action on Pi is (5,7) [57,1,8] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi2^2 phi4) Order of center |Z^F|: phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 1/32 q^3 ( q-2 ) q congruent 3 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 1/32 q^3 ( q-2 ) q congruent 5 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 1/32 q^3 ( q-2 ) q congruent 9 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 1/32 q^3 ( q-2 ) q congruent 17 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 1/32 q^3 ( q-2 ) q congruent 37 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 76, 18, 20, 74, 20, 74, 71, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 48, 1, 9, 16 ], [ 49, 1, 4, 32 ], [ 52, 1, 5, 16 ] ] k = 9: F-action on Pi is (5,7) [57,1,9] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 2 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) q congruent 4 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 7 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) q congruent 8 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 11 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 16 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 19 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 23 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 27 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 31 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) q congruent 32 modulo 60: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 43 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) q congruent 47 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 59 modulo 60: 1/32 ( q^4-10*q^3+36*q^2-62*q+51 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 76, 69, 20, 69, 20, 5, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 10 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 2, 16 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 4, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 4, 8 ], [ 30, 1, 3, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 4, 16 ], [ 33, 1, 6, 32 ], [ 34, 1, 4, 16 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 16 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 16 ], [ 39, 1, 2, 4 ], [ 39, 1, 3, 8 ], [ 40, 1, 2, 16 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 47, 1, 10, 32 ], [ 48, 1, 3, 16 ], [ 48, 1, 6, 16 ], [ 48, 1, 10, 16 ], [ 49, 1, 8, 32 ], [ 52, 1, 4, 16 ] ] k = 10: F-action on Pi is () [57,1,10] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^4) Order of center |Z^F|: phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 ( q^3-31*q^2+327*q-1209 ) q congruent 2 modulo 60: 1/384 ( q^4-28*q^3+252*q^2-848*q+896 ) q congruent 3 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 ) q congruent 4 modulo 60: 1/384 ( q^4-28*q^3+252*q^2-720*q+384 ) q congruent 5 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1664*q+2745 ) q congruent 7 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 ) q congruent 8 modulo 60: 1/384 ( q^4-28*q^3+252*q^2-848*q+896 ) q congruent 9 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1536*q+1593 ) q congruent 11 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1760*q+3993 ) q congruent 13 modulo 60: 1/384 phi1 ( q^3-31*q^2+327*q-1209 ) q congruent 16 modulo 60: 1/384 q ( q^3-28*q^2+252*q-720 ) q congruent 17 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1664*q+2745 ) q congruent 19 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1632*q+2841 ) q congruent 21 modulo 60: 1/384 phi1 ( q^3-31*q^2+327*q-1209 ) q congruent 23 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1760*q+3993 ) q congruent 25 modulo 60: 1/384 phi1 ( q^3-31*q^2+327*q-1209 ) q congruent 27 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 ) q congruent 29 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1664*q+3129 ) q congruent 31 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 ) q congruent 32 modulo 60: 1/384 ( q^4-28*q^3+252*q^2-848*q+896 ) q congruent 37 modulo 60: 1/384 phi1 ( q^3-31*q^2+327*q-1209 ) q congruent 41 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1664*q+2745 ) q congruent 43 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 ) q congruent 47 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1760*q+3993 ) q congruent 49 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1536*q+1593 ) q congruent 53 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1664*q+2745 ) q congruent 59 modulo 60: 1/384 ( q^4-32*q^3+358*q^2-1760*q+4377 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 69, 69, 5, 69, 5, 5, 67, 69, 5, 5, 67, 5, 67, 67, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 72 ], [ 5, 1, 2, 96 ], [ 6, 1, 2, 128 ], [ 7, 1, 2, 32 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 8 ], [ 11, 1, 2, 32 ], [ 12, 1, 2, 96 ], [ 13, 1, 4, 144 ], [ 14, 1, 2, 96 ], [ 15, 1, 2, 192 ], [ 16, 1, 3, 384 ], [ 17, 1, 4, 384 ], [ 18, 1, 2, 64 ], [ 19, 1, 2, 128 ], [ 20, 1, 4, 192 ], [ 21, 1, 2, 16 ], [ 22, 1, 4, 64 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 56 ], [ 25, 1, 3, 144 ], [ 28, 1, 4, 96 ], [ 30, 1, 3, 192 ], [ 31, 1, 4, 192 ], [ 32, 1, 3, 384 ], [ 33, 1, 8, 768 ], [ 34, 1, 4, 64 ], [ 35, 1, 8, 384 ], [ 37, 1, 3, 96 ], [ 39, 1, 3, 48 ], [ 40, 1, 6, 192 ], [ 41, 1, 9, 288 ], [ 47, 1, 8, 384 ], [ 48, 1, 6, 192 ], [ 49, 1, 10, 768 ], [ 52, 1, 10, 192 ] ] k = 11: F-action on Pi is (5,7) [57,1,11] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi4) Order of center |Z^F|: phi1^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 2 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 16 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 32 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/32 phi1 phi2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 16, 19, 73, 19, 73, 76, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 1, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 48, 1, 8, 16 ], [ 49, 1, 7, 32 ], [ 52, 1, 8, 16 ] ] k = 12: F-action on Pi is (2,5,7) [57,1,12] Dynkin type is A_1(q) + A_1(q^3) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 phi2 ( q^2-4*q+2 ) q congruent 2 modulo 60: 1/12 q phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/12 q phi1 ( q^2-2*q-2 ) q congruent 5 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/12 phi1 phi2 ( q^2-4*q+2 ) q congruent 8 modulo 60: 1/12 q phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/12 phi1 phi2 ( q^2-4*q+2 ) q congruent 16 modulo 60: 1/12 q phi1 ( q^2-2*q-2 ) q congruent 17 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/12 phi1 phi2 ( q^2-4*q+2 ) q congruent 21 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/12 phi1 phi2 ( q^2-4*q+2 ) q congruent 27 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/12 phi1 phi2 ( q^2-4*q+2 ) q congruent 32 modulo 60: 1/12 q phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/12 phi1 phi2 ( q^2-4*q+2 ) q congruent 41 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/12 phi1 phi2 ( q^2-4*q+2 ) q congruent 47 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/12 phi1 phi2 ( q^2-4*q+2 ) q congruent 53 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/12 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 87, 83, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 5, 12 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 33, 1, 3, 6 ], [ 34, 1, 1, 4 ], [ 40, 1, 5, 6 ], [ 47, 1, 5, 12 ], [ 49, 1, 3, 6 ], [ 52, 1, 6, 6 ] ] k = 13: F-action on Pi is (2,5,7) [57,1,13] Dynkin type is A_1(q) + A_1(q^3) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 2 modulo 60: 1/12 q^2 phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 60: 1/12 q phi1 ( q^2-2 ) q congruent 5 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 8 modulo 60: 1/12 q^2 phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 13 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 16 modulo 60: 1/12 q phi1 ( q^2-2 ) q congruent 17 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 19 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 23 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 25 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 29 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 31 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 32 modulo 60: 1/12 q^2 phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 41 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 43 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 47 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 49 modulo 60: 1/12 phi1^2 ( q^2-2 ) q congruent 53 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 59 modulo 60: 1/12 q phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 83, 35, 37, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 19, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 2 ], [ 33, 1, 3, 6 ], [ 34, 1, 2, 4 ], [ 40, 1, 5, 6 ], [ 47, 1, 6, 12 ], [ 49, 1, 3, 6 ], [ 52, 1, 6, 6 ] ] k = 14: F-action on Pi is (2,5,7) [57,1,14] Dynkin type is A_1(q) + A_1(q^3) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 2 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 3 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 4 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 7 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 8 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 9 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 11 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 13 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 16 modulo 60: 1/12 q^2 phi1 ( q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 19 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 21 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 23 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 25 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 27 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 29 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 31 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 32 modulo 60: 1/12 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 37 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 41 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 43 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 47 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 49 modulo 60: 1/12 q^2 phi1 ( q-3 ) q congruent 53 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^3-5*q^2+8*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 38, 35, 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 19, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 2 ], [ 33, 1, 7, 6 ], [ 34, 1, 3, 4 ], [ 40, 1, 4, 6 ], [ 47, 1, 11, 12 ], [ 49, 1, 6, 6 ], [ 52, 1, 7, 6 ] ] k = 15: F-action on Pi is (2,5,7) [57,1,15] Dynkin type is A_1(q) + A_1(q^3) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1^2 q congruent 2 modulo 60: 1/12 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 3 modulo 60: 1/12 q^2 phi1^2 q congruent 4 modulo 60: 1/12 q^3 phi1 q congruent 5 modulo 60: 1/12 phi2 ( q^3-3*q^2+4*q-6 ) q congruent 7 modulo 60: 1/12 q^2 phi1^2 q congruent 8 modulo 60: 1/12 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 9 modulo 60: 1/12 q^2 phi1^2 q congruent 11 modulo 60: 1/12 phi2 ( q^3-3*q^2+4*q-6 ) q congruent 13 modulo 60: 1/12 q^2 phi1^2 q congruent 16 modulo 60: 1/12 q^3 phi1 q congruent 17 modulo 60: 1/12 phi2 ( q^3-3*q^2+4*q-6 ) q congruent 19 modulo 60: 1/12 q^2 phi1^2 q congruent 21 modulo 60: 1/12 q^2 phi1^2 q congruent 23 modulo 60: 1/12 phi2 ( q^3-3*q^2+4*q-6 ) q congruent 25 modulo 60: 1/12 q^2 phi1^2 q congruent 27 modulo 60: 1/12 q^2 phi1^2 q congruent 29 modulo 60: 1/12 phi2 ( q^3-3*q^2+4*q-6 ) q congruent 31 modulo 60: 1/12 q^2 phi1^2 q congruent 32 modulo 60: 1/12 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 37 modulo 60: 1/12 q^2 phi1^2 q congruent 41 modulo 60: 1/12 phi2 ( q^3-3*q^2+4*q-6 ) q congruent 43 modulo 60: 1/12 q^2 phi1^2 q congruent 47 modulo 60: 1/12 phi2 ( q^3-3*q^2+4*q-6 ) q congruent 49 modulo 60: 1/12 q^2 phi1^2 q congruent 53 modulo 60: 1/12 phi2 ( q^3-3*q^2+4*q-6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^3-3*q^2+4*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 40, 84, 88, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 6, 12 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ], [ 33, 1, 7, 6 ], [ 34, 1, 4, 4 ], [ 40, 1, 4, 6 ], [ 47, 1, 12, 12 ], [ 49, 1, 6, 6 ], [ 52, 1, 7, 6 ] ] k = 16: F-action on Pi is (1,2)(5,7) [57,1,16] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 1/32 q ( q^3-4*q^2+8 ) q congruent 3 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 1/32 q ( q^3-4*q^2+8 ) q congruent 5 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 1/32 q ( q^3-4*q^2+8 ) q congruent 9 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 1/32 q ( q^3-4*q^2+8 ) q congruent 17 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 1/32 q ( q^3-4*q^2+8 ) q congruent 37 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/32 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 76, 76, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 8 ], [ 5, 1, 2, 8 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 8 ], [ 13, 1, 3, 8 ], [ 14, 1, 1, 8 ], [ 14, 1, 2, 8 ], [ 21, 1, 1, 4 ], [ 21, 1, 2, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 8 ], [ 30, 1, 2, 16 ], [ 30, 1, 4, 16 ], [ 37, 1, 1, 8 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 8 ], [ 37, 1, 4, 16 ], [ 39, 1, 2, 8 ], [ 41, 1, 2, 16 ], [ 48, 1, 7, 16 ], [ 48, 1, 10, 16 ] ] k = 17: F-action on Pi is (1,2)(5,7) [57,1,17] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^3 phi2 q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1^3 phi2 q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1^3 phi2 q congruent 7 modulo 60: 1/16 phi1^3 phi2 q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1^3 phi2 q congruent 11 modulo 60: 1/16 phi1^3 phi2 q congruent 13 modulo 60: 1/16 phi1^3 phi2 q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1^3 phi2 q congruent 19 modulo 60: 1/16 phi1^3 phi2 q congruent 21 modulo 60: 1/16 phi1^3 phi2 q congruent 23 modulo 60: 1/16 phi1^3 phi2 q congruent 25 modulo 60: 1/16 phi1^3 phi2 q congruent 27 modulo 60: 1/16 phi1^3 phi2 q congruent 29 modulo 60: 1/16 phi1^3 phi2 q congruent 31 modulo 60: 1/16 phi1^3 phi2 q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1^3 phi2 q congruent 41 modulo 60: 1/16 phi1^3 phi2 q congruent 43 modulo 60: 1/16 phi1^3 phi2 q congruent 47 modulo 60: 1/16 phi1^3 phi2 q congruent 49 modulo 60: 1/16 phi1^3 phi2 q congruent 53 modulo 60: 1/16 phi1^3 phi2 q congruent 59 modulo 60: 1/16 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 76, 22, 18, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 8 ], [ 41, 1, 5, 8 ], [ 48, 1, 8, 8 ], [ 48, 1, 9, 8 ] ] k = 18: F-action on Pi is (1,2)(5,7) [57,1,18] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi4^2) Order of center |Z^F|: phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 2 modulo 60: 1/32 ( q^4-12*q^2+32 ) q congruent 3 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 4 modulo 60: 1/32 q^2 ( q^2-12 ) q congruent 5 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 7 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 8 modulo 60: 1/32 ( q^4-12*q^2+32 ) q congruent 9 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 11 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 13 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 16 modulo 60: 1/32 q^2 ( q^2-12 ) q congruent 17 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 19 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 21 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 23 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 25 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 27 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 29 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 31 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 32 modulo 60: 1/32 ( q^4-12*q^2+32 ) q congruent 37 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 41 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 43 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 47 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 49 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) q congruent 53 modulo 60: 1/32 ( q^4-14*q^2+45 ) q congruent 59 modulo 60: 1/32 phi1 phi2 ( q^2-13 ) Fusion of maximal tori of C^F in those of G^F: [ 22, 75, 75, 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 16 ], [ 5, 1, 4, 16 ], [ 9, 1, 1, 3 ], [ 32, 1, 5, 32 ], [ 37, 1, 5, 16 ], [ 39, 1, 5, 8 ], [ 41, 1, 5, 16 ] ] k = 19: F-action on Pi is (1,2,5,7) [57,1,19] Dynkin type is A_1(q^4) + T(phi8) Order of center |Z^F|: phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 phi4 q congruent 2 modulo 60: 1/8 q^4 q congruent 3 modulo 60: 1/8 phi1 phi2 phi4 q congruent 4 modulo 60: 1/8 q^4 q congruent 5 modulo 60: 1/8 phi1 phi2 phi4 q congruent 7 modulo 60: 1/8 phi1 phi2 phi4 q congruent 8 modulo 60: 1/8 q^4 q congruent 9 modulo 60: 1/8 phi1 phi2 phi4 q congruent 11 modulo 60: 1/8 phi1 phi2 phi4 q congruent 13 modulo 60: 1/8 phi1 phi2 phi4 q congruent 16 modulo 60: 1/8 q^4 q congruent 17 modulo 60: 1/8 phi1 phi2 phi4 q congruent 19 modulo 60: 1/8 phi1 phi2 phi4 q congruent 21 modulo 60: 1/8 phi1 phi2 phi4 q congruent 23 modulo 60: 1/8 phi1 phi2 phi4 q congruent 25 modulo 60: 1/8 phi1 phi2 phi4 q congruent 27 modulo 60: 1/8 phi1 phi2 phi4 q congruent 29 modulo 60: 1/8 phi1 phi2 phi4 q congruent 31 modulo 60: 1/8 phi1 phi2 phi4 q congruent 32 modulo 60: 1/8 q^4 q congruent 37 modulo 60: 1/8 phi1 phi2 phi4 q congruent 41 modulo 60: 1/8 phi1 phi2 phi4 q congruent 43 modulo 60: 1/8 phi1 phi2 phi4 q congruent 47 modulo 60: 1/8 phi1 phi2 phi4 q congruent 49 modulo 60: 1/8 phi1 phi2 phi4 q congruent 53 modulo 60: 1/8 phi1 phi2 phi4 q congruent 59 modulo 60: 1/8 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 92, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ] k = 20: F-action on Pi is (1,2,5,7) [57,1,20] Dynkin type is A_1(q^4) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1^2 phi2^2 q congruent 2 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 3 modulo 60: 1/8 phi1^2 phi2^2 q congruent 4 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 5 modulo 60: 1/8 phi1^2 phi2^2 q congruent 7 modulo 60: 1/8 phi1^2 phi2^2 q congruent 8 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 9 modulo 60: 1/8 phi1^2 phi2^2 q congruent 11 modulo 60: 1/8 phi1^2 phi2^2 q congruent 13 modulo 60: 1/8 phi1^2 phi2^2 q congruent 16 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 17 modulo 60: 1/8 phi1^2 phi2^2 q congruent 19 modulo 60: 1/8 phi1^2 phi2^2 q congruent 21 modulo 60: 1/8 phi1^2 phi2^2 q congruent 23 modulo 60: 1/8 phi1^2 phi2^2 q congruent 25 modulo 60: 1/8 phi1^2 phi2^2 q congruent 27 modulo 60: 1/8 phi1^2 phi2^2 q congruent 29 modulo 60: 1/8 phi1^2 phi2^2 q congruent 31 modulo 60: 1/8 phi1^2 phi2^2 q congruent 32 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 37 modulo 60: 1/8 phi1^2 phi2^2 q congruent 41 modulo 60: 1/8 phi1^2 phi2^2 q congruent 43 modulo 60: 1/8 phi1^2 phi2^2 q congruent 47 modulo 60: 1/8 phi1^2 phi2^2 q congruent 49 modulo 60: 1/8 phi1^2 phi2^2 q congruent 53 modulo 60: 1/8 phi1^2 phi2^2 q congruent 59 modulo 60: 1/8 phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 22, 92 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 21, 1, 1, 2 ], [ 21, 1, 2, 2 ], [ 37, 1, 4, 4 ], [ 37, 1, 5, 4 ] ] i = 58: Pi = [ 1, 3, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [58,1,1] Dynkin type is A_2(q) + A_2(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 ( q^4-34*q^3+423*q^2-2368*q+5722 ) q congruent 2 modulo 60: 1/288 ( q^4-34*q^3+400*q^2-1824*q+2304 ) q congruent 3 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 ) q congruent 4 modulo 60: 1/288 ( q^4-34*q^3+408*q^2-2032*q+3520 ) q congruent 5 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 ) q congruent 7 modulo 60: 1/288 ( q^4-34*q^3+423*q^2-2332*q+4858 ) q congruent 8 modulo 60: 1/288 ( q^4-34*q^3+400*q^2-1824*q+2304 ) q congruent 9 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 ) q congruent 11 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2124*q+3762 ) q congruent 13 modulo 60: 1/288 ( q^4-34*q^3+423*q^2-2368*q+5434 ) q congruent 16 modulo 60: 1/288 ( q^4-34*q^3+408*q^2-2032*q+3808 ) q congruent 17 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 ) q congruent 19 modulo 60: 1/288 ( q^4-34*q^3+423*q^2-2332*q+4858 ) q congruent 21 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2160*q+4338 ) q congruent 23 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 ) q congruent 25 modulo 60: 1/288 ( q^4-34*q^3+423*q^2-2368*q+5434 ) q congruent 27 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 ) q congruent 29 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 ) q congruent 31 modulo 60: 1/288 ( q^4-34*q^3+423*q^2-2332*q+5146 ) q congruent 32 modulo 60: 1/288 ( q^4-34*q^3+400*q^2-1824*q+2304 ) q congruent 37 modulo 60: 1/288 ( q^4-34*q^3+423*q^2-2368*q+5434 ) q congruent 41 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2160*q+4338 ) q congruent 43 modulo 60: 1/288 ( q^4-34*q^3+423*q^2-2332*q+4858 ) q congruent 47 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 ) q congruent 49 modulo 60: 1/288 ( q^4-34*q^3+423*q^2-2368*q+5434 ) q congruent 53 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 ) q congruent 59 modulo 60: 1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 8, 66, 4, 77, 8, 77, 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], [ 5, 1, 1, 72 ], [ 6, 1, 1, 36 ], [ 7, 1, 1, 36 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 9 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 36 ], [ 14, 1, 1, 144 ], [ 15, 1, 1, 72 ], [ 16, 1, 1, 72 ], [ 17, 1, 1, 72 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 36 ], [ 20, 1, 1, 144 ], [ 21, 1, 1, 72 ], [ 22, 1, 1, 72 ], [ 23, 1, 1, 36 ], [ 24, 1, 1, 36 ], [ 25, 1, 1, 144 ], [ 26, 1, 1, 72 ], [ 27, 1, 1, 24 ], [ 29, 1, 1, 144 ], [ 31, 1, 1, 144 ], [ 32, 1, 1, 72 ], [ 34, 1, 1, 72 ], [ 36, 1, 1, 144 ], [ 37, 1, 1, 288 ], [ 38, 1, 1, 144 ], [ 39, 1, 1, 72 ], [ 40, 1, 1, 144 ], [ 42, 1, 1, 72 ], [ 43, 1, 1, 288 ], [ 46, 1, 1, 144 ], [ 50, 1, 1, 144 ], [ 51, 1, 1, 288 ] ] k = 2: F-action on Pi is () [58,1,2] Dynkin type is A_2(q) + A_2(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 phi1 ( q^3-15*q^2+72*q-118 ) q congruent 2 modulo 60: 1/48 q ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 60: 1/48 ( q^4-16*q^3+83*q^2-146*q+42 ) q congruent 4 modulo 60: 1/48 q ( q^3-16*q^2+80*q-128 ) q congruent 5 modulo 60: 1/48 phi1 ( q^3-15*q^2+68*q-90 ) q congruent 7 modulo 60: 1/48 ( q^4-16*q^3+87*q^2-178*q+70 ) q congruent 8 modulo 60: 1/48 q ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 60: 1/48 phi1 ( q^3-15*q^2+68*q-90 ) q congruent 11 modulo 60: 1/48 ( q^4-16*q^3+83*q^2-146*q+42 ) q congruent 13 modulo 60: 1/48 phi1 ( q^3-15*q^2+72*q-118 ) q congruent 16 modulo 60: 1/48 q ( q^3-16*q^2+80*q-128 ) q congruent 17 modulo 60: 1/48 phi1 ( q^3-15*q^2+68*q-90 ) q congruent 19 modulo 60: 1/48 ( q^4-16*q^3+87*q^2-178*q+70 ) q congruent 21 modulo 60: 1/48 phi1 ( q^3-15*q^2+68*q-90 ) q congruent 23 modulo 60: 1/48 ( q^4-16*q^3+83*q^2-146*q+42 ) q congruent 25 modulo 60: 1/48 phi1 ( q^3-15*q^2+72*q-118 ) q congruent 27 modulo 60: 1/48 ( q^4-16*q^3+83*q^2-146*q+42 ) q congruent 29 modulo 60: 1/48 phi1 ( q^3-15*q^2+68*q-90 ) q congruent 31 modulo 60: 1/48 ( q^4-16*q^3+87*q^2-178*q+70 ) q congruent 32 modulo 60: 1/48 q ( q^3-16*q^2+76*q-96 ) q congruent 37 modulo 60: 1/48 phi1 ( q^3-15*q^2+72*q-118 ) q congruent 41 modulo 60: 1/48 phi1 ( q^3-15*q^2+68*q-90 ) q congruent 43 modulo 60: 1/48 ( q^4-16*q^3+87*q^2-178*q+70 ) q congruent 47 modulo 60: 1/48 ( q^4-16*q^3+83*q^2-146*q+42 ) q congruent 49 modulo 60: 1/48 phi1 ( q^3-15*q^2+72*q-118 ) q congruent 53 modulo 60: 1/48 phi1 ( q^3-15*q^2+68*q-90 ) q congruent 59 modulo 60: 1/48 ( q^4-16*q^3+83*q^2-146*q+42 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 77, 4, 68, 30, 77, 30, 83 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 48 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 24 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 36 ], [ 22, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 1, 12 ], [ 26, 1, 3, 12 ], [ 27, 1, 1, 12 ], [ 27, 1, 2, 4 ], [ 29, 1, 1, 24 ], [ 29, 1, 2, 24 ], [ 31, 1, 1, 24 ], [ 31, 1, 2, 24 ], [ 32, 1, 1, 24 ], [ 34, 1, 1, 12 ], [ 34, 1, 2, 12 ], [ 36, 1, 2, 24 ], [ 38, 1, 1, 72 ], [ 38, 1, 5, 24 ], [ 39, 1, 4, 12 ], [ 42, 1, 1, 12 ], [ 42, 1, 4, 12 ], [ 43, 1, 2, 48 ], [ 46, 1, 1, 24 ], [ 46, 1, 2, 24 ], [ 50, 1, 2, 24 ], [ 50, 1, 4, 24 ], [ 51, 1, 2, 48 ] ] k = 3: F-action on Pi is () [58,1,3] Dynkin type is A_2(q) + A_2(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 ( q^3-6*q^2+3*q+38 ) q congruent 2 modulo 60: 1/72 q phi2 ( q^2-8*q+12 ) q congruent 3 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/72 phi1 ( q^3-6*q^2+32 ) q congruent 5 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/72 phi1 ( q^3-6*q^2+3*q+38 ) q congruent 8 modulo 60: 1/72 q phi2 ( q^2-8*q+12 ) q congruent 9 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/72 phi1 ( q^3-6*q^2+3*q+38 ) q congruent 16 modulo 60: 1/72 phi1 ( q^3-6*q^2+32 ) q congruent 17 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/72 phi1 ( q^3-6*q^2+3*q+38 ) q congruent 21 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/72 phi1 ( q^3-6*q^2+3*q+38 ) q congruent 27 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/72 phi1 ( q^3-6*q^2+3*q+38 ) q congruent 32 modulo 60: 1/72 q phi2 ( q^2-8*q+12 ) q congruent 37 modulo 60: 1/72 phi1 ( q^3-6*q^2+3*q+38 ) q congruent 41 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/72 phi1 ( q^3-6*q^2+3*q+38 ) q congruent 47 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/72 phi1 ( q^3-6*q^2+3*q+38 ) q congruent 53 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/72 q phi2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 14, 77, 30, 83, 14, 83, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 18 ], [ 8, 1, 1, 12 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 22, 1, 1, 36 ], [ 27, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 38, 1, 1, 72 ], [ 38, 1, 3, 36 ], [ 42, 1, 3, 18 ], [ 46, 1, 3, 36 ], [ 50, 1, 3, 36 ] ] k = 4: F-action on Pi is (5,6) [58,1,4] Dynkin type is A_2(q) + ^2A_2(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 2 modulo 60: 1/24 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/24 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/24 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/24 q^2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/24 q^2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/24 q phi1 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 28, 69, 7, 82, 27, 81, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 12, 1, 2, 6 ], [ 16, 1, 2, 12 ], [ 16, 1, 4, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 12 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 12 ], [ 32, 1, 2, 12 ], [ 37, 1, 2, 24 ], [ 39, 1, 2, 12 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 12 ], [ 40, 1, 3, 12 ], [ 40, 1, 6, 12 ], [ 43, 1, 8, 24 ], [ 51, 1, 3, 24 ], [ 51, 1, 6, 24 ] ] k = 5: F-action on Pi is (5,6) [58,1,5] Dynkin type is A_2(q) + ^2A_2(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 2 modulo 60: 1/8 q^3 ( q-2 ) q congruent 3 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 4 modulo 60: 1/8 q^3 ( q-2 ) q congruent 5 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 8 modulo 60: 1/8 q^3 ( q-2 ) q congruent 9 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 11 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 13 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 16 modulo 60: 1/8 q^3 ( q-2 ) q congruent 17 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 19 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 21 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 23 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 25 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 27 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 29 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 31 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 32 modulo 60: 1/8 q^3 ( q-2 ) q congruent 37 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 41 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 43 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 47 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 49 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 53 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) q congruent 59 modulo 60: 1/8 phi1 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 19, 96, 20, 76, 60, 95, 59, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 32, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 43, 1, 9, 8 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 8 ] ] k = 6: F-action on Pi is (5,6) [58,1,6] Dynkin type is A_2(q) + ^2A_2(q) + T(phi3 phi6) Order of center |Z^F|: phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1 phi2 q congruent 2 modulo 60: 1/12 q^2 phi1 phi2 q congruent 3 modulo 60: 1/12 q^2 phi1 phi2 q congruent 4 modulo 60: 1/12 q^2 phi1 phi2 q congruent 5 modulo 60: 1/12 q^2 phi1 phi2 q congruent 7 modulo 60: 1/12 q^2 phi1 phi2 q congruent 8 modulo 60: 1/12 q^2 phi1 phi2 q congruent 9 modulo 60: 1/12 q^2 phi1 phi2 q congruent 11 modulo 60: 1/12 q^2 phi1 phi2 q congruent 13 modulo 60: 1/12 q^2 phi1 phi2 q congruent 16 modulo 60: 1/12 q^2 phi1 phi2 q congruent 17 modulo 60: 1/12 q^2 phi1 phi2 q congruent 19 modulo 60: 1/12 q^2 phi1 phi2 q congruent 21 modulo 60: 1/12 q^2 phi1 phi2 q congruent 23 modulo 60: 1/12 q^2 phi1 phi2 q congruent 25 modulo 60: 1/12 q^2 phi1 phi2 q congruent 27 modulo 60: 1/12 q^2 phi1 phi2 q congruent 29 modulo 60: 1/12 q^2 phi1 phi2 q congruent 31 modulo 60: 1/12 q^2 phi1 phi2 q congruent 32 modulo 60: 1/12 q^2 phi1 phi2 q congruent 37 modulo 60: 1/12 q^2 phi1 phi2 q congruent 41 modulo 60: 1/12 q^2 phi1 phi2 q congruent 43 modulo 60: 1/12 q^2 phi1 phi2 q congruent 47 modulo 60: 1/12 q^2 phi1 phi2 q congruent 49 modulo 60: 1/12 q^2 phi1 phi2 q congruent 53 modulo 60: 1/12 q^2 phi1 phi2 q congruent 59 modulo 60: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 35, 87, 33, 88, 40, 86, 34, 85, 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ] ] k = 7: F-action on Pi is () [58,1,7] Dynkin type is A_2(q) + A_2(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 2 modulo 60: 1/24 q^2 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q phi1^2 phi2 q congruent 4 modulo 60: 1/24 q phi1 ( q^2-4 ) q congruent 5 modulo 60: 1/24 q phi1^2 phi2 q congruent 7 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 8 modulo 60: 1/24 q^2 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q phi1^2 phi2 q congruent 11 modulo 60: 1/24 q phi1^2 phi2 q congruent 13 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 16 modulo 60: 1/24 q phi1 ( q^2-4 ) q congruent 17 modulo 60: 1/24 q phi1^2 phi2 q congruent 19 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 21 modulo 60: 1/24 q phi1^2 phi2 q congruent 23 modulo 60: 1/24 q phi1^2 phi2 q congruent 25 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 27 modulo 60: 1/24 q phi1^2 phi2 q congruent 29 modulo 60: 1/24 q phi1^2 phi2 q congruent 31 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 32 modulo 60: 1/24 q^2 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 41 modulo 60: 1/24 q phi1^2 phi2 q congruent 43 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 47 modulo 60: 1/24 q phi1^2 phi2 q congruent 49 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 53 modulo 60: 1/24 q phi1^2 phi2 q congruent 59 modulo 60: 1/24 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 77, 30, 83, 30, 81, 37, 83, 37, 79 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 1, 12 ], [ 22, 1, 2, 12 ], [ 27, 1, 2, 4 ], [ 27, 1, 5, 6 ], [ 38, 1, 3, 36 ], [ 38, 1, 5, 24 ], [ 42, 1, 3, 6 ], [ 46, 1, 3, 12 ], [ 50, 1, 6, 12 ] ] k = 8: F-action on Pi is () [58,1,8] Dynkin type is A_2(q) + A_2(q) + T(phi3^2) Order of center |Z^F|: phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 2 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 3 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 4 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 5 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 7 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 8 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 9 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 11 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 13 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 16 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 17 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 19 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 21 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 23 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 25 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 27 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 29 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 31 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 32 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 37 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 41 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 43 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 47 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 49 modulo 60: 1/72 phi1 ( q^3+3*q^2-6*q-16 ) q congruent 53 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 59 modulo 60: 1/72 q phi2 ( q^2+q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 83, 12, 83, 37, 79, 12, 79, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 27, 1, 5, 12 ], [ 38, 1, 3, 72 ], [ 40, 1, 5, 36 ] ] k = 9: F-action on Pi is () [58,1,9] Dynkin type is A_2(q) + A_2(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 2 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) q congruent 4 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 7 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) q congruent 8 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 11 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 16 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 19 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 23 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 27 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 31 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) q congruent 32 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 43 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) q congruent 47 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-5*q^2+6*q-6 ) q congruent 59 modulo 60: 1/32 ( q^4-6*q^3+11*q^2-8*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 30, 68, 7, 81, 30, 81, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 24 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 16 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 29, 1, 2, 16 ], [ 31, 1, 2, 16 ], [ 32, 1, 1, 8 ], [ 34, 1, 2, 8 ], [ 38, 1, 5, 48 ], [ 39, 1, 3, 8 ], [ 40, 1, 3, 16 ], [ 42, 1, 4, 8 ], [ 43, 1, 12, 32 ], [ 46, 1, 2, 16 ], [ 50, 1, 5, 16 ], [ 51, 1, 5, 32 ] ] k = 10: F-action on Pi is (1,3)(5,6) [58,1,10] Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^3 q congruent 2 modulo 60: 1/24 q phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/24 q phi1^3 q congruent 4 modulo 60: 1/24 q^2 phi1 ( q-2 ) q congruent 5 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 7 modulo 60: 1/24 q phi1^3 q congruent 8 modulo 60: 1/24 q phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/24 q phi1^3 q congruent 11 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 13 modulo 60: 1/24 q phi1^3 q congruent 16 modulo 60: 1/24 q^2 phi1 ( q-2 ) q congruent 17 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 19 modulo 60: 1/24 q phi1^3 q congruent 21 modulo 60: 1/24 q phi1^3 q congruent 23 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 25 modulo 60: 1/24 q phi1^3 q congruent 27 modulo 60: 1/24 q phi1^3 q congruent 29 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 31 modulo 60: 1/24 q phi1^3 q congruent 32 modulo 60: 1/24 q phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/24 q phi1^3 q congruent 41 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 43 modulo 60: 1/24 q phi1^3 q congruent 47 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 49 modulo 60: 1/24 q phi1^3 q congruent 53 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 59 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 31, 84, 31, 82, 38, 84, 38, 80 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 4, 12 ], [ 22, 1, 3, 12 ], [ 27, 1, 3, 4 ], [ 27, 1, 4, 6 ], [ 38, 1, 8, 24 ], [ 38, 1, 11, 36 ], [ 42, 1, 5, 6 ], [ 46, 1, 4, 12 ], [ 50, 1, 7, 12 ] ] k = 11: F-action on Pi is (1,3)(5,6) [58,1,11] Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 2 modulo 60: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) q congruent 4 modulo 60: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 5 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 7 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) q congruent 8 modulo 60: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 11 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) q congruent 13 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 16 modulo 60: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 17 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 19 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) q congruent 21 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 23 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) q congruent 25 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 27 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) q congruent 29 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 31 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) q congruent 32 modulo 60: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 41 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 43 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) q congruent 47 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) q congruent 49 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 53 modulo 60: 1/32 phi1 ( q^3-5*q^2+10*q-10 ) q congruent 59 modulo 60: 1/32 ( q^4-6*q^3+15*q^2-24*q+18 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 69, 31, 69, 7, 82, 31, 82, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 20, 1, 3, 16 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 16 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 29, 1, 3, 16 ], [ 31, 1, 3, 16 ], [ 32, 1, 3, 8 ], [ 34, 1, 3, 8 ], [ 38, 1, 8, 48 ], [ 39, 1, 1, 8 ], [ 40, 1, 2, 16 ], [ 42, 1, 2, 8 ], [ 43, 1, 3, 32 ], [ 46, 1, 5, 16 ], [ 50, 1, 8, 16 ], [ 51, 1, 10, 32 ] ] k = 12: F-action on Pi is (1,3)(5,6) [58,1,12] Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 phi1 ( q^3-11*q^2+40*q-54 ) q congruent 2 modulo 60: 1/48 ( q^4-12*q^3+48*q^2-80*q+48 ) q congruent 3 modulo 60: 1/48 ( q^4-12*q^3+51*q^2-106*q+102 ) q congruent 4 modulo 60: 1/48 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/48 ( q^4-12*q^3+55*q^2-126*q+130 ) q congruent 7 modulo 60: 1/48 ( q^4-12*q^3+51*q^2-106*q+102 ) q congruent 8 modulo 60: 1/48 ( q^4-12*q^3+48*q^2-80*q+48 ) q congruent 9 modulo 60: 1/48 phi1 ( q^3-11*q^2+40*q-54 ) q congruent 11 modulo 60: 1/48 ( q^4-12*q^3+55*q^2-138*q+178 ) q congruent 13 modulo 60: 1/48 phi1 ( q^3-11*q^2+40*q-54 ) q congruent 16 modulo 60: 1/48 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/48 ( q^4-12*q^3+55*q^2-126*q+130 ) q congruent 19 modulo 60: 1/48 ( q^4-12*q^3+51*q^2-106*q+102 ) q congruent 21 modulo 60: 1/48 phi1 ( q^3-11*q^2+40*q-54 ) q congruent 23 modulo 60: 1/48 ( q^4-12*q^3+55*q^2-138*q+178 ) q congruent 25 modulo 60: 1/48 phi1 ( q^3-11*q^2+40*q-54 ) q congruent 27 modulo 60: 1/48 ( q^4-12*q^3+51*q^2-106*q+102 ) q congruent 29 modulo 60: 1/48 ( q^4-12*q^3+55*q^2-126*q+130 ) q congruent 31 modulo 60: 1/48 ( q^4-12*q^3+51*q^2-106*q+102 ) q congruent 32 modulo 60: 1/48 ( q^4-12*q^3+48*q^2-80*q+48 ) q congruent 37 modulo 60: 1/48 phi1 ( q^3-11*q^2+40*q-54 ) q congruent 41 modulo 60: 1/48 ( q^4-12*q^3+55*q^2-126*q+130 ) q congruent 43 modulo 60: 1/48 ( q^4-12*q^3+51*q^2-106*q+102 ) q congruent 47 modulo 60: 1/48 ( q^4-12*q^3+55*q^2-138*q+178 ) q congruent 49 modulo 60: 1/48 phi1 ( q^3-11*q^2+40*q-54 ) q congruent 53 modulo 60: 1/48 ( q^4-12*q^3+55*q^2-126*q+130 ) q congruent 59 modulo 60: 1/48 ( q^4-12*q^3+55*q^2-138*q+178 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 78, 5, 69, 31, 78, 31, 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 12 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 24 ], [ 16, 1, 3, 24 ], [ 17, 1, 4, 48 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 20, 1, 3, 24 ], [ 20, 1, 4, 24 ], [ 21, 1, 2, 12 ], [ 22, 1, 3, 12 ], [ 22, 1, 4, 36 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 2, 12 ], [ 26, 1, 4, 12 ], [ 27, 1, 3, 4 ], [ 27, 1, 6, 12 ], [ 29, 1, 3, 24 ], [ 29, 1, 4, 24 ], [ 31, 1, 3, 24 ], [ 31, 1, 4, 24 ], [ 32, 1, 3, 24 ], [ 34, 1, 3, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 3, 24 ], [ 38, 1, 8, 24 ], [ 38, 1, 12, 72 ], [ 39, 1, 4, 12 ], [ 42, 1, 2, 12 ], [ 42, 1, 6, 12 ], [ 43, 1, 4, 48 ], [ 46, 1, 5, 24 ], [ 46, 1, 6, 24 ], [ 50, 1, 9, 24 ], [ 50, 1, 11, 24 ], [ 51, 1, 8, 48 ] ] k = 13: F-action on Pi is (1,3)(5,6) [58,1,13] Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi6^2) Order of center |Z^F|: phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 2 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 3 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 5 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 7 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 8 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 9 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 11 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 13 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 17 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 19 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 21 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 23 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 25 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 27 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 29 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 31 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 32 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 37 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 41 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 43 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 47 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 49 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 53 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) q congruent 59 modulo 60: 1/72 phi2 ( q^3-3*q^2-6*q+16 ) Fusion of maximal tori of C^F in those of G^F: [ 15, 84, 13, 84, 38, 80, 13, 80, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 27, 1, 4, 12 ], [ 38, 1, 11, 72 ], [ 40, 1, 4, 36 ] ] k = 14: F-action on Pi is (1,3)(5,6) [58,1,14] Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 2 modulo 60: 1/72 phi2 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 4 modulo 60: 1/72 q^2 phi1 ( q-4 ) q congruent 5 modulo 60: 1/72 phi2 ( q^3-6*q^2+15*q-14 ) q congruent 7 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 8 modulo 60: 1/72 phi2 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 11 modulo 60: 1/72 phi2 ( q^3-6*q^2+15*q-14 ) q congruent 13 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 16 modulo 60: 1/72 q^2 phi1 ( q-4 ) q congruent 17 modulo 60: 1/72 phi2 ( q^3-6*q^2+15*q-14 ) q congruent 19 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 21 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 23 modulo 60: 1/72 phi2 ( q^3-6*q^2+15*q-14 ) q congruent 25 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 27 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/72 phi2 ( q^3-6*q^2+15*q-14 ) q congruent 31 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 32 modulo 60: 1/72 phi2 ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 41 modulo 60: 1/72 phi2 ( q^3-6*q^2+15*q-14 ) q congruent 43 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 47 modulo 60: 1/72 phi2 ( q^3-6*q^2+15*q-14 ) q congruent 49 modulo 60: 1/72 q phi1^2 ( q-3 ) q congruent 53 modulo 60: 1/72 phi2 ( q^3-6*q^2+15*q-14 ) q congruent 59 modulo 60: 1/72 phi2 ( q^3-6*q^2+15*q-14 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 78, 15, 78, 31, 84, 15, 84, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 18 ], [ 8, 1, 2, 12 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 4, 36 ], [ 22, 1, 4, 36 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 12 ], [ 38, 1, 11, 36 ], [ 38, 1, 12, 72 ], [ 42, 1, 5, 18 ], [ 46, 1, 4, 36 ], [ 50, 1, 10, 36 ] ] k = 15: F-action on Pi is (1,3)(5,6) [58,1,15] Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi2^4) Order of center |Z^F|: phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 phi1 ( q^3-25*q^2+210*q-630 ) q congruent 2 modulo 60: 1/288 ( q^4-26*q^3+228*q^2-776*q+832 ) q congruent 3 modulo 60: 1/288 ( q^4-26*q^3+235*q^2-876*q+1134 ) q congruent 4 modulo 60: 1/288 ( q^4-26*q^3+220*q^2-600*q+288 ) q congruent 5 modulo 60: 1/288 ( q^4-26*q^3+243*q^2-1016*q+1630 ) q congruent 7 modulo 60: 1/288 ( q^4-26*q^3+235*q^2-876*q+1134 ) q congruent 8 modulo 60: 1/288 ( q^4-26*q^3+228*q^2-776*q+832 ) q congruent 9 modulo 60: 1/288 ( q^4-26*q^3+235*q^2-840*q+918 ) q congruent 11 modulo 60: 1/288 ( q^4-26*q^3+243*q^2-1052*q+2134 ) q congruent 13 modulo 60: 1/288 phi1 ( q^3-25*q^2+210*q-630 ) q congruent 16 modulo 60: 1/288 q ( q^3-26*q^2+220*q-600 ) q congruent 17 modulo 60: 1/288 ( q^4-26*q^3+243*q^2-1016*q+1630 ) q congruent 19 modulo 60: 1/288 ( q^4-26*q^3+235*q^2-876*q+1422 ) q congruent 21 modulo 60: 1/288 phi1 ( q^3-25*q^2+210*q-630 ) q congruent 23 modulo 60: 1/288 ( q^4-26*q^3+243*q^2-1052*q+2134 ) q congruent 25 modulo 60: 1/288 phi1 ( q^3-25*q^2+210*q-630 ) q congruent 27 modulo 60: 1/288 ( q^4-26*q^3+235*q^2-876*q+1134 ) q congruent 29 modulo 60: 1/288 ( q^4-26*q^3+243*q^2-1016*q+1918 ) q congruent 31 modulo 60: 1/288 ( q^4-26*q^3+235*q^2-876*q+1134 ) q congruent 32 modulo 60: 1/288 ( q^4-26*q^3+228*q^2-776*q+832 ) q congruent 37 modulo 60: 1/288 phi1 ( q^3-25*q^2+210*q-630 ) q congruent 41 modulo 60: 1/288 ( q^4-26*q^3+243*q^2-1016*q+1630 ) q congruent 43 modulo 60: 1/288 ( q^4-26*q^3+235*q^2-876*q+1134 ) q congruent 47 modulo 60: 1/288 ( q^4-26*q^3+243*q^2-1052*q+2134 ) q congruent 49 modulo 60: 1/288 ( q^4-26*q^3+235*q^2-840*q+918 ) q congruent 53 modulo 60: 1/288 ( q^4-26*q^3+243*q^2-1016*q+1630 ) q congruent 59 modulo 60: 1/288 ( q^4-26*q^3+243*q^2-1052*q+2422 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 9, 67, 5, 78, 9, 78, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 36 ], [ 5, 1, 2, 72 ], [ 6, 1, 2, 36 ], [ 7, 1, 2, 36 ], [ 8, 1, 2, 24 ], [ 9, 1, 1, 9 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 36 ], [ 14, 1, 2, 144 ], [ 15, 1, 2, 72 ], [ 16, 1, 3, 72 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 36 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 72 ], [ 22, 1, 4, 72 ], [ 23, 1, 2, 36 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 144 ], [ 26, 1, 4, 72 ], [ 27, 1, 6, 24 ], [ 29, 1, 4, 144 ], [ 31, 1, 4, 144 ], [ 32, 1, 3, 72 ], [ 34, 1, 4, 72 ], [ 36, 1, 4, 144 ], [ 37, 1, 3, 288 ], [ 38, 1, 12, 144 ], [ 39, 1, 3, 72 ], [ 40, 1, 6, 144 ], [ 42, 1, 6, 72 ], [ 43, 1, 13, 288 ], [ 46, 1, 6, 144 ], [ 50, 1, 12, 144 ], [ 51, 1, 9, 288 ] ] k = 16: F-action on Pi is (1,5)(3,6) [58,1,16] Dynkin type is A_2(q^2) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 phi1 ( q^3-9*q^2+24*q-4 ) q congruent 2 modulo 60: 1/48 q ( q^3-10*q^2+28*q-24 ) q congruent 3 modulo 60: 1/48 ( q^4-10*q^3+29*q^2-20*q-12 ) q congruent 4 modulo 60: 1/48 q ( q^3-10*q^2+32*q-32 ) q congruent 5 modulo 60: 1/48 q phi1 ( q^2-9*q+20 ) q congruent 7 modulo 60: 1/48 ( q^4-10*q^3+33*q^2-28*q-8 ) q congruent 8 modulo 60: 1/48 q ( q^3-10*q^2+28*q-24 ) q congruent 9 modulo 60: 1/48 q phi1 ( q^2-9*q+20 ) q congruent 11 modulo 60: 1/48 ( q^4-10*q^3+29*q^2-20*q-12 ) q congruent 13 modulo 60: 1/48 phi1 ( q^3-9*q^2+24*q-4 ) q congruent 16 modulo 60: 1/48 q ( q^3-10*q^2+32*q-32 ) q congruent 17 modulo 60: 1/48 q phi1 ( q^2-9*q+20 ) q congruent 19 modulo 60: 1/48 ( q^4-10*q^3+33*q^2-28*q-8 ) q congruent 21 modulo 60: 1/48 q phi1 ( q^2-9*q+20 ) q congruent 23 modulo 60: 1/48 ( q^4-10*q^3+29*q^2-20*q-12 ) q congruent 25 modulo 60: 1/48 phi1 ( q^3-9*q^2+24*q-4 ) q congruent 27 modulo 60: 1/48 ( q^4-10*q^3+29*q^2-20*q-12 ) q congruent 29 modulo 60: 1/48 q phi1 ( q^2-9*q+20 ) q congruent 31 modulo 60: 1/48 ( q^4-10*q^3+33*q^2-28*q-8 ) q congruent 32 modulo 60: 1/48 q ( q^3-10*q^2+28*q-24 ) q congruent 37 modulo 60: 1/48 phi1 ( q^3-9*q^2+24*q-4 ) q congruent 41 modulo 60: 1/48 q phi1 ( q^2-9*q+20 ) q congruent 43 modulo 60: 1/48 ( q^4-10*q^3+33*q^2-28*q-8 ) q congruent 47 modulo 60: 1/48 ( q^4-10*q^3+29*q^2-20*q-12 ) q congruent 49 modulo 60: 1/48 phi1 ( q^3-9*q^2+24*q-4 ) q congruent 53 modulo 60: 1/48 q phi1 ( q^2-9*q+20 ) q congruent 59 modulo 60: 1/48 ( q^4-10*q^3+29*q^2-20*q-12 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 87 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 8 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 12 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 6, 24 ], [ 20, 1, 8, 24 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 12 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 12 ], [ 26, 1, 1, 12 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 12 ], [ 27, 1, 3, 4 ], [ 32, 1, 4, 12 ], [ 34, 1, 1, 12 ], [ 34, 1, 3, 12 ], [ 36, 1, 1, 24 ], [ 38, 1, 2, 8 ], [ 38, 1, 7, 24 ], [ 39, 1, 1, 24 ], [ 42, 1, 1, 12 ], [ 42, 1, 2, 12 ], [ 43, 1, 6, 48 ], [ 46, 1, 7, 24 ], [ 46, 1, 11, 24 ], [ 50, 1, 1, 24 ], [ 50, 1, 8, 24 ] ] k = 17: F-action on Pi is (1,5)(3,6) [58,1,17] Dynkin type is A_2(q^2) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 3 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 5 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 7 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 9 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 11 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 16 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 17 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 19 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 23 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 27 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 31 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/16 q ( q^3-4*q^2+8 ) q congruent 37 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 41 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 43 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 53 modulo 60: 1/16 phi1^2 ( q^2-2*q-4 ) q congruent 59 modulo 60: 1/16 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 76, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ], [ 20, 1, 6, 8 ], [ 20, 1, 7, 8 ], [ 21, 1, 1, 4 ], [ 21, 1, 2, 4 ], [ 22, 1, 1, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 2, 4 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 32, 1, 4, 4 ], [ 34, 1, 1, 4 ], [ 34, 1, 4, 4 ], [ 36, 1, 2, 8 ], [ 36, 1, 3, 8 ], [ 37, 1, 4, 16 ], [ 38, 1, 2, 8 ], [ 38, 1, 10, 8 ], [ 39, 1, 4, 4 ], [ 42, 1, 2, 4 ], [ 42, 1, 4, 4 ], [ 43, 1, 7, 16 ], [ 46, 1, 8, 8 ], [ 46, 1, 11, 8 ], [ 50, 1, 2, 8 ], [ 50, 1, 11, 8 ] ] k = 18: F-action on Pi is (1,5)(3,6) [58,1,18] Dynkin type is A_2(q^2) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 2 modulo 60: 1/24 q^2 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q phi1^2 phi2 q congruent 4 modulo 60: 1/24 q phi1 ( q^2-4 ) q congruent 5 modulo 60: 1/24 q phi1^2 phi2 q congruent 7 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 8 modulo 60: 1/24 q^2 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q phi1^2 phi2 q congruent 11 modulo 60: 1/24 q phi1^2 phi2 q congruent 13 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 16 modulo 60: 1/24 q phi1 ( q^2-4 ) q congruent 17 modulo 60: 1/24 q phi1^2 phi2 q congruent 19 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 21 modulo 60: 1/24 q phi1^2 phi2 q congruent 23 modulo 60: 1/24 q phi1^2 phi2 q congruent 25 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 27 modulo 60: 1/24 q phi1^2 phi2 q congruent 29 modulo 60: 1/24 q phi1^2 phi2 q congruent 31 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 32 modulo 60: 1/24 q^2 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 41 modulo 60: 1/24 q phi1^2 phi2 q congruent 43 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 47 modulo 60: 1/24 q phi1^2 phi2 q congruent 49 modulo 60: 1/24 phi1^3 ( q+2 ) q congruent 53 modulo 60: 1/24 q phi1^2 phi2 q congruent 59 modulo 60: 1/24 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 81, 59, 85 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 22, 1, 1, 4 ], [ 27, 1, 3, 4 ], [ 27, 1, 5, 6 ], [ 38, 1, 2, 8 ], [ 38, 1, 9, 12 ], [ 42, 1, 3, 6 ], [ 46, 1, 9, 12 ], [ 50, 1, 3, 12 ] ] k = 19: F-action on Pi is (1,5,3,6) [58,1,19] Dynkin type is ^2A_2(q^2) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 2 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 3 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 4 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 5 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 7 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 8 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 9 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 11 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 13 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 16 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 17 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 19 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 21 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 23 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 25 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 27 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 29 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 31 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 32 modulo 60: 1/8 q^2 ( q^2-2 ) q congruent 37 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 41 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 43 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 47 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 49 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 53 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) q congruent 59 modulo 60: 1/8 phi1 phi2 ( q^2-2 ) Fusion of maximal tori of C^F in those of G^F: [ 75, 22, 100 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 32, 1, 5, 4 ], [ 39, 1, 2, 4 ], [ 43, 1, 11, 8 ] ] k = 20: F-action on Pi is (1,5,3,6) [58,1,20] Dynkin type is ^2A_2(q^2) + T(phi12) Order of center |Z^F|: phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1 phi2 q congruent 2 modulo 60: 1/12 q^2 phi1 phi2 q congruent 3 modulo 60: 1/12 q^2 phi1 phi2 q congruent 4 modulo 60: 1/12 q^2 phi1 phi2 q congruent 5 modulo 60: 1/12 q^2 phi1 phi2 q congruent 7 modulo 60: 1/12 q^2 phi1 phi2 q congruent 8 modulo 60: 1/12 q^2 phi1 phi2 q congruent 9 modulo 60: 1/12 q^2 phi1 phi2 q congruent 11 modulo 60: 1/12 q^2 phi1 phi2 q congruent 13 modulo 60: 1/12 q^2 phi1 phi2 q congruent 16 modulo 60: 1/12 q^2 phi1 phi2 q congruent 17 modulo 60: 1/12 q^2 phi1 phi2 q congruent 19 modulo 60: 1/12 q^2 phi1 phi2 q congruent 21 modulo 60: 1/12 q^2 phi1 phi2 q congruent 23 modulo 60: 1/12 q^2 phi1 phi2 q congruent 25 modulo 60: 1/12 q^2 phi1 phi2 q congruent 27 modulo 60: 1/12 q^2 phi1 phi2 q congruent 29 modulo 60: 1/12 q^2 phi1 phi2 q congruent 31 modulo 60: 1/12 q^2 phi1 phi2 q congruent 32 modulo 60: 1/12 q^2 phi1 phi2 q congruent 37 modulo 60: 1/12 q^2 phi1 phi2 q congruent 41 modulo 60: 1/12 q^2 phi1 phi2 q congruent 43 modulo 60: 1/12 q^2 phi1 phi2 q congruent 47 modulo 60: 1/12 q^2 phi1 phi2 q congruent 49 modulo 60: 1/12 q^2 phi1 phi2 q congruent 53 modulo 60: 1/12 q^2 phi1 phi2 q congruent 59 modulo 60: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 39, 100, 32 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 21: F-action on Pi is (1,5,3,6) [58,1,21] Dynkin type is ^2A_2(q^2) + T(phi4^2) Order of center |Z^F|: phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 2 modulo 60: 1/24 ( q^4-10*q^2+24 ) q congruent 3 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 4 modulo 60: 1/24 q^2 ( q^2-10 ) q congruent 5 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 7 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 8 modulo 60: 1/24 ( q^4-10*q^2+24 ) q congruent 9 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 11 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 13 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 16 modulo 60: 1/24 q^2 ( q^2-10 ) q congruent 17 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 19 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 21 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 23 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 25 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 27 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 29 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 31 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 32 modulo 60: 1/24 ( q^4-10*q^2+24 ) q congruent 37 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 41 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 43 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 47 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 49 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) q congruent 53 modulo 60: 1/24 ( q^4-13*q^2+36 ) q congruent 59 modulo 60: 1/24 phi1 phi2 ( q^2-12 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 75, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 12 ], [ 5, 1, 4, 12 ], [ 9, 1, 1, 3 ], [ 32, 1, 5, 12 ], [ 37, 1, 5, 24 ], [ 39, 1, 5, 12 ], [ 43, 1, 10, 24 ] ] k = 22: F-action on Pi is (1,5)(3,6) [58,1,22] Dynkin type is A_2(q^2) + T(phi1^2 phi6) Order of center |Z^F|: phi1^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1 ( q^2-8*q+19 ) q congruent 2 modulo 60: 1/72 phi2 ( q^3-10*q^2+28*q-24 ) q congruent 3 modulo 60: 1/72 q phi1 ( q^2-8*q+15 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^2-8*q+16 ) q congruent 5 modulo 60: 1/72 phi2 ( q^3-10*q^2+31*q-30 ) q congruent 7 modulo 60: 1/72 q phi1 ( q^2-8*q+19 ) q congruent 8 modulo 60: 1/72 phi2 ( q^3-10*q^2+28*q-24 ) q congruent 9 modulo 60: 1/72 q phi1 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/72 phi2 ( q^3-10*q^2+31*q-30 ) q congruent 13 modulo 60: 1/72 q phi1 ( q^2-8*q+19 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^2-8*q+16 ) q congruent 17 modulo 60: 1/72 phi2 ( q^3-10*q^2+31*q-30 ) q congruent 19 modulo 60: 1/72 q phi1 ( q^2-8*q+19 ) q congruent 21 modulo 60: 1/72 q phi1 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/72 phi2 ( q^3-10*q^2+31*q-30 ) q congruent 25 modulo 60: 1/72 q phi1 ( q^2-8*q+19 ) q congruent 27 modulo 60: 1/72 q phi1 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/72 phi2 ( q^3-10*q^2+31*q-30 ) q congruent 31 modulo 60: 1/72 q phi1 ( q^2-8*q+19 ) q congruent 32 modulo 60: 1/72 phi2 ( q^3-10*q^2+28*q-24 ) q congruent 37 modulo 60: 1/72 q phi1 ( q^2-8*q+19 ) q congruent 41 modulo 60: 1/72 phi2 ( q^3-10*q^2+31*q-30 ) q congruent 43 modulo 60: 1/72 q phi1 ( q^2-8*q+19 ) q congruent 47 modulo 60: 1/72 phi2 ( q^3-10*q^2+31*q-30 ) q congruent 49 modulo 60: 1/72 q phi1 ( q^2-8*q+19 ) q congruent 53 modulo 60: 1/72 phi2 ( q^3-10*q^2+31*q-30 ) q congruent 59 modulo 60: 1/72 phi2 ( q^3-10*q^2+31*q-30 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 96, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 6 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 3, 12 ], [ 22, 1, 3, 12 ], [ 27, 1, 1, 12 ], [ 27, 1, 4, 6 ], [ 38, 1, 4, 12 ], [ 38, 1, 7, 24 ], [ 42, 1, 5, 18 ], [ 46, 1, 10, 36 ], [ 50, 1, 7, 36 ] ] k = 23: F-action on Pi is (1,5)(3,6) [58,1,23] Dynkin type is A_2(q^2) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^3 q congruent 2 modulo 60: 1/24 q phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/24 q phi1^3 q congruent 4 modulo 60: 1/24 q^2 phi1 ( q-2 ) q congruent 5 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 7 modulo 60: 1/24 q phi1^3 q congruent 8 modulo 60: 1/24 q phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/24 q phi1^3 q congruent 11 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 13 modulo 60: 1/24 q phi1^3 q congruent 16 modulo 60: 1/24 q^2 phi1 ( q-2 ) q congruent 17 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 19 modulo 60: 1/24 q phi1^3 q congruent 21 modulo 60: 1/24 q phi1^3 q congruent 23 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 25 modulo 60: 1/24 q phi1^3 q congruent 27 modulo 60: 1/24 q phi1^3 q congruent 29 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 31 modulo 60: 1/24 q phi1^3 q congruent 32 modulo 60: 1/24 q phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/24 q phi1^3 q congruent 41 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 43 modulo 60: 1/24 q phi1^3 q congruent 47 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 49 modulo 60: 1/24 q phi1^3 q congruent 53 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) q congruent 59 modulo 60: 1/24 phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 82, 60, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 27, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 38, 1, 4, 12 ], [ 38, 1, 10, 8 ], [ 42, 1, 5, 6 ], [ 46, 1, 10, 12 ], [ 50, 1, 10, 12 ] ] k = 24: F-action on Pi is (1,5)(3,6) [58,1,24] Dynkin type is A_2(q^2) + T(phi3 phi6) Order of center |Z^F|: phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 2 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 3 modulo 60: 1/36 q^2 phi1 phi2 q congruent 4 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 5 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 7 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 8 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 9 modulo 60: 1/36 q^2 phi1 phi2 q congruent 11 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 13 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 16 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 17 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 19 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 21 modulo 60: 1/36 q^2 phi1 phi2 q congruent 23 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 25 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 27 modulo 60: 1/36 q^2 phi1 phi2 q congruent 29 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 31 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 32 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 37 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 41 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 43 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 47 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 49 modulo 60: 1/36 q phi1^2 ( q+2 ) q congruent 53 modulo 60: 1/36 q phi2^2 ( q-2 ) q congruent 59 modulo 60: 1/36 q phi2^2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 36, 99, 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 27, 1, 4, 6 ], [ 27, 1, 5, 6 ], [ 38, 1, 4, 12 ], [ 38, 1, 9, 12 ] ] k = 25: F-action on Pi is (1,5)(3,6) [58,1,25] Dynkin type is A_2(q^2) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 phi1 ( q^3-11*q^2+34*q-12 ) q congruent 2 modulo 60: 1/144 ( q^4-12*q^3+48*q^2-80*q+48 ) q congruent 3 modulo 60: 1/144 ( q^4-12*q^3+41*q^2-30*q-36 ) q congruent 4 modulo 60: 1/144 q ( q^3-12*q^2+48*q-64 ) q congruent 5 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-62*q+60 ) q congruent 7 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-46*q-24 ) q congruent 8 modulo 60: 1/144 ( q^4-12*q^3+48*q^2-80*q+48 ) q congruent 9 modulo 60: 1/144 q phi1 ( q^2-11*q+30 ) q congruent 11 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-62*q+24 ) q congruent 13 modulo 60: 1/144 phi1 ( q^3-11*q^2+34*q-12 ) q congruent 16 modulo 60: 1/144 q ( q^3-12*q^2+48*q-64 ) q congruent 17 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-62*q+60 ) q congruent 19 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-46*q-24 ) q congruent 21 modulo 60: 1/144 q phi1 ( q^2-11*q+30 ) q congruent 23 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-62*q+24 ) q congruent 25 modulo 60: 1/144 phi1 ( q^3-11*q^2+34*q-12 ) q congruent 27 modulo 60: 1/144 ( q^4-12*q^3+41*q^2-30*q-36 ) q congruent 29 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-62*q+60 ) q congruent 31 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-46*q-24 ) q congruent 32 modulo 60: 1/144 ( q^4-12*q^3+48*q^2-80*q+48 ) q congruent 37 modulo 60: 1/144 phi1 ( q^3-11*q^2+34*q-12 ) q congruent 41 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-62*q+60 ) q congruent 43 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-46*q-24 ) q congruent 47 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-62*q+24 ) q congruent 49 modulo 60: 1/144 phi1 ( q^3-11*q^2+34*q-12 ) q congruent 53 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-62*q+60 ) q congruent 59 modulo 60: 1/144 ( q^4-12*q^3+45*q^2-62*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 6 ], [ 6, 1, 2, 6 ], [ 7, 1, 1, 18 ], [ 7, 1, 2, 18 ], [ 9, 1, 1, 9 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 17, 1, 3, 12 ], [ 19, 1, 1, 18 ], [ 19, 1, 2, 18 ], [ 20, 1, 5, 72 ], [ 20, 1, 8, 72 ], [ 22, 1, 2, 12 ], [ 22, 1, 3, 12 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 18 ], [ 26, 1, 1, 36 ], [ 26, 1, 4, 36 ], [ 27, 1, 1, 12 ], [ 27, 1, 6, 12 ], [ 32, 1, 4, 36 ], [ 34, 1, 2, 36 ], [ 34, 1, 3, 36 ], [ 38, 1, 6, 24 ], [ 38, 1, 7, 24 ], [ 39, 1, 4, 36 ], [ 42, 1, 1, 36 ], [ 42, 1, 6, 36 ], [ 43, 1, 5, 144 ], [ 46, 1, 7, 72 ], [ 46, 1, 12, 72 ], [ 50, 1, 4, 72 ], [ 50, 1, 9, 72 ] ] k = 26: F-action on Pi is (1,5)(3,6) [58,1,26] Dynkin type is A_2(q^2) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 ( q-4 ) q congruent 2 modulo 60: 1/48 q ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/48 ( q^4-6*q^3+9*q^2-4*q+12 ) q congruent 4 modulo 60: 1/48 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/48 phi1^2 ( q^2-4*q+4 ) q congruent 7 modulo 60: 1/48 ( q^4-6*q^3+9*q^2-4*q+12 ) q congruent 8 modulo 60: 1/48 q ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/48 q phi1^2 ( q-4 ) q congruent 11 modulo 60: 1/48 ( q^4-6*q^3+13*q^2-12*q+16 ) q congruent 13 modulo 60: 1/48 q phi1^2 ( q-4 ) q congruent 16 modulo 60: 1/48 q^2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/48 phi1^2 ( q^2-4*q+4 ) q congruent 19 modulo 60: 1/48 ( q^4-6*q^3+9*q^2-4*q+12 ) q congruent 21 modulo 60: 1/48 q phi1^2 ( q-4 ) q congruent 23 modulo 60: 1/48 ( q^4-6*q^3+13*q^2-12*q+16 ) q congruent 25 modulo 60: 1/48 q phi1^2 ( q-4 ) q congruent 27 modulo 60: 1/48 ( q^4-6*q^3+9*q^2-4*q+12 ) q congruent 29 modulo 60: 1/48 phi1^2 ( q^2-4*q+4 ) q congruent 31 modulo 60: 1/48 ( q^4-6*q^3+9*q^2-4*q+12 ) q congruent 32 modulo 60: 1/48 q ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/48 q phi1^2 ( q-4 ) q congruent 41 modulo 60: 1/48 phi1^2 ( q^2-4*q+4 ) q congruent 43 modulo 60: 1/48 ( q^4-6*q^3+9*q^2-4*q+12 ) q congruent 47 modulo 60: 1/48 ( q^4-6*q^3+13*q^2-12*q+16 ) q congruent 49 modulo 60: 1/48 q phi1^2 ( q-4 ) q congruent 53 modulo 60: 1/48 phi1^2 ( q^2-4*q+4 ) q congruent 59 modulo 60: 1/48 ( q^4-6*q^3+13*q^2-12*q+16 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 6 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 8 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 12 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 5, 24 ], [ 20, 1, 7, 24 ], [ 21, 1, 2, 12 ], [ 22, 1, 2, 12 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 12 ], [ 26, 1, 3, 12 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 4 ], [ 27, 1, 6, 12 ], [ 32, 1, 4, 12 ], [ 34, 1, 2, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 4, 24 ], [ 38, 1, 6, 24 ], [ 38, 1, 10, 8 ], [ 39, 1, 3, 24 ], [ 42, 1, 4, 12 ], [ 42, 1, 6, 12 ], [ 43, 1, 14, 48 ], [ 46, 1, 8, 24 ], [ 46, 1, 12, 24 ], [ 50, 1, 5, 24 ], [ 50, 1, 12, 24 ] ] k = 27: F-action on Pi is (1,5)(3,6) [58,1,27] Dynkin type is A_2(q^2) + T(phi2^2 phi3) Order of center |Z^F|: phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1^2 ( q^2-q-6 ) q congruent 2 modulo 60: 1/72 q phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/72 q phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^2-2*q-8 ) q congruent 5 modulo 60: 1/72 q phi2 ( q^2-4*q+7 ) q congruent 7 modulo 60: 1/72 phi1^2 ( q^2-q-6 ) q congruent 8 modulo 60: 1/72 q phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/72 q phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/72 q phi2 ( q^2-4*q+7 ) q congruent 13 modulo 60: 1/72 phi1^2 ( q^2-q-6 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^2-2*q-8 ) q congruent 17 modulo 60: 1/72 q phi2 ( q^2-4*q+7 ) q congruent 19 modulo 60: 1/72 phi1^2 ( q^2-q-6 ) q congruent 21 modulo 60: 1/72 q phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/72 q phi2 ( q^2-4*q+7 ) q congruent 25 modulo 60: 1/72 phi1^2 ( q^2-q-6 ) q congruent 27 modulo 60: 1/72 q phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/72 q phi2 ( q^2-4*q+7 ) q congruent 31 modulo 60: 1/72 phi1^2 ( q^2-q-6 ) q congruent 32 modulo 60: 1/72 q phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/72 phi1^2 ( q^2-q-6 ) q congruent 41 modulo 60: 1/72 q phi2 ( q^2-4*q+7 ) q congruent 43 modulo 60: 1/72 phi1^2 ( q^2-q-6 ) q congruent 47 modulo 60: 1/72 q phi2 ( q^2-4*q+7 ) q congruent 49 modulo 60: 1/72 phi1^2 ( q^2-q-6 ) q congruent 53 modulo 60: 1/72 q phi2 ( q^2-4*q+7 ) q congruent 59 modulo 60: 1/72 q phi2 ( q^2-4*q+7 ) Fusion of maximal tori of C^F in those of G^F: [ 27, 95, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 22, 1, 2, 12 ], [ 27, 1, 5, 6 ], [ 27, 1, 6, 12 ], [ 38, 1, 6, 24 ], [ 38, 1, 9, 12 ], [ 42, 1, 3, 18 ], [ 46, 1, 9, 36 ], [ 50, 1, 6, 36 ] ] i = 59: Pi = [ 2, 3, 4, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [59,1,1] Dynkin type is D_4(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 2 modulo 60: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 3 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 4 modulo 60: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1280 ) q congruent 5 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 7 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 8 modulo 60: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 9 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 11 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 13 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 16 modulo 60: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1280 ) q congruent 17 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 19 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 21 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 23 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 25 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 27 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 29 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 31 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 32 modulo 60: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 37 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 41 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 43 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 47 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 49 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 53 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 59 modulo 60: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 4, 3, 66, 70, 68, 4, 4, 16, 8, 28, 70, 70 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 144 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 39, 1, 1, 144 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 288 ], [ 44, 1, 1, 576 ], [ 52, 1, 1, 576 ] ] k = 2: F-action on Pi is () [59,1,2] Dynkin type is D_4(q) + T(phi2^4) Order of center |Z^F|: phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 2 modulo 60: 1/1152 ( q^4-20*q^3+124*q^2-240*q+128 ) q congruent 3 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 4 modulo 60: 1/1152 q ( q^3-20*q^2+124*q-240 ) q congruent 5 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+425 ) q congruent 7 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 8 modulo 60: 1/1152 ( q^4-20*q^3+124*q^2-240*q+128 ) q congruent 9 modulo 60: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 11 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+569 ) q congruent 13 modulo 60: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 16 modulo 60: 1/1152 q ( q^3-20*q^2+124*q-240 ) q congruent 17 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+425 ) q congruent 19 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 21 modulo 60: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 23 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+569 ) q congruent 25 modulo 60: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 27 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 29 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+425 ) q congruent 31 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 32 modulo 60: 1/1152 ( q^4-20*q^3+124*q^2-240*q+128 ) q congruent 37 modulo 60: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 41 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+425 ) q congruent 43 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 47 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+569 ) q congruent 49 modulo 60: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 53 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+425 ) q congruent 59 modulo 60: 1/1152 ( q^4-20*q^3+142*q^2-420*q+569 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 5, 2, 69, 71, 67, 5, 5, 17, 27, 9, 71, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 4, 144 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 72 ], [ 25, 1, 3, 48 ], [ 27, 1, 6, 192 ], [ 28, 1, 4, 288 ], [ 39, 1, 3, 144 ], [ 40, 1, 6, 192 ], [ 41, 1, 9, 288 ], [ 44, 1, 10, 576 ], [ 52, 1, 10, 576 ] ] k = 3: F-action on Pi is () [59,1,3] Dynkin type is D_4(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/64 phi1^2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 7, 5, 68, 76, 69, 3, 7, 18, 30, 31, 72, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 8 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 8 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 32 ], [ 41, 1, 6, 32 ], [ 41, 1, 9, 16 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ] ] k = 4: F-action on Pi is () [59,1,4] Dynkin type is D_4(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 16 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 17 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 21 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 27 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 32 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 41 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 47 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 53 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 30, 27, 77, 97, 81, 30, 30, 53, 14, 36, 97, 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 40, 1, 1, 12 ], [ 44, 1, 3, 18 ] ] k = 5: F-action on Pi is () [59,1,5] Dynkin type is D_4(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 q^2 phi1^2 q congruent 2 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 60: 1/36 q^2 phi1^2 q congruent 4 modulo 60: 1/36 q^2 phi1^2 q congruent 5 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 60: 1/36 q^2 phi1^2 q congruent 8 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 9 modulo 60: 1/36 q^2 phi1^2 q congruent 11 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 13 modulo 60: 1/36 q^2 phi1^2 q congruent 16 modulo 60: 1/36 q^2 phi1^2 q congruent 17 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 19 modulo 60: 1/36 q^2 phi1^2 q congruent 21 modulo 60: 1/36 q^2 phi1^2 q congruent 23 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 25 modulo 60: 1/36 q^2 phi1^2 q congruent 27 modulo 60: 1/36 q^2 phi1^2 q congruent 29 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 31 modulo 60: 1/36 q^2 phi1^2 q congruent 32 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 37 modulo 60: 1/36 q^2 phi1^2 q congruent 41 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 43 modulo 60: 1/36 q^2 phi1^2 q congruent 47 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 49 modulo 60: 1/36 q^2 phi1^2 q congruent 53 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 59 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 31, 9, 82, 98, 78, 31, 31, 54, 36, 15, 98, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], [ 40, 1, 6, 12 ], [ 44, 1, 7, 18 ] ] k = 6: F-action on Pi is () [59,1,6] Dynkin type is D_4(q) + T(phi4^2) Order of center |Z^F|: phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 60: 1/96 q^2 ( q^2-4 ) q congruent 3 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 60: 1/96 q^2 ( q^2-4 ) q congruent 5 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 60: 1/96 q^2 ( q^2-4 ) q congruent 9 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 13 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 16 modulo 60: 1/96 q^2 ( q^2-4 ) q congruent 17 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 19 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 21 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 23 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 25 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 27 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 29 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 31 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 32 modulo 60: 1/96 q^2 ( q^2-4 ) q congruent 37 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 41 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 43 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 47 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 49 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 53 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) q congruent 59 modulo 60: 1/96 phi1 phi2 ( q^2-9 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 18, 17, 73, 75, 74, 18, 18, 6, 53, 54, 75, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 3 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ] ] k = 7: F-action on Pi is (2,3,5) [59,1,7] Dynkin type is ^3D_4(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 16 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 17 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 21 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 27 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 32 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 41 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 47 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 53 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 87, 83, 35, 12, 57, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 27, 1, 1, 12 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 18 ] ] k = 8: F-action on Pi is (2,5,3) [59,1,8] Dynkin type is ^3D_4(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 q^2 phi1^2 q congruent 2 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 60: 1/36 q^2 phi1^2 q congruent 4 modulo 60: 1/36 q^2 phi1^2 q congruent 5 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 60: 1/36 q^2 phi1^2 q congruent 8 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 9 modulo 60: 1/36 q^2 phi1^2 q congruent 11 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 13 modulo 60: 1/36 q^2 phi1^2 q congruent 16 modulo 60: 1/36 q^2 phi1^2 q congruent 17 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 19 modulo 60: 1/36 q^2 phi1^2 q congruent 21 modulo 60: 1/36 q^2 phi1^2 q congruent 23 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 25 modulo 60: 1/36 q^2 phi1^2 q congruent 27 modulo 60: 1/36 q^2 phi1^2 q congruent 29 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 31 modulo 60: 1/36 q^2 phi1^2 q congruent 32 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 37 modulo 60: 1/36 q^2 phi1^2 q congruent 41 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 43 modulo 60: 1/36 q^2 phi1^2 q congruent 47 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 49 modulo 60: 1/36 q^2 phi1^2 q congruent 53 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 59 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 84, 88, 15, 34, 58, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 27, 1, 6, 12 ], [ 40, 1, 4, 6 ], [ 52, 1, 7, 18 ] ] k = 9: F-action on Pi is (2,3,5) [59,1,9] Dynkin type is ^3D_4(q) + T(phi3^2) Order of center |Z^F|: phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 2 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 3 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 4 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 5 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 7 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 8 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 9 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 11 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 13 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 16 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 17 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 19 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 21 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 23 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 25 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 27 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 29 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 31 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 32 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 37 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 41 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 43 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 47 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 49 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 53 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 59 modulo 60: 1/72 q phi2 ( q^2+q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 85, 79, 34, 10, 55, 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 27, 1, 5, 24 ], [ 40, 1, 5, 24 ] ] k = 10: F-action on Pi is (2,3,5) [59,1,10] Dynkin type is ^3D_4(q) + T(phi6^2) Order of center |Z^F|: phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 2 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 5 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 7 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 8 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 9 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 11 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 13 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 17 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 19 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 21 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 23 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 25 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 27 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 29 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 31 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 32 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 37 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 41 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 43 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 47 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 49 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 53 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 59 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 80, 86, 13, 29, 56, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 27, 1, 4, 24 ], [ 40, 1, 4, 24 ] ] k = 11: F-action on Pi is (2,3,5) [59,1,11] Dynkin type is ^3D_4(q) + T(phi12) Order of center |Z^F|: phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1 phi2 q congruent 2 modulo 60: 1/12 q^2 phi1 phi2 q congruent 3 modulo 60: 1/12 q^2 phi1 phi2 q congruent 4 modulo 60: 1/12 q^2 phi1 phi2 q congruent 5 modulo 60: 1/12 q^2 phi1 phi2 q congruent 7 modulo 60: 1/12 q^2 phi1 phi2 q congruent 8 modulo 60: 1/12 q^2 phi1 phi2 q congruent 9 modulo 60: 1/12 q^2 phi1 phi2 q congruent 11 modulo 60: 1/12 q^2 phi1 phi2 q congruent 13 modulo 60: 1/12 q^2 phi1 phi2 q congruent 16 modulo 60: 1/12 q^2 phi1 phi2 q congruent 17 modulo 60: 1/12 q^2 phi1 phi2 q congruent 19 modulo 60: 1/12 q^2 phi1 phi2 q congruent 21 modulo 60: 1/12 q^2 phi1 phi2 q congruent 23 modulo 60: 1/12 q^2 phi1 phi2 q congruent 25 modulo 60: 1/12 q^2 phi1 phi2 q congruent 27 modulo 60: 1/12 q^2 phi1 phi2 q congruent 29 modulo 60: 1/12 q^2 phi1 phi2 q congruent 31 modulo 60: 1/12 q^2 phi1 phi2 q congruent 32 modulo 60: 1/12 q^2 phi1 phi2 q congruent 37 modulo 60: 1/12 q^2 phi1 phi2 q congruent 41 modulo 60: 1/12 q^2 phi1 phi2 q congruent 43 modulo 60: 1/12 q^2 phi1 phi2 q congruent 47 modulo 60: 1/12 q^2 phi1 phi2 q congruent 49 modulo 60: 1/12 q^2 phi1 phi2 q congruent 53 modulo 60: 1/12 q^2 phi1 phi2 q congruent 59 modulo 60: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 57, 102, 101, 58, 55, 32, 56 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 12: F-action on Pi is () [59,1,12] Dynkin type is D_4(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 16 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 19 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 23 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 27 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 29 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 31 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 32 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 41 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 43 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 47 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 49 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 53 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 59 modulo 60: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 68, 69, 4, 19, 7, 68, 68, 73, 77, 82, 19, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 24 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 6, 24 ], [ 44, 1, 2, 48 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ] ] k = 13: F-action on Pi is () [59,1,13] Dynkin type is D_4(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 2 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 4 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 7 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 8 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 11 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 16 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 19 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 23 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 27 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 29 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 31 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 32 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 41 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 43 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 47 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 49 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 53 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 59 modulo 60: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 69, 67, 7, 20, 5, 69, 69, 74, 81, 78, 20, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 4, 24 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 27, 1, 3, 16 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 6, 48 ], [ 41, 1, 6, 24 ], [ 41, 1, 9, 48 ], [ 44, 1, 8, 48 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ] ] k = 14: F-action on Pi is (2,3,5) [59,1,14] Dynkin type is ^3D_4(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1 phi2 q congruent 2 modulo 60: 1/12 q^2 phi1 phi2 q congruent 3 modulo 60: 1/12 q^2 phi1 phi2 q congruent 4 modulo 60: 1/12 q^2 phi1 phi2 q congruent 5 modulo 60: 1/12 q^2 phi1 phi2 q congruent 7 modulo 60: 1/12 q^2 phi1 phi2 q congruent 8 modulo 60: 1/12 q^2 phi1 phi2 q congruent 9 modulo 60: 1/12 q^2 phi1 phi2 q congruent 11 modulo 60: 1/12 q^2 phi1 phi2 q congruent 13 modulo 60: 1/12 q^2 phi1 phi2 q congruent 16 modulo 60: 1/12 q^2 phi1 phi2 q congruent 17 modulo 60: 1/12 q^2 phi1 phi2 q congruent 19 modulo 60: 1/12 q^2 phi1 phi2 q congruent 21 modulo 60: 1/12 q^2 phi1 phi2 q congruent 23 modulo 60: 1/12 q^2 phi1 phi2 q congruent 25 modulo 60: 1/12 q^2 phi1 phi2 q congruent 27 modulo 60: 1/12 q^2 phi1 phi2 q congruent 29 modulo 60: 1/12 q^2 phi1 phi2 q congruent 31 modulo 60: 1/12 q^2 phi1 phi2 q congruent 32 modulo 60: 1/12 q^2 phi1 phi2 q congruent 37 modulo 60: 1/12 q^2 phi1 phi2 q congruent 41 modulo 60: 1/12 q^2 phi1 phi2 q congruent 43 modulo 60: 1/12 q^2 phi1 phi2 q congruent 47 modulo 60: 1/12 q^2 phi1 phi2 q congruent 49 modulo 60: 1/12 q^2 phi1 phi2 q congruent 53 modulo 60: 1/12 q^2 phi1 phi2 q congruent 59 modulo 60: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 83, 40, 37, 88, 79, 101, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 27, 1, 2, 4 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 6 ] ] k = 15: F-action on Pi is (2,5,3) [59,1,15] Dynkin type is ^3D_4(q) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 2 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 13 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 16 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 19 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 23 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 25 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 29 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 31 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 32 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 41 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 43 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 47 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 49 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 53 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 59 modulo 60: 1/12 q phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 38, 40, 84, 85, 102, 80 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 27, 1, 3, 4 ], [ 40, 1, 4, 6 ], [ 52, 1, 7, 6 ] ] k = 16: F-action on Pi is () [59,1,16] Dynkin type is D_4(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 13 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 19 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 21 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 23 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 25 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 27 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 29 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 31 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 41 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 43 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 49 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 53 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 59 modulo 60: 1/16 phi1 phi2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 76, 71, 19, 22, 20, 72, 76, 75, 97, 98, 18, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 8 ], [ 41, 1, 5, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ] ] k = 17: F-action on Pi is (2,5) [59,1,17] Dynkin type is ^2D_4(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 2 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 4 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 7 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 8 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 11 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 16 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 19 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 23 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 27 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 29 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 31 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 32 modulo 60: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 41 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 43 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 47 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 49 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 53 modulo 60: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 59 modulo 60: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 3, 70, 68, 72, 19, 28, 30, 89 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 12 ], [ 25, 1, 4, 4 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 24 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 12 ], [ 40, 1, 3, 16 ], [ 41, 1, 3, 48 ], [ 41, 1, 4, 24 ], [ 44, 1, 1, 48 ], [ 44, 1, 9, 48 ], [ 52, 1, 3, 48 ] ] k = 18: F-action on Pi is (2,5) [59,1,18] Dynkin type is ^2D_4(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 2 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 4 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 7 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 8 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 11 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 13 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 16 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 19 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 21 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 23 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 25 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 27 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 29 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 31 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 32 modulo 60: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 41 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 43 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 47 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 49 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 53 modulo 60: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 59 modulo 60: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 5, 72, 69, 71, 20, 31, 27, 90 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 12 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 12 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 24 ], [ 28, 1, 4, 24 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 24 ], [ 40, 1, 2, 16 ], [ 41, 1, 4, 24 ], [ 41, 1, 10, 48 ], [ 44, 1, 5, 48 ], [ 44, 1, 10, 48 ], [ 52, 1, 4, 48 ] ] k = 19: F-action on Pi is (2,5) [59,1,19] Dynkin type is ^2D_4(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1 phi2 q congruent 2 modulo 60: 1/12 q^2 phi1 phi2 q congruent 3 modulo 60: 1/12 q^2 phi1 phi2 q congruent 4 modulo 60: 1/12 q^2 phi1 phi2 q congruent 5 modulo 60: 1/12 q^2 phi1 phi2 q congruent 7 modulo 60: 1/12 q^2 phi1 phi2 q congruent 8 modulo 60: 1/12 q^2 phi1 phi2 q congruent 9 modulo 60: 1/12 q^2 phi1 phi2 q congruent 11 modulo 60: 1/12 q^2 phi1 phi2 q congruent 13 modulo 60: 1/12 q^2 phi1 phi2 q congruent 16 modulo 60: 1/12 q^2 phi1 phi2 q congruent 17 modulo 60: 1/12 q^2 phi1 phi2 q congruent 19 modulo 60: 1/12 q^2 phi1 phi2 q congruent 21 modulo 60: 1/12 q^2 phi1 phi2 q congruent 23 modulo 60: 1/12 q^2 phi1 phi2 q congruent 25 modulo 60: 1/12 q^2 phi1 phi2 q congruent 27 modulo 60: 1/12 q^2 phi1 phi2 q congruent 29 modulo 60: 1/12 q^2 phi1 phi2 q congruent 31 modulo 60: 1/12 q^2 phi1 phi2 q congruent 32 modulo 60: 1/12 q^2 phi1 phi2 q congruent 37 modulo 60: 1/12 q^2 phi1 phi2 q congruent 41 modulo 60: 1/12 q^2 phi1 phi2 q congruent 43 modulo 60: 1/12 q^2 phi1 phi2 q congruent 47 modulo 60: 1/12 q^2 phi1 phi2 q congruent 49 modulo 60: 1/12 q^2 phi1 phi2 q congruent 53 modulo 60: 1/12 q^2 phi1 phi2 q congruent 59 modulo 60: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 30, 27, 97, 81, 95, 59, 36, 37, 109 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 40, 1, 3, 4 ], [ 44, 1, 3, 6 ] ] k = 20: F-action on Pi is (2,3) [59,1,20] Dynkin type is ^2D_4(q) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 2 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 13 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 16 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 19 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 23 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 25 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 29 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 31 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 32 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 41 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 43 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 47 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 49 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 53 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 59 modulo 60: 1/12 q phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 31, 96, 82, 98, 60, 38, 36, 110 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 40, 1, 2, 4 ], [ 44, 1, 7, 6 ] ] k = 21: F-action on Pi is (2,3) [59,1,21] Dynkin type is ^2D_4(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^3 phi2 q congruent 2 modulo 60: 1/16 q^3 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1^3 phi2 q congruent 4 modulo 60: 1/16 q^3 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1^3 phi2 q congruent 7 modulo 60: 1/16 phi1^3 phi2 q congruent 8 modulo 60: 1/16 q^3 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1^3 phi2 q congruent 11 modulo 60: 1/16 phi1^3 phi2 q congruent 13 modulo 60: 1/16 phi1^3 phi2 q congruent 16 modulo 60: 1/16 q^3 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1^3 phi2 q congruent 19 modulo 60: 1/16 phi1^3 phi2 q congruent 21 modulo 60: 1/16 phi1^3 phi2 q congruent 23 modulo 60: 1/16 phi1^3 phi2 q congruent 25 modulo 60: 1/16 phi1^3 phi2 q congruent 27 modulo 60: 1/16 phi1^3 phi2 q congruent 29 modulo 60: 1/16 phi1^3 phi2 q congruent 31 modulo 60: 1/16 phi1^3 phi2 q congruent 32 modulo 60: 1/16 q^3 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1^3 phi2 q congruent 41 modulo 60: 1/16 phi1^3 phi2 q congruent 43 modulo 60: 1/16 phi1^3 phi2 q congruent 47 modulo 60: 1/16 phi1^3 phi2 q congruent 49 modulo 60: 1/16 phi1^3 phi2 q congruent 53 modulo 60: 1/16 phi1^3 phi2 q congruent 59 modulo 60: 1/16 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 19, 20, 73, 76, 74, 18, 60, 59, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ] ] k = 22: F-action on Pi is (2,5) [59,1,22] Dynkin type is ^2D_4(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 2 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 4 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 7 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 8 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 11 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 16 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 19 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 23 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 27 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 31 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 32 modulo 60: 1/16 q^2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 41 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 43 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 53 modulo 60: 1/16 phi1 phi4 ( q-3 ) q congruent 59 modulo 60: 1/16 phi1 phi4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 69, 19, 7, 20, 76, 82, 81, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 8 ], [ 41, 1, 4, 8 ], [ 41, 1, 7, 8 ], [ 44, 1, 2, 8 ], [ 44, 1, 8, 8 ], [ 52, 1, 3, 8 ], [ 52, 1, 4, 8 ] ] k = 23: F-action on Pi is (2,3) [59,1,23] Dynkin type is ^2D_4(q) + T(phi1^2 phi4) Order of center |Z^F|: phi1^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/32 q^2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/32 phi1 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 72, 16, 19, 18, 73, 96, 97, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 3, 16 ], [ 41, 1, 8, 8 ], [ 44, 1, 6, 16 ], [ 52, 1, 8, 16 ] ] k = 24: F-action on Pi is (2,5) [59,1,24] Dynkin type is ^2D_4(q) + T(phi2^2 phi4) Order of center |Z^F|: phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^3 phi2 q congruent 2 modulo 60: 1/32 q^3 ( q-2 ) q congruent 3 modulo 60: 1/32 phi1^3 phi2 q congruent 4 modulo 60: 1/32 q^3 ( q-2 ) q congruent 5 modulo 60: 1/32 phi1^3 phi2 q congruent 7 modulo 60: 1/32 phi1^3 phi2 q congruent 8 modulo 60: 1/32 q^3 ( q-2 ) q congruent 9 modulo 60: 1/32 phi1^3 phi2 q congruent 11 modulo 60: 1/32 phi1^3 phi2 q congruent 13 modulo 60: 1/32 phi1^3 phi2 q congruent 16 modulo 60: 1/32 q^3 ( q-2 ) q congruent 17 modulo 60: 1/32 phi1^3 phi2 q congruent 19 modulo 60: 1/32 phi1^3 phi2 q congruent 21 modulo 60: 1/32 phi1^3 phi2 q congruent 23 modulo 60: 1/32 phi1^3 phi2 q congruent 25 modulo 60: 1/32 phi1^3 phi2 q congruent 27 modulo 60: 1/32 phi1^3 phi2 q congruent 29 modulo 60: 1/32 phi1^3 phi2 q congruent 31 modulo 60: 1/32 phi1^3 phi2 q congruent 32 modulo 60: 1/32 q^3 ( q-2 ) q congruent 37 modulo 60: 1/32 phi1^3 phi2 q congruent 41 modulo 60: 1/32 phi1^3 phi2 q congruent 43 modulo 60: 1/32 phi1^3 phi2 q congruent 47 modulo 60: 1/32 phi1^3 phi2 q congruent 49 modulo 60: 1/32 phi1^3 phi2 q congruent 53 modulo 60: 1/32 phi1^3 phi2 q congruent 59 modulo 60: 1/32 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 72, 71, 18, 20, 17, 74, 98, 95, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 41, 1, 10, 16 ], [ 44, 1, 4, 16 ], [ 52, 1, 5, 16 ] ] k = 25: F-action on Pi is (2,3) [59,1,25] Dynkin type is ^2D_4(q) + T(phi8) Order of center |Z^F|: phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/8 phi1 phi2 phi4 q congruent 2 modulo 60: 1/8 q^4 q congruent 3 modulo 60: 1/8 phi1 phi2 phi4 q congruent 4 modulo 60: 1/8 q^4 q congruent 5 modulo 60: 1/8 phi1 phi2 phi4 q congruent 7 modulo 60: 1/8 phi1 phi2 phi4 q congruent 8 modulo 60: 1/8 q^4 q congruent 9 modulo 60: 1/8 phi1 phi2 phi4 q congruent 11 modulo 60: 1/8 phi1 phi2 phi4 q congruent 13 modulo 60: 1/8 phi1 phi2 phi4 q congruent 16 modulo 60: 1/8 q^4 q congruent 17 modulo 60: 1/8 phi1 phi2 phi4 q congruent 19 modulo 60: 1/8 phi1 phi2 phi4 q congruent 21 modulo 60: 1/8 phi1 phi2 phi4 q congruent 23 modulo 60: 1/8 phi1 phi2 phi4 q congruent 25 modulo 60: 1/8 phi1 phi2 phi4 q congruent 27 modulo 60: 1/8 phi1 phi2 phi4 q congruent 29 modulo 60: 1/8 phi1 phi2 phi4 q congruent 31 modulo 60: 1/8 phi1 phi2 phi4 q congruent 32 modulo 60: 1/8 q^4 q congruent 37 modulo 60: 1/8 phi1 phi2 phi4 q congruent 41 modulo 60: 1/8 phi1 phi2 phi4 q congruent 43 modulo 60: 1/8 phi1 phi2 phi4 q congruent 47 modulo 60: 1/8 phi1 phi2 phi4 q congruent 49 modulo 60: 1/8 phi1 phi2 phi4 q congruent 53 modulo 60: 1/8 phi1 phi2 phi4 q congruent 59 modulo 60: 1/8 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 89, 90, 44, 43, 45, 91, 110, 109, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ] i = 60: Pi = [ 2, 5, 7, 240 ] j = 1: Omega trivial k = 1: F-action on Pi is () [60,1,1] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^4) Order of center |Z^F|: phi1^4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 7 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 11 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) q congruent 13 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 19 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 ) q congruent 21 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 23 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) q congruent 25 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 ) q congruent 27 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) q congruent 29 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 31 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 ) q congruent 41 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 43 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 ) q congruent 47 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) q congruent 49 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 ) q congruent 53 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 59 modulo 60: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 72 ], [ 6, 1, 1, 128 ], [ 7, 1, 1, 96 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 240 ], [ 16, 1, 1, 384 ], [ 19, 1, 1, 384 ], [ 20, 1, 1, 576 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 168 ], [ 25, 1, 1, 336 ], [ 26, 1, 1, 192 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 33, 1, 1, 768 ], [ 35, 1, 1, 1152 ], [ 39, 1, 1, 144 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 864 ], [ 42, 1, 1, 768 ], [ 43, 1, 1, 1152 ], [ 44, 1, 1, 576 ], [ 49, 1, 1, 2304 ], [ 52, 1, 1, 576 ], [ 53, 1, 1, 2304 ], [ 59, 1, 1, 1152 ] ] k = 2: F-action on Pi is () [60,1,2] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 21 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 27 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 41 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 47 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 53 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/144 q phi2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30, 77, 30, 30, 81, 77, 30, 30, 81, 30, 81, 81, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 33, 1, 1, 48 ], [ 40, 1, 1, 12 ], [ 42, 1, 3, 24 ], [ 44, 1, 3, 18 ], [ 53, 1, 16, 72 ], [ 59, 1, 4, 36 ] ] k = 3: F-action on Pi is ( 5, 7,240) [60,1,3] Dynkin type is A_1(q) + A_1(q^3) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 21 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 27 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 41 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 47 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 53 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/36 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 87, 83, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 19, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 33, 1, 3, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 1, 12 ], [ 49, 1, 3, 18 ], [ 52, 1, 6, 18 ], [ 59, 1, 7, 36 ] ] k = 4: F-action on Pi is ( 5, 7,240) [60,1,4] Dynkin type is A_1(q) + A_1(q^3) + T(phi3^2) Order of center |Z^F|: phi3^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 7 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 11 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 13 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 19 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 21 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 23 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 25 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 27 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 29 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 31 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 41 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 43 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 47 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 49 modulo 60: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 53 modulo 60: 1/72 q phi2 ( q^2+q-6 ) q congruent 59 modulo 60: 1/72 q phi2 ( q^2+q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 85, 79, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 27, 1, 5, 24 ], [ 33, 1, 3, 24 ], [ 40, 1, 5, 24 ], [ 42, 1, 3, 24 ], [ 59, 1, 9, 72 ] ] k = 5: F-action on Pi is ( 2, 7)( 5,240) [60,1,5] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/48 q phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/48 q phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 30, 97, 97, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 3, 8 ], [ 16, 1, 2, 8 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 33, 1, 4, 16 ], [ 40, 1, 1, 12 ], [ 44, 1, 3, 18 ], [ 53, 1, 17, 24 ], [ 59, 1, 4, 36 ] ] k = 6: F-action on Pi is ( 2,240, 7, 5) [60,1,6] Dynkin type is A_1(q^4) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^2 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/24 q phi1^2 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/24 q phi1^2 phi2 q congruent 7 modulo 60: 1/24 q phi1^2 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/24 q phi1^2 phi2 q congruent 11 modulo 60: 1/24 q phi1^2 phi2 q congruent 13 modulo 60: 1/24 q phi1^2 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/24 q phi1^2 phi2 q congruent 19 modulo 60: 1/24 q phi1^2 phi2 q congruent 21 modulo 60: 1/24 q phi1^2 phi2 q congruent 23 modulo 60: 1/24 q phi1^2 phi2 q congruent 25 modulo 60: 1/24 q phi1^2 phi2 q congruent 27 modulo 60: 1/24 q phi1^2 phi2 q congruent 29 modulo 60: 1/24 q phi1^2 phi2 q congruent 31 modulo 60: 1/24 q phi1^2 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/24 q phi1^2 phi2 q congruent 41 modulo 60: 1/24 q phi1^2 phi2 q congruent 43 modulo 60: 1/24 q phi1^2 phi2 q congruent 47 modulo 60: 1/24 q phi1^2 phi2 q congruent 49 modulo 60: 1/24 q phi1^2 phi2 q congruent 53 modulo 60: 1/24 q phi1^2 phi2 q congruent 59 modulo 60: 1/24 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 60, 110 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 33, 1, 9, 8 ], [ 40, 1, 2, 4 ], [ 44, 1, 7, 6 ], [ 59, 1, 20, 12 ] ] k = 7: F-action on Pi is ( 2,240, 7, 5) [60,1,7] Dynkin type is A_1(q^4) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1 phi2^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/24 q phi1 phi2^2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/24 q phi1 phi2^2 q congruent 7 modulo 60: 1/24 q phi1 phi2^2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/24 q phi1 phi2^2 q congruent 11 modulo 60: 1/24 q phi1 phi2^2 q congruent 13 modulo 60: 1/24 q phi1 phi2^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/24 q phi1 phi2^2 q congruent 19 modulo 60: 1/24 q phi1 phi2^2 q congruent 21 modulo 60: 1/24 q phi1 phi2^2 q congruent 23 modulo 60: 1/24 q phi1 phi2^2 q congruent 25 modulo 60: 1/24 q phi1 phi2^2 q congruent 27 modulo 60: 1/24 q phi1 phi2^2 q congruent 29 modulo 60: 1/24 q phi1 phi2^2 q congruent 31 modulo 60: 1/24 q phi1 phi2^2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/24 q phi1 phi2^2 q congruent 41 modulo 60: 1/24 q phi1 phi2^2 q congruent 43 modulo 60: 1/24 q phi1 phi2^2 q congruent 47 modulo 60: 1/24 q phi1 phi2^2 q congruent 49 modulo 60: 1/24 q phi1 phi2^2 q congruent 53 modulo 60: 1/24 q phi1 phi2^2 q congruent 59 modulo 60: 1/24 q phi1 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 59, 109 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 33, 1, 5, 8 ], [ 40, 1, 3, 4 ], [ 44, 1, 3, 6 ], [ 59, 1, 19, 12 ] ] k = 8: F-action on Pi is () [60,1,8] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 7 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 11 modulo 60: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 13 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 19 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 21 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 23 modulo 60: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 25 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 27 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 31 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 41 modulo 60: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 43 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 47 modulo 60: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 49 modulo 60: 1/144 q phi1^2 ( q-3 ) q congruent 53 modulo 60: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 59 modulo 60: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 82, 82, 31, 82, 31, 31, 78, 82, 31, 31, 78, 31, 78, 78, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 18 ], [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 24 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], [ 33, 1, 8, 48 ], [ 40, 1, 6, 12 ], [ 42, 1, 5, 24 ], [ 44, 1, 7, 18 ], [ 53, 1, 18, 72 ], [ 59, 1, 5, 36 ] ] k = 9: F-action on Pi is ( 2, 7)( 5,240) [60,1,9] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/48 q phi1^2 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/48 q phi1^2 phi2 q congruent 7 modulo 60: 1/48 q phi1^2 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/48 q phi1^2 phi2 q congruent 11 modulo 60: 1/48 q phi1^2 phi2 q congruent 13 modulo 60: 1/48 q phi1^2 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/48 q phi1^2 phi2 q congruent 19 modulo 60: 1/48 q phi1^2 phi2 q congruent 21 modulo 60: 1/48 q phi1^2 phi2 q congruent 23 modulo 60: 1/48 q phi1^2 phi2 q congruent 25 modulo 60: 1/48 q phi1^2 phi2 q congruent 27 modulo 60: 1/48 q phi1^2 phi2 q congruent 29 modulo 60: 1/48 q phi1^2 phi2 q congruent 31 modulo 60: 1/48 q phi1^2 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/48 q phi1^2 phi2 q congruent 41 modulo 60: 1/48 q phi1^2 phi2 q congruent 43 modulo 60: 1/48 q phi1^2 phi2 q congruent 47 modulo 60: 1/48 q phi1^2 phi2 q congruent 49 modulo 60: 1/48 q phi1^2 phi2 q congruent 53 modulo 60: 1/48 q phi1^2 phi2 q congruent 59 modulo 60: 1/48 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 31, 98, 98, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 2, 8 ], [ 16, 1, 4, 8 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], [ 33, 1, 10, 16 ], [ 40, 1, 6, 12 ], [ 44, 1, 7, 18 ], [ 53, 1, 15, 24 ], [ 59, 1, 5, 36 ] ] k = 10: F-action on Pi is ( 5,240) [60,1,10] Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/24 q phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/24 q phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 82, 96, 60, 82, 31, 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 33, 1, 6, 8 ], [ 40, 1, 2, 4 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 12 ], [ 59, 1, 20, 12 ] ] k = 11: F-action on Pi is ( 5,240) [60,1,11] Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^2 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/24 q phi1^2 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/24 q phi1^2 phi2 q congruent 7 modulo 60: 1/24 q phi1^2 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/24 q phi1^2 phi2 q congruent 11 modulo 60: 1/24 q phi1^2 phi2 q congruent 13 modulo 60: 1/24 q phi1^2 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/24 q phi1^2 phi2 q congruent 19 modulo 60: 1/24 q phi1^2 phi2 q congruent 21 modulo 60: 1/24 q phi1^2 phi2 q congruent 23 modulo 60: 1/24 q phi1^2 phi2 q congruent 25 modulo 60: 1/24 q phi1^2 phi2 q congruent 27 modulo 60: 1/24 q phi1^2 phi2 q congruent 29 modulo 60: 1/24 q phi1^2 phi2 q congruent 31 modulo 60: 1/24 q phi1^2 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/24 q phi1^2 phi2 q congruent 41 modulo 60: 1/24 q phi1^2 phi2 q congruent 43 modulo 60: 1/24 q phi1^2 phi2 q congruent 47 modulo 60: 1/24 q phi1^2 phi2 q congruent 49 modulo 60: 1/24 q phi1^2 phi2 q congruent 53 modulo 60: 1/24 q phi1^2 phi2 q congruent 59 modulo 60: 1/24 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 30, 81, 97, 59, 81, 27, 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 33, 1, 2, 8 ], [ 40, 1, 3, 4 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 12 ], [ 59, 1, 19, 12 ] ] k = 12: F-action on Pi is ( 5,240, 7) [60,1,12] Dynkin type is A_1(q) + A_1(q^3) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/12 q^2 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 q^2 phi1 phi2 q congruent 7 modulo 60: 1/12 q^2 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/12 q^2 phi1 phi2 q congruent 11 modulo 60: 1/12 q^2 phi1 phi2 q congruent 13 modulo 60: 1/12 q^2 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 q^2 phi1 phi2 q congruent 19 modulo 60: 1/12 q^2 phi1 phi2 q congruent 21 modulo 60: 1/12 q^2 phi1 phi2 q congruent 23 modulo 60: 1/12 q^2 phi1 phi2 q congruent 25 modulo 60: 1/12 q^2 phi1 phi2 q congruent 27 modulo 60: 1/12 q^2 phi1 phi2 q congruent 29 modulo 60: 1/12 q^2 phi1 phi2 q congruent 31 modulo 60: 1/12 q^2 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 q^2 phi1 phi2 q congruent 41 modulo 60: 1/12 q^2 phi1 phi2 q congruent 43 modulo 60: 1/12 q^2 phi1 phi2 q congruent 47 modulo 60: 1/12 q^2 phi1 phi2 q congruent 49 modulo 60: 1/12 q^2 phi1 phi2 q congruent 53 modulo 60: 1/12 q^2 phi1 phi2 q congruent 59 modulo 60: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 83, 40, 37, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 19, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 33, 1, 3, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 4, 4 ], [ 49, 1, 3, 6 ], [ 52, 1, 6, 6 ], [ 59, 1, 14, 12 ] ] k = 13: F-action on Pi is ( 5,240, 7) [60,1,13] Dynkin type is A_1(q) + A_1(q^3) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 13 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 19 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 23 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 25 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 29 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 31 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 41 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 43 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 47 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 49 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 53 modulo 60: 1/12 q phi1 phi2 ( q-2 ) q congruent 59 modulo 60: 1/12 q phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 38, 40, 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 19, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ], [ 42, 1, 2, 4 ], [ 49, 1, 6, 6 ], [ 52, 1, 7, 6 ], [ 59, 1, 15, 12 ] ] k = 14: F-action on Pi is ( 5,240, 7) [60,1,14] Dynkin type is A_1(q) + A_1(q^3) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 q^2 phi1^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/36 q^2 phi1^2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 60: 1/36 q^2 phi1^2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/36 q^2 phi1^2 q congruent 11 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 13 modulo 60: 1/36 q^2 phi1^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 19 modulo 60: 1/36 q^2 phi1^2 q congruent 21 modulo 60: 1/36 q^2 phi1^2 q congruent 23 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 25 modulo 60: 1/36 q^2 phi1^2 q congruent 27 modulo 60: 1/36 q^2 phi1^2 q congruent 29 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 31 modulo 60: 1/36 q^2 phi1^2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/36 q^2 phi1^2 q congruent 41 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 43 modulo 60: 1/36 q^2 phi1^2 q congruent 47 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 49 modulo 60: 1/36 q^2 phi1^2 q congruent 53 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 59 modulo 60: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 84, 88, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 19, 1, 2, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ], [ 42, 1, 6, 12 ], [ 49, 1, 6, 18 ], [ 52, 1, 7, 18 ], [ 59, 1, 8, 36 ] ] k = 15: F-action on Pi is ( 5,240, 7) [60,1,15] Dynkin type is A_1(q) + A_1(q^3) + T(phi6^2) Order of center |Z^F|: phi6^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 7 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 11 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 13 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 19 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 21 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 23 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 25 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 27 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 29 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 31 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 41 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 43 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 47 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 49 modulo 60: 1/72 q phi1 ( q^2-q-6 ) q congruent 53 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 59 modulo 60: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 80, 86, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 27, 1, 4, 24 ], [ 33, 1, 7, 24 ], [ 40, 1, 4, 24 ], [ 42, 1, 5, 24 ], [ 59, 1, 10, 72 ] ] k = 16: F-action on Pi is ( 5, 7,240) [60,1,16] Dynkin type is A_1(q) + A_1(q^3) + T(phi12) Order of center |Z^F|: phi12 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^2 phi1 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/12 q^2 phi1 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/12 q^2 phi1 phi2 q congruent 7 modulo 60: 1/12 q^2 phi1 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/12 q^2 phi1 phi2 q congruent 11 modulo 60: 1/12 q^2 phi1 phi2 q congruent 13 modulo 60: 1/12 q^2 phi1 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/12 q^2 phi1 phi2 q congruent 19 modulo 60: 1/12 q^2 phi1 phi2 q congruent 21 modulo 60: 1/12 q^2 phi1 phi2 q congruent 23 modulo 60: 1/12 q^2 phi1 phi2 q congruent 25 modulo 60: 1/12 q^2 phi1 phi2 q congruent 27 modulo 60: 1/12 q^2 phi1 phi2 q congruent 29 modulo 60: 1/12 q^2 phi1 phi2 q congruent 31 modulo 60: 1/12 q^2 phi1 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/12 q^2 phi1 phi2 q congruent 41 modulo 60: 1/12 q^2 phi1 phi2 q congruent 43 modulo 60: 1/12 q^2 phi1 phi2 q congruent 47 modulo 60: 1/12 q^2 phi1 phi2 q congruent 49 modulo 60: 1/12 q^2 phi1 phi2 q congruent 53 modulo 60: 1/12 q^2 phi1 phi2 q congruent 59 modulo 60: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 57, 102, 101, 58 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 59, 1, 11, 12 ] ] k = 17: F-action on Pi is () [60,1,17] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^4) Order of center |Z^F|: phi2^4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 ) q congruent 7 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 11 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 ) q congruent 13 modulo 60: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 ) q congruent 19 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 21 modulo 60: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 23 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 ) q congruent 25 modulo 60: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 27 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 29 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 ) q congruent 31 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 41 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 ) q congruent 43 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 47 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 ) q congruent 49 modulo 60: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 53 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 ) q congruent 59 modulo 60: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 69, 5, 69, 5, 5, 67, 69, 5, 5, 67, 5, 67, 67, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 72 ], [ 6, 1, 2, 128 ], [ 7, 1, 2, 96 ], [ 9, 1, 1, 15 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 4, 240 ], [ 16, 1, 3, 384 ], [ 19, 1, 2, 384 ], [ 20, 1, 4, 576 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 168 ], [ 25, 1, 3, 336 ], [ 26, 1, 4, 192 ], [ 27, 1, 6, 192 ], [ 28, 1, 4, 288 ], [ 33, 1, 8, 768 ], [ 35, 1, 8, 1152 ], [ 39, 1, 3, 144 ], [ 40, 1, 6, 192 ], [ 41, 1, 9, 864 ], [ 42, 1, 6, 768 ], [ 43, 1, 13, 1152 ], [ 44, 1, 10, 576 ], [ 49, 1, 10, 2304 ], [ 52, 1, 10, 576 ], [ 53, 1, 20, 2304 ], [ 59, 1, 2, 1152 ] ] k = 18: F-action on Pi is () [60,1,18] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi4^2) Order of center |Z^F|: phi4^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 13 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 19 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 21 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 23 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 25 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 27 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 29 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 31 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 41 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 43 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 47 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 49 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 53 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) q congruent 59 modulo 60: 1/384 phi1 phi2 ( q^2-9 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 73, 73, 18, 73, 18, 18, 74, 73, 18, 18, 74, 18, 74, 74, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ], [ 41, 1, 8, 96 ], [ 59, 1, 6, 96 ] ] k = 19: F-action on Pi is ( 5,240) [60,1,19] Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi8) Order of center |Z^F|: phi8 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 phi4 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 phi2 phi4 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 phi2 phi4 q congruent 7 modulo 60: 1/16 phi1 phi2 phi4 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 phi2 phi4 q congruent 11 modulo 60: 1/16 phi1 phi2 phi4 q congruent 13 modulo 60: 1/16 phi1 phi2 phi4 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 phi2 phi4 q congruent 19 modulo 60: 1/16 phi1 phi2 phi4 q congruent 21 modulo 60: 1/16 phi1 phi2 phi4 q congruent 23 modulo 60: 1/16 phi1 phi2 phi4 q congruent 25 modulo 60: 1/16 phi1 phi2 phi4 q congruent 27 modulo 60: 1/16 phi1 phi2 phi4 q congruent 29 modulo 60: 1/16 phi1 phi2 phi4 q congruent 31 modulo 60: 1/16 phi1 phi2 phi4 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 phi2 phi4 q congruent 41 modulo 60: 1/16 phi1 phi2 phi4 q congruent 43 modulo 60: 1/16 phi1 phi2 phi4 q congruent 47 modulo 60: 1/16 phi1 phi2 phi4 q congruent 49 modulo 60: 1/16 phi1 phi2 phi4 q congruent 53 modulo 60: 1/16 phi1 phi2 phi4 q congruent 59 modulo 60: 1/16 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 89, 43, 44, 91, 43, 90, 91, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 59, 1, 25, 8 ] ] k = 20: F-action on Pi is ( 2, 7)( 5,240) [60,1,20] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi4^2) Order of center |Z^F|: phi4^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 13 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 19 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 21 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 23 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 25 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 27 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 29 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 31 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 41 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 43 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 47 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 49 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 53 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) q congruent 59 modulo 60: 1/128 phi1 phi2 ( q^2-9 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 75, 75, 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 7 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 80 ], [ 43, 1, 10, 64 ], [ 59, 1, 6, 96 ] ] k = 21: F-action on Pi is ( 2,240, 7, 5) [60,1,21] Dynkin type is A_1(q^4) + T(phi8) Order of center |Z^F|: phi8 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 phi4 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/16 phi1 phi2 phi4 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/16 phi1 phi2 phi4 q congruent 7 modulo 60: 1/16 phi1 phi2 phi4 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/16 phi1 phi2 phi4 q congruent 11 modulo 60: 1/16 phi1 phi2 phi4 q congruent 13 modulo 60: 1/16 phi1 phi2 phi4 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/16 phi1 phi2 phi4 q congruent 19 modulo 60: 1/16 phi1 phi2 phi4 q congruent 21 modulo 60: 1/16 phi1 phi2 phi4 q congruent 23 modulo 60: 1/16 phi1 phi2 phi4 q congruent 25 modulo 60: 1/16 phi1 phi2 phi4 q congruent 27 modulo 60: 1/16 phi1 phi2 phi4 q congruent 29 modulo 60: 1/16 phi1 phi2 phi4 q congruent 31 modulo 60: 1/16 phi1 phi2 phi4 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/16 phi1 phi2 phi4 q congruent 41 modulo 60: 1/16 phi1 phi2 phi4 q congruent 43 modulo 60: 1/16 phi1 phi2 phi4 q congruent 47 modulo 60: 1/16 phi1 phi2 phi4 q congruent 49 modulo 60: 1/16 phi1 phi2 phi4 q congruent 53 modulo 60: 1/16 phi1 phi2 phi4 q congruent 59 modulo 60: 1/16 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 91, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 3 ], [ 59, 1, 25, 8 ] ] k = 22: F-action on Pi is ( 2, 7)( 5,240) [60,1,22] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^4) Order of center |Z^F|: phi1^4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 7 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 11 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 13 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 19 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 21 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 23 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 25 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 27 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 29 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 31 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 41 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 43 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 47 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 49 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 53 modulo 60: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 59 modulo 60: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 70, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 16 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 144 ], [ 13, 1, 3, 32 ], [ 16, 1, 2, 128 ], [ 20, 1, 3, 192 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 25, 1, 2, 96 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 33, 1, 4, 256 ], [ 35, 1, 5, 384 ], [ 39, 1, 1, 144 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 288 ], [ 41, 1, 3, 192 ], [ 43, 1, 3, 384 ], [ 44, 1, 1, 576 ], [ 49, 1, 11, 768 ], [ 52, 1, 1, 576 ], [ 53, 1, 5, 768 ], [ 59, 1, 1, 1152 ] ] k = 23: F-action on Pi is ( 2,240, 7, 5) [60,1,23] Dynkin type is A_1(q^4) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/192 phi1 phi2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 89 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 12 ], [ 25, 1, 4, 4 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 24 ], [ 33, 1, 5, 32 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 12 ], [ 40, 1, 3, 16 ], [ 41, 1, 3, 48 ], [ 41, 1, 4, 24 ], [ 44, 1, 1, 48 ], [ 44, 1, 9, 48 ], [ 49, 1, 12, 96 ], [ 52, 1, 3, 48 ], [ 59, 1, 17, 96 ] ] k = 24: F-action on Pi is ( 2,240, 7, 5) [60,1,24] Dynkin type is A_1(q^4) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/192 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 90 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 12 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 12 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 9, 32 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 24 ], [ 40, 1, 2, 16 ], [ 41, 1, 4, 24 ], [ 41, 1, 10, 48 ], [ 44, 1, 5, 48 ], [ 44, 1, 10, 48 ], [ 49, 1, 16, 96 ], [ 52, 1, 4, 48 ], [ 59, 1, 18, 96 ] ] k = 25: F-action on Pi is ( 2, 5, 7,240) [60,1,25] Dynkin type is A_1(q^4) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 7 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 11 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 19 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 23 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 27 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 31 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 41 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 43 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 53 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 59 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 76, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 5, 16 ], [ 33, 1, 9, 16 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 8 ], [ 41, 1, 4, 8 ], [ 41, 1, 7, 8 ], [ 43, 1, 11, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 8, 8 ], [ 49, 1, 12, 16 ], [ 49, 1, 16, 16 ], [ 52, 1, 3, 8 ], [ 52, 1, 4, 8 ], [ 59, 1, 22, 16 ] ] k = 26: F-action on Pi is ( 2, 7)( 5,240) [60,1,26] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi2^4) Order of center |Z^F|: phi2^4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 7 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 11 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 13 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 19 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 21 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 23 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 25 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 27 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 29 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 31 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 41 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 43 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 47 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 49 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 53 modulo 60: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 59 modulo 60: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 71, 71, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 16 ], [ 4, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 2, 32 ], [ 13, 1, 4, 144 ], [ 16, 1, 4, 128 ], [ 20, 1, 2, 192 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 72 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 96 ], [ 27, 1, 6, 192 ], [ 28, 1, 4, 288 ], [ 33, 1, 10, 256 ], [ 35, 1, 4, 384 ], [ 39, 1, 3, 144 ], [ 40, 1, 6, 192 ], [ 41, 1, 9, 288 ], [ 41, 1, 10, 192 ], [ 43, 1, 12, 384 ], [ 44, 1, 10, 576 ], [ 49, 1, 19, 768 ], [ 52, 1, 10, 576 ], [ 53, 1, 19, 768 ], [ 59, 1, 2, 1152 ] ] k = 27: F-action on Pi is () [60,1,27] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 7 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 11 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 13 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 19 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 21 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 23 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 25 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 27 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 29 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 31 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 41 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 43 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 47 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 49 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 53 modulo 60: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 59 modulo 60: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 7, 68, 3, 7, 69, 68, 7, 3, 69, 7, 69, 69, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 24 ], [ 20, 1, 2, 32 ], [ 20, 1, 3, 32 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 28 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 32 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 35, 1, 3, 64 ], [ 35, 1, 6, 64 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 32 ], [ 41, 1, 4, 64 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], [ 43, 1, 3, 64 ], [ 43, 1, 8, 64 ], [ 43, 1, 12, 64 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 49, 1, 5, 128 ], [ 49, 1, 9, 128 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ], [ 53, 1, 6, 128 ], [ 53, 1, 9, 128 ], [ 59, 1, 3, 64 ] ] k = 28: F-action on Pi is () [60,1,28] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 19, 76, 19, 72, 76, 20, 19, 76, 72, 20, 76, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 59, 1, 16, 16 ] ] k = 29: F-action on Pi is ( 2, 7)( 5,240) [60,1,29] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 18, 18, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 7 ], [ 13, 1, 2, 12 ], [ 13, 1, 3, 12 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 12 ], [ 25, 1, 3, 12 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 24 ], [ 41, 1, 5, 24 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 53, 1, 10, 32 ], [ 53, 1, 14, 32 ], [ 59, 1, 16, 16 ] ] k = 30: F-action on Pi is ( 5,240) [60,1,30] Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi2^2 phi4) Order of center |Z^F|: phi2^2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20, 18, 74, 20, 71, 74, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 16 ], [ 49, 1, 4, 32 ], [ 52, 1, 5, 16 ], [ 53, 1, 11, 32 ], [ 53, 1, 14, 32 ], [ 59, 1, 24, 32 ] ] k = 31: F-action on Pi is ( 5,240) [60,1,31] Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1^2 phi4) Order of center |Z^F|: phi1^2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 7 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 11 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 13 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 19 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 21 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 23 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 25 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 27 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 29 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 31 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 41 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 43 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 47 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 49 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 53 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 59 modulo 60: 1/64 phi1 phi2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 16, 73, 19, 72, 73, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 1, 16 ], [ 41, 1, 3, 32 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 6, 16 ], [ 49, 1, 7, 32 ], [ 52, 1, 8, 16 ], [ 53, 1, 10, 32 ], [ 53, 1, 13, 32 ], [ 59, 1, 23, 32 ] ] k = 32: F-action on Pi is ( 2,240)( 5, 7) [60,1,32] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 phi2^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi1^2 phi2^2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1^2 phi2^2 q congruent 7 modulo 60: 1/32 phi1^2 phi2^2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1^2 phi2^2 q congruent 11 modulo 60: 1/32 phi1^2 phi2^2 q congruent 13 modulo 60: 1/32 phi1^2 phi2^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1^2 phi2^2 q congruent 19 modulo 60: 1/32 phi1^2 phi2^2 q congruent 21 modulo 60: 1/32 phi1^2 phi2^2 q congruent 23 modulo 60: 1/32 phi1^2 phi2^2 q congruent 25 modulo 60: 1/32 phi1^2 phi2^2 q congruent 27 modulo 60: 1/32 phi1^2 phi2^2 q congruent 29 modulo 60: 1/32 phi1^2 phi2^2 q congruent 31 modulo 60: 1/32 phi1^2 phi2^2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1^2 phi2^2 q congruent 41 modulo 60: 1/32 phi1^2 phi2^2 q congruent 43 modulo 60: 1/32 phi1^2 phi2^2 q congruent 47 modulo 60: 1/32 phi1^2 phi2^2 q congruent 49 modulo 60: 1/32 phi1^2 phi2^2 q congruent 53 modulo 60: 1/32 phi1^2 phi2^2 q congruent 59 modulo 60: 1/32 phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 76, 22, 22, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 8 ], [ 41, 1, 5, 8 ], [ 43, 1, 11, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 59, 1, 16, 16 ] ] k = 33: F-action on Pi is ( 5,240) [60,1,33] Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^3 phi2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi1^3 phi2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1^3 phi2 q congruent 7 modulo 60: 1/32 phi1^3 phi2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1^3 phi2 q congruent 11 modulo 60: 1/32 phi1^3 phi2 q congruent 13 modulo 60: 1/32 phi1^3 phi2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1^3 phi2 q congruent 19 modulo 60: 1/32 phi1^3 phi2 q congruent 21 modulo 60: 1/32 phi1^3 phi2 q congruent 23 modulo 60: 1/32 phi1^3 phi2 q congruent 25 modulo 60: 1/32 phi1^3 phi2 q congruent 27 modulo 60: 1/32 phi1^3 phi2 q congruent 29 modulo 60: 1/32 phi1^3 phi2 q congruent 31 modulo 60: 1/32 phi1^3 phi2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1^3 phi2 q congruent 41 modulo 60: 1/32 phi1^3 phi2 q congruent 43 modulo 60: 1/32 phi1^3 phi2 q congruent 47 modulo 60: 1/32 phi1^3 phi2 q congruent 49 modulo 60: 1/32 phi1^3 phi2 q congruent 53 modulo 60: 1/32 phi1^3 phi2 q congruent 59 modulo 60: 1/32 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 19, 76, 73, 18, 76, 20, 18, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 8 ], [ 41, 1, 7, 16 ], [ 41, 1, 8, 16 ], [ 49, 1, 4, 16 ], [ 49, 1, 7, 16 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 59, 1, 21, 16 ] ] k = 34: F-action on Pi is ( 2, 7)( 5,240) [60,1,34] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 7 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 11 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 13 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 19 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 21 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 23 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 25 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 27 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 29 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 31 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 41 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 43 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 47 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 49 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 53 modulo 60: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 59 modulo 60: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 72, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ], [ 9, 1, 1, 11 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 32 ], [ 13, 1, 3, 32 ], [ 13, 1, 4, 8 ], [ 20, 1, 1, 32 ], [ 20, 1, 4, 32 ], [ 20, 1, 5, 64 ], [ 20, 1, 8, 64 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 40 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 40 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 32 ], [ 26, 1, 4, 32 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 35, 1, 2, 64 ], [ 35, 1, 7, 64 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 96 ], [ 41, 1, 3, 32 ], [ 41, 1, 6, 32 ], [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], [ 43, 1, 1, 64 ], [ 43, 1, 5, 128 ], [ 43, 1, 8, 64 ], [ 43, 1, 13, 64 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 49, 1, 14, 128 ], [ 49, 1, 20, 128 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ], [ 53, 1, 2, 128 ], [ 53, 1, 12, 128 ], [ 59, 1, 3, 64 ] ] k = 35: F-action on Pi is ( 2,240, 7, 5) [60,1,35] Dynkin type is A_1(q^4) + T(phi1^2 phi4) Order of center |Z^F|: phi1^2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/64 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 73, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 20, 1, 6, 16 ], [ 20, 1, 8, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 26, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 3, 16 ], [ 41, 1, 8, 8 ], [ 43, 1, 6, 32 ], [ 44, 1, 6, 16 ], [ 49, 1, 17, 32 ], [ 52, 1, 8, 16 ], [ 59, 1, 23, 32 ] ] k = 36: F-action on Pi is ( 2,240, 7, 5) [60,1,36] Dynkin type is A_1(q^4) + T(phi2^2 phi4) Order of center |Z^F|: phi2^2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2^2 q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/64 phi1^2 phi2^2 q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/64 phi1^2 phi2^2 q congruent 7 modulo 60: 1/64 phi1^2 phi2^2 q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/64 phi1^2 phi2^2 q congruent 11 modulo 60: 1/64 phi1^2 phi2^2 q congruent 13 modulo 60: 1/64 phi1^2 phi2^2 q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/64 phi1^2 phi2^2 q congruent 19 modulo 60: 1/64 phi1^2 phi2^2 q congruent 21 modulo 60: 1/64 phi1^2 phi2^2 q congruent 23 modulo 60: 1/64 phi1^2 phi2^2 q congruent 25 modulo 60: 1/64 phi1^2 phi2^2 q congruent 27 modulo 60: 1/64 phi1^2 phi2^2 q congruent 29 modulo 60: 1/64 phi1^2 phi2^2 q congruent 31 modulo 60: 1/64 phi1^2 phi2^2 q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/64 phi1^2 phi2^2 q congruent 41 modulo 60: 1/64 phi1^2 phi2^2 q congruent 43 modulo 60: 1/64 phi1^2 phi2^2 q congruent 47 modulo 60: 1/64 phi1^2 phi2^2 q congruent 49 modulo 60: 1/64 phi1^2 phi2^2 q congruent 53 modulo 60: 1/64 phi1^2 phi2^2 q congruent 59 modulo 60: 1/64 phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 74, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 20, 1, 5, 16 ], [ 20, 1, 7, 16 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 8 ], [ 26, 1, 3, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 41, 1, 10, 16 ], [ 43, 1, 14, 32 ], [ 44, 1, 4, 16 ], [ 49, 1, 13, 32 ], [ 52, 1, 5, 16 ], [ 59, 1, 24, 32 ] ] k = 37: F-action on Pi is ( 2,240, 7, 5) [60,1,37] Dynkin type is A_1(q^4) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 7 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 11 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 19 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 23 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 27 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 31 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 41 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 43 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 53 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) q congruent 59 modulo 60: 1/32 phi1 phi2^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 5, 8 ], [ 20, 1, 6, 8 ], [ 20, 1, 7, 8 ], [ 20, 1, 8, 8 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 43, 1, 5, 16 ], [ 43, 1, 7, 16 ], [ 43, 1, 10, 16 ], [ 49, 1, 13, 16 ], [ 49, 1, 17, 16 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 59, 1, 21, 16 ] ] k = 38: F-action on Pi is ( 2, 7)( 5,240) [60,1,38] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 7 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 11 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 19 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 23 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 27 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 31 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 41 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 43 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 53 modulo 60: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 59 modulo 60: 1/128 phi2^2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 76, 76, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 8 ], [ 20, 1, 6, 32 ], [ 20, 1, 7, 32 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 8 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 32 ], [ 41, 1, 6, 32 ], [ 41, 1, 7, 32 ], [ 41, 1, 9, 16 ], [ 43, 1, 7, 64 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 49, 1, 15, 64 ], [ 49, 1, 18, 64 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ], [ 59, 1, 3, 64 ] ] k = 39: F-action on Pi is ( 2, 7)( 5,240) [60,1,39] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 7 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 11 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 13 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 19 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 21 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 23 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 25 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 27 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 29 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 31 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 41 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 43 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 47 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 49 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 53 modulo 60: 1/128 phi1^2 phi2 ( q-5 ) q congruent 59 modulo 60: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 20, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 24 ], [ 16, 1, 4, 32 ], [ 20, 1, 1, 16 ], [ 20, 1, 2, 16 ], [ 20, 1, 5, 32 ], [ 20, 1, 7, 32 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 26, 1, 3, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 10, 64 ], [ 35, 1, 2, 32 ], [ 35, 1, 4, 32 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 6, 48 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 16 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 32 ], [ 43, 1, 2, 32 ], [ 43, 1, 14, 64 ], [ 44, 1, 8, 48 ], [ 49, 1, 14, 64 ], [ 49, 1, 15, 64 ], [ 49, 1, 19, 64 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ], [ 53, 1, 4, 64 ], [ 59, 1, 13, 96 ] ] k = 40: F-action on Pi is () [60,1,40] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 7 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 11 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 13 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 19 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 21 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 23 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 25 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 27 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 29 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 31 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 41 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 43 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 47 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 49 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 53 modulo 60: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 59 modulo 60: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 7, 4, 68, 68, 7, 68, 7, 7, 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 72 ], [ 16, 1, 1, 96 ], [ 19, 1, 1, 32 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 48 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 42 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 72 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 33, 1, 1, 192 ], [ 35, 1, 1, 96 ], [ 35, 1, 3, 96 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 144 ], [ 41, 1, 6, 72 ], [ 42, 1, 4, 64 ], [ 43, 1, 2, 96 ], [ 44, 1, 2, 48 ], [ 49, 1, 1, 192 ], [ 49, 1, 9, 192 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ], [ 53, 1, 3, 192 ], [ 59, 1, 12, 96 ] ] k = 41: F-action on Pi is () [60,1,41] Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 7 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 11 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 13 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 19 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 21 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 23 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 25 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 27 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 29 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 31 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 41 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 43 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 47 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 49 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 53 modulo 60: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 59 modulo 60: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 7, 69, 7, 69, 69, 5, 7, 69, 69, 5, 69, 5, 5, 67 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 36 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 4, 72 ], [ 16, 1, 3, 96 ], [ 19, 1, 2, 32 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 48 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 42 ], [ 25, 1, 3, 72 ], [ 26, 1, 2, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 8, 192 ], [ 35, 1, 6, 96 ], [ 35, 1, 8, 96 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 6, 48 ], [ 41, 1, 6, 72 ], [ 41, 1, 9, 144 ], [ 42, 1, 2, 64 ], [ 43, 1, 4, 96 ], [ 44, 1, 8, 48 ], [ 49, 1, 5, 192 ], [ 49, 1, 10, 192 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ], [ 53, 1, 8, 192 ], [ 59, 1, 13, 96 ] ] k = 42: F-action on Pi is ( 2, 7)( 5,240) [60,1,42] Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 7 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 11 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 13 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 19 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 21 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 23 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 25 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 27 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 29 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 31 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 41 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 43 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 47 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 49 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 53 modulo 60: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 59 modulo 60: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 19, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 16 ], [ 16, 1, 2, 32 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 16 ], [ 20, 1, 6, 32 ], [ 20, 1, 8, 32 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 26, 1, 2, 16 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 33, 1, 4, 64 ], [ 35, 1, 5, 32 ], [ 35, 1, 7, 32 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 3, 32 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 16 ], [ 43, 1, 4, 32 ], [ 43, 1, 6, 64 ], [ 44, 1, 2, 48 ], [ 49, 1, 11, 64 ], [ 49, 1, 18, 64 ], [ 49, 1, 20, 64 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ], [ 53, 1, 7, 64 ], [ 59, 1, 12, 96 ] ] k = 43: F-action on Pi is ( 5,240) [60,1,43] Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 13 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 19 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 21 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 23 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 25 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 27 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 29 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 31 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 41 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 43 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 47 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 49 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 53 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 59 modulo 60: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 72, 20, 69, 5, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 14 ], [ 4, 1, 2, 10 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 36 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 48 ], [ 20, 1, 4, 48 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 36 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 36 ], [ 25, 1, 4, 48 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 6, 32 ], [ 35, 1, 3, 48 ], [ 35, 1, 4, 48 ], [ 35, 1, 7, 48 ], [ 35, 1, 8, 48 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 24 ], [ 40, 1, 2, 16 ], [ 41, 1, 2, 24 ], [ 41, 1, 4, 48 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 96 ], [ 42, 1, 6, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 5, 48 ], [ 44, 1, 10, 48 ], [ 49, 1, 8, 96 ], [ 52, 1, 4, 48 ], [ 53, 1, 9, 96 ], [ 53, 1, 12, 96 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 96 ], [ 59, 1, 18, 96 ] ] k = 44: F-action on Pi is ( 5,240) [60,1,44] Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 7 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 11 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 13 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 19 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 21 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 23 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 25 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 27 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 29 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 31 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 41 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 43 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 47 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 49 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 53 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 59 modulo 60: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 70, 19, 68, 3, 19, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 14 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 36 ], [ 13, 1, 4, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 48 ], [ 20, 1, 3, 48 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 36 ], [ 25, 1, 1, 36 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 24 ], [ 33, 1, 2, 32 ], [ 35, 1, 1, 48 ], [ 35, 1, 2, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 48 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 12 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 24 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 43, 1, 3, 96 ], [ 43, 1, 8, 48 ], [ 44, 1, 1, 48 ], [ 44, 1, 9, 48 ], [ 49, 1, 2, 96 ], [ 52, 1, 3, 48 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 96 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 96 ], [ 59, 1, 17, 96 ] ] k = 45: F-action on Pi is (2,7) [60,1,45] Dynkin type is A_1(q^2) + A_1(q) + A_1(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 2 modulo 60: 0 q congruent 3 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 4 modulo 60: 0 q congruent 5 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 7 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 8 modulo 60: 0 q congruent 9 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 11 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 16 modulo 60: 0 q congruent 17 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 19 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 23 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 27 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 31 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 32 modulo 60: 0 q congruent 37 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 41 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 43 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 47 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 53 modulo 60: 1/32 phi1^3 ( q-3 ) q congruent 59 modulo 60: 1/32 phi1^3 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 7, 69, 19, 76, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 6, 1, 1, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 16, 1, 4, 8 ], [ 19, 1, 1, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 2, 16 ], [ 33, 1, 6, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 8 ], [ 41, 1, 7, 16 ], [ 42, 1, 2, 16 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 8, 8 ], [ 49, 1, 2, 16 ], [ 49, 1, 8, 16 ], [ 52, 1, 3, 8 ], [ 52, 1, 4, 8 ], [ 53, 1, 3, 16 ], [ 53, 1, 4, 16 ], [ 53, 1, 7, 16 ], [ 53, 1, 8, 16 ], [ 59, 1, 22, 16 ] ] i = 61: Pi = [ 1, 2, 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [61,1,1] Dynkin type is A_2(q) + A_1(q) + T(phi1^5) Order of center |Z^F|: phi1^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9451*q^2+44448*q-93546 ) q congruent 2 modulo 60: 1/1440 ( q^5-51*q^4+984*q^3-8756*q^2+34128*q-40320 ) q congruent 3 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+41508*q-63270 ) q congruent 4 modulo 60: 1/1440 ( q^5-51*q^4+984*q^3-8836*q^2+36528*q-55680 ) q congruent 5 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+42048*q-72090 ) q congruent 7 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9451*q^2+43908*q-81270 ) q congruent 8 modulo 60: 1/1440 ( q^5-51*q^4+984*q^3-8756*q^2+34128*q-40320 ) q congruent 9 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+42048*q-72090 ) q congruent 11 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+41508*q-66726 ) q congruent 13 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9451*q^2+44448*q-90090 ) q congruent 16 modulo 60: 1/1440 ( q^5-51*q^4+984*q^3-8836*q^2+36528*q-59136 ) q congruent 17 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+42048*q-72090 ) q congruent 19 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9451*q^2+43908*q-81270 ) q congruent 21 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+42048*q-75546 ) q congruent 23 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+41508*q-63270 ) q congruent 25 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9451*q^2+44448*q-90090 ) q congruent 27 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+41508*q-63270 ) q congruent 29 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+42048*q-72090 ) q congruent 31 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9451*q^2+43908*q-84726 ) q congruent 32 modulo 60: 1/1440 ( q^5-51*q^4+984*q^3-8756*q^2+34128*q-40320 ) q congruent 37 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9451*q^2+44448*q-90090 ) q congruent 41 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+42048*q-75546 ) q congruent 43 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9451*q^2+43908*q-81270 ) q congruent 47 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+41508*q-63270 ) q congruent 49 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9451*q^2+44448*q-90090 ) q congruent 53 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+42048*q-72090 ) q congruent 59 modulo 60: 1/1440 ( q^5-51*q^4+999*q^3-9371*q^2+41508*q-63270 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 8, 77 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 62 ], [ 4, 1, 1, 150 ], [ 5, 1, 1, 264 ], [ 6, 1, 1, 312 ], [ 7, 1, 1, 132 ], [ 8, 1, 1, 60 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 30 ], [ 11, 1, 1, 140 ], [ 12, 1, 1, 330 ], [ 13, 1, 1, 360 ], [ 14, 1, 1, 660 ], [ 15, 1, 1, 732 ], [ 16, 1, 1, 840 ], [ 17, 1, 1, 840 ], [ 18, 1, 1, 420 ], [ 19, 1, 1, 600 ], [ 20, 1, 1, 840 ], [ 21, 1, 1, 240 ], [ 22, 1, 1, 540 ], [ 23, 1, 1, 90 ], [ 24, 1, 1, 210 ], [ 25, 1, 1, 540 ], [ 26, 1, 1, 240 ], [ 27, 1, 1, 240 ], [ 28, 1, 1, 540 ], [ 29, 1, 1, 1200 ], [ 30, 1, 1, 1080 ], [ 31, 1, 1, 1380 ], [ 32, 1, 1, 1200 ], [ 33, 1, 1, 720 ], [ 34, 1, 1, 960 ], [ 35, 1, 1, 1080 ], [ 36, 1, 1, 720 ], [ 37, 1, 1, 1440 ], [ 38, 1, 1, 1440 ], [ 39, 1, 1, 360 ], [ 40, 1, 1, 900 ], [ 41, 1, 1, 720 ], [ 42, 1, 1, 960 ], [ 43, 1, 1, 1440 ], [ 44, 1, 1, 720 ], [ 45, 1, 1, 1440 ], [ 46, 1, 1, 1920 ], [ 47, 1, 1, 1080 ], [ 48, 1, 1, 1440 ], [ 50, 1, 1, 1440 ], [ 51, 1, 1, 2160 ], [ 52, 1, 1, 720 ], [ 53, 1, 1, 1440 ], [ 54, 1, 1, 1440 ], [ 55, 1, 1, 1440 ], [ 56, 1, 1, 1440 ], [ 58, 1, 1, 2880 ] ] k = 2: F-action on Pi is () [61,1,2] Dynkin type is A_2(q) + A_1(q) + T(phi1 phi5) Order of center |Z^F|: phi1 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 2 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 13 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 17 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 23 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 32 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 43 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/10 q phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 23, 93, 93, 50, 62, 111 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 15, 1, 1, 2 ], [ 54, 1, 6, 10 ] ] k = 3: F-action on Pi is (1,3) [61,1,3] Dynkin type is ^2A_2(q) + A_1(q) + T(phi2 phi10) Order of center |Z^F|: phi2 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/10 q^2 phi1 phi4 q congruent 2 modulo 60: 1/10 q^2 phi1 phi4 q congruent 3 modulo 60: 1/10 q^2 phi1 phi4 q congruent 4 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 5 modulo 60: 1/10 q^2 phi1 phi4 q congruent 7 modulo 60: 1/10 q^2 phi1 phi4 q congruent 8 modulo 60: 1/10 q^2 phi1 phi4 q congruent 9 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 11 modulo 60: 1/10 q^2 phi1 phi4 q congruent 13 modulo 60: 1/10 q^2 phi1 phi4 q congruent 16 modulo 60: 1/10 q^2 phi1 phi4 q congruent 17 modulo 60: 1/10 q^2 phi1 phi4 q congruent 19 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 21 modulo 60: 1/10 q^2 phi1 phi4 q congruent 23 modulo 60: 1/10 q^2 phi1 phi4 q congruent 25 modulo 60: 1/10 q^2 phi1 phi4 q congruent 27 modulo 60: 1/10 q^2 phi1 phi4 q congruent 29 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 31 modulo 60: 1/10 q^2 phi1 phi4 q congruent 32 modulo 60: 1/10 q^2 phi1 phi4 q congruent 37 modulo 60: 1/10 q^2 phi1 phi4 q congruent 41 modulo 60: 1/10 q^2 phi1 phi4 q congruent 43 modulo 60: 1/10 q^2 phi1 phi4 q congruent 47 modulo 60: 1/10 q^2 phi1 phi4 q congruent 49 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 53 modulo 60: 1/10 q^2 phi1 phi4 q congruent 59 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 94, 24, 51, 94, 112, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 15, 1, 2, 2 ], [ 54, 1, 8, 10 ] ] k = 4: F-action on Pi is () [61,1,4] Dynkin type is A_2(q) + A_1(q) + T(phi1^3 phi3) Order of center |Z^F|: phi1^3 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 phi1 ( q^4-11*q^3+31*q^2+9*q-96 ) q congruent 2 modulo 60: 1/36 q phi2 ( q^3-13*q^2+52*q-60 ) q congruent 3 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 4 modulo 60: 1/36 phi1 ( q^4-11*q^3+28*q^2+18*q-72 ) q congruent 5 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 7 modulo 60: 1/36 phi1 ( q^4-11*q^3+31*q^2+9*q-96 ) q congruent 8 modulo 60: 1/36 q phi2 ( q^3-13*q^2+52*q-60 ) q congruent 9 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 11 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 13 modulo 60: 1/36 phi1 ( q^4-11*q^3+31*q^2+9*q-96 ) q congruent 16 modulo 60: 1/36 phi1 ( q^4-11*q^3+28*q^2+18*q-72 ) q congruent 17 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 19 modulo 60: 1/36 phi1 ( q^4-11*q^3+31*q^2+9*q-96 ) q congruent 21 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 23 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 25 modulo 60: 1/36 phi1 ( q^4-11*q^3+31*q^2+9*q-96 ) q congruent 27 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 29 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 31 modulo 60: 1/36 phi1 ( q^4-11*q^3+31*q^2+9*q-96 ) q congruent 32 modulo 60: 1/36 q phi2 ( q^3-13*q^2+52*q-60 ) q congruent 37 modulo 60: 1/36 phi1 ( q^4-11*q^3+31*q^2+9*q-96 ) q congruent 41 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 43 modulo 60: 1/36 phi1 ( q^4-11*q^3+31*q^2+9*q-96 ) q congruent 47 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 49 modulo 60: 1/36 phi1 ( q^4-11*q^3+31*q^2+9*q-96 ) q congruent 53 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) q congruent 59 modulo 60: 1/36 q phi2 ( q^3-13*q^2+55*q-75 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30, 14, 83 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 48 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 20, 1, 1, 24 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 36 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 29, 1, 1, 24 ], [ 31, 1, 1, 24 ], [ 32, 1, 1, 24 ], [ 34, 1, 1, 12 ], [ 38, 1, 1, 72 ], [ 38, 1, 3, 36 ], [ 42, 1, 1, 12 ], [ 42, 1, 3, 24 ], [ 44, 1, 3, 18 ], [ 45, 1, 3, 36 ], [ 46, 1, 1, 24 ], [ 46, 1, 3, 48 ], [ 50, 1, 3, 36 ], [ 53, 1, 16, 36 ], [ 54, 1, 3, 36 ], [ 55, 1, 3, 36 ], [ 56, 1, 3, 36 ], [ 58, 1, 3, 72 ] ] k = 5: F-action on Pi is () [61,1,5] Dynkin type is A_2(q) + A_1(q) + T(phi1 phi3^2) Order of center |Z^F|: phi1 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 phi1^2 ( q^3+2*q^2-3*q-6 ) q congruent 2 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+6 ) q congruent 3 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 4 modulo 60: 1/36 phi1 ( q^4+q^3-5*q^2+12 ) q congruent 5 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 7 modulo 60: 1/36 phi1^2 ( q^3+2*q^2-3*q-6 ) q congruent 8 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+6 ) q congruent 9 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 11 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 13 modulo 60: 1/36 phi1^2 ( q^3+2*q^2-3*q-6 ) q congruent 16 modulo 60: 1/36 phi1 ( q^4+q^3-5*q^2+12 ) q congruent 17 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 19 modulo 60: 1/36 phi1^2 ( q^3+2*q^2-3*q-6 ) q congruent 21 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 23 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 25 modulo 60: 1/36 phi1^2 ( q^3+2*q^2-3*q-6 ) q congruent 27 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 29 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 31 modulo 60: 1/36 phi1^2 ( q^3+2*q^2-3*q-6 ) q congruent 32 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+6 ) q congruent 37 modulo 60: 1/36 phi1^2 ( q^3+2*q^2-3*q-6 ) q congruent 41 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 43 modulo 60: 1/36 phi1^2 ( q^3+2*q^2-3*q-6 ) q congruent 47 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 49 modulo 60: 1/36 phi1^2 ( q^3+2*q^2-3*q-6 ) q congruent 53 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) q congruent 59 modulo 60: 1/36 q phi2 ( q^3-q^2-5*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 83, 83, 37, 12, 79 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], [ 11, 1, 1, 2 ], [ 17, 1, 1, 12 ], [ 27, 1, 5, 12 ], [ 33, 1, 3, 18 ], [ 38, 1, 3, 72 ], [ 40, 1, 5, 36 ], [ 42, 1, 3, 12 ], [ 46, 1, 3, 24 ], [ 52, 1, 6, 18 ], [ 58, 1, 8, 72 ] ] k = 6: F-action on Pi is (1,3) [61,1,6] Dynkin type is ^2A_2(q) + A_1(q) + T(phi2^3 phi6) Order of center |Z^F|: phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/36 phi2 ( q^4-9*q^3+28*q^2-42*q+28 ) q congruent 3 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/36 q^2 phi1 ( q^2-7*q+12 ) q congruent 5 modulo 60: 1/36 phi2 ( q^4-9*q^3+31*q^2-57*q+52 ) q congruent 7 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/36 phi2 ( q^4-9*q^3+28*q^2-42*q+28 ) q congruent 9 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/36 phi2 ( q^4-9*q^3+31*q^2-57*q+52 ) q congruent 13 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/36 q^2 phi1 ( q^2-7*q+12 ) q congruent 17 modulo 60: 1/36 phi2 ( q^4-9*q^3+31*q^2-57*q+52 ) q congruent 19 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/36 phi2 ( q^4-9*q^3+31*q^2-57*q+52 ) q congruent 25 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/36 phi2 ( q^4-9*q^3+31*q^2-57*q+52 ) q congruent 31 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/36 phi2 ( q^4-9*q^3+28*q^2-42*q+28 ) q congruent 37 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/36 phi2 ( q^4-9*q^3+31*q^2-57*q+52 ) q congruent 43 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/36 phi2 ( q^4-9*q^3+31*q^2-57*q+52 ) q congruent 49 modulo 60: 1/36 q phi1^2 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/36 phi2 ( q^4-9*q^3+31*q^2-57*q+52 ) q congruent 59 modulo 60: 1/36 phi2 ( q^4-9*q^3+31*q^2-57*q+52 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 9, 31, 78, 84, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 12 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 24 ], [ 16, 1, 3, 24 ], [ 17, 1, 4, 48 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 20, 1, 4, 24 ], [ 21, 1, 2, 12 ], [ 22, 1, 4, 36 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 12 ], [ 29, 1, 4, 24 ], [ 31, 1, 4, 24 ], [ 32, 1, 3, 24 ], [ 34, 1, 4, 12 ], [ 38, 1, 11, 36 ], [ 38, 1, 12, 72 ], [ 42, 1, 5, 24 ], [ 42, 1, 6, 12 ], [ 44, 1, 7, 18 ], [ 45, 1, 4, 36 ], [ 46, 1, 4, 48 ], [ 46, 1, 6, 24 ], [ 50, 1, 10, 36 ], [ 53, 1, 18, 36 ], [ 54, 1, 10, 36 ], [ 55, 1, 12, 36 ], [ 56, 1, 17, 36 ], [ 58, 1, 14, 72 ] ] k = 7: F-action on Pi is () [61,1,7] Dynkin type is A_2(q) + A_1(q) + T(phi1^2 phi2 phi3) Order of center |Z^F|: phi1^2 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^4-3*q^3-q^2+5*q-4 ) q congruent 2 modulo 60: 1/12 q^2 phi2 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 1/12 q phi1 ( q^3-3*q^2-2*q+6 ) q congruent 5 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/12 phi1 ( q^4-3*q^3-q^2+5*q-4 ) q congruent 8 modulo 60: 1/12 q^2 phi2 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/12 phi1 ( q^4-3*q^3-q^2+5*q-4 ) q congruent 16 modulo 60: 1/12 q phi1 ( q^3-3*q^2-2*q+6 ) q congruent 17 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/12 phi1 ( q^4-3*q^3-q^2+5*q-4 ) q congruent 21 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/12 phi1 ( q^4-3*q^3-q^2+5*q-4 ) q congruent 27 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/12 phi1 ( q^4-3*q^3-q^2+5*q-4 ) q congruent 32 modulo 60: 1/12 q^2 phi2 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/12 phi1 ( q^4-3*q^3-q^2+5*q-4 ) q congruent 41 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/12 phi1 ( q^4-3*q^3-q^2+5*q-4 ) q congruent 47 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/12 phi1 ( q^4-3*q^3-q^2+5*q-4 ) q congruent 53 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/12 q phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 77, 30, 30, 81, 83, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 12 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 27, 1, 5, 6 ], [ 29, 1, 2, 8 ], [ 31, 1, 2, 8 ], [ 32, 1, 1, 8 ], [ 34, 1, 2, 4 ], [ 38, 1, 3, 36 ], [ 38, 1, 5, 24 ], [ 42, 1, 3, 12 ], [ 42, 1, 4, 4 ], [ 44, 1, 3, 6 ], [ 45, 1, 3, 12 ], [ 46, 1, 2, 8 ], [ 46, 1, 3, 24 ], [ 50, 1, 6, 12 ], [ 53, 1, 16, 12 ], [ 54, 1, 7, 12 ], [ 55, 1, 3, 12 ], [ 56, 1, 8, 12 ], [ 58, 1, 7, 24 ] ] k = 8: F-action on Pi is (1,3) [61,1,8] Dynkin type is ^2A_2(q) + A_1(q) + T(phi1 phi2^2 phi6) Order of center |Z^F|: phi1 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1^4 q congruent 2 modulo 60: 1/12 phi1 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 3 modulo 60: 1/12 q phi1^4 q congruent 4 modulo 60: 1/12 q^2 phi1^2 ( q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^4-5*q^3+11*q^2-13*q+8 ) q congruent 7 modulo 60: 1/12 q phi1^4 q congruent 8 modulo 60: 1/12 phi1 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 9 modulo 60: 1/12 q phi1^4 q congruent 11 modulo 60: 1/12 phi2 ( q^4-5*q^3+11*q^2-13*q+8 ) q congruent 13 modulo 60: 1/12 q phi1^4 q congruent 16 modulo 60: 1/12 q^2 phi1^2 ( q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^4-5*q^3+11*q^2-13*q+8 ) q congruent 19 modulo 60: 1/12 q phi1^4 q congruent 21 modulo 60: 1/12 q phi1^4 q congruent 23 modulo 60: 1/12 phi2 ( q^4-5*q^3+11*q^2-13*q+8 ) q congruent 25 modulo 60: 1/12 q phi1^4 q congruent 27 modulo 60: 1/12 q phi1^4 q congruent 29 modulo 60: 1/12 phi2 ( q^4-5*q^3+11*q^2-13*q+8 ) q congruent 31 modulo 60: 1/12 q phi1^4 q congruent 32 modulo 60: 1/12 phi1 phi2 ( q^3-4*q^2+6*q-4 ) q congruent 37 modulo 60: 1/12 q phi1^4 q congruent 41 modulo 60: 1/12 phi2 ( q^4-5*q^3+11*q^2-13*q+8 ) q congruent 43 modulo 60: 1/12 q phi1^4 q congruent 47 modulo 60: 1/12 phi2 ( q^4-5*q^3+11*q^2-13*q+8 ) q congruent 49 modulo 60: 1/12 q phi1^4 q congruent 53 modulo 60: 1/12 phi2 ( q^4-5*q^3+11*q^2-13*q+8 ) q congruent 59 modulo 60: 1/12 phi2 ( q^4-5*q^3+11*q^2-13*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 78, 82, 31, 38, 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 12 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 27, 1, 4, 6 ], [ 29, 1, 3, 8 ], [ 31, 1, 3, 8 ], [ 32, 1, 3, 8 ], [ 34, 1, 3, 4 ], [ 38, 1, 8, 24 ], [ 38, 1, 11, 36 ], [ 42, 1, 2, 4 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 46, 1, 4, 24 ], [ 46, 1, 5, 8 ], [ 50, 1, 7, 12 ], [ 53, 1, 18, 12 ], [ 54, 1, 11, 12 ], [ 55, 1, 12, 12 ], [ 56, 1, 12, 12 ], [ 58, 1, 10, 24 ] ] k = 9: F-action on Pi is (1,3) [61,1,9] Dynkin type is ^2A_2(q) + A_1(q) + T(phi2 phi6^2) Order of center |Z^F|: phi2 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 2 modulo 60: 1/36 phi2 ( q^4-3*q^3+q^2+6*q-8 ) q congruent 3 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 4 modulo 60: 1/36 q^2 phi1 ( q^2-q-3 ) q congruent 5 modulo 60: 1/36 phi1^2 phi2^2 ( q-2 ) q congruent 7 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 8 modulo 60: 1/36 phi2 ( q^4-3*q^3+q^2+6*q-8 ) q congruent 9 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 11 modulo 60: 1/36 phi1^2 phi2^2 ( q-2 ) q congruent 13 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 16 modulo 60: 1/36 q^2 phi1 ( q^2-q-3 ) q congruent 17 modulo 60: 1/36 phi1^2 phi2^2 ( q-2 ) q congruent 19 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 21 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 23 modulo 60: 1/36 phi1^2 phi2^2 ( q-2 ) q congruent 25 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 27 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 29 modulo 60: 1/36 phi1^2 phi2^2 ( q-2 ) q congruent 31 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 32 modulo 60: 1/36 phi2 ( q^4-3*q^3+q^2+6*q-8 ) q congruent 37 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 41 modulo 60: 1/36 phi1^2 phi2^2 ( q-2 ) q congruent 43 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 47 modulo 60: 1/36 phi1^2 phi2^2 ( q-2 ) q congruent 49 modulo 60: 1/36 q phi1 ( q^3-q^2-3*q-3 ) q congruent 53 modulo 60: 1/36 phi1^2 phi2^2 ( q-2 ) q congruent 59 modulo 60: 1/36 phi1^2 phi2^2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 84, 15, 38, 84, 80, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], [ 11, 1, 2, 2 ], [ 17, 1, 4, 12 ], [ 27, 1, 4, 12 ], [ 33, 1, 7, 18 ], [ 38, 1, 11, 72 ], [ 40, 1, 4, 36 ], [ 42, 1, 5, 12 ], [ 46, 1, 4, 24 ], [ 52, 1, 7, 18 ], [ 58, 1, 13, 72 ] ] k = 10: F-action on Pi is (1,3) [61,1,10] Dynkin type is ^2A_2(q) + A_1(q) + T(phi1 phi3 phi6) Order of center |Z^F|: phi1 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 2 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-4*q+4 ) q congruent 3 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 4 modulo 60: 1/12 q phi1 phi3 ( q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-5*q+6 ) q congruent 7 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 8 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-4*q+4 ) q congruent 9 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 11 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-5*q+6 ) q congruent 13 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 16 modulo 60: 1/12 q phi1 phi3 ( q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-5*q+6 ) q congruent 19 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 21 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 23 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-5*q+6 ) q congruent 25 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 27 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 29 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-5*q+6 ) q congruent 31 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 32 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-4*q+4 ) q congruent 37 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 41 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-5*q+6 ) q congruent 43 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 47 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-5*q+6 ) q congruent 49 modulo 60: 1/12 q phi1 ( q^3-q^2-q-3 ) q congruent 53 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-5*q+6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^4-3*q^3+3*q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 88, 87, 40, 33, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 3, 4 ], [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 6 ], [ 58, 1, 6, 12 ] ] k = 11: F-action on Pi is () [61,1,11] Dynkin type is A_2(q) + A_1(q) + T(phi2 phi3 phi6) Order of center |Z^F|: phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^4+q^3+q^2+q-2 ) q congruent 2 modulo 60: 1/12 q^2 phi2 phi6 q congruent 3 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 4 modulo 60: 1/12 q phi1 ( q^3+q^2+q+2 ) q congruent 5 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 7 modulo 60: 1/12 phi1 ( q^4+q^3+q^2+q-2 ) q congruent 8 modulo 60: 1/12 q^2 phi2 phi6 q congruent 9 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 11 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 13 modulo 60: 1/12 phi1 ( q^4+q^3+q^2+q-2 ) q congruent 16 modulo 60: 1/12 q phi1 ( q^3+q^2+q+2 ) q congruent 17 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 19 modulo 60: 1/12 phi1 ( q^4+q^3+q^2+q-2 ) q congruent 21 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 23 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 25 modulo 60: 1/12 phi1 ( q^4+q^3+q^2+q-2 ) q congruent 27 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 29 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 31 modulo 60: 1/12 phi1 ( q^4+q^3+q^2+q-2 ) q congruent 32 modulo 60: 1/12 q^2 phi2 phi6 q congruent 37 modulo 60: 1/12 phi1 ( q^4+q^3+q^2+q-2 ) q congruent 41 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 43 modulo 60: 1/12 phi1 ( q^4+q^3+q^2+q-2 ) q congruent 47 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 49 modulo 60: 1/12 phi1 ( q^4+q^3+q^2+q-2 ) q congruent 53 modulo 60: 1/12 q phi1 phi2 phi4 q congruent 59 modulo 60: 1/12 q phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 87, 35, 40, 88, 85, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 33, 1, 3, 6 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 52, 1, 7, 6 ], [ 58, 1, 6, 12 ] ] k = 12: F-action on Pi is () [61,1,12] Dynkin type is A_2(q) + A_1(q) + T(phi1^3 phi2^2) Order of center |Z^F|: phi1^3 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 2 modulo 60: 1/32 q ( q^4-11*q^3+36*q^2-28*q-16 ) q congruent 3 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) q congruent 4 modulo 60: 1/32 q ( q^4-11*q^3+36*q^2-28*q-16 ) q congruent 5 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 7 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) q congruent 8 modulo 60: 1/32 q ( q^4-11*q^3+36*q^2-28*q-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 11 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) q congruent 13 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 16 modulo 60: 1/32 q ( q^4-11*q^3+36*q^2-28*q-16 ) q congruent 17 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 19 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) q congruent 21 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 23 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) q congruent 25 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 27 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) q congruent 29 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 31 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) q congruent 32 modulo 60: 1/32 q ( q^4-11*q^3+36*q^2-28*q-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 41 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 43 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) q congruent 47 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) q congruent 49 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 53 modulo 60: 1/32 phi1 ( q^4-10*q^3+29*q^2-22*q+10 ) q congruent 59 modulo 60: 1/32 ( q^5-11*q^4+39*q^3-51*q^2+28*q-30 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 7, 30, 81 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 4, 1, 1, 18 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 18 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 8 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], [ 16, 1, 1, 48 ], [ 16, 1, 2, 8 ], [ 17, 1, 1, 72 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 48 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 40 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 12 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 8 ], [ 29, 1, 2, 48 ], [ 30, 1, 1, 24 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 12 ], [ 31, 1, 2, 56 ], [ 32, 1, 1, 48 ], [ 33, 1, 1, 48 ], [ 33, 1, 2, 16 ], [ 34, 1, 2, 32 ], [ 35, 1, 1, 24 ], [ 35, 1, 2, 16 ], [ 35, 1, 3, 48 ], [ 36, 1, 2, 16 ], [ 37, 1, 2, 16 ], [ 38, 1, 5, 96 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 40, 1, 1, 12 ], [ 40, 1, 3, 24 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 4, 32 ], [ 43, 1, 2, 32 ], [ 43, 1, 8, 16 ], [ 43, 1, 12, 32 ], [ 44, 1, 2, 16 ], [ 44, 1, 5, 16 ], [ 45, 1, 2, 32 ], [ 46, 1, 2, 64 ], [ 47, 1, 1, 24 ], [ 47, 1, 2, 48 ], [ 47, 1, 3, 16 ], [ 48, 1, 2, 32 ], [ 48, 1, 3, 32 ], [ 50, 1, 5, 32 ], [ 51, 1, 2, 16 ], [ 51, 1, 5, 48 ], [ 51, 1, 6, 16 ], [ 52, 1, 3, 16 ], [ 52, 1, 9, 16 ], [ 53, 1, 3, 32 ], [ 53, 1, 9, 32 ], [ 54, 1, 5, 32 ], [ 55, 1, 2, 32 ], [ 55, 1, 5, 32 ], [ 56, 1, 5, 32 ], [ 56, 1, 7, 32 ], [ 58, 1, 9, 64 ] ] k = 13: F-action on Pi is () [61,1,13] Dynkin type is A_2(q) + A_1(q) + T(phi1^2 phi2 phi4) Order of center |Z^F|: phi1^2 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 2 modulo 60: 1/16 q^2 phi2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 4 modulo 60: 1/16 q^2 phi2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 7 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 8 modulo 60: 1/16 q^2 phi2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 11 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 13 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 16 modulo 60: 1/16 q^2 phi2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 19 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 21 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 23 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 25 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 27 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 29 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 31 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 32 modulo 60: 1/16 q^2 phi2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 41 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 43 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 49 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 53 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 59 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+4*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 19, 76, 97, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 4, 4 ], [ 28, 1, 3, 4 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 33, 1, 2, 8 ], [ 35, 1, 2, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 47, 1, 3, 8 ], [ 51, 1, 7, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 11, 16 ], [ 54, 1, 4, 16 ], [ 55, 1, 4, 16 ], [ 56, 1, 4, 16 ] ] k = 14: F-action on Pi is (1,3) [61,1,14] Dynkin type is ^2A_2(q) + A_1(q) + T(phi1^2 phi2 phi4) Order of center |Z^F|: phi1^2 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 2 modulo 60: 1/16 q^3 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 4 modulo 60: 1/16 q^3 ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 7 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 8 modulo 60: 1/16 q^3 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 11 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 13 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 16 modulo 60: 1/16 q^3 ( q^2-5*q+6 ) q congruent 17 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 19 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 21 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 23 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 25 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 27 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 29 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 31 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 32 modulo 60: 1/16 q^3 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 41 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 43 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 47 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 49 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 53 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) q congruent 59 modulo 60: 1/16 phi1 phi2 ( q^3-5*q^2+8*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20, 19, 76, 96, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 28, 1, 1, 4 ], [ 31, 1, 3, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 35, 1, 5, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 47, 1, 9, 8 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 16 ], [ 52, 1, 8, 8 ], [ 53, 1, 13, 16 ], [ 55, 1, 11, 16 ], [ 56, 1, 11, 16 ], [ 58, 1, 5, 16 ] ] k = 15: F-action on Pi is () [61,1,15] Dynkin type is A_2(q) + A_1(q) + T(phi1 phi2^2 phi4) Order of center |Z^F|: phi1 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 2 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 4 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 8 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 11 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 13 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 16 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 19 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 21 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 23 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 25 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 27 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 29 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 31 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 32 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 41 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 43 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 47 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 49 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 53 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 59 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 72, 76, 20, 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 28, 1, 4, 4 ], [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 47, 1, 4, 8 ], [ 51, 1, 4, 16 ], [ 51, 1, 7, 8 ], [ 52, 1, 5, 8 ], [ 53, 1, 11, 16 ], [ 55, 1, 4, 16 ], [ 56, 1, 9, 16 ], [ 58, 1, 5, 16 ] ] k = 16: F-action on Pi is (1,3) [61,1,16] Dynkin type is ^2A_2(q) + A_1(q) + T(phi1 phi2^2 phi4) Order of center |Z^F|: phi1 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 2 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 4 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 8 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 11 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 13 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 16 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 19 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 21 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 23 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 25 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 27 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 29 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 31 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 32 modulo 60: 1/16 q^3 phi1 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 41 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 43 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 47 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 49 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 53 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 59 modulo 60: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 71, 76, 20, 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 4, 8 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 28, 1, 2, 4 ], [ 30, 1, 4, 8 ], [ 31, 1, 4, 4 ], [ 33, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 47, 1, 10, 8 ], [ 51, 1, 4, 8 ], [ 52, 1, 5, 8 ], [ 53, 1, 13, 16 ], [ 54, 1, 9, 16 ], [ 55, 1, 11, 16 ], [ 56, 1, 16, 16 ] ] k = 17: F-action on Pi is () [61,1,17] Dynkin type is A_2(q) + A_1(q) + T(phi1^2 phi2^3) Order of center |Z^F|: phi1^2 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+10 ) q congruent 2 modulo 60: 1/96 q^2 ( q^3-9*q^2+24*q-20 ) q congruent 3 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+6 ) q congruent 4 modulo 60: 1/96 q ( q^4-9*q^3+24*q^2-20*q+16 ) q congruent 5 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q-6 ) q congruent 7 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+22 ) q congruent 8 modulo 60: 1/96 q^2 ( q^3-9*q^2+24*q-20 ) q congruent 9 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q-6 ) q congruent 11 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+6 ) q congruent 13 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+10 ) q congruent 16 modulo 60: 1/96 q ( q^4-9*q^3+24*q^2-20*q+16 ) q congruent 17 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q-6 ) q congruent 19 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+22 ) q congruent 21 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q-6 ) q congruent 23 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+6 ) q congruent 25 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+10 ) q congruent 27 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+6 ) q congruent 29 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q-6 ) q congruent 31 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+22 ) q congruent 32 modulo 60: 1/96 q^2 ( q^3-9*q^2+24*q-20 ) q congruent 37 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+10 ) q congruent 41 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q-6 ) q congruent 43 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+22 ) q congruent 47 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+6 ) q congruent 49 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+10 ) q congruent 53 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q-6 ) q congruent 59 modulo 60: 1/96 phi1 ( q^4-8*q^3+19*q^2-14*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 3, 7, 69, 81, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 18 ], [ 4, 1, 2, 12 ], [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 6 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 24 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 24 ], [ 16, 1, 4, 48 ], [ 17, 1, 2, 16 ], [ 20, 1, 2, 72 ], [ 22, 1, 2, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 18 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 24 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 48 ], [ 28, 1, 2, 36 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 36 ], [ 32, 1, 2, 48 ], [ 33, 1, 1, 48 ], [ 33, 1, 2, 48 ], [ 35, 1, 3, 72 ], [ 35, 1, 4, 48 ], [ 37, 1, 2, 48 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 24 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 48 ], [ 40, 1, 3, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 4, 48 ], [ 41, 1, 9, 48 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 96 ], [ 44, 1, 5, 48 ], [ 47, 1, 2, 72 ], [ 47, 1, 4, 48 ], [ 48, 1, 3, 96 ], [ 51, 1, 3, 96 ], [ 51, 1, 5, 48 ], [ 51, 1, 6, 48 ], [ 52, 1, 4, 48 ], [ 52, 1, 10, 48 ], [ 53, 1, 9, 96 ], [ 55, 1, 5, 96 ], [ 56, 1, 10, 96 ], [ 58, 1, 4, 96 ] ] k = 18: F-action on Pi is (1,3) [61,1,18] Dynkin type is ^2A_2(q) + A_1(q) + T(phi1^2 phi2^3) Order of center |Z^F|: phi1^2 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 2 modulo 60: 1/32 q phi1 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) q congruent 4 modulo 60: 1/32 q phi1 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 7 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) q congruent 8 modulo 60: 1/32 q phi1 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 11 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) q congruent 13 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 16 modulo 60: 1/32 q phi1 ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 19 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) q congruent 21 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 23 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) q congruent 25 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 27 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) q congruent 29 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 31 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) q congruent 32 modulo 60: 1/32 q phi1 ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 41 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 43 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) q congruent 47 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) q congruent 49 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 53 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+26 ) q congruent 59 modulo 60: 1/32 phi1 ( q^4-8*q^3+23*q^2-34*q+30 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 7, 69, 82, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 14 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 18 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 18 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], [ 16, 1, 3, 48 ], [ 16, 1, 4, 8 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 24 ], [ 22, 1, 3, 40 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 12 ], [ 29, 1, 3, 48 ], [ 30, 1, 3, 24 ], [ 30, 1, 4, 16 ], [ 31, 1, 3, 56 ], [ 31, 1, 4, 12 ], [ 32, 1, 3, 48 ], [ 33, 1, 6, 16 ], [ 33, 1, 8, 48 ], [ 34, 1, 3, 32 ], [ 35, 1, 6, 48 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 24 ], [ 36, 1, 3, 16 ], [ 37, 1, 2, 16 ], [ 38, 1, 8, 96 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 4, 8 ], [ 40, 1, 2, 24 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 42, 1, 2, 32 ], [ 43, 1, 3, 32 ], [ 43, 1, 4, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 45, 1, 5, 32 ], [ 46, 1, 5, 64 ], [ 47, 1, 7, 48 ], [ 47, 1, 8, 24 ], [ 47, 1, 10, 16 ], [ 48, 1, 4, 32 ], [ 48, 1, 5, 32 ], [ 50, 1, 8, 32 ], [ 51, 1, 3, 16 ], [ 51, 1, 8, 16 ], [ 51, 1, 10, 48 ], [ 52, 1, 2, 16 ], [ 52, 1, 4, 16 ], [ 53, 1, 6, 32 ], [ 53, 1, 8, 32 ], [ 54, 1, 13, 32 ], [ 55, 1, 13, 32 ], [ 55, 1, 14, 32 ], [ 56, 1, 13, 32 ], [ 56, 1, 19, 32 ], [ 58, 1, 11, 64 ] ] k = 19: F-action on Pi is () [61,1,19] Dynkin type is A_2(q) + A_1(q) + T(phi1^4 phi2) Order of center |Z^F|: phi1^4 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-718*q+938 ) q congruent 2 modulo 60: 1/96 q ( q^4-25*q^3+220*q^2-780*q+864 ) q congruent 3 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-905*q^2+1452*q-558 ) q congruent 4 modulo 60: 1/96 q ( q^4-25*q^3+220*q^2-796*q+1008 ) q congruent 5 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-702*q+810 ) q congruent 7 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-921*q^2+1596*q-686 ) q congruent 8 modulo 60: 1/96 q ( q^4-25*q^3+220*q^2-780*q+864 ) q congruent 9 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-702*q+810 ) q congruent 11 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-905*q^2+1452*q-558 ) q congruent 13 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-718*q+938 ) q congruent 16 modulo 60: 1/96 q ( q^4-25*q^3+220*q^2-796*q+1008 ) q congruent 17 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-702*q+810 ) q congruent 19 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-921*q^2+1596*q-686 ) q congruent 21 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-702*q+810 ) q congruent 23 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-905*q^2+1452*q-558 ) q congruent 25 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-718*q+938 ) q congruent 27 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-905*q^2+1452*q-558 ) q congruent 29 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-702*q+810 ) q congruent 31 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-921*q^2+1596*q-686 ) q congruent 32 modulo 60: 1/96 q ( q^4-25*q^3+220*q^2-780*q+864 ) q congruent 37 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-718*q+938 ) q congruent 41 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-702*q+810 ) q congruent 43 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-921*q^2+1596*q-686 ) q congruent 47 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-905*q^2+1452*q-558 ) q congruent 49 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-718*q+938 ) q congruent 53 modulo 60: 1/96 phi1 ( q^4-24*q^3+203*q^2-702*q+810 ) q congruent 59 modulo 60: 1/96 ( q^5-25*q^4+227*q^3-905*q^2+1452*q-558 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 77, 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 26 ], [ 4, 1, 1, 46 ], [ 5, 1, 1, 80 ], [ 6, 1, 1, 96 ], [ 7, 1, 1, 40 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 40 ], [ 12, 1, 1, 70 ], [ 13, 1, 1, 72 ], [ 14, 1, 1, 120 ], [ 15, 1, 1, 152 ], [ 16, 1, 1, 176 ], [ 17, 1, 1, 240 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 112 ], [ 20, 1, 1, 144 ], [ 20, 1, 2, 56 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 120 ], [ 22, 1, 2, 36 ], [ 23, 1, 1, 18 ], [ 24, 1, 1, 36 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 60 ], [ 26, 1, 1, 48 ], [ 26, 1, 3, 16 ], [ 27, 1, 1, 48 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 72 ], [ 28, 1, 2, 36 ], [ 29, 1, 1, 144 ], [ 29, 1, 2, 80 ], [ 30, 1, 1, 144 ], [ 31, 1, 1, 168 ], [ 31, 1, 2, 92 ], [ 32, 1, 1, 224 ], [ 33, 1, 1, 144 ], [ 34, 1, 1, 96 ], [ 34, 1, 2, 64 ], [ 35, 1, 1, 144 ], [ 35, 1, 3, 72 ], [ 36, 1, 1, 48 ], [ 36, 1, 2, 48 ], [ 37, 1, 1, 96 ], [ 38, 1, 1, 288 ], [ 38, 1, 5, 96 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 24 ], [ 40, 1, 1, 36 ], [ 41, 1, 1, 48 ], [ 41, 1, 6, 48 ], [ 42, 1, 1, 96 ], [ 42, 1, 4, 64 ], [ 43, 1, 1, 96 ], [ 43, 1, 2, 96 ], [ 44, 1, 1, 48 ], [ 44, 1, 2, 48 ], [ 45, 1, 1, 96 ], [ 45, 1, 2, 96 ], [ 46, 1, 1, 192 ], [ 46, 1, 2, 128 ], [ 47, 1, 1, 144 ], [ 47, 1, 2, 72 ], [ 48, 1, 1, 96 ], [ 48, 1, 2, 96 ], [ 50, 1, 2, 96 ], [ 50, 1, 4, 96 ], [ 51, 1, 1, 48 ], [ 51, 1, 2, 144 ], [ 52, 1, 2, 48 ], [ 53, 1, 1, 96 ], [ 53, 1, 3, 96 ], [ 54, 1, 2, 96 ], [ 55, 1, 1, 96 ], [ 55, 1, 2, 96 ], [ 56, 1, 2, 96 ], [ 56, 1, 6, 96 ], [ 58, 1, 2, 192 ] ] k = 20: F-action on Pi is (1,3) [61,1,20] Dynkin type is ^2A_2(q) + A_1(q) + T(phi1 phi2^4) Order of center |Z^F|: phi1 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^4-18*q^3+117*q^2-346*q+438 ) q congruent 2 modulo 60: 1/96 ( q^5-19*q^4+128*q^3-372*q^2+480*q-224 ) q congruent 3 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-463*q^2+844*q-714 ) q congruent 4 modulo 60: 1/96 q ( q^4-19*q^3+128*q^2-356*q+336 ) q congruent 5 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-479*q^2+928*q-790 ) q congruent 7 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-463*q^2+844*q-714 ) q congruent 8 modulo 60: 1/96 ( q^5-19*q^4+128*q^3-372*q^2+480*q-224 ) q congruent 9 modulo 60: 1/96 phi1 ( q^4-18*q^3+117*q^2-346*q+438 ) q congruent 11 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-479*q^2+988*q-1066 ) q congruent 13 modulo 60: 1/96 phi1 ( q^4-18*q^3+117*q^2-346*q+438 ) q congruent 16 modulo 60: 1/96 q ( q^4-19*q^3+128*q^2-356*q+336 ) q congruent 17 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-479*q^2+928*q-790 ) q congruent 19 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-463*q^2+844*q-714 ) q congruent 21 modulo 60: 1/96 phi1 ( q^4-18*q^3+117*q^2-346*q+438 ) q congruent 23 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-479*q^2+988*q-1066 ) q congruent 25 modulo 60: 1/96 phi1 ( q^4-18*q^3+117*q^2-346*q+438 ) q congruent 27 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-463*q^2+844*q-714 ) q congruent 29 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-479*q^2+928*q-790 ) q congruent 31 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-463*q^2+844*q-714 ) q congruent 32 modulo 60: 1/96 ( q^5-19*q^4+128*q^3-372*q^2+480*q-224 ) q congruent 37 modulo 60: 1/96 phi1 ( q^4-18*q^3+117*q^2-346*q+438 ) q congruent 41 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-479*q^2+928*q-790 ) q congruent 43 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-463*q^2+844*q-714 ) q congruent 47 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-479*q^2+988*q-1066 ) q congruent 49 modulo 60: 1/96 phi1 ( q^4-18*q^3+117*q^2-346*q+438 ) q congruent 53 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-479*q^2+928*q-790 ) q congruent 59 modulo 60: 1/96 ( q^5-19*q^4+135*q^3-479*q^2+988*q-1066 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 69, 5, 31, 78 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 26 ], [ 4, 1, 2, 46 ], [ 5, 1, 2, 80 ], [ 6, 1, 2, 96 ], [ 7, 1, 2, 40 ], [ 8, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 40 ], [ 12, 1, 2, 70 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 120 ], [ 15, 1, 2, 152 ], [ 16, 1, 3, 176 ], [ 17, 1, 4, 240 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 112 ], [ 20, 1, 3, 56 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 48 ], [ 22, 1, 3, 36 ], [ 22, 1, 4, 120 ], [ 23, 1, 2, 18 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 60 ], [ 26, 1, 2, 16 ], [ 26, 1, 4, 48 ], [ 27, 1, 3, 16 ], [ 27, 1, 6, 48 ], [ 28, 1, 3, 36 ], [ 28, 1, 4, 72 ], [ 29, 1, 3, 80 ], [ 29, 1, 4, 144 ], [ 30, 1, 3, 144 ], [ 31, 1, 3, 92 ], [ 31, 1, 4, 168 ], [ 32, 1, 3, 224 ], [ 33, 1, 8, 144 ], [ 34, 1, 3, 64 ], [ 34, 1, 4, 96 ], [ 35, 1, 6, 72 ], [ 35, 1, 8, 144 ], [ 36, 1, 3, 48 ], [ 36, 1, 4, 48 ], [ 37, 1, 3, 96 ], [ 38, 1, 8, 96 ], [ 38, 1, 12, 288 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 24 ], [ 40, 1, 6, 36 ], [ 41, 1, 6, 48 ], [ 41, 1, 9, 48 ], [ 42, 1, 2, 64 ], [ 42, 1, 6, 96 ], [ 43, 1, 4, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 8, 48 ], [ 44, 1, 10, 48 ], [ 45, 1, 5, 96 ], [ 45, 1, 6, 96 ], [ 46, 1, 5, 128 ], [ 46, 1, 6, 192 ], [ 47, 1, 7, 72 ], [ 47, 1, 8, 144 ], [ 48, 1, 5, 96 ], [ 48, 1, 6, 96 ], [ 50, 1, 9, 96 ], [ 50, 1, 11, 96 ], [ 51, 1, 8, 144 ], [ 51, 1, 9, 48 ], [ 52, 1, 9, 48 ], [ 53, 1, 8, 96 ], [ 53, 1, 20, 96 ], [ 54, 1, 12, 96 ], [ 55, 1, 13, 96 ], [ 55, 1, 15, 96 ], [ 56, 1, 15, 96 ], [ 56, 1, 18, 96 ], [ 58, 1, 12, 192 ] ] k = 21: F-action on Pi is (1,3) [61,1,21] Dynkin type is ^2A_2(q) + A_1(q) + T(phi2^5) Order of center |Z^F|: phi2^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/1440 phi1 ( q^4-40*q^3+591*q^2-3930*q+10530 ) q congruent 2 modulo 60: 1/1440 ( q^5-41*q^4+616*q^3-4076*q^2+11440*q-10880 ) q congruent 3 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4521*q^2+15000*q-18270 ) q congruent 4 modulo 60: 1/1440 ( q^5-41*q^4+616*q^3-3996*q^2+9360*q-3456 ) q congruent 5 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4601*q^2+16540*q-24050 ) q congruent 7 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4521*q^2+15000*q-18270 ) q congruent 8 modulo 60: 1/1440 ( q^5-41*q^4+616*q^3-4076*q^2+11440*q-10880 ) q congruent 9 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4521*q^2+14460*q-13986 ) q congruent 11 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4601*q^2+17080*q-31790 ) q congruent 13 modulo 60: 1/1440 phi1 ( q^4-40*q^3+591*q^2-3930*q+10530 ) q congruent 16 modulo 60: 1/1440 q ( q^4-41*q^3+616*q^2-3996*q+9360 ) q congruent 17 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4601*q^2+16540*q-24050 ) q congruent 19 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4521*q^2+15000*q-21726 ) q congruent 21 modulo 60: 1/1440 phi1 ( q^4-40*q^3+591*q^2-3930*q+10530 ) q congruent 23 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4601*q^2+17080*q-31790 ) q congruent 25 modulo 60: 1/1440 phi1 ( q^4-40*q^3+591*q^2-3930*q+10530 ) q congruent 27 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4521*q^2+15000*q-18270 ) q congruent 29 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4601*q^2+16540*q-27506 ) q congruent 31 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4521*q^2+15000*q-18270 ) q congruent 32 modulo 60: 1/1440 ( q^5-41*q^4+616*q^3-4076*q^2+11440*q-10880 ) q congruent 37 modulo 60: 1/1440 phi1 ( q^4-40*q^3+591*q^2-3930*q+10530 ) q congruent 41 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4601*q^2+16540*q-24050 ) q congruent 43 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4521*q^2+15000*q-18270 ) q congruent 47 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4601*q^2+17080*q-31790 ) q congruent 49 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4521*q^2+14460*q-13986 ) q congruent 53 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4601*q^2+16540*q-24050 ) q congruent 59 modulo 60: 1/1440 ( q^5-41*q^4+631*q^3-4601*q^2+17080*q-35246 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2, 5, 67, 78, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 62 ], [ 4, 1, 2, 150 ], [ 5, 1, 2, 264 ], [ 6, 1, 2, 312 ], [ 7, 1, 2, 132 ], [ 8, 1, 2, 60 ], [ 9, 1, 1, 15 ], [ 10, 1, 2, 30 ], [ 11, 1, 2, 140 ], [ 12, 1, 2, 330 ], [ 13, 1, 4, 360 ], [ 14, 1, 2, 660 ], [ 15, 1, 2, 732 ], [ 16, 1, 3, 840 ], [ 17, 1, 4, 840 ], [ 18, 1, 2, 420 ], [ 19, 1, 2, 600 ], [ 20, 1, 4, 840 ], [ 21, 1, 2, 240 ], [ 22, 1, 4, 540 ], [ 23, 1, 2, 90 ], [ 24, 1, 2, 210 ], [ 25, 1, 3, 540 ], [ 26, 1, 4, 240 ], [ 27, 1, 6, 240 ], [ 28, 1, 4, 540 ], [ 29, 1, 4, 1200 ], [ 30, 1, 3, 1080 ], [ 31, 1, 4, 1380 ], [ 32, 1, 3, 1200 ], [ 33, 1, 8, 720 ], [ 34, 1, 4, 960 ], [ 35, 1, 8, 1080 ], [ 36, 1, 4, 720 ], [ 37, 1, 3, 1440 ], [ 38, 1, 12, 1440 ], [ 39, 1, 3, 360 ], [ 40, 1, 6, 900 ], [ 41, 1, 9, 720 ], [ 42, 1, 6, 960 ], [ 43, 1, 13, 1440 ], [ 44, 1, 10, 720 ], [ 45, 1, 6, 1440 ], [ 46, 1, 6, 1920 ], [ 47, 1, 8, 1080 ], [ 48, 1, 6, 1440 ], [ 50, 1, 12, 1440 ], [ 51, 1, 9, 2160 ], [ 52, 1, 10, 720 ], [ 53, 1, 20, 1440 ], [ 54, 1, 14, 1440 ], [ 55, 1, 15, 1440 ], [ 56, 1, 20, 1440 ], [ 58, 1, 15, 2880 ] ] k = 22: F-action on Pi is (1,3) [61,1,22] Dynkin type is ^2A_2(q) + A_1(q) + T(phi1^3 phi2^2) Order of center |Z^F|: phi1^3 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 phi1 ( q^4-10*q^3+29*q^2-18*q-18 ) q congruent 2 modulo 60: 1/96 ( q^5-11*q^4+36*q^3-28*q^2-32 ) q congruent 3 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2-12*q+54 ) q congruent 4 modulo 60: 1/96 q ( q^4-11*q^3+36*q^2-28*q-16 ) q congruent 5 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2+16*q-30 ) q congruent 7 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2-12*q+54 ) q congruent 8 modulo 60: 1/96 ( q^5-11*q^4+36*q^3-28*q^2-32 ) q congruent 9 modulo 60: 1/96 phi1 ( q^4-10*q^3+29*q^2-18*q-18 ) q congruent 11 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2+4*q+6 ) q congruent 13 modulo 60: 1/96 phi1 ( q^4-10*q^3+29*q^2-18*q-18 ) q congruent 16 modulo 60: 1/96 q ( q^4-11*q^3+36*q^2-28*q-16 ) q congruent 17 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2+16*q-30 ) q congruent 19 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2-12*q+54 ) q congruent 21 modulo 60: 1/96 phi1 ( q^4-10*q^3+29*q^2-18*q-18 ) q congruent 23 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2+4*q+6 ) q congruent 25 modulo 60: 1/96 phi1 ( q^4-10*q^3+29*q^2-18*q-18 ) q congruent 27 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2-12*q+54 ) q congruent 29 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2+16*q-30 ) q congruent 31 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2-12*q+54 ) q congruent 32 modulo 60: 1/96 ( q^5-11*q^4+36*q^3-28*q^2-32 ) q congruent 37 modulo 60: 1/96 phi1 ( q^4-10*q^3+29*q^2-18*q-18 ) q congruent 41 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2+16*q-30 ) q congruent 43 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2-12*q+54 ) q congruent 47 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2+4*q+6 ) q congruent 49 modulo 60: 1/96 phi1 ( q^4-10*q^3+29*q^2-18*q-18 ) q congruent 53 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2+16*q-30 ) q congruent 59 modulo 60: 1/96 ( q^5-11*q^4+39*q^3-47*q^2+4*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 68, 7, 28, 82 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 18 ], [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 6 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 24 ], [ 16, 1, 2, 48 ], [ 16, 1, 3, 24 ], [ 16, 1, 4, 24 ], [ 17, 1, 3, 16 ], [ 20, 1, 3, 72 ], [ 22, 1, 3, 12 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 24 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 36 ], [ 31, 1, 3, 36 ], [ 32, 1, 2, 48 ], [ 33, 1, 6, 48 ], [ 33, 1, 8, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 72 ], [ 37, 1, 2, 48 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 24 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 24 ], [ 40, 1, 3, 48 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 48 ], [ 41, 1, 4, 48 ], [ 43, 1, 3, 96 ], [ 43, 1, 8, 48 ], [ 44, 1, 9, 48 ], [ 47, 1, 7, 72 ], [ 47, 1, 9, 48 ], [ 48, 1, 4, 96 ], [ 51, 1, 3, 48 ], [ 51, 1, 6, 96 ], [ 51, 1, 10, 48 ], [ 52, 1, 1, 48 ], [ 52, 1, 3, 48 ], [ 53, 1, 6, 96 ], [ 55, 1, 14, 96 ], [ 56, 1, 14, 96 ], [ 58, 1, 4, 96 ] ] i = 62: Pi = [ 1, 2, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [62,1,1] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^5) Order of center |Z^F|: phi1^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11806*q^2+59125*q-131371 ) q congruent 2 modulo 60: 1/2304 ( q^5-54*q^4+1092*q^3-10088*q^2+40416*q-48384 ) q congruent 3 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+55557*q-88155 ) q congruent 4 modulo 60: 1/2304 ( q^5-54*q^4+1092*q^3-10152*q^2+42976*q-66560 ) q congruent 5 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+56565*q-103275 ) q congruent 7 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11806*q^2+58117*q-111643 ) q congruent 8 modulo 60: 1/2304 ( q^5-54*q^4+1092*q^3-10088*q^2+40416*q-48384 ) q congruent 9 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+56565*q-103275 ) q congruent 11 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+55557*q-92763 ) q congruent 13 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11806*q^2+59125*q-126763 ) q congruent 16 modulo 60: 1/2304 ( q^5-54*q^4+1092*q^3-10152*q^2+42976*q-71168 ) q congruent 17 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+56565*q-103275 ) q congruent 19 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11806*q^2+58117*q-111643 ) q congruent 21 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+56565*q-107883 ) q congruent 23 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+55557*q-88155 ) q congruent 25 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11806*q^2+59125*q-126763 ) q congruent 27 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+55557*q-88155 ) q congruent 29 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+56565*q-103275 ) q congruent 31 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11806*q^2+58117*q-116251 ) q congruent 32 modulo 60: 1/2304 ( q^5-54*q^4+1092*q^3-10088*q^2+40416*q-48384 ) q congruent 37 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11806*q^2+59125*q-126763 ) q congruent 41 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+56565*q-107883 ) q congruent 43 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11806*q^2+58117*q-111643 ) q congruent 47 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+55557*q-88155 ) q congruent 49 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11806*q^2+59125*q-126763 ) q congruent 53 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+56565*q-103275 ) q congruent 59 modulo 60: 1/2304 ( q^5-55*q^4+1162*q^3-11742*q^2+55557*q-88155 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4, 66, 4, 4, 68 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 80 ], [ 4, 1, 1, 216 ], [ 5, 1, 1, 384 ], [ 6, 1, 1, 512 ], [ 7, 1, 1, 144 ], [ 8, 1, 1, 64 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 26 ], [ 11, 1, 1, 144 ], [ 12, 1, 1, 432 ], [ 13, 1, 1, 528 ], [ 14, 1, 1, 768 ], [ 15, 1, 1, 1152 ], [ 16, 1, 1, 1920 ], [ 17, 1, 1, 2304 ], [ 18, 1, 1, 384 ], [ 19, 1, 1, 768 ], [ 20, 1, 1, 1248 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 640 ], [ 23, 1, 1, 72 ], [ 24, 1, 1, 198 ], [ 25, 1, 1, 624 ], [ 26, 1, 1, 192 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 624 ], [ 29, 1, 1, 1152 ], [ 30, 1, 1, 1536 ], [ 31, 1, 1, 1920 ], [ 32, 1, 1, 3072 ], [ 33, 1, 1, 4224 ], [ 34, 1, 1, 768 ], [ 35, 1, 1, 2688 ], [ 36, 1, 1, 384 ], [ 37, 1, 1, 1152 ], [ 38, 1, 1, 2304 ], [ 39, 1, 1, 240 ], [ 40, 1, 1, 1056 ], [ 41, 1, 1, 1440 ], [ 42, 1, 1, 768 ], [ 43, 1, 1, 1152 ], [ 44, 1, 1, 576 ], [ 45, 1, 1, 1152 ], [ 46, 1, 1, 2304 ], [ 47, 1, 1, 3840 ], [ 48, 1, 1, 2304 ], [ 49, 1, 1, 5760 ], [ 50, 1, 1, 384 ], [ 51, 1, 1, 1152 ], [ 52, 1, 1, 1440 ], [ 53, 1, 1, 2304 ], [ 55, 1, 1, 2304 ], [ 56, 1, 1, 1152 ], [ 57, 1, 1, 4608 ], [ 59, 1, 1, 1152 ], [ 60, 1, 1, 4608 ] ] k = 2: F-action on Pi is () [62,1,2] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^3 phi3) Order of center |Z^F|: phi1^3 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 ( q^4-12*q^3+37*q^2+6*q-104 ) q congruent 2 modulo 60: 1/72 q phi2 ( q^3-13*q^2+52*q-60 ) q congruent 3 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 4 modulo 60: 1/72 phi1 ( q^4-11*q^3+28*q^2+16*q-64 ) q congruent 5 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 7 modulo 60: 1/72 phi1 ( q^4-12*q^3+37*q^2+6*q-104 ) q congruent 8 modulo 60: 1/72 q phi2 ( q^3-13*q^2+52*q-60 ) q congruent 9 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 11 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 13 modulo 60: 1/72 phi1 ( q^4-12*q^3+37*q^2+6*q-104 ) q congruent 16 modulo 60: 1/72 phi1 ( q^4-11*q^3+28*q^2+16*q-64 ) q congruent 17 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 19 modulo 60: 1/72 phi1 ( q^4-12*q^3+37*q^2+6*q-104 ) q congruent 21 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 23 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 25 modulo 60: 1/72 phi1 ( q^4-12*q^3+37*q^2+6*q-104 ) q congruent 27 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 29 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 31 modulo 60: 1/72 phi1 ( q^4-12*q^3+37*q^2+6*q-104 ) q congruent 32 modulo 60: 1/72 q phi2 ( q^3-13*q^2+52*q-60 ) q congruent 37 modulo 60: 1/72 phi1 ( q^4-12*q^3+37*q^2+6*q-104 ) q congruent 41 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 43 modulo 60: 1/72 phi1 ( q^4-12*q^3+37*q^2+6*q-104 ) q congruent 47 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 49 modulo 60: 1/72 phi1 ( q^4-12*q^3+37*q^2+6*q-104 ) q congruent 53 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) q congruent 59 modulo 60: 1/72 q phi2 ( q^3-14*q^2+63*q-90 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30, 77, 30, 30, 81 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 4, 1, 1, 18 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 18 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], [ 16, 1, 1, 48 ], [ 17, 1, 1, 72 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], [ 20, 1, 1, 24 ], [ 22, 1, 1, 4 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 12 ], [ 30, 1, 1, 24 ], [ 31, 1, 1, 12 ], [ 32, 1, 1, 48 ], [ 33, 1, 1, 48 ], [ 35, 1, 1, 24 ], [ 38, 1, 3, 72 ], [ 40, 1, 1, 12 ], [ 42, 1, 3, 24 ], [ 44, 1, 3, 18 ], [ 45, 1, 3, 36 ], [ 46, 1, 3, 72 ], [ 47, 1, 1, 24 ], [ 50, 1, 3, 12 ], [ 53, 1, 16, 72 ], [ 55, 1, 3, 72 ], [ 56, 1, 3, 36 ], [ 59, 1, 4, 36 ], [ 60, 1, 2, 144 ] ] k = 3: F-action on Pi is (1,2,5) [62,1,3] Dynkin type is A_1(q^3) + T(phi1 phi3^2) Order of center |Z^F|: phi1 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 phi1 phi2^2 ( q^2-2*q-8 ) q congruent 2 modulo 60: 1/144 q phi2 ( q^3-q^2-8*q+12 ) q congruent 3 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 4 modulo 60: 1/144 phi1 ( q^4+q^3-8*q^2-20*q-16 ) q congruent 5 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 7 modulo 60: 1/144 phi1 phi2^2 ( q^2-2*q-8 ) q congruent 8 modulo 60: 1/144 q phi2 ( q^3-q^2-8*q+12 ) q congruent 9 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 11 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 13 modulo 60: 1/144 phi1 phi2^2 ( q^2-2*q-8 ) q congruent 16 modulo 60: 1/144 phi1 ( q^4+q^3-8*q^2-20*q-16 ) q congruent 17 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 19 modulo 60: 1/144 phi1 phi2^2 ( q^2-2*q-8 ) q congruent 21 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 23 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 25 modulo 60: 1/144 phi1 phi2^2 ( q^2-2*q-8 ) q congruent 27 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 29 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 31 modulo 60: 1/144 phi1 phi2^2 ( q^2-2*q-8 ) q congruent 32 modulo 60: 1/144 q phi2 ( q^3-q^2-8*q+12 ) q congruent 37 modulo 60: 1/144 phi1 phi2^2 ( q^2-2*q-8 ) q congruent 41 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 43 modulo 60: 1/144 phi1 phi2^2 ( q^2-2*q-8 ) q congruent 47 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 49 modulo 60: 1/144 phi1 phi2^2 ( q^2-2*q-8 ) q congruent 53 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) q congruent 59 modulo 60: 1/144 q phi2 ( q^3-2*q^2-9*q+18 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 85 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 8, 1, 1, 16 ], [ 10, 1, 1, 2 ], [ 22, 1, 1, 16 ], [ 27, 1, 5, 24 ], [ 33, 1, 3, 24 ], [ 38, 1, 14, 144 ], [ 40, 1, 5, 24 ], [ 42, 1, 3, 24 ], [ 47, 1, 5, 48 ], [ 50, 1, 3, 48 ], [ 59, 1, 9, 72 ], [ 60, 1, 4, 72 ] ] k = 4: F-action on Pi is (1,2,5) [62,1,4] Dynkin type is A_1(q^3) + T(phi1^3 phi3) Order of center |Z^F|: phi1^3 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 ( q^4-6*q^3+7*q^2+6*q+4 ) q congruent 2 modulo 60: 1/72 q phi2 ( q^3-7*q^2+16*q-12 ) q congruent 3 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 4 modulo 60: 1/72 phi1 ( q^4-5*q^3+4*q^2+4*q+8 ) q congruent 5 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 7 modulo 60: 1/72 phi1 ( q^4-6*q^3+7*q^2+6*q+4 ) q congruent 8 modulo 60: 1/72 q phi2 ( q^3-7*q^2+16*q-12 ) q congruent 9 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 11 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 13 modulo 60: 1/72 phi1 ( q^4-6*q^3+7*q^2+6*q+4 ) q congruent 16 modulo 60: 1/72 phi1 ( q^4-5*q^3+4*q^2+4*q+8 ) q congruent 17 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 19 modulo 60: 1/72 phi1 ( q^4-6*q^3+7*q^2+6*q+4 ) q congruent 21 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 23 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 25 modulo 60: 1/72 phi1 ( q^4-6*q^3+7*q^2+6*q+4 ) q congruent 27 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 29 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 31 modulo 60: 1/72 phi1 ( q^4-6*q^3+7*q^2+6*q+4 ) q congruent 32 modulo 60: 1/72 q phi2 ( q^3-7*q^2+16*q-12 ) q congruent 37 modulo 60: 1/72 phi1 ( q^4-6*q^3+7*q^2+6*q+4 ) q congruent 41 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 43 modulo 60: 1/72 phi1 ( q^4-6*q^3+7*q^2+6*q+4 ) q congruent 47 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 49 modulo 60: 1/72 phi1 ( q^4-6*q^3+7*q^2+6*q+4 ) q congruent 53 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) q congruent 59 modulo 60: 1/72 q phi2 ( q^3-8*q^2+21*q-18 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 87 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 8 ], [ 11, 1, 1, 6 ], [ 17, 1, 5, 36 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 6 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 4 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 12 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 33, 1, 3, 6 ], [ 34, 1, 1, 12 ], [ 36, 1, 1, 24 ], [ 38, 1, 13, 72 ], [ 39, 1, 1, 24 ], [ 40, 1, 5, 6 ], [ 42, 1, 1, 12 ], [ 47, 1, 5, 12 ], [ 49, 1, 3, 18 ], [ 50, 1, 1, 24 ], [ 52, 1, 6, 18 ], [ 57, 1, 12, 36 ], [ 59, 1, 7, 36 ], [ 60, 1, 3, 36 ] ] k = 5: F-action on Pi is () [62,1,5] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2 phi3) Order of center |Z^F|: phi1^2 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 2 modulo 60: 1/72 q^2 phi2 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/72 q phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 8 modulo 60: 1/72 q^2 phi2 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 16 modulo 60: 1/72 q phi1^2 ( q^2-2*q-4 ) q congruent 17 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 21 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 27 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 32 modulo 60: 1/72 q^2 phi2 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 41 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 47 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 53 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 77, 30, 30, 81, 30, 81, 81, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 6 ], [ 13, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 20, 1, 2, 24 ], [ 22, 1, 2, 4 ], [ 23, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 28, 1, 2, 12 ], [ 31, 1, 2, 12 ], [ 33, 1, 1, 48 ], [ 35, 1, 3, 24 ], [ 40, 1, 1, 12 ], [ 42, 1, 3, 24 ], [ 44, 1, 3, 18 ], [ 47, 1, 2, 24 ], [ 50, 1, 6, 12 ], [ 53, 1, 16, 72 ], [ 56, 1, 8, 36 ], [ 59, 1, 4, 36 ], [ 60, 1, 2, 144 ] ] k = 6: F-action on Pi is () [62,1,6] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2 phi6) Order of center |Z^F|: phi1 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 2 modulo 60: 1/72 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 3 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 4 modulo 60: 1/72 q^2 phi1^2 ( q-2 ) q congruent 5 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 7 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 8 modulo 60: 1/72 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 9 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 11 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 13 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 16 modulo 60: 1/72 q^2 phi1^2 ( q-2 ) q congruent 17 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 19 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 21 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 23 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 25 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 27 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 31 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 32 modulo 60: 1/72 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 37 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 41 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 43 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 47 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 49 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 53 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 59 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 82, 82, 31, 82, 31, 31, 78 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 18 ], [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 12, 1, 2, 6 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 24 ], [ 20, 1, 3, 24 ], [ 22, 1, 3, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], [ 28, 1, 3, 12 ], [ 31, 1, 3, 12 ], [ 33, 1, 8, 48 ], [ 35, 1, 6, 24 ], [ 40, 1, 6, 12 ], [ 42, 1, 5, 24 ], [ 44, 1, 7, 18 ], [ 47, 1, 7, 24 ], [ 50, 1, 7, 12 ], [ 53, 1, 18, 72 ], [ 56, 1, 12, 36 ], [ 59, 1, 5, 36 ], [ 60, 1, 8, 144 ] ] k = 7: F-action on Pi is () [62,1,7] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi2^3 phi6) Order of center |Z^F|: phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 2 modulo 60: 1/72 phi2 ( q^4-9*q^3+28*q^2-44*q+32 ) q congruent 3 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 4 modulo 60: 1/72 q^2 phi1 ( q^2-7*q+12 ) q congruent 5 modulo 60: 1/72 phi2 ( q^4-10*q^3+37*q^2-72*q+72 ) q congruent 7 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 8 modulo 60: 1/72 phi2 ( q^4-9*q^3+28*q^2-44*q+32 ) q congruent 9 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 11 modulo 60: 1/72 phi2 ( q^4-10*q^3+37*q^2-72*q+72 ) q congruent 13 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 16 modulo 60: 1/72 q^2 phi1 ( q^2-7*q+12 ) q congruent 17 modulo 60: 1/72 phi2 ( q^4-10*q^3+37*q^2-72*q+72 ) q congruent 19 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 21 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 23 modulo 60: 1/72 phi2 ( q^4-10*q^3+37*q^2-72*q+72 ) q congruent 25 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 27 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 29 modulo 60: 1/72 phi2 ( q^4-10*q^3+37*q^2-72*q+72 ) q congruent 31 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 32 modulo 60: 1/72 phi2 ( q^4-9*q^3+28*q^2-44*q+32 ) q congruent 37 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 41 modulo 60: 1/72 phi2 ( q^4-10*q^3+37*q^2-72*q+72 ) q congruent 43 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 47 modulo 60: 1/72 phi2 ( q^4-10*q^3+37*q^2-72*q+72 ) q congruent 49 modulo 60: 1/72 q phi1^2 ( q^2-7*q+12 ) q congruent 53 modulo 60: 1/72 phi2 ( q^4-10*q^3+37*q^2-72*q+72 ) q congruent 59 modulo 60: 1/72 phi2 ( q^4-10*q^3+37*q^2-72*q+72 ) Fusion of maximal tori of C^F in those of G^F: [ 82, 31, 31, 78, 31, 78, 78, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 14 ], [ 4, 1, 2, 18 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 18 ], [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], [ 16, 1, 3, 48 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], [ 20, 1, 4, 24 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], [ 28, 1, 4, 12 ], [ 30, 1, 3, 24 ], [ 31, 1, 4, 12 ], [ 32, 1, 3, 48 ], [ 33, 1, 8, 48 ], [ 35, 1, 8, 24 ], [ 38, 1, 11, 72 ], [ 40, 1, 6, 12 ], [ 42, 1, 5, 24 ], [ 44, 1, 7, 18 ], [ 45, 1, 4, 36 ], [ 46, 1, 4, 72 ], [ 47, 1, 8, 24 ], [ 50, 1, 10, 12 ], [ 53, 1, 18, 72 ], [ 55, 1, 12, 72 ], [ 56, 1, 17, 36 ], [ 59, 1, 5, 36 ], [ 60, 1, 8, 144 ] ] k = 8: F-action on Pi is (2,5) [62,1,8] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^2 phi2 phi6) Order of center |Z^F|: phi1^2 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+22 ) q congruent 2 modulo 60: 1/24 phi2 ( q^4-7*q^3+12*q^2-8 ) q congruent 3 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+18 ) q congruent 4 modulo 60: 1/24 q phi1 ( q^3-5*q^2+16 ) q congruent 5 modulo 60: 1/24 phi2 ( q^4-8*q^3+17*q^2-2*q-12 ) q congruent 7 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+22 ) q congruent 8 modulo 60: 1/24 phi2 ( q^4-7*q^3+12*q^2-8 ) q congruent 9 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+18 ) q congruent 11 modulo 60: 1/24 phi2 ( q^4-8*q^3+17*q^2-2*q-12 ) q congruent 13 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+22 ) q congruent 16 modulo 60: 1/24 q phi1 ( q^3-5*q^2+16 ) q congruent 17 modulo 60: 1/24 phi2 ( q^4-8*q^3+17*q^2-2*q-12 ) q congruent 19 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+22 ) q congruent 21 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+18 ) q congruent 23 modulo 60: 1/24 phi2 ( q^4-8*q^3+17*q^2-2*q-12 ) q congruent 25 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+22 ) q congruent 27 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+18 ) q congruent 29 modulo 60: 1/24 phi2 ( q^4-8*q^3+17*q^2-2*q-12 ) q congruent 31 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+22 ) q congruent 32 modulo 60: 1/24 phi2 ( q^4-7*q^3+12*q^2-8 ) q congruent 37 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+22 ) q congruent 41 modulo 60: 1/24 phi2 ( q^4-8*q^3+17*q^2-2*q-12 ) q congruent 43 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+22 ) q congruent 47 modulo 60: 1/24 phi2 ( q^4-8*q^3+17*q^2-2*q-12 ) q congruent 49 modulo 60: 1/24 q phi1 ( q^3-6*q^2+3*q+22 ) q congruent 53 modulo 60: 1/24 phi2 ( q^4-8*q^3+17*q^2-2*q-12 ) q congruent 59 modulo 60: 1/24 phi2 ( q^4-8*q^3+17*q^2-2*q-12 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 96, 82, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 28, 1, 1, 4 ], [ 31, 1, 3, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 35, 1, 5, 8 ], [ 38, 1, 4, 24 ], [ 40, 1, 2, 4 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 46, 1, 10, 24 ], [ 47, 1, 9, 8 ], [ 50, 1, 7, 12 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 12 ], [ 55, 1, 7, 24 ], [ 56, 1, 12, 12 ], [ 59, 1, 20, 12 ], [ 60, 1, 10, 24 ] ] k = 9: F-action on Pi is (2,5) [62,1,9] Dynkin type is A_1(q) + A_1(q^2) + T(phi1 phi2^2 phi6) Order of center |Z^F|: phi1 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 2 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 4 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 7 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 8 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 11 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 13 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 16 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 19 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 21 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 23 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 25 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 27 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 29 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 31 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 32 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 41 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 43 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 47 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 49 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 53 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 59 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 82, 60, 31, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 4, 8 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 28, 1, 2, 4 ], [ 30, 1, 4, 8 ], [ 31, 1, 4, 4 ], [ 33, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 40, 1, 2, 4 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 47, 1, 10, 8 ], [ 50, 1, 10, 12 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 12 ], [ 56, 1, 17, 12 ], [ 59, 1, 20, 12 ], [ 60, 1, 10, 24 ] ] k = 10: F-action on Pi is (2,5) [62,1,10] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^2 phi2 phi3) Order of center |Z^F|: phi1^2 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 30, 97, 81, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 28, 1, 3, 4 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 33, 1, 2, 8 ], [ 35, 1, 2, 8 ], [ 40, 1, 3, 4 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], [ 45, 1, 3, 12 ], [ 47, 1, 3, 8 ], [ 50, 1, 3, 12 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 12 ], [ 56, 1, 3, 12 ], [ 59, 1, 19, 12 ], [ 60, 1, 11, 24 ] ] k = 11: F-action on Pi is (2,5) [62,1,11] Dynkin type is A_1(q) + A_1(q^2) + T(phi1 phi2^2 phi3) Order of center |Z^F|: phi1 phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1^2 ( q^3-q^2-4*q-4 ) q congruent 2 modulo 60: 1/24 q phi2^2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/24 q phi1 ( q^3-q^2-4*q-4 ) q congruent 5 modulo 60: 1/24 q phi2 ( q^3-4*q^2+3*q+4 ) q congruent 7 modulo 60: 1/24 phi1^2 ( q^3-q^2-4*q-4 ) q congruent 8 modulo 60: 1/24 q phi2^2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/24 q phi2 ( q^3-4*q^2+3*q+4 ) q congruent 13 modulo 60: 1/24 phi1^2 ( q^3-q^2-4*q-4 ) q congruent 16 modulo 60: 1/24 q phi1 ( q^3-q^2-4*q-4 ) q congruent 17 modulo 60: 1/24 q phi2 ( q^3-4*q^2+3*q+4 ) q congruent 19 modulo 60: 1/24 phi1^2 ( q^3-q^2-4*q-4 ) q congruent 21 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/24 q phi2 ( q^3-4*q^2+3*q+4 ) q congruent 25 modulo 60: 1/24 phi1^2 ( q^3-q^2-4*q-4 ) q congruent 27 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/24 q phi2 ( q^3-4*q^2+3*q+4 ) q congruent 31 modulo 60: 1/24 phi1^2 ( q^3-q^2-4*q-4 ) q congruent 32 modulo 60: 1/24 q phi2^2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/24 phi1^2 ( q^3-q^2-4*q-4 ) q congruent 41 modulo 60: 1/24 q phi2 ( q^3-4*q^2+3*q+4 ) q congruent 43 modulo 60: 1/24 phi1^2 ( q^3-q^2-4*q-4 ) q congruent 47 modulo 60: 1/24 q phi2 ( q^3-4*q^2+3*q+4 ) q congruent 49 modulo 60: 1/24 phi1^2 ( q^3-q^2-4*q-4 ) q congruent 53 modulo 60: 1/24 q phi2 ( q^3-4*q^2+3*q+4 ) q congruent 59 modulo 60: 1/24 q phi2 ( q^3-4*q^2+3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 81, 59, 27, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 28, 1, 4, 4 ], [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 38, 1, 9, 24 ], [ 40, 1, 3, 4 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], [ 46, 1, 9, 24 ], [ 47, 1, 4, 8 ], [ 50, 1, 6, 12 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 12 ], [ 55, 1, 18, 24 ], [ 56, 1, 8, 12 ], [ 59, 1, 19, 12 ], [ 60, 1, 11, 24 ] ] k = 12: F-action on Pi is (1,5,2) [62,1,12] Dynkin type is A_1(q^3) + T(phi2 phi3^2) Order of center |Z^F|: phi2 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 phi1^2 ( q^3+3*q^2-2*q-8 ) q congruent 2 modulo 60: 1/144 q^2 phi2 ( q^2+q-6 ) q congruent 3 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 4 modulo 60: 1/144 q phi1 ( q^3+3*q^2-2*q-8 ) q congruent 5 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 7 modulo 60: 1/144 phi1^2 ( q^3+3*q^2-2*q-8 ) q congruent 8 modulo 60: 1/144 q^2 phi2 ( q^2+q-6 ) q congruent 9 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 11 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 13 modulo 60: 1/144 phi1^2 ( q^3+3*q^2-2*q-8 ) q congruent 16 modulo 60: 1/144 q phi1 ( q^3+3*q^2-2*q-8 ) q congruent 17 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 19 modulo 60: 1/144 phi1^2 ( q^3+3*q^2-2*q-8 ) q congruent 21 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 23 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 25 modulo 60: 1/144 phi1^2 ( q^3+3*q^2-2*q-8 ) q congruent 27 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 29 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 31 modulo 60: 1/144 phi1^2 ( q^3+3*q^2-2*q-8 ) q congruent 32 modulo 60: 1/144 q^2 phi2 ( q^2+q-6 ) q congruent 37 modulo 60: 1/144 phi1^2 ( q^3+3*q^2-2*q-8 ) q congruent 41 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 43 modulo 60: 1/144 phi1^2 ( q^3+3*q^2-2*q-8 ) q congruent 47 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 49 modulo 60: 1/144 phi1^2 ( q^3+3*q^2-2*q-8 ) q congruent 53 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) q congruent 59 modulo 60: 1/144 q phi1 phi2 ( q^2+q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 79, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 10, 1, 2, 2 ], [ 22, 1, 2, 16 ], [ 27, 1, 5, 24 ], [ 33, 1, 3, 24 ], [ 40, 1, 5, 24 ], [ 42, 1, 3, 24 ], [ 47, 1, 6, 48 ], [ 50, 1, 6, 48 ], [ 59, 1, 9, 72 ], [ 60, 1, 4, 72 ] ] k = 13: F-action on Pi is (1,5,2) [62,1,13] Dynkin type is A_1(q^3) + T(phi1 phi6^2) Order of center |Z^F|: phi1 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 2 modulo 60: 1/144 phi2 ( q^4-5*q^3+4*q^2+12*q-16 ) q congruent 3 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 4 modulo 60: 1/144 q phi1 ( q^3-3*q^2-4*q+12 ) q congruent 5 modulo 60: 1/144 phi2 ( q^4-6*q^3+7*q^2+14*q-24 ) q congruent 7 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 8 modulo 60: 1/144 phi2 ( q^4-5*q^3+4*q^2+12*q-16 ) q congruent 9 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 11 modulo 60: 1/144 phi2 ( q^4-6*q^3+7*q^2+14*q-24 ) q congruent 13 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 16 modulo 60: 1/144 q phi1 ( q^3-3*q^2-4*q+12 ) q congruent 17 modulo 60: 1/144 phi2 ( q^4-6*q^3+7*q^2+14*q-24 ) q congruent 19 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 21 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 23 modulo 60: 1/144 phi2 ( q^4-6*q^3+7*q^2+14*q-24 ) q congruent 25 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 27 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 29 modulo 60: 1/144 phi2 ( q^4-6*q^3+7*q^2+14*q-24 ) q congruent 31 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 32 modulo 60: 1/144 phi2 ( q^4-5*q^3+4*q^2+12*q-16 ) q congruent 37 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 41 modulo 60: 1/144 phi2 ( q^4-6*q^3+7*q^2+14*q-24 ) q congruent 43 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 47 modulo 60: 1/144 phi2 ( q^4-6*q^3+7*q^2+14*q-24 ) q congruent 49 modulo 60: 1/144 q phi1 ( q^3-4*q^2-3*q+18 ) q congruent 53 modulo 60: 1/144 phi2 ( q^4-6*q^3+7*q^2+14*q-24 ) q congruent 59 modulo 60: 1/144 phi2 ( q^4-6*q^3+7*q^2+14*q-24 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 80 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 10, 1, 1, 2 ], [ 22, 1, 3, 16 ], [ 27, 1, 4, 24 ], [ 33, 1, 7, 24 ], [ 40, 1, 4, 24 ], [ 42, 1, 5, 24 ], [ 47, 1, 11, 48 ], [ 50, 1, 7, 48 ], [ 59, 1, 10, 72 ], [ 60, 1, 15, 72 ] ] k = 14: F-action on Pi is (1,2,5) [62,1,14] Dynkin type is A_1(q^3) + T(phi1 phi12) Order of center |Z^F|: phi1 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 2 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 8 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 16 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 21 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 27 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 32 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 41 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 47 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 53 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 57, 102 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 59, 1, 11, 12 ], [ 60, 1, 16, 12 ] ] k = 15: F-action on Pi is (1,2,5) [62,1,15] Dynkin type is A_1(q^3) + T(phi2 phi12) Order of center |Z^F|: phi2 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 2 modulo 60: 1/24 q^3 phi1 phi2 q congruent 3 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 4 modulo 60: 1/24 q^3 phi1 phi2 q congruent 5 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 7 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 8 modulo 60: 1/24 q^3 phi1 phi2 q congruent 9 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 11 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 13 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 16 modulo 60: 1/24 q^3 phi1 phi2 q congruent 17 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 19 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 21 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 23 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 25 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 27 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 29 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 31 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 32 modulo 60: 1/24 q^3 phi1 phi2 q congruent 37 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 41 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 43 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 47 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 49 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 53 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 59 modulo 60: 1/24 q^2 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 101, 58 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 59, 1, 11, 12 ], [ 60, 1, 16, 12 ] ] k = 16: F-action on Pi is (1,5,2) [62,1,16] Dynkin type is A_1(q^3) + T(phi2 phi6^2) Order of center |Z^F|: phi2 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 2 modulo 60: 1/144 phi2 ( q^4-3*q^3-2*q^2-8*q+32 ) q congruent 3 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 4 modulo 60: 1/144 q^2 phi1 ( q^2-q-6 ) q congruent 5 modulo 60: 1/144 phi2 ( q^4-4*q^3+q^2-6*q+24 ) q congruent 7 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 8 modulo 60: 1/144 phi2 ( q^4-3*q^3-2*q^2-8*q+32 ) q congruent 9 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 11 modulo 60: 1/144 phi2 ( q^4-4*q^3+q^2-6*q+24 ) q congruent 13 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 16 modulo 60: 1/144 q^2 phi1 ( q^2-q-6 ) q congruent 17 modulo 60: 1/144 phi2 ( q^4-4*q^3+q^2-6*q+24 ) q congruent 19 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 21 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 23 modulo 60: 1/144 phi2 ( q^4-4*q^3+q^2-6*q+24 ) q congruent 25 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 27 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 29 modulo 60: 1/144 phi2 ( q^4-4*q^3+q^2-6*q+24 ) q congruent 31 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 32 modulo 60: 1/144 phi2 ( q^4-3*q^3-2*q^2-8*q+32 ) q congruent 37 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 41 modulo 60: 1/144 phi2 ( q^4-4*q^3+q^2-6*q+24 ) q congruent 43 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 47 modulo 60: 1/144 phi2 ( q^4-4*q^3+q^2-6*q+24 ) q congruent 49 modulo 60: 1/144 q phi1^2 ( q^2-q-6 ) q congruent 53 modulo 60: 1/144 phi2 ( q^4-4*q^3+q^2-6*q+24 ) q congruent 59 modulo 60: 1/144 phi2 ( q^4-4*q^3+q^2-6*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 86, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 8, 1, 2, 16 ], [ 10, 1, 2, 2 ], [ 22, 1, 4, 16 ], [ 27, 1, 4, 24 ], [ 33, 1, 7, 24 ], [ 38, 1, 17, 144 ], [ 40, 1, 4, 24 ], [ 42, 1, 5, 24 ], [ 47, 1, 12, 48 ], [ 50, 1, 10, 48 ], [ 59, 1, 10, 72 ], [ 60, 1, 15, 72 ] ] k = 17: F-action on Pi is (1,5,2) [62,1,17] Dynkin type is A_1(q^3) + T(phi1 phi2^2 phi6) Order of center |Z^F|: phi1 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 2 modulo 60: 1/24 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 3 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 4 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/24 phi2 ( q^4-4*q^3+5*q^2-6*q+8 ) q congruent 7 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 8 modulo 60: 1/24 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 9 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 11 modulo 60: 1/24 phi2 ( q^4-4*q^3+5*q^2-6*q+8 ) q congruent 13 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 16 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/24 phi2 ( q^4-4*q^3+5*q^2-6*q+8 ) q congruent 19 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 21 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 23 modulo 60: 1/24 phi2 ( q^4-4*q^3+5*q^2-6*q+8 ) q congruent 25 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 27 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 29 modulo 60: 1/24 phi2 ( q^4-4*q^3+5*q^2-6*q+8 ) q congruent 31 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 32 modulo 60: 1/24 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 37 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 41 modulo 60: 1/24 phi2 ( q^4-4*q^3+5*q^2-6*q+8 ) q congruent 43 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 47 modulo 60: 1/24 phi2 ( q^4-4*q^3+5*q^2-6*q+8 ) q congruent 49 modulo 60: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 53 modulo 60: 1/24 phi2 ( q^4-4*q^3+5*q^2-6*q+8 ) q congruent 59 modulo 60: 1/24 phi2 ( q^4-4*q^3+5*q^2-6*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 40, 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 6, 12 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 33, 1, 7, 6 ], [ 34, 1, 4, 4 ], [ 36, 1, 3, 8 ], [ 38, 1, 16, 24 ], [ 39, 1, 4, 4 ], [ 40, 1, 4, 6 ], [ 42, 1, 2, 4 ], [ 47, 1, 12, 12 ], [ 49, 1, 6, 6 ], [ 50, 1, 11, 8 ], [ 52, 1, 7, 6 ], [ 57, 1, 15, 12 ], [ 59, 1, 15, 12 ], [ 60, 1, 13, 12 ] ] k = 18: F-action on Pi is (1,5,2) [62,1,18] Dynkin type is A_1(q^3) + T(phi1^2 phi2 phi3) Order of center |Z^F|: phi1^2 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 2 modulo 60: 1/72 q^2 phi2 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/72 q phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 8 modulo 60: 1/72 q^2 phi2 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 16 modulo 60: 1/72 q phi1^2 ( q^2-2*q-4 ) q congruent 17 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 21 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 27 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 32 modulo 60: 1/72 q^2 phi2 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 41 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 47 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/72 phi1^3 ( q^2-2*q-4 ) q congruent 53 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/72 q phi1 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 83, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 6 ], [ 19, 1, 1, 6 ], [ 22, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 33, 1, 3, 6 ], [ 34, 1, 2, 12 ], [ 39, 1, 4, 12 ], [ 40, 1, 5, 6 ], [ 42, 1, 1, 12 ], [ 47, 1, 6, 12 ], [ 49, 1, 3, 18 ], [ 50, 1, 4, 24 ], [ 52, 1, 6, 18 ], [ 57, 1, 13, 36 ], [ 59, 1, 7, 36 ], [ 60, 1, 3, 36 ] ] k = 19: F-action on Pi is (1,5,2) [62,1,19] Dynkin type is A_1(q^3) + T(phi1^2 phi2 phi6) Order of center |Z^F|: phi1^2 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 2 modulo 60: 1/24 q phi1 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/24 q phi1 phi2 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/24 q phi1 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/24 q phi1 phi2 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/24 q phi1 phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/24 q phi1 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 11, 1, 2, 2 ], [ 19, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 33, 1, 7, 6 ], [ 34, 1, 3, 4 ], [ 39, 1, 1, 8 ], [ 40, 1, 4, 6 ], [ 42, 1, 2, 4 ], [ 47, 1, 11, 12 ], [ 49, 1, 6, 6 ], [ 50, 1, 8, 8 ], [ 52, 1, 7, 6 ], [ 57, 1, 14, 12 ], [ 59, 1, 15, 12 ], [ 60, 1, 13, 12 ] ] k = 20: F-action on Pi is (1,5,2) [62,1,20] Dynkin type is A_1(q^3) + T(phi1^2 phi2 phi3) Order of center |Z^F|: phi1^2 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1 ( q^3-2*q^2-3*q-4 ) q congruent 2 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 4 modulo 60: 1/24 q phi1 ( q^3-q^2-2*q-4 ) q congruent 5 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 7 modulo 60: 1/24 q phi1 ( q^3-2*q^2-3*q-4 ) q congruent 8 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 11 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 13 modulo 60: 1/24 q phi1 ( q^3-2*q^2-3*q-4 ) q congruent 16 modulo 60: 1/24 q phi1 ( q^3-q^2-2*q-4 ) q congruent 17 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 19 modulo 60: 1/24 q phi1 ( q^3-2*q^2-3*q-4 ) q congruent 21 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 23 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 25 modulo 60: 1/24 q phi1 ( q^3-2*q^2-3*q-4 ) q congruent 27 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 29 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 31 modulo 60: 1/24 q phi1 ( q^3-2*q^2-3*q-4 ) q congruent 32 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 q phi1 ( q^3-2*q^2-3*q-4 ) q congruent 41 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 43 modulo 60: 1/24 q phi1 ( q^3-2*q^2-3*q-4 ) q congruent 47 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 49 modulo 60: 1/24 q phi1 ( q^3-2*q^2-3*q-4 ) q congruent 53 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 59 modulo 60: 1/24 q^2 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 83, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 5, 12 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 33, 1, 3, 6 ], [ 34, 1, 1, 4 ], [ 36, 1, 2, 8 ], [ 38, 1, 15, 24 ], [ 39, 1, 4, 4 ], [ 40, 1, 5, 6 ], [ 42, 1, 4, 4 ], [ 47, 1, 5, 12 ], [ 49, 1, 3, 6 ], [ 50, 1, 2, 8 ], [ 52, 1, 6, 6 ], [ 57, 1, 12, 12 ], [ 59, 1, 14, 12 ], [ 60, 1, 12, 12 ] ] k = 21: F-action on Pi is (1,5,2) [62,1,21] Dynkin type is A_1(q^3) + T(phi2^3 phi6) Order of center |Z^F|: phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q^2 phi1^3 q congruent 2 modulo 60: 1/72 phi2 ( q^4-3*q^3+4*q^2-8*q+8 ) q congruent 3 modulo 60: 1/72 q^2 phi1^3 q congruent 4 modulo 60: 1/72 q^3 phi1^2 q congruent 5 modulo 60: 1/72 phi2 ( q^4-4*q^3+7*q^2-12*q+12 ) q congruent 7 modulo 60: 1/72 q^2 phi1^3 q congruent 8 modulo 60: 1/72 phi2 ( q^4-3*q^3+4*q^2-8*q+8 ) q congruent 9 modulo 60: 1/72 q^2 phi1^3 q congruent 11 modulo 60: 1/72 phi2 ( q^4-4*q^3+7*q^2-12*q+12 ) q congruent 13 modulo 60: 1/72 q^2 phi1^3 q congruent 16 modulo 60: 1/72 q^3 phi1^2 q congruent 17 modulo 60: 1/72 phi2 ( q^4-4*q^3+7*q^2-12*q+12 ) q congruent 19 modulo 60: 1/72 q^2 phi1^3 q congruent 21 modulo 60: 1/72 q^2 phi1^3 q congruent 23 modulo 60: 1/72 phi2 ( q^4-4*q^3+7*q^2-12*q+12 ) q congruent 25 modulo 60: 1/72 q^2 phi1^3 q congruent 27 modulo 60: 1/72 q^2 phi1^3 q congruent 29 modulo 60: 1/72 phi2 ( q^4-4*q^3+7*q^2-12*q+12 ) q congruent 31 modulo 60: 1/72 q^2 phi1^3 q congruent 32 modulo 60: 1/72 phi2 ( q^4-3*q^3+4*q^2-8*q+8 ) q congruent 37 modulo 60: 1/72 q^2 phi1^3 q congruent 41 modulo 60: 1/72 phi2 ( q^4-4*q^3+7*q^2-12*q+12 ) q congruent 43 modulo 60: 1/72 q^2 phi1^3 q congruent 47 modulo 60: 1/72 phi2 ( q^4-4*q^3+7*q^2-12*q+12 ) q congruent 49 modulo 60: 1/72 q^2 phi1^3 q congruent 53 modulo 60: 1/72 phi2 ( q^4-4*q^3+7*q^2-12*q+12 ) q congruent 59 modulo 60: 1/72 phi2 ( q^4-4*q^3+7*q^2-12*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 88, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 8 ], [ 11, 1, 2, 6 ], [ 17, 1, 6, 36 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 6 ], [ 21, 1, 2, 12 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 12 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 33, 1, 7, 6 ], [ 34, 1, 4, 12 ], [ 36, 1, 4, 24 ], [ 38, 1, 18, 72 ], [ 39, 1, 3, 24 ], [ 40, 1, 4, 6 ], [ 42, 1, 6, 12 ], [ 47, 1, 12, 12 ], [ 49, 1, 6, 18 ], [ 50, 1, 12, 24 ], [ 52, 1, 7, 18 ], [ 57, 1, 15, 36 ], [ 59, 1, 8, 36 ], [ 60, 1, 14, 36 ] ] k = 22: F-action on Pi is (1,5,2) [62,1,22] Dynkin type is A_1(q^3) + T(phi1 phi2^2 phi3) Order of center |Z^F|: phi1 phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 2 modulo 60: 1/24 q^3 phi1 phi2 q congruent 3 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 4 modulo 60: 1/24 q^3 phi1 phi2 q congruent 5 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 7 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 8 modulo 60: 1/24 q^3 phi1 phi2 q congruent 9 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 11 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 13 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 16 modulo 60: 1/24 q^3 phi1 phi2 q congruent 17 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 19 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 21 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 23 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 25 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 27 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 29 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 31 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 32 modulo 60: 1/24 q^3 phi1 phi2 q congruent 37 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 41 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 43 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 47 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 49 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 53 modulo 60: 1/24 q^2 phi1^2 phi2 q congruent 59 modulo 60: 1/24 q^2 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 37, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 2 ], [ 19, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 33, 1, 3, 6 ], [ 34, 1, 2, 4 ], [ 39, 1, 3, 8 ], [ 40, 1, 5, 6 ], [ 42, 1, 4, 4 ], [ 47, 1, 6, 12 ], [ 49, 1, 3, 6 ], [ 50, 1, 5, 8 ], [ 52, 1, 6, 6 ], [ 57, 1, 13, 12 ], [ 59, 1, 14, 12 ], [ 60, 1, 12, 12 ] ] k = 23: F-action on Pi is (1,5,2) [62,1,23] Dynkin type is A_1(q^3) + T(phi1 phi2^2 phi6) Order of center |Z^F|: phi1 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 2 modulo 60: 1/72 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 3 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 4 modulo 60: 1/72 q^2 phi1^2 ( q-2 ) q congruent 5 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 7 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 8 modulo 60: 1/72 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 9 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 11 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 13 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 16 modulo 60: 1/72 q^2 phi1^2 ( q-2 ) q congruent 17 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 19 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 21 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 23 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 25 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 27 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 29 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 31 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 32 modulo 60: 1/72 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 37 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 41 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 43 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 47 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 49 modulo 60: 1/72 q^2 phi1^2 ( q-3 ) q congruent 53 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) q congruent 59 modulo 60: 1/72 phi2 ( q^4-6*q^3+13*q^2-16*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 19, 1, 2, 6 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 33, 1, 7, 6 ], [ 34, 1, 3, 12 ], [ 39, 1, 4, 12 ], [ 40, 1, 4, 6 ], [ 42, 1, 6, 12 ], [ 47, 1, 11, 12 ], [ 49, 1, 6, 18 ], [ 50, 1, 9, 24 ], [ 52, 1, 7, 18 ], [ 57, 1, 14, 36 ], [ 59, 1, 8, 36 ], [ 60, 1, 14, 36 ] ] k = 24: F-action on Pi is () [62,1,24] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^4) Order of center |Z^F|: phi1 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/2304 phi1 ( q^4-22*q^3+180*q^2-666*q+891 ) q congruent 2 modulo 60: 1/2304 ( q^5-22*q^4+164*q^3-488*q^2+608*q-256 ) q congruent 3 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1701*q-1323 ) q congruent 4 modulo 60: 1/2304 q ( q^4-22*q^3+164*q^2-488*q+480 ) q congruent 5 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1685*q-1275 ) q congruent 7 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1701*q-1323 ) q congruent 8 modulo 60: 1/2304 ( q^5-22*q^4+164*q^3-488*q^2+608*q-256 ) q congruent 9 modulo 60: 1/2304 phi1 ( q^4-22*q^3+180*q^2-666*q+891 ) q congruent 11 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1829*q-1707 ) q congruent 13 modulo 60: 1/2304 phi1 ( q^4-22*q^3+180*q^2-666*q+891 ) q congruent 16 modulo 60: 1/2304 q ( q^4-22*q^3+164*q^2-488*q+480 ) q congruent 17 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1685*q-1275 ) q congruent 19 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1701*q-1323 ) q congruent 21 modulo 60: 1/2304 phi1 ( q^4-22*q^3+180*q^2-666*q+891 ) q congruent 23 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1829*q-1707 ) q congruent 25 modulo 60: 1/2304 phi1 ( q^4-22*q^3+180*q^2-666*q+891 ) q congruent 27 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1701*q-1323 ) q congruent 29 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1685*q-1275 ) q congruent 31 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1701*q-1323 ) q congruent 32 modulo 60: 1/2304 ( q^5-22*q^4+164*q^3-488*q^2+608*q-256 ) q congruent 37 modulo 60: 1/2304 phi1 ( q^4-22*q^3+180*q^2-666*q+891 ) q congruent 41 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1685*q-1275 ) q congruent 43 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1701*q-1323 ) q congruent 47 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1829*q-1707 ) q congruent 49 modulo 60: 1/2304 phi1 ( q^4-22*q^3+180*q^2-666*q+891 ) q congruent 53 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1685*q-1275 ) q congruent 59 modulo 60: 1/2304 ( q^5-23*q^4+202*q^3-846*q^2+1829*q-1707 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 69, 5, 69, 5, 5, 67 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 72 ], [ 6, 1, 2, 128 ], [ 7, 1, 2, 96 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 4, 240 ], [ 16, 1, 3, 384 ], [ 19, 1, 2, 384 ], [ 20, 1, 3, 96 ], [ 20, 1, 4, 576 ], [ 22, 1, 3, 64 ], [ 23, 1, 2, 24 ], [ 24, 1, 1, 30 ], [ 24, 1, 2, 168 ], [ 25, 1, 3, 336 ], [ 26, 1, 4, 192 ], [ 27, 1, 6, 192 ], [ 28, 1, 3, 48 ], [ 28, 1, 4, 288 ], [ 31, 1, 3, 192 ], [ 33, 1, 8, 768 ], [ 34, 1, 3, 192 ], [ 35, 1, 6, 384 ], [ 35, 1, 8, 1152 ], [ 39, 1, 3, 144 ], [ 39, 1, 4, 48 ], [ 40, 1, 6, 192 ], [ 41, 1, 6, 288 ], [ 41, 1, 9, 864 ], [ 42, 1, 6, 768 ], [ 43, 1, 13, 1152 ], [ 44, 1, 10, 576 ], [ 47, 1, 7, 384 ], [ 48, 1, 5, 576 ], [ 49, 1, 5, 1152 ], [ 49, 1, 10, 2304 ], [ 50, 1, 9, 384 ], [ 52, 1, 9, 288 ], [ 52, 1, 10, 576 ], [ 53, 1, 20, 2304 ], [ 56, 1, 15, 1152 ], [ 57, 1, 6, 1152 ], [ 59, 1, 2, 1152 ], [ 60, 1, 17, 4608 ] ] k = 25: F-action on Pi is () [62,1,25] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi2 phi4^2) Order of center |Z^F|: phi2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 2 modulo 60: 1/192 q^3 ( q^2-4 ) q congruent 3 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 4 modulo 60: 1/192 q^3 ( q^2-4 ) q congruent 5 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 7 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 8 modulo 60: 1/192 q^3 ( q^2-4 ) q congruent 9 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 11 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 13 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 16 modulo 60: 1/192 q^3 ( q^2-4 ) q congruent 17 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 19 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 21 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 23 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 25 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 27 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 29 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 31 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 32 modulo 60: 1/192 q^3 ( q^2-4 ) q congruent 37 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 41 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 43 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 47 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 49 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 53 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) q congruent 59 modulo 60: 1/192 phi1^2 phi2 ( q^2-9 ) Fusion of maximal tori of C^F in those of G^F: [ 73, 18, 18, 74, 18, 74, 74, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 24, 1, 2, 6 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ], [ 41, 1, 8, 96 ], [ 49, 1, 4, 96 ], [ 52, 1, 5, 48 ], [ 59, 1, 6, 96 ], [ 60, 1, 18, 384 ] ] k = 26: F-action on Pi is () [62,1,26] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1 phi4^2) Order of center |Z^F|: phi1 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 2 modulo 60: 1/192 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 4 modulo 60: 1/192 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 7 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 8 modulo 60: 1/192 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 11 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 13 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 16 modulo 60: 1/192 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 17 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 19 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 21 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 23 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 25 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 27 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 29 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 31 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 32 modulo 60: 1/192 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 37 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 41 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 43 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 47 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 49 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 53 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 59 modulo 60: 1/192 phi1 phi2 ( q^3-3*q^2-9*q+27 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 73, 73, 18, 73, 18, 18, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 24, 1, 1, 6 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ], [ 41, 1, 8, 96 ], [ 49, 1, 7, 96 ], [ 52, 1, 8, 48 ], [ 59, 1, 6, 96 ], [ 60, 1, 18, 384 ] ] k = 27: F-action on Pi is (2,5) [62,1,27] Dynkin type is A_1(q) + A_1(q^2) + T(phi2 phi8) Order of center |Z^F|: phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 2 modulo 60: 1/16 q^5 q congruent 3 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 4 modulo 60: 1/16 q^5 q congruent 5 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 7 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 8 modulo 60: 1/16 q^5 q congruent 9 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 11 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 13 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 16 modulo 60: 1/16 q^5 q congruent 17 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 19 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 21 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 23 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 25 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 27 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 29 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 31 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 32 modulo 60: 1/16 q^5 q congruent 37 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 41 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 43 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 47 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 49 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 53 modulo 60: 1/16 phi1^2 phi2 phi4 q congruent 59 modulo 60: 1/16 phi1^2 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 43, 91, 90, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ] ] k = 28: F-action on Pi is (2,5) [62,1,28] Dynkin type is A_1(q) + A_1(q^2) + T(phi1 phi8) Order of center |Z^F|: phi1 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 2 modulo 60: 1/16 q^4 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 4 modulo 60: 1/16 q^4 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 7 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 8 modulo 60: 1/16 q^4 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 11 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 13 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 16 modulo 60: 1/16 q^4 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 19 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 21 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 23 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 25 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 27 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 29 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 31 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 32 modulo 60: 1/16 q^4 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 41 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 43 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 47 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 49 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 53 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 59 modulo 60: 1/16 phi1 phi2 phi4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 89, 44, 43, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ] ] k = 29: F-action on Pi is () [62,1,29] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi2^5) Order of center |Z^F|: phi2^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/2304 phi1 ( q^4-44*q^3+718*q^2-5292*q+15561 ) q congruent 2 modulo 60: 1/2304 ( q^5-44*q^4+700*q^3-4816*q^2+13824*q-13312 ) q congruent 3 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6010*q^2+21861*q-28665 ) q congruent 4 modulo 60: 1/2304 ( q^5-44*q^4+700*q^3-4752*q^2+11520*q-4608 ) q congruent 5 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6074*q^2+23157*q-34185 ) q congruent 7 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6010*q^2+21861*q-28665 ) q congruent 8 modulo 60: 1/2304 ( q^5-44*q^4+700*q^3-4816*q^2+13824*q-13312 ) q congruent 9 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6010*q^2+20853*q-20169 ) q congruent 11 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6074*q^2+24165*q-47289 ) q congruent 13 modulo 60: 1/2304 phi1 ( q^4-44*q^3+718*q^2-5292*q+15561 ) q congruent 16 modulo 60: 1/2304 q ( q^4-44*q^3+700*q^2-4752*q+11520 ) q congruent 17 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6074*q^2+23157*q-34185 ) q congruent 19 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6010*q^2+21861*q-33273 ) q congruent 21 modulo 60: 1/2304 phi1 ( q^4-44*q^3+718*q^2-5292*q+15561 ) q congruent 23 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6074*q^2+24165*q-47289 ) q congruent 25 modulo 60: 1/2304 phi1 ( q^4-44*q^3+718*q^2-5292*q+15561 ) q congruent 27 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6010*q^2+21861*q-28665 ) q congruent 29 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6074*q^2+23157*q-38793 ) q congruent 31 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6010*q^2+21861*q-28665 ) q congruent 32 modulo 60: 1/2304 ( q^5-44*q^4+700*q^3-4816*q^2+13824*q-13312 ) q congruent 37 modulo 60: 1/2304 phi1 ( q^4-44*q^3+718*q^2-5292*q+15561 ) q congruent 41 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6074*q^2+23157*q-34185 ) q congruent 43 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6010*q^2+21861*q-28665 ) q congruent 47 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6074*q^2+24165*q-47289 ) q congruent 49 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6010*q^2+20853*q-20169 ) q congruent 53 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6074*q^2+23157*q-34185 ) q congruent 59 modulo 60: 1/2304 ( q^5-45*q^4+762*q^3-6074*q^2+24165*q-51897 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 5, 67, 5, 67, 67, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 80 ], [ 4, 1, 2, 216 ], [ 5, 1, 2, 384 ], [ 6, 1, 2, 512 ], [ 7, 1, 2, 144 ], [ 8, 1, 2, 64 ], [ 9, 1, 1, 15 ], [ 10, 1, 2, 26 ], [ 11, 1, 2, 144 ], [ 12, 1, 2, 432 ], [ 13, 1, 4, 528 ], [ 14, 1, 2, 768 ], [ 15, 1, 2, 1152 ], [ 16, 1, 3, 1920 ], [ 17, 1, 4, 2304 ], [ 18, 1, 2, 384 ], [ 19, 1, 2, 768 ], [ 20, 1, 4, 1248 ], [ 21, 1, 2, 192 ], [ 22, 1, 4, 640 ], [ 23, 1, 2, 72 ], [ 24, 1, 2, 198 ], [ 25, 1, 3, 624 ], [ 26, 1, 4, 192 ], [ 27, 1, 6, 192 ], [ 28, 1, 4, 624 ], [ 29, 1, 4, 1152 ], [ 30, 1, 3, 1536 ], [ 31, 1, 4, 1920 ], [ 32, 1, 3, 3072 ], [ 33, 1, 8, 4224 ], [ 34, 1, 4, 768 ], [ 35, 1, 8, 2688 ], [ 36, 1, 4, 384 ], [ 37, 1, 3, 1152 ], [ 38, 1, 12, 2304 ], [ 39, 1, 3, 240 ], [ 40, 1, 6, 1056 ], [ 41, 1, 9, 1440 ], [ 42, 1, 6, 768 ], [ 43, 1, 13, 1152 ], [ 44, 1, 10, 576 ], [ 45, 1, 6, 1152 ], [ 46, 1, 6, 2304 ], [ 47, 1, 8, 3840 ], [ 48, 1, 6, 2304 ], [ 49, 1, 10, 5760 ], [ 50, 1, 12, 384 ], [ 51, 1, 9, 1152 ], [ 52, 1, 10, 1440 ], [ 53, 1, 20, 2304 ], [ 55, 1, 15, 2304 ], [ 56, 1, 20, 1152 ], [ 57, 1, 10, 4608 ], [ 59, 1, 2, 1152 ], [ 60, 1, 17, 4608 ] ] k = 30: F-action on Pi is () [62,1,30] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^4 phi2) Order of center |Z^F|: phi1^4 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 2 modulo 60: 1/2304 q ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 3 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 4 modulo 60: 1/2304 q ( q^4-28*q^3+268*q^2-1008*q+1280 ) q congruent 5 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 7 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 8 modulo 60: 1/2304 q ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 9 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 11 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 13 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 16 modulo 60: 1/2304 q ( q^4-28*q^3+268*q^2-1008*q+1280 ) q congruent 17 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 19 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 21 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 23 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 25 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 27 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 29 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 31 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 32 modulo 60: 1/2304 q ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 37 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 41 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 43 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 47 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 49 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 53 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 59 modulo 60: 1/2304 phi1 ( q^4-28*q^3+286*q^2-1260*q+1881 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 72 ], [ 6, 1, 1, 128 ], [ 7, 1, 1, 96 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 24 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 240 ], [ 16, 1, 1, 384 ], [ 19, 1, 1, 384 ], [ 20, 1, 1, 576 ], [ 20, 1, 2, 96 ], [ 22, 1, 2, 64 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 168 ], [ 24, 1, 2, 30 ], [ 25, 1, 1, 336 ], [ 26, 1, 1, 192 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 28, 1, 2, 48 ], [ 31, 1, 2, 192 ], [ 33, 1, 1, 768 ], [ 34, 1, 2, 192 ], [ 35, 1, 1, 1152 ], [ 35, 1, 3, 384 ], [ 39, 1, 1, 144 ], [ 39, 1, 4, 48 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 864 ], [ 41, 1, 6, 288 ], [ 42, 1, 1, 768 ], [ 43, 1, 1, 1152 ], [ 44, 1, 1, 576 ], [ 47, 1, 2, 384 ], [ 48, 1, 2, 576 ], [ 49, 1, 1, 2304 ], [ 49, 1, 9, 1152 ], [ 50, 1, 4, 384 ], [ 52, 1, 1, 576 ], [ 52, 1, 2, 288 ], [ 53, 1, 1, 2304 ], [ 56, 1, 6, 1152 ], [ 57, 1, 2, 1152 ], [ 59, 1, 1, 1152 ], [ 60, 1, 1, 4608 ] ] k = 31: F-action on Pi is () [62,1,31] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^3) Order of center |Z^F|: phi1^2 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 2 modulo 60: 1/128 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 3 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) q congruent 4 modulo 60: 1/128 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 5 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 7 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) q congruent 8 modulo 60: 1/128 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 9 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 11 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) q congruent 13 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 16 modulo 60: 1/128 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 17 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 19 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) q congruent 21 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 23 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) q congruent 25 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 27 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) q congruent 29 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 31 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) q congruent 32 modulo 60: 1/128 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 37 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 41 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 43 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) q congruent 47 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) q congruent 49 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 53 modulo 60: 1/128 phi1 ( q^4-12*q^3+54*q^2-116*q+105 ) q congruent 59 modulo 60: 1/128 ( q^5-13*q^4+66*q^3-170*q^2+237*q-153 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 7, 69, 3, 69, 69, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 36 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 72 ], [ 16, 1, 3, 96 ], [ 16, 1, 4, 32 ], [ 19, 1, 2, 32 ], [ 20, 1, 2, 48 ], [ 20, 1, 3, 96 ], [ 20, 1, 4, 48 ], [ 22, 1, 3, 32 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 42 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 72 ], [ 25, 1, 4, 32 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 48 ], [ 28, 1, 4, 24 ], [ 31, 1, 3, 96 ], [ 33, 1, 6, 64 ], [ 33, 1, 8, 192 ], [ 34, 1, 3, 32 ], [ 35, 1, 3, 96 ], [ 35, 1, 4, 32 ], [ 35, 1, 6, 192 ], [ 35, 1, 7, 32 ], [ 35, 1, 8, 96 ], [ 37, 1, 2, 32 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 24 ], [ 40, 1, 2, 32 ], [ 40, 1, 6, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 32 ], [ 41, 1, 4, 64 ], [ 41, 1, 6, 144 ], [ 41, 1, 9, 144 ], [ 43, 1, 3, 64 ], [ 43, 1, 8, 64 ], [ 43, 1, 12, 64 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 47, 1, 7, 192 ], [ 48, 1, 3, 64 ], [ 48, 1, 4, 64 ], [ 48, 1, 5, 96 ], [ 49, 1, 5, 384 ], [ 49, 1, 8, 64 ], [ 49, 1, 9, 192 ], [ 49, 1, 10, 192 ], [ 51, 1, 3, 64 ], [ 51, 1, 10, 64 ], [ 52, 1, 2, 48 ], [ 52, 1, 4, 32 ], [ 52, 1, 9, 96 ], [ 52, 1, 10, 48 ], [ 53, 1, 6, 128 ], [ 53, 1, 9, 128 ], [ 55, 1, 14, 128 ], [ 56, 1, 10, 64 ], [ 56, 1, 19, 64 ], [ 57, 1, 5, 128 ], [ 57, 1, 6, 192 ], [ 59, 1, 3, 64 ], [ 60, 1, 27, 256 ] ] k = 32: F-action on Pi is () [62,1,32] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^3 phi2^2) Order of center |Z^F|: phi1^3 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 2 modulo 60: 1/128 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 3 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) q congruent 4 modulo 60: 1/128 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 5 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 7 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) q congruent 8 modulo 60: 1/128 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 9 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 11 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) q congruent 13 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 16 modulo 60: 1/128 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 17 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 19 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) q congruent 21 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 23 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) q congruent 25 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 27 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) q congruent 29 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 31 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) q congruent 32 modulo 60: 1/128 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 37 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 41 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 43 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) q congruent 47 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) q congruent 49 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 53 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+115 ) q congruent 59 modulo 60: 1/128 phi1 ( q^4-14*q^3+68*q^2-138*q+99 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 3, 68, 7, 7, 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], [ 4, 1, 2, 12 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 24 ], [ 16, 1, 1, 96 ], [ 16, 1, 2, 32 ], [ 19, 1, 1, 32 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 96 ], [ 20, 1, 3, 48 ], [ 22, 1, 2, 32 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 42 ], [ 24, 1, 2, 28 ], [ 25, 1, 1, 72 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 32 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 48 ], [ 28, 1, 3, 24 ], [ 31, 1, 2, 96 ], [ 33, 1, 1, 192 ], [ 33, 1, 2, 64 ], [ 34, 1, 2, 32 ], [ 35, 1, 1, 96 ], [ 35, 1, 2, 32 ], [ 35, 1, 3, 192 ], [ 35, 1, 5, 32 ], [ 35, 1, 6, 96 ], [ 37, 1, 2, 32 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 24 ], [ 40, 1, 1, 48 ], [ 40, 1, 3, 32 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 32 ], [ 41, 1, 4, 64 ], [ 41, 1, 6, 144 ], [ 41, 1, 9, 48 ], [ 43, 1, 3, 64 ], [ 43, 1, 8, 64 ], [ 43, 1, 12, 64 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 47, 1, 2, 192 ], [ 48, 1, 2, 96 ], [ 48, 1, 3, 64 ], [ 48, 1, 4, 64 ], [ 49, 1, 1, 192 ], [ 49, 1, 2, 64 ], [ 49, 1, 5, 192 ], [ 49, 1, 9, 384 ], [ 51, 1, 5, 64 ], [ 51, 1, 6, 64 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 96 ], [ 52, 1, 3, 32 ], [ 52, 1, 9, 48 ], [ 53, 1, 6, 128 ], [ 53, 1, 9, 128 ], [ 55, 1, 5, 128 ], [ 56, 1, 5, 64 ], [ 56, 1, 14, 64 ], [ 57, 1, 2, 192 ], [ 57, 1, 5, 128 ], [ 59, 1, 3, 64 ], [ 60, 1, 27, 256 ] ] k = 33: F-action on Pi is (2,5) [62,1,33] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^3 phi4) Order of center |Z^F|: phi1^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 2 modulo 60: 1/64 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 4 modulo 60: 1/64 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 7 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 8 modulo 60: 1/64 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 11 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 13 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 16 modulo 60: 1/64 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 19 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 21 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 23 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 25 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 27 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 29 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 31 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 32 modulo 60: 1/64 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 41 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 43 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 47 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 49 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 53 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) q congruent 59 modulo 60: 1/64 phi1 phi2 ( q^3-13*q^2+55*q-75 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 16, 19, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 16 ], [ 16, 1, 2, 32 ], [ 20, 1, 3, 16 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 33, 1, 4, 64 ], [ 35, 1, 5, 32 ], [ 39, 1, 1, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 3, 32 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 6, 16 ], [ 48, 1, 8, 32 ], [ 49, 1, 7, 48 ], [ 49, 1, 11, 64 ], [ 51, 1, 7, 32 ], [ 52, 1, 1, 48 ], [ 52, 1, 8, 24 ], [ 53, 1, 10, 32 ], [ 53, 1, 13, 32 ], [ 55, 1, 6, 64 ], [ 56, 1, 11, 32 ], [ 57, 1, 11, 64 ], [ 59, 1, 23, 32 ], [ 60, 1, 31, 64 ] ] k = 34: F-action on Pi is (2,5) [62,1,34] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^2 phi2 phi4) Order of center |Z^F|: phi1^2 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 73, 72, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 16 ], [ 20, 1, 4, 16 ], [ 20, 1, 8, 32 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 28, 1, 2, 8 ], [ 35, 1, 7, 32 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 1, 16 ], [ 41, 1, 3, 32 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 6, 16 ], [ 49, 1, 4, 16 ], [ 49, 1, 7, 32 ], [ 49, 1, 20, 64 ], [ 52, 1, 2, 16 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 16 ], [ 53, 1, 10, 32 ], [ 53, 1, 13, 32 ], [ 56, 1, 16, 32 ], [ 57, 1, 7, 32 ], [ 59, 1, 23, 32 ], [ 60, 1, 31, 64 ] ] k = 35: F-action on Pi is (2,5) [62,1,35] Dynkin type is A_1(q) + A_1(q^2) + T(phi2^3 phi4) Order of center |Z^F|: phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 74, 71, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 24 ], [ 16, 1, 4, 32 ], [ 20, 1, 2, 16 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 28, 1, 4, 24 ], [ 33, 1, 10, 64 ], [ 35, 1, 4, 32 ], [ 39, 1, 3, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 6, 48 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 32 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 16 ], [ 48, 1, 9, 32 ], [ 49, 1, 4, 48 ], [ 49, 1, 19, 64 ], [ 51, 1, 4, 32 ], [ 52, 1, 5, 24 ], [ 52, 1, 10, 48 ], [ 53, 1, 11, 32 ], [ 53, 1, 14, 32 ], [ 55, 1, 19, 64 ], [ 56, 1, 9, 32 ], [ 57, 1, 8, 64 ], [ 59, 1, 24, 32 ], [ 60, 1, 30, 64 ] ] k = 36: F-action on Pi is (2,5) [62,1,36] Dynkin type is A_1(q) + A_1(q^2) + T(phi1 phi2^2 phi4) Order of center |Z^F|: phi1 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 2 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 4 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 7 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 8 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 11 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 13 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 16 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 19 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 21 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 23 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 25 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 27 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 29 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 31 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 32 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 41 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 43 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 47 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 49 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 53 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) q congruent 59 modulo 60: 1/64 phi1^3 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 18, 20, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 8 ], [ 20, 1, 1, 16 ], [ 20, 1, 5, 32 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 28, 1, 3, 8 ], [ 35, 1, 2, 32 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 16 ], [ 49, 1, 4, 32 ], [ 49, 1, 7, 16 ], [ 49, 1, 14, 64 ], [ 52, 1, 5, 16 ], [ 52, 1, 8, 8 ], [ 52, 1, 9, 16 ], [ 53, 1, 11, 32 ], [ 53, 1, 14, 32 ], [ 56, 1, 4, 32 ], [ 57, 1, 7, 32 ], [ 59, 1, 24, 32 ], [ 60, 1, 30, 64 ] ] k = 37: F-action on Pi is () [62,1,37] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2 phi4) Order of center |Z^F|: phi1^2 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 2 modulo 60: 1/32 q^3 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 4 modulo 60: 1/32 q^3 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 7 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 8 modulo 60: 1/32 q^3 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 11 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 13 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 16 modulo 60: 1/32 q^3 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 19 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 21 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 23 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 25 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 27 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 29 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 31 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 32 modulo 60: 1/32 q^3 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 41 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 43 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 47 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 49 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 53 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 59 modulo 60: 1/32 phi1 phi2 ( q^3-7*q^2+11*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 19, 72, 19, 76, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 3, 4 ], [ 33, 1, 2, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 49, 1, 2, 16 ], [ 49, 1, 7, 16 ], [ 51, 1, 7, 16 ], [ 52, 1, 3, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 55, 1, 4, 32 ], [ 56, 1, 4, 16 ], [ 56, 1, 11, 16 ], [ 59, 1, 16, 16 ], [ 60, 1, 28, 64 ] ] k = 38: F-action on Pi is (2,5) [62,1,38] Dynkin type is A_1(q) + A_1(q^2) + T(phi1 phi2^2 phi4) Order of center |Z^F|: phi1 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^4 phi2 q congruent 2 modulo 60: 1/32 q^4 ( q-2 ) q congruent 3 modulo 60: 1/32 phi1^4 phi2 q congruent 4 modulo 60: 1/32 q^4 ( q-2 ) q congruent 5 modulo 60: 1/32 phi1^4 phi2 q congruent 7 modulo 60: 1/32 phi1^4 phi2 q congruent 8 modulo 60: 1/32 q^4 ( q-2 ) q congruent 9 modulo 60: 1/32 phi1^4 phi2 q congruent 11 modulo 60: 1/32 phi1^4 phi2 q congruent 13 modulo 60: 1/32 phi1^4 phi2 q congruent 16 modulo 60: 1/32 q^4 ( q-2 ) q congruent 17 modulo 60: 1/32 phi1^4 phi2 q congruent 19 modulo 60: 1/32 phi1^4 phi2 q congruent 21 modulo 60: 1/32 phi1^4 phi2 q congruent 23 modulo 60: 1/32 phi1^4 phi2 q congruent 25 modulo 60: 1/32 phi1^4 phi2 q congruent 27 modulo 60: 1/32 phi1^4 phi2 q congruent 29 modulo 60: 1/32 phi1^4 phi2 q congruent 31 modulo 60: 1/32 phi1^4 phi2 q congruent 32 modulo 60: 1/32 q^4 ( q-2 ) q congruent 37 modulo 60: 1/32 phi1^4 phi2 q congruent 41 modulo 60: 1/32 phi1^4 phi2 q congruent 43 modulo 60: 1/32 phi1^4 phi2 q congruent 47 modulo 60: 1/32 phi1^4 phi2 q congruent 49 modulo 60: 1/32 phi1^4 phi2 q congruent 53 modulo 60: 1/32 phi1^4 phi2 q congruent 59 modulo 60: 1/32 phi1^4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 76, 18, 20, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 20, 1, 7, 16 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 28, 1, 3, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 16 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 48, 1, 9, 16 ], [ 49, 1, 4, 32 ], [ 49, 1, 7, 16 ], [ 49, 1, 15, 32 ], [ 52, 1, 5, 16 ], [ 52, 1, 8, 8 ], [ 52, 1, 9, 16 ], [ 57, 1, 7, 16 ], [ 57, 1, 8, 32 ], [ 59, 1, 21, 16 ], [ 60, 1, 33, 32 ] ] k = 39: F-action on Pi is () [62,1,39] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2 phi4) Order of center |Z^F|: phi1 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 2 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 4 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 7 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 8 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 11 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 16 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 19 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 23 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 27 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 31 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 32 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 41 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 43 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 53 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 59 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 76, 76, 20, 72, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], [ 16, 1, 4, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 8 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 2, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 6, 16 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 49, 1, 4, 16 ], [ 49, 1, 8, 16 ], [ 51, 1, 4, 16 ], [ 52, 1, 4, 8 ], [ 52, 1, 5, 8 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 55, 1, 11, 32 ], [ 56, 1, 9, 16 ], [ 56, 1, 16, 16 ], [ 59, 1, 16, 16 ], [ 60, 1, 28, 64 ] ] k = 40: F-action on Pi is (2,5) [62,1,40] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^2 phi2 phi4) Order of center |Z^F|: phi1^2 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 2 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 4 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 7 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 8 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 11 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 16 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 19 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 23 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 27 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 31 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 32 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 41 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 43 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 53 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) q congruent 59 modulo 60: 1/32 phi1^3 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 73, 76, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 20, 1, 6, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 28, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 1, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 16 ], [ 41, 1, 8, 16 ], [ 48, 1, 8, 16 ], [ 49, 1, 4, 16 ], [ 49, 1, 7, 32 ], [ 49, 1, 18, 32 ], [ 52, 1, 2, 16 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 16 ], [ 57, 1, 7, 16 ], [ 57, 1, 11, 32 ], [ 59, 1, 21, 16 ], [ 60, 1, 33, 32 ] ] k = 41: F-action on Pi is () [62,1,41] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^4 phi2) Order of center |Z^F|: phi1^4 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-934*q+1359 ) q congruent 2 modulo 60: 1/192 q ( q^4-26*q^3+236*q^2-856*q+960 ) q congruent 3 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1158*q^2+2037*q-927 ) q congruent 4 modulo 60: 1/192 q ( q^4-26*q^3+236*q^2-872*q+1120 ) q congruent 5 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-918*q+1215 ) q congruent 7 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1174*q^2+2197*q-1071 ) q congruent 8 modulo 60: 1/192 q ( q^4-26*q^3+236*q^2-856*q+960 ) q congruent 9 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-918*q+1215 ) q congruent 11 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1158*q^2+2037*q-927 ) q congruent 13 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-934*q+1359 ) q congruent 16 modulo 60: 1/192 q ( q^4-26*q^3+236*q^2-872*q+1120 ) q congruent 17 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-918*q+1215 ) q congruent 19 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1174*q^2+2197*q-1071 ) q congruent 21 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-918*q+1215 ) q congruent 23 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1158*q^2+2037*q-927 ) q congruent 25 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-934*q+1359 ) q congruent 27 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1158*q^2+2037*q-927 ) q congruent 29 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-918*q+1215 ) q congruent 31 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1174*q^2+2197*q-1071 ) q congruent 32 modulo 60: 1/192 q ( q^4-26*q^3+236*q^2-856*q+960 ) q congruent 37 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-934*q+1359 ) q congruent 41 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-918*q+1215 ) q congruent 43 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1174*q^2+2197*q-1071 ) q congruent 47 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1158*q^2+2037*q-927 ) q congruent 49 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-934*q+1359 ) q congruent 53 modulo 60: 1/192 phi1 ( q^4-26*q^3+240*q^2-918*q+1215 ) q congruent 59 modulo 60: 1/192 ( q^5-27*q^4+266*q^3-1158*q^2+2037*q-927 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68, 4, 68, 68, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 72 ], [ 5, 1, 1, 96 ], [ 6, 1, 1, 128 ], [ 7, 1, 1, 32 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 8 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 144 ], [ 14, 1, 1, 96 ], [ 15, 1, 1, 192 ], [ 16, 1, 1, 384 ], [ 17, 1, 1, 384 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 128 ], [ 20, 1, 1, 192 ], [ 20, 1, 2, 96 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 64 ], [ 22, 1, 2, 48 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 56 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 144 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 96 ], [ 28, 1, 2, 48 ], [ 29, 1, 2, 96 ], [ 30, 1, 1, 192 ], [ 31, 1, 1, 192 ], [ 31, 1, 2, 144 ], [ 32, 1, 1, 384 ], [ 33, 1, 1, 768 ], [ 34, 1, 1, 64 ], [ 34, 1, 2, 48 ], [ 35, 1, 1, 384 ], [ 35, 1, 3, 192 ], [ 36, 1, 2, 32 ], [ 37, 1, 1, 96 ], [ 38, 1, 5, 192 ], [ 39, 1, 1, 48 ], [ 39, 1, 4, 16 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 288 ], [ 41, 1, 6, 96 ], [ 42, 1, 4, 64 ], [ 43, 1, 2, 96 ], [ 44, 1, 2, 48 ], [ 45, 1, 2, 96 ], [ 46, 1, 2, 192 ], [ 47, 1, 1, 384 ], [ 47, 1, 2, 288 ], [ 48, 1, 1, 192 ], [ 48, 1, 2, 144 ], [ 49, 1, 1, 768 ], [ 49, 1, 9, 384 ], [ 50, 1, 2, 32 ], [ 51, 1, 2, 96 ], [ 52, 1, 1, 192 ], [ 52, 1, 2, 96 ], [ 53, 1, 3, 192 ], [ 55, 1, 2, 192 ], [ 56, 1, 2, 96 ], [ 57, 1, 1, 384 ], [ 57, 1, 2, 288 ], [ 59, 1, 12, 96 ], [ 60, 1, 40, 384 ] ] k = 42: F-action on Pi is () [62,1,42] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^3) Order of center |Z^F|: phi1^2 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 2 modulo 60: 1/192 q ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 3 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 4 modulo 60: 1/192 q ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 5 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 7 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 8 modulo 60: 1/192 q ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 9 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 11 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 13 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 16 modulo 60: 1/192 q ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 17 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 19 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 21 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 23 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 25 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 27 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 29 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 31 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 32 modulo 60: 1/192 q ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 37 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 41 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 43 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 47 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 49 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 53 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) q congruent 59 modulo 60: 1/192 phi1 ( q^4-10*q^3+40*q^2-78*q+63 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 7, 69, 7, 69, 69, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 36 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 4, 72 ], [ 16, 1, 3, 96 ], [ 19, 1, 2, 32 ], [ 20, 1, 2, 48 ], [ 20, 1, 3, 96 ], [ 20, 1, 4, 48 ], [ 22, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 42 ], [ 25, 1, 1, 24 ], [ 25, 1, 3, 72 ], [ 26, 1, 2, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 48 ], [ 28, 1, 4, 24 ], [ 31, 1, 3, 48 ], [ 33, 1, 8, 192 ], [ 34, 1, 3, 16 ], [ 35, 1, 3, 96 ], [ 35, 1, 6, 192 ], [ 35, 1, 8, 96 ], [ 37, 1, 2, 48 ], [ 39, 1, 1, 8 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 6, 144 ], [ 41, 1, 9, 144 ], [ 42, 1, 2, 64 ], [ 43, 1, 4, 96 ], [ 44, 1, 8, 48 ], [ 47, 1, 7, 96 ], [ 48, 1, 3, 96 ], [ 48, 1, 4, 96 ], [ 48, 1, 5, 48 ], [ 49, 1, 5, 384 ], [ 49, 1, 9, 192 ], [ 49, 1, 10, 192 ], [ 50, 1, 8, 32 ], [ 52, 1, 2, 48 ], [ 52, 1, 9, 96 ], [ 52, 1, 10, 48 ], [ 53, 1, 8, 192 ], [ 56, 1, 13, 96 ], [ 57, 1, 5, 192 ], [ 57, 1, 6, 96 ], [ 59, 1, 13, 96 ], [ 60, 1, 41, 384 ] ] k = 43: F-action on Pi is () [62,1,43] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^4) Order of center |Z^F|: phi1 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^4-20*q^3+146*q^2-484*q+645 ) q congruent 2 modulo 60: 1/192 ( q^5-20*q^4+140*q^3-416*q^2+544*q-256 ) q congruent 3 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-630*q^2+1225*q-1029 ) q congruent 4 modulo 60: 1/192 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 5 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-646*q^2+1289*q-1045 ) q congruent 7 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-630*q^2+1225*q-1029 ) q congruent 8 modulo 60: 1/192 ( q^5-20*q^4+140*q^3-416*q^2+544*q-256 ) q congruent 9 modulo 60: 1/192 phi1 ( q^4-20*q^3+146*q^2-484*q+645 ) q congruent 11 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-646*q^2+1385*q-1429 ) q congruent 13 modulo 60: 1/192 phi1 ( q^4-20*q^3+146*q^2-484*q+645 ) q congruent 16 modulo 60: 1/192 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 17 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-646*q^2+1289*q-1045 ) q congruent 19 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-630*q^2+1225*q-1029 ) q congruent 21 modulo 60: 1/192 phi1 ( q^4-20*q^3+146*q^2-484*q+645 ) q congruent 23 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-646*q^2+1385*q-1429 ) q congruent 25 modulo 60: 1/192 phi1 ( q^4-20*q^3+146*q^2-484*q+645 ) q congruent 27 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-630*q^2+1225*q-1029 ) q congruent 29 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-646*q^2+1289*q-1045 ) q congruent 31 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-630*q^2+1225*q-1029 ) q congruent 32 modulo 60: 1/192 ( q^5-20*q^4+140*q^3-416*q^2+544*q-256 ) q congruent 37 modulo 60: 1/192 phi1 ( q^4-20*q^3+146*q^2-484*q+645 ) q congruent 41 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-646*q^2+1289*q-1045 ) q congruent 43 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-630*q^2+1225*q-1029 ) q congruent 47 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-646*q^2+1385*q-1429 ) q congruent 49 modulo 60: 1/192 phi1 ( q^4-20*q^3+146*q^2-484*q+645 ) q congruent 53 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-646*q^2+1289*q-1045 ) q congruent 59 modulo 60: 1/192 ( q^5-21*q^4+166*q^3-646*q^2+1385*q-1429 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 69, 69, 5, 69, 5, 5, 67 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 72 ], [ 5, 1, 2, 96 ], [ 6, 1, 2, 128 ], [ 7, 1, 2, 32 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 8 ], [ 11, 1, 2, 32 ], [ 12, 1, 2, 96 ], [ 13, 1, 4, 144 ], [ 14, 1, 2, 96 ], [ 15, 1, 2, 192 ], [ 16, 1, 3, 384 ], [ 17, 1, 4, 384 ], [ 18, 1, 2, 64 ], [ 19, 1, 2, 128 ], [ 20, 1, 3, 96 ], [ 20, 1, 4, 192 ], [ 21, 1, 2, 16 ], [ 22, 1, 3, 48 ], [ 22, 1, 4, 64 ], [ 23, 1, 2, 24 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 56 ], [ 25, 1, 3, 144 ], [ 26, 1, 2, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 3, 48 ], [ 28, 1, 4, 96 ], [ 29, 1, 3, 96 ], [ 30, 1, 3, 192 ], [ 31, 1, 3, 144 ], [ 31, 1, 4, 192 ], [ 32, 1, 3, 384 ], [ 33, 1, 8, 768 ], [ 34, 1, 3, 48 ], [ 34, 1, 4, 64 ], [ 35, 1, 6, 192 ], [ 35, 1, 8, 384 ], [ 36, 1, 3, 32 ], [ 37, 1, 3, 96 ], [ 38, 1, 8, 192 ], [ 39, 1, 3, 48 ], [ 39, 1, 4, 16 ], [ 40, 1, 6, 192 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 288 ], [ 42, 1, 2, 64 ], [ 43, 1, 4, 96 ], [ 44, 1, 8, 48 ], [ 45, 1, 5, 96 ], [ 46, 1, 5, 192 ], [ 47, 1, 7, 288 ], [ 47, 1, 8, 384 ], [ 48, 1, 5, 144 ], [ 48, 1, 6, 192 ], [ 49, 1, 5, 384 ], [ 49, 1, 10, 768 ], [ 50, 1, 11, 32 ], [ 51, 1, 8, 96 ], [ 52, 1, 9, 96 ], [ 52, 1, 10, 192 ], [ 53, 1, 8, 192 ], [ 55, 1, 13, 192 ], [ 56, 1, 18, 96 ], [ 57, 1, 6, 288 ], [ 57, 1, 10, 384 ], [ 59, 1, 13, 96 ], [ 60, 1, 41, 384 ] ] k = 44: F-action on Pi is (2,5) [62,1,44] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^2 phi2^3) Order of center |Z^F|: phi1^2 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^4-12*q^3+42*q^2-32*q+33 ) q congruent 2 modulo 60: 1/192 ( q^5-12*q^4+44*q^3-48*q^2-32*q+64 ) q congruent 3 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+81*q-81 ) q congruent 4 modulo 60: 1/192 q ( q^4-12*q^3+44*q^2-32*q-64 ) q congruent 5 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+97*q+15 ) q congruent 7 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-74*q^2+17*q-33 ) q congruent 8 modulo 60: 1/192 ( q^5-12*q^4+44*q^3-48*q^2-32*q+64 ) q congruent 9 modulo 60: 1/192 phi1 ( q^4-12*q^3+42*q^2-48*q+81 ) q congruent 11 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+49*q+15 ) q congruent 13 modulo 60: 1/192 phi1 ( q^4-12*q^3+42*q^2-32*q+33 ) q congruent 16 modulo 60: 1/192 q ( q^4-12*q^3+44*q^2-32*q-64 ) q congruent 17 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+97*q+15 ) q congruent 19 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-74*q^2+17*q-33 ) q congruent 21 modulo 60: 1/192 phi1 ( q^4-12*q^3+42*q^2-48*q+81 ) q congruent 23 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+49*q+15 ) q congruent 25 modulo 60: 1/192 phi1 ( q^4-12*q^3+42*q^2-32*q+33 ) q congruent 27 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+81*q-81 ) q congruent 29 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+97*q+15 ) q congruent 31 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-74*q^2+17*q-33 ) q congruent 32 modulo 60: 1/192 ( q^5-12*q^4+44*q^3-48*q^2-32*q+64 ) q congruent 37 modulo 60: 1/192 phi1 ( q^4-12*q^3+42*q^2-32*q+33 ) q congruent 41 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+97*q+15 ) q congruent 43 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-74*q^2+17*q-33 ) q congruent 47 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+49*q+15 ) q congruent 49 modulo 60: 1/192 phi1 ( q^4-12*q^3+42*q^2-32*q+33 ) q congruent 53 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+97*q+15 ) q congruent 59 modulo 60: 1/192 ( q^5-13*q^4+54*q^3-90*q^2+49*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72, 69, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 14 ], [ 4, 1, 2, 10 ], [ 6, 1, 1, 24 ], [ 6, 1, 2, 16 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 12 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 24 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 36 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 24 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 96 ], [ 17, 1, 3, 32 ], [ 19, 1, 1, 24 ], [ 19, 1, 2, 48 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 48 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 48 ], [ 20, 1, 5, 96 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 36 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 36 ], [ 25, 1, 4, 48 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 48 ], [ 31, 1, 3, 16 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 96 ], [ 33, 1, 2, 48 ], [ 33, 1, 6, 32 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 1, 24 ], [ 35, 1, 2, 72 ], [ 35, 1, 3, 48 ], [ 35, 1, 4, 48 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 48 ], [ 35, 1, 8, 48 ], [ 38, 1, 6, 192 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 24 ], [ 40, 1, 2, 16 ], [ 40, 1, 3, 24 ], [ 41, 1, 2, 24 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 48 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 96 ], [ 42, 1, 6, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 5, 48 ], [ 44, 1, 10, 48 ], [ 46, 1, 12, 192 ], [ 47, 1, 4, 96 ], [ 47, 1, 9, 32 ], [ 48, 1, 2, 48 ], [ 48, 1, 5, 48 ], [ 49, 1, 2, 48 ], [ 49, 1, 8, 96 ], [ 49, 1, 14, 192 ], [ 50, 1, 9, 96 ], [ 51, 1, 5, 96 ], [ 52, 1, 3, 24 ], [ 52, 1, 4, 48 ], [ 52, 1, 9, 48 ], [ 53, 1, 9, 96 ], [ 53, 1, 12, 96 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 96 ], [ 55, 1, 10, 192 ], [ 56, 1, 5, 96 ], [ 56, 1, 15, 96 ], [ 57, 1, 4, 96 ], [ 59, 1, 18, 96 ], [ 60, 1, 43, 192 ] ] k = 45: F-action on Pi is (2,5) [62,1,45] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^3 phi2^2) Order of center |Z^F|: phi1^3 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^4-14*q^3+60*q^2-78*q-17 ) q congruent 2 modulo 60: 1/192 ( q^5-14*q^4+60*q^3-56*q^2-128*q+192 ) q congruent 3 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-138*q^2+141*q-207 ) q congruent 4 modulo 60: 1/192 q ( q^4-14*q^3+60*q^2-72*q-32 ) q congruent 5 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-122*q^2-35*q+225 ) q congruent 7 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-138*q^2+109*q-175 ) q congruent 8 modulo 60: 1/192 ( q^5-14*q^4+60*q^3-56*q^2-128*q+192 ) q congruent 9 modulo 60: 1/192 phi1 ( q^4-14*q^3+60*q^2-78*q+15 ) q congruent 11 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-122*q^2+13*q+33 ) q congruent 13 modulo 60: 1/192 phi1 ( q^4-14*q^3+60*q^2-78*q-17 ) q congruent 16 modulo 60: 1/192 q ( q^4-14*q^3+60*q^2-72*q-32 ) q congruent 17 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-122*q^2-35*q+225 ) q congruent 19 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-138*q^2+109*q-175 ) q congruent 21 modulo 60: 1/192 phi1 ( q^4-14*q^3+60*q^2-78*q+15 ) q congruent 23 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-122*q^2+13*q+33 ) q congruent 25 modulo 60: 1/192 phi1 ( q^4-14*q^3+60*q^2-78*q-17 ) q congruent 27 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-138*q^2+141*q-207 ) q congruent 29 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-122*q^2-35*q+225 ) q congruent 31 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-138*q^2+109*q-175 ) q congruent 32 modulo 60: 1/192 ( q^5-14*q^4+60*q^3-56*q^2-128*q+192 ) q congruent 37 modulo 60: 1/192 phi1 ( q^4-14*q^3+60*q^2-78*q-17 ) q congruent 41 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-122*q^2-35*q+225 ) q congruent 43 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-138*q^2+109*q-175 ) q congruent 47 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-122*q^2+13*q+33 ) q congruent 49 modulo 60: 1/192 phi1 ( q^4-14*q^3+60*q^2-78*q-17 ) q congruent 53 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-122*q^2-35*q+225 ) q congruent 59 modulo 60: 1/192 ( q^5-15*q^4+74*q^3-122*q^2+13*q+33 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 3, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 14 ], [ 6, 1, 1, 16 ], [ 6, 1, 2, 24 ], [ 7, 1, 1, 24 ], [ 7, 1, 2, 12 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 24 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 36 ], [ 13, 1, 4, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 24 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 32 ], [ 17, 1, 3, 96 ], [ 19, 1, 1, 48 ], [ 19, 1, 2, 24 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 24 ], [ 20, 1, 8, 96 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 48 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 36 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 36 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 12 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 4 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 48 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 96 ], [ 33, 1, 2, 32 ], [ 33, 1, 6, 48 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 2, 48 ], [ 35, 1, 3, 24 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 48 ], [ 35, 1, 7, 72 ], [ 35, 1, 8, 24 ], [ 38, 1, 7, 192 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 12 ], [ 39, 1, 4, 24 ], [ 40, 1, 2, 24 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 24 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 48 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 43, 1, 3, 96 ], [ 43, 1, 8, 48 ], [ 44, 1, 1, 48 ], [ 44, 1, 9, 48 ], [ 46, 1, 7, 192 ], [ 47, 1, 4, 32 ], [ 47, 1, 9, 96 ], [ 48, 1, 2, 48 ], [ 48, 1, 5, 48 ], [ 49, 1, 2, 96 ], [ 49, 1, 8, 48 ], [ 49, 1, 20, 192 ], [ 50, 1, 4, 96 ], [ 51, 1, 10, 96 ], [ 52, 1, 2, 48 ], [ 52, 1, 3, 48 ], [ 52, 1, 4, 24 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 96 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 96 ], [ 55, 1, 16, 192 ], [ 56, 1, 6, 96 ], [ 56, 1, 19, 96 ], [ 57, 1, 4, 96 ], [ 59, 1, 17, 96 ], [ 60, 1, 44, 192 ] ] k = 46: F-action on Pi is () [62,1,46] Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1^3 phi2^2) Order of center |Z^F|: phi1^3 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 13 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 16 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 19 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 21 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 23 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 25 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 27 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 29 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 31 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 32 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 41 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 43 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 47 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 49 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 53 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) q congruent 59 modulo 60: 1/192 phi1^2 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 7, 68, 7, 7, 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], [ 4, 1, 2, 12 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 72 ], [ 13, 1, 4, 24 ], [ 16, 1, 1, 96 ], [ 19, 1, 1, 32 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 96 ], [ 20, 1, 3, 48 ], [ 22, 1, 2, 16 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 42 ], [ 24, 1, 2, 28 ], [ 25, 1, 1, 72 ], [ 25, 1, 3, 24 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 48 ], [ 28, 1, 3, 24 ], [ 31, 1, 2, 48 ], [ 33, 1, 1, 192 ], [ 34, 1, 2, 16 ], [ 35, 1, 1, 96 ], [ 35, 1, 3, 192 ], [ 35, 1, 6, 96 ], [ 37, 1, 2, 48 ], [ 39, 1, 1, 24 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 24 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 144 ], [ 41, 1, 6, 144 ], [ 41, 1, 9, 48 ], [ 42, 1, 4, 64 ], [ 43, 1, 2, 96 ], [ 44, 1, 2, 48 ], [ 47, 1, 2, 96 ], [ 48, 1, 2, 48 ], [ 48, 1, 3, 96 ], [ 48, 1, 4, 96 ], [ 49, 1, 1, 192 ], [ 49, 1, 5, 192 ], [ 49, 1, 9, 384 ], [ 50, 1, 5, 32 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 96 ], [ 52, 1, 9, 48 ], [ 53, 1, 3, 192 ], [ 56, 1, 7, 96 ], [ 57, 1, 2, 96 ], [ 57, 1, 5, 192 ], [ 59, 1, 12, 96 ], [ 60, 1, 40, 384 ] ] k = 47: F-action on Pi is (2,5) [62,1,47] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^4 phi2) Order of center |Z^F|: phi1^4 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 2 modulo 60: 1/192 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 3 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) q congruent 4 modulo 60: 1/192 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 5 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 7 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) q congruent 8 modulo 60: 1/192 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 9 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 11 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) q congruent 13 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 16 modulo 60: 1/192 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 17 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 19 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) q congruent 21 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 23 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) q congruent 25 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 27 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) q congruent 29 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 31 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) q congruent 32 modulo 60: 1/192 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 37 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 41 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 43 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) q congruent 47 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) q congruent 49 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 53 modulo 60: 1/192 phi1 ( q^4-20*q^3+138*q^2-360*q+225 ) q congruent 59 modulo 60: 1/192 ( q^5-21*q^4+158*q^3-498*q^2+537*q+63 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70, 68, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 20 ], [ 4, 1, 1, 34 ], [ 4, 1, 2, 14 ], [ 5, 1, 1, 32 ], [ 6, 1, 1, 40 ], [ 7, 1, 1, 28 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 14 ], [ 11, 1, 1, 36 ], [ 12, 1, 1, 68 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 36 ], [ 13, 1, 4, 16 ], [ 14, 1, 1, 64 ], [ 15, 1, 1, 64 ], [ 16, 1, 1, 40 ], [ 16, 1, 2, 88 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 72 ], [ 20, 1, 1, 56 ], [ 20, 1, 3, 72 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 64 ], [ 23, 1, 1, 30 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 50 ], [ 25, 1, 1, 84 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 84 ], [ 28, 1, 3, 28 ], [ 29, 1, 1, 96 ], [ 30, 1, 1, 96 ], [ 30, 1, 2, 32 ], [ 31, 1, 1, 64 ], [ 33, 1, 2, 80 ], [ 33, 1, 4, 192 ], [ 34, 1, 1, 96 ], [ 35, 1, 1, 72 ], [ 35, 1, 2, 56 ], [ 35, 1, 5, 120 ], [ 35, 1, 6, 72 ], [ 36, 1, 1, 96 ], [ 37, 1, 1, 96 ], [ 37, 1, 2, 48 ], [ 39, 1, 1, 72 ], [ 39, 1, 2, 12 ], [ 40, 1, 1, 144 ], [ 40, 1, 3, 40 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 24 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 43, 1, 3, 96 ], [ 43, 1, 8, 48 ], [ 44, 1, 1, 48 ], [ 44, 1, 9, 48 ], [ 45, 1, 1, 96 ], [ 47, 1, 3, 128 ], [ 48, 1, 1, 96 ], [ 48, 1, 4, 96 ], [ 48, 1, 7, 96 ], [ 49, 1, 2, 144 ], [ 49, 1, 11, 192 ], [ 50, 1, 1, 96 ], [ 51, 1, 1, 96 ], [ 51, 1, 6, 96 ], [ 52, 1, 1, 144 ], [ 52, 1, 3, 72 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 96 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 96 ], [ 55, 1, 9, 192 ], [ 56, 1, 1, 96 ], [ 56, 1, 14, 96 ], [ 57, 1, 3, 192 ], [ 59, 1, 17, 96 ], [ 60, 1, 44, 192 ] ] k = 48: F-action on Pi is (2,5) [62,1,48] Dynkin type is A_1(q) + A_1(q^2) + T(phi1 phi2^4) Order of center |Z^F|: phi1 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 2 modulo 60: 1/192 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 3 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) q congruent 4 modulo 60: 1/192 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 5 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 7 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) q congruent 8 modulo 60: 1/192 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 9 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 11 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) q congruent 13 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 16 modulo 60: 1/192 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 17 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 19 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) q congruent 21 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 23 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) q congruent 25 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 27 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) q congruent 29 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 31 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) q congruent 32 modulo 60: 1/192 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 37 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 41 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 43 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) q congruent 47 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) q congruent 49 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 53 modulo 60: 1/192 phi1 ( q^4-14*q^3+68*q^2-142*q+135 ) q congruent 59 modulo 60: 1/192 ( q^5-15*q^4+82*q^3-210*q^2+325*q-327 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20, 5, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 20 ], [ 4, 1, 1, 14 ], [ 4, 1, 2, 34 ], [ 5, 1, 2, 32 ], [ 6, 1, 2, 40 ], [ 7, 1, 2, 28 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 14 ], [ 11, 1, 2, 36 ], [ 12, 1, 2, 68 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 36 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 64 ], [ 15, 1, 2, 64 ], [ 16, 1, 3, 40 ], [ 16, 1, 4, 88 ], [ 18, 1, 2, 64 ], [ 19, 1, 2, 72 ], [ 20, 1, 2, 72 ], [ 20, 1, 4, 56 ], [ 21, 1, 2, 48 ], [ 22, 1, 4, 64 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 30 ], [ 24, 1, 2, 50 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 84 ], [ 25, 1, 4, 48 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 28 ], [ 28, 1, 4, 84 ], [ 29, 1, 4, 96 ], [ 30, 1, 3, 96 ], [ 30, 1, 4, 32 ], [ 31, 1, 4, 64 ], [ 33, 1, 6, 80 ], [ 33, 1, 10, 192 ], [ 34, 1, 4, 96 ], [ 35, 1, 3, 72 ], [ 35, 1, 4, 120 ], [ 35, 1, 7, 56 ], [ 35, 1, 8, 72 ], [ 36, 1, 4, 96 ], [ 37, 1, 2, 48 ], [ 37, 1, 3, 96 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 72 ], [ 40, 1, 2, 40 ], [ 40, 1, 6, 144 ], [ 41, 1, 2, 24 ], [ 41, 1, 4, 48 ], [ 41, 1, 9, 144 ], [ 41, 1, 10, 96 ], [ 42, 1, 6, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 5, 48 ], [ 44, 1, 10, 48 ], [ 45, 1, 6, 96 ], [ 47, 1, 10, 128 ], [ 48, 1, 3, 96 ], [ 48, 1, 6, 96 ], [ 48, 1, 10, 96 ], [ 49, 1, 8, 144 ], [ 49, 1, 19, 192 ], [ 50, 1, 12, 96 ], [ 51, 1, 3, 96 ], [ 51, 1, 9, 96 ], [ 52, 1, 4, 72 ], [ 52, 1, 10, 144 ], [ 53, 1, 9, 96 ], [ 53, 1, 12, 96 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 96 ], [ 55, 1, 20, 192 ], [ 56, 1, 10, 96 ], [ 56, 1, 20, 96 ], [ 57, 1, 9, 192 ], [ 59, 1, 18, 96 ], [ 60, 1, 43, 192 ] ] k = 49: F-action on Pi is (2,5) [62,1,49] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^2 phi2^3) Order of center |Z^F|: phi1^2 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q-3 ) q congruent 2 modulo 60: 1/32 q ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 3 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-14*q^2+25*q-3 ) q congruent 4 modulo 60: 1/32 q^3 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q+5 ) q congruent 7 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-14*q^2+25*q-3 ) q congruent 8 modulo 60: 1/32 q ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 9 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q-3 ) q congruent 11 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-6*q^2+9*q+5 ) q congruent 13 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q-3 ) q congruent 16 modulo 60: 1/32 q^3 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q+5 ) q congruent 19 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-14*q^2+25*q-3 ) q congruent 21 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q-3 ) q congruent 23 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-6*q^2+9*q+5 ) q congruent 25 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q-3 ) q congruent 27 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-14*q^2+25*q-3 ) q congruent 29 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q+5 ) q congruent 31 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-14*q^2+25*q-3 ) q congruent 32 modulo 60: 1/32 q ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 37 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q-3 ) q congruent 41 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q+5 ) q congruent 43 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-14*q^2+25*q-3 ) q congruent 47 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-6*q^2+9*q+5 ) q congruent 49 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q-3 ) q congruent 53 modulo 60: 1/32 phi1^2 ( q^3-5*q^2+3*q+5 ) q congruent 59 modulo 60: 1/32 ( q^5-7*q^4+14*q^3-6*q^2+9*q+5 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 76, 69, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 10 ], [ 5, 1, 2, 16 ], [ 6, 1, 1, 8 ], [ 6, 1, 2, 16 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 1, 8 ], [ 19, 1, 2, 16 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 16 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 16 ], [ 20, 1, 7, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 8 ], [ 22, 1, 4, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 8 ], [ 29, 1, 3, 16 ], [ 30, 1, 3, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 31, 1, 4, 16 ], [ 32, 1, 2, 16 ], [ 32, 1, 4, 16 ], [ 33, 1, 2, 16 ], [ 33, 1, 6, 32 ], [ 34, 1, 2, 8 ], [ 34, 1, 3, 8 ], [ 34, 1, 4, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 16 ], [ 36, 1, 3, 16 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 16 ], [ 38, 1, 10, 32 ], [ 39, 1, 2, 4 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 40, 1, 2, 16 ], [ 40, 1, 3, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 2, 16 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 8, 8 ], [ 45, 1, 5, 16 ], [ 46, 1, 8, 32 ], [ 47, 1, 4, 16 ], [ 47, 1, 9, 16 ], [ 47, 1, 10, 32 ], [ 48, 1, 2, 8 ], [ 48, 1, 3, 16 ], [ 48, 1, 5, 8 ], [ 48, 1, 6, 16 ], [ 48, 1, 10, 16 ], [ 49, 1, 2, 16 ], [ 49, 1, 8, 32 ], [ 49, 1, 15, 32 ], [ 50, 1, 5, 16 ], [ 50, 1, 11, 16 ], [ 51, 1, 8, 16 ], [ 52, 1, 3, 8 ], [ 52, 1, 4, 16 ], [ 52, 1, 9, 16 ], [ 53, 1, 3, 16 ], [ 53, 1, 4, 16 ], [ 53, 1, 7, 16 ], [ 53, 1, 8, 16 ], [ 55, 1, 17, 32 ], [ 56, 1, 7, 16 ], [ 56, 1, 18, 16 ], [ 57, 1, 4, 16 ], [ 57, 1, 9, 32 ], [ 59, 1, 22, 16 ], [ 60, 1, 45, 32 ] ] k = 50: F-action on Pi is (2,5) [62,1,50] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^3 phi2^2) Order of center |Z^F|: phi1^3 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+12*q+5 ) q congruent 2 modulo 60: 1/32 q ( q^4-8*q^3+16*q^2-16 ) q congruent 3 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q-3 ) q congruent 4 modulo 60: 1/32 q ( q^4-8*q^3+16*q^2+8*q-32 ) q congruent 5 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q+13 ) q congruent 7 modulo 60: 1/32 phi1 phi2 ( q^3-9*q^2+23*q-11 ) q congruent 8 modulo 60: 1/32 q ( q^4-8*q^3+16*q^2-16 ) q congruent 9 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q+13 ) q congruent 11 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q-3 ) q congruent 13 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+12*q+5 ) q congruent 16 modulo 60: 1/32 q ( q^4-8*q^3+16*q^2+8*q-32 ) q congruent 17 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q+13 ) q congruent 19 modulo 60: 1/32 phi1 phi2 ( q^3-9*q^2+23*q-11 ) q congruent 21 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q+13 ) q congruent 23 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q-3 ) q congruent 25 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+12*q+5 ) q congruent 27 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q-3 ) q congruent 29 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q+13 ) q congruent 31 modulo 60: 1/32 phi1 phi2 ( q^3-9*q^2+23*q-11 ) q congruent 32 modulo 60: 1/32 q ( q^4-8*q^3+16*q^2-16 ) q congruent 37 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+12*q+5 ) q congruent 41 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q+13 ) q congruent 43 modulo 60: 1/32 phi1 phi2 ( q^3-9*q^2+23*q-11 ) q congruent 47 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q-3 ) q congruent 49 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+12*q+5 ) q congruent 53 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q+13 ) q congruent 59 modulo 60: 1/32 phi1 ( q^4-8*q^3+14*q^2+4*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19, 7, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 8 ], [ 7, 1, 2, 4 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 8 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 16 ], [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 19, 1, 2, 8 ], [ 20, 1, 1, 16 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 8 ], [ 20, 1, 6, 16 ], [ 21, 1, 1, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 8 ], [ 28, 1, 2, 12 ], [ 28, 1, 3, 8 ], [ 28, 1, 4, 4 ], [ 29, 1, 2, 16 ], [ 30, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 16 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 32, 1, 2, 16 ], [ 32, 1, 4, 16 ], [ 33, 1, 2, 32 ], [ 33, 1, 6, 16 ], [ 34, 1, 1, 16 ], [ 34, 1, 2, 8 ], [ 34, 1, 3, 8 ], [ 35, 1, 1, 16 ], [ 35, 1, 2, 16 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 16 ], [ 35, 1, 6, 16 ], [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 36, 1, 2, 16 ], [ 37, 1, 1, 16 ], [ 37, 1, 2, 8 ], [ 38, 1, 2, 32 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 8 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 16 ], [ 42, 1, 2, 16 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 8, 8 ], [ 45, 1, 2, 16 ], [ 46, 1, 11, 32 ], [ 47, 1, 3, 32 ], [ 47, 1, 4, 16 ], [ 47, 1, 9, 16 ], [ 48, 1, 1, 16 ], [ 48, 1, 2, 8 ], [ 48, 1, 4, 16 ], [ 48, 1, 5, 8 ], [ 48, 1, 7, 16 ], [ 49, 1, 2, 32 ], [ 49, 1, 8, 16 ], [ 49, 1, 18, 32 ], [ 50, 1, 2, 16 ], [ 50, 1, 8, 16 ], [ 51, 1, 2, 16 ], [ 52, 1, 2, 16 ], [ 52, 1, 3, 16 ], [ 52, 1, 4, 8 ], [ 53, 1, 3, 16 ], [ 53, 1, 4, 16 ], [ 53, 1, 7, 16 ], [ 53, 1, 8, 16 ], [ 55, 1, 8, 32 ], [ 56, 1, 2, 16 ], [ 56, 1, 13, 16 ], [ 57, 1, 3, 32 ], [ 57, 1, 4, 16 ], [ 59, 1, 22, 16 ], [ 60, 1, 45, 32 ] ] i = 63: Pi = [ 1, 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [63,1,1] Dynkin type is A_3(q) + T(phi1^5) Order of center |Z^F|: phi1^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+29113*q-53666 ) q congruent 2 modulo 60: 1/3840 ( q^5-46*q^4+804*q^3-6536*q^2+23648*q-26880 ) q congruent 3 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28233*q-40770 ) q congruent 4 modulo 60: 1/3840 ( q^5-46*q^4+804*q^3-6536*q^2+24288*q-33280 ) q congruent 5 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28473*q-45090 ) q congruent 7 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28873*q-47810 ) q congruent 8 modulo 60: 1/3840 ( q^5-46*q^4+804*q^3-6536*q^2+23648*q-26880 ) q congruent 9 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28473*q-45090 ) q congruent 11 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28233*q-42306 ) q congruent 13 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+29113*q-52130 ) q congruent 16 modulo 60: 1/3840 ( q^5-46*q^4+804*q^3-6536*q^2+24288*q-34816 ) q congruent 17 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28473*q-45090 ) q congruent 19 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28873*q-47810 ) q congruent 21 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28473*q-46626 ) q congruent 23 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28233*q-40770 ) q congruent 25 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+29113*q-52130 ) q congruent 27 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28233*q-40770 ) q congruent 29 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28473*q-45090 ) q congruent 31 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28873*q-49346 ) q congruent 32 modulo 60: 1/3840 ( q^5-46*q^4+804*q^3-6536*q^2+23648*q-26880 ) q congruent 37 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+29113*q-52130 ) q congruent 41 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28473*q-46626 ) q congruent 43 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28873*q-47810 ) q congruent 47 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28233*q-40770 ) q congruent 49 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+29113*q-52130 ) q congruent 53 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28473*q-45090 ) q congruent 59 modulo 60: 1/3840 ( q^5-46*q^4+814*q^3-6936*q^2+28233*q-40770 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 4, 8, 70 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 20 ], [ 3, 1, 1, 80 ], [ 4, 1, 1, 102 ], [ 5, 1, 1, 64 ], [ 6, 1, 1, 160 ], [ 7, 1, 1, 80 ], [ 8, 1, 1, 32 ], [ 9, 1, 1, 11 ], [ 10, 1, 1, 40 ], [ 11, 1, 1, 240 ], [ 12, 1, 1, 400 ], [ 13, 1, 1, 600 ], [ 14, 1, 1, 192 ], [ 15, 1, 1, 320 ], [ 16, 1, 1, 160 ], [ 18, 1, 1, 320 ], [ 19, 1, 1, 480 ], [ 20, 1, 1, 160 ], [ 21, 1, 1, 160 ], [ 22, 1, 1, 320 ], [ 23, 1, 1, 90 ], [ 24, 1, 1, 280 ], [ 25, 1, 1, 260 ], [ 26, 1, 1, 160 ], [ 27, 1, 1, 480 ], [ 28, 1, 1, 1200 ], [ 29, 1, 1, 640 ], [ 30, 1, 1, 960 ], [ 31, 1, 1, 320 ], [ 34, 1, 1, 960 ], [ 35, 1, 1, 480 ], [ 36, 1, 1, 640 ], [ 37, 1, 1, 320 ], [ 39, 1, 1, 560 ], [ 40, 1, 1, 960 ], [ 41, 1, 1, 1440 ], [ 42, 1, 1, 960 ], [ 43, 1, 1, 320 ], [ 44, 1, 1, 2400 ], [ 45, 1, 1, 1920 ], [ 48, 1, 1, 960 ], [ 50, 1, 1, 1920 ], [ 51, 1, 1, 640 ], [ 52, 1, 1, 2880 ], [ 53, 1, 1, 960 ], [ 54, 1, 1, 3840 ], [ 56, 1, 1, 1920 ], [ 59, 1, 1, 5760 ] ] k = 2: F-action on Pi is () [63,1,2] Dynkin type is A_3(q) + T(phi1 phi5) Order of center |Z^F|: phi1 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 2 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 13 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 17 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 23 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 32 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/10 phi1 ( q^4-q^2-2*q-4 ) q congruent 43 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/10 q phi2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/10 q phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 23, 93, 50, 62, 107 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 14, 1, 1, 2 ], [ 54, 1, 6, 10 ] ] k = 3: F-action on Pi is (1,4) [63,1,3] Dynkin type is ^2A_3(q) + T(phi2 phi10) Order of center |Z^F|: phi2 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/10 q^2 phi1 phi4 q congruent 2 modulo 60: 1/10 q^2 phi1 phi4 q congruent 3 modulo 60: 1/10 q^2 phi1 phi4 q congruent 4 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 5 modulo 60: 1/10 q^2 phi1 phi4 q congruent 7 modulo 60: 1/10 q^2 phi1 phi4 q congruent 8 modulo 60: 1/10 q^2 phi1 phi4 q congruent 9 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 11 modulo 60: 1/10 q^2 phi1 phi4 q congruent 13 modulo 60: 1/10 q^2 phi1 phi4 q congruent 16 modulo 60: 1/10 q^2 phi1 phi4 q congruent 17 modulo 60: 1/10 q^2 phi1 phi4 q congruent 19 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 21 modulo 60: 1/10 q^2 phi1 phi4 q congruent 23 modulo 60: 1/10 q^2 phi1 phi4 q congruent 25 modulo 60: 1/10 q^2 phi1 phi4 q congruent 27 modulo 60: 1/10 q^2 phi1 phi4 q congruent 29 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 31 modulo 60: 1/10 q^2 phi1 phi4 q congruent 32 modulo 60: 1/10 q^2 phi1 phi4 q congruent 37 modulo 60: 1/10 q^2 phi1 phi4 q congruent 41 modulo 60: 1/10 q^2 phi1 phi4 q congruent 43 modulo 60: 1/10 q^2 phi1 phi4 q congruent 47 modulo 60: 1/10 q^2 phi1 phi4 q congruent 49 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) q congruent 53 modulo 60: 1/10 q^2 phi1 phi4 q congruent 59 modulo 60: 1/10 phi2 ( q^4-2*q^3+3*q^2-4*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 24, 94, 51, 63, 108 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 14, 1, 2, 2 ], [ 54, 1, 8, 10 ] ] k = 4: F-action on Pi is () [63,1,4] Dynkin type is A_3(q) + T(phi1^3 phi3) Order of center |Z^F|: phi1^3 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 phi1 ( q^4-9*q^3+19*q^2+13*q-40 ) q congruent 2 modulo 60: 1/48 q phi2 ( q^3-11*q^2+38*q-40 ) q congruent 3 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 60: 1/48 phi1 ( q^4-9*q^3+18*q^2+16*q-32 ) q congruent 5 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 60: 1/48 phi1 ( q^4-9*q^3+19*q^2+13*q-40 ) q congruent 8 modulo 60: 1/48 q phi2 ( q^3-11*q^2+38*q-40 ) q congruent 9 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 13 modulo 60: 1/48 phi1 ( q^4-9*q^3+19*q^2+13*q-40 ) q congruent 16 modulo 60: 1/48 phi1 ( q^4-9*q^3+18*q^2+16*q-32 ) q congruent 17 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 19 modulo 60: 1/48 phi1 ( q^4-9*q^3+19*q^2+13*q-40 ) q congruent 21 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 23 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 25 modulo 60: 1/48 phi1 ( q^4-9*q^3+19*q^2+13*q-40 ) q congruent 27 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 29 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 31 modulo 60: 1/48 phi1 ( q^4-9*q^3+19*q^2+13*q-40 ) q congruent 32 modulo 60: 1/48 q phi2 ( q^3-11*q^2+38*q-40 ) q congruent 37 modulo 60: 1/48 phi1 ( q^4-9*q^3+19*q^2+13*q-40 ) q congruent 41 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 43 modulo 60: 1/48 phi1 ( q^4-9*q^3+19*q^2+13*q-40 ) q congruent 47 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 49 modulo 60: 1/48 phi1 ( q^4-9*q^3+19*q^2+13*q-40 ) q congruent 53 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) q congruent 59 modulo 60: 1/48 q phi2 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 30, 14, 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 12, 1, 1, 10 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 8 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 32 ], [ 26, 1, 1, 16 ], [ 27, 1, 5, 6 ], [ 29, 1, 1, 16 ], [ 31, 1, 1, 8 ], [ 36, 1, 1, 16 ], [ 37, 1, 1, 32 ], [ 39, 1, 1, 8 ], [ 40, 1, 1, 24 ], [ 42, 1, 3, 12 ], [ 43, 1, 1, 32 ], [ 44, 1, 3, 30 ], [ 45, 1, 3, 24 ], [ 50, 1, 3, 24 ], [ 51, 1, 1, 16 ], [ 53, 1, 16, 12 ], [ 54, 1, 3, 48 ], [ 56, 1, 3, 24 ], [ 59, 1, 4, 72 ] ] k = 5: F-action on Pi is () [63,1,5] Dynkin type is A_3(q) + T(phi1 phi2^2 phi3) Order of center |Z^F|: phi1 phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^3 phi2 q congruent 2 modulo 60: 1/48 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/48 q phi1^3 phi2 q congruent 4 modulo 60: 1/48 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/48 q phi1^3 phi2 q congruent 7 modulo 60: 1/48 q phi1^3 phi2 q congruent 8 modulo 60: 1/48 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/48 q phi1^3 phi2 q congruent 11 modulo 60: 1/48 q phi1^3 phi2 q congruent 13 modulo 60: 1/48 q phi1^3 phi2 q congruent 16 modulo 60: 1/48 q^2 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/48 q phi1^3 phi2 q congruent 19 modulo 60: 1/48 q phi1^3 phi2 q congruent 21 modulo 60: 1/48 q phi1^3 phi2 q congruent 23 modulo 60: 1/48 q phi1^3 phi2 q congruent 25 modulo 60: 1/48 q phi1^3 phi2 q congruent 27 modulo 60: 1/48 q phi1^3 phi2 q congruent 29 modulo 60: 1/48 q phi1^3 phi2 q congruent 31 modulo 60: 1/48 q phi1^3 phi2 q congruent 32 modulo 60: 1/48 q^2 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/48 q phi1^3 phi2 q congruent 41 modulo 60: 1/48 q phi1^3 phi2 q congruent 43 modulo 60: 1/48 q phi1^3 phi2 q congruent 47 modulo 60: 1/48 q phi1^3 phi2 q congruent 49 modulo 60: 1/48 q phi1^3 phi2 q congruent 53 modulo 60: 1/48 q phi1^3 phi2 q congruent 59 modulo 60: 1/48 q phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 30, 81, 27, 37, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 16, 1, 1, 4 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 16 ], [ 27, 1, 5, 6 ], [ 31, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 40, 1, 3, 8 ], [ 42, 1, 3, 12 ], [ 43, 1, 12, 32 ], [ 44, 1, 3, 6 ], [ 50, 1, 6, 24 ], [ 51, 1, 5, 16 ], [ 53, 1, 16, 12 ], [ 56, 1, 8, 24 ], [ 59, 1, 19, 24 ] ] k = 6: F-action on Pi is () [63,1,6] Dynkin type is A_3(q) + T(phi2 phi4 phi6) Order of center |Z^F|: phi2 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 2 modulo 60: 1/24 q^3 phi1 phi2 q congruent 3 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 4 modulo 60: 1/24 q^3 phi1 phi2 q congruent 5 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 7 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 8 modulo 60: 1/24 q^3 phi1 phi2 q congruent 9 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 11 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 13 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 16 modulo 60: 1/24 q^3 phi1 phi2 q congruent 17 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 19 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 21 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 23 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 25 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 27 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 29 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 31 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 32 modulo 60: 1/24 q^3 phi1 phi2 q congruent 37 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 41 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 43 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 47 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 49 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 53 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 59 modulo 60: 1/24 q phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 96, 60, 98, 99, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 16, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 39, 1, 5, 4 ], [ 43, 1, 9, 8 ], [ 44, 1, 7, 6 ], [ 51, 1, 4, 8 ], [ 53, 1, 15, 12 ] ] k = 7: F-action on Pi is (1,4) [63,1,7] Dynkin type is ^2A_3(q) + T(phi1 phi3 phi4) Order of center |Z^F|: phi1 phi3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 2 modulo 60: 1/24 q^3 phi1 phi2 q congruent 3 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 4 modulo 60: 1/24 q^3 phi1 phi2 q congruent 5 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 7 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 8 modulo 60: 1/24 q^3 phi1 phi2 q congruent 9 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 11 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 13 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 16 modulo 60: 1/24 q^3 phi1 phi2 q congruent 17 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 19 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 21 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 23 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 25 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 27 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 29 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 31 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 32 modulo 60: 1/24 q^3 phi1 phi2 q congruent 37 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 41 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 43 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 47 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 49 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 53 modulo 60: 1/24 q phi1^2 phi2^2 q congruent 59 modulo 60: 1/24 q phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 95, 59, 97, 99, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 27, 1, 5, 6 ], [ 39, 1, 5, 4 ], [ 43, 1, 9, 8 ], [ 44, 1, 3, 6 ], [ 51, 1, 7, 8 ], [ 53, 1, 17, 12 ] ] k = 8: F-action on Pi is (1,4) [63,1,8] Dynkin type is ^2A_3(q) + T(phi1^2 phi2 phi6) Order of center |Z^F|: phi1^2 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/48 q phi1 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 82, 28, 38, 96 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 16, 1, 3, 4 ], [ 20, 1, 3, 16 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 16 ], [ 27, 1, 4, 6 ], [ 31, 1, 3, 8 ], [ 39, 1, 1, 8 ], [ 40, 1, 2, 8 ], [ 42, 1, 5, 12 ], [ 43, 1, 3, 32 ], [ 44, 1, 7, 6 ], [ 50, 1, 7, 24 ], [ 51, 1, 10, 16 ], [ 53, 1, 18, 12 ], [ 56, 1, 12, 24 ], [ 59, 1, 20, 24 ] ] k = 9: F-action on Pi is (1,4) [63,1,9] Dynkin type is ^2A_3(q) + T(phi2^3 phi6) Order of center |Z^F|: phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 2 modulo 60: 1/48 phi2 ( q^4-7*q^3+18*q^2-24*q+16 ) q congruent 3 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 4 modulo 60: 1/48 q^2 phi1 ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/48 phi2 ( q^4-7*q^3+19*q^2-29*q+24 ) q congruent 7 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 8 modulo 60: 1/48 phi2 ( q^4-7*q^3+18*q^2-24*q+16 ) q congruent 9 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 11 modulo 60: 1/48 phi2 ( q^4-7*q^3+19*q^2-29*q+24 ) q congruent 13 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 16 modulo 60: 1/48 q^2 phi1 ( q^2-5*q+6 ) q congruent 17 modulo 60: 1/48 phi2 ( q^4-7*q^3+19*q^2-29*q+24 ) q congruent 19 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 21 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 23 modulo 60: 1/48 phi2 ( q^4-7*q^3+19*q^2-29*q+24 ) q congruent 25 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 27 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 29 modulo 60: 1/48 phi2 ( q^4-7*q^3+19*q^2-29*q+24 ) q congruent 31 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 32 modulo 60: 1/48 phi2 ( q^4-7*q^3+18*q^2-24*q+16 ) q congruent 37 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 41 modulo 60: 1/48 phi2 ( q^4-7*q^3+19*q^2-29*q+24 ) q congruent 43 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 47 modulo 60: 1/48 phi2 ( q^4-7*q^3+19*q^2-29*q+24 ) q congruent 49 modulo 60: 1/48 q phi1^3 ( q-3 ) q congruent 53 modulo 60: 1/48 phi2 ( q^4-7*q^3+19*q^2-29*q+24 ) q congruent 59 modulo 60: 1/48 phi2 ( q^4-7*q^3+19*q^2-29*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 78, 31, 15, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 10 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 4 ], [ 25, 1, 3, 32 ], [ 26, 1, 4, 16 ], [ 27, 1, 4, 6 ], [ 29, 1, 4, 16 ], [ 31, 1, 4, 8 ], [ 36, 1, 4, 16 ], [ 37, 1, 3, 32 ], [ 39, 1, 3, 8 ], [ 40, 1, 6, 24 ], [ 42, 1, 5, 12 ], [ 43, 1, 13, 32 ], [ 44, 1, 7, 30 ], [ 45, 1, 4, 24 ], [ 50, 1, 10, 24 ], [ 51, 1, 9, 16 ], [ 53, 1, 18, 12 ], [ 54, 1, 10, 48 ], [ 56, 1, 17, 24 ], [ 59, 1, 5, 72 ] ] k = 10: F-action on Pi is () [63,1,10] Dynkin type is A_3(q) + T(phi1^2 phi2 phi3) Order of center |Z^F|: phi1^2 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^4-3*q^3-q^2+3*q-4 ) q congruent 2 modulo 60: 1/24 q^2 phi2 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 1/24 q phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/24 phi1 ( q^4-3*q^3-q^2+3*q-4 ) q congruent 8 modulo 60: 1/24 q^2 phi2 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/24 phi1 ( q^4-3*q^3-q^2+3*q-4 ) q congruent 16 modulo 60: 1/24 q phi1^2 ( q^2-2*q-4 ) q congruent 17 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/24 phi1 ( q^4-3*q^3-q^2+3*q-4 ) q congruent 21 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/24 phi1 ( q^4-3*q^3-q^2+3*q-4 ) q congruent 27 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/24 phi1 ( q^4-3*q^3-q^2+3*q-4 ) q congruent 32 modulo 60: 1/24 q^2 phi2 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/24 phi1 ( q^4-3*q^3-q^2+3*q-4 ) q congruent 41 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/24 phi1 ( q^4-3*q^3-q^2+3*q-4 ) q congruent 47 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/24 phi1 ( q^4-3*q^3-q^2+3*q-4 ) q congruent 53 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/24 q phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 77, 30, 81, 83, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 2 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 8 ], [ 27, 1, 5, 6 ], [ 29, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 31, 1, 2, 4 ], [ 36, 1, 2, 8 ], [ 39, 1, 4, 4 ], [ 42, 1, 3, 12 ], [ 43, 1, 2, 16 ], [ 44, 1, 3, 6 ], [ 45, 1, 3, 12 ], [ 50, 1, 3, 12 ], [ 50, 1, 6, 12 ], [ 51, 1, 2, 8 ], [ 53, 1, 16, 12 ], [ 54, 1, 7, 24 ], [ 56, 1, 3, 12 ], [ 56, 1, 8, 12 ] ] k = 11: F-action on Pi is (1,4) [63,1,11] Dynkin type is ^2A_3(q) + T(phi1 phi2^2 phi6) Order of center |Z^F|: phi1 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^4 q congruent 2 modulo 60: 1/24 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 3 modulo 60: 1/24 q phi1^4 q congruent 4 modulo 60: 1/24 q^2 phi1^2 ( q-2 ) q congruent 5 modulo 60: 1/24 phi2 ( q^4-5*q^3+11*q^2-15*q+12 ) q congruent 7 modulo 60: 1/24 q phi1^4 q congruent 8 modulo 60: 1/24 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 9 modulo 60: 1/24 q phi1^4 q congruent 11 modulo 60: 1/24 phi2 ( q^4-5*q^3+11*q^2-15*q+12 ) q congruent 13 modulo 60: 1/24 q phi1^4 q congruent 16 modulo 60: 1/24 q^2 phi1^2 ( q-2 ) q congruent 17 modulo 60: 1/24 phi2 ( q^4-5*q^3+11*q^2-15*q+12 ) q congruent 19 modulo 60: 1/24 q phi1^4 q congruent 21 modulo 60: 1/24 q phi1^4 q congruent 23 modulo 60: 1/24 phi2 ( q^4-5*q^3+11*q^2-15*q+12 ) q congruent 25 modulo 60: 1/24 q phi1^4 q congruent 27 modulo 60: 1/24 q phi1^4 q congruent 29 modulo 60: 1/24 phi2 ( q^4-5*q^3+11*q^2-15*q+12 ) q congruent 31 modulo 60: 1/24 q phi1^4 q congruent 32 modulo 60: 1/24 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 37 modulo 60: 1/24 q phi1^4 q congruent 41 modulo 60: 1/24 phi2 ( q^4-5*q^3+11*q^2-15*q+12 ) q congruent 43 modulo 60: 1/24 q phi1^4 q congruent 47 modulo 60: 1/24 phi2 ( q^4-5*q^3+11*q^2-15*q+12 ) q congruent 49 modulo 60: 1/24 q phi1^4 q congruent 53 modulo 60: 1/24 phi2 ( q^4-5*q^3+11*q^2-15*q+12 ) q congruent 59 modulo 60: 1/24 phi2 ( q^4-5*q^3+11*q^2-15*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 31, 82, 84, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 2, 8 ], [ 27, 1, 4, 6 ], [ 29, 1, 3, 8 ], [ 31, 1, 3, 4 ], [ 31, 1, 4, 4 ], [ 36, 1, 3, 8 ], [ 39, 1, 4, 4 ], [ 42, 1, 5, 12 ], [ 43, 1, 4, 16 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 50, 1, 7, 12 ], [ 50, 1, 10, 12 ], [ 51, 1, 8, 8 ], [ 53, 1, 18, 12 ], [ 54, 1, 11, 24 ], [ 56, 1, 12, 12 ], [ 56, 1, 17, 12 ] ] k = 12: F-action on Pi is () [63,1,12] Dynkin type is A_3(q) + T(phi1 phi2^2 phi6) Order of center |Z^F|: phi1 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 13 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 16 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 19 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 21 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 23 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 25 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 27 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 29 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 31 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 32 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 41 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 43 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 47 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 49 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 53 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 59 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 82, 31, 36, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 16, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 37, 1, 2, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 2, 4 ], [ 40, 1, 6, 12 ], [ 43, 1, 8, 8 ], [ 44, 1, 7, 18 ], [ 51, 1, 3, 8 ], [ 53, 1, 15, 12 ], [ 59, 1, 5, 36 ], [ 59, 1, 20, 12 ] ] k = 13: F-action on Pi is (1,4) [63,1,13] Dynkin type is ^2A_3(q) + T(phi1^2 phi2 phi3) Order of center |Z^F|: phi1^2 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 13 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 16 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 19 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 21 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 23 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 25 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 27 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 29 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 31 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 32 modulo 60: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 41 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 43 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 47 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 49 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 53 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 59 modulo 60: 1/24 q phi1 phi2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 27, 81, 30, 36, 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 16, 1, 2, 4 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 37, 1, 2, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 1, 12 ], [ 40, 1, 3, 4 ], [ 43, 1, 8, 8 ], [ 44, 1, 3, 18 ], [ 51, 1, 6, 8 ], [ 53, 1, 17, 12 ], [ 59, 1, 4, 36 ], [ 59, 1, 19, 12 ] ] k = 14: F-action on Pi is () [63,1,14] Dynkin type is A_3(q) + T(phi1 phi2^4) Order of center |Z^F|: phi1 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 2 modulo 60: 1/768 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 3 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) q congruent 4 modulo 60: 1/768 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 5 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 7 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) q congruent 8 modulo 60: 1/768 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 9 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 11 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) q congruent 13 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 16 modulo 60: 1/768 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 17 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 19 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) q congruent 21 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 23 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) q congruent 25 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 27 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) q congruent 29 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 31 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) q congruent 32 modulo 60: 1/768 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 37 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 41 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 43 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) q congruent 47 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) q congruent 49 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 53 modulo 60: 1/768 phi1 ( q^4-13*q^3+57*q^2-103*q+90 ) q congruent 59 modulo 60: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 5, 27, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 14 ], [ 4, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 48 ], [ 13, 1, 4, 144 ], [ 16, 1, 4, 64 ], [ 20, 1, 2, 96 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 72 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 64 ], [ 27, 1, 6, 192 ], [ 28, 1, 2, 48 ], [ 28, 1, 4, 288 ], [ 35, 1, 3, 96 ], [ 35, 1, 4, 192 ], [ 37, 1, 2, 32 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 144 ], [ 40, 1, 2, 64 ], [ 40, 1, 6, 192 ], [ 41, 1, 4, 96 ], [ 41, 1, 9, 288 ], [ 41, 1, 10, 192 ], [ 43, 1, 8, 32 ], [ 43, 1, 12, 192 ], [ 44, 1, 5, 96 ], [ 44, 1, 10, 576 ], [ 48, 1, 3, 192 ], [ 51, 1, 3, 128 ], [ 52, 1, 4, 192 ], [ 52, 1, 10, 576 ], [ 53, 1, 9, 192 ], [ 53, 1, 19, 384 ], [ 56, 1, 10, 384 ], [ 59, 1, 2, 1152 ], [ 59, 1, 18, 384 ] ] k = 15: F-action on Pi is (1,4) [63,1,15] Dynkin type is ^2A_3(q) + T(phi2 phi4^2) Order of center |Z^F|: phi2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 2 modulo 60: 1/64 q^3 ( q^2-4 ) q congruent 3 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 4 modulo 60: 1/64 q^3 ( q^2-4 ) q congruent 5 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 7 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 8 modulo 60: 1/64 q^3 ( q^2-4 ) q congruent 9 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 11 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 13 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 16 modulo 60: 1/64 q^3 ( q^2-4 ) q congruent 17 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 19 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 21 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 23 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 25 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 27 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 29 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 31 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 32 modulo 60: 1/64 q^3 ( q^2-4 ) q congruent 37 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 41 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 43 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 47 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 49 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 53 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 59 modulo 60: 1/64 phi1^2 phi2 ( q^2+q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 74, 18, 54, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 8 ], [ 23, 1, 2, 2 ], [ 25, 1, 3, 4 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 16 ], [ 48, 1, 9, 32 ], [ 53, 1, 14, 32 ], [ 59, 1, 6, 96 ] ] k = 16: F-action on Pi is () [63,1,16] Dynkin type is A_3(q) + T(phi1 phi4^2) Order of center |Z^F|: phi1 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 2 modulo 60: 1/64 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 4 modulo 60: 1/64 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 7 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 8 modulo 60: 1/64 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 11 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 13 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 16 modulo 60: 1/64 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 17 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 19 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 21 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 23 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 25 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 27 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 29 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 31 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 32 modulo 60: 1/64 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 37 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 41 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 43 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 47 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 49 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 53 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) q congruent 59 modulo 60: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 73, 18, 53, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 25, 1, 1, 4 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ], [ 43, 1, 9, 16 ], [ 44, 1, 6, 16 ], [ 48, 1, 8, 32 ], [ 53, 1, 10, 32 ], [ 59, 1, 6, 96 ] ] k = 17: F-action on Pi is (1,4) [63,1,17] Dynkin type is ^2A_3(q) + T(phi1 phi8) Order of center |Z^F|: phi1 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/16 q^4 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/16 q^4 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/16 q^4 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/16 q^4 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/16 q^4 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/16 phi1 phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 90, 43, 89, 110, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 59, 1, 25, 8 ] ] k = 18: F-action on Pi is () [63,1,18] Dynkin type is A_3(q) + T(phi2 phi8) Order of center |Z^F|: phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 2 modulo 60: 1/16 q^5 q congruent 3 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 4 modulo 60: 1/16 q^5 q congruent 5 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 7 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 8 modulo 60: 1/16 q^5 q congruent 9 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 11 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 13 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 16 modulo 60: 1/16 q^5 q congruent 17 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 19 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 21 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 23 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 25 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 27 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 29 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 31 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 32 modulo 60: 1/16 q^5 q congruent 37 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 41 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 43 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 47 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 49 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 53 modulo 60: 1/16 q phi1 phi2 phi4 q congruent 59 modulo 60: 1/16 q phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 89, 43, 90, 109, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 59, 1, 25, 8 ] ] k = 19: F-action on Pi is (1,4) [63,1,19] Dynkin type is ^2A_3(q) + T(phi2^5) Order of center |Z^F|: phi2^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/3840 phi1 ( q^4-35*q^3+451*q^2-2625*q+6240 ) q congruent 2 modulo 60: 1/3840 ( q^5-36*q^4+476*q^3-2736*q^2+6400*q-5120 ) q congruent 3 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9105*q-10080 ) q congruent 4 modulo 60: 1/3840 ( q^5-36*q^4+476*q^3-2736*q^2+5760*q-1536 ) q congruent 5 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9505*q-12000 ) q congruent 7 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9105*q-10080 ) q congruent 8 modulo 60: 1/3840 ( q^5-36*q^4+476*q^3-2736*q^2+6400*q-5120 ) q congruent 9 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+8865*q-7776 ) q congruent 11 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9745*q-15840 ) q congruent 13 modulo 60: 1/3840 phi1 ( q^4-35*q^3+451*q^2-2625*q+6240 ) q congruent 16 modulo 60: 1/3840 q ( q^4-36*q^3+476*q^2-2736*q+5760 ) q congruent 17 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9505*q-12000 ) q congruent 19 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9105*q-11616 ) q congruent 21 modulo 60: 1/3840 phi1 ( q^4-35*q^3+451*q^2-2625*q+6240 ) q congruent 23 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9745*q-15840 ) q congruent 25 modulo 60: 1/3840 phi1 ( q^4-35*q^3+451*q^2-2625*q+6240 ) q congruent 27 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9105*q-10080 ) q congruent 29 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9505*q-13536 ) q congruent 31 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9105*q-10080 ) q congruent 32 modulo 60: 1/3840 ( q^5-36*q^4+476*q^3-2736*q^2+6400*q-5120 ) q congruent 37 modulo 60: 1/3840 phi1 ( q^4-35*q^3+451*q^2-2625*q+6240 ) q congruent 41 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9505*q-12000 ) q congruent 43 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9105*q-10080 ) q congruent 47 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9745*q-15840 ) q congruent 49 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+8865*q-7776 ) q congruent 53 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9505*q-12000 ) q congruent 59 modulo 60: 1/3840 ( q^5-36*q^4+486*q^3-3076*q^2+9745*q-17376 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 5, 9, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 20 ], [ 3, 1, 2, 80 ], [ 4, 1, 2, 102 ], [ 5, 1, 2, 64 ], [ 6, 1, 2, 160 ], [ 7, 1, 2, 80 ], [ 8, 1, 2, 32 ], [ 9, 1, 1, 11 ], [ 10, 1, 2, 40 ], [ 11, 1, 2, 240 ], [ 12, 1, 2, 400 ], [ 13, 1, 4, 600 ], [ 14, 1, 2, 192 ], [ 15, 1, 2, 320 ], [ 16, 1, 3, 160 ], [ 18, 1, 2, 320 ], [ 19, 1, 2, 480 ], [ 20, 1, 4, 160 ], [ 21, 1, 2, 160 ], [ 22, 1, 4, 320 ], [ 23, 1, 2, 90 ], [ 24, 1, 2, 280 ], [ 25, 1, 3, 260 ], [ 26, 1, 4, 160 ], [ 27, 1, 6, 480 ], [ 28, 1, 4, 1200 ], [ 29, 1, 4, 640 ], [ 30, 1, 3, 960 ], [ 31, 1, 4, 320 ], [ 34, 1, 4, 960 ], [ 35, 1, 8, 480 ], [ 36, 1, 4, 640 ], [ 37, 1, 3, 320 ], [ 39, 1, 3, 560 ], [ 40, 1, 6, 960 ], [ 41, 1, 9, 1440 ], [ 42, 1, 6, 960 ], [ 43, 1, 13, 320 ], [ 44, 1, 10, 2400 ], [ 45, 1, 6, 1920 ], [ 48, 1, 6, 960 ], [ 50, 1, 12, 1920 ], [ 51, 1, 9, 640 ], [ 52, 1, 10, 2880 ], [ 53, 1, 20, 960 ], [ 54, 1, 14, 3840 ], [ 56, 1, 20, 1920 ], [ 59, 1, 2, 5760 ] ] k = 20: F-action on Pi is (1,4) [63,1,20] Dynkin type is ^2A_3(q) + T(phi1^4 phi2) Order of center |Z^F|: phi1^4 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 2 modulo 60: 1/768 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 3 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) q congruent 4 modulo 60: 1/768 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 5 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 7 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) q congruent 8 modulo 60: 1/768 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 9 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 11 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) q congruent 13 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 16 modulo 60: 1/768 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 17 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 19 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) q congruent 21 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 23 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) q congruent 25 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 27 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) q congruent 29 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 31 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) q congruent 32 modulo 60: 1/768 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 37 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 41 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 43 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) q congruent 47 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) q congruent 49 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 53 modulo 60: 1/768 phi1 ( q^4-19*q^3+123*q^2-289*q+120 ) q congruent 59 modulo 60: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 4, 28, 70 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 14 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 144 ], [ 13, 1, 3, 48 ], [ 13, 1, 4, 24 ], [ 16, 1, 2, 64 ], [ 20, 1, 3, 96 ], [ 23, 1, 1, 24 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 25, 1, 2, 64 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 16 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 28, 1, 3, 48 ], [ 35, 1, 5, 192 ], [ 35, 1, 6, 96 ], [ 37, 1, 2, 32 ], [ 39, 1, 1, 144 ], [ 39, 1, 2, 16 ], [ 40, 1, 1, 192 ], [ 40, 1, 3, 64 ], [ 41, 1, 1, 288 ], [ 41, 1, 3, 192 ], [ 41, 1, 4, 96 ], [ 43, 1, 3, 192 ], [ 43, 1, 8, 32 ], [ 44, 1, 1, 576 ], [ 44, 1, 9, 96 ], [ 48, 1, 4, 192 ], [ 51, 1, 6, 128 ], [ 52, 1, 1, 576 ], [ 52, 1, 3, 192 ], [ 53, 1, 5, 384 ], [ 53, 1, 6, 192 ], [ 56, 1, 14, 384 ], [ 59, 1, 1, 1152 ], [ 59, 1, 17, 384 ] ] k = 21: F-action on Pi is () [63,1,21] Dynkin type is A_3(q) + T(phi1^3 phi2^2) Order of center |Z^F|: phi1^3 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 2 modulo 60: 1/384 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 3 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) q congruent 4 modulo 60: 1/384 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 5 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 7 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) q congruent 8 modulo 60: 1/384 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 9 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 11 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) q congruent 13 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 16 modulo 60: 1/384 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 17 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 19 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) q congruent 21 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 23 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) q congruent 25 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 27 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) q congruent 29 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 31 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) q congruent 32 modulo 60: 1/384 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 37 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 41 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 43 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) q congruent 47 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) q congruent 49 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 53 modulo 60: 1/384 phi1^3 ( q^2-11*q+30 ) q congruent 59 modulo 60: 1/384 ( q^5-14*q^4+66*q^3-124*q^2+101*q-78 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 3, 30, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 12 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 24 ], [ 13, 1, 3, 48 ], [ 13, 1, 4, 24 ], [ 16, 1, 1, 16 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 32 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 36 ], [ 24, 1, 2, 28 ], [ 25, 1, 1, 36 ], [ 25, 1, 2, 24 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 48 ], [ 31, 1, 2, 32 ], [ 34, 1, 2, 96 ], [ 35, 1, 1, 48 ], [ 35, 1, 2, 96 ], [ 35, 1, 3, 48 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 48 ], [ 40, 1, 3, 32 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 96 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 32 ], [ 44, 1, 1, 48 ], [ 44, 1, 5, 48 ], [ 44, 1, 9, 96 ], [ 48, 1, 2, 96 ], [ 50, 1, 4, 192 ], [ 51, 1, 5, 64 ], [ 52, 1, 2, 96 ], [ 52, 1, 3, 96 ], [ 52, 1, 9, 96 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 192 ], [ 53, 1, 9, 96 ], [ 56, 1, 5, 192 ], [ 56, 1, 6, 192 ], [ 59, 1, 3, 192 ], [ 59, 1, 17, 192 ] ] k = 22: F-action on Pi is () [63,1,22] Dynkin type is A_3(q) + T(phi2^3 phi4) Order of center |Z^F|: phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 2 modulo 60: 1/192 q^3 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/192 q^3 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/192 q^3 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/192 q^3 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/192 q^3 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/192 phi1^2 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20, 71, 95, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 16, 1, 4, 16 ], [ 20, 1, 2, 48 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 4, 36 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], [ 35, 1, 4, 48 ], [ 39, 1, 3, 24 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 24 ], [ 41, 1, 10, 48 ], [ 43, 1, 9, 8 ], [ 43, 1, 12, 96 ], [ 44, 1, 4, 24 ], [ 44, 1, 10, 48 ], [ 51, 1, 4, 32 ], [ 52, 1, 5, 48 ], [ 53, 1, 11, 48 ], [ 53, 1, 19, 96 ], [ 56, 1, 9, 96 ], [ 59, 1, 24, 96 ] ] k = 23: F-action on Pi is () [63,1,23] Dynkin type is A_3(q) + T(phi1^2 phi2 phi4) Order of center |Z^F|: phi1^2 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 2 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 4 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 7 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 8 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 11 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 13 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 16 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 19 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 21 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 23 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 25 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 27 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 29 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 31 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 32 modulo 60: 1/64 q^3 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 41 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 43 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 47 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 49 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 53 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 59 modulo 60: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 72, 97, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 4 ], [ 20, 1, 1, 16 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 16 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 4 ], [ 26, 1, 1, 16 ], [ 28, 1, 3, 8 ], [ 35, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 16 ], [ 41, 1, 3, 16 ], [ 41, 1, 5, 16 ], [ 41, 1, 8, 8 ], [ 43, 1, 1, 32 ], [ 43, 1, 8, 16 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 16 ], [ 44, 1, 9, 16 ], [ 52, 1, 8, 16 ], [ 53, 1, 2, 32 ], [ 53, 1, 10, 32 ], [ 53, 1, 11, 16 ], [ 56, 1, 4, 32 ], [ 59, 1, 16, 32 ], [ 59, 1, 23, 32 ] ] k = 24: F-action on Pi is (1,4) [63,1,24] Dynkin type is ^2A_3(q) + T(phi1^3 phi4) Order of center |Z^F|: phi1^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 2 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 4 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 7 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 8 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 11 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 13 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 16 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 19 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 21 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 23 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 25 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 27 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 29 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 31 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 32 modulo 60: 1/192 q^2 ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 41 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 43 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 47 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 49 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 53 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) q congruent 59 modulo 60: 1/192 phi1 phi2 ( q^3-12*q^2+47*q-60 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 19, 70, 96, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 8 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 12 ], [ 16, 1, 2, 16 ], [ 20, 1, 3, 48 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 36 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 35, 1, 5, 48 ], [ 39, 1, 1, 24 ], [ 39, 1, 5, 4 ], [ 41, 1, 3, 48 ], [ 41, 1, 8, 24 ], [ 43, 1, 3, 96 ], [ 43, 1, 9, 8 ], [ 44, 1, 1, 48 ], [ 44, 1, 6, 24 ], [ 51, 1, 7, 32 ], [ 52, 1, 8, 48 ], [ 53, 1, 5, 96 ], [ 53, 1, 13, 48 ], [ 56, 1, 11, 96 ], [ 59, 1, 23, 96 ] ] k = 25: F-action on Pi is (1,4) [63,1,25] Dynkin type is ^2A_3(q) + T(phi1 phi2^2 phi4) Order of center |Z^F|: phi1 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 1/64 q^3 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/64 q phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 71, 20, 72, 98, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 4 ], [ 20, 1, 4, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 16 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 16 ], [ 28, 1, 2, 8 ], [ 35, 1, 7, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 16 ], [ 41, 1, 5, 16 ], [ 41, 1, 8, 8 ], [ 41, 1, 10, 16 ], [ 43, 1, 8, 16 ], [ 43, 1, 9, 8 ], [ 43, 1, 13, 32 ], [ 44, 1, 4, 16 ], [ 44, 1, 5, 16 ], [ 44, 1, 6, 8 ], [ 52, 1, 5, 16 ], [ 53, 1, 12, 32 ], [ 53, 1, 13, 16 ], [ 53, 1, 14, 32 ], [ 56, 1, 16, 32 ], [ 59, 1, 16, 32 ], [ 59, 1, 24, 32 ] ] k = 26: F-action on Pi is (1,4) [63,1,26] Dynkin type is ^2A_3(q) + T(phi1^2 phi2 phi4) Order of center |Z^F|: phi1^2 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 2 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 4 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 7 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 8 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 11 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 13 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 16 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 19 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 21 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 23 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 25 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 27 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 29 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 31 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 32 modulo 60: 1/32 q^3 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 41 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 43 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 47 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 49 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 53 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) q congruent 59 modulo 60: 1/32 phi1^3 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 76, 19, 60, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 35, 1, 5, 8 ], [ 35, 1, 7, 8 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 43, 1, 4, 16 ], [ 43, 1, 9, 8 ], [ 44, 1, 2, 8 ], [ 44, 1, 6, 8 ], [ 51, 1, 7, 16 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 7, 16 ], [ 53, 1, 13, 16 ], [ 56, 1, 11, 16 ], [ 56, 1, 16, 16 ], [ 59, 1, 21, 16 ] ] k = 27: F-action on Pi is () [63,1,27] Dynkin type is A_3(q) + T(phi1 phi2^2 phi4) Order of center |Z^F|: phi1 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 q phi1^3 phi2 q congruent 2 modulo 60: 1/32 q^4 ( q-2 ) q congruent 3 modulo 60: 1/32 q phi1^3 phi2 q congruent 4 modulo 60: 1/32 q^4 ( q-2 ) q congruent 5 modulo 60: 1/32 q phi1^3 phi2 q congruent 7 modulo 60: 1/32 q phi1^3 phi2 q congruent 8 modulo 60: 1/32 q^4 ( q-2 ) q congruent 9 modulo 60: 1/32 q phi1^3 phi2 q congruent 11 modulo 60: 1/32 q phi1^3 phi2 q congruent 13 modulo 60: 1/32 q phi1^3 phi2 q congruent 16 modulo 60: 1/32 q^4 ( q-2 ) q congruent 17 modulo 60: 1/32 q phi1^3 phi2 q congruent 19 modulo 60: 1/32 q phi1^3 phi2 q congruent 21 modulo 60: 1/32 q phi1^3 phi2 q congruent 23 modulo 60: 1/32 q phi1^3 phi2 q congruent 25 modulo 60: 1/32 q phi1^3 phi2 q congruent 27 modulo 60: 1/32 q phi1^3 phi2 q congruent 29 modulo 60: 1/32 q phi1^3 phi2 q congruent 31 modulo 60: 1/32 q phi1^3 phi2 q congruent 32 modulo 60: 1/32 q^4 ( q-2 ) q congruent 37 modulo 60: 1/32 q phi1^3 phi2 q congruent 41 modulo 60: 1/32 q phi1^3 phi2 q congruent 43 modulo 60: 1/32 q phi1^3 phi2 q congruent 47 modulo 60: 1/32 q phi1^3 phi2 q congruent 49 modulo 60: 1/32 q phi1^3 phi2 q congruent 53 modulo 60: 1/32 q phi1^3 phi2 q congruent 59 modulo 60: 1/32 q phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 19, 76, 20, 59, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 4, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 43, 1, 2, 16 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 8, 8 ], [ 51, 1, 4, 16 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 4, 16 ], [ 53, 1, 11, 16 ], [ 56, 1, 4, 16 ], [ 56, 1, 9, 16 ], [ 59, 1, 21, 16 ] ] k = 28: F-action on Pi is (1,4) [63,1,28] Dynkin type is ^2A_3(q) + T(phi1^2 phi2^3) Order of center |Z^F|: phi1^2 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 2 modulo 60: 1/384 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 3 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) q congruent 4 modulo 60: 1/384 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 5 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 7 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) q congruent 8 modulo 60: 1/384 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 9 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 11 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) q congruent 13 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 16 modulo 60: 1/384 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 17 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 19 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) q congruent 21 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 23 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) q congruent 25 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 27 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) q congruent 29 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 31 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) q congruent 32 modulo 60: 1/384 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 37 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 41 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 43 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) q congruent 47 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) q congruent 49 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 53 modulo 60: 1/384 phi1 ( q^4-11*q^3+39*q^2-57*q+60 ) q congruent 59 modulo 60: 1/384 ( q^5-12*q^4+50*q^3-96*q^2+117*q-108 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 69, 3, 31, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 10 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 48 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 16 ], [ 19, 1, 2, 48 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 48 ], [ 22, 1, 3, 32 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 36 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 36 ], [ 25, 1, 4, 24 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 48 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 31, 1, 3, 32 ], [ 34, 1, 3, 96 ], [ 35, 1, 6, 48 ], [ 35, 1, 7, 96 ], [ 35, 1, 8, 48 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 48 ], [ 40, 1, 2, 32 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 96 ], [ 42, 1, 6, 96 ], [ 43, 1, 3, 32 ], [ 43, 1, 8, 48 ], [ 43, 1, 13, 96 ], [ 44, 1, 5, 96 ], [ 44, 1, 9, 48 ], [ 44, 1, 10, 48 ], [ 48, 1, 5, 96 ], [ 50, 1, 9, 192 ], [ 51, 1, 10, 64 ], [ 52, 1, 2, 96 ], [ 52, 1, 4, 96 ], [ 52, 1, 9, 96 ], [ 53, 1, 6, 96 ], [ 53, 1, 12, 192 ], [ 53, 1, 20, 96 ], [ 56, 1, 15, 192 ], [ 56, 1, 19, 192 ], [ 59, 1, 3, 192 ], [ 59, 1, 18, 192 ] ] k = 29: F-action on Pi is () [63,1,29] Dynkin type is A_3(q) + T(phi1^3 phi2^2) Order of center |Z^F|: phi1^3 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 2 modulo 60: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 3 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) q congruent 4 modulo 60: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 5 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 7 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) q congruent 8 modulo 60: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 9 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 11 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) q congruent 13 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 16 modulo 60: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 17 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 19 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) q congruent 21 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 23 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) q congruent 25 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 27 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) q congruent 29 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 31 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) q congruent 32 modulo 60: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 37 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 41 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 43 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) q congruent 47 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) q congruent 49 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 53 modulo 60: 1/64 phi1^2 ( q^3-8*q^2+13*q+10 ) q congruent 59 modulo 60: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 7, 30, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 8 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 16 ], [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 20, 1, 1, 16 ], [ 20, 1, 2, 16 ], [ 21, 1, 1, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 16 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 3, 8 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 8 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 16 ], [ 29, 1, 2, 32 ], [ 30, 1, 1, 16 ], [ 30, 1, 2, 32 ], [ 31, 1, 1, 16 ], [ 31, 1, 2, 16 ], [ 34, 1, 1, 16 ], [ 34, 1, 2, 16 ], [ 35, 1, 1, 16 ], [ 35, 1, 3, 16 ], [ 36, 1, 2, 32 ], [ 37, 1, 1, 16 ], [ 37, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 32 ], [ 41, 1, 6, 32 ], [ 41, 1, 9, 16 ], [ 42, 1, 4, 32 ], [ 43, 1, 2, 32 ], [ 44, 1, 2, 16 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 45, 1, 2, 32 ], [ 48, 1, 1, 16 ], [ 48, 1, 2, 16 ], [ 48, 1, 3, 16 ], [ 48, 1, 7, 32 ], [ 50, 1, 2, 32 ], [ 50, 1, 5, 32 ], [ 51, 1, 2, 32 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ], [ 53, 1, 3, 32 ], [ 54, 1, 5, 64 ], [ 56, 1, 2, 32 ], [ 56, 1, 7, 32 ], [ 59, 1, 3, 64 ] ] k = 30: F-action on Pi is (1,4) [63,1,30] Dynkin type is ^2A_3(q) + T(phi1 phi2^2 phi4) Order of center |Z^F|: phi1 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 q phi1^3 phi2 q congruent 2 modulo 60: 1/16 q^4 ( q-2 ) q congruent 3 modulo 60: 1/16 q phi1^3 phi2 q congruent 4 modulo 60: 1/16 q^4 ( q-2 ) q congruent 5 modulo 60: 1/16 q phi1^3 phi2 q congruent 7 modulo 60: 1/16 q phi1^3 phi2 q congruent 8 modulo 60: 1/16 q^4 ( q-2 ) q congruent 9 modulo 60: 1/16 q phi1^3 phi2 q congruent 11 modulo 60: 1/16 q phi1^3 phi2 q congruent 13 modulo 60: 1/16 q phi1^3 phi2 q congruent 16 modulo 60: 1/16 q^4 ( q-2 ) q congruent 17 modulo 60: 1/16 q phi1^3 phi2 q congruent 19 modulo 60: 1/16 q phi1^3 phi2 q congruent 21 modulo 60: 1/16 q phi1^3 phi2 q congruent 23 modulo 60: 1/16 q phi1^3 phi2 q congruent 25 modulo 60: 1/16 q phi1^3 phi2 q congruent 27 modulo 60: 1/16 q phi1^3 phi2 q congruent 29 modulo 60: 1/16 q phi1^3 phi2 q congruent 31 modulo 60: 1/16 q phi1^3 phi2 q congruent 32 modulo 60: 1/16 q^4 ( q-2 ) q congruent 37 modulo 60: 1/16 q phi1^3 phi2 q congruent 41 modulo 60: 1/16 q phi1^3 phi2 q congruent 43 modulo 60: 1/16 q phi1^3 phi2 q congruent 47 modulo 60: 1/16 q phi1^3 phi2 q congruent 49 modulo 60: 1/16 q phi1^3 phi2 q congruent 53 modulo 60: 1/16 q phi1^3 phi2 q congruent 59 modulo 60: 1/16 q phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 71, 20, 76, 98, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 8 ], [ 21, 1, 2, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 8 ], [ 30, 1, 4, 8 ], [ 37, 1, 2, 4 ], [ 37, 1, 3, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 8 ], [ 41, 1, 5, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 48, 1, 9, 8 ], [ 48, 1, 10, 8 ], [ 54, 1, 9, 16 ], [ 59, 1, 16, 16 ] ] k = 31: F-action on Pi is () [63,1,31] Dynkin type is A_3(q) + T(phi1^2 phi2 phi4) Order of center |Z^F|: phi1^2 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 2 modulo 60: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 3 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 5 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 9 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 17 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 37 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 76, 97, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 1, 8 ], [ 21, 1, 1, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 4 ], [ 30, 1, 2, 8 ], [ 37, 1, 1, 8 ], [ 37, 1, 2, 4 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 8 ], [ 41, 1, 5, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 48, 1, 7, 8 ], [ 48, 1, 8, 8 ], [ 54, 1, 4, 16 ], [ 59, 1, 16, 16 ] ] k = 32: F-action on Pi is () [63,1,32] Dynkin type is A_3(q) + T(phi1^2 phi2^3) Order of center |Z^F|: phi1^2 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 2 modulo 60: 1/64 q^2 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) q congruent 4 modulo 60: 1/64 q^2 ( q^3-6*q^2+12*q-8 ) q congruent 5 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 7 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) q congruent 8 modulo 60: 1/64 q^2 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 11 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) q congruent 13 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 16 modulo 60: 1/64 q^2 ( q^3-6*q^2+12*q-8 ) q congruent 17 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 19 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) q congruent 21 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 23 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) q congruent 25 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 27 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) q congruent 29 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 31 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) q congruent 32 modulo 60: 1/64 q^2 ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 41 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 43 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) q congruent 47 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) q congruent 49 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 53 modulo 60: 1/64 phi1^2 ( q^3-4*q^2+3*q-4 ) q congruent 59 modulo 60: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 69, 81, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 12 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 24 ], [ 16, 1, 1, 8 ], [ 16, 1, 4, 16 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 24 ], [ 22, 1, 2, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 18 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 16 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 12 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 16 ], [ 34, 1, 2, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 16 ], [ 35, 1, 3, 24 ], [ 35, 1, 4, 16 ], [ 37, 1, 2, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 2, 16 ], [ 40, 1, 3, 16 ], [ 40, 1, 6, 48 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 16 ], [ 41, 1, 9, 48 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 43, 1, 8, 16 ], [ 43, 1, 12, 32 ], [ 44, 1, 2, 8 ], [ 44, 1, 5, 16 ], [ 44, 1, 8, 48 ], [ 48, 1, 2, 16 ], [ 48, 1, 3, 32 ], [ 50, 1, 5, 32 ], [ 51, 1, 3, 32 ], [ 51, 1, 5, 32 ], [ 52, 1, 3, 16 ], [ 52, 1, 4, 16 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ], [ 53, 1, 3, 16 ], [ 53, 1, 4, 32 ], [ 53, 1, 9, 32 ], [ 56, 1, 5, 32 ], [ 56, 1, 7, 32 ], [ 56, 1, 10, 32 ], [ 59, 1, 13, 96 ], [ 59, 1, 22, 32 ] ] k = 33: F-action on Pi is () [63,1,33] Dynkin type is A_3(q) + T(phi1^4 phi2) Order of center |Z^F|: phi1^4 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+512 ) q congruent 2 modulo 60: 1/192 q ( q^4-22*q^3+172*q^2-552*q+576 ) q congruent 3 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+927*q-360 ) q congruent 4 modulo 60: 1/192 q ( q^4-22*q^3+172*q^2-552*q+608 ) q congruent 5 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+480 ) q congruent 7 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+959*q-392 ) q congruent 8 modulo 60: 1/192 q ( q^4-22*q^3+172*q^2-552*q+576 ) q congruent 9 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+480 ) q congruent 11 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+927*q-360 ) q congruent 13 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+512 ) q congruent 16 modulo 60: 1/192 q ( q^4-22*q^3+172*q^2-552*q+608 ) q congruent 17 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+480 ) q congruent 19 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+959*q-392 ) q congruent 21 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+480 ) q congruent 23 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+927*q-360 ) q congruent 25 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+512 ) q congruent 27 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+927*q-360 ) q congruent 29 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+480 ) q congruent 31 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+959*q-392 ) q congruent 32 modulo 60: 1/192 q ( q^4-22*q^3+172*q^2-552*q+576 ) q congruent 37 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+512 ) q congruent 41 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+480 ) q congruent 43 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+959*q-392 ) q congruent 47 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+927*q-360 ) q congruent 49 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+512 ) q congruent 53 modulo 60: 1/192 phi1 ( q^4-21*q^3+155*q^2-471*q+480 ) q congruent 59 modulo 60: 1/192 ( q^5-22*q^4+176*q^3-626*q^2+927*q-360 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 68, 77, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 20 ], [ 4, 1, 1, 34 ], [ 5, 1, 1, 32 ], [ 6, 1, 1, 40 ], [ 7, 1, 1, 28 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 14 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 36 ], [ 12, 1, 1, 68 ], [ 13, 1, 1, 72 ], [ 14, 1, 1, 64 ], [ 15, 1, 1, 64 ], [ 16, 1, 1, 40 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 72 ], [ 20, 1, 1, 56 ], [ 20, 1, 2, 8 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 64 ], [ 22, 1, 2, 16 ], [ 23, 1, 1, 30 ], [ 24, 1, 1, 50 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 84 ], [ 26, 1, 1, 48 ], [ 26, 1, 3, 8 ], [ 27, 1, 1, 48 ], [ 27, 1, 2, 24 ], [ 28, 1, 1, 84 ], [ 28, 1, 2, 60 ], [ 29, 1, 1, 96 ], [ 29, 1, 2, 32 ], [ 30, 1, 1, 96 ], [ 31, 1, 1, 64 ], [ 31, 1, 2, 16 ], [ 34, 1, 1, 96 ], [ 34, 1, 2, 48 ], [ 35, 1, 1, 72 ], [ 35, 1, 3, 24 ], [ 36, 1, 1, 96 ], [ 36, 1, 2, 32 ], [ 37, 1, 1, 96 ], [ 39, 1, 1, 72 ], [ 39, 1, 4, 28 ], [ 40, 1, 1, 144 ], [ 41, 1, 1, 144 ], [ 41, 1, 6, 72 ], [ 42, 1, 1, 96 ], [ 42, 1, 4, 48 ], [ 43, 1, 1, 96 ], [ 43, 1, 2, 16 ], [ 44, 1, 1, 48 ], [ 44, 1, 2, 120 ], [ 45, 1, 1, 96 ], [ 45, 1, 2, 96 ], [ 48, 1, 1, 96 ], [ 48, 1, 2, 48 ], [ 50, 1, 1, 96 ], [ 50, 1, 2, 96 ], [ 50, 1, 4, 96 ], [ 51, 1, 1, 96 ], [ 51, 1, 2, 32 ], [ 52, 1, 1, 144 ], [ 52, 1, 2, 144 ], [ 53, 1, 1, 96 ], [ 53, 1, 3, 48 ], [ 54, 1, 2, 192 ], [ 56, 1, 1, 96 ], [ 56, 1, 2, 96 ], [ 56, 1, 6, 96 ], [ 59, 1, 12, 288 ] ] k = 34: F-action on Pi is (1,4) [63,1,34] Dynkin type is ^2A_3(q) + T(phi1^2 phi2^3) Order of center |Z^F|: phi1^2 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 2 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 4 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 7 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 8 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 11 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 13 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 16 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 19 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 21 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 23 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 25 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 27 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 29 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 31 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 32 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 41 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 43 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 47 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 49 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 53 modulo 60: 1/64 phi1^4 ( q-4 ) q congruent 59 modulo 60: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 69, 7, 31, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 10 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 3, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 16 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 12 ], [ 26, 1, 2, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 8 ], [ 29, 1, 3, 32 ], [ 30, 1, 3, 16 ], [ 30, 1, 4, 32 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 4, 16 ], [ 35, 1, 6, 16 ], [ 35, 1, 8, 16 ], [ 36, 1, 3, 32 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 32 ], [ 41, 1, 6, 32 ], [ 41, 1, 9, 16 ], [ 42, 1, 2, 32 ], [ 43, 1, 4, 32 ], [ 44, 1, 5, 32 ], [ 44, 1, 8, 16 ], [ 44, 1, 9, 32 ], [ 45, 1, 5, 32 ], [ 48, 1, 4, 16 ], [ 48, 1, 5, 16 ], [ 48, 1, 6, 16 ], [ 48, 1, 10, 32 ], [ 50, 1, 8, 32 ], [ 50, 1, 11, 32 ], [ 51, 1, 8, 32 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ], [ 53, 1, 8, 32 ], [ 54, 1, 13, 64 ], [ 56, 1, 13, 32 ], [ 56, 1, 18, 32 ], [ 59, 1, 3, 64 ] ] k = 35: F-action on Pi is (1,4) [63,1,35] Dynkin type is ^2A_3(q) + T(phi1^3 phi2^2) Order of center |Z^F|: phi1^3 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 2 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) q congruent 4 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 7 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) q congruent 8 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 11 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) q congruent 13 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 16 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 19 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) q congruent 21 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 23 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) q congruent 25 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 27 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) q congruent 29 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 31 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) q congruent 32 modulo 60: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 41 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 43 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) q congruent 47 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) q congruent 49 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 53 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 59 modulo 60: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 7, 68, 82, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 3, 24 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 16 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 2, 16 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 4 ], [ 31, 1, 3, 16 ], [ 34, 1, 3, 16 ], [ 35, 1, 5, 16 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 8 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 8 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 16 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 16 ], [ 42, 1, 2, 16 ], [ 43, 1, 3, 32 ], [ 43, 1, 4, 16 ], [ 43, 1, 8, 16 ], [ 44, 1, 2, 48 ], [ 44, 1, 8, 8 ], [ 44, 1, 9, 16 ], [ 48, 1, 4, 32 ], [ 48, 1, 5, 16 ], [ 50, 1, 8, 32 ], [ 51, 1, 6, 32 ], [ 51, 1, 10, 32 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ], [ 52, 1, 3, 16 ], [ 52, 1, 4, 16 ], [ 53, 1, 6, 32 ], [ 53, 1, 7, 32 ], [ 53, 1, 8, 16 ], [ 56, 1, 13, 32 ], [ 56, 1, 14, 32 ], [ 56, 1, 19, 32 ], [ 59, 1, 12, 96 ], [ 59, 1, 22, 32 ] ] k = 36: F-action on Pi is (1,4) [63,1,36] Dynkin type is ^2A_3(q) + T(phi1 phi2^4) Order of center |Z^F|: phi1 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^4-15*q^3+81*q^2-205*q+234 ) q congruent 2 modulo 60: 1/192 ( q^5-16*q^4+92*q^3-224*q^2+224*q-64 ) q congruent 3 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+463*q-354 ) q congruent 4 modulo 60: 1/192 q ( q^4-16*q^3+92*q^2-224*q+192 ) q congruent 5 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+471*q-330 ) q congruent 7 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+463*q-354 ) q congruent 8 modulo 60: 1/192 ( q^5-16*q^4+92*q^3-224*q^2+224*q-64 ) q congruent 9 modulo 60: 1/192 phi1 ( q^4-15*q^3+81*q^2-205*q+234 ) q congruent 11 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+495*q-450 ) q congruent 13 modulo 60: 1/192 phi1 ( q^4-15*q^3+81*q^2-205*q+234 ) q congruent 16 modulo 60: 1/192 q ( q^4-16*q^3+92*q^2-224*q+192 ) q congruent 17 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+471*q-330 ) q congruent 19 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+463*q-354 ) q congruent 21 modulo 60: 1/192 phi1 ( q^4-15*q^3+81*q^2-205*q+234 ) q congruent 23 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+495*q-450 ) q congruent 25 modulo 60: 1/192 phi1 ( q^4-15*q^3+81*q^2-205*q+234 ) q congruent 27 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+463*q-354 ) q congruent 29 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+471*q-330 ) q congruent 31 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+463*q-354 ) q congruent 32 modulo 60: 1/192 ( q^5-16*q^4+92*q^3-224*q^2+224*q-64 ) q congruent 37 modulo 60: 1/192 phi1 ( q^4-15*q^3+81*q^2-205*q+234 ) q congruent 41 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+471*q-330 ) q congruent 43 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+463*q-354 ) q congruent 47 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+495*q-450 ) q congruent 49 modulo 60: 1/192 phi1 ( q^4-15*q^3+81*q^2-205*q+234 ) q congruent 53 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+471*q-330 ) q congruent 59 modulo 60: 1/192 ( q^5-16*q^4+96*q^3-286*q^2+495*q-450 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 69, 78, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 20 ], [ 4, 1, 2, 34 ], [ 5, 1, 2, 32 ], [ 6, 1, 2, 40 ], [ 7, 1, 2, 28 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 14 ], [ 11, 1, 2, 36 ], [ 12, 1, 2, 68 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 64 ], [ 15, 1, 2, 64 ], [ 16, 1, 3, 40 ], [ 18, 1, 2, 64 ], [ 19, 1, 2, 72 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 56 ], [ 21, 1, 2, 48 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 64 ], [ 23, 1, 2, 30 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 50 ], [ 25, 1, 3, 84 ], [ 26, 1, 2, 8 ], [ 26, 1, 4, 48 ], [ 27, 1, 3, 24 ], [ 27, 1, 6, 48 ], [ 28, 1, 3, 60 ], [ 28, 1, 4, 84 ], [ 29, 1, 3, 32 ], [ 29, 1, 4, 96 ], [ 30, 1, 3, 96 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 64 ], [ 34, 1, 3, 48 ], [ 34, 1, 4, 96 ], [ 35, 1, 6, 24 ], [ 35, 1, 8, 72 ], [ 36, 1, 3, 32 ], [ 36, 1, 4, 96 ], [ 37, 1, 3, 96 ], [ 39, 1, 3, 72 ], [ 39, 1, 4, 28 ], [ 40, 1, 6, 144 ], [ 41, 1, 6, 72 ], [ 41, 1, 9, 144 ], [ 42, 1, 2, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 4, 16 ], [ 43, 1, 13, 96 ], [ 44, 1, 8, 120 ], [ 44, 1, 10, 48 ], [ 45, 1, 5, 96 ], [ 45, 1, 6, 96 ], [ 48, 1, 5, 48 ], [ 48, 1, 6, 96 ], [ 50, 1, 9, 96 ], [ 50, 1, 11, 96 ], [ 50, 1, 12, 96 ], [ 51, 1, 8, 32 ], [ 51, 1, 9, 96 ], [ 52, 1, 9, 144 ], [ 52, 1, 10, 144 ], [ 53, 1, 8, 48 ], [ 53, 1, 20, 96 ], [ 54, 1, 12, 192 ], [ 56, 1, 15, 96 ], [ 56, 1, 18, 96 ], [ 56, 1, 20, 96 ], [ 59, 1, 13, 288 ] ] i = 64: Pi = [ 1, 2 ] j = 1: Omega trivial k = 1: F-action on Pi is () [64,1,1] Dynkin type is A_1(q) + A_1(q) + T(phi1^6) Order of center |Z^F|: phi1^6 Numbers of classes in class type: q congruent 1 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+267471*q^2-1134914*q+2188517 ) q congruent 2 modulo 60: 1/46080 ( q^6-74*q^5+2172*q^4-31928*q^3+242176*q^2-856704*q+967680 ) q congruent 3 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1078434*q+1569285 ) q congruent 4 modulo 60: 1/46080 ( q^6-74*q^5+2172*q^4-31928*q^3+243456*q^2-900224*q+1264640 ) q congruent 5 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1091394*q+1769445 ) q congruent 7 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+267471*q^2-1121954*q+1923845 ) q congruent 8 modulo 60: 1/46080 ( q^6-74*q^5+2172*q^4-31928*q^3+242176*q^2-856704*q+967680 ) q congruent 9 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1091394*q+1769445 ) q congruent 11 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1078434*q+1633797 ) q congruent 13 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+267471*q^2-1134914*q+2124005 ) q congruent 16 modulo 60: 1/46080 ( q^6-74*q^5+2172*q^4-31928*q^3+243456*q^2-900224*q+1329152 ) q congruent 17 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1091394*q+1769445 ) q congruent 19 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+267471*q^2-1121954*q+1923845 ) q congruent 21 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1091394*q+1833957 ) q congruent 23 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1078434*q+1569285 ) q congruent 25 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+267471*q^2-1134914*q+2124005 ) q congruent 27 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1078434*q+1569285 ) q congruent 29 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1091394*q+1769445 ) q congruent 31 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+267471*q^2-1121954*q+1988357 ) q congruent 32 modulo 60: 1/46080 ( q^6-74*q^5+2172*q^4-31928*q^3+242176*q^2-856704*q+967680 ) q congruent 37 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+267471*q^2-1134914*q+2124005 ) q congruent 41 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1091394*q+1833957 ) q congruent 43 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+267471*q^2-1121954*q+1923845 ) q congruent 47 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1078434*q+1569285 ) q congruent 49 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+267471*q^2-1134914*q+2124005 ) q congruent 53 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1091394*q+1769445 ) q congruent 59 modulo 60: 1/46080 ( q^6-74*q^5+2187*q^4-32948*q^3+266191*q^2-1078434*q+1569285 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 66, 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 32 ], [ 3, 1, 1, 224 ], [ 4, 1, 1, 772 ], [ 5, 1, 1, 1664 ], [ 6, 1, 1, 2304 ], [ 7, 1, 1, 544 ], [ 8, 1, 1, 192 ], [ 9, 1, 1, 31 ], [ 10, 1, 1, 60 ], [ 11, 1, 1, 544 ], [ 12, 1, 1, 2080 ], [ 13, 1, 1, 2664 ], [ 14, 1, 1, 4992 ], [ 15, 1, 1, 7424 ], [ 16, 1, 1, 12800 ], [ 17, 1, 1, 15360 ], [ 18, 1, 1, 2304 ], [ 19, 1, 1, 4864 ], [ 20, 1, 1, 8640 ], [ 21, 1, 1, 960 ], [ 22, 1, 1, 3840 ], [ 23, 1, 1, 252 ], [ 24, 1, 1, 900 ], [ 25, 1, 1, 3720 ], [ 26, 1, 1, 960 ], [ 27, 1, 1, 960 ], [ 28, 1, 1, 4320 ], [ 29, 1, 1, 11520 ], [ 30, 1, 1, 13824 ], [ 31, 1, 1, 19200 ], [ 32, 1, 1, 28160 ], [ 33, 1, 1, 34560 ], [ 34, 1, 1, 7680 ], [ 35, 1, 1, 23040 ], [ 36, 1, 1, 3840 ], [ 37, 1, 1, 13440 ], [ 38, 1, 1, 23040 ], [ 39, 1, 1, 1560 ], [ 40, 1, 1, 8640 ], [ 41, 1, 1, 10320 ], [ 42, 1, 1, 7680 ], [ 43, 1, 1, 13440 ], [ 44, 1, 1, 6720 ], [ 45, 1, 1, 19200 ], [ 46, 1, 1, 38400 ], [ 47, 1, 1, 46080 ], [ 48, 1, 1, 30720 ], [ 49, 1, 1, 57600 ], [ 50, 1, 1, 11520 ], [ 51, 1, 1, 26880 ], [ 52, 1, 1, 14400 ], [ 53, 1, 1, 30720 ], [ 54, 1, 1, 23040 ], [ 55, 1, 1, 53760 ], [ 56, 1, 1, 34560 ], [ 57, 1, 1, 69120 ], [ 58, 1, 1, 46080 ], [ 59, 1, 1, 17280 ], [ 60, 1, 1, 69120 ], [ 61, 1, 1, 46080 ], [ 62, 1, 1, 69120 ], [ 63, 1, 1, 23040 ] ] k = 2: F-action on Pi is () [64,1,2] Dynkin type is A_1(q) + A_1(q) + T(phi1^2 phi5) Order of center |Z^F|: phi1^2 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 2 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 13 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 17 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 23 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 32 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 43 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 23, 93, 93, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 15, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 4 ], [ 23, 1, 1, 2 ], [ 30, 1, 1, 4 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 20 ], [ 63, 1, 2, 10 ] ] k = 3: F-action on Pi is (1,2) [64,1,3] Dynkin type is A_1(q^2) + T(phi1 phi2 phi5) Order of center |Z^F|: phi1 phi2 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 2 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 3 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 4 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 5 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 7 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 8 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 9 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 11 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 13 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 16 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 17 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 19 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 21 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 23 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 25 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 27 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 29 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 31 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 32 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 37 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 41 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 43 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 47 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 49 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 53 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 59 modulo 60: 1/20 q^2 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 50, 107 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], [ 14, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 30, 1, 2, 4 ], [ 54, 1, 6, 10 ], [ 63, 1, 2, 10 ] ] k = 4: F-action on Pi is (1,2) [64,1,4] Dynkin type is A_1(q^2) + T(phi1 phi2 phi10) Order of center |Z^F|: phi1 phi2 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 17 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 51, 108 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 30, 1, 4, 4 ], [ 54, 1, 8, 10 ], [ 63, 1, 3, 10 ] ] k = 5: F-action on Pi is () [64,1,5] Dynkin type is A_1(q) + A_1(q) + T(phi2^2 phi10) Order of center |Z^F|: phi2^2 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 2 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 3 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 4 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 5 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 7 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 8 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 9 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 11 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 13 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 16 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 17 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 19 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 21 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 23 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 25 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 27 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 29 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 31 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 32 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 37 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 41 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 43 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 47 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 49 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 53 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 59 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) Fusion of maximal tori of C^F in those of G^F: [ 51, 94, 94, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 30, 1, 3, 4 ], [ 54, 1, 8, 10 ], [ 61, 1, 3, 20 ], [ 63, 1, 3, 10 ] ] k = 6: F-action on Pi is () [64,1,6] Dynkin type is A_1(q) + A_1(q) + T(phi1^4 phi3) Order of center |Z^F|: phi1^4 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 phi1 ( q^5-19*q^4+119*q^3-237*q^2-144*q+616 ) q congruent 2 modulo 60: 1/288 q phi2 ( q^4-21*q^3+156*q^2-476*q+480 ) q congruent 3 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 4 modulo 60: 1/288 phi1 ( q^5-19*q^4+116*q^3-204*q^2-192*q+448 ) q congruent 5 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 7 modulo 60: 1/288 phi1 ( q^5-19*q^4+119*q^3-237*q^2-144*q+616 ) q congruent 8 modulo 60: 1/288 q phi2 ( q^4-21*q^3+156*q^2-476*q+480 ) q congruent 9 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 11 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 13 modulo 60: 1/288 phi1 ( q^5-19*q^4+119*q^3-237*q^2-144*q+616 ) q congruent 16 modulo 60: 1/288 phi1 ( q^5-19*q^4+116*q^3-204*q^2-192*q+448 ) q congruent 17 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 19 modulo 60: 1/288 phi1 ( q^5-19*q^4+119*q^3-237*q^2-144*q+616 ) q congruent 21 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 23 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 25 modulo 60: 1/288 phi1 ( q^5-19*q^4+119*q^3-237*q^2-144*q+616 ) q congruent 27 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 29 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 31 modulo 60: 1/288 phi1 ( q^5-19*q^4+119*q^3-237*q^2-144*q+616 ) q congruent 32 modulo 60: 1/288 q phi2 ( q^4-21*q^3+156*q^2-476*q+480 ) q congruent 37 modulo 60: 1/288 phi1 ( q^5-19*q^4+119*q^3-237*q^2-144*q+616 ) q congruent 41 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 43 modulo 60: 1/288 phi1 ( q^5-19*q^4+119*q^3-237*q^2-144*q+616 ) q congruent 47 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 49 modulo 60: 1/288 phi1 ( q^5-19*q^4+119*q^3-237*q^2-144*q+616 ) q congruent 53 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 59 modulo 60: 1/288 q phi2 ( q^4-21*q^3+159*q^2-515*q+600 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 77, 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 26 ], [ 4, 1, 1, 46 ], [ 5, 1, 1, 80 ], [ 6, 1, 1, 96 ], [ 7, 1, 1, 40 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 40 ], [ 12, 1, 1, 70 ], [ 13, 1, 1, 72 ], [ 14, 1, 1, 120 ], [ 15, 1, 1, 152 ], [ 16, 1, 1, 176 ], [ 17, 1, 1, 240 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 112 ], [ 20, 1, 1, 144 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 120 ], [ 23, 1, 1, 18 ], [ 24, 1, 1, 36 ], [ 25, 1, 1, 60 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 72 ], [ 29, 1, 1, 144 ], [ 30, 1, 1, 144 ], [ 31, 1, 1, 168 ], [ 32, 1, 1, 224 ], [ 33, 1, 1, 144 ], [ 34, 1, 1, 96 ], [ 35, 1, 1, 144 ], [ 36, 1, 1, 48 ], [ 37, 1, 1, 96 ], [ 38, 1, 1, 288 ], [ 38, 1, 3, 144 ], [ 39, 1, 1, 24 ], [ 40, 1, 1, 36 ], [ 41, 1, 1, 48 ], [ 42, 1, 1, 96 ], [ 42, 1, 3, 48 ], [ 43, 1, 1, 96 ], [ 44, 1, 1, 48 ], [ 44, 1, 3, 42 ], [ 45, 1, 1, 96 ], [ 45, 1, 3, 120 ], [ 46, 1, 1, 192 ], [ 46, 1, 3, 240 ], [ 47, 1, 1, 144 ], [ 48, 1, 1, 96 ], [ 50, 1, 3, 72 ], [ 51, 1, 1, 48 ], [ 53, 1, 1, 96 ], [ 53, 1, 16, 192 ], [ 54, 1, 3, 144 ], [ 55, 1, 1, 96 ], [ 55, 1, 3, 336 ], [ 56, 1, 3, 216 ], [ 58, 1, 3, 288 ], [ 59, 1, 4, 108 ], [ 60, 1, 2, 432 ], [ 61, 1, 4, 288 ], [ 62, 1, 2, 432 ], [ 63, 1, 4, 144 ] ] k = 7: F-action on Pi is () [64,1,7] Dynkin type is A_1(q) + A_1(q) + T(phi1^2 phi3^2) Order of center |Z^F|: phi1^2 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 phi2 ( q^4-2*q^3-2*q^2-4*q+4 ) q congruent 2 modulo 60: 1/72 q^2 phi2^2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 4 modulo 60: 1/72 phi1 ( q^5-q^4-4*q^3-8 ) q congruent 5 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 7 modulo 60: 1/72 phi1 phi2 ( q^4-2*q^3-2*q^2-4*q+4 ) q congruent 8 modulo 60: 1/72 q^2 phi2^2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 11 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 13 modulo 60: 1/72 phi1 phi2 ( q^4-2*q^3-2*q^2-4*q+4 ) q congruent 16 modulo 60: 1/72 phi1 ( q^5-q^4-4*q^3-8 ) q congruent 17 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 19 modulo 60: 1/72 phi1 phi2 ( q^4-2*q^3-2*q^2-4*q+4 ) q congruent 21 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 23 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 25 modulo 60: 1/72 phi1 phi2 ( q^4-2*q^3-2*q^2-4*q+4 ) q congruent 27 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 29 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 31 modulo 60: 1/72 phi1 phi2 ( q^4-2*q^3-2*q^2-4*q+4 ) q congruent 32 modulo 60: 1/72 q^2 phi2^2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/72 phi1 phi2 ( q^4-2*q^3-2*q^2-4*q+4 ) q congruent 41 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 43 modulo 60: 1/72 phi1 phi2 ( q^4-2*q^3-2*q^2-4*q+4 ) q congruent 47 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 49 modulo 60: 1/72 phi1 phi2 ( q^4-2*q^3-2*q^2-4*q+4 ) q congruent 53 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) q congruent 59 modulo 60: 1/72 q phi2 ( q^4-3*q^3-2*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 83, 83, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 27, 1, 5, 12 ], [ 32, 1, 1, 8 ], [ 33, 1, 3, 36 ], [ 38, 1, 3, 72 ], [ 40, 1, 5, 36 ], [ 42, 1, 3, 24 ], [ 44, 1, 3, 12 ], [ 45, 1, 3, 24 ], [ 46, 1, 3, 48 ], [ 49, 1, 3, 36 ], [ 52, 1, 6, 36 ], [ 53, 1, 16, 24 ], [ 55, 1, 3, 24 ], [ 58, 1, 8, 72 ], [ 61, 1, 5, 72 ] ] k = 8: F-action on Pi is () [64,1,8] Dynkin type is A_1(q) + A_1(q) + T(phi1^2 phi2^2 phi3) Order of center |Z^F|: phi1^2 phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 30, 81, 81, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 12, 1, 1, 6 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 8 ], [ 20, 1, 2, 48 ], [ 22, 1, 2, 8 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 27, 1, 5, 6 ], [ 28, 1, 2, 24 ], [ 31, 1, 2, 24 ], [ 33, 1, 1, 48 ], [ 33, 1, 2, 16 ], [ 35, 1, 3, 48 ], [ 37, 1, 2, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 40, 1, 1, 12 ], [ 40, 1, 3, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 3, 24 ], [ 43, 1, 8, 16 ], [ 43, 1, 12, 32 ], [ 44, 1, 3, 18 ], [ 44, 1, 5, 16 ], [ 47, 1, 2, 48 ], [ 48, 1, 3, 32 ], [ 50, 1, 6, 24 ], [ 51, 1, 5, 16 ], [ 51, 1, 6, 16 ], [ 53, 1, 9, 32 ], [ 53, 1, 16, 72 ], [ 53, 1, 17, 24 ], [ 55, 1, 5, 32 ], [ 56, 1, 8, 72 ], [ 59, 1, 4, 36 ], [ 59, 1, 19, 24 ], [ 60, 1, 2, 144 ], [ 60, 1, 11, 48 ], [ 62, 1, 5, 144 ], [ 63, 1, 5, 48 ], [ 63, 1, 13, 48 ] ] k = 9: F-action on Pi is (1,2) [64,1,9] Dynkin type is A_1(q^2) + T(phi1^2 phi3 phi4) Order of center |Z^F|: phi1^2 phi3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 2 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 4 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 7 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 8 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 11 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 13 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 16 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 19 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 21 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 23 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 25 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 27 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 29 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 31 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 32 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 41 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 43 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 47 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 49 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 53 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 59 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 97, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 3, 8 ], [ 16, 1, 2, 8 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 33, 1, 4, 16 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 12 ], [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 3, 18 ], [ 44, 1, 6, 8 ], [ 48, 1, 8, 16 ], [ 51, 1, 7, 8 ], [ 53, 1, 10, 16 ], [ 53, 1, 17, 24 ], [ 55, 1, 6, 16 ], [ 59, 1, 4, 36 ], [ 60, 1, 5, 48 ], [ 63, 1, 7, 24 ] ] k = 10: F-action on Pi is () [64,1,10] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2 phi3 phi4) Order of center |Z^F|: phi1 phi2 phi3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 2 modulo 60: 1/48 q^4 phi1 phi2 q congruent 3 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 4 modulo 60: 1/48 q^4 phi1 phi2 q congruent 5 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 7 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 8 modulo 60: 1/48 q^4 phi1 phi2 q congruent 9 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 11 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 13 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 16 modulo 60: 1/48 q^4 phi1 phi2 q congruent 17 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 19 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 21 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 23 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 25 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 27 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 29 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 31 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 32 modulo 60: 1/48 q^4 phi1 phi2 q congruent 37 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 41 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 43 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 47 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 49 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 53 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 59 modulo 60: 1/48 q^2 phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 97, 59, 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 33, 1, 2, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 8, 8 ], [ 42, 1, 3, 12 ], [ 43, 1, 9, 8 ], [ 44, 1, 3, 6 ], [ 44, 1, 4, 8 ], [ 51, 1, 7, 8 ], [ 53, 1, 11, 16 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 12 ], [ 55, 1, 4, 16 ], [ 59, 1, 19, 12 ], [ 60, 1, 11, 24 ], [ 63, 1, 7, 24 ] ] k = 11: F-action on Pi is () [64,1,11] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2 phi4 phi6) Order of center |Z^F|: phi1 phi2 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 2 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 4 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 7 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 8 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 11 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 13 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 16 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 19 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 21 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 23 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 25 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 27 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 29 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 31 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 32 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 41 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 43 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 47 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 49 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 53 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 59 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 96, 60, 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 33, 1, 6, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 8, 8 ], [ 42, 1, 5, 12 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 44, 1, 7, 6 ], [ 51, 1, 4, 8 ], [ 53, 1, 13, 16 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 12 ], [ 55, 1, 11, 16 ], [ 59, 1, 20, 12 ], [ 60, 1, 10, 24 ], [ 63, 1, 6, 24 ] ] k = 12: F-action on Pi is (1,2) [64,1,12] Dynkin type is A_1(q^2) + T(phi2^2 phi4 phi6) Order of center |Z^F|: phi2^2 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 2 modulo 60: 1/48 q^4 phi1 phi2 q congruent 3 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 4 modulo 60: 1/48 q^4 phi1 phi2 q congruent 5 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 7 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 8 modulo 60: 1/48 q^4 phi1 phi2 q congruent 9 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 11 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 13 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 16 modulo 60: 1/48 q^4 phi1 phi2 q congruent 17 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 19 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 21 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 23 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 25 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 27 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 29 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 31 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 32 modulo 60: 1/48 q^4 phi1 phi2 q congruent 37 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 41 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 43 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 47 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 49 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 53 modulo 60: 1/48 q^2 phi1^2 phi2^2 q congruent 59 modulo 60: 1/48 q^2 phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 98, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 2, 8 ], [ 16, 1, 4, 8 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], [ 33, 1, 10, 16 ], [ 39, 1, 5, 4 ], [ 40, 1, 6, 12 ], [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 7, 18 ], [ 48, 1, 9, 16 ], [ 51, 1, 4, 8 ], [ 53, 1, 14, 16 ], [ 53, 1, 15, 24 ], [ 55, 1, 19, 16 ], [ 59, 1, 5, 36 ], [ 60, 1, 9, 48 ], [ 63, 1, 6, 24 ] ] k = 13: F-action on Pi is (1,2) [64,1,13] Dynkin type is A_1(q^2) + T(phi1 phi2^3 phi3) Order of center |Z^F|: phi1 phi2^3 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 phi1^2 ( q^4-4*q^3-3*q^2+10*q+24 ) q congruent 2 modulo 60: 1/288 q phi2 ( q^4-7*q^3+10*q^2+8*q-16 ) q congruent 3 modulo 60: 1/288 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 4 modulo 60: 1/288 q phi1 ( q^4-5*q^3-2*q^2+16*q+32 ) q congruent 5 modulo 60: 1/288 q phi2^2 ( q^3-8*q^2+21*q-22 ) q congruent 7 modulo 60: 1/288 phi1^2 ( q^4-4*q^3-3*q^2+10*q+24 ) q congruent 8 modulo 60: 1/288 q phi2 ( q^4-7*q^3+10*q^2+8*q-16 ) q congruent 9 modulo 60: 1/288 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 11 modulo 60: 1/288 q phi2^2 ( q^3-8*q^2+21*q-22 ) q congruent 13 modulo 60: 1/288 phi1^2 ( q^4-4*q^3-3*q^2+10*q+24 ) q congruent 16 modulo 60: 1/288 q phi1 ( q^4-5*q^3-2*q^2+16*q+32 ) q congruent 17 modulo 60: 1/288 q phi2^2 ( q^3-8*q^2+21*q-22 ) q congruent 19 modulo 60: 1/288 phi1^2 ( q^4-4*q^3-3*q^2+10*q+24 ) q congruent 21 modulo 60: 1/288 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 23 modulo 60: 1/288 q phi2^2 ( q^3-8*q^2+21*q-22 ) q congruent 25 modulo 60: 1/288 phi1^2 ( q^4-4*q^3-3*q^2+10*q+24 ) q congruent 27 modulo 60: 1/288 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 29 modulo 60: 1/288 q phi2^2 ( q^3-8*q^2+21*q-22 ) q congruent 31 modulo 60: 1/288 phi1^2 ( q^4-4*q^3-3*q^2+10*q+24 ) q congruent 32 modulo 60: 1/288 q phi2 ( q^4-7*q^3+10*q^2+8*q-16 ) q congruent 37 modulo 60: 1/288 phi1^2 ( q^4-4*q^3-3*q^2+10*q+24 ) q congruent 41 modulo 60: 1/288 q phi2^2 ( q^3-8*q^2+21*q-22 ) q congruent 43 modulo 60: 1/288 phi1^2 ( q^4-4*q^3-3*q^2+10*q+24 ) q congruent 47 modulo 60: 1/288 q phi2^2 ( q^3-8*q^2+21*q-22 ) q congruent 49 modulo 60: 1/288 phi1^2 ( q^4-4*q^3-3*q^2+10*q+24 ) q congruent 53 modulo 60: 1/288 q phi2^2 ( q^3-8*q^2+21*q-22 ) q congruent 59 modulo 60: 1/288 q phi2^2 ( q^3-8*q^2+21*q-22 ) Fusion of maximal tori of C^F in those of G^F: [ 27, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 12 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 8 ], [ 13, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 48 ], [ 20, 1, 2, 48 ], [ 22, 1, 2, 24 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 4, 36 ], [ 27, 1, 5, 6 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 2, 24 ], [ 35, 1, 4, 48 ], [ 38, 1, 6, 96 ], [ 38, 1, 9, 48 ], [ 39, 1, 3, 24 ], [ 40, 1, 3, 12 ], [ 41, 1, 10, 48 ], [ 42, 1, 3, 36 ], [ 43, 1, 12, 96 ], [ 44, 1, 3, 6 ], [ 44, 1, 10, 48 ], [ 46, 1, 9, 144 ], [ 47, 1, 4, 48 ], [ 50, 1, 6, 72 ], [ 51, 1, 5, 48 ], [ 53, 1, 16, 36 ], [ 53, 1, 17, 12 ], [ 53, 1, 19, 96 ], [ 55, 1, 10, 96 ], [ 55, 1, 18, 48 ], [ 56, 1, 8, 72 ], [ 58, 1, 27, 288 ], [ 59, 1, 19, 36 ], [ 60, 1, 11, 72 ], [ 62, 1, 11, 144 ], [ 63, 1, 5, 144 ] ] k = 14: F-action on Pi is (1,2) [64,1,14] Dynkin type is A_1(q^2) + T(phi1^3 phi2 phi3) Order of center |Z^F|: phi1^3 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 2 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 4 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 7 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 8 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 11 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 13 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 16 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 19 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 21 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 23 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 25 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 27 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 29 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 31 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 32 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 41 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 43 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 47 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 49 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 53 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 59 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 30, 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 12, 1, 1, 10 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 12 ], [ 18, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 8 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 32 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 4 ], [ 26, 1, 1, 16 ], [ 27, 1, 5, 6 ], [ 28, 1, 3, 8 ], [ 29, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 8 ], [ 33, 1, 2, 8 ], [ 33, 1, 4, 32 ], [ 35, 1, 2, 16 ], [ 36, 1, 1, 16 ], [ 37, 1, 1, 32 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 40, 1, 1, 24 ], [ 40, 1, 3, 4 ], [ 41, 1, 2, 16 ], [ 41, 1, 3, 16 ], [ 42, 1, 3, 12 ], [ 43, 1, 1, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 3, 30 ], [ 44, 1, 9, 16 ], [ 45, 1, 3, 24 ], [ 47, 1, 3, 16 ], [ 48, 1, 7, 32 ], [ 50, 1, 3, 24 ], [ 51, 1, 1, 16 ], [ 51, 1, 6, 16 ], [ 53, 1, 2, 32 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 36 ], [ 54, 1, 3, 48 ], [ 55, 1, 9, 32 ], [ 56, 1, 3, 24 ], [ 59, 1, 4, 72 ], [ 59, 1, 19, 12 ], [ 60, 1, 5, 96 ], [ 60, 1, 11, 24 ], [ 62, 1, 10, 48 ], [ 63, 1, 4, 48 ], [ 63, 1, 13, 48 ] ] k = 15: F-action on Pi is () [64,1,15] Dynkin type is A_1(q) + A_1(q) + T(phi2^4 phi6) Order of center |Z^F|: phi2^4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 2 modulo 60: 1/288 phi2 ( q^5-15*q^4+82*q^3-208*q^2+288*q-192 ) q congruent 3 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 4 modulo 60: 1/288 q^2 phi1 ( q^3-13*q^2+54*q-72 ) q congruent 5 modulo 60: 1/288 phi2 ( q^5-15*q^4+85*q^3-241*q^2+402*q-360 ) q congruent 7 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 8 modulo 60: 1/288 phi2 ( q^5-15*q^4+82*q^3-208*q^2+288*q-192 ) q congruent 9 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 11 modulo 60: 1/288 phi2 ( q^5-15*q^4+85*q^3-241*q^2+402*q-360 ) q congruent 13 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 16 modulo 60: 1/288 q^2 phi1 ( q^3-13*q^2+54*q-72 ) q congruent 17 modulo 60: 1/288 phi2 ( q^5-15*q^4+85*q^3-241*q^2+402*q-360 ) q congruent 19 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 21 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 23 modulo 60: 1/288 phi2 ( q^5-15*q^4+85*q^3-241*q^2+402*q-360 ) q congruent 25 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 27 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 29 modulo 60: 1/288 phi2 ( q^5-15*q^4+85*q^3-241*q^2+402*q-360 ) q congruent 31 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 32 modulo 60: 1/288 phi2 ( q^5-15*q^4+82*q^3-208*q^2+288*q-192 ) q congruent 37 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 41 modulo 60: 1/288 phi2 ( q^5-15*q^4+85*q^3-241*q^2+402*q-360 ) q congruent 43 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 47 modulo 60: 1/288 phi2 ( q^5-15*q^4+85*q^3-241*q^2+402*q-360 ) q congruent 49 modulo 60: 1/288 q phi1^2 ( q^3-12*q^2+45*q-54 ) q congruent 53 modulo 60: 1/288 phi2 ( q^5-15*q^4+85*q^3-241*q^2+402*q-360 ) q congruent 59 modulo 60: 1/288 phi2 ( q^5-15*q^4+85*q^3-241*q^2+402*q-360 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 78, 78, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 26 ], [ 4, 1, 2, 46 ], [ 5, 1, 2, 80 ], [ 6, 1, 2, 96 ], [ 7, 1, 2, 40 ], [ 8, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 40 ], [ 12, 1, 2, 70 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 120 ], [ 15, 1, 2, 152 ], [ 16, 1, 3, 176 ], [ 17, 1, 4, 240 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 112 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 48 ], [ 22, 1, 4, 120 ], [ 23, 1, 2, 18 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 60 ], [ 26, 1, 4, 48 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 72 ], [ 29, 1, 4, 144 ], [ 30, 1, 3, 144 ], [ 31, 1, 4, 168 ], [ 32, 1, 3, 224 ], [ 33, 1, 8, 144 ], [ 34, 1, 4, 96 ], [ 35, 1, 8, 144 ], [ 36, 1, 4, 48 ], [ 37, 1, 3, 96 ], [ 38, 1, 11, 144 ], [ 38, 1, 12, 288 ], [ 39, 1, 3, 24 ], [ 40, 1, 6, 36 ], [ 41, 1, 9, 48 ], [ 42, 1, 5, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 7, 42 ], [ 44, 1, 10, 48 ], [ 45, 1, 4, 120 ], [ 45, 1, 6, 96 ], [ 46, 1, 4, 240 ], [ 46, 1, 6, 192 ], [ 47, 1, 8, 144 ], [ 48, 1, 6, 96 ], [ 50, 1, 10, 72 ], [ 51, 1, 9, 48 ], [ 53, 1, 18, 192 ], [ 53, 1, 20, 96 ], [ 54, 1, 10, 144 ], [ 55, 1, 12, 336 ], [ 55, 1, 15, 96 ], [ 56, 1, 17, 216 ], [ 58, 1, 14, 288 ], [ 59, 1, 5, 108 ], [ 60, 1, 8, 432 ], [ 61, 1, 6, 288 ], [ 62, 1, 7, 432 ], [ 63, 1, 9, 144 ] ] k = 16: F-action on Pi is () [64,1,16] Dynkin type is A_1(q) + A_1(q) + T(phi1^2 phi2^2 phi6) Order of center |Z^F|: phi1^2 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 2 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 4 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 7 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 8 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 11 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 13 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 16 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 19 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 21 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 23 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 25 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 27 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 29 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 31 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 32 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 41 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 43 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 47 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 49 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 53 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 59 modulo 60: 1/96 q phi1 phi2 ( q^3-6*q^2+7*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 82, 82, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 18 ], [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 12, 1, 2, 6 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 24 ], [ 16, 1, 4, 8 ], [ 20, 1, 3, 48 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 27, 1, 4, 6 ], [ 28, 1, 3, 24 ], [ 31, 1, 3, 24 ], [ 33, 1, 6, 16 ], [ 33, 1, 8, 48 ], [ 35, 1, 6, 48 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 40, 1, 2, 8 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 16 ], [ 41, 1, 4, 16 ], [ 42, 1, 5, 24 ], [ 43, 1, 3, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 7, 18 ], [ 44, 1, 9, 16 ], [ 47, 1, 7, 48 ], [ 48, 1, 4, 32 ], [ 50, 1, 7, 24 ], [ 51, 1, 3, 16 ], [ 51, 1, 10, 16 ], [ 53, 1, 6, 32 ], [ 53, 1, 15, 24 ], [ 53, 1, 18, 72 ], [ 55, 1, 14, 32 ], [ 56, 1, 12, 72 ], [ 59, 1, 5, 36 ], [ 59, 1, 20, 24 ], [ 60, 1, 8, 144 ], [ 60, 1, 10, 48 ], [ 62, 1, 6, 144 ], [ 63, 1, 8, 48 ], [ 63, 1, 12, 48 ] ] k = 17: F-action on Pi is (1,2) [64,1,17] Dynkin type is A_1(q^2) + T(phi1^3 phi2 phi6) Order of center |Z^F|: phi1^3 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-136 ) q congruent 2 modulo 60: 1/288 phi2 ( q^5-13*q^4+52*q^3-52*q^2-64*q+96 ) q congruent 3 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-120 ) q congruent 4 modulo 60: 1/288 q phi1 ( q^4-11*q^3+28*q^2+28*q-112 ) q congruent 5 modulo 60: 1/288 phi2 ( q^5-13*q^4+55*q^3-67*q^2-64*q+120 ) q congruent 7 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-136 ) q congruent 8 modulo 60: 1/288 phi2 ( q^5-13*q^4+52*q^3-52*q^2-64*q+96 ) q congruent 9 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-120 ) q congruent 11 modulo 60: 1/288 phi2 ( q^5-13*q^4+55*q^3-67*q^2-64*q+120 ) q congruent 13 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-136 ) q congruent 16 modulo 60: 1/288 q phi1 ( q^4-11*q^3+28*q^2+28*q-112 ) q congruent 17 modulo 60: 1/288 phi2 ( q^5-13*q^4+55*q^3-67*q^2-64*q+120 ) q congruent 19 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-136 ) q congruent 21 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-120 ) q congruent 23 modulo 60: 1/288 phi2 ( q^5-13*q^4+55*q^3-67*q^2-64*q+120 ) q congruent 25 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-136 ) q congruent 27 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-120 ) q congruent 29 modulo 60: 1/288 phi2 ( q^5-13*q^4+55*q^3-67*q^2-64*q+120 ) q congruent 31 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-136 ) q congruent 32 modulo 60: 1/288 phi2 ( q^5-13*q^4+52*q^3-52*q^2-64*q+96 ) q congruent 37 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-136 ) q congruent 41 modulo 60: 1/288 phi2 ( q^5-13*q^4+55*q^3-67*q^2-64*q+120 ) q congruent 43 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-136 ) q congruent 47 modulo 60: 1/288 phi2 ( q^5-13*q^4+55*q^3-67*q^2-64*q+120 ) q congruent 49 modulo 60: 1/288 q phi1 ( q^4-11*q^3+31*q^2+19*q-136 ) q congruent 53 modulo 60: 1/288 phi2 ( q^5-13*q^4+55*q^3-67*q^2-64*q+120 ) q congruent 59 modulo 60: 1/288 phi2 ( q^5-13*q^4+55*q^3-67*q^2-64*q+120 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 96 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 12 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 12 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 48 ], [ 20, 1, 3, 48 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 36 ], [ 27, 1, 1, 48 ], [ 27, 1, 4, 6 ], [ 28, 1, 1, 24 ], [ 31, 1, 3, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 6, 24 ], [ 35, 1, 5, 48 ], [ 38, 1, 4, 48 ], [ 38, 1, 7, 96 ], [ 39, 1, 1, 24 ], [ 40, 1, 2, 12 ], [ 41, 1, 3, 48 ], [ 42, 1, 5, 36 ], [ 43, 1, 3, 96 ], [ 44, 1, 1, 48 ], [ 44, 1, 7, 6 ], [ 46, 1, 10, 144 ], [ 47, 1, 9, 48 ], [ 50, 1, 7, 72 ], [ 51, 1, 10, 48 ], [ 53, 1, 5, 96 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 36 ], [ 55, 1, 7, 48 ], [ 55, 1, 16, 96 ], [ 56, 1, 12, 72 ], [ 58, 1, 22, 288 ], [ 59, 1, 20, 36 ], [ 60, 1, 10, 72 ], [ 62, 1, 8, 144 ], [ 63, 1, 8, 144 ] ] k = 18: F-action on Pi is (1,2) [64,1,18] Dynkin type is A_1(q^2) + T(phi1 phi2^3 phi6) Order of center |Z^F|: phi1 phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 13 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 16 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 19 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 21 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 23 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 25 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 27 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 29 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 31 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 32 modulo 60: 1/96 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 41 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 43 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 47 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 49 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 53 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) q congruent 59 modulo 60: 1/96 q^2 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 10 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 12 ], [ 18, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 32 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 16 ], [ 27, 1, 4, 6 ], [ 28, 1, 2, 8 ], [ 29, 1, 4, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 4, 8 ], [ 33, 1, 6, 8 ], [ 33, 1, 10, 32 ], [ 35, 1, 7, 16 ], [ 36, 1, 4, 16 ], [ 37, 1, 2, 16 ], [ 37, 1, 3, 32 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 40, 1, 2, 4 ], [ 40, 1, 6, 24 ], [ 41, 1, 2, 16 ], [ 41, 1, 10, 16 ], [ 42, 1, 5, 12 ], [ 43, 1, 8, 16 ], [ 43, 1, 13, 32 ], [ 44, 1, 5, 16 ], [ 44, 1, 7, 30 ], [ 45, 1, 4, 24 ], [ 47, 1, 10, 16 ], [ 48, 1, 10, 32 ], [ 50, 1, 10, 24 ], [ 51, 1, 3, 16 ], [ 51, 1, 9, 16 ], [ 53, 1, 12, 32 ], [ 53, 1, 15, 36 ], [ 53, 1, 18, 12 ], [ 54, 1, 10, 48 ], [ 55, 1, 20, 32 ], [ 56, 1, 17, 24 ], [ 59, 1, 5, 72 ], [ 59, 1, 20, 12 ], [ 60, 1, 9, 96 ], [ 60, 1, 10, 24 ], [ 62, 1, 9, 48 ], [ 63, 1, 9, 48 ], [ 63, 1, 12, 48 ] ] k = 19: F-action on Pi is () [64,1,19] Dynkin type is A_1(q) + A_1(q) + T(phi1^3 phi2 phi3) Order of center |Z^F|: phi1^3 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 phi1 ( q^5-7*q^4+11*q^3+7*q^2-16*q+12 ) q congruent 2 modulo 60: 1/48 q^2 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 4 modulo 60: 1/48 q phi1^2 ( q^3-6*q^2+4*q+16 ) q congruent 5 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 7 modulo 60: 1/48 phi1 ( q^5-7*q^4+11*q^3+7*q^2-16*q+12 ) q congruent 8 modulo 60: 1/48 q^2 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 9 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 11 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 13 modulo 60: 1/48 phi1 ( q^5-7*q^4+11*q^3+7*q^2-16*q+12 ) q congruent 16 modulo 60: 1/48 q phi1^2 ( q^3-6*q^2+4*q+16 ) q congruent 17 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 19 modulo 60: 1/48 phi1 ( q^5-7*q^4+11*q^3+7*q^2-16*q+12 ) q congruent 21 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 23 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 25 modulo 60: 1/48 phi1 ( q^5-7*q^4+11*q^3+7*q^2-16*q+12 ) q congruent 27 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 29 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 31 modulo 60: 1/48 phi1 ( q^5-7*q^4+11*q^3+7*q^2-16*q+12 ) q congruent 32 modulo 60: 1/48 q^2 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 37 modulo 60: 1/48 phi1 ( q^5-7*q^4+11*q^3+7*q^2-16*q+12 ) q congruent 41 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 43 modulo 60: 1/48 phi1 ( q^5-7*q^4+11*q^3+7*q^2-16*q+12 ) q congruent 47 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 49 modulo 60: 1/48 phi1 ( q^5-7*q^4+11*q^3+7*q^2-16*q+12 ) q congruent 53 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) q congruent 59 modulo 60: 1/48 q phi1^2 phi2 ( q^2-7*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 77, 30, 30, 81 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 4, 1, 1, 18 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 18 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], [ 16, 1, 1, 48 ], [ 17, 1, 1, 72 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 24 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 20 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 12 ], [ 28, 1, 2, 12 ], [ 29, 1, 2, 24 ], [ 30, 1, 1, 24 ], [ 31, 1, 1, 12 ], [ 31, 1, 2, 28 ], [ 32, 1, 1, 48 ], [ 33, 1, 1, 48 ], [ 34, 1, 2, 16 ], [ 35, 1, 1, 24 ], [ 35, 1, 3, 24 ], [ 36, 1, 2, 8 ], [ 38, 1, 3, 72 ], [ 38, 1, 5, 48 ], [ 39, 1, 4, 4 ], [ 40, 1, 1, 12 ], [ 41, 1, 6, 8 ], [ 42, 1, 3, 24 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 3, 18 ], [ 45, 1, 2, 16 ], [ 45, 1, 3, 36 ], [ 46, 1, 2, 32 ], [ 46, 1, 3, 72 ], [ 47, 1, 1, 24 ], [ 47, 1, 2, 24 ], [ 48, 1, 2, 16 ], [ 50, 1, 3, 12 ], [ 50, 1, 6, 12 ], [ 51, 1, 2, 8 ], [ 53, 1, 3, 16 ], [ 53, 1, 16, 72 ], [ 54, 1, 7, 24 ], [ 55, 1, 2, 16 ], [ 55, 1, 3, 72 ], [ 56, 1, 3, 36 ], [ 56, 1, 8, 36 ], [ 58, 1, 7, 48 ], [ 59, 1, 4, 36 ], [ 60, 1, 2, 144 ], [ 61, 1, 7, 48 ], [ 62, 1, 2, 72 ], [ 62, 1, 5, 72 ], [ 63, 1, 10, 24 ] ] k = 20: F-action on Pi is (1,2) [64,1,20] Dynkin type is A_1(q^2) + T(phi1^2 phi2^2 phi3) Order of center |Z^F|: phi1^2 phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 phi1^3 ( q^3+q^2-2*q-4 ) q congruent 2 modulo 60: 1/48 q^2 phi2^2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 4 modulo 60: 1/48 q phi1 ( q^4-q^3-4*q^2+8 ) q congruent 5 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 7 modulo 60: 1/48 phi1^3 ( q^3+q^2-2*q-4 ) q congruent 8 modulo 60: 1/48 q^2 phi2^2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 11 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 13 modulo 60: 1/48 phi1^3 ( q^3+q^2-2*q-4 ) q congruent 16 modulo 60: 1/48 q phi1 ( q^4-q^3-4*q^2+8 ) q congruent 17 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 19 modulo 60: 1/48 phi1^3 ( q^3+q^2-2*q-4 ) q congruent 21 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 23 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 25 modulo 60: 1/48 phi1^3 ( q^3+q^2-2*q-4 ) q congruent 27 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 29 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 31 modulo 60: 1/48 phi1^3 ( q^3+q^2-2*q-4 ) q congruent 32 modulo 60: 1/48 q^2 phi2^2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/48 phi1^3 ( q^3+q^2-2*q-4 ) q congruent 41 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 43 modulo 60: 1/48 phi1^3 ( q^3+q^2-2*q-4 ) q congruent 47 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 49 modulo 60: 1/48 phi1^3 ( q^3+q^2-2*q-4 ) q congruent 53 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) q congruent 59 modulo 60: 1/48 q phi1^2 phi2^2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 81, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 3, 8 ], [ 27, 1, 5, 6 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 29, 1, 2, 8 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 36, 1, 2, 8 ], [ 38, 1, 2, 16 ], [ 38, 1, 9, 24 ], [ 39, 1, 4, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 7, 8 ], [ 42, 1, 3, 12 ], [ 43, 1, 2, 16 ], [ 44, 1, 3, 6 ], [ 44, 1, 8, 8 ], [ 45, 1, 3, 12 ], [ 46, 1, 9, 24 ], [ 47, 1, 3, 8 ], [ 47, 1, 4, 8 ], [ 50, 1, 3, 12 ], [ 50, 1, 6, 12 ], [ 51, 1, 2, 8 ], [ 53, 1, 4, 16 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 12 ], [ 54, 1, 7, 24 ], [ 55, 1, 8, 16 ], [ 55, 1, 18, 24 ], [ 56, 1, 3, 12 ], [ 56, 1, 8, 12 ], [ 58, 1, 18, 48 ], [ 59, 1, 19, 12 ], [ 60, 1, 11, 24 ], [ 62, 1, 10, 24 ], [ 62, 1, 11, 24 ], [ 63, 1, 10, 24 ] ] k = 21: F-action on Pi is (1,2) [64,1,21] Dynkin type is A_1(q^2) + T(phi1^2 phi2^2 phi6) Order of center |Z^F|: phi1^2 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 2 modulo 60: 1/48 q phi2^2 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 4 modulo 60: 1/48 q^2 phi1 ( q^3-3*q^2-2*q+8 ) q congruent 5 modulo 60: 1/48 phi1^2 phi2^2 ( q^2-4*q+4 ) q congruent 7 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 8 modulo 60: 1/48 q phi2^2 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 11 modulo 60: 1/48 phi1^2 phi2^2 ( q^2-4*q+4 ) q congruent 13 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 16 modulo 60: 1/48 q^2 phi1 ( q^3-3*q^2-2*q+8 ) q congruent 17 modulo 60: 1/48 phi1^2 phi2^2 ( q^2-4*q+4 ) q congruent 19 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 21 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 23 modulo 60: 1/48 phi1^2 phi2^2 ( q^2-4*q+4 ) q congruent 25 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 27 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 29 modulo 60: 1/48 phi1^2 phi2^2 ( q^2-4*q+4 ) q congruent 31 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 32 modulo 60: 1/48 q phi2^2 ( q^3-6*q^2+12*q-8 ) q congruent 37 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 41 modulo 60: 1/48 phi1^2 phi2^2 ( q^2-4*q+4 ) q congruent 43 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 47 modulo 60: 1/48 phi1^2 phi2^2 ( q^2-4*q+4 ) q congruent 49 modulo 60: 1/48 q phi1^3 ( q^2-q-4 ) q congruent 53 modulo 60: 1/48 phi1^2 phi2^2 ( q^2-4*q+4 ) q congruent 59 modulo 60: 1/48 phi1^2 phi2^2 ( q^2-4*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 82, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 4, 6 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 29, 1, 3, 8 ], [ 30, 1, 4, 8 ], [ 31, 1, 3, 4 ], [ 31, 1, 4, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 35, 1, 5, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 3, 8 ], [ 38, 1, 4, 24 ], [ 38, 1, 10, 16 ], [ 39, 1, 4, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 7, 8 ], [ 42, 1, 5, 12 ], [ 43, 1, 4, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 46, 1, 10, 24 ], [ 47, 1, 9, 8 ], [ 47, 1, 10, 8 ], [ 50, 1, 7, 12 ], [ 50, 1, 10, 12 ], [ 51, 1, 8, 8 ], [ 53, 1, 7, 16 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 12 ], [ 54, 1, 11, 24 ], [ 55, 1, 7, 24 ], [ 55, 1, 17, 16 ], [ 56, 1, 12, 12 ], [ 56, 1, 17, 12 ], [ 58, 1, 23, 48 ], [ 59, 1, 20, 12 ], [ 60, 1, 10, 24 ], [ 62, 1, 8, 24 ], [ 62, 1, 9, 24 ], [ 63, 1, 11, 24 ] ] k = 22: F-action on Pi is () [64,1,22] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2^3 phi6) Order of center |Z^F|: phi1 phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 2 modulo 60: 1/48 phi2 ( q^5-7*q^4+20*q^3-32*q^2+32*q-16 ) q congruent 3 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 4 modulo 60: 1/48 q^2 phi1^2 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/48 phi2 ( q^5-7*q^4+21*q^3-37*q^2+42*q-28 ) q congruent 7 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 8 modulo 60: 1/48 phi2 ( q^5-7*q^4+20*q^3-32*q^2+32*q-16 ) q congruent 9 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 11 modulo 60: 1/48 phi2 ( q^5-7*q^4+21*q^3-37*q^2+42*q-28 ) q congruent 13 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 16 modulo 60: 1/48 q^2 phi1^2 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/48 phi2 ( q^5-7*q^4+21*q^3-37*q^2+42*q-28 ) q congruent 19 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 21 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 23 modulo 60: 1/48 phi2 ( q^5-7*q^4+21*q^3-37*q^2+42*q-28 ) q congruent 25 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 27 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 29 modulo 60: 1/48 phi2 ( q^5-7*q^4+21*q^3-37*q^2+42*q-28 ) q congruent 31 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 32 modulo 60: 1/48 phi2 ( q^5-7*q^4+20*q^3-32*q^2+32*q-16 ) q congruent 37 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 41 modulo 60: 1/48 phi2 ( q^5-7*q^4+21*q^3-37*q^2+42*q-28 ) q congruent 43 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 47 modulo 60: 1/48 phi2 ( q^5-7*q^4+21*q^3-37*q^2+42*q-28 ) q congruent 49 modulo 60: 1/48 q phi1^4 ( q-2 ) q congruent 53 modulo 60: 1/48 phi2 ( q^5-7*q^4+21*q^3-37*q^2+42*q-28 ) q congruent 59 modulo 60: 1/48 phi2 ( q^5-7*q^4+21*q^3-37*q^2+42*q-28 ) Fusion of maximal tori of C^F in those of G^F: [ 82, 31, 31, 78 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 14 ], [ 4, 1, 2, 18 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 18 ], [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], [ 16, 1, 3, 48 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], [ 20, 1, 3, 24 ], [ 20, 1, 4, 24 ], [ 22, 1, 3, 20 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 27, 1, 4, 6 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 12 ], [ 29, 1, 3, 24 ], [ 30, 1, 3, 24 ], [ 31, 1, 3, 28 ], [ 31, 1, 4, 12 ], [ 32, 1, 3, 48 ], [ 33, 1, 8, 48 ], [ 34, 1, 3, 16 ], [ 35, 1, 6, 24 ], [ 35, 1, 8, 24 ], [ 36, 1, 3, 8 ], [ 38, 1, 8, 48 ], [ 38, 1, 11, 72 ], [ 39, 1, 4, 4 ], [ 40, 1, 6, 12 ], [ 41, 1, 6, 8 ], [ 42, 1, 2, 16 ], [ 42, 1, 5, 24 ], [ 43, 1, 4, 16 ], [ 44, 1, 7, 18 ], [ 44, 1, 8, 8 ], [ 45, 1, 4, 36 ], [ 45, 1, 5, 16 ], [ 46, 1, 4, 72 ], [ 46, 1, 5, 32 ], [ 47, 1, 7, 24 ], [ 47, 1, 8, 24 ], [ 48, 1, 5, 16 ], [ 50, 1, 7, 12 ], [ 50, 1, 10, 12 ], [ 51, 1, 8, 8 ], [ 53, 1, 8, 16 ], [ 53, 1, 18, 72 ], [ 54, 1, 11, 24 ], [ 55, 1, 12, 72 ], [ 55, 1, 13, 16 ], [ 56, 1, 12, 36 ], [ 56, 1, 17, 36 ], [ 58, 1, 10, 48 ], [ 59, 1, 5, 36 ], [ 60, 1, 8, 144 ], [ 61, 1, 8, 48 ], [ 62, 1, 6, 72 ], [ 62, 1, 7, 72 ], [ 63, 1, 11, 24 ] ] k = 23: F-action on Pi is () [64,1,23] Dynkin type is A_1(q) + A_1(q) + T(phi2^2 phi6^2) Order of center |Z^F|: phi2^2 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 2 modulo 60: 1/72 q^2 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 4 modulo 60: 1/72 q^4 phi1^2 q congruent 5 modulo 60: 1/72 phi2 ( q^5-3*q^4+4*q^3-10*q^2+12*q-12 ) q congruent 7 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 8 modulo 60: 1/72 q^2 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 9 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 11 modulo 60: 1/72 phi2 ( q^5-3*q^4+4*q^3-10*q^2+12*q-12 ) q congruent 13 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 16 modulo 60: 1/72 q^4 phi1^2 q congruent 17 modulo 60: 1/72 phi2 ( q^5-3*q^4+4*q^3-10*q^2+12*q-12 ) q congruent 19 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 21 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 23 modulo 60: 1/72 phi2 ( q^5-3*q^4+4*q^3-10*q^2+12*q-12 ) q congruent 25 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 27 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 29 modulo 60: 1/72 phi2 ( q^5-3*q^4+4*q^3-10*q^2+12*q-12 ) q congruent 31 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 32 modulo 60: 1/72 q^2 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 37 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 41 modulo 60: 1/72 phi2 ( q^5-3*q^4+4*q^3-10*q^2+12*q-12 ) q congruent 43 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 47 modulo 60: 1/72 phi2 ( q^5-3*q^4+4*q^3-10*q^2+12*q-12 ) q congruent 49 modulo 60: 1/72 q^2 phi1 ( q^3-q^2-6 ) q congruent 53 modulo 60: 1/72 phi2 ( q^5-3*q^4+4*q^3-10*q^2+12*q-12 ) q congruent 59 modulo 60: 1/72 phi2 ( q^5-3*q^4+4*q^3-10*q^2+12*q-12 ) Fusion of maximal tori of C^F in those of G^F: [ 38, 84, 84, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 27, 1, 4, 12 ], [ 32, 1, 3, 8 ], [ 33, 1, 7, 36 ], [ 38, 1, 11, 72 ], [ 40, 1, 4, 36 ], [ 42, 1, 5, 24 ], [ 44, 1, 7, 12 ], [ 45, 1, 4, 24 ], [ 46, 1, 4, 48 ], [ 49, 1, 6, 36 ], [ 52, 1, 7, 36 ], [ 53, 1, 18, 24 ], [ 55, 1, 12, 24 ], [ 58, 1, 13, 72 ], [ 61, 1, 9, 72 ] ] k = 24: F-action on Pi is (1,2) [64,1,24] Dynkin type is A_1(q^2) + T(phi4 phi12) Order of center |Z^F|: phi4 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 q^4 phi1 phi2 q congruent 2 modulo 60: 1/12 q^4 phi1 phi2 q congruent 3 modulo 60: 1/12 q^4 phi1 phi2 q congruent 4 modulo 60: 1/12 q^4 phi1 phi2 q congruent 5 modulo 60: 1/12 q^4 phi1 phi2 q congruent 7 modulo 60: 1/12 q^4 phi1 phi2 q congruent 8 modulo 60: 1/12 q^4 phi1 phi2 q congruent 9 modulo 60: 1/12 q^4 phi1 phi2 q congruent 11 modulo 60: 1/12 q^4 phi1 phi2 q congruent 13 modulo 60: 1/12 q^4 phi1 phi2 q congruent 16 modulo 60: 1/12 q^4 phi1 phi2 q congruent 17 modulo 60: 1/12 q^4 phi1 phi2 q congruent 19 modulo 60: 1/12 q^4 phi1 phi2 q congruent 21 modulo 60: 1/12 q^4 phi1 phi2 q congruent 23 modulo 60: 1/12 q^4 phi1 phi2 q congruent 25 modulo 60: 1/12 q^4 phi1 phi2 q congruent 27 modulo 60: 1/12 q^4 phi1 phi2 q congruent 29 modulo 60: 1/12 q^4 phi1 phi2 q congruent 31 modulo 60: 1/12 q^4 phi1 phi2 q congruent 32 modulo 60: 1/12 q^4 phi1 phi2 q congruent 37 modulo 60: 1/12 q^4 phi1 phi2 q congruent 41 modulo 60: 1/12 q^4 phi1 phi2 q congruent 43 modulo 60: 1/12 q^4 phi1 phi2 q congruent 47 modulo 60: 1/12 q^4 phi1 phi2 q congruent 49 modulo 60: 1/12 q^4 phi1 phi2 q congruent 53 modulo 60: 1/12 q^4 phi1 phi2 q congruent 59 modulo 60: 1/12 q^4 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 100, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 9, 1, 1, 1 ], [ 32, 1, 5, 4 ], [ 58, 1, 20, 12 ] ] k = 25: F-action on Pi is () [64,1,25] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2 phi3 phi6) Order of center |Z^F|: phi1 phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/12 phi1 ( q^5-q^4-4*q^2-2*q+2 ) q congruent 2 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-6*q^2+6*q-4 ) q congruent 3 modulo 60: 1/12 q phi1 ( q^4-q^3-4*q-2 ) q congruent 4 modulo 60: 1/12 q phi1 ( q^4-q^3-2*q-2 ) q congruent 5 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-8*q^2+10*q-6 ) q congruent 7 modulo 60: 1/12 phi1 ( q^5-q^4-4*q^2-2*q+2 ) q congruent 8 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-6*q^2+6*q-4 ) q congruent 9 modulo 60: 1/12 q phi1 ( q^4-q^3-4*q-2 ) q congruent 11 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-8*q^2+10*q-6 ) q congruent 13 modulo 60: 1/12 phi1 ( q^5-q^4-4*q^2-2*q+2 ) q congruent 16 modulo 60: 1/12 q phi1 ( q^4-q^3-2*q-2 ) q congruent 17 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-8*q^2+10*q-6 ) q congruent 19 modulo 60: 1/12 phi1 ( q^5-q^4-4*q^2-2*q+2 ) q congruent 21 modulo 60: 1/12 q phi1 ( q^4-q^3-4*q-2 ) q congruent 23 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-8*q^2+10*q-6 ) q congruent 25 modulo 60: 1/12 phi1 ( q^5-q^4-4*q^2-2*q+2 ) q congruent 27 modulo 60: 1/12 q phi1 ( q^4-q^3-4*q-2 ) q congruent 29 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-8*q^2+10*q-6 ) q congruent 31 modulo 60: 1/12 phi1 ( q^5-q^4-4*q^2-2*q+2 ) q congruent 32 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-6*q^2+6*q-4 ) q congruent 37 modulo 60: 1/12 phi1 ( q^5-q^4-4*q^2-2*q+2 ) q congruent 41 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-8*q^2+10*q-6 ) q congruent 43 modulo 60: 1/12 phi1 ( q^5-q^4-4*q^2-2*q+2 ) q congruent 47 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-8*q^2+10*q-6 ) q congruent 49 modulo 60: 1/12 phi1 ( q^5-q^4-4*q^2-2*q+2 ) q congruent 53 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-8*q^2+10*q-6 ) q congruent 59 modulo 60: 1/12 phi2 ( q^5-3*q^4+4*q^3-8*q^2+10*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 40, 35, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ], [ 32, 1, 4, 4 ], [ 33, 1, 3, 6 ], [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 49, 1, 3, 6 ], [ 49, 1, 6, 6 ], [ 52, 1, 6, 6 ], [ 52, 1, 7, 6 ], [ 58, 1, 6, 12 ], [ 61, 1, 10, 12 ], [ 61, 1, 11, 12 ] ] k = 26: F-action on Pi is (1,2) [64,1,26] Dynkin type is A_1(q^2) + T(phi1 phi2 phi3 phi6) Order of center |Z^F|: phi1 phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 2 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 3 modulo 60: 1/36 q^2 phi1 phi2 ( q^2-2 ) q congruent 4 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 5 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 7 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 8 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 9 modulo 60: 1/36 q^2 phi1 phi2 ( q^2-2 ) q congruent 11 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 13 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 16 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 17 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 19 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 21 modulo 60: 1/36 q^2 phi1 phi2 ( q^2-2 ) q congruent 23 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 25 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 27 modulo 60: 1/36 q^2 phi1 phi2 ( q^2-2 ) q congruent 29 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 31 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 32 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 37 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 41 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 43 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 47 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 49 modulo 60: 1/36 q phi1^2 ( q^3+2*q^2-2 ) q congruent 53 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) q congruent 59 modulo 60: 1/36 q phi2^2 ( q^3-2*q^2+2 ) Fusion of maximal tori of C^F in those of G^F: [ 36, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 27, 1, 5, 6 ], [ 32, 1, 2, 4 ], [ 38, 1, 4, 12 ], [ 38, 1, 9, 12 ], [ 44, 1, 3, 6 ], [ 44, 1, 7, 6 ], [ 53, 1, 15, 12 ], [ 53, 1, 17, 12 ], [ 55, 1, 7, 12 ], [ 55, 1, 18, 12 ], [ 58, 1, 24, 36 ] ] k = 27: F-action on Pi is () [64,1,27] Dynkin type is A_1(q) + A_1(q) + T(phi1^2 phi2^4) Order of center |Z^F|: phi1^2 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 2 modulo 60: 1/3072 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 ) q congruent 3 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) q congruent 4 modulo 60: 1/3072 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 ) q congruent 5 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 7 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) q congruent 8 modulo 60: 1/3072 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 ) q congruent 9 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 11 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) q congruent 13 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 16 modulo 60: 1/3072 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 ) q congruent 17 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 19 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) q congruent 21 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 23 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) q congruent 25 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 27 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) q congruent 29 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 31 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) q congruent 32 modulo 60: 1/3072 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 ) q congruent 37 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 41 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 43 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) q congruent 47 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) q congruent 49 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 53 modulo 60: 1/3072 phi1 ( q^5-17*q^4+106*q^3-314*q^2+501*q-405 ) q congruent 59 modulo 60: 1/3072 ( q^6-18*q^5+123*q^4-420*q^3+815*q^2-1002*q+693 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 69, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 28 ], [ 4, 1, 2, 72 ], [ 6, 1, 2, 128 ], [ 7, 1, 2, 96 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 1, 56 ], [ 13, 1, 2, 96 ], [ 13, 1, 3, 32 ], [ 13, 1, 4, 240 ], [ 16, 1, 3, 384 ], [ 16, 1, 4, 128 ], [ 19, 1, 2, 384 ], [ 20, 1, 2, 192 ], [ 20, 1, 3, 192 ], [ 20, 1, 4, 576 ], [ 22, 1, 3, 128 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 24 ], [ 24, 1, 1, 60 ], [ 24, 1, 2, 168 ], [ 25, 1, 1, 56 ], [ 25, 1, 2, 64 ], [ 25, 1, 3, 336 ], [ 25, 1, 4, 128 ], [ 26, 1, 4, 192 ], [ 27, 1, 6, 192 ], [ 28, 1, 2, 96 ], [ 28, 1, 3, 96 ], [ 28, 1, 4, 288 ], [ 31, 1, 3, 384 ], [ 33, 1, 6, 256 ], [ 33, 1, 8, 768 ], [ 34, 1, 3, 384 ], [ 35, 1, 3, 384 ], [ 35, 1, 4, 384 ], [ 35, 1, 6, 768 ], [ 35, 1, 7, 384 ], [ 35, 1, 8, 1152 ], [ 37, 1, 2, 64 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 32 ], [ 39, 1, 3, 144 ], [ 39, 1, 4, 96 ], [ 40, 1, 2, 128 ], [ 40, 1, 6, 192 ], [ 41, 1, 1, 112 ], [ 41, 1, 2, 192 ], [ 41, 1, 4, 256 ], [ 41, 1, 6, 576 ], [ 41, 1, 9, 864 ], [ 41, 1, 10, 384 ], [ 42, 1, 6, 768 ], [ 43, 1, 3, 128 ], [ 43, 1, 8, 256 ], [ 43, 1, 12, 384 ], [ 43, 1, 13, 1152 ], [ 44, 1, 5, 192 ], [ 44, 1, 9, 64 ], [ 44, 1, 10, 576 ], [ 47, 1, 7, 768 ], [ 48, 1, 3, 384 ], [ 48, 1, 4, 128 ], [ 48, 1, 5, 1152 ], [ 49, 1, 5, 2304 ], [ 49, 1, 8, 768 ], [ 49, 1, 9, 768 ], [ 49, 1, 10, 2304 ], [ 50, 1, 9, 768 ], [ 51, 1, 3, 256 ], [ 51, 1, 10, 256 ], [ 52, 1, 2, 192 ], [ 52, 1, 4, 384 ], [ 52, 1, 9, 576 ], [ 52, 1, 10, 576 ], [ 53, 1, 6, 512 ], [ 53, 1, 9, 768 ], [ 53, 1, 12, 768 ], [ 53, 1, 19, 768 ], [ 53, 1, 20, 2304 ], [ 55, 1, 14, 512 ], [ 56, 1, 10, 768 ], [ 56, 1, 15, 2304 ], [ 56, 1, 19, 768 ], [ 57, 1, 5, 768 ], [ 57, 1, 6, 2304 ], [ 59, 1, 2, 1152 ], [ 59, 1, 3, 384 ], [ 59, 1, 18, 768 ], [ 60, 1, 17, 4608 ], [ 60, 1, 27, 1536 ], [ 60, 1, 43, 1536 ], [ 62, 1, 24, 4608 ], [ 62, 1, 31, 1536 ], [ 63, 1, 14, 1536 ], [ 63, 1, 28, 1536 ] ] k = 28: F-action on Pi is () [64,1,28] Dynkin type is A_1(q) + A_1(q) + T(phi1^2 phi4^2) Order of center |Z^F|: phi1^2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 2 modulo 60: 1/256 q^2 ( q^4-6*q^3+4*q^2+24*q-32 ) q congruent 3 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 4 modulo 60: 1/256 q^2 ( q^4-6*q^3+4*q^2+24*q-32 ) q congruent 5 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 7 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 8 modulo 60: 1/256 q^2 ( q^4-6*q^3+4*q^2+24*q-32 ) q congruent 9 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 11 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 13 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 16 modulo 60: 1/256 q^2 ( q^4-6*q^3+4*q^2+24*q-32 ) q congruent 17 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 19 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 21 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 23 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 25 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 27 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 29 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 31 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 32 modulo 60: 1/256 q^2 ( q^4-6*q^3+4*q^2+24*q-32 ) q congruent 37 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 41 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 43 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 47 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 49 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 53 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) q congruent 59 modulo 60: 1/256 phi1 phi2 ( q^4-6*q^3+4*q^2+38*q-69 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 73, 73, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 5, 24 ], [ 41, 1, 1, 16 ], [ 41, 1, 3, 32 ], [ 41, 1, 5, 48 ], [ 41, 1, 8, 96 ], [ 43, 1, 9, 32 ], [ 44, 1, 6, 32 ], [ 48, 1, 8, 64 ], [ 49, 1, 7, 192 ], [ 52, 1, 8, 96 ], [ 53, 1, 10, 64 ], [ 53, 1, 13, 64 ], [ 57, 1, 11, 128 ], [ 59, 1, 6, 96 ], [ 59, 1, 23, 64 ], [ 60, 1, 18, 384 ], [ 60, 1, 31, 128 ], [ 62, 1, 26, 384 ], [ 63, 1, 16, 128 ] ] k = 29: F-action on Pi is (1,2) [64,1,29] Dynkin type is A_1(q^2) + T(phi2^2 phi8) Order of center |Z^F|: phi2^2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 2 modulo 60: 1/64 q^5 ( q-2 ) q congruent 3 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 4 modulo 60: 1/64 q^5 ( q-2 ) q congruent 5 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 7 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 8 modulo 60: 1/64 q^5 ( q-2 ) q congruent 9 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 11 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 13 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 16 modulo 60: 1/64 q^5 ( q-2 ) q congruent 17 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 19 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 21 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 23 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 25 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 27 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 29 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 31 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 32 modulo 60: 1/64 q^5 ( q-2 ) q congruent 37 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 41 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 43 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 47 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 49 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 53 modulo 60: 1/64 phi1^3 phi2 phi4 q congruent 59 modulo 60: 1/64 phi1^3 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 90, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 8 ], [ 39, 1, 3, 8 ], [ 41, 1, 10, 16 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 62, 1, 27, 32 ], [ 63, 1, 18, 32 ] ] k = 30: F-action on Pi is (1,2) [64,1,30] Dynkin type is A_1(q^2) + T(phi1^2 phi8) Order of center |Z^F|: phi1^2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/64 q^4 ( q^2-6*q+8 ) q congruent 3 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/64 q^4 ( q^2-6*q+8 ) q congruent 5 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/64 q^4 ( q^2-6*q+8 ) q congruent 9 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/64 q^4 ( q^2-6*q+8 ) q congruent 17 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/64 q^4 ( q^2-6*q+8 ) q congruent 37 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/64 phi1 phi2 phi4 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 89, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 41, 1, 3, 16 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 62, 1, 28, 32 ], [ 63, 1, 17, 32 ] ] k = 31: F-action on Pi is () [64,1,31] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2 phi8) Order of center |Z^F|: phi1 phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 2 modulo 60: 1/32 q^5 ( q-2 ) q congruent 3 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 4 modulo 60: 1/32 q^5 ( q-2 ) q congruent 5 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 7 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 8 modulo 60: 1/32 q^5 ( q-2 ) q congruent 9 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 11 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 13 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 16 modulo 60: 1/32 q^5 ( q-2 ) q congruent 17 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 19 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 21 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 23 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 25 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 27 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 29 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 31 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 32 modulo 60: 1/32 q^5 ( q-2 ) q congruent 37 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 41 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 43 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 47 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 49 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 53 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) q congruent 59 modulo 60: 1/32 phi1 phi2 phi4 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 89, 43, 43, 90 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 39, 1, 2, 4 ], [ 41, 1, 4, 8 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 63, 1, 17, 16 ], [ 63, 1, 18, 16 ] ] k = 32: F-action on Pi is (1,2) [64,1,32] Dynkin type is A_1(q^2) + T(phi1 phi2 phi8) Order of center |Z^F|: phi1 phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 2 modulo 60: 1/32 q^5 ( q-2 ) q congruent 3 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 4 modulo 60: 1/32 q^5 ( q-2 ) q congruent 5 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 7 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 8 modulo 60: 1/32 q^5 ( q-2 ) q congruent 9 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 11 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 13 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 16 modulo 60: 1/32 q^5 ( q-2 ) q congruent 17 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 19 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 21 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 23 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 25 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 27 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 29 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 31 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 32 modulo 60: 1/32 q^5 ( q-2 ) q congruent 37 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 41 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 43 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 47 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 49 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 53 modulo 60: 1/32 phi1^3 phi2 phi4 q congruent 59 modulo 60: 1/32 phi1^3 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 43, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 39, 1, 4, 4 ], [ 41, 1, 7, 8 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 62, 1, 27, 16 ], [ 62, 1, 28, 16 ] ] k = 33: F-action on Pi is () [64,1,33] Dynkin type is A_1(q) + A_1(q) + T(phi2^2 phi4^2) Order of center |Z^F|: phi2^2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 2 modulo 60: 1/256 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 4 modulo 60: 1/256 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 7 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 8 modulo 60: 1/256 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 11 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 13 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 16 modulo 60: 1/256 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 17 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 19 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 21 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 23 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 25 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 27 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 29 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 31 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 32 modulo 60: 1/256 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 37 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 41 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 43 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 47 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 49 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 53 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 59 modulo 60: 1/256 phi1^2 phi2 ( q^3-q^2-5*q+13 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 74, 74, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ], [ 41, 1, 8, 96 ], [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], [ 43, 1, 9, 32 ], [ 44, 1, 4, 32 ], [ 48, 1, 9, 64 ], [ 49, 1, 4, 192 ], [ 52, 1, 5, 96 ], [ 53, 1, 11, 64 ], [ 53, 1, 14, 64 ], [ 57, 1, 8, 128 ], [ 59, 1, 6, 96 ], [ 59, 1, 24, 64 ], [ 60, 1, 18, 384 ], [ 60, 1, 30, 128 ], [ 62, 1, 25, 384 ], [ 63, 1, 15, 128 ] ] k = 34: F-action on Pi is () [64,1,34] Dynkin type is A_1(q) + A_1(q) + T(phi4 phi8) Order of center |Z^F|: phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 2 modulo 60: 1/32 q^6 q congruent 3 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 4 modulo 60: 1/32 q^6 q congruent 5 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 7 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 8 modulo 60: 1/32 q^6 q congruent 9 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 11 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 13 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 16 modulo 60: 1/32 q^6 q congruent 17 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 19 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 21 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 23 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 25 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 27 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 29 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 31 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 32 modulo 60: 1/32 q^6 q congruent 37 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 41 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 43 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 47 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 49 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 53 modulo 60: 1/32 phi1^2 phi2^2 phi4 q congruent 59 modulo 60: 1/32 phi1^2 phi2^2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 44, 91, 91, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ] ] k = 35: F-action on Pi is () [64,1,35] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2 phi4^2) Order of center |Z^F|: phi1 phi2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 2 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 4 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 7 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 8 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 11 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 13 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 16 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 17 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 19 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 21 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 23 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 25 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 27 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 29 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 31 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 32 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 37 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 41 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 43 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 47 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 49 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 53 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 59 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-5*q+13 ) Fusion of maximal tori of C^F in those of G^F: [ 73, 18, 18, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ], [ 41, 1, 6, 8 ], [ 41, 1, 7, 16 ], [ 41, 1, 8, 96 ], [ 49, 1, 4, 96 ], [ 49, 1, 7, 96 ], [ 52, 1, 5, 48 ], [ 52, 1, 8, 48 ], [ 57, 1, 7, 64 ], [ 59, 1, 6, 96 ], [ 59, 1, 21, 32 ], [ 60, 1, 18, 384 ], [ 60, 1, 33, 64 ], [ 62, 1, 25, 192 ], [ 62, 1, 26, 192 ] ] k = 36: F-action on Pi is (1,2) [64,1,36] Dynkin type is A_1(q^2) + T(phi1 phi2 phi4^2) Order of center |Z^F|: phi1 phi2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 2 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 4 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 7 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 8 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 11 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 13 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 16 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 17 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 19 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 21 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 23 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 25 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 27 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 29 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 31 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 32 modulo 60: 1/128 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 37 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 41 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 43 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 47 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 49 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 53 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) q congruent 59 modulo 60: 1/128 phi1^2 phi2 ( q^3-q^2-7*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 7 ], [ 13, 1, 2, 12 ], [ 13, 1, 3, 12 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 12 ], [ 25, 1, 3, 12 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 24 ], [ 41, 1, 2, 24 ], [ 41, 1, 5, 80 ], [ 43, 1, 9, 32 ], [ 43, 1, 10, 64 ], [ 44, 1, 4, 16 ], [ 44, 1, 6, 16 ], [ 48, 1, 8, 32 ], [ 48, 1, 9, 32 ], [ 53, 1, 10, 64 ], [ 53, 1, 14, 64 ], [ 57, 1, 17, 64 ], [ 59, 1, 6, 96 ], [ 59, 1, 16, 32 ], [ 60, 1, 20, 128 ], [ 60, 1, 29, 128 ], [ 63, 1, 15, 64 ], [ 63, 1, 16, 64 ] ] k = 37: F-action on Pi is () [64,1,37] Dynkin type is A_1(q) + A_1(q) + T(phi1^4 phi2^2) Order of center |Z^F|: phi1^4 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 2 modulo 60: 1/3072 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 3 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) q congruent 4 modulo 60: 1/3072 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 5 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 7 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) q congruent 8 modulo 60: 1/3072 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 9 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 11 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) q congruent 13 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 16 modulo 60: 1/3072 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 17 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 19 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) q congruent 21 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 23 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) q congruent 25 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 27 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) q congruent 29 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 31 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) q congruent 32 modulo 60: 1/3072 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 37 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 41 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 43 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) q congruent 47 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) q congruent 49 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 53 modulo 60: 1/3072 phi1^2 ( q^4-20*q^3+138*q^2-372*q+285 ) q congruent 59 modulo 60: 1/3072 phi1 ( q^5-21*q^4+158*q^3-510*q^2+657*q-189 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 72 ], [ 4, 1, 2, 28 ], [ 6, 1, 1, 128 ], [ 7, 1, 1, 96 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 24 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 240 ], [ 13, 1, 2, 32 ], [ 13, 1, 3, 96 ], [ 13, 1, 4, 56 ], [ 16, 1, 1, 384 ], [ 16, 1, 2, 128 ], [ 19, 1, 1, 384 ], [ 20, 1, 1, 576 ], [ 20, 1, 2, 192 ], [ 20, 1, 3, 192 ], [ 22, 1, 2, 128 ], [ 23, 1, 1, 24 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 168 ], [ 24, 1, 2, 60 ], [ 25, 1, 1, 336 ], [ 25, 1, 2, 128 ], [ 25, 1, 3, 56 ], [ 25, 1, 4, 64 ], [ 26, 1, 1, 192 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 28, 1, 2, 96 ], [ 28, 1, 3, 96 ], [ 31, 1, 2, 384 ], [ 33, 1, 1, 768 ], [ 33, 1, 2, 256 ], [ 34, 1, 2, 384 ], [ 35, 1, 1, 1152 ], [ 35, 1, 2, 384 ], [ 35, 1, 3, 768 ], [ 35, 1, 5, 384 ], [ 35, 1, 6, 384 ], [ 37, 1, 2, 64 ], [ 39, 1, 1, 144 ], [ 39, 1, 2, 32 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 96 ], [ 40, 1, 1, 192 ], [ 40, 1, 3, 128 ], [ 41, 1, 1, 864 ], [ 41, 1, 2, 192 ], [ 41, 1, 3, 384 ], [ 41, 1, 4, 256 ], [ 41, 1, 6, 576 ], [ 41, 1, 9, 112 ], [ 42, 1, 1, 768 ], [ 43, 1, 1, 1152 ], [ 43, 1, 3, 384 ], [ 43, 1, 8, 256 ], [ 43, 1, 12, 128 ], [ 44, 1, 1, 576 ], [ 44, 1, 5, 64 ], [ 44, 1, 9, 192 ], [ 47, 1, 2, 768 ], [ 48, 1, 2, 1152 ], [ 48, 1, 3, 128 ], [ 48, 1, 4, 384 ], [ 49, 1, 1, 2304 ], [ 49, 1, 2, 768 ], [ 49, 1, 5, 768 ], [ 49, 1, 9, 2304 ], [ 50, 1, 4, 768 ], [ 51, 1, 5, 256 ], [ 51, 1, 6, 256 ], [ 52, 1, 1, 576 ], [ 52, 1, 2, 576 ], [ 52, 1, 3, 384 ], [ 52, 1, 9, 192 ], [ 53, 1, 1, 2304 ], [ 53, 1, 2, 768 ], [ 53, 1, 5, 768 ], [ 53, 1, 6, 768 ], [ 53, 1, 9, 512 ], [ 55, 1, 5, 512 ], [ 56, 1, 5, 768 ], [ 56, 1, 6, 2304 ], [ 56, 1, 14, 768 ], [ 57, 1, 2, 2304 ], [ 57, 1, 5, 768 ], [ 59, 1, 1, 1152 ], [ 59, 1, 3, 384 ], [ 59, 1, 17, 768 ], [ 60, 1, 1, 4608 ], [ 60, 1, 27, 1536 ], [ 60, 1, 44, 1536 ], [ 62, 1, 30, 4608 ], [ 62, 1, 32, 1536 ], [ 63, 1, 20, 1536 ], [ 63, 1, 21, 1536 ] ] k = 38: F-action on Pi is (1,2) [64,1,38] Dynkin type is A_1(q^2) + T(phi1^4 phi4) Order of center |Z^F|: phi1^4 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 2 modulo 60: 1/1536 q^2 ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 3 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 4 modulo 60: 1/1536 q^2 ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 5 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 7 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 8 modulo 60: 1/1536 q^2 ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 9 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 11 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 13 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 16 modulo 60: 1/1536 q^2 ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 17 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 19 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 21 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 23 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 25 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 27 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 29 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 31 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 32 modulo 60: 1/1536 q^2 ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 37 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 41 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 43 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 47 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 49 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 53 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) q congruent 59 modulo 60: 1/1536 phi1 phi2 ( q^4-20*q^3+146*q^2-460*q+525 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 16 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 144 ], [ 13, 1, 3, 32 ], [ 16, 1, 2, 128 ], [ 20, 1, 3, 192 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 25, 1, 2, 96 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 33, 1, 4, 256 ], [ 35, 1, 5, 384 ], [ 39, 1, 1, 144 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 288 ], [ 41, 1, 3, 192 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 48 ], [ 43, 1, 3, 384 ], [ 43, 1, 9, 32 ], [ 44, 1, 1, 576 ], [ 44, 1, 6, 32 ], [ 48, 1, 8, 64 ], [ 49, 1, 7, 192 ], [ 49, 1, 11, 768 ], [ 51, 1, 7, 128 ], [ 52, 1, 1, 576 ], [ 52, 1, 8, 96 ], [ 53, 1, 5, 768 ], [ 53, 1, 10, 64 ], [ 53, 1, 13, 192 ], [ 55, 1, 6, 256 ], [ 56, 1, 11, 384 ], [ 57, 1, 11, 384 ], [ 59, 1, 1, 1152 ], [ 59, 1, 23, 192 ], [ 60, 1, 22, 1536 ], [ 60, 1, 31, 384 ], [ 62, 1, 33, 768 ], [ 63, 1, 24, 768 ] ] k = 39: F-action on Pi is (1,2) [64,1,39] Dynkin type is A_1(q^2) + T(phi2^4 phi4) Order of center |Z^F|: phi2^4 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 60: 1/1536 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 60: 1/1536 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 60: 1/1536 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 13 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 16 modulo 60: 1/1536 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 19 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 21 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 23 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 25 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 27 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 29 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 31 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 32 modulo 60: 1/1536 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 41 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 43 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 47 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 49 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 53 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) q congruent 59 modulo 60: 1/1536 phi1^2 phi2 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 71, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 16 ], [ 4, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 2, 32 ], [ 13, 1, 4, 144 ], [ 16, 1, 4, 128 ], [ 20, 1, 2, 192 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 72 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 96 ], [ 27, 1, 6, 192 ], [ 28, 1, 4, 288 ], [ 33, 1, 10, 256 ], [ 35, 1, 4, 384 ], [ 39, 1, 3, 144 ], [ 39, 1, 5, 4 ], [ 40, 1, 6, 192 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 48 ], [ 41, 1, 9, 288 ], [ 41, 1, 10, 192 ], [ 43, 1, 9, 32 ], [ 43, 1, 12, 384 ], [ 44, 1, 4, 32 ], [ 44, 1, 10, 576 ], [ 48, 1, 9, 64 ], [ 49, 1, 4, 192 ], [ 49, 1, 19, 768 ], [ 51, 1, 4, 128 ], [ 52, 1, 5, 96 ], [ 52, 1, 10, 576 ], [ 53, 1, 11, 192 ], [ 53, 1, 14, 64 ], [ 53, 1, 19, 768 ], [ 55, 1, 19, 256 ], [ 56, 1, 9, 384 ], [ 57, 1, 8, 384 ], [ 59, 1, 2, 1152 ], [ 59, 1, 24, 192 ], [ 60, 1, 26, 1536 ], [ 60, 1, 30, 384 ], [ 62, 1, 35, 768 ], [ 63, 1, 22, 768 ] ] k = 40: F-action on Pi is (1,2) [64,1,40] Dynkin type is A_1(q^2) + T(phi1^2 phi2^2 phi4) Order of center |Z^F|: phi1^2 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 2 modulo 60: 1/256 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 4 modulo 60: 1/256 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 7 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 8 modulo 60: 1/256 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 11 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 13 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 16 modulo 60: 1/256 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 19 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 21 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 23 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 25 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 27 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 29 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 31 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 32 modulo 60: 1/256 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 41 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 43 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 47 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 49 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 53 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 59 modulo 60: 1/256 phi1^2 phi2 ( q^3-7*q^2+11*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ], [ 9, 1, 1, 11 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 32 ], [ 13, 1, 3, 32 ], [ 13, 1, 4, 8 ], [ 20, 1, 1, 32 ], [ 20, 1, 4, 32 ], [ 20, 1, 5, 64 ], [ 20, 1, 8, 64 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 40 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 40 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 32 ], [ 26, 1, 4, 32 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 35, 1, 2, 64 ], [ 35, 1, 7, 64 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 39, 1, 5, 4 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 96 ], [ 41, 1, 3, 32 ], [ 41, 1, 5, 40 ], [ 41, 1, 6, 32 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], [ 43, 1, 1, 64 ], [ 43, 1, 5, 128 ], [ 43, 1, 8, 64 ], [ 43, 1, 9, 32 ], [ 43, 1, 13, 64 ], [ 44, 1, 4, 16 ], [ 44, 1, 5, 32 ], [ 44, 1, 6, 16 ], [ 44, 1, 9, 32 ], [ 49, 1, 4, 32 ], [ 49, 1, 7, 32 ], [ 49, 1, 14, 128 ], [ 49, 1, 20, 128 ], [ 52, 1, 2, 32 ], [ 52, 1, 5, 16 ], [ 52, 1, 8, 16 ], [ 52, 1, 9, 32 ], [ 53, 1, 2, 128 ], [ 53, 1, 10, 96 ], [ 53, 1, 11, 32 ], [ 53, 1, 12, 128 ], [ 53, 1, 13, 32 ], [ 53, 1, 14, 96 ], [ 56, 1, 4, 64 ], [ 56, 1, 16, 64 ], [ 57, 1, 7, 64 ], [ 59, 1, 3, 64 ], [ 59, 1, 16, 64 ], [ 59, 1, 23, 32 ], [ 59, 1, 24, 32 ], [ 60, 1, 29, 256 ], [ 60, 1, 30, 64 ], [ 60, 1, 31, 64 ], [ 60, 1, 34, 256 ], [ 62, 1, 34, 128 ], [ 62, 1, 36, 128 ], [ 63, 1, 23, 128 ], [ 63, 1, 25, 128 ] ] k = 41: F-action on Pi is (1,2) [64,1,41] Dynkin type is A_1(q^2) + T(phi1^2 phi2^2 phi4) Order of center |Z^F|: phi1^2 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 2 modulo 60: 1/128 q^3 ( q^3-4*q^2+8 ) q congruent 3 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 4 modulo 60: 1/128 q^3 ( q^3-4*q^2+8 ) q congruent 5 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 7 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 8 modulo 60: 1/128 q^3 ( q^3-4*q^2+8 ) q congruent 9 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 11 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 13 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 16 modulo 60: 1/128 q^3 ( q^3-4*q^2+8 ) q congruent 17 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 19 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 21 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 23 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 25 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 27 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 29 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 31 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 32 modulo 60: 1/128 q^3 ( q^3-4*q^2+8 ) q congruent 37 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 41 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 43 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 47 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 49 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 53 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) q congruent 59 modulo 60: 1/128 phi1^3 phi2^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 76, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 8 ], [ 20, 1, 6, 32 ], [ 20, 1, 7, 32 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 8 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 39, 1, 5, 4 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 32 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 32 ], [ 41, 1, 7, 32 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 43, 1, 7, 64 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 48, 1, 8, 16 ], [ 48, 1, 9, 16 ], [ 49, 1, 4, 32 ], [ 49, 1, 7, 32 ], [ 49, 1, 15, 64 ], [ 49, 1, 18, 64 ], [ 52, 1, 2, 32 ], [ 52, 1, 5, 16 ], [ 52, 1, 8, 16 ], [ 52, 1, 9, 32 ], [ 57, 1, 7, 32 ], [ 57, 1, 8, 32 ], [ 57, 1, 11, 32 ], [ 57, 1, 17, 64 ], [ 59, 1, 3, 64 ], [ 59, 1, 21, 32 ], [ 60, 1, 33, 64 ], [ 60, 1, 38, 128 ], [ 62, 1, 38, 64 ], [ 62, 1, 40, 64 ] ] k = 42: F-action on Pi is () [64,1,42] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2^3 phi4) Order of center |Z^F|: phi1 phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 2 modulo 60: 1/384 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 4 modulo 60: 1/384 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 7 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 8 modulo 60: 1/384 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 11 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 13 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 16 modulo 60: 1/384 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 19 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 21 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 23 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 25 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 27 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 29 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 31 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 32 modulo 60: 1/384 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 41 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 43 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 47 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 49 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 53 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 59 modulo 60: 1/384 phi1^2 phi2 ( q^3-7*q^2+13*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 14 ], [ 4, 1, 2, 10 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 36 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 48 ], [ 20, 1, 4, 48 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 36 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 36 ], [ 25, 1, 4, 48 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 6, 32 ], [ 35, 1, 3, 48 ], [ 35, 1, 4, 48 ], [ 35, 1, 7, 48 ], [ 35, 1, 8, 48 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 16 ], [ 41, 1, 2, 24 ], [ 41, 1, 4, 48 ], [ 41, 1, 5, 24 ], [ 41, 1, 8, 32 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 96 ], [ 42, 1, 6, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 9, 32 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 4, 24 ], [ 44, 1, 5, 48 ], [ 44, 1, 6, 8 ], [ 44, 1, 10, 48 ], [ 49, 1, 4, 96 ], [ 49, 1, 8, 96 ], [ 51, 1, 4, 32 ], [ 52, 1, 4, 48 ], [ 52, 1, 5, 48 ], [ 53, 1, 9, 96 ], [ 53, 1, 11, 96 ], [ 53, 1, 12, 96 ], [ 53, 1, 13, 64 ], [ 53, 1, 14, 96 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 96 ], [ 55, 1, 11, 64 ], [ 56, 1, 9, 96 ], [ 56, 1, 16, 96 ], [ 59, 1, 16, 48 ], [ 59, 1, 18, 96 ], [ 59, 1, 24, 96 ], [ 60, 1, 28, 192 ], [ 60, 1, 30, 192 ], [ 60, 1, 43, 192 ], [ 62, 1, 39, 192 ], [ 63, 1, 22, 192 ], [ 63, 1, 25, 192 ] ] k = 43: F-action on Pi is () [64,1,43] Dynkin type is A_1(q) + A_1(q) + T(phi1^3 phi2 phi4) Order of center |Z^F|: phi1^3 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 2 modulo 60: 1/384 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 4 modulo 60: 1/384 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 7 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 8 modulo 60: 1/384 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 11 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 13 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 16 modulo 60: 1/384 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 17 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 19 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 21 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 23 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 25 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 27 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 29 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 31 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 32 modulo 60: 1/384 q^3 ( q^3-12*q^2+44*q-48 ) q congruent 37 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 41 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 43 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 47 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 49 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 53 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) q congruent 59 modulo 60: 1/384 phi1 phi2 ( q^4-12*q^3+44*q^2-36*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 19, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 14 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 36 ], [ 13, 1, 4, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 48 ], [ 20, 1, 3, 48 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 36 ], [ 25, 1, 1, 36 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 24 ], [ 33, 1, 2, 32 ], [ 35, 1, 1, 48 ], [ 35, 1, 2, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 48 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 12 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 24 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 5, 24 ], [ 41, 1, 8, 32 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 43, 1, 3, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 9, 32 ], [ 44, 1, 1, 48 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 24 ], [ 44, 1, 9, 48 ], [ 49, 1, 2, 96 ], [ 49, 1, 7, 96 ], [ 51, 1, 7, 32 ], [ 52, 1, 3, 48 ], [ 52, 1, 8, 48 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 96 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 96 ], [ 53, 1, 10, 96 ], [ 53, 1, 11, 64 ], [ 53, 1, 13, 96 ], [ 55, 1, 4, 64 ], [ 56, 1, 4, 96 ], [ 56, 1, 11, 96 ], [ 59, 1, 16, 48 ], [ 59, 1, 17, 96 ], [ 59, 1, 23, 96 ], [ 60, 1, 28, 192 ], [ 60, 1, 31, 192 ], [ 60, 1, 44, 192 ], [ 62, 1, 37, 192 ], [ 63, 1, 23, 192 ], [ 63, 1, 24, 192 ] ] k = 44: F-action on Pi is (1,2) [64,1,44] Dynkin type is A_1(q^2) + T(phi1 phi2^3 phi4) Order of center |Z^F|: phi1 phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^5 phi2 q congruent 2 modulo 60: 1/128 q^4 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/128 phi1^5 phi2 q congruent 4 modulo 60: 1/128 q^4 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/128 phi1^5 phi2 q congruent 7 modulo 60: 1/128 phi1^5 phi2 q congruent 8 modulo 60: 1/128 q^4 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/128 phi1^5 phi2 q congruent 11 modulo 60: 1/128 phi1^5 phi2 q congruent 13 modulo 60: 1/128 phi1^5 phi2 q congruent 16 modulo 60: 1/128 q^4 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/128 phi1^5 phi2 q congruent 19 modulo 60: 1/128 phi1^5 phi2 q congruent 21 modulo 60: 1/128 phi1^5 phi2 q congruent 23 modulo 60: 1/128 phi1^5 phi2 q congruent 25 modulo 60: 1/128 phi1^5 phi2 q congruent 27 modulo 60: 1/128 phi1^5 phi2 q congruent 29 modulo 60: 1/128 phi1^5 phi2 q congruent 31 modulo 60: 1/128 phi1^5 phi2 q congruent 32 modulo 60: 1/128 q^4 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/128 phi1^5 phi2 q congruent 41 modulo 60: 1/128 phi1^5 phi2 q congruent 43 modulo 60: 1/128 phi1^5 phi2 q congruent 47 modulo 60: 1/128 phi1^5 phi2 q congruent 49 modulo 60: 1/128 phi1^5 phi2 q congruent 53 modulo 60: 1/128 phi1^5 phi2 q congruent 59 modulo 60: 1/128 phi1^5 phi2 Fusion of maximal tori of C^F in those of G^F: [ 20, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 24 ], [ 16, 1, 4, 32 ], [ 20, 1, 1, 16 ], [ 20, 1, 2, 16 ], [ 20, 1, 5, 32 ], [ 20, 1, 7, 32 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 26, 1, 3, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 10, 64 ], [ 35, 1, 2, 32 ], [ 35, 1, 4, 32 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 39, 1, 5, 4 ], [ 40, 1, 6, 48 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 16 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 32 ], [ 43, 1, 2, 32 ], [ 43, 1, 9, 16 ], [ 43, 1, 14, 64 ], [ 44, 1, 4, 16 ], [ 44, 1, 8, 48 ], [ 48, 1, 9, 32 ], [ 49, 1, 4, 48 ], [ 49, 1, 7, 16 ], [ 49, 1, 14, 64 ], [ 49, 1, 15, 64 ], [ 49, 1, 19, 64 ], [ 51, 1, 4, 32 ], [ 52, 1, 5, 24 ], [ 52, 1, 8, 8 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ], [ 53, 1, 4, 64 ], [ 53, 1, 11, 32 ], [ 53, 1, 14, 32 ], [ 55, 1, 19, 64 ], [ 56, 1, 4, 32 ], [ 56, 1, 9, 32 ], [ 57, 1, 7, 32 ], [ 57, 1, 8, 64 ], [ 59, 1, 13, 96 ], [ 59, 1, 21, 16 ], [ 59, 1, 24, 32 ], [ 60, 1, 30, 64 ], [ 60, 1, 33, 32 ], [ 60, 1, 39, 128 ], [ 62, 1, 35, 64 ], [ 62, 1, 36, 64 ], [ 62, 1, 38, 64 ], [ 63, 1, 27, 64 ] ] k = 45: F-action on Pi is (1,2) [64,1,45] Dynkin type is A_1(q^2) + T(phi1^3 phi2 phi4) Order of center |Z^F|: phi1^3 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/128 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/128 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/128 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/128 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/128 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/128 phi1^3 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 16 ], [ 16, 1, 2, 32 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 16 ], [ 20, 1, 6, 32 ], [ 20, 1, 8, 32 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 26, 1, 2, 16 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 33, 1, 4, 64 ], [ 35, 1, 5, 32 ], [ 35, 1, 7, 32 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 12 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 3, 32 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 16 ], [ 41, 1, 8, 16 ], [ 43, 1, 4, 32 ], [ 43, 1, 6, 64 ], [ 43, 1, 9, 16 ], [ 44, 1, 2, 48 ], [ 44, 1, 6, 16 ], [ 48, 1, 8, 32 ], [ 49, 1, 4, 16 ], [ 49, 1, 7, 48 ], [ 49, 1, 11, 64 ], [ 49, 1, 18, 64 ], [ 49, 1, 20, 64 ], [ 51, 1, 7, 32 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 24 ], [ 53, 1, 7, 64 ], [ 53, 1, 10, 32 ], [ 53, 1, 13, 32 ], [ 55, 1, 6, 64 ], [ 56, 1, 11, 32 ], [ 56, 1, 16, 32 ], [ 57, 1, 7, 32 ], [ 57, 1, 11, 64 ], [ 59, 1, 12, 96 ], [ 59, 1, 21, 16 ], [ 59, 1, 23, 32 ], [ 60, 1, 31, 64 ], [ 60, 1, 33, 32 ], [ 60, 1, 42, 128 ], [ 62, 1, 33, 64 ], [ 62, 1, 34, 64 ], [ 62, 1, 40, 64 ], [ 63, 1, 26, 64 ] ] k = 46: F-action on Pi is () [64,1,46] Dynkin type is A_1(q) + A_1(q) + T(phi1^2 phi2^2 phi4) Order of center |Z^F|: phi1^2 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 60: 1/64 q^4 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 60: 1/64 q^4 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 60: 1/64 q^4 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 13 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 16 modulo 60: 1/64 q^4 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 19 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 21 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 23 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 25 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 27 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 29 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 31 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 32 modulo 60: 1/64 q^4 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 41 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 43 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 47 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 49 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 53 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) q congruent 59 modulo 60: 1/64 phi1^3 phi2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 76, 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 6, 1, 1, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 16, 1, 4, 8 ], [ 19, 1, 1, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 2, 16 ], [ 33, 1, 6, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 8 ], [ 41, 1, 7, 16 ], [ 41, 1, 8, 16 ], [ 42, 1, 2, 16 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 44, 1, 8, 8 ], [ 49, 1, 2, 16 ], [ 49, 1, 4, 16 ], [ 49, 1, 7, 16 ], [ 49, 1, 8, 16 ], [ 51, 1, 4, 16 ], [ 51, 1, 7, 16 ], [ 52, 1, 3, 8 ], [ 52, 1, 4, 8 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 3, 16 ], [ 53, 1, 4, 16 ], [ 53, 1, 7, 16 ], [ 53, 1, 8, 16 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 55, 1, 4, 32 ], [ 55, 1, 11, 32 ], [ 56, 1, 4, 16 ], [ 56, 1, 9, 16 ], [ 56, 1, 11, 16 ], [ 56, 1, 16, 16 ], [ 59, 1, 16, 16 ], [ 59, 1, 21, 16 ], [ 59, 1, 22, 16 ], [ 60, 1, 28, 64 ], [ 60, 1, 33, 32 ], [ 60, 1, 45, 32 ], [ 62, 1, 37, 32 ], [ 62, 1, 39, 32 ], [ 63, 1, 26, 32 ], [ 63, 1, 27, 32 ] ] k = 47: F-action on Pi is () [64,1,47] Dynkin type is A_1(q) + A_1(q) + T(phi2^6) Order of center |Z^F|: phi2^6 Numbers of classes in class type: q congruent 1 modulo 60: 1/46080 phi1 ( q^5-61*q^4+1446*q^3-16806*q^2+98505*q-246285 ) q congruent 2 modulo 60: 1/46080 ( q^6-62*q^5+1492*q^4-17352*q^3+98336*q^2-245760*q+215040 ) q congruent 3 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+115311*q^2-357750*q+420525 ) q congruent 4 modulo 60: 1/46080 ( q^6-62*q^5+1492*q^4-17352*q^3+97056*q^2-207360*q+64512 ) q congruent 5 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+116591*q^2-383190*q+518925 ) q congruent 7 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+115311*q^2-357750*q+420525 ) q congruent 8 modulo 60: 1/46080 ( q^6-62*q^5+1492*q^4-17352*q^3+98336*q^2-245760*q+215040 ) q congruent 9 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+115311*q^2-344790*q+310797 ) q congruent 11 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+116591*q^2-396150*q+693165 ) q congruent 13 modulo 60: 1/46080 phi1 ( q^5-61*q^4+1446*q^3-16806*q^2+98505*q-246285 ) q congruent 16 modulo 60: 1/46080 q ( q^5-62*q^4+1492*q^3-17352*q^2+97056*q-207360 ) q congruent 17 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+116591*q^2-383190*q+518925 ) q congruent 19 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+115311*q^2-357750*q+485037 ) q congruent 21 modulo 60: 1/46080 phi1 ( q^5-61*q^4+1446*q^3-16806*q^2+98505*q-246285 ) q congruent 23 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+116591*q^2-396150*q+693165 ) q congruent 25 modulo 60: 1/46080 phi1 ( q^5-61*q^4+1446*q^3-16806*q^2+98505*q-246285 ) q congruent 27 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+115311*q^2-357750*q+420525 ) q congruent 29 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+116591*q^2-383190*q+583437 ) q congruent 31 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+115311*q^2-357750*q+420525 ) q congruent 32 modulo 60: 1/46080 ( q^6-62*q^5+1492*q^4-17352*q^3+98336*q^2-245760*q+215040 ) q congruent 37 modulo 60: 1/46080 phi1 ( q^5-61*q^4+1446*q^3-16806*q^2+98505*q-246285 ) q congruent 41 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+116591*q^2-383190*q+518925 ) q congruent 43 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+115311*q^2-357750*q+420525 ) q congruent 47 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+116591*q^2-396150*q+693165 ) q congruent 49 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+115311*q^2-344790*q+310797 ) q congruent 53 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+116591*q^2-383190*q+518925 ) q congruent 59 modulo 60: 1/46080 ( q^6-62*q^5+1507*q^4-18252*q^3+116591*q^2-396150*q+757677 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67, 67, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 32 ], [ 3, 1, 2, 224 ], [ 4, 1, 2, 772 ], [ 5, 1, 2, 1664 ], [ 6, 1, 2, 2304 ], [ 7, 1, 2, 544 ], [ 8, 1, 2, 192 ], [ 9, 1, 1, 31 ], [ 10, 1, 2, 60 ], [ 11, 1, 2, 544 ], [ 12, 1, 2, 2080 ], [ 13, 1, 4, 2664 ], [ 14, 1, 2, 4992 ], [ 15, 1, 2, 7424 ], [ 16, 1, 3, 12800 ], [ 17, 1, 4, 15360 ], [ 18, 1, 2, 2304 ], [ 19, 1, 2, 4864 ], [ 20, 1, 4, 8640 ], [ 21, 1, 2, 960 ], [ 22, 1, 4, 3840 ], [ 23, 1, 2, 252 ], [ 24, 1, 2, 900 ], [ 25, 1, 3, 3720 ], [ 26, 1, 4, 960 ], [ 27, 1, 6, 960 ], [ 28, 1, 4, 4320 ], [ 29, 1, 4, 11520 ], [ 30, 1, 3, 13824 ], [ 31, 1, 4, 19200 ], [ 32, 1, 3, 28160 ], [ 33, 1, 8, 34560 ], [ 34, 1, 4, 7680 ], [ 35, 1, 8, 23040 ], [ 36, 1, 4, 3840 ], [ 37, 1, 3, 13440 ], [ 38, 1, 12, 23040 ], [ 39, 1, 3, 1560 ], [ 40, 1, 6, 8640 ], [ 41, 1, 9, 10320 ], [ 42, 1, 6, 7680 ], [ 43, 1, 13, 13440 ], [ 44, 1, 10, 6720 ], [ 45, 1, 6, 19200 ], [ 46, 1, 6, 38400 ], [ 47, 1, 8, 46080 ], [ 48, 1, 6, 30720 ], [ 49, 1, 10, 57600 ], [ 50, 1, 12, 11520 ], [ 51, 1, 9, 26880 ], [ 52, 1, 10, 14400 ], [ 53, 1, 20, 30720 ], [ 54, 1, 14, 23040 ], [ 55, 1, 15, 53760 ], [ 56, 1, 20, 34560 ], [ 57, 1, 10, 69120 ], [ 58, 1, 15, 46080 ], [ 59, 1, 2, 17280 ], [ 60, 1, 17, 69120 ], [ 61, 1, 21, 46080 ], [ 62, 1, 29, 69120 ], [ 63, 1, 19, 23040 ] ] k = 48: F-action on Pi is (1,2) [64,1,48] Dynkin type is A_1(q^2) + T(phi4^3) Order of center |Z^F|: phi4^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 2 modulo 60: 1/384 ( q^6-28*q^4+192*q^2-384 ) q congruent 3 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 4 modulo 60: 1/384 q^2 ( q^4-28*q^2+192 ) q congruent 5 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 7 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 8 modulo 60: 1/384 ( q^6-28*q^4+192*q^2-384 ) q congruent 9 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 11 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 13 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 16 modulo 60: 1/384 q^2 ( q^4-28*q^2+192 ) q congruent 17 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 19 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 21 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 23 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 25 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 27 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 29 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 31 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 32 modulo 60: 1/384 ( q^6-28*q^4+192*q^2-384 ) q congruent 37 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 41 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 43 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 47 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 49 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) q congruent 53 modulo 60: 1/384 ( q^6-31*q^4+267*q^2-621 ) q congruent 59 modulo 60: 1/384 phi1 phi2 ( q^4-30*q^2+237 ) Fusion of maximal tori of C^F in those of G^F: [ 75, 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 64 ], [ 5, 1, 4, 64 ], [ 9, 1, 1, 7 ], [ 32, 1, 5, 256 ], [ 37, 1, 5, 192 ], [ 39, 1, 5, 60 ], [ 41, 1, 5, 168 ], [ 43, 1, 10, 192 ], [ 57, 1, 18, 384 ], [ 58, 1, 21, 384 ], [ 59, 1, 6, 288 ], [ 60, 1, 20, 384 ] ] k = 49: F-action on Pi is (1,2) [64,1,49] Dynkin type is A_1(q^2) + T(phi1^5 phi2) Order of center |Z^F|: phi1^5 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 2 modulo 60: 1/7680 q ( q^5-30*q^4+340*q^3-1800*q^2+4384*q-3840 ) q congruent 3 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) q congruent 4 modulo 60: 1/7680 q ( q^5-30*q^4+340*q^3-1800*q^2+4384*q-3840 ) q congruent 5 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 7 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) q congruent 8 modulo 60: 1/7680 q ( q^5-30*q^4+340*q^3-1800*q^2+4384*q-3840 ) q congruent 9 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 11 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) q congruent 13 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 16 modulo 60: 1/7680 q ( q^5-30*q^4+340*q^3-1800*q^2+4384*q-3840 ) q congruent 17 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 19 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) q congruent 21 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 23 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) q congruent 25 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 27 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) q congruent 29 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 31 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) q congruent 32 modulo 60: 1/7680 q ( q^5-30*q^4+340*q^3-1800*q^2+4384*q-3840 ) q congruent 37 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 41 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 43 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) q congruent 47 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) q congruent 49 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 53 modulo 60: 1/7680 phi1 ( q^5-29*q^4+316*q^3-1544*q^2+2955*q-675 ) q congruent 59 modulo 60: 1/7680 ( q^6-30*q^5+345*q^4-1860*q^3+4499*q^2-3150*q-2205 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 70 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 20 ], [ 3, 1, 1, 80 ], [ 4, 1, 1, 102 ], [ 4, 1, 2, 30 ], [ 5, 1, 1, 64 ], [ 6, 1, 1, 160 ], [ 7, 1, 1, 80 ], [ 8, 1, 1, 32 ], [ 9, 1, 1, 11 ], [ 10, 1, 1, 40 ], [ 11, 1, 1, 240 ], [ 12, 1, 1, 400 ], [ 13, 1, 1, 600 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 100 ], [ 13, 1, 4, 40 ], [ 14, 1, 1, 192 ], [ 15, 1, 1, 320 ], [ 16, 1, 1, 160 ], [ 16, 1, 2, 480 ], [ 18, 1, 1, 320 ], [ 19, 1, 1, 480 ], [ 20, 1, 1, 160 ], [ 20, 1, 3, 480 ], [ 21, 1, 1, 160 ], [ 22, 1, 1, 320 ], [ 23, 1, 1, 90 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 280 ], [ 25, 1, 1, 260 ], [ 25, 1, 2, 200 ], [ 25, 1, 3, 20 ], [ 25, 1, 4, 40 ], [ 26, 1, 1, 160 ], [ 27, 1, 1, 480 ], [ 28, 1, 1, 1200 ], [ 28, 1, 3, 80 ], [ 29, 1, 1, 640 ], [ 30, 1, 1, 960 ], [ 30, 1, 2, 64 ], [ 31, 1, 1, 320 ], [ 33, 1, 2, 320 ], [ 33, 1, 4, 1280 ], [ 34, 1, 1, 960 ], [ 35, 1, 1, 480 ], [ 35, 1, 2, 160 ], [ 35, 1, 5, 1440 ], [ 35, 1, 6, 480 ], [ 36, 1, 1, 640 ], [ 37, 1, 1, 320 ], [ 37, 1, 2, 160 ], [ 39, 1, 1, 560 ], [ 39, 1, 2, 20 ], [ 40, 1, 1, 960 ], [ 40, 1, 3, 160 ], [ 41, 1, 1, 1440 ], [ 41, 1, 2, 40 ], [ 41, 1, 3, 640 ], [ 41, 1, 4, 240 ], [ 42, 1, 1, 960 ], [ 43, 1, 1, 320 ], [ 43, 1, 3, 960 ], [ 43, 1, 8, 160 ], [ 44, 1, 1, 2400 ], [ 44, 1, 9, 160 ], [ 45, 1, 1, 1920 ], [ 47, 1, 3, 640 ], [ 48, 1, 1, 960 ], [ 48, 1, 4, 960 ], [ 48, 1, 7, 320 ], [ 49, 1, 2, 960 ], [ 49, 1, 11, 3840 ], [ 50, 1, 1, 1920 ], [ 51, 1, 1, 640 ], [ 51, 1, 6, 640 ], [ 52, 1, 1, 2880 ], [ 52, 1, 3, 480 ], [ 53, 1, 1, 960 ], [ 53, 1, 2, 320 ], [ 53, 1, 5, 2880 ], [ 53, 1, 6, 960 ], [ 54, 1, 1, 3840 ], [ 55, 1, 9, 1280 ], [ 56, 1, 1, 1920 ], [ 56, 1, 14, 1920 ], [ 57, 1, 3, 1920 ], [ 59, 1, 1, 5760 ], [ 59, 1, 17, 960 ], [ 60, 1, 22, 7680 ], [ 60, 1, 44, 1920 ], [ 62, 1, 47, 3840 ], [ 63, 1, 1, 3840 ], [ 63, 1, 20, 3840 ] ] k = 50: F-action on Pi is (1,2) [64,1,50] Dynkin type is A_1(q^2) + T(phi1 phi2^5) Order of center |Z^F|: phi1 phi2^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 2 modulo 60: 1/7680 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 3 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) q congruent 4 modulo 60: 1/7680 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 5 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 7 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) q congruent 8 modulo 60: 1/7680 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 9 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 11 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) q congruent 13 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 16 modulo 60: 1/7680 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 17 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 19 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) q congruent 21 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 23 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) q congruent 25 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 27 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) q congruent 29 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 31 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) q congruent 32 modulo 60: 1/7680 q ( q^5-22*q^4+180*q^3-680*q^2+1184*q-768 ) q congruent 37 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 41 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 43 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) q congruent 47 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) q congruent 49 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 53 modulo 60: 1/7680 phi1 ( q^5-21*q^4+164*q^3-576*q^2+963*q-915 ) q congruent 59 modulo 60: 1/7680 ( q^6-22*q^5+185*q^4-740*q^3+1539*q^2-2358*q+2835 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 20 ], [ 3, 1, 2, 80 ], [ 4, 1, 1, 30 ], [ 4, 1, 2, 102 ], [ 5, 1, 2, 64 ], [ 6, 1, 2, 160 ], [ 7, 1, 2, 80 ], [ 8, 1, 2, 32 ], [ 9, 1, 1, 11 ], [ 10, 1, 2, 40 ], [ 11, 1, 2, 240 ], [ 12, 1, 2, 400 ], [ 13, 1, 1, 40 ], [ 13, 1, 2, 100 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 600 ], [ 14, 1, 2, 192 ], [ 15, 1, 2, 320 ], [ 16, 1, 3, 160 ], [ 16, 1, 4, 480 ], [ 18, 1, 2, 320 ], [ 19, 1, 2, 480 ], [ 20, 1, 2, 480 ], [ 20, 1, 4, 160 ], [ 21, 1, 2, 160 ], [ 22, 1, 4, 320 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 90 ], [ 24, 1, 2, 280 ], [ 25, 1, 1, 20 ], [ 25, 1, 2, 40 ], [ 25, 1, 3, 260 ], [ 25, 1, 4, 200 ], [ 26, 1, 4, 160 ], [ 27, 1, 6, 480 ], [ 28, 1, 2, 80 ], [ 28, 1, 4, 1200 ], [ 29, 1, 4, 640 ], [ 30, 1, 3, 960 ], [ 30, 1, 4, 64 ], [ 31, 1, 4, 320 ], [ 33, 1, 6, 320 ], [ 33, 1, 10, 1280 ], [ 34, 1, 4, 960 ], [ 35, 1, 3, 480 ], [ 35, 1, 4, 1440 ], [ 35, 1, 7, 160 ], [ 35, 1, 8, 480 ], [ 36, 1, 4, 640 ], [ 37, 1, 2, 160 ], [ 37, 1, 3, 320 ], [ 39, 1, 2, 20 ], [ 39, 1, 3, 560 ], [ 40, 1, 2, 160 ], [ 40, 1, 6, 960 ], [ 41, 1, 2, 40 ], [ 41, 1, 4, 240 ], [ 41, 1, 9, 1440 ], [ 41, 1, 10, 640 ], [ 42, 1, 6, 960 ], [ 43, 1, 8, 160 ], [ 43, 1, 12, 960 ], [ 43, 1, 13, 320 ], [ 44, 1, 5, 160 ], [ 44, 1, 10, 2400 ], [ 45, 1, 6, 1920 ], [ 47, 1, 10, 640 ], [ 48, 1, 3, 960 ], [ 48, 1, 6, 960 ], [ 48, 1, 10, 320 ], [ 49, 1, 8, 960 ], [ 49, 1, 19, 3840 ], [ 50, 1, 12, 1920 ], [ 51, 1, 3, 640 ], [ 51, 1, 9, 640 ], [ 52, 1, 4, 480 ], [ 52, 1, 10, 2880 ], [ 53, 1, 9, 960 ], [ 53, 1, 12, 320 ], [ 53, 1, 19, 2880 ], [ 53, 1, 20, 960 ], [ 54, 1, 14, 3840 ], [ 55, 1, 20, 1280 ], [ 56, 1, 10, 1920 ], [ 56, 1, 20, 1920 ], [ 57, 1, 9, 1920 ], [ 59, 1, 2, 5760 ], [ 59, 1, 18, 960 ], [ 60, 1, 26, 7680 ], [ 60, 1, 43, 1920 ], [ 62, 1, 48, 3840 ], [ 63, 1, 14, 3840 ], [ 63, 1, 19, 3840 ] ] k = 51: F-action on Pi is () [64,1,51] Dynkin type is A_1(q) + A_1(q) + T(phi1^5 phi2) Order of center |Z^F|: phi1^5 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10409*q-12357 ) q congruent 2 modulo 60: 1/1536 q ( q^5-38*q^4+548*q^3-3688*q^2+11232*q-11520 ) q congruent 3 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13679*q^2-20814*q+8613 ) q congruent 4 modulo 60: 1/1536 q ( q^5-38*q^4+548*q^3-3688*q^2+11360*q-12800 ) q congruent 5 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10281*q-11205 ) q congruent 7 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13807*q^2-22094*q+9765 ) q congruent 8 modulo 60: 1/1536 q ( q^5-38*q^4+548*q^3-3688*q^2+11232*q-11520 ) q congruent 9 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10281*q-11205 ) q congruent 11 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13679*q^2-20814*q+8613 ) q congruent 13 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10409*q-12357 ) q congruent 16 modulo 60: 1/1536 q ( q^5-38*q^4+548*q^3-3688*q^2+11360*q-12800 ) q congruent 17 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10281*q-11205 ) q congruent 19 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13807*q^2-22094*q+9765 ) q congruent 21 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10281*q-11205 ) q congruent 23 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13679*q^2-20814*q+8613 ) q congruent 25 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10409*q-12357 ) q congruent 27 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13679*q^2-20814*q+8613 ) q congruent 29 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10281*q-11205 ) q congruent 31 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13807*q^2-22094*q+9765 ) q congruent 32 modulo 60: 1/1536 q ( q^5-38*q^4+548*q^3-3688*q^2+11232*q-11520 ) q congruent 37 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10409*q-12357 ) q congruent 41 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10281*q-11205 ) q congruent 43 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13807*q^2-22094*q+9765 ) q congruent 47 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13679*q^2-20814*q+8613 ) q congruent 49 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10409*q-12357 ) q congruent 53 modulo 60: 1/1536 phi1 ( q^5-37*q^4+518*q^3-3398*q^2+10281*q-11205 ) q congruent 59 modulo 60: 1/1536 ( q^6-38*q^5+555*q^4-3916*q^3+13679*q^2-20814*q+8613 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 4, 68 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 80 ], [ 4, 1, 1, 216 ], [ 5, 1, 1, 384 ], [ 6, 1, 1, 512 ], [ 7, 1, 1, 144 ], [ 8, 1, 1, 64 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 26 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 144 ], [ 12, 1, 1, 432 ], [ 13, 1, 1, 528 ], [ 14, 1, 1, 768 ], [ 15, 1, 1, 1152 ], [ 16, 1, 1, 1920 ], [ 17, 1, 1, 2304 ], [ 18, 1, 1, 384 ], [ 19, 1, 1, 768 ], [ 20, 1, 1, 1248 ], [ 20, 1, 2, 288 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 640 ], [ 22, 1, 2, 128 ], [ 23, 1, 1, 72 ], [ 24, 1, 1, 198 ], [ 24, 1, 2, 30 ], [ 25, 1, 1, 624 ], [ 26, 1, 1, 192 ], [ 26, 1, 3, 32 ], [ 27, 1, 1, 192 ], [ 27, 1, 2, 32 ], [ 28, 1, 1, 624 ], [ 28, 1, 2, 144 ], [ 29, 1, 1, 1152 ], [ 29, 1, 2, 384 ], [ 30, 1, 1, 1536 ], [ 31, 1, 1, 1920 ], [ 31, 1, 2, 640 ], [ 32, 1, 1, 3072 ], [ 33, 1, 1, 4224 ], [ 34, 1, 1, 768 ], [ 34, 1, 2, 256 ], [ 35, 1, 1, 2688 ], [ 35, 1, 3, 768 ], [ 36, 1, 1, 384 ], [ 36, 1, 2, 128 ], [ 37, 1, 1, 1152 ], [ 38, 1, 1, 2304 ], [ 38, 1, 5, 768 ], [ 39, 1, 1, 240 ], [ 39, 1, 4, 52 ], [ 40, 1, 1, 1056 ], [ 41, 1, 1, 1440 ], [ 41, 1, 6, 344 ], [ 42, 1, 1, 768 ], [ 42, 1, 4, 256 ], [ 43, 1, 1, 1152 ], [ 43, 1, 2, 448 ], [ 44, 1, 1, 576 ], [ 44, 1, 2, 224 ], [ 45, 1, 1, 1152 ], [ 45, 1, 2, 640 ], [ 46, 1, 1, 2304 ], [ 46, 1, 2, 1280 ], [ 47, 1, 1, 3840 ], [ 47, 1, 2, 1536 ], [ 48, 1, 1, 2304 ], [ 48, 1, 2, 1024 ], [ 49, 1, 1, 5760 ], [ 49, 1, 9, 1920 ], [ 50, 1, 1, 384 ], [ 50, 1, 2, 384 ], [ 50, 1, 4, 384 ], [ 51, 1, 1, 1152 ], [ 51, 1, 2, 896 ], [ 52, 1, 1, 1440 ], [ 52, 1, 2, 480 ], [ 53, 1, 1, 2304 ], [ 53, 1, 3, 1024 ], [ 54, 1, 2, 768 ], [ 55, 1, 1, 2304 ], [ 55, 1, 2, 1792 ], [ 56, 1, 1, 1152 ], [ 56, 1, 2, 1152 ], [ 56, 1, 6, 1152 ], [ 57, 1, 1, 4608 ], [ 57, 1, 2, 2304 ], [ 58, 1, 2, 1536 ], [ 59, 1, 1, 1152 ], [ 59, 1, 12, 576 ], [ 60, 1, 1, 4608 ], [ 60, 1, 40, 2304 ], [ 61, 1, 19, 1536 ], [ 62, 1, 1, 2304 ], [ 62, 1, 30, 2304 ], [ 62, 1, 41, 2304 ], [ 63, 1, 33, 768 ] ] k = 52: F-action on Pi is () [64,1,52] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2^5) Order of center |Z^F|: phi1 phi2^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/1536 phi1 ( q^5-29*q^4+318*q^3-1678*q^2+4529*q-5445 ) q congruent 2 modulo 60: 1/1536 ( q^6-30*q^5+340*q^4-1800*q^3+4512*q^2-5120*q+2048 ) q congruent 3 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6207*q^2-10646*q+8421 ) q congruent 4 modulo 60: 1/1536 q ( q^5-30*q^4+340*q^3-1800*q^2+4384*q-3840 ) q congruent 5 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6335*q^2-11254*q+8645 ) q congruent 7 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6207*q^2-10646*q+8421 ) q congruent 8 modulo 60: 1/1536 ( q^6-30*q^5+340*q^4-1800*q^3+4512*q^2-5120*q+2048 ) q congruent 9 modulo 60: 1/1536 phi1 ( q^5-29*q^4+318*q^3-1678*q^2+4529*q-5445 ) q congruent 11 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6335*q^2-11926*q+11621 ) q congruent 13 modulo 60: 1/1536 phi1 ( q^5-29*q^4+318*q^3-1678*q^2+4529*q-5445 ) q congruent 16 modulo 60: 1/1536 q ( q^5-30*q^4+340*q^3-1800*q^2+4384*q-3840 ) q congruent 17 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6335*q^2-11254*q+8645 ) q congruent 19 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6207*q^2-10646*q+8421 ) q congruent 21 modulo 60: 1/1536 phi1 ( q^5-29*q^4+318*q^3-1678*q^2+4529*q-5445 ) q congruent 23 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6335*q^2-11926*q+11621 ) q congruent 25 modulo 60: 1/1536 phi1 ( q^5-29*q^4+318*q^3-1678*q^2+4529*q-5445 ) q congruent 27 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6207*q^2-10646*q+8421 ) q congruent 29 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6335*q^2-11254*q+8645 ) q congruent 31 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6207*q^2-10646*q+8421 ) q congruent 32 modulo 60: 1/1536 ( q^6-30*q^5+340*q^4-1800*q^3+4512*q^2-5120*q+2048 ) q congruent 37 modulo 60: 1/1536 phi1 ( q^5-29*q^4+318*q^3-1678*q^2+4529*q-5445 ) q congruent 41 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6335*q^2-11254*q+8645 ) q congruent 43 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6207*q^2-10646*q+8421 ) q congruent 47 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6335*q^2-11926*q+11621 ) q congruent 49 modulo 60: 1/1536 phi1 ( q^5-29*q^4+318*q^3-1678*q^2+4529*q-5445 ) q congruent 53 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6335*q^2-11254*q+8645 ) q congruent 59 modulo 60: 1/1536 ( q^6-30*q^5+347*q^4-1996*q^3+6335*q^2-11926*q+11621 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5, 5, 67 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 80 ], [ 4, 1, 2, 216 ], [ 5, 1, 2, 384 ], [ 6, 1, 2, 512 ], [ 7, 1, 2, 144 ], [ 8, 1, 2, 64 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 26 ], [ 11, 1, 2, 144 ], [ 12, 1, 2, 432 ], [ 13, 1, 4, 528 ], [ 14, 1, 2, 768 ], [ 15, 1, 2, 1152 ], [ 16, 1, 3, 1920 ], [ 17, 1, 4, 2304 ], [ 18, 1, 2, 384 ], [ 19, 1, 2, 768 ], [ 20, 1, 3, 288 ], [ 20, 1, 4, 1248 ], [ 21, 1, 2, 192 ], [ 22, 1, 3, 128 ], [ 22, 1, 4, 640 ], [ 23, 1, 2, 72 ], [ 24, 1, 1, 30 ], [ 24, 1, 2, 198 ], [ 25, 1, 3, 624 ], [ 26, 1, 2, 32 ], [ 26, 1, 4, 192 ], [ 27, 1, 3, 32 ], [ 27, 1, 6, 192 ], [ 28, 1, 3, 144 ], [ 28, 1, 4, 624 ], [ 29, 1, 3, 384 ], [ 29, 1, 4, 1152 ], [ 30, 1, 3, 1536 ], [ 31, 1, 3, 640 ], [ 31, 1, 4, 1920 ], [ 32, 1, 3, 3072 ], [ 33, 1, 8, 4224 ], [ 34, 1, 3, 256 ], [ 34, 1, 4, 768 ], [ 35, 1, 6, 768 ], [ 35, 1, 8, 2688 ], [ 36, 1, 3, 128 ], [ 36, 1, 4, 384 ], [ 37, 1, 3, 1152 ], [ 38, 1, 8, 768 ], [ 38, 1, 12, 2304 ], [ 39, 1, 3, 240 ], [ 39, 1, 4, 52 ], [ 40, 1, 6, 1056 ], [ 41, 1, 6, 344 ], [ 41, 1, 9, 1440 ], [ 42, 1, 2, 256 ], [ 42, 1, 6, 768 ], [ 43, 1, 4, 448 ], [ 43, 1, 13, 1152 ], [ 44, 1, 8, 224 ], [ 44, 1, 10, 576 ], [ 45, 1, 5, 640 ], [ 45, 1, 6, 1152 ], [ 46, 1, 5, 1280 ], [ 46, 1, 6, 2304 ], [ 47, 1, 7, 1536 ], [ 47, 1, 8, 3840 ], [ 48, 1, 5, 1024 ], [ 48, 1, 6, 2304 ], [ 49, 1, 5, 1920 ], [ 49, 1, 10, 5760 ], [ 50, 1, 9, 384 ], [ 50, 1, 11, 384 ], [ 50, 1, 12, 384 ], [ 51, 1, 8, 896 ], [ 51, 1, 9, 1152 ], [ 52, 1, 9, 480 ], [ 52, 1, 10, 1440 ], [ 53, 1, 8, 1024 ], [ 53, 1, 20, 2304 ], [ 54, 1, 12, 768 ], [ 55, 1, 13, 1792 ], [ 55, 1, 15, 2304 ], [ 56, 1, 15, 1152 ], [ 56, 1, 18, 1152 ], [ 56, 1, 20, 1152 ], [ 57, 1, 6, 2304 ], [ 57, 1, 10, 4608 ], [ 58, 1, 12, 1536 ], [ 59, 1, 2, 1152 ], [ 59, 1, 13, 576 ], [ 60, 1, 17, 4608 ], [ 60, 1, 41, 2304 ], [ 61, 1, 20, 1536 ], [ 62, 1, 24, 2304 ], [ 62, 1, 29, 2304 ], [ 62, 1, 43, 2304 ], [ 63, 1, 36, 768 ] ] k = 53: F-action on Pi is () [64,1,53] Dynkin type is A_1(q) + A_1(q) + T(phi1^4 phi2^2) Order of center |Z^F|: phi1^4 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 2 modulo 60: 1/256 q ( q^5-18*q^4+112*q^3-264*q^2+112*q+192 ) q congruent 3 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) q congruent 4 modulo 60: 1/256 q ( q^5-18*q^4+112*q^3-264*q^2+112*q+192 ) q congruent 5 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 7 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) q congruent 8 modulo 60: 1/256 q ( q^5-18*q^4+112*q^3-264*q^2+112*q+192 ) q congruent 9 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 11 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) q congruent 13 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 16 modulo 60: 1/256 q ( q^5-18*q^4+112*q^3-264*q^2+112*q+192 ) q congruent 17 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 19 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) q congruent 21 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 23 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) q congruent 25 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 27 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) q congruent 29 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 31 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) q congruent 32 modulo 60: 1/256 q ( q^5-18*q^4+112*q^3-264*q^2+112*q+192 ) q congruent 37 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 41 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 43 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) q congruent 47 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) q congruent 49 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 53 modulo 60: 1/256 phi1 ( q^5-17*q^4+98*q^3-210*q^2+101*q-5 ) q congruent 59 modulo 60: 1/256 ( q^6-18*q^5+115*q^4-308*q^3+311*q^2-106*q+165 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 68, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 72 ], [ 4, 1, 2, 12 ], [ 5, 1, 1, 96 ], [ 6, 1, 1, 128 ], [ 7, 1, 1, 32 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 8 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 144 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 24 ], [ 14, 1, 1, 96 ], [ 15, 1, 1, 192 ], [ 16, 1, 1, 384 ], [ 16, 1, 2, 64 ], [ 17, 1, 1, 384 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 128 ], [ 20, 1, 1, 192 ], [ 20, 1, 2, 192 ], [ 20, 1, 3, 64 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 64 ], [ 22, 1, 2, 96 ], [ 23, 1, 1, 24 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 56 ], [ 24, 1, 2, 28 ], [ 25, 1, 1, 144 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 32 ], [ 26, 1, 3, 32 ], [ 27, 1, 2, 32 ], [ 28, 1, 1, 96 ], [ 28, 1, 2, 96 ], [ 28, 1, 3, 32 ], [ 29, 1, 2, 192 ], [ 30, 1, 1, 192 ], [ 30, 1, 2, 64 ], [ 31, 1, 1, 192 ], [ 31, 1, 2, 288 ], [ 32, 1, 1, 384 ], [ 33, 1, 1, 768 ], [ 33, 1, 2, 128 ], [ 34, 1, 1, 64 ], [ 34, 1, 2, 96 ], [ 35, 1, 1, 384 ], [ 35, 1, 2, 64 ], [ 35, 1, 3, 384 ], [ 35, 1, 5, 64 ], [ 35, 1, 6, 128 ], [ 36, 1, 2, 64 ], [ 37, 1, 1, 96 ], [ 37, 1, 2, 80 ], [ 38, 1, 5, 384 ], [ 39, 1, 1, 48 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 32 ], [ 40, 1, 1, 192 ], [ 40, 1, 3, 64 ], [ 41, 1, 1, 288 ], [ 41, 1, 2, 32 ], [ 41, 1, 4, 64 ], [ 41, 1, 6, 192 ], [ 41, 1, 9, 48 ], [ 42, 1, 4, 128 ], [ 43, 1, 2, 192 ], [ 43, 1, 3, 64 ], [ 43, 1, 8, 64 ], [ 43, 1, 12, 64 ], [ 44, 1, 2, 96 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 45, 1, 2, 192 ], [ 46, 1, 2, 384 ], [ 47, 1, 1, 384 ], [ 47, 1, 2, 576 ], [ 47, 1, 3, 128 ], [ 48, 1, 1, 192 ], [ 48, 1, 2, 288 ], [ 48, 1, 3, 160 ], [ 48, 1, 4, 160 ], [ 48, 1, 7, 64 ], [ 49, 1, 1, 768 ], [ 49, 1, 2, 128 ], [ 49, 1, 5, 256 ], [ 49, 1, 9, 768 ], [ 50, 1, 2, 64 ], [ 50, 1, 5, 64 ], [ 51, 1, 2, 192 ], [ 51, 1, 5, 128 ], [ 51, 1, 6, 128 ], [ 52, 1, 1, 192 ], [ 52, 1, 2, 192 ], [ 52, 1, 3, 64 ], [ 52, 1, 9, 64 ], [ 53, 1, 3, 384 ], [ 53, 1, 6, 128 ], [ 53, 1, 9, 128 ], [ 54, 1, 5, 128 ], [ 55, 1, 2, 384 ], [ 55, 1, 5, 256 ], [ 56, 1, 2, 192 ], [ 56, 1, 5, 128 ], [ 56, 1, 7, 192 ], [ 56, 1, 14, 128 ], [ 57, 1, 1, 384 ], [ 57, 1, 2, 576 ], [ 57, 1, 3, 128 ], [ 57, 1, 5, 320 ], [ 58, 1, 9, 256 ], [ 59, 1, 3, 64 ], [ 59, 1, 12, 192 ], [ 60, 1, 27, 256 ], [ 60, 1, 40, 768 ], [ 61, 1, 12, 256 ], [ 62, 1, 32, 256 ], [ 62, 1, 41, 384 ], [ 62, 1, 46, 384 ], [ 63, 1, 29, 128 ] ] k = 54: F-action on Pi is () [64,1,54] Dynkin type is A_1(q) + A_1(q) + T(phi1^3 phi2 phi4) Order of center |Z^F|: phi1^3 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 60: 1/64 q^2 ( q^4-10*q^3+26*q^2+4*q-48 ) q congruent 3 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 60: 1/64 q^2 ( q^4-10*q^3+26*q^2+4*q-48 ) q congruent 5 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 60: 1/64 q^2 ( q^4-10*q^3+26*q^2+4*q-48 ) q congruent 9 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 13 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 16 modulo 60: 1/64 q^2 ( q^4-10*q^3+26*q^2+4*q-48 ) q congruent 17 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 19 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 21 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 23 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 25 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 27 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 29 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 31 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 32 modulo 60: 1/64 q^2 ( q^4-10*q^3+26*q^2+4*q-48 ) q congruent 37 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 41 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 43 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 47 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 49 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 53 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) q congruent 59 modulo 60: 1/64 phi1 phi2^2 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 19, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 20, 1, 1, 16 ], [ 20, 1, 3, 16 ], [ 21, 1, 1, 8 ], [ 22, 1, 1, 16 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 8 ], [ 28, 1, 3, 8 ], [ 30, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 16 ], [ 33, 1, 2, 32 ], [ 34, 1, 1, 16 ], [ 35, 1, 1, 16 ], [ 35, 1, 2, 16 ], [ 35, 1, 5, 16 ], [ 35, 1, 6, 16 ], [ 37, 1, 1, 16 ], [ 37, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 47, 1, 3, 32 ], [ 48, 1, 1, 16 ], [ 48, 1, 4, 16 ], [ 48, 1, 7, 16 ], [ 48, 1, 8, 16 ], [ 49, 1, 2, 32 ], [ 49, 1, 7, 32 ], [ 51, 1, 7, 32 ], [ 52, 1, 3, 16 ], [ 52, 1, 8, 16 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 54, 1, 4, 32 ], [ 55, 1, 4, 64 ], [ 56, 1, 4, 32 ], [ 56, 1, 11, 32 ], [ 57, 1, 3, 32 ], [ 57, 1, 11, 32 ], [ 59, 1, 16, 16 ], [ 60, 1, 28, 64 ], [ 61, 1, 13, 64 ], [ 62, 1, 37, 64 ], [ 63, 1, 31, 32 ] ] k = 55: F-action on Pi is () [64,1,55] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2^3 phi4) Order of center |Z^F|: phi1 phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 2 modulo 60: 1/64 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 3 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 4 modulo 60: 1/64 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 5 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 7 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 8 modulo 60: 1/64 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 9 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 11 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 13 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 16 modulo 60: 1/64 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 17 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 19 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 21 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 23 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 25 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 27 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 29 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 31 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 32 modulo 60: 1/64 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 37 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 41 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 43 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 47 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 49 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 53 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) q congruent 59 modulo 60: 1/64 phi1^4 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 76, 20, 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 10 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 2, 16 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 4, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 4, 8 ], [ 30, 1, 3, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 4, 16 ], [ 33, 1, 6, 32 ], [ 34, 1, 4, 16 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 16 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 16 ], [ 39, 1, 2, 4 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 16 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 47, 1, 10, 32 ], [ 48, 1, 3, 16 ], [ 48, 1, 6, 16 ], [ 48, 1, 9, 16 ], [ 48, 1, 10, 16 ], [ 49, 1, 4, 32 ], [ 49, 1, 8, 32 ], [ 51, 1, 4, 32 ], [ 52, 1, 4, 16 ], [ 52, 1, 5, 16 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 54, 1, 9, 32 ], [ 55, 1, 11, 64 ], [ 56, 1, 9, 32 ], [ 56, 1, 16, 32 ], [ 57, 1, 8, 32 ], [ 57, 1, 9, 32 ], [ 59, 1, 16, 16 ], [ 60, 1, 28, 64 ], [ 61, 1, 16, 64 ], [ 62, 1, 39, 64 ], [ 63, 1, 30, 32 ] ] k = 56: F-action on Pi is () [64,1,56] Dynkin type is A_1(q) + A_1(q) + T(phi1^2 phi2^2 phi4) Order of center |Z^F|: phi1^2 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 2 modulo 60: 1/32 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 3 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 4 modulo 60: 1/32 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 5 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 7 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 8 modulo 60: 1/32 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 9 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 11 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 13 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 16 modulo 60: 1/32 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 17 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 19 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 21 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 23 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 25 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 27 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 29 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 31 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 32 modulo 60: 1/32 q^3 ( q^3-6*q^2+10*q-4 ) q congruent 37 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 41 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 43 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 47 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 49 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 53 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) q congruent 59 modulo 60: 1/32 phi1^4 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 76, 72, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 6, 1, 1, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 16 ], [ 19, 1, 1, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 32, 1, 2, 16 ], [ 32, 1, 4, 16 ], [ 33, 1, 2, 16 ], [ 33, 1, 6, 16 ], [ 34, 1, 2, 8 ], [ 34, 1, 3, 8 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 8 ], [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 47, 1, 4, 16 ], [ 47, 1, 9, 16 ], [ 48, 1, 2, 8 ], [ 48, 1, 5, 8 ], [ 49, 1, 2, 16 ], [ 49, 1, 4, 16 ], [ 49, 1, 7, 16 ], [ 49, 1, 8, 16 ], [ 51, 1, 4, 16 ], [ 51, 1, 7, 16 ], [ 52, 1, 3, 8 ], [ 52, 1, 4, 8 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 55, 1, 4, 32 ], [ 55, 1, 11, 32 ], [ 56, 1, 4, 16 ], [ 56, 1, 9, 16 ], [ 56, 1, 11, 16 ], [ 56, 1, 16, 16 ], [ 57, 1, 4, 16 ], [ 57, 1, 7, 16 ], [ 58, 1, 5, 32 ], [ 59, 1, 16, 16 ], [ 60, 1, 28, 64 ], [ 61, 1, 14, 32 ], [ 61, 1, 15, 32 ], [ 62, 1, 37, 32 ], [ 62, 1, 39, 32 ] ] k = 57: F-action on Pi is (1,2) [64,1,57] Dynkin type is A_1(q^2) + T(phi1^2 phi2^2 phi4) Order of center |Z^F|: phi1^2 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 2 modulo 60: 1/32 q^3 ( q^3-2*q^2-2*q+4 ) q congruent 3 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 4 modulo 60: 1/32 q^3 ( q^3-2*q^2-2*q+4 ) q congruent 5 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 7 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 8 modulo 60: 1/32 q^3 ( q^3-2*q^2-2*q+4 ) q congruent 9 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 11 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 13 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 16 modulo 60: 1/32 q^3 ( q^3-2*q^2-2*q+4 ) q congruent 17 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 19 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 21 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 23 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 25 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 27 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 29 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 31 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 32 modulo 60: 1/32 q^3 ( q^3-2*q^2-2*q+4 ) q congruent 37 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 41 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 43 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 47 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 49 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 53 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) q congruent 59 modulo 60: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2+2*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 76, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 8 ], [ 5, 1, 2, 8 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 8 ], [ 13, 1, 3, 8 ], [ 14, 1, 1, 8 ], [ 14, 1, 2, 8 ], [ 21, 1, 1, 4 ], [ 21, 1, 2, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 8 ], [ 30, 1, 2, 16 ], [ 30, 1, 4, 16 ], [ 37, 1, 1, 8 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 8 ], [ 37, 1, 4, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 2, 16 ], [ 41, 1, 5, 8 ], [ 43, 1, 11, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 48, 1, 7, 16 ], [ 48, 1, 8, 8 ], [ 48, 1, 9, 8 ], [ 48, 1, 10, 16 ], [ 54, 1, 4, 16 ], [ 54, 1, 9, 16 ], [ 57, 1, 16, 32 ], [ 57, 1, 17, 16 ], [ 59, 1, 16, 16 ], [ 60, 1, 32, 32 ], [ 63, 1, 30, 16 ], [ 63, 1, 31, 16 ] ] k = 58: F-action on Pi is () [64,1,58] Dynkin type is A_1(q) + A_1(q) + T(phi1^2 phi2^4) Order of center |Z^F|: phi1^2 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 2 modulo 60: 1/256 q ( q^5-14*q^4+72*q^3-168*q^2+176*q-64 ) q congruent 3 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) q congruent 4 modulo 60: 1/256 q ( q^5-14*q^4+72*q^3-168*q^2+176*q-64 ) q congruent 5 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 7 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) q congruent 8 modulo 60: 1/256 q ( q^5-14*q^4+72*q^3-168*q^2+176*q-64 ) q congruent 9 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 11 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) q congruent 13 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 16 modulo 60: 1/256 q ( q^5-14*q^4+72*q^3-168*q^2+176*q-64 ) q congruent 17 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 19 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) q congruent 21 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 23 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) q congruent 25 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 27 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) q congruent 29 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 31 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) q congruent 32 modulo 60: 1/256 q ( q^5-14*q^4+72*q^3-168*q^2+176*q-64 ) q congruent 37 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 41 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 43 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) q congruent 47 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) q congruent 49 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 53 modulo 60: 1/256 phi1 ( q^5-13*q^4+62*q^3-142*q^2+185*q-125 ) q congruent 59 modulo 60: 1/256 ( q^6-14*q^5+75*q^4-204*q^3+327*q^2-310*q+93 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 69, 69, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 72 ], [ 5, 1, 2, 96 ], [ 6, 1, 2, 128 ], [ 7, 1, 2, 32 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 11, 1, 2, 32 ], [ 12, 1, 2, 96 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 144 ], [ 14, 1, 2, 96 ], [ 15, 1, 2, 192 ], [ 16, 1, 3, 384 ], [ 16, 1, 4, 64 ], [ 17, 1, 4, 384 ], [ 18, 1, 2, 64 ], [ 19, 1, 2, 128 ], [ 20, 1, 2, 64 ], [ 20, 1, 3, 192 ], [ 20, 1, 4, 192 ], [ 21, 1, 2, 16 ], [ 22, 1, 3, 96 ], [ 22, 1, 4, 64 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 24 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 56 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 144 ], [ 25, 1, 4, 32 ], [ 26, 1, 2, 32 ], [ 27, 1, 3, 32 ], [ 28, 1, 2, 32 ], [ 28, 1, 3, 96 ], [ 28, 1, 4, 96 ], [ 29, 1, 3, 192 ], [ 30, 1, 3, 192 ], [ 30, 1, 4, 64 ], [ 31, 1, 3, 288 ], [ 31, 1, 4, 192 ], [ 32, 1, 3, 384 ], [ 33, 1, 6, 128 ], [ 33, 1, 8, 768 ], [ 34, 1, 3, 96 ], [ 34, 1, 4, 64 ], [ 35, 1, 3, 128 ], [ 35, 1, 4, 64 ], [ 35, 1, 6, 384 ], [ 35, 1, 7, 64 ], [ 35, 1, 8, 384 ], [ 36, 1, 3, 64 ], [ 37, 1, 2, 80 ], [ 37, 1, 3, 96 ], [ 38, 1, 8, 384 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 48 ], [ 39, 1, 4, 32 ], [ 40, 1, 2, 64 ], [ 40, 1, 6, 192 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 32 ], [ 41, 1, 4, 64 ], [ 41, 1, 6, 192 ], [ 41, 1, 9, 288 ], [ 42, 1, 2, 128 ], [ 43, 1, 3, 64 ], [ 43, 1, 4, 192 ], [ 43, 1, 8, 64 ], [ 43, 1, 12, 64 ], [ 44, 1, 5, 32 ], [ 44, 1, 8, 96 ], [ 44, 1, 9, 32 ], [ 45, 1, 5, 192 ], [ 46, 1, 5, 384 ], [ 47, 1, 7, 576 ], [ 47, 1, 8, 384 ], [ 47, 1, 10, 128 ], [ 48, 1, 3, 160 ], [ 48, 1, 4, 160 ], [ 48, 1, 5, 288 ], [ 48, 1, 6, 192 ], [ 48, 1, 10, 64 ], [ 49, 1, 5, 768 ], [ 49, 1, 8, 128 ], [ 49, 1, 9, 256 ], [ 49, 1, 10, 768 ], [ 50, 1, 8, 64 ], [ 50, 1, 11, 64 ], [ 51, 1, 3, 128 ], [ 51, 1, 8, 192 ], [ 51, 1, 10, 128 ], [ 52, 1, 2, 64 ], [ 52, 1, 4, 64 ], [ 52, 1, 9, 192 ], [ 52, 1, 10, 192 ], [ 53, 1, 6, 128 ], [ 53, 1, 8, 384 ], [ 53, 1, 9, 128 ], [ 54, 1, 13, 128 ], [ 55, 1, 13, 384 ], [ 55, 1, 14, 256 ], [ 56, 1, 10, 128 ], [ 56, 1, 13, 192 ], [ 56, 1, 18, 192 ], [ 56, 1, 19, 128 ], [ 57, 1, 5, 320 ], [ 57, 1, 6, 576 ], [ 57, 1, 9, 128 ], [ 57, 1, 10, 384 ], [ 58, 1, 11, 256 ], [ 59, 1, 3, 64 ], [ 59, 1, 13, 192 ], [ 60, 1, 27, 256 ], [ 60, 1, 41, 768 ], [ 61, 1, 18, 256 ], [ 62, 1, 31, 256 ], [ 62, 1, 42, 384 ], [ 62, 1, 43, 384 ], [ 63, 1, 34, 128 ] ] k = 59: F-action on Pi is (1,2) [64,1,59] Dynkin type is A_1(q^2) + T(phi1 phi2 phi4^2) Order of center |Z^F|: phi1 phi2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 2 modulo 60: 1/32 q^2 ( q^4-6*q^2+8 ) q congruent 3 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 4 modulo 60: 1/32 q^2 ( q^4-6*q^2+8 ) q congruent 5 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 7 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 8 modulo 60: 1/32 q^2 ( q^4-6*q^2+8 ) q congruent 9 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 11 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 13 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 16 modulo 60: 1/32 q^2 ( q^4-6*q^2+8 ) q congruent 17 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 19 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 21 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 23 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 25 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 27 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 29 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 31 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 32 modulo 60: 1/32 q^2 ( q^4-6*q^2+8 ) q congruent 37 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 41 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 43 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 47 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 49 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 53 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) q congruent 59 modulo 60: 1/32 phi1 phi2 ( q^4-6*q^2+9 ) Fusion of maximal tori of C^F in those of G^F: [ 22, 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 5, 1, 3, 16 ], [ 5, 1, 4, 16 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ], [ 32, 1, 5, 32 ], [ 37, 1, 5, 16 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 5, 16 ], [ 43, 1, 11, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 48, 1, 8, 8 ], [ 48, 1, 9, 8 ], [ 57, 1, 17, 16 ], [ 57, 1, 18, 32 ], [ 58, 1, 19, 32 ], [ 59, 1, 16, 16 ], [ 60, 1, 32, 32 ] ] k = 60: F-action on Pi is () [64,1,60] Dynkin type is A_1(q) + A_1(q) + T(phi1^3 phi2^3) Order of center |Z^F|: phi1^3 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 2 modulo 60: 1/256 q^2 ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 3 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 4 modulo 60: 1/256 q^2 ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 5 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 7 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 8 modulo 60: 1/256 q^2 ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 9 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 11 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 13 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 16 modulo 60: 1/256 q^2 ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 17 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 19 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 21 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 23 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 25 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 27 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 29 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 31 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 32 modulo 60: 1/256 q^2 ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 37 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 41 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 43 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 47 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 49 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 53 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) q congruent 59 modulo 60: 1/256 phi1^2 ( q^4-8*q^3+18*q^2-16*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 7, 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 36 ], [ 4, 1, 2, 36 ], [ 6, 1, 1, 32 ], [ 6, 1, 2, 32 ], [ 7, 1, 1, 8 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 72 ], [ 16, 1, 1, 96 ], [ 16, 1, 2, 32 ], [ 16, 1, 3, 96 ], [ 16, 1, 4, 32 ], [ 19, 1, 1, 32 ], [ 19, 1, 2, 32 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 144 ], [ 20, 1, 3, 144 ], [ 20, 1, 4, 48 ], [ 22, 1, 2, 32 ], [ 22, 1, 3, 32 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 42 ], [ 24, 1, 2, 42 ], [ 25, 1, 1, 72 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 72 ], [ 25, 1, 4, 32 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 72 ], [ 28, 1, 3, 72 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 96 ], [ 31, 1, 3, 96 ], [ 33, 1, 1, 192 ], [ 33, 1, 2, 64 ], [ 33, 1, 6, 64 ], [ 33, 1, 8, 192 ], [ 34, 1, 2, 32 ], [ 34, 1, 3, 32 ], [ 35, 1, 1, 96 ], [ 35, 1, 2, 32 ], [ 35, 1, 3, 288 ], [ 35, 1, 4, 32 ], [ 35, 1, 5, 32 ], [ 35, 1, 6, 288 ], [ 35, 1, 7, 32 ], [ 35, 1, 8, 96 ], [ 37, 1, 2, 128 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 36 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 32 ], [ 40, 1, 3, 32 ], [ 40, 1, 6, 48 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 32 ], [ 41, 1, 4, 64 ], [ 41, 1, 6, 216 ], [ 41, 1, 7, 32 ], [ 41, 1, 9, 144 ], [ 42, 1, 2, 64 ], [ 42, 1, 4, 64 ], [ 43, 1, 2, 96 ], [ 43, 1, 3, 64 ], [ 43, 1, 4, 96 ], [ 43, 1, 8, 64 ], [ 43, 1, 12, 64 ], [ 44, 1, 2, 48 ], [ 44, 1, 5, 32 ], [ 44, 1, 8, 48 ], [ 44, 1, 9, 32 ], [ 47, 1, 2, 192 ], [ 47, 1, 7, 192 ], [ 48, 1, 2, 96 ], [ 48, 1, 3, 256 ], [ 48, 1, 4, 256 ], [ 48, 1, 5, 96 ], [ 49, 1, 1, 192 ], [ 49, 1, 2, 64 ], [ 49, 1, 5, 576 ], [ 49, 1, 8, 64 ], [ 49, 1, 9, 576 ], [ 49, 1, 10, 192 ], [ 50, 1, 5, 64 ], [ 50, 1, 8, 64 ], [ 51, 1, 3, 64 ], [ 51, 1, 5, 64 ], [ 51, 1, 6, 64 ], [ 51, 1, 10, 64 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 144 ], [ 52, 1, 3, 32 ], [ 52, 1, 4, 32 ], [ 52, 1, 9, 144 ], [ 52, 1, 10, 48 ], [ 53, 1, 3, 192 ], [ 53, 1, 4, 64 ], [ 53, 1, 6, 128 ], [ 53, 1, 7, 64 ], [ 53, 1, 8, 192 ], [ 53, 1, 9, 128 ], [ 55, 1, 5, 128 ], [ 55, 1, 14, 128 ], [ 56, 1, 5, 64 ], [ 56, 1, 7, 192 ], [ 56, 1, 10, 64 ], [ 56, 1, 13, 192 ], [ 56, 1, 14, 64 ], [ 56, 1, 19, 64 ], [ 57, 1, 2, 192 ], [ 57, 1, 5, 512 ], [ 57, 1, 6, 192 ], [ 59, 1, 3, 64 ], [ 59, 1, 12, 96 ], [ 59, 1, 13, 96 ], [ 59, 1, 22, 64 ], [ 60, 1, 27, 256 ], [ 60, 1, 40, 384 ], [ 60, 1, 41, 384 ], [ 60, 1, 45, 128 ], [ 62, 1, 31, 128 ], [ 62, 1, 32, 128 ], [ 62, 1, 42, 384 ], [ 62, 1, 46, 384 ], [ 63, 1, 32, 128 ], [ 63, 1, 35, 128 ] ] k = 61: F-action on Pi is (1,2) [64,1,61] Dynkin type is A_1(q^2) + T(phi1^3 phi2^3) Order of center |Z^F|: phi1^3 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/2304 phi1 ( q^5-17*q^4+88*q^3-92*q^2-241*q-123 ) q congruent 2 modulo 60: 1/2304 ( q^6-18*q^5+108*q^4-216*q^3-128*q^2+896*q-768 ) q congruent 3 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-85*q^2-138*q+1179 ) q congruent 4 modulo 60: 1/2304 q ( q^5-18*q^4+108*q^3-216*q^2-128*q+640 ) q congruent 5 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-149*q^2+374*q-645 ) q congruent 7 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-149*q^2+118*q+987 ) q congruent 8 modulo 60: 1/2304 ( q^6-18*q^5+108*q^4-216*q^3-128*q^2+896*q-768 ) q congruent 9 modulo 60: 1/2304 phi1 ( q^5-17*q^4+88*q^3-92*q^2-177*q-315 ) q congruent 11 modulo 60: 1/2304 phi2 ( q^5-19*q^4+124*q^3-304*q^2+155*q+219 ) q congruent 13 modulo 60: 1/2304 phi1 ( q^5-17*q^4+88*q^3-92*q^2-241*q-123 ) q congruent 16 modulo 60: 1/2304 q ( q^5-18*q^4+108*q^3-216*q^2-128*q+640 ) q congruent 17 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-149*q^2+374*q-645 ) q congruent 19 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-149*q^2+118*q+987 ) q congruent 21 modulo 60: 1/2304 phi1 ( q^5-17*q^4+88*q^3-92*q^2-177*q-315 ) q congruent 23 modulo 60: 1/2304 phi2 ( q^5-19*q^4+124*q^3-304*q^2+155*q+219 ) q congruent 25 modulo 60: 1/2304 phi1 ( q^5-17*q^4+88*q^3-92*q^2-241*q-123 ) q congruent 27 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-85*q^2-138*q+1179 ) q congruent 29 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-149*q^2+374*q-645 ) q congruent 31 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-149*q^2+118*q+987 ) q congruent 32 modulo 60: 1/2304 ( q^6-18*q^5+108*q^4-216*q^3-128*q^2+896*q-768 ) q congruent 37 modulo 60: 1/2304 phi1 ( q^5-17*q^4+88*q^3-92*q^2-241*q-123 ) q congruent 41 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-149*q^2+374*q-645 ) q congruent 43 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-149*q^2+118*q+987 ) q congruent 47 modulo 60: 1/2304 phi2 ( q^5-19*q^4+124*q^3-304*q^2+155*q+219 ) q congruent 49 modulo 60: 1/2304 phi1 ( q^5-17*q^4+88*q^3-92*q^2-241*q-123 ) q congruent 53 modulo 60: 1/2304 ( q^6-18*q^5+105*q^4-180*q^3-149*q^2+374*q-645 ) q congruent 59 modulo 60: 1/2304 phi2 ( q^5-19*q^4+124*q^3-304*q^2+155*q+219 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 26 ], [ 4, 1, 2, 26 ], [ 6, 1, 1, 48 ], [ 6, 1, 2, 48 ], [ 7, 1, 1, 72 ], [ 7, 1, 2, 72 ], [ 9, 1, 1, 19 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 12 ], [ 11, 1, 1, 24 ], [ 11, 1, 2, 24 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 48 ], [ 13, 1, 2, 84 ], [ 13, 1, 3, 84 ], [ 13, 1, 4, 48 ], [ 16, 1, 1, 48 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 48 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 192 ], [ 17, 1, 3, 192 ], [ 19, 1, 1, 144 ], [ 19, 1, 2, 144 ], [ 20, 1, 1, 144 ], [ 20, 1, 2, 48 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 144 ], [ 20, 1, 5, 576 ], [ 20, 1, 8, 576 ], [ 22, 1, 2, 96 ], [ 22, 1, 3, 96 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 84 ], [ 24, 1, 2, 84 ], [ 25, 1, 1, 108 ], [ 25, 1, 2, 72 ], [ 25, 1, 3, 108 ], [ 25, 1, 4, 72 ], [ 26, 1, 1, 144 ], [ 26, 1, 4, 144 ], [ 27, 1, 1, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 72 ], [ 28, 1, 3, 72 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 96 ], [ 31, 1, 3, 96 ], [ 32, 1, 2, 64 ], [ 32, 1, 4, 576 ], [ 33, 1, 2, 96 ], [ 33, 1, 6, 96 ], [ 34, 1, 2, 288 ], [ 34, 1, 3, 288 ], [ 35, 1, 1, 144 ], [ 35, 1, 2, 432 ], [ 35, 1, 3, 144 ], [ 35, 1, 4, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 144 ], [ 35, 1, 7, 432 ], [ 35, 1, 8, 144 ], [ 38, 1, 6, 384 ], [ 38, 1, 7, 384 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 36 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 144 ], [ 40, 1, 2, 48 ], [ 40, 1, 3, 48 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 360 ], [ 41, 1, 3, 192 ], [ 41, 1, 4, 144 ], [ 41, 1, 6, 288 ], [ 41, 1, 9, 144 ], [ 41, 1, 10, 192 ], [ 42, 1, 1, 288 ], [ 42, 1, 6, 288 ], [ 43, 1, 1, 288 ], [ 43, 1, 3, 96 ], [ 43, 1, 5, 1152 ], [ 43, 1, 8, 288 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 288 ], [ 44, 1, 1, 48 ], [ 44, 1, 5, 144 ], [ 44, 1, 9, 144 ], [ 44, 1, 10, 48 ], [ 46, 1, 7, 1152 ], [ 46, 1, 12, 1152 ], [ 47, 1, 4, 192 ], [ 47, 1, 9, 192 ], [ 48, 1, 2, 288 ], [ 48, 1, 5, 288 ], [ 49, 1, 2, 288 ], [ 49, 1, 8, 288 ], [ 49, 1, 14, 1152 ], [ 49, 1, 20, 1152 ], [ 50, 1, 4, 576 ], [ 50, 1, 9, 576 ], [ 51, 1, 5, 192 ], [ 51, 1, 10, 192 ], [ 52, 1, 2, 288 ], [ 52, 1, 3, 144 ], [ 52, 1, 4, 144 ], [ 52, 1, 9, 288 ], [ 53, 1, 1, 288 ], [ 53, 1, 2, 864 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 288 ], [ 53, 1, 9, 288 ], [ 53, 1, 12, 864 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 288 ], [ 55, 1, 10, 384 ], [ 55, 1, 16, 384 ], [ 56, 1, 5, 576 ], [ 56, 1, 6, 576 ], [ 56, 1, 15, 576 ], [ 56, 1, 19, 576 ], [ 57, 1, 4, 576 ], [ 58, 1, 25, 2304 ], [ 59, 1, 3, 576 ], [ 59, 1, 17, 288 ], [ 59, 1, 18, 288 ], [ 60, 1, 34, 2304 ], [ 60, 1, 43, 576 ], [ 60, 1, 44, 576 ], [ 62, 1, 44, 1152 ], [ 62, 1, 45, 1152 ], [ 63, 1, 21, 1152 ], [ 63, 1, 28, 1152 ] ] k = 62: F-action on Pi is (1,2) [64,1,62] Dynkin type is A_1(q^2) + T(phi1^4 phi2^2) Order of center |Z^F|: phi1^4 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 ( q^5-13*q^4+48*q^3-8*q^2-177*q-43 ) q congruent 2 modulo 60: 1/384 q ( q^5-14*q^4+60*q^3-56*q^2-128*q+192 ) q congruent 3 modulo 60: 1/384 phi2 ( q^5-15*q^4+76*q^3-132*q^2-5*q+123 ) q congruent 4 modulo 60: 1/384 q ( q^5-14*q^4+60*q^3-56*q^2-160*q+256 ) q congruent 5 modulo 60: 1/384 phi1 phi2 ( q^4-14*q^3+62*q^2-70*q-75 ) q congruent 7 modulo 60: 1/384 ( q^6-14*q^5+61*q^4-56*q^3-169*q^2+182*q+91 ) q congruent 8 modulo 60: 1/384 q ( q^5-14*q^4+60*q^3-56*q^2-128*q+192 ) q congruent 9 modulo 60: 1/384 phi1 phi2 ( q^4-14*q^3+62*q^2-70*q-75 ) q congruent 11 modulo 60: 1/384 phi2 ( q^5-15*q^4+76*q^3-132*q^2-5*q+123 ) q congruent 13 modulo 60: 1/384 phi1 ( q^5-13*q^4+48*q^3-8*q^2-177*q-43 ) q congruent 16 modulo 60: 1/384 q ( q^5-14*q^4+60*q^3-56*q^2-160*q+256 ) q congruent 17 modulo 60: 1/384 phi1 phi2 ( q^4-14*q^3+62*q^2-70*q-75 ) q congruent 19 modulo 60: 1/384 ( q^6-14*q^5+61*q^4-56*q^3-169*q^2+182*q+91 ) q congruent 21 modulo 60: 1/384 phi1 phi2 ( q^4-14*q^3+62*q^2-70*q-75 ) q congruent 23 modulo 60: 1/384 phi2 ( q^5-15*q^4+76*q^3-132*q^2-5*q+123 ) q congruent 25 modulo 60: 1/384 phi1 ( q^5-13*q^4+48*q^3-8*q^2-177*q-43 ) q congruent 27 modulo 60: 1/384 phi2 ( q^5-15*q^4+76*q^3-132*q^2-5*q+123 ) q congruent 29 modulo 60: 1/384 phi1 phi2 ( q^4-14*q^3+62*q^2-70*q-75 ) q congruent 31 modulo 60: 1/384 ( q^6-14*q^5+61*q^4-56*q^3-169*q^2+182*q+91 ) q congruent 32 modulo 60: 1/384 q ( q^5-14*q^4+60*q^3-56*q^2-128*q+192 ) q congruent 37 modulo 60: 1/384 phi1 ( q^5-13*q^4+48*q^3-8*q^2-177*q-43 ) q congruent 41 modulo 60: 1/384 phi1 phi2 ( q^4-14*q^3+62*q^2-70*q-75 ) q congruent 43 modulo 60: 1/384 ( q^6-14*q^5+61*q^4-56*q^3-169*q^2+182*q+91 ) q congruent 47 modulo 60: 1/384 phi2 ( q^5-15*q^4+76*q^3-132*q^2-5*q+123 ) q congruent 49 modulo 60: 1/384 phi1 ( q^5-13*q^4+48*q^3-8*q^2-177*q-43 ) q congruent 53 modulo 60: 1/384 phi1 phi2 ( q^4-14*q^3+62*q^2-70*q-75 ) q congruent 59 modulo 60: 1/384 phi2 ( q^5-15*q^4+76*q^3-132*q^2-5*q+123 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 20 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 34 ], [ 4, 1, 2, 14 ], [ 5, 1, 1, 32 ], [ 6, 1, 1, 40 ], [ 6, 1, 2, 24 ], [ 7, 1, 1, 28 ], [ 7, 1, 2, 12 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 14 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 36 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 68 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 36 ], [ 13, 1, 4, 16 ], [ 14, 1, 1, 64 ], [ 15, 1, 1, 64 ], [ 16, 1, 1, 40 ], [ 16, 1, 2, 88 ], [ 16, 1, 3, 24 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 32 ], [ 17, 1, 3, 96 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 72 ], [ 19, 1, 2, 24 ], [ 20, 1, 1, 56 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 72 ], [ 20, 1, 4, 24 ], [ 20, 1, 6, 96 ], [ 20, 1, 8, 96 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 64 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 48 ], [ 23, 1, 1, 30 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 50 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 84 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 8 ], [ 27, 1, 1, 48 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 84 ], [ 28, 1, 2, 60 ], [ 28, 1, 3, 28 ], [ 28, 1, 4, 4 ], [ 29, 1, 1, 96 ], [ 29, 1, 2, 32 ], [ 30, 1, 1, 96 ], [ 30, 1, 2, 32 ], [ 31, 1, 1, 64 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 48 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 96 ], [ 33, 1, 2, 80 ], [ 33, 1, 4, 192 ], [ 33, 1, 6, 48 ], [ 34, 1, 1, 96 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 1, 72 ], [ 35, 1, 2, 56 ], [ 35, 1, 3, 24 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 120 ], [ 35, 1, 6, 72 ], [ 35, 1, 7, 72 ], [ 35, 1, 8, 24 ], [ 36, 1, 1, 96 ], [ 36, 1, 2, 32 ], [ 37, 1, 1, 96 ], [ 37, 1, 2, 48 ], [ 38, 1, 2, 64 ], [ 38, 1, 7, 192 ], [ 39, 1, 1, 72 ], [ 39, 1, 2, 12 ], [ 39, 1, 4, 28 ], [ 40, 1, 1, 144 ], [ 40, 1, 2, 24 ], [ 40, 1, 3, 40 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 24 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 72 ], [ 41, 1, 7, 32 ], [ 42, 1, 1, 96 ], [ 42, 1, 2, 48 ], [ 42, 1, 4, 48 ], [ 43, 1, 1, 96 ], [ 43, 1, 2, 16 ], [ 43, 1, 3, 96 ], [ 43, 1, 4, 48 ], [ 43, 1, 6, 192 ], [ 43, 1, 8, 48 ], [ 44, 1, 1, 48 ], [ 44, 1, 2, 120 ], [ 44, 1, 8, 8 ], [ 44, 1, 9, 48 ], [ 45, 1, 1, 96 ], [ 45, 1, 2, 96 ], [ 46, 1, 7, 192 ], [ 46, 1, 11, 192 ], [ 47, 1, 3, 128 ], [ 47, 1, 4, 32 ], [ 47, 1, 9, 96 ], [ 48, 1, 1, 96 ], [ 48, 1, 2, 48 ], [ 48, 1, 4, 96 ], [ 48, 1, 5, 48 ], [ 48, 1, 7, 96 ], [ 49, 1, 2, 144 ], [ 49, 1, 8, 48 ], [ 49, 1, 11, 192 ], [ 49, 1, 18, 192 ], [ 49, 1, 20, 192 ], [ 50, 1, 1, 96 ], [ 50, 1, 2, 96 ], [ 50, 1, 4, 96 ], [ 50, 1, 8, 96 ], [ 51, 1, 1, 96 ], [ 51, 1, 2, 32 ], [ 51, 1, 6, 96 ], [ 51, 1, 10, 96 ], [ 52, 1, 1, 144 ], [ 52, 1, 2, 144 ], [ 52, 1, 3, 72 ], [ 52, 1, 4, 24 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 96 ], [ 53, 1, 3, 48 ], [ 53, 1, 4, 16 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 96 ], [ 53, 1, 7, 144 ], [ 53, 1, 8, 48 ], [ 54, 1, 2, 192 ], [ 55, 1, 8, 64 ], [ 55, 1, 9, 192 ], [ 55, 1, 16, 192 ], [ 56, 1, 1, 96 ], [ 56, 1, 2, 96 ], [ 56, 1, 6, 96 ], [ 56, 1, 13, 96 ], [ 56, 1, 14, 96 ], [ 56, 1, 19, 96 ], [ 57, 1, 3, 192 ], [ 57, 1, 4, 96 ], [ 58, 1, 16, 384 ], [ 59, 1, 12, 288 ], [ 59, 1, 17, 96 ], [ 59, 1, 22, 48 ], [ 60, 1, 42, 384 ], [ 60, 1, 44, 192 ], [ 60, 1, 45, 96 ], [ 62, 1, 45, 192 ], [ 62, 1, 47, 192 ], [ 62, 1, 50, 192 ], [ 63, 1, 33, 192 ], [ 63, 1, 35, 192 ] ] k = 63: F-action on Pi is (1,2) [64,1,63] Dynkin type is A_1(q^2) + T(phi1^2 phi2^4) Order of center |Z^F|: phi1^2 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1^2 ( q^4-8*q^3+12*q^2+16*q+27 ) q congruent 2 modulo 60: 1/384 q ( q^5-10*q^4+28*q^3-8*q^2-64*q+64 ) q congruent 3 modulo 60: 1/384 ( q^6-10*q^5+29*q^4-16*q^3+7*q^2-86*q-21 ) q congruent 4 modulo 60: 1/384 q^2 ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 5 modulo 60: 1/384 phi1^2 phi2 ( q^3-9*q^2+21*q-5 ) q congruent 7 modulo 60: 1/384 ( q^6-10*q^5+29*q^4-16*q^3+7*q^2-86*q-21 ) q congruent 8 modulo 60: 1/384 q ( q^5-10*q^4+28*q^3-8*q^2-64*q+64 ) q congruent 9 modulo 60: 1/384 phi1^2 ( q^4-8*q^3+12*q^2+16*q+27 ) q congruent 11 modulo 60: 1/384 phi2 ( q^5-11*q^4+40*q^3-56*q^2+31*q-53 ) q congruent 13 modulo 60: 1/384 phi1^2 ( q^4-8*q^3+12*q^2+16*q+27 ) q congruent 16 modulo 60: 1/384 q^2 ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 17 modulo 60: 1/384 phi1^2 phi2 ( q^3-9*q^2+21*q-5 ) q congruent 19 modulo 60: 1/384 ( q^6-10*q^5+29*q^4-16*q^3+7*q^2-86*q-21 ) q congruent 21 modulo 60: 1/384 phi1^2 ( q^4-8*q^3+12*q^2+16*q+27 ) q congruent 23 modulo 60: 1/384 phi2 ( q^5-11*q^4+40*q^3-56*q^2+31*q-53 ) q congruent 25 modulo 60: 1/384 phi1^2 ( q^4-8*q^3+12*q^2+16*q+27 ) q congruent 27 modulo 60: 1/384 ( q^6-10*q^5+29*q^4-16*q^3+7*q^2-86*q-21 ) q congruent 29 modulo 60: 1/384 phi1^2 phi2 ( q^3-9*q^2+21*q-5 ) q congruent 31 modulo 60: 1/384 ( q^6-10*q^5+29*q^4-16*q^3+7*q^2-86*q-21 ) q congruent 32 modulo 60: 1/384 q ( q^5-10*q^4+28*q^3-8*q^2-64*q+64 ) q congruent 37 modulo 60: 1/384 phi1^2 ( q^4-8*q^3+12*q^2+16*q+27 ) q congruent 41 modulo 60: 1/384 phi1^2 phi2 ( q^3-9*q^2+21*q-5 ) q congruent 43 modulo 60: 1/384 ( q^6-10*q^5+29*q^4-16*q^3+7*q^2-86*q-21 ) q congruent 47 modulo 60: 1/384 phi2 ( q^5-11*q^4+40*q^3-56*q^2+31*q-53 ) q congruent 49 modulo 60: 1/384 phi1^2 ( q^4-8*q^3+12*q^2+16*q+27 ) q congruent 53 modulo 60: 1/384 phi1^2 phi2 ( q^3-9*q^2+21*q-5 ) q congruent 59 modulo 60: 1/384 phi2 ( q^5-11*q^4+40*q^3-56*q^2+31*q-53 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 20 ], [ 4, 1, 1, 14 ], [ 4, 1, 2, 34 ], [ 5, 1, 2, 32 ], [ 6, 1, 1, 24 ], [ 6, 1, 2, 40 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 28 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 14 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 36 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 68 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 36 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 64 ], [ 15, 1, 2, 64 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 40 ], [ 16, 1, 4, 88 ], [ 17, 1, 2, 96 ], [ 17, 1, 3, 32 ], [ 18, 1, 2, 64 ], [ 19, 1, 1, 24 ], [ 19, 1, 2, 72 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 72 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 56 ], [ 20, 1, 5, 96 ], [ 20, 1, 7, 96 ], [ 21, 1, 2, 48 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 64 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 30 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 50 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 84 ], [ 25, 1, 4, 48 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 48 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 24 ], [ 27, 1, 6, 48 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 28 ], [ 28, 1, 3, 60 ], [ 28, 1, 4, 84 ], [ 29, 1, 3, 32 ], [ 29, 1, 4, 96 ], [ 30, 1, 3, 96 ], [ 30, 1, 4, 32 ], [ 31, 1, 2, 48 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 64 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 96 ], [ 33, 1, 2, 48 ], [ 33, 1, 6, 80 ], [ 33, 1, 10, 192 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 34, 1, 4, 96 ], [ 35, 1, 1, 24 ], [ 35, 1, 2, 72 ], [ 35, 1, 3, 72 ], [ 35, 1, 4, 120 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 56 ], [ 35, 1, 8, 72 ], [ 36, 1, 3, 32 ], [ 36, 1, 4, 96 ], [ 37, 1, 2, 48 ], [ 37, 1, 3, 96 ], [ 38, 1, 6, 192 ], [ 38, 1, 10, 64 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 72 ], [ 39, 1, 4, 28 ], [ 40, 1, 2, 40 ], [ 40, 1, 3, 24 ], [ 40, 1, 6, 144 ], [ 41, 1, 2, 24 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 72 ], [ 41, 1, 7, 32 ], [ 41, 1, 9, 144 ], [ 41, 1, 10, 96 ], [ 42, 1, 2, 48 ], [ 42, 1, 4, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 2, 48 ], [ 43, 1, 4, 16 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 96 ], [ 43, 1, 14, 192 ], [ 44, 1, 2, 8 ], [ 44, 1, 5, 48 ], [ 44, 1, 8, 120 ], [ 44, 1, 10, 48 ], [ 45, 1, 5, 96 ], [ 45, 1, 6, 96 ], [ 46, 1, 8, 192 ], [ 46, 1, 12, 192 ], [ 47, 1, 4, 96 ], [ 47, 1, 9, 32 ], [ 47, 1, 10, 128 ], [ 48, 1, 2, 48 ], [ 48, 1, 3, 96 ], [ 48, 1, 5, 48 ], [ 48, 1, 6, 96 ], [ 48, 1, 10, 96 ], [ 49, 1, 2, 48 ], [ 49, 1, 8, 144 ], [ 49, 1, 14, 192 ], [ 49, 1, 15, 192 ], [ 49, 1, 19, 192 ], [ 50, 1, 5, 96 ], [ 50, 1, 9, 96 ], [ 50, 1, 11, 96 ], [ 50, 1, 12, 96 ], [ 51, 1, 3, 96 ], [ 51, 1, 5, 96 ], [ 51, 1, 8, 32 ], [ 51, 1, 9, 96 ], [ 52, 1, 3, 24 ], [ 52, 1, 4, 72 ], [ 52, 1, 9, 144 ], [ 52, 1, 10, 144 ], [ 53, 1, 3, 48 ], [ 53, 1, 4, 144 ], [ 53, 1, 7, 16 ], [ 53, 1, 8, 48 ], [ 53, 1, 9, 96 ], [ 53, 1, 12, 96 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 96 ], [ 54, 1, 12, 192 ], [ 55, 1, 10, 192 ], [ 55, 1, 17, 64 ], [ 55, 1, 20, 192 ], [ 56, 1, 5, 96 ], [ 56, 1, 7, 96 ], [ 56, 1, 10, 96 ], [ 56, 1, 15, 96 ], [ 56, 1, 18, 96 ], [ 56, 1, 20, 96 ], [ 57, 1, 4, 96 ], [ 57, 1, 9, 192 ], [ 58, 1, 26, 384 ], [ 59, 1, 13, 288 ], [ 59, 1, 18, 96 ], [ 59, 1, 22, 48 ], [ 60, 1, 39, 384 ], [ 60, 1, 43, 192 ], [ 60, 1, 45, 96 ], [ 62, 1, 44, 192 ], [ 62, 1, 48, 192 ], [ 62, 1, 49, 192 ], [ 63, 1, 32, 192 ], [ 63, 1, 36, 192 ] ] k = 64: F-action on Pi is () [64,1,64] Dynkin type is A_1(q) + A_1(q) + T(phi1^3 phi2^3) Order of center |Z^F|: phi1^3 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 ( q^5-13*q^4+54*q^3-70*q^2+q-37 ) q congruent 2 modulo 60: 1/384 ( q^6-14*q^5+64*q^4-104*q^3+48*q^2-64*q+128 ) q congruent 3 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2+26*q-123 ) q congruent 4 modulo 60: 1/384 q ( q^5-14*q^4+64*q^3-104*q^2+48*q-64 ) q congruent 5 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q+165 ) q congruent 7 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q-59 ) q congruent 8 modulo 60: 1/384 ( q^6-14*q^5+64*q^4-104*q^3+48*q^2-64*q+128 ) q congruent 9 modulo 60: 1/384 phi1^2 ( q^4-12*q^3+42*q^2-28*q-27 ) q congruent 11 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q+69 ) q congruent 13 modulo 60: 1/384 phi1 ( q^5-13*q^4+54*q^3-70*q^2+q-37 ) q congruent 16 modulo 60: 1/384 q ( q^5-14*q^4+64*q^3-104*q^2+48*q-64 ) q congruent 17 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q+165 ) q congruent 19 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q-59 ) q congruent 21 modulo 60: 1/384 phi1^2 ( q^4-12*q^3+42*q^2-28*q-27 ) q congruent 23 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q+69 ) q congruent 25 modulo 60: 1/384 phi1 ( q^5-13*q^4+54*q^3-70*q^2+q-37 ) q congruent 27 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2+26*q-123 ) q congruent 29 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q+165 ) q congruent 31 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q-59 ) q congruent 32 modulo 60: 1/384 ( q^6-14*q^5+64*q^4-104*q^3+48*q^2-64*q+128 ) q congruent 37 modulo 60: 1/384 phi1 ( q^5-13*q^4+54*q^3-70*q^2+q-37 ) q congruent 41 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q+165 ) q congruent 43 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q-59 ) q congruent 47 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q+69 ) q congruent 49 modulo 60: 1/384 phi1 ( q^5-13*q^4+54*q^3-70*q^2+q-37 ) q congruent 53 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q+165 ) q congruent 59 modulo 60: 1/384 ( q^6-14*q^5+67*q^4-124*q^3+71*q^2-38*q+69 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 3, 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 36 ], [ 4, 1, 2, 36 ], [ 6, 1, 1, 32 ], [ 6, 1, 2, 32 ], [ 7, 1, 1, 8 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 48 ], [ 13, 1, 3, 48 ], [ 13, 1, 4, 72 ], [ 16, 1, 1, 96 ], [ 16, 1, 2, 96 ], [ 16, 1, 3, 96 ], [ 16, 1, 4, 96 ], [ 17, 1, 2, 64 ], [ 17, 1, 3, 64 ], [ 19, 1, 1, 32 ], [ 19, 1, 2, 32 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 144 ], [ 20, 1, 3, 144 ], [ 20, 1, 4, 48 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 48 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 42 ], [ 24, 1, 2, 42 ], [ 25, 1, 1, 72 ], [ 25, 1, 2, 96 ], [ 25, 1, 3, 72 ], [ 25, 1, 4, 96 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 72 ], [ 28, 1, 3, 72 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 144 ], [ 31, 1, 3, 144 ], [ 32, 1, 2, 192 ], [ 32, 1, 4, 64 ], [ 33, 1, 1, 192 ], [ 33, 1, 2, 192 ], [ 33, 1, 6, 192 ], [ 33, 1, 8, 192 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 1, 96 ], [ 35, 1, 2, 96 ], [ 35, 1, 3, 288 ], [ 35, 1, 4, 96 ], [ 35, 1, 5, 96 ], [ 35, 1, 6, 288 ], [ 35, 1, 7, 96 ], [ 35, 1, 8, 96 ], [ 37, 1, 2, 96 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 48 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 36 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 96 ], [ 40, 1, 3, 96 ], [ 40, 1, 6, 48 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 96 ], [ 41, 1, 4, 192 ], [ 41, 1, 6, 216 ], [ 41, 1, 9, 144 ], [ 43, 1, 3, 192 ], [ 43, 1, 8, 192 ], [ 43, 1, 12, 192 ], [ 44, 1, 5, 96 ], [ 44, 1, 9, 96 ], [ 47, 1, 2, 288 ], [ 47, 1, 4, 192 ], [ 47, 1, 7, 288 ], [ 47, 1, 9, 192 ], [ 48, 1, 2, 144 ], [ 48, 1, 3, 192 ], [ 48, 1, 4, 192 ], [ 48, 1, 5, 144 ], [ 49, 1, 1, 192 ], [ 49, 1, 2, 192 ], [ 49, 1, 5, 576 ], [ 49, 1, 8, 192 ], [ 49, 1, 9, 576 ], [ 49, 1, 10, 192 ], [ 51, 1, 3, 192 ], [ 51, 1, 5, 192 ], [ 51, 1, 6, 192 ], [ 51, 1, 10, 192 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 144 ], [ 52, 1, 3, 96 ], [ 52, 1, 4, 96 ], [ 52, 1, 9, 144 ], [ 52, 1, 10, 48 ], [ 53, 1, 6, 384 ], [ 53, 1, 9, 384 ], [ 55, 1, 5, 384 ], [ 55, 1, 14, 384 ], [ 56, 1, 5, 192 ], [ 56, 1, 10, 192 ], [ 56, 1, 14, 192 ], [ 56, 1, 19, 192 ], [ 57, 1, 2, 288 ], [ 57, 1, 4, 192 ], [ 57, 1, 5, 384 ], [ 57, 1, 6, 288 ], [ 58, 1, 4, 384 ], [ 59, 1, 3, 192 ], [ 60, 1, 27, 768 ], [ 61, 1, 17, 384 ], [ 61, 1, 22, 384 ], [ 62, 1, 31, 384 ], [ 62, 1, 32, 384 ] ] k = 65: F-action on Pi is (1,2) [64,1,65] Dynkin type is A_1(q^2) + T(phi1^3 phi2^3) Order of center |Z^F|: phi1^3 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 2 modulo 60: 1/128 q ( q^5-6*q^4+40*q^2-16*q-64 ) q congruent 3 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) q congruent 4 modulo 60: 1/128 q ( q^5-6*q^4+40*q^2-16*q-64 ) q congruent 5 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 7 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) q congruent 8 modulo 60: 1/128 q ( q^5-6*q^4+40*q^2-16*q-64 ) q congruent 9 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 11 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) q congruent 13 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 16 modulo 60: 1/128 q ( q^5-6*q^4+40*q^2-16*q-64 ) q congruent 17 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 19 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) q congruent 21 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 23 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) q congruent 25 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 27 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) q congruent 29 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 31 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) q congruent 32 modulo 60: 1/128 q ( q^5-6*q^4+40*q^2-16*q-64 ) q congruent 37 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 41 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 43 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) q congruent 47 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) q congruent 49 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 53 modulo 60: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+24*q+35 ) q congruent 59 modulo 60: 1/128 phi2 ( q^5-7*q^4+8*q^3+28*q^2-49*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 10 ], [ 5, 1, 1, 16 ], [ 5, 1, 2, 16 ], [ 6, 1, 1, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 1, 8 ], [ 7, 1, 2, 8 ], [ 8, 1, 1, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 20 ], [ 13, 1, 3, 20 ], [ 13, 1, 4, 16 ], [ 14, 1, 1, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 32 ], [ 17, 1, 3, 32 ], [ 18, 1, 1, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 1, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 1, 16 ], [ 20, 1, 2, 16 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 16 ], [ 20, 1, 6, 32 ], [ 20, 1, 7, 32 ], [ 21, 1, 1, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 16 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 1, 8 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 8 ], [ 29, 1, 2, 32 ], [ 29, 1, 3, 32 ], [ 30, 1, 1, 16 ], [ 30, 1, 2, 48 ], [ 30, 1, 3, 16 ], [ 30, 1, 4, 48 ], [ 31, 1, 1, 16 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 16 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 32 ], [ 33, 1, 2, 32 ], [ 33, 1, 6, 32 ], [ 34, 1, 1, 16 ], [ 34, 1, 2, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 4, 16 ], [ 35, 1, 1, 16 ], [ 35, 1, 2, 16 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 1, 5, 16 ], [ 35, 1, 6, 16 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 16 ], [ 36, 1, 2, 32 ], [ 36, 1, 3, 32 ], [ 37, 1, 1, 16 ], [ 37, 1, 2, 16 ], [ 37, 1, 3, 16 ], [ 37, 1, 4, 64 ], [ 38, 1, 2, 64 ], [ 38, 1, 10, 64 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 20 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 40, 1, 2, 16 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 40 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 32 ], [ 41, 1, 7, 32 ], [ 41, 1, 9, 16 ], [ 42, 1, 2, 32 ], [ 42, 1, 4, 32 ], [ 43, 1, 2, 32 ], [ 43, 1, 4, 32 ], [ 43, 1, 7, 64 ], [ 44, 1, 2, 16 ], [ 44, 1, 5, 32 ], [ 44, 1, 8, 16 ], [ 44, 1, 9, 32 ], [ 45, 1, 2, 32 ], [ 45, 1, 5, 32 ], [ 46, 1, 8, 64 ], [ 46, 1, 11, 64 ], [ 47, 1, 3, 32 ], [ 47, 1, 4, 32 ], [ 47, 1, 9, 32 ], [ 47, 1, 10, 32 ], [ 48, 1, 1, 16 ], [ 48, 1, 2, 16 ], [ 48, 1, 3, 16 ], [ 48, 1, 4, 16 ], [ 48, 1, 5, 16 ], [ 48, 1, 6, 16 ], [ 48, 1, 7, 48 ], [ 48, 1, 10, 48 ], [ 49, 1, 2, 32 ], [ 49, 1, 8, 32 ], [ 49, 1, 15, 64 ], [ 49, 1, 18, 64 ], [ 50, 1, 2, 32 ], [ 50, 1, 5, 32 ], [ 50, 1, 8, 32 ], [ 50, 1, 11, 32 ], [ 51, 1, 2, 32 ], [ 51, 1, 8, 32 ], [ 52, 1, 2, 32 ], [ 52, 1, 3, 16 ], [ 52, 1, 4, 16 ], [ 52, 1, 9, 32 ], [ 53, 1, 3, 32 ], [ 53, 1, 4, 32 ], [ 53, 1, 7, 32 ], [ 53, 1, 8, 32 ], [ 54, 1, 5, 64 ], [ 54, 1, 13, 64 ], [ 55, 1, 8, 64 ], [ 55, 1, 17, 64 ], [ 56, 1, 2, 32 ], [ 56, 1, 7, 32 ], [ 56, 1, 13, 32 ], [ 56, 1, 18, 32 ], [ 57, 1, 3, 32 ], [ 57, 1, 4, 32 ], [ 57, 1, 9, 32 ], [ 57, 1, 16, 128 ], [ 58, 1, 17, 128 ], [ 59, 1, 3, 64 ], [ 59, 1, 22, 32 ], [ 60, 1, 38, 128 ], [ 60, 1, 45, 64 ], [ 62, 1, 49, 64 ], [ 62, 1, 50, 64 ], [ 63, 1, 29, 64 ], [ 63, 1, 34, 64 ] ] i = 65: Pi = [ 1, 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [65,1,1] Dynkin type is A_2(q) + T(phi1^6) Order of center |Z^F|: phi1^6 Numbers of classes in class type: q congruent 1 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+202821*q^2-806169*q+1457692 ) q congruent 2 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26468*q^3+191736*q^2-654624*q+725760 ) q congruent 3 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-768969*q+1074060 ) q congruent 4 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26468*q^3+192696*q^2-685344*q+931840 ) q congruent 5 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-775449*q+1184220 ) q congruent 7 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+202821*q^2-799689*q+1306060 ) q congruent 8 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26468*q^3+191736*q^2-654624*q+725760 ) q congruent 9 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-775449*q+1184220 ) q congruent 11 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-768969*q+1115532 ) q congruent 13 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+202821*q^2-806169*q+1416220 ) q congruent 16 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26468*q^3+192696*q^2-685344*q+973312 ) q congruent 17 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-775449*q+1184220 ) q congruent 19 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+202821*q^2-799689*q+1306060 ) q congruent 21 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-775449*q+1225692 ) q congruent 23 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-768969*q+1074060 ) q congruent 25 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+202821*q^2-806169*q+1416220 ) q congruent 27 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-768969*q+1074060 ) q congruent 29 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-775449*q+1184220 ) q congruent 31 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+202821*q^2-799689*q+1347532 ) q congruent 32 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26468*q^3+191736*q^2-654624*q+725760 ) q congruent 37 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+202821*q^2-806169*q+1416220 ) q congruent 41 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-775449*q+1225692 ) q congruent 43 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+202821*q^2-799689*q+1306060 ) q congruent 47 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-768969*q+1074060 ) q congruent 49 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+202821*q^2-806169*q+1416220 ) q congruent 53 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-775449*q+1184220 ) q congruent 59 modulo 60: 1/103680 ( q^6-69*q^5+1902*q^4-26738*q^3+201861*q^2-768969*q+1074060 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 36 ], [ 3, 1, 1, 242 ], [ 4, 1, 1, 594 ], [ 5, 1, 1, 864 ], [ 6, 1, 1, 1512 ], [ 7, 1, 1, 432 ], [ 8, 1, 1, 144 ], [ 9, 1, 1, 27 ], [ 10, 1, 1, 72 ], [ 11, 1, 1, 720 ], [ 12, 1, 1, 2214 ], [ 13, 1, 1, 3240 ], [ 14, 1, 1, 3024 ], [ 15, 1, 1, 4752 ], [ 16, 1, 1, 5400 ], [ 17, 1, 1, 4320 ], [ 18, 1, 1, 2160 ], [ 19, 1, 1, 4320 ], [ 20, 1, 1, 4320 ], [ 21, 1, 1, 864 ], [ 22, 1, 1, 3024 ], [ 23, 1, 1, 270 ], [ 24, 1, 1, 1080 ], [ 25, 1, 1, 2700 ], [ 26, 1, 1, 864 ], [ 27, 1, 1, 1440 ], [ 28, 1, 1, 6480 ], [ 29, 1, 1, 9504 ], [ 30, 1, 1, 12960 ], [ 31, 1, 1, 10800 ], [ 32, 1, 1, 8640 ], [ 33, 1, 1, 6480 ], [ 34, 1, 1, 8640 ], [ 35, 1, 1, 12960 ], [ 36, 1, 1, 4320 ], [ 37, 1, 1, 8640 ], [ 38, 1, 1, 8640 ], [ 39, 1, 1, 2160 ], [ 40, 1, 1, 9180 ], [ 41, 1, 1, 12960 ], [ 42, 1, 1, 8640 ], [ 43, 1, 1, 8640 ], [ 44, 1, 1, 12960 ], [ 45, 1, 1, 25920 ], [ 46, 1, 1, 17280 ], [ 47, 1, 1, 12960 ], [ 48, 1, 1, 25920 ], [ 50, 1, 1, 17280 ], [ 51, 1, 1, 21600 ], [ 52, 1, 1, 25920 ], [ 53, 1, 1, 25920 ], [ 54, 1, 1, 51840 ], [ 55, 1, 1, 25920 ], [ 56, 1, 1, 51840 ], [ 58, 1, 1, 34560 ], [ 59, 1, 1, 51840 ], [ 61, 1, 1, 51840 ], [ 63, 1, 1, 103680 ] ] k = 2: F-action on Pi is () [65,1,2] Dynkin type is A_2(q) + T(phi1^2 phi5) Order of center |Z^F|: phi1^2 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 2 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 13 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 17 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 23 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 32 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/20 phi1 ( q^5-3*q^4-q^3+q^2+2*q+8 ) q congruent 43 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/20 q phi2 phi4 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 23, 93, 62 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 26, 1, 1, 4 ], [ 29, 1, 1, 4 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 10 ], [ 63, 1, 2, 20 ] ] k = 3: F-action on Pi is () [65,1,3] Dynkin type is A_2(q) + T(phi1 phi2 phi5) Order of center |Z^F|: phi1 phi2 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 2 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 3 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 4 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 5 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 7 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 8 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 9 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 11 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 13 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 16 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 17 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 19 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 21 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 23 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 25 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 27 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 29 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 31 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 32 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 37 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 41 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 43 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 47 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 49 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 53 modulo 60: 1/20 q^2 phi1 phi2 phi4 q congruent 59 modulo 60: 1/20 q^2 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 93, 50, 111 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 15, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 26, 1, 3, 4 ], [ 29, 1, 2, 4 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 10 ] ] k = 4: F-action on Pi is (1,3) [65,1,4] Dynkin type is ^2A_2(q) + T(phi2^2 phi10) Order of center |Z^F|: phi2^2 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 2 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 3 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 4 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 5 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 7 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 8 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 9 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 11 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 13 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 16 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 17 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 19 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 21 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 23 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 25 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 27 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 29 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 31 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 32 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 37 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 41 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 43 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 47 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 49 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) q congruent 53 modulo 60: 1/20 q^2 phi1^2 phi4 q congruent 59 modulo 60: 1/20 phi2 ( q^5-3*q^4+5*q^3-7*q^2+8*q-8 ) Fusion of maximal tori of C^F in those of G^F: [ 24, 94, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 29, 1, 4, 4 ], [ 54, 1, 8, 10 ], [ 61, 1, 3, 10 ], [ 63, 1, 3, 20 ] ] k = 5: F-action on Pi is (1,3) [65,1,5] Dynkin type is ^2A_2(q) + T(phi1 phi2 phi10) Order of center |Z^F|: phi1 phi2 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 17 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/20 q phi1 phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 94, 51, 112 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 15, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 26, 1, 2, 4 ], [ 29, 1, 3, 4 ], [ 54, 1, 8, 10 ], [ 61, 1, 3, 10 ] ] k = 6: F-action on Pi is () [65,1,6] Dynkin type is A_2(q) + T(phi3^3) Order of center |Z^F|: phi3^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 2 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 3 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 4 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 5 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 7 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 8 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 9 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 11 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 13 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 16 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 17 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 19 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 21 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 23 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 25 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 27 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 29 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 31 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 32 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 37 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 41 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 43 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 47 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 49 modulo 60: 1/1296 phi1 ( q^5+4*q^4-11*q^3-46*q^2+32*q+128 ) q congruent 53 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) q congruent 59 modulo 60: 1/1296 q phi2 ( q^4+2*q^3-17*q^2-18*q+72 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 79, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 26 ], [ 27, 1, 5, 72 ], [ 38, 1, 3, 432 ], [ 40, 1, 5, 270 ], [ 58, 1, 8, 864 ], [ 59, 1, 9, 648 ] ] k = 7: F-action on Pi is () [65,1,7] Dynkin type is A_2(q) + T(phi9) Order of center |Z^F|: phi9 Numbers of classes in class type: q congruent 1 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 2 modulo 60: 1/18 q^3 phi2 phi6 q congruent 3 modulo 60: 1/18 q^3 phi2 phi6 q congruent 4 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 5 modulo 60: 1/18 q^3 phi2 phi6 q congruent 7 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 8 modulo 60: 1/18 q^3 phi2 phi6 q congruent 9 modulo 60: 1/18 q^3 phi2 phi6 q congruent 11 modulo 60: 1/18 q^3 phi2 phi6 q congruent 13 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 16 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 17 modulo 60: 1/18 q^3 phi2 phi6 q congruent 19 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 21 modulo 60: 1/18 q^3 phi2 phi6 q congruent 23 modulo 60: 1/18 q^3 phi2 phi6 q congruent 25 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 27 modulo 60: 1/18 q^3 phi2 phi6 q congruent 29 modulo 60: 1/18 q^3 phi2 phi6 q congruent 31 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 32 modulo 60: 1/18 q^3 phi2 phi6 q congruent 37 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 41 modulo 60: 1/18 q^3 phi2 phi6 q congruent 43 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 47 modulo 60: 1/18 q^3 phi2 phi6 q congruent 49 modulo 60: 1/18 phi1 phi3 ( q^3+2 ) q congruent 53 modulo 60: 1/18 q^3 phi2 phi6 q congruent 59 modulo 60: 1/18 q^3 phi2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 46, 105, 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ] ] k = 8: F-action on Pi is () [65,1,8] Dynkin type is A_2(q) + T(phi1^2 phi3^2) Order of center |Z^F|: phi1^2 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+17*q+26 ) q congruent 2 modulo 60: 1/216 q^2 phi2 ( q^3-4*q^2-2*q+12 ) q congruent 3 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+8*q+8 ) q congruent 5 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 7 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+17*q+26 ) q congruent 8 modulo 60: 1/216 q^2 phi2 ( q^3-4*q^2-2*q+12 ) q congruent 9 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 13 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+17*q+26 ) q congruent 16 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+8*q+8 ) q congruent 17 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 19 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+17*q+26 ) q congruent 21 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 25 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+17*q+26 ) q congruent 27 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 31 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+17*q+26 ) q congruent 32 modulo 60: 1/216 q^2 phi2 ( q^3-4*q^2-2*q+12 ) q congruent 37 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+17*q+26 ) q congruent 41 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 43 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+17*q+26 ) q congruent 47 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 49 modulo 60: 1/216 phi1 ( q^5-2*q^4-8*q^3+2*q^2+17*q+26 ) q congruent 53 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) q congruent 59 modulo 60: 1/216 q phi2^3 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 83, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 18 ], [ 8, 1, 1, 12 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 22, 1, 1, 36 ], [ 27, 1, 1, 12 ], [ 27, 1, 5, 12 ], [ 33, 1, 3, 54 ], [ 38, 1, 1, 72 ], [ 38, 1, 3, 72 ], [ 40, 1, 5, 36 ], [ 42, 1, 3, 36 ], [ 46, 1, 3, 72 ], [ 47, 1, 5, 108 ], [ 50, 1, 3, 72 ], [ 52, 1, 6, 54 ], [ 58, 1, 3, 144 ], [ 58, 1, 8, 72 ], [ 59, 1, 7, 108 ], [ 61, 1, 5, 108 ] ] k = 9: F-action on Pi is () [65,1,9] Dynkin type is A_2(q) + T(phi1^4 phi3) Order of center |Z^F|: phi1^4 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-157*q^2-133*q+392 ) q congruent 2 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-372*q+360 ) q congruent 3 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 4 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-148*q^2-160*q+320 ) q congruent 5 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 7 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-157*q^2-133*q+392 ) q congruent 8 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-372*q+360 ) q congruent 9 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 11 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 13 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-157*q^2-133*q+392 ) q congruent 16 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-148*q^2-160*q+320 ) q congruent 17 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 19 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-157*q^2-133*q+392 ) q congruent 21 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 23 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 25 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-157*q^2-133*q+392 ) q congruent 27 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 29 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 31 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-157*q^2-133*q+392 ) q congruent 32 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-372*q+360 ) q congruent 37 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-157*q^2-133*q+392 ) q congruent 41 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 43 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-157*q^2-133*q+392 ) q congruent 47 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 49 modulo 60: 1/432 phi1 ( q^5-17*q^4+94*q^3-157*q^2-133*q+392 ) q congruent 53 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 59 modulo 60: 1/432 q phi2 ( q^4-19*q^3+130*q^2-381*q+405 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77, 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], [ 5, 1, 1, 72 ], [ 6, 1, 1, 36 ], [ 7, 1, 1, 36 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 9 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 36 ], [ 14, 1, 1, 144 ], [ 15, 1, 1, 72 ], [ 16, 1, 1, 72 ], [ 17, 1, 1, 72 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 36 ], [ 20, 1, 1, 144 ], [ 21, 1, 1, 72 ], [ 22, 1, 1, 72 ], [ 23, 1, 1, 36 ], [ 24, 1, 1, 36 ], [ 25, 1, 1, 144 ], [ 26, 1, 1, 72 ], [ 27, 1, 1, 24 ], [ 27, 1, 5, 6 ], [ 29, 1, 1, 144 ], [ 31, 1, 1, 144 ], [ 32, 1, 1, 72 ], [ 34, 1, 1, 72 ], [ 36, 1, 1, 144 ], [ 37, 1, 1, 288 ], [ 38, 1, 1, 144 ], [ 38, 1, 3, 36 ], [ 39, 1, 1, 72 ], [ 40, 1, 1, 144 ], [ 42, 1, 1, 72 ], [ 42, 1, 3, 36 ], [ 43, 1, 1, 288 ], [ 44, 1, 3, 54 ], [ 45, 1, 3, 108 ], [ 46, 1, 1, 144 ], [ 46, 1, 3, 72 ], [ 50, 1, 1, 144 ], [ 50, 1, 3, 72 ], [ 51, 1, 1, 288 ], [ 53, 1, 16, 108 ], [ 54, 1, 3, 216 ], [ 55, 1, 3, 108 ], [ 56, 1, 3, 216 ], [ 58, 1, 1, 288 ], [ 58, 1, 3, 144 ], [ 59, 1, 4, 216 ], [ 61, 1, 4, 216 ], [ 63, 1, 4, 432 ] ] k = 10: F-action on Pi is (1,3) [65,1,10] Dynkin type is ^2A_2(q) + T(phi6^3) Order of center |Z^F|: phi6^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 2 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 3 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 4 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 5 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 7 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 8 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 9 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 11 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 13 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 16 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 17 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 19 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 21 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 23 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 25 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 27 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 29 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 31 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 32 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 37 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 41 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 43 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 47 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 49 modulo 60: 1/1296 q phi1 ( q^4-2*q^3-17*q^2+18*q+72 ) q congruent 53 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) q congruent 59 modulo 60: 1/1296 phi2 ( q^5-4*q^4-11*q^3+46*q^2+32*q-128 ) Fusion of maximal tori of C^F in those of G^F: [ 13, 80, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 26 ], [ 27, 1, 4, 72 ], [ 38, 1, 11, 432 ], [ 40, 1, 4, 270 ], [ 58, 1, 13, 864 ], [ 59, 1, 10, 648 ] ] k = 11: F-action on Pi is () [65,1,11] Dynkin type is A_2(q) + T(phi3 phi6^2) Order of center |Z^F|: phi3 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 2 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 3 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 4 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 5 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 7 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 8 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 9 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 11 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 13 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 16 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 17 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 19 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 21 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 23 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 25 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 27 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 29 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 31 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 32 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 37 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 41 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 43 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 47 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 49 modulo 60: 1/144 q phi1 ( q^4-3*q^2-2*q-8 ) q congruent 53 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) q congruent 59 modulo 60: 1/144 q^2 phi1 phi2^2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 86, 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 27, 1, 4, 24 ], [ 38, 1, 4, 48 ], [ 40, 1, 4, 24 ], [ 40, 1, 5, 6 ], [ 58, 1, 6, 48 ], [ 59, 1, 10, 72 ] ] k = 12: F-action on Pi is () [65,1,12] Dynkin type is A_2(q) + T(phi3 phi12) Order of center |Z^F|: phi3 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 2 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 3 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 4 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 5 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 7 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 8 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 9 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 11 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 13 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 16 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 17 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 19 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 21 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 23 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 25 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 27 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 29 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 31 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 32 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 37 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 41 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 43 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 47 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 49 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 53 modulo 60: 1/24 q^3 phi1 phi2^2 q congruent 59 modulo 60: 1/24 q^3 phi1 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 57, 101, 55 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 40, 1, 5, 6 ], [ 59, 1, 11, 12 ] ] k = 13: F-action on Pi is (1,3) [65,1,13] Dynkin type is ^2A_2(q) + T(phi6 phi12) Order of center |Z^F|: phi6 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 2 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 3 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 4 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 5 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 7 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 8 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 9 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 11 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 13 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 16 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 17 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 19 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 21 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 23 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 25 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 27 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 29 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 31 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 32 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 37 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 41 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 43 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 47 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 49 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 53 modulo 60: 1/24 q^3 phi1^2 phi2 q congruent 59 modulo 60: 1/24 q^3 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 58, 102, 56 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 40, 1, 4, 6 ], [ 59, 1, 11, 12 ] ] k = 14: F-action on Pi is (1,3) [65,1,14] Dynkin type is ^2A_2(q) + T(phi3^2 phi6) Order of center |Z^F|: phi3^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 2 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 3 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 4 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 5 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 7 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 8 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 9 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 11 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 13 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 16 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 17 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 19 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 21 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 23 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 25 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 27 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 29 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 31 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 32 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 37 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 41 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 43 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 47 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 49 modulo 60: 1/144 q^2 phi1^2 phi2 ( q+2 ) q congruent 53 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) q congruent 59 modulo 60: 1/144 q phi2 ( q^4-3*q^2+2*q-8 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 85, 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 27, 1, 5, 24 ], [ 38, 1, 9, 48 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 24 ], [ 58, 1, 6, 48 ], [ 59, 1, 9, 72 ] ] k = 15: F-action on Pi is (1,3) [65,1,15] Dynkin type is ^2A_2(q) + T(phi18) Order of center |Z^F|: phi18 Numbers of classes in class type: q congruent 1 modulo 60: 1/18 q^3 phi1 phi3 q congruent 2 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 3 modulo 60: 1/18 q^3 phi1 phi3 q congruent 4 modulo 60: 1/18 q^3 phi1 phi3 q congruent 5 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 7 modulo 60: 1/18 q^3 phi1 phi3 q congruent 8 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 9 modulo 60: 1/18 q^3 phi1 phi3 q congruent 11 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 13 modulo 60: 1/18 q^3 phi1 phi3 q congruent 16 modulo 60: 1/18 q^3 phi1 phi3 q congruent 17 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 19 modulo 60: 1/18 q^3 phi1 phi3 q congruent 21 modulo 60: 1/18 q^3 phi1 phi3 q congruent 23 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 25 modulo 60: 1/18 q^3 phi1 phi3 q congruent 27 modulo 60: 1/18 q^3 phi1 phi3 q congruent 29 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 31 modulo 60: 1/18 q^3 phi1 phi3 q congruent 32 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 37 modulo 60: 1/18 q^3 phi1 phi3 q congruent 41 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 43 modulo 60: 1/18 q^3 phi1 phi3 q congruent 47 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 49 modulo 60: 1/18 q^3 phi1 phi3 q congruent 53 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) q congruent 59 modulo 60: 1/18 phi2 phi6 ( q^3-2 ) Fusion of maximal tori of C^F in those of G^F: [ 47, 106, 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ] ] k = 16: F-action on Pi is (1,3) [65,1,16] Dynkin type is ^2A_2(q) + T(phi1 phi2 phi6^2) Order of center |Z^F|: phi1 phi2 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 2 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+8*q-16 ) q congruent 3 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+12 ) q congruent 5 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+11*q-22 ) q congruent 7 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 8 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+8*q-16 ) q congruent 9 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 11 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+11*q-22 ) q congruent 13 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+12 ) q congruent 17 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+11*q-22 ) q congruent 19 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 21 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 23 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+11*q-22 ) q congruent 25 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 27 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 29 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+11*q-22 ) q congruent 31 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 32 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+8*q-16 ) q congruent 37 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 41 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+11*q-22 ) q congruent 43 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 47 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+11*q-22 ) q congruent 49 modulo 60: 1/72 q phi1 ( q^4-2*q^3-4*q^2+2*q+15 ) q congruent 53 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+11*q-22 ) q congruent 59 modulo 60: 1/72 phi2 ( q^5-4*q^4+2*q^3+4*q^2+11*q-22 ) Fusion of maximal tori of C^F in those of G^F: [ 84, 38, 80 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 4, 12 ], [ 22, 1, 3, 12 ], [ 27, 1, 3, 4 ], [ 27, 1, 4, 12 ], [ 33, 1, 7, 18 ], [ 38, 1, 8, 24 ], [ 38, 1, 11, 72 ], [ 40, 1, 4, 36 ], [ 42, 1, 5, 12 ], [ 46, 1, 4, 24 ], [ 47, 1, 11, 36 ], [ 50, 1, 7, 24 ], [ 52, 1, 7, 18 ], [ 58, 1, 10, 48 ], [ 58, 1, 13, 72 ], [ 59, 1, 15, 36 ], [ 61, 1, 9, 36 ] ] k = 17: F-action on Pi is () [65,1,17] Dynkin type is A_2(q) + T(phi1 phi2 phi3^2) Order of center |Z^F|: phi1 phi2 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1^2 ( q^4+3*q^3+q^2-5*q-6 ) q congruent 2 modulo 60: 1/72 q^3 phi2 ( q^2-4 ) q congruent 3 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^4+2*q^3-2*q^2-6*q-4 ) q congruent 5 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 7 modulo 60: 1/72 phi1^2 ( q^4+3*q^3+q^2-5*q-6 ) q congruent 8 modulo 60: 1/72 q^3 phi2 ( q^2-4 ) q congruent 9 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 11 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 13 modulo 60: 1/72 phi1^2 ( q^4+3*q^3+q^2-5*q-6 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^4+2*q^3-2*q^2-6*q-4 ) q congruent 17 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 19 modulo 60: 1/72 phi1^2 ( q^4+3*q^3+q^2-5*q-6 ) q congruent 21 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 23 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 25 modulo 60: 1/72 phi1^2 ( q^4+3*q^3+q^2-5*q-6 ) q congruent 27 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 29 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 31 modulo 60: 1/72 phi1^2 ( q^4+3*q^3+q^2-5*q-6 ) q congruent 32 modulo 60: 1/72 q^3 phi2 ( q^2-4 ) q congruent 37 modulo 60: 1/72 phi1^2 ( q^4+3*q^3+q^2-5*q-6 ) q congruent 41 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 43 modulo 60: 1/72 phi1^2 ( q^4+3*q^3+q^2-5*q-6 ) q congruent 47 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 49 modulo 60: 1/72 phi1^2 ( q^4+3*q^3+q^2-5*q-6 ) q congruent 53 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) q congruent 59 modulo 60: 1/72 q phi1 phi2^2 ( q^2-3 ) Fusion of maximal tori of C^F in those of G^F: [ 83, 37, 79 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 1, 12 ], [ 22, 1, 2, 12 ], [ 27, 1, 2, 4 ], [ 27, 1, 5, 12 ], [ 33, 1, 3, 18 ], [ 38, 1, 3, 72 ], [ 38, 1, 5, 24 ], [ 40, 1, 5, 36 ], [ 42, 1, 3, 12 ], [ 46, 1, 3, 24 ], [ 47, 1, 6, 36 ], [ 50, 1, 6, 24 ], [ 52, 1, 6, 18 ], [ 58, 1, 7, 48 ], [ 58, 1, 8, 72 ], [ 59, 1, 14, 36 ], [ 61, 1, 5, 36 ] ] k = 18: F-action on Pi is (1,3) [65,1,18] Dynkin type is ^2A_2(q) + T(phi2^2 phi6^2) Order of center |Z^F|: phi2^2 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 2 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+8*q+16 ) q congruent 3 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 4 modulo 60: 1/216 q^2 phi1 ( q^3-2*q^2-2*q-6 ) q congruent 5 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+17*q-2 ) q congruent 7 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 8 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+8*q+16 ) q congruent 9 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 11 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+17*q-2 ) q congruent 13 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 16 modulo 60: 1/216 q^2 phi1 ( q^3-2*q^2-2*q-6 ) q congruent 17 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+17*q-2 ) q congruent 19 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 21 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 23 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+17*q-2 ) q congruent 25 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 27 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 29 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+17*q-2 ) q congruent 31 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 32 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+8*q+16 ) q congruent 37 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 41 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+17*q-2 ) q congruent 43 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 47 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+17*q-2 ) q congruent 49 modulo 60: 1/216 q phi1^2 ( q^3-q^2-3*q-9 ) q congruent 53 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+17*q-2 ) q congruent 59 modulo 60: 1/216 phi2 ( q^5-4*q^4+4*q^3-8*q^2+17*q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 15, 84, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 18 ], [ 8, 1, 2, 12 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 4, 36 ], [ 22, 1, 4, 36 ], [ 27, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 33, 1, 7, 54 ], [ 38, 1, 11, 72 ], [ 38, 1, 12, 72 ], [ 40, 1, 4, 36 ], [ 42, 1, 5, 36 ], [ 46, 1, 4, 72 ], [ 47, 1, 12, 108 ], [ 50, 1, 10, 72 ], [ 52, 1, 7, 54 ], [ 58, 1, 13, 72 ], [ 58, 1, 14, 144 ], [ 59, 1, 8, 108 ], [ 61, 1, 9, 108 ] ] k = 19: F-action on Pi is (1,3) [65,1,19] Dynkin type is ^2A_2(q) + T(phi1^2 phi3 phi6) Order of center |Z^F|: phi1^2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 2 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+28*q-24 ) q congruent 3 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+12 ) q congruent 5 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+31*q-30 ) q congruent 7 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 8 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+28*q-24 ) q congruent 9 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 11 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+31*q-30 ) q congruent 13 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+12 ) q congruent 17 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+31*q-30 ) q congruent 19 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 21 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 23 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+31*q-30 ) q congruent 25 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 27 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 29 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+31*q-30 ) q congruent 31 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 32 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+28*q-24 ) q congruent 37 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 41 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+31*q-30 ) q congruent 43 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 47 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+31*q-30 ) q congruent 49 modulo 60: 1/72 q phi1 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 53 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+31*q-30 ) q congruent 59 modulo 60: 1/72 phi2 ( q^5-6*q^4+12*q^3-16*q^2+31*q-30 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 87, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 6 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 3, 12 ], [ 22, 1, 3, 12 ], [ 27, 1, 1, 12 ], [ 33, 1, 7, 18 ], [ 38, 1, 7, 24 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 47, 1, 11, 36 ], [ 52, 1, 6, 18 ], [ 58, 1, 6, 12 ], [ 59, 1, 7, 36 ], [ 61, 1, 10, 36 ] ] k = 20: F-action on Pi is () [65,1,20] Dynkin type is A_2(q) + T(phi1 phi2 phi3 phi6) Order of center |Z^F|: phi1 phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^5-2*q^3-2*q^2-3*q+2 ) q congruent 2 modulo 60: 1/24 q^4 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 4 modulo 60: 1/24 q phi1 ( q^4-2*q^2-2*q-4 ) q congruent 5 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 7 modulo 60: 1/24 phi1 ( q^5-2*q^3-2*q^2-3*q+2 ) q congruent 8 modulo 60: 1/24 q^4 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 11 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 13 modulo 60: 1/24 phi1 ( q^5-2*q^3-2*q^2-3*q+2 ) q congruent 16 modulo 60: 1/24 q phi1 ( q^4-2*q^2-2*q-4 ) q congruent 17 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 19 modulo 60: 1/24 phi1 ( q^5-2*q^3-2*q^2-3*q+2 ) q congruent 21 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 23 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 25 modulo 60: 1/24 phi1 ( q^5-2*q^3-2*q^2-3*q+2 ) q congruent 27 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 29 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 31 modulo 60: 1/24 phi1 ( q^5-2*q^3-2*q^2-3*q+2 ) q congruent 32 modulo 60: 1/24 q^4 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 phi1 ( q^5-2*q^3-2*q^2-3*q+2 ) q congruent 41 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 43 modulo 60: 1/24 phi1 ( q^5-2*q^3-2*q^2-3*q+2 ) q congruent 47 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 49 modulo 60: 1/24 phi1 ( q^5-2*q^3-2*q^2-3*q+2 ) q congruent 53 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) q congruent 59 modulo 60: 1/24 q phi1 phi2 ( q^3-q^2-q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 40, 85 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 22, 1, 1, 4 ], [ 27, 1, 3, 4 ], [ 33, 1, 3, 6 ], [ 38, 1, 2, 8 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 47, 1, 5, 12 ], [ 52, 1, 7, 6 ], [ 58, 1, 6, 12 ], [ 59, 1, 15, 12 ], [ 61, 1, 11, 12 ] ] k = 21: F-action on Pi is (1,3) [65,1,21] Dynkin type is ^2A_2(q) + T(phi1 phi2 phi3 phi6) Order of center |Z^F|: phi1 phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 2 modulo 60: 1/24 q phi2 ( q^4-2*q^3+2*q^2-4*q+4 ) q congruent 3 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 4 modulo 60: 1/24 q^2 phi1 ( q^3-2 ) q congruent 5 modulo 60: 1/24 phi1^3 phi2 ( q^2+q+2 ) q congruent 7 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 8 modulo 60: 1/24 q phi2 ( q^4-2*q^3+2*q^2-4*q+4 ) q congruent 9 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 11 modulo 60: 1/24 phi1^3 phi2 ( q^2+q+2 ) q congruent 13 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 16 modulo 60: 1/24 q^2 phi1 ( q^3-2 ) q congruent 17 modulo 60: 1/24 phi1^3 phi2 ( q^2+q+2 ) q congruent 19 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 21 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 23 modulo 60: 1/24 phi1^3 phi2 ( q^2+q+2 ) q congruent 25 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 27 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 29 modulo 60: 1/24 phi1^3 phi2 ( q^2+q+2 ) q congruent 31 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 32 modulo 60: 1/24 q phi2 ( q^4-2*q^3+2*q^2-4*q+4 ) q congruent 37 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 41 modulo 60: 1/24 phi1^3 phi2 ( q^2+q+2 ) q congruent 43 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 47 modulo 60: 1/24 phi1^3 phi2 ( q^2+q+2 ) q congruent 49 modulo 60: 1/24 q phi1^2 ( q^3+q^2+q-1 ) q congruent 53 modulo 60: 1/24 phi1^3 phi2 ( q^2+q+2 ) q congruent 59 modulo 60: 1/24 phi1^3 phi2 ( q^2+q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 88, 40, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 27, 1, 2, 4 ], [ 33, 1, 7, 6 ], [ 38, 1, 10, 8 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 47, 1, 12, 12 ], [ 52, 1, 6, 6 ], [ 58, 1, 6, 12 ], [ 59, 1, 14, 12 ], [ 61, 1, 10, 12 ] ] k = 22: F-action on Pi is () [65,1,22] Dynkin type is A_2(q) + T(phi2^2 phi3 phi6) Order of center |Z^F|: phi2^2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1^2 ( q^4+q^3+q^2-q-6 ) q congruent 2 modulo 60: 1/72 q^2 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 3 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^4-2*q-8 ) q congruent 5 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 7 modulo 60: 1/72 phi1^2 ( q^4+q^3+q^2-q-6 ) q congruent 8 modulo 60: 1/72 q^2 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 9 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 11 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 13 modulo 60: 1/72 phi1^2 ( q^4+q^3+q^2-q-6 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^4-2*q-8 ) q congruent 17 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 19 modulo 60: 1/72 phi1^2 ( q^4+q^3+q^2-q-6 ) q congruent 21 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 23 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 25 modulo 60: 1/72 phi1^2 ( q^4+q^3+q^2-q-6 ) q congruent 27 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 29 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 31 modulo 60: 1/72 phi1^2 ( q^4+q^3+q^2-q-6 ) q congruent 32 modulo 60: 1/72 q^2 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 37 modulo 60: 1/72 phi1^2 ( q^4+q^3+q^2-q-6 ) q congruent 41 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 43 modulo 60: 1/72 phi1^2 ( q^4+q^3+q^2-q-6 ) q congruent 47 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 49 modulo 60: 1/72 phi1^2 ( q^4+q^3+q^2-q-6 ) q congruent 53 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) q congruent 59 modulo 60: 1/72 q phi1 phi2 ( q^3-q^2+q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 88, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 22, 1, 2, 12 ], [ 27, 1, 6, 12 ], [ 33, 1, 3, 18 ], [ 38, 1, 6, 24 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 47, 1, 6, 36 ], [ 52, 1, 7, 18 ], [ 58, 1, 6, 12 ], [ 59, 1, 8, 36 ], [ 61, 1, 11, 36 ] ] k = 23: F-action on Pi is () [65,1,23] Dynkin type is A_2(q) + T(phi1^2 phi2^2 phi3) Order of center |Z^F|: phi1^2 phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 2 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 4 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 7 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 8 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 11 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 13 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 16 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 19 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 21 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 23 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 25 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 27 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 29 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 31 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 32 modulo 60: 1/48 q^3 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 41 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 43 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 47 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 49 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 53 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) q congruent 59 modulo 60: 1/48 q phi1 phi2 ( q^3-2*q^2-1 ) Fusion of maximal tori of C^F in those of G^F: [ 30, 81, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 24 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 16 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 5, 6 ], [ 29, 1, 2, 16 ], [ 31, 1, 2, 16 ], [ 32, 1, 1, 8 ], [ 34, 1, 2, 8 ], [ 38, 1, 3, 36 ], [ 38, 1, 5, 48 ], [ 39, 1, 3, 8 ], [ 40, 1, 3, 16 ], [ 42, 1, 3, 12 ], [ 42, 1, 4, 8 ], [ 43, 1, 12, 32 ], [ 44, 1, 3, 6 ], [ 45, 1, 3, 12 ], [ 46, 1, 2, 16 ], [ 46, 1, 3, 24 ], [ 50, 1, 5, 16 ], [ 50, 1, 6, 24 ], [ 51, 1, 5, 32 ], [ 53, 1, 16, 12 ], [ 54, 1, 7, 24 ], [ 55, 1, 3, 12 ], [ 56, 1, 8, 24 ], [ 58, 1, 7, 48 ], [ 58, 1, 9, 32 ], [ 59, 1, 19, 24 ], [ 61, 1, 7, 24 ], [ 63, 1, 5, 48 ] ] k = 24: F-action on Pi is (1,3) [65,1,24] Dynkin type is ^2A_2(q) + T(phi1 phi2 phi3 phi4) Order of center |Z^F|: phi1 phi2 phi3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 2 modulo 60: 1/24 q^4 phi1 phi2 q congruent 3 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 4 modulo 60: 1/24 q^4 phi1 phi2 q congruent 5 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 7 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 8 modulo 60: 1/24 q^4 phi1 phi2 q congruent 9 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 11 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 13 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 16 modulo 60: 1/24 q^4 phi1 phi2 q congruent 17 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 19 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 21 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 23 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 25 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 27 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 29 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 31 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 32 modulo 60: 1/24 q^4 phi1 phi2 q congruent 37 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 41 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 43 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 47 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 49 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 53 modulo 60: 1/24 q phi1 phi2^2 phi6 q congruent 59 modulo 60: 1/24 q phi1 phi2^2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 95, 59, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 32, 1, 2, 4 ], [ 38, 1, 9, 12 ], [ 39, 1, 5, 4 ], [ 43, 1, 9, 8 ], [ 44, 1, 3, 6 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 8 ], [ 53, 1, 17, 12 ], [ 55, 1, 18, 12 ], [ 58, 1, 5, 8 ], [ 63, 1, 7, 24 ] ] k = 25: F-action on Pi is () [65,1,25] Dynkin type is A_2(q) + T(phi1 phi2 phi4 phi6) Order of center |Z^F|: phi1 phi2 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 2 modulo 60: 1/24 q^3 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 4 modulo 60: 1/24 q^3 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 7 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 8 modulo 60: 1/24 q^3 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 11 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 13 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 16 modulo 60: 1/24 q^3 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 19 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 21 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 23 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 25 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 27 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 29 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 31 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 32 modulo 60: 1/24 q^3 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 41 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 43 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 47 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 49 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 53 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) q congruent 59 modulo 60: 1/24 q phi1^2 phi2 ( q^2-q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 96, 60, 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 32, 1, 2, 4 ], [ 38, 1, 4, 12 ], [ 39, 1, 5, 4 ], [ 43, 1, 9, 8 ], [ 44, 1, 7, 6 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 8 ], [ 53, 1, 15, 12 ], [ 55, 1, 7, 12 ], [ 58, 1, 5, 8 ], [ 63, 1, 6, 24 ] ] k = 26: F-action on Pi is (1,3) [65,1,26] Dynkin type is ^2A_2(q) + T(phi1^2 phi2^2 phi6) Order of center |Z^F|: phi1^2 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 2 modulo 60: 1/48 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 4 modulo 60: 1/48 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 7 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 8 modulo 60: 1/48 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 11 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 13 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 16 modulo 60: 1/48 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 19 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 21 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 23 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 25 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 27 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 29 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 31 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 32 modulo 60: 1/48 q^2 phi1 phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 41 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 43 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 47 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 49 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 53 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) q congruent 59 modulo 60: 1/48 q phi1^2 phi2 ( q^2-3*q+1 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 82, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 20, 1, 3, 16 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 16 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 27, 1, 4, 6 ], [ 29, 1, 3, 16 ], [ 31, 1, 3, 16 ], [ 32, 1, 3, 8 ], [ 34, 1, 3, 8 ], [ 38, 1, 8, 48 ], [ 38, 1, 11, 36 ], [ 39, 1, 1, 8 ], [ 40, 1, 2, 16 ], [ 42, 1, 2, 8 ], [ 42, 1, 5, 12 ], [ 43, 1, 3, 32 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 46, 1, 4, 24 ], [ 46, 1, 5, 16 ], [ 50, 1, 7, 24 ], [ 50, 1, 8, 16 ], [ 51, 1, 10, 32 ], [ 53, 1, 18, 12 ], [ 54, 1, 11, 24 ], [ 55, 1, 12, 12 ], [ 56, 1, 12, 24 ], [ 58, 1, 10, 48 ], [ 58, 1, 11, 32 ], [ 59, 1, 20, 24 ], [ 61, 1, 8, 24 ], [ 63, 1, 8, 48 ] ] k = 27: F-action on Pi is (1,3) [65,1,27] Dynkin type is ^2A_2(q) + T(phi2^4 phi6) Order of center |Z^F|: phi2^4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 2 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-152*q^2+200*q-128 ) q congruent 3 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 4 modulo 60: 1/432 q^2 phi1 ( q^3-11*q^2+40*q-48 ) q congruent 5 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-161*q^2+245*q-200 ) q congruent 7 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 8 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-152*q^2+200*q-128 ) q congruent 9 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 11 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-161*q^2+245*q-200 ) q congruent 13 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 16 modulo 60: 1/432 q^2 phi1 ( q^3-11*q^2+40*q-48 ) q congruent 17 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-161*q^2+245*q-200 ) q congruent 19 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 21 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 23 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-161*q^2+245*q-200 ) q congruent 25 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 27 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 29 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-161*q^2+245*q-200 ) q congruent 31 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 32 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-152*q^2+200*q-128 ) q congruent 37 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 41 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-161*q^2+245*q-200 ) q congruent 43 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 47 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-161*q^2+245*q-200 ) q congruent 49 modulo 60: 1/432 q phi1^2 ( q^3-10*q^2+30*q-27 ) q congruent 53 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-161*q^2+245*q-200 ) q congruent 59 modulo 60: 1/432 phi2 ( q^5-13*q^4+64*q^3-161*q^2+245*q-200 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 78, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 36 ], [ 5, 1, 2, 72 ], [ 6, 1, 2, 36 ], [ 7, 1, 2, 36 ], [ 8, 1, 2, 24 ], [ 9, 1, 1, 9 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 36 ], [ 14, 1, 2, 144 ], [ 15, 1, 2, 72 ], [ 16, 1, 3, 72 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 36 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 72 ], [ 22, 1, 4, 72 ], [ 23, 1, 2, 36 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 144 ], [ 26, 1, 4, 72 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 24 ], [ 29, 1, 4, 144 ], [ 31, 1, 4, 144 ], [ 32, 1, 3, 72 ], [ 34, 1, 4, 72 ], [ 36, 1, 4, 144 ], [ 37, 1, 3, 288 ], [ 38, 1, 11, 36 ], [ 38, 1, 12, 144 ], [ 39, 1, 3, 72 ], [ 40, 1, 6, 144 ], [ 42, 1, 5, 36 ], [ 42, 1, 6, 72 ], [ 43, 1, 13, 288 ], [ 44, 1, 7, 54 ], [ 45, 1, 4, 108 ], [ 46, 1, 4, 72 ], [ 46, 1, 6, 144 ], [ 50, 1, 10, 72 ], [ 50, 1, 12, 144 ], [ 51, 1, 9, 288 ], [ 53, 1, 18, 108 ], [ 54, 1, 10, 216 ], [ 55, 1, 12, 108 ], [ 56, 1, 17, 216 ], [ 58, 1, 14, 144 ], [ 58, 1, 15, 288 ], [ 59, 1, 5, 216 ], [ 61, 1, 6, 216 ], [ 63, 1, 9, 432 ] ] k = 28: F-action on Pi is () [65,1,28] Dynkin type is A_2(q) + T(phi1^3 phi2 phi3) Order of center |Z^F|: phi1^3 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 ( q^5-7*q^4+10*q^3+9*q^2-13*q+12 ) q congruent 2 modulo 60: 1/72 q^2 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 4 modulo 60: 1/72 q phi1^2 ( q^3-6*q^2+4*q+16 ) q congruent 5 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 7 modulo 60: 1/72 phi1 ( q^5-7*q^4+10*q^3+9*q^2-13*q+12 ) q congruent 8 modulo 60: 1/72 q^2 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 9 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 11 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 13 modulo 60: 1/72 phi1 ( q^5-7*q^4+10*q^3+9*q^2-13*q+12 ) q congruent 16 modulo 60: 1/72 q phi1^2 ( q^3-6*q^2+4*q+16 ) q congruent 17 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 19 modulo 60: 1/72 phi1 ( q^5-7*q^4+10*q^3+9*q^2-13*q+12 ) q congruent 21 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 23 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 25 modulo 60: 1/72 phi1 ( q^5-7*q^4+10*q^3+9*q^2-13*q+12 ) q congruent 27 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 29 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 31 modulo 60: 1/72 phi1 ( q^5-7*q^4+10*q^3+9*q^2-13*q+12 ) q congruent 32 modulo 60: 1/72 q^2 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 37 modulo 60: 1/72 phi1 ( q^5-7*q^4+10*q^3+9*q^2-13*q+12 ) q congruent 41 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 43 modulo 60: 1/72 phi1 ( q^5-7*q^4+10*q^3+9*q^2-13*q+12 ) q congruent 47 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 49 modulo 60: 1/72 phi1 ( q^5-7*q^4+10*q^3+9*q^2-13*q+12 ) q congruent 53 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 59 modulo 60: 1/72 q phi1 phi2 ( q^3-8*q^2+18*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 77, 30, 83 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 48 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 24 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 36 ], [ 22, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 1, 12 ], [ 26, 1, 3, 12 ], [ 27, 1, 1, 12 ], [ 27, 1, 2, 4 ], [ 27, 1, 5, 6 ], [ 29, 1, 1, 24 ], [ 29, 1, 2, 24 ], [ 31, 1, 1, 24 ], [ 31, 1, 2, 24 ], [ 32, 1, 1, 24 ], [ 34, 1, 1, 12 ], [ 34, 1, 2, 12 ], [ 36, 1, 2, 24 ], [ 38, 1, 1, 72 ], [ 38, 1, 3, 36 ], [ 38, 1, 5, 24 ], [ 39, 1, 4, 12 ], [ 42, 1, 1, 12 ], [ 42, 1, 3, 24 ], [ 42, 1, 4, 12 ], [ 43, 1, 2, 48 ], [ 44, 1, 3, 18 ], [ 45, 1, 3, 36 ], [ 46, 1, 1, 24 ], [ 46, 1, 2, 24 ], [ 46, 1, 3, 48 ], [ 50, 1, 2, 24 ], [ 50, 1, 3, 36 ], [ 50, 1, 4, 24 ], [ 50, 1, 6, 12 ], [ 51, 1, 2, 48 ], [ 53, 1, 16, 36 ], [ 54, 1, 3, 36 ], [ 54, 1, 7, 36 ], [ 55, 1, 3, 36 ], [ 56, 1, 3, 36 ], [ 56, 1, 8, 36 ], [ 58, 1, 2, 48 ], [ 58, 1, 3, 72 ], [ 58, 1, 7, 24 ], [ 61, 1, 4, 36 ], [ 61, 1, 7, 36 ], [ 63, 1, 10, 72 ] ] k = 29: F-action on Pi is (1,3) [65,1,29] Dynkin type is ^2A_2(q) + T(phi1 phi2^3 phi6) Order of center |Z^F|: phi1 phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 2 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-32*q^2+32*q-16 ) q congruent 3 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 4 modulo 60: 1/72 q^2 phi1^2 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-35*q^2+41*q-28 ) q congruent 7 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 8 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-32*q^2+32*q-16 ) q congruent 9 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 11 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-35*q^2+41*q-28 ) q congruent 13 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 16 modulo 60: 1/72 q^2 phi1^2 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-35*q^2+41*q-28 ) q congruent 19 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 21 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 23 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-35*q^2+41*q-28 ) q congruent 25 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 27 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 29 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-35*q^2+41*q-28 ) q congruent 31 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 32 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-32*q^2+32*q-16 ) q congruent 37 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 41 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-35*q^2+41*q-28 ) q congruent 43 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 47 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-35*q^2+41*q-28 ) q congruent 49 modulo 60: 1/72 q phi1^2 phi6 ( q-3 ) q congruent 53 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-35*q^2+41*q-28 ) q congruent 59 modulo 60: 1/72 phi2 ( q^5-7*q^4+20*q^3-35*q^2+41*q-28 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 31, 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 12 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 24 ], [ 16, 1, 3, 24 ], [ 17, 1, 4, 48 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 20, 1, 3, 24 ], [ 20, 1, 4, 24 ], [ 21, 1, 2, 12 ], [ 22, 1, 3, 12 ], [ 22, 1, 4, 36 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 2, 12 ], [ 26, 1, 4, 12 ], [ 27, 1, 3, 4 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 12 ], [ 29, 1, 3, 24 ], [ 29, 1, 4, 24 ], [ 31, 1, 3, 24 ], [ 31, 1, 4, 24 ], [ 32, 1, 3, 24 ], [ 34, 1, 3, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 3, 24 ], [ 38, 1, 8, 24 ], [ 38, 1, 11, 36 ], [ 38, 1, 12, 72 ], [ 39, 1, 4, 12 ], [ 42, 1, 2, 12 ], [ 42, 1, 5, 24 ], [ 42, 1, 6, 12 ], [ 43, 1, 4, 48 ], [ 44, 1, 7, 18 ], [ 45, 1, 4, 36 ], [ 46, 1, 4, 48 ], [ 46, 1, 5, 24 ], [ 46, 1, 6, 24 ], [ 50, 1, 7, 12 ], [ 50, 1, 9, 24 ], [ 50, 1, 10, 36 ], [ 50, 1, 11, 24 ], [ 51, 1, 8, 48 ], [ 53, 1, 18, 36 ], [ 54, 1, 10, 36 ], [ 54, 1, 11, 36 ], [ 55, 1, 12, 36 ], [ 56, 1, 12, 36 ], [ 56, 1, 17, 36 ], [ 58, 1, 10, 24 ], [ 58, 1, 12, 48 ], [ 58, 1, 14, 72 ], [ 61, 1, 6, 36 ], [ 61, 1, 8, 36 ], [ 63, 1, 11, 72 ] ] k = 30: F-action on Pi is (1,3) [65,1,30] Dynkin type is ^2A_2(q) + T(phi1^2 phi2^2 phi3) Order of center |Z^F|: phi1^2 phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 2 modulo 60: 1/72 q phi2 ( q^4-3*q^3+2*q+4 ) q congruent 3 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 4 modulo 60: 1/72 q^2 phi1 phi2 ( q^2-2*q-2 ) q congruent 5 modulo 60: 1/72 q phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 7 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 8 modulo 60: 1/72 q phi2 ( q^4-3*q^3+2*q+4 ) q congruent 9 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 11 modulo 60: 1/72 q phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 13 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 16 modulo 60: 1/72 q^2 phi1 phi2 ( q^2-2*q-2 ) q congruent 17 modulo 60: 1/72 q phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 19 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 21 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 23 modulo 60: 1/72 q phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 25 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 27 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 29 modulo 60: 1/72 q phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 31 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 32 modulo 60: 1/72 q phi2 ( q^4-3*q^3+2*q+4 ) q congruent 37 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 41 modulo 60: 1/72 q phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 43 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 47 modulo 60: 1/72 q phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 49 modulo 60: 1/72 q phi1^2 phi2 ( q^2-q-3 ) q congruent 53 modulo 60: 1/72 q phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 59 modulo 60: 1/72 q phi2^2 ( q^3-4*q^2+4*q+1 ) Fusion of maximal tori of C^F in those of G^F: [ 27, 81, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 12, 1, 2, 6 ], [ 16, 1, 2, 12 ], [ 16, 1, 4, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 12 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 12 ], [ 27, 1, 5, 6 ], [ 32, 1, 2, 12 ], [ 37, 1, 2, 24 ], [ 38, 1, 9, 12 ], [ 39, 1, 2, 12 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 12 ], [ 40, 1, 3, 12 ], [ 40, 1, 6, 12 ], [ 43, 1, 8, 24 ], [ 44, 1, 3, 18 ], [ 51, 1, 3, 24 ], [ 51, 1, 6, 24 ], [ 53, 1, 17, 36 ], [ 55, 1, 18, 36 ], [ 58, 1, 4, 24 ], [ 59, 1, 4, 36 ], [ 59, 1, 19, 36 ], [ 63, 1, 13, 72 ] ] k = 31: F-action on Pi is () [65,1,31] Dynkin type is A_2(q) + T(phi1^2 phi2^2 phi6) Order of center |Z^F|: phi1^2 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+13*q+19 ) q congruent 2 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+12 ) q congruent 3 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+10*q+16 ) q congruent 5 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 7 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+13*q+19 ) q congruent 8 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+12 ) q congruent 9 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 11 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 13 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+13*q+19 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+10*q+16 ) q congruent 17 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 19 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+13*q+19 ) q congruent 21 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 23 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 25 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+13*q+19 ) q congruent 27 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 29 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 31 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+13*q+19 ) q congruent 32 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+12 ) q congruent 37 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+13*q+19 ) q congruent 41 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 43 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+13*q+19 ) q congruent 47 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 49 modulo 60: 1/72 q phi1 ( q^4-3*q^3-6*q^2+13*q+19 ) q congruent 53 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) q congruent 59 modulo 60: 1/72 q phi1 phi2 ( q^3-4*q^2-2*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 82, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 12, 1, 2, 6 ], [ 16, 1, 2, 12 ], [ 16, 1, 4, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 12 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 12 ], [ 27, 1, 4, 6 ], [ 32, 1, 2, 12 ], [ 37, 1, 2, 24 ], [ 38, 1, 4, 12 ], [ 39, 1, 2, 12 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 12 ], [ 40, 1, 3, 12 ], [ 40, 1, 6, 12 ], [ 43, 1, 8, 24 ], [ 44, 1, 7, 18 ], [ 51, 1, 3, 24 ], [ 51, 1, 6, 24 ], [ 53, 1, 15, 36 ], [ 55, 1, 7, 36 ], [ 58, 1, 4, 24 ], [ 59, 1, 5, 36 ], [ 59, 1, 20, 36 ], [ 63, 1, 12, 72 ] ] k = 32: F-action on Pi is () [65,1,32] Dynkin type is A_2(q) + T(phi1^2 phi2^4) Order of center |Z^F|: phi1^2 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/2304 phi1^2 ( q^4-11*q^3+31*q^2-q+12 ) q congruent 2 modulo 60: 1/2304 q phi2 ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 3 modulo 60: 1/2304 phi1 phi2 ( q^4-13*q^3+55*q^2-87*q+36 ) q congruent 4 modulo 60: 1/2304 q ( q^5-13*q^4+54*q^3-68*q^2+24*q-160 ) q congruent 5 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2-51*q+180 ) q congruent 7 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2+13*q-156 ) q congruent 8 modulo 60: 1/2304 q phi2 ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 9 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2-51*q+180 ) q congruent 11 modulo 60: 1/2304 phi1 phi2 ( q^4-13*q^3+55*q^2-87*q+36 ) q congruent 13 modulo 60: 1/2304 phi1^2 ( q^4-11*q^3+31*q^2-q+12 ) q congruent 16 modulo 60: 1/2304 q ( q^5-13*q^4+54*q^3-68*q^2+24*q-160 ) q congruent 17 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2-51*q+180 ) q congruent 19 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2+13*q-156 ) q congruent 21 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2-51*q+180 ) q congruent 23 modulo 60: 1/2304 phi1 phi2 ( q^4-13*q^3+55*q^2-87*q+36 ) q congruent 25 modulo 60: 1/2304 phi1^2 ( q^4-11*q^3+31*q^2-q+12 ) q congruent 27 modulo 60: 1/2304 phi1 phi2 ( q^4-13*q^3+55*q^2-87*q+36 ) q congruent 29 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2-51*q+180 ) q congruent 31 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2+13*q-156 ) q congruent 32 modulo 60: 1/2304 q phi2 ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 37 modulo 60: 1/2304 phi1^2 ( q^4-11*q^3+31*q^2-q+12 ) q congruent 41 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2-51*q+180 ) q congruent 43 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2+13*q-156 ) q congruent 47 modulo 60: 1/2304 phi1 phi2 ( q^4-13*q^3+55*q^2-87*q+36 ) q congruent 49 modulo 60: 1/2304 phi1^2 ( q^4-11*q^3+31*q^2-q+12 ) q congruent 53 modulo 60: 1/2304 phi1 ( q^5-12*q^4+42*q^3-32*q^2-51*q+180 ) q congruent 59 modulo 60: 1/2304 phi1 phi2 ( q^4-13*q^3+55*q^2-87*q+36 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 42 ], [ 4, 1, 2, 24 ], [ 6, 1, 1, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 1, 6 ], [ 12, 1, 2, 96 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 144 ], [ 13, 1, 4, 144 ], [ 16, 1, 1, 72 ], [ 16, 1, 2, 48 ], [ 16, 1, 4, 192 ], [ 17, 1, 2, 192 ], [ 20, 1, 2, 288 ], [ 22, 1, 2, 48 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 72 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 192 ], [ 27, 1, 6, 192 ], [ 28, 1, 2, 144 ], [ 28, 1, 4, 288 ], [ 31, 1, 2, 144 ], [ 32, 1, 2, 192 ], [ 33, 1, 1, 144 ], [ 33, 1, 2, 288 ], [ 35, 1, 3, 288 ], [ 35, 1, 4, 576 ], [ 37, 1, 2, 96 ], [ 38, 1, 6, 384 ], [ 39, 1, 2, 48 ], [ 39, 1, 3, 144 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 192 ], [ 40, 1, 3, 48 ], [ 40, 1, 6, 192 ], [ 41, 1, 4, 288 ], [ 41, 1, 9, 288 ], [ 41, 1, 10, 576 ], [ 43, 1, 8, 96 ], [ 43, 1, 12, 576 ], [ 44, 1, 5, 288 ], [ 44, 1, 10, 576 ], [ 47, 1, 2, 288 ], [ 47, 1, 4, 576 ], [ 48, 1, 3, 576 ], [ 51, 1, 3, 384 ], [ 51, 1, 5, 288 ], [ 51, 1, 6, 96 ], [ 52, 1, 4, 576 ], [ 52, 1, 10, 576 ], [ 53, 1, 9, 576 ], [ 53, 1, 19, 1152 ], [ 55, 1, 5, 576 ], [ 55, 1, 10, 1152 ], [ 56, 1, 10, 1152 ], [ 58, 1, 4, 384 ], [ 59, 1, 2, 1152 ], [ 59, 1, 18, 1152 ], [ 61, 1, 17, 1152 ], [ 63, 1, 14, 2304 ] ] k = 33: F-action on Pi is () [65,1,33] Dynkin type is A_2(q) + T(phi1^2 phi4^2) Order of center |Z^F|: phi1^2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 2 modulo 60: 1/192 q^2 ( q^4-5*q^3+2*q^2+20*q-24 ) q congruent 3 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 4 modulo 60: 1/192 q^2 ( q^4-5*q^3+2*q^2+20*q-24 ) q congruent 5 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 7 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 8 modulo 60: 1/192 q^2 ( q^4-5*q^3+2*q^2+20*q-24 ) q congruent 9 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 11 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 13 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 16 modulo 60: 1/192 q^2 ( q^4-5*q^3+2*q^2+20*q-24 ) q congruent 17 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 19 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 21 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 23 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 25 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 27 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 29 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 31 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 32 modulo 60: 1/192 q^2 ( q^4-5*q^3+2*q^2+20*q-24 ) q congruent 37 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 41 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 43 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 47 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 49 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 53 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) q congruent 59 modulo 60: 1/192 phi1 phi2 ( q^4-5*q^3+3*q^2+21*q-36 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 73, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 3, 24 ], [ 16, 1, 2, 24 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 33, 1, 4, 48 ], [ 39, 1, 5, 24 ], [ 40, 1, 1, 12 ], [ 41, 1, 5, 48 ], [ 43, 1, 9, 48 ], [ 44, 1, 6, 48 ], [ 48, 1, 8, 96 ], [ 51, 1, 7, 48 ], [ 53, 1, 10, 96 ], [ 55, 1, 6, 96 ], [ 59, 1, 6, 96 ], [ 63, 1, 16, 192 ] ] k = 34: F-action on Pi is () [65,1,34] Dynkin type is A_2(q) + T(phi1 phi2 phi8) Order of center |Z^F|: phi1 phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/16 q^4 phi2 ( q-2 ) q congruent 3 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/16 q^4 phi2 ( q-2 ) q congruent 5 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/16 q^4 phi2 ( q-2 ) q congruent 9 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/16 q^4 phi2 ( q-2 ) q congruent 17 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/16 q^4 phi2 ( q-2 ) q congruent 37 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/16 phi1 phi2^2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 89, 43, 109 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 33, 1, 5, 8 ], [ 40, 1, 3, 4 ], [ 59, 1, 25, 8 ], [ 63, 1, 18, 16 ] ] k = 35: F-action on Pi is (1,3) [65,1,35] Dynkin type is ^2A_2(q) + T(phi1 phi2 phi8) Order of center |Z^F|: phi1 phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 2 modulo 60: 1/16 q^5 phi1 q congruent 3 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 4 modulo 60: 1/16 q^5 phi1 q congruent 5 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 7 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 8 modulo 60: 1/16 q^5 phi1 q congruent 9 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 11 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 13 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 16 modulo 60: 1/16 q^5 phi1 q congruent 17 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 19 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 21 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 23 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 25 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 27 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 29 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 31 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 32 modulo 60: 1/16 q^5 phi1 q congruent 37 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 41 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 43 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 47 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 49 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 53 modulo 60: 1/16 q phi1^2 phi2 phi4 q congruent 59 modulo 60: 1/16 q phi1^2 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 90, 43, 110 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 33, 1, 9, 8 ], [ 40, 1, 2, 4 ], [ 59, 1, 25, 8 ], [ 63, 1, 17, 16 ] ] k = 36: F-action on Pi is (1,3) [65,1,36] Dynkin type is ^2A_2(q) + T(phi2^2 phi4^2) Order of center |Z^F|: phi2^2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 2 modulo 60: 1/192 q^3 phi1 ( q^2-4 ) q congruent 3 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 4 modulo 60: 1/192 q^3 phi1 ( q^2-4 ) q congruent 5 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 7 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 8 modulo 60: 1/192 q^3 phi1 ( q^2-4 ) q congruent 9 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 11 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 13 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 16 modulo 60: 1/192 q^3 phi1 ( q^2-4 ) q congruent 17 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 19 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 21 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 23 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 25 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 27 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 29 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 31 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 32 modulo 60: 1/192 q^3 phi1 ( q^2-4 ) q congruent 37 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 41 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 43 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 47 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 49 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 53 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) q congruent 59 modulo 60: 1/192 phi1^2 phi2 ( q^3-3*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 74, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 2, 24 ], [ 16, 1, 4, 24 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 33, 1, 10, 48 ], [ 39, 1, 5, 24 ], [ 40, 1, 6, 12 ], [ 41, 1, 5, 48 ], [ 43, 1, 9, 48 ], [ 44, 1, 4, 48 ], [ 48, 1, 9, 96 ], [ 51, 1, 4, 48 ], [ 53, 1, 14, 96 ], [ 55, 1, 19, 96 ], [ 59, 1, 6, 96 ], [ 63, 1, 15, 192 ] ] k = 37: F-action on Pi is (1,3) [65,1,37] Dynkin type is ^2A_2(q) + T(phi1^4 phi2^2) Order of center |Z^F|: phi1^4 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2304 phi1 ( q^5-16*q^4+80*q^3-98*q^2-225*q+450 ) q congruent 2 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-172*q^3-48*q^2-128*q+768 ) q congruent 3 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-127*q^2+819*q-882 ) q congruent 4 modulo 60: 1/2304 q ( q^5-17*q^4+96*q^3-172*q^2-112*q+384 ) q congruent 5 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-63*q^2+163*q+510 ) q congruent 7 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-127*q^2+819*q-882 ) q congruent 8 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-172*q^3-48*q^2-128*q+768 ) q congruent 9 modulo 60: 1/2304 phi1 ( q^5-16*q^4+80*q^3-98*q^2-225*q+450 ) q congruent 11 modulo 60: 1/2304 phi2 ( q^5-18*q^4+114*q^3-292*q^2+229*q+78 ) q congruent 13 modulo 60: 1/2304 phi1 ( q^5-16*q^4+80*q^3-98*q^2-225*q+450 ) q congruent 16 modulo 60: 1/2304 q ( q^5-17*q^4+96*q^3-172*q^2-112*q+384 ) q congruent 17 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-63*q^2+163*q+510 ) q congruent 19 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-127*q^2+819*q-882 ) q congruent 21 modulo 60: 1/2304 phi1 ( q^5-16*q^4+80*q^3-98*q^2-225*q+450 ) q congruent 23 modulo 60: 1/2304 phi2 ( q^5-18*q^4+114*q^3-292*q^2+229*q+78 ) q congruent 25 modulo 60: 1/2304 phi1 ( q^5-16*q^4+80*q^3-98*q^2-225*q+450 ) q congruent 27 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-127*q^2+819*q-882 ) q congruent 29 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-63*q^2+163*q+510 ) q congruent 31 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-127*q^2+819*q-882 ) q congruent 32 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-172*q^3-48*q^2-128*q+768 ) q congruent 37 modulo 60: 1/2304 phi1 ( q^5-16*q^4+80*q^3-98*q^2-225*q+450 ) q congruent 41 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-63*q^2+163*q+510 ) q congruent 43 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-127*q^2+819*q-882 ) q congruent 47 modulo 60: 1/2304 phi2 ( q^5-18*q^4+114*q^3-292*q^2+229*q+78 ) q congruent 49 modulo 60: 1/2304 phi1 ( q^5-16*q^4+80*q^3-98*q^2-225*q+450 ) q congruent 53 modulo 60: 1/2304 ( q^6-17*q^5+96*q^4-178*q^3-63*q^2+163*q+510 ) q congruent 59 modulo 60: 1/2304 phi2 ( q^5-18*q^4+114*q^3-292*q^2+229*q+78 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 68, 28 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 32 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 42 ], [ 6, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 12, 1, 2, 6 ], [ 13, 1, 1, 144 ], [ 13, 1, 3, 144 ], [ 13, 1, 4, 72 ], [ 16, 1, 2, 192 ], [ 16, 1, 3, 72 ], [ 16, 1, 4, 48 ], [ 17, 1, 3, 192 ], [ 20, 1, 3, 288 ], [ 22, 1, 3, 48 ], [ 23, 1, 1, 24 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 25, 1, 2, 192 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 48 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 28, 1, 3, 144 ], [ 31, 1, 3, 144 ], [ 32, 1, 2, 192 ], [ 33, 1, 6, 288 ], [ 33, 1, 8, 144 ], [ 35, 1, 5, 576 ], [ 35, 1, 6, 288 ], [ 37, 1, 2, 96 ], [ 38, 1, 7, 384 ], [ 39, 1, 1, 144 ], [ 39, 1, 2, 48 ], [ 40, 1, 1, 192 ], [ 40, 1, 2, 48 ], [ 40, 1, 3, 192 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 288 ], [ 41, 1, 3, 576 ], [ 41, 1, 4, 288 ], [ 43, 1, 3, 576 ], [ 43, 1, 8, 96 ], [ 44, 1, 1, 576 ], [ 44, 1, 9, 288 ], [ 47, 1, 7, 288 ], [ 47, 1, 9, 576 ], [ 48, 1, 4, 576 ], [ 51, 1, 3, 96 ], [ 51, 1, 6, 384 ], [ 51, 1, 10, 288 ], [ 52, 1, 1, 576 ], [ 52, 1, 3, 576 ], [ 53, 1, 5, 1152 ], [ 53, 1, 6, 576 ], [ 55, 1, 14, 576 ], [ 55, 1, 16, 1152 ], [ 56, 1, 14, 1152 ], [ 58, 1, 4, 384 ], [ 59, 1, 1, 1152 ], [ 59, 1, 17, 1152 ], [ 61, 1, 22, 1152 ], [ 63, 1, 20, 2304 ] ] k = 38: F-action on Pi is (1,3) [65,1,38] Dynkin type is ^2A_2(q) + T(phi2^6) Order of center |Z^F|: phi2^6 Numbers of classes in class type: q congruent 1 modulo 60: 1/103680 phi1 ( q^5-56*q^4+1216*q^3-12906*q^2+68895*q-157950 ) q congruent 2 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-13852*q^3+74256*q^2-176640*q+148480 ) q congruent 3 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+81801*q^2-233325*q+255150 ) q congruent 4 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-13852*q^3+73296*q^2-149760*q+41472 ) q congruent 5 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+82761*q^2-253725*q+332350 ) q congruent 7 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+81801*q^2-233325*q+255150 ) q congruent 8 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-13852*q^3+74256*q^2-176640*q+148480 ) q congruent 9 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+81801*q^2-226845*q+199422 ) q congruent 11 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+82761*q^2-260205*q+429550 ) q congruent 13 modulo 60: 1/103680 phi1 ( q^5-56*q^4+1216*q^3-12906*q^2+68895*q-157950 ) q congruent 16 modulo 60: 1/103680 q ( q^5-57*q^4+1272*q^3-13852*q^2+73296*q-149760 ) q congruent 17 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+82761*q^2-253725*q+332350 ) q congruent 19 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+81801*q^2-233325*q+296622 ) q congruent 21 modulo 60: 1/103680 phi1 ( q^5-56*q^4+1216*q^3-12906*q^2+68895*q-157950 ) q congruent 23 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+82761*q^2-260205*q+429550 ) q congruent 25 modulo 60: 1/103680 phi1 ( q^5-56*q^4+1216*q^3-12906*q^2+68895*q-157950 ) q congruent 27 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+81801*q^2-233325*q+255150 ) q congruent 29 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+82761*q^2-253725*q+373822 ) q congruent 31 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+81801*q^2-233325*q+255150 ) q congruent 32 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-13852*q^3+74256*q^2-176640*q+148480 ) q congruent 37 modulo 60: 1/103680 phi1 ( q^5-56*q^4+1216*q^3-12906*q^2+68895*q-157950 ) q congruent 41 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+82761*q^2-253725*q+332350 ) q congruent 43 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+81801*q^2-233325*q+255150 ) q congruent 47 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+82761*q^2-260205*q+429550 ) q congruent 49 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+81801*q^2-226845*q+199422 ) q congruent 53 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+82761*q^2-253725*q+332350 ) q congruent 59 modulo 60: 1/103680 ( q^6-57*q^5+1272*q^4-14122*q^3+82761*q^2-260205*q+471022 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 67, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 36 ], [ 3, 1, 2, 242 ], [ 4, 1, 2, 594 ], [ 5, 1, 2, 864 ], [ 6, 1, 2, 1512 ], [ 7, 1, 2, 432 ], [ 8, 1, 2, 144 ], [ 9, 1, 1, 27 ], [ 10, 1, 2, 72 ], [ 11, 1, 2, 720 ], [ 12, 1, 2, 2214 ], [ 13, 1, 4, 3240 ], [ 14, 1, 2, 3024 ], [ 15, 1, 2, 4752 ], [ 16, 1, 3, 5400 ], [ 17, 1, 4, 4320 ], [ 18, 1, 2, 2160 ], [ 19, 1, 2, 4320 ], [ 20, 1, 4, 4320 ], [ 21, 1, 2, 864 ], [ 22, 1, 4, 3024 ], [ 23, 1, 2, 270 ], [ 24, 1, 2, 1080 ], [ 25, 1, 3, 2700 ], [ 26, 1, 4, 864 ], [ 27, 1, 6, 1440 ], [ 28, 1, 4, 6480 ], [ 29, 1, 4, 9504 ], [ 30, 1, 3, 12960 ], [ 31, 1, 4, 10800 ], [ 32, 1, 3, 8640 ], [ 33, 1, 8, 6480 ], [ 34, 1, 4, 8640 ], [ 35, 1, 8, 12960 ], [ 36, 1, 4, 4320 ], [ 37, 1, 3, 8640 ], [ 38, 1, 12, 8640 ], [ 39, 1, 3, 2160 ], [ 40, 1, 6, 9180 ], [ 41, 1, 9, 12960 ], [ 42, 1, 6, 8640 ], [ 43, 1, 13, 8640 ], [ 44, 1, 10, 12960 ], [ 45, 1, 6, 25920 ], [ 46, 1, 6, 17280 ], [ 47, 1, 8, 12960 ], [ 48, 1, 6, 25920 ], [ 50, 1, 12, 17280 ], [ 51, 1, 9, 21600 ], [ 52, 1, 10, 25920 ], [ 53, 1, 20, 25920 ], [ 54, 1, 14, 51840 ], [ 55, 1, 15, 25920 ], [ 56, 1, 20, 51840 ], [ 58, 1, 15, 34560 ], [ 59, 1, 2, 51840 ], [ 61, 1, 21, 51840 ], [ 63, 1, 19, 103680 ] ] k = 39: F-action on Pi is () [65,1,39] Dynkin type is A_2(q) + T(phi1^4 phi2^2) Order of center |Z^F|: phi1^4 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 2 modulo 60: 1/384 q phi2 ( q^4-18*q^3+116*q^2-312*q+288 ) q congruent 3 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) q congruent 4 modulo 60: 1/384 q phi2 ( q^4-18*q^3+116*q^2-312*q+288 ) q congruent 5 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 7 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) q congruent 8 modulo 60: 1/384 q phi2 ( q^4-18*q^3+116*q^2-312*q+288 ) q congruent 9 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 11 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) q congruent 13 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 16 modulo 60: 1/384 q phi2 ( q^4-18*q^3+116*q^2-312*q+288 ) q congruent 17 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 19 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) q congruent 21 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 23 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) q congruent 25 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 27 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) q congruent 29 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 31 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) q congruent 32 modulo 60: 1/384 q phi2 ( q^4-18*q^3+116*q^2-312*q+288 ) q congruent 37 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 41 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 43 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) q congruent 47 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) q congruent 49 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 53 modulo 60: 1/384 phi1 ( q^5-16*q^4+82*q^3-124*q^2-67*q+60 ) q congruent 59 modulo 60: 1/384 ( q^6-17*q^5+98*q^4-206*q^3+57*q^2+127*q+132 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68, 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 26 ], [ 4, 1, 1, 46 ], [ 4, 1, 2, 12 ], [ 5, 1, 1, 80 ], [ 6, 1, 1, 96 ], [ 7, 1, 1, 40 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 40 ], [ 12, 1, 1, 70 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 24 ], [ 13, 1, 3, 48 ], [ 13, 1, 4, 24 ], [ 14, 1, 1, 120 ], [ 15, 1, 1, 152 ], [ 16, 1, 1, 176 ], [ 16, 1, 2, 24 ], [ 17, 1, 1, 240 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 112 ], [ 20, 1, 1, 144 ], [ 20, 1, 2, 112 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 120 ], [ 22, 1, 2, 72 ], [ 23, 1, 1, 18 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 36 ], [ 24, 1, 2, 28 ], [ 25, 1, 1, 60 ], [ 25, 1, 2, 24 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 26, 1, 3, 32 ], [ 27, 1, 1, 48 ], [ 27, 1, 2, 32 ], [ 28, 1, 1, 72 ], [ 28, 1, 2, 72 ], [ 28, 1, 3, 48 ], [ 29, 1, 1, 144 ], [ 29, 1, 2, 160 ], [ 30, 1, 1, 144 ], [ 30, 1, 2, 96 ], [ 31, 1, 1, 168 ], [ 31, 1, 2, 184 ], [ 32, 1, 1, 224 ], [ 33, 1, 1, 144 ], [ 33, 1, 2, 48 ], [ 33, 1, 4, 96 ], [ 34, 1, 1, 96 ], [ 34, 1, 2, 128 ], [ 35, 1, 1, 144 ], [ 35, 1, 2, 96 ], [ 35, 1, 3, 144 ], [ 36, 1, 1, 48 ], [ 36, 1, 2, 96 ], [ 37, 1, 1, 96 ], [ 37, 1, 2, 48 ], [ 38, 1, 1, 288 ], [ 38, 1, 5, 192 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 48 ], [ 40, 1, 1, 36 ], [ 40, 1, 3, 40 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 96 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], [ 42, 1, 1, 96 ], [ 42, 1, 4, 128 ], [ 43, 1, 1, 96 ], [ 43, 1, 2, 192 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 32 ], [ 44, 1, 1, 48 ], [ 44, 1, 2, 96 ], [ 44, 1, 5, 48 ], [ 44, 1, 9, 96 ], [ 45, 1, 1, 96 ], [ 45, 1, 2, 192 ], [ 46, 1, 1, 192 ], [ 46, 1, 2, 256 ], [ 47, 1, 1, 144 ], [ 47, 1, 2, 144 ], [ 47, 1, 3, 96 ], [ 48, 1, 1, 96 ], [ 48, 1, 2, 192 ], [ 48, 1, 3, 96 ], [ 48, 1, 7, 192 ], [ 50, 1, 2, 192 ], [ 50, 1, 4, 192 ], [ 50, 1, 5, 64 ], [ 51, 1, 1, 48 ], [ 51, 1, 2, 288 ], [ 51, 1, 5, 80 ], [ 51, 1, 6, 48 ], [ 52, 1, 2, 96 ], [ 52, 1, 3, 96 ], [ 52, 1, 9, 96 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 192 ], [ 53, 1, 3, 192 ], [ 53, 1, 9, 96 ], [ 54, 1, 2, 192 ], [ 54, 1, 5, 192 ], [ 55, 1, 1, 96 ], [ 55, 1, 2, 192 ], [ 55, 1, 5, 96 ], [ 55, 1, 9, 192 ], [ 56, 1, 2, 192 ], [ 56, 1, 5, 192 ], [ 56, 1, 6, 192 ], [ 56, 1, 7, 192 ], [ 58, 1, 2, 384 ], [ 58, 1, 9, 128 ], [ 59, 1, 3, 192 ], [ 59, 1, 17, 192 ], [ 61, 1, 12, 192 ], [ 61, 1, 19, 192 ], [ 63, 1, 21, 384 ], [ 63, 1, 29, 384 ] ] k = 40: F-action on Pi is () [65,1,40] Dynkin type is A_2(q) + T(phi1^3 phi2 phi4) Order of center |Z^F|: phi1^3 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 2 modulo 60: 1/64 q^2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 3 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 4 modulo 60: 1/64 q^2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 5 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 7 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 8 modulo 60: 1/64 q^2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 9 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 11 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 13 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 16 modulo 60: 1/64 q^2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 17 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 19 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 21 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 23 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 25 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 27 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 29 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 31 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 32 modulo 60: 1/64 q^2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 37 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 41 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 43 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 47 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 49 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 53 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) q congruent 59 modulo 60: 1/64 phi1 phi2 ( q^4-9*q^3+21*q^2+5*q-42 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19, 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 12, 1, 1, 10 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 12 ], [ 18, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 8 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 32 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 4 ], [ 26, 1, 1, 16 ], [ 28, 1, 3, 8 ], [ 29, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 8 ], [ 33, 1, 2, 8 ], [ 33, 1, 4, 32 ], [ 35, 1, 2, 16 ], [ 36, 1, 1, 16 ], [ 37, 1, 1, 32 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 24 ], [ 40, 1, 3, 4 ], [ 41, 1, 2, 16 ], [ 41, 1, 3, 16 ], [ 41, 1, 5, 16 ], [ 41, 1, 8, 8 ], [ 43, 1, 1, 32 ], [ 43, 1, 8, 16 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 16 ], [ 44, 1, 9, 16 ], [ 47, 1, 3, 16 ], [ 48, 1, 7, 32 ], [ 48, 1, 8, 32 ], [ 51, 1, 1, 16 ], [ 51, 1, 6, 16 ], [ 51, 1, 7, 8 ], [ 52, 1, 8, 16 ], [ 53, 1, 2, 32 ], [ 53, 1, 10, 32 ], [ 53, 1, 11, 16 ], [ 54, 1, 4, 32 ], [ 55, 1, 4, 16 ], [ 55, 1, 6, 32 ], [ 55, 1, 9, 32 ], [ 56, 1, 4, 32 ], [ 59, 1, 16, 32 ], [ 59, 1, 23, 32 ], [ 61, 1, 13, 32 ], [ 63, 1, 23, 64 ], [ 63, 1, 31, 64 ] ] k = 41: F-action on Pi is () [65,1,41] Dynkin type is A_2(q) + T(phi1 phi2^3 phi4) Order of center |Z^F|: phi1 phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 2 modulo 60: 1/192 q^3 phi1 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 4 modulo 60: 1/192 q^3 phi1 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 7 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 8 modulo 60: 1/192 q^3 phi1 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 11 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 13 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 16 modulo 60: 1/192 q^3 phi1 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 19 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 21 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 23 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 25 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 27 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 29 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 31 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 32 modulo 60: 1/192 q^3 phi1 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 41 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 43 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 47 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 49 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 53 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) q congruent 59 modulo 60: 1/192 phi1^2 phi2 ( q^3-4*q^2+5*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 12 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 8 ], [ 13, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 48 ], [ 20, 1, 2, 48 ], [ 22, 1, 2, 24 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 4, 36 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 2, 24 ], [ 35, 1, 4, 48 ], [ 38, 1, 6, 96 ], [ 39, 1, 3, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 12 ], [ 41, 1, 8, 24 ], [ 41, 1, 10, 48 ], [ 43, 1, 9, 8 ], [ 43, 1, 12, 96 ], [ 44, 1, 4, 24 ], [ 44, 1, 10, 48 ], [ 47, 1, 4, 48 ], [ 51, 1, 4, 32 ], [ 51, 1, 5, 48 ], [ 51, 1, 7, 8 ], [ 52, 1, 5, 48 ], [ 53, 1, 11, 48 ], [ 53, 1, 19, 96 ], [ 55, 1, 4, 48 ], [ 55, 1, 10, 96 ], [ 56, 1, 9, 96 ], [ 58, 1, 5, 32 ], [ 59, 1, 24, 96 ], [ 61, 1, 15, 96 ], [ 63, 1, 22, 192 ] ] k = 42: F-action on Pi is (1,3) [65,1,42] Dynkin type is ^2A_2(q) + T(phi1 phi2^3 phi4) Order of center |Z^F|: phi1 phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 2 modulo 60: 1/64 q^4 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 4 modulo 60: 1/64 q^4 ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 7 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 8 modulo 60: 1/64 q^4 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 11 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 13 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 16 modulo 60: 1/64 q^4 ( q^2-5*q+6 ) q congruent 17 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 19 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 21 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 23 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 25 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 27 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 29 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 31 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 32 modulo 60: 1/64 q^4 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 41 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 43 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 47 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 49 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 53 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) q congruent 59 modulo 60: 1/64 q phi1^3 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 71, 20, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 10 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 12 ], [ 18, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 32 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 16 ], [ 28, 1, 2, 8 ], [ 29, 1, 4, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 4, 8 ], [ 33, 1, 6, 8 ], [ 33, 1, 10, 32 ], [ 35, 1, 7, 16 ], [ 36, 1, 4, 16 ], [ 37, 1, 2, 16 ], [ 37, 1, 3, 32 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 40, 1, 6, 24 ], [ 41, 1, 2, 16 ], [ 41, 1, 5, 16 ], [ 41, 1, 8, 8 ], [ 41, 1, 10, 16 ], [ 43, 1, 8, 16 ], [ 43, 1, 9, 8 ], [ 43, 1, 13, 32 ], [ 44, 1, 4, 16 ], [ 44, 1, 5, 16 ], [ 44, 1, 6, 8 ], [ 47, 1, 10, 16 ], [ 48, 1, 9, 32 ], [ 48, 1, 10, 32 ], [ 51, 1, 3, 16 ], [ 51, 1, 4, 8 ], [ 51, 1, 9, 16 ], [ 52, 1, 5, 16 ], [ 53, 1, 12, 32 ], [ 53, 1, 13, 16 ], [ 53, 1, 14, 32 ], [ 54, 1, 9, 32 ], [ 55, 1, 11, 16 ], [ 55, 1, 19, 32 ], [ 55, 1, 20, 32 ], [ 56, 1, 16, 32 ], [ 59, 1, 16, 32 ], [ 59, 1, 24, 32 ], [ 61, 1, 16, 32 ], [ 63, 1, 25, 64 ], [ 63, 1, 30, 64 ] ] k = 43: F-action on Pi is (1,3) [65,1,43] Dynkin type is ^2A_2(q) + T(phi1^3 phi2 phi4) Order of center |Z^F|: phi1^3 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 2 modulo 60: 1/192 q^3 ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 4 modulo 60: 1/192 q^3 ( q^3-9*q^2+26*q-24 ) q congruent 5 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 7 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 8 modulo 60: 1/192 q^3 ( q^3-9*q^2+26*q-24 ) q congruent 9 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 11 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 13 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 16 modulo 60: 1/192 q^3 ( q^3-9*q^2+26*q-24 ) q congruent 17 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 19 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 21 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 23 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 25 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 27 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 29 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 31 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 32 modulo 60: 1/192 q^3 ( q^3-9*q^2+26*q-24 ) q congruent 37 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 41 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 43 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 47 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 49 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 53 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) q congruent 59 modulo 60: 1/192 phi1 phi2 ( q^4-9*q^3+27*q^2-35*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 19, 96 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 12 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 12 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 48 ], [ 20, 1, 3, 48 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 36 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 31, 1, 3, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 6, 24 ], [ 35, 1, 5, 48 ], [ 38, 1, 7, 96 ], [ 39, 1, 1, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 12 ], [ 41, 1, 3, 48 ], [ 41, 1, 8, 24 ], [ 43, 1, 3, 96 ], [ 43, 1, 9, 8 ], [ 44, 1, 1, 48 ], [ 44, 1, 6, 24 ], [ 47, 1, 9, 48 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 32 ], [ 51, 1, 10, 48 ], [ 52, 1, 8, 48 ], [ 53, 1, 5, 96 ], [ 53, 1, 13, 48 ], [ 55, 1, 11, 48 ], [ 55, 1, 16, 96 ], [ 56, 1, 11, 96 ], [ 58, 1, 5, 32 ], [ 59, 1, 23, 96 ], [ 61, 1, 14, 96 ], [ 63, 1, 24, 192 ] ] k = 44: F-action on Pi is (1,3) [65,1,44] Dynkin type is ^2A_2(q) + T(phi1^2 phi2^2 phi4) Order of center |Z^F|: phi1^2 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 2 modulo 60: 1/32 q^4 phi1 ( q-2 ) q congruent 3 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 4 modulo 60: 1/32 q^4 phi1 ( q-2 ) q congruent 5 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 7 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 8 modulo 60: 1/32 q^4 phi1 ( q-2 ) q congruent 9 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 11 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 13 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 16 modulo 60: 1/32 q^4 phi1 ( q-2 ) q congruent 17 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 19 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 21 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 23 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 25 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 27 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 29 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 31 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 32 modulo 60: 1/32 q^4 phi1 ( q-2 ) q congruent 37 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 41 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 43 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 47 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 49 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 53 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) q congruent 59 modulo 60: 1/32 phi1 phi2 ( q^4-3*q^3+3*q^2-3*q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 76, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 29, 1, 3, 8 ], [ 30, 1, 4, 8 ], [ 31, 1, 3, 4 ], [ 31, 1, 4, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 33, 1, 9, 16 ], [ 35, 1, 5, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 3, 8 ], [ 38, 1, 10, 16 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 43, 1, 4, 16 ], [ 43, 1, 9, 8 ], [ 44, 1, 2, 8 ], [ 44, 1, 6, 8 ], [ 47, 1, 9, 8 ], [ 47, 1, 10, 8 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 16 ], [ 51, 1, 8, 8 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 7, 16 ], [ 53, 1, 13, 16 ], [ 54, 1, 9, 16 ], [ 55, 1, 11, 16 ], [ 55, 1, 17, 16 ], [ 56, 1, 11, 16 ], [ 56, 1, 16, 16 ], [ 58, 1, 5, 16 ], [ 59, 1, 21, 16 ], [ 61, 1, 14, 16 ], [ 61, 1, 16, 16 ], [ 63, 1, 26, 32 ] ] k = 45: F-action on Pi is () [65,1,45] Dynkin type is A_2(q) + T(phi1^2 phi2^2 phi4) Order of center |Z^F|: phi1^2 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 2 modulo 60: 1/32 q^3 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 4 modulo 60: 1/32 q^3 phi2 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 7 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 8 modulo 60: 1/32 q^3 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 11 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 13 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 16 modulo 60: 1/32 q^3 phi2 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 19 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 21 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 23 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 25 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 27 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 29 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 31 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 32 modulo 60: 1/32 q^3 phi2 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 41 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 43 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 47 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 49 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 53 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) q congruent 59 modulo 60: 1/32 phi1 phi2^2 ( q^3-4*q^2+5*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 76, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 29, 1, 2, 8 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 33, 1, 5, 16 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 36, 1, 2, 8 ], [ 38, 1, 2, 16 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 43, 1, 2, 16 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 8, 8 ], [ 47, 1, 3, 8 ], [ 47, 1, 4, 8 ], [ 51, 1, 2, 8 ], [ 51, 1, 4, 16 ], [ 51, 1, 7, 8 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 4, 16 ], [ 53, 1, 11, 16 ], [ 54, 1, 4, 16 ], [ 55, 1, 4, 16 ], [ 55, 1, 8, 16 ], [ 56, 1, 4, 16 ], [ 56, 1, 9, 16 ], [ 58, 1, 5, 16 ], [ 59, 1, 21, 16 ], [ 61, 1, 13, 16 ], [ 61, 1, 15, 16 ], [ 63, 1, 27, 32 ] ] k = 46: F-action on Pi is (1,3) [65,1,46] Dynkin type is ^2A_2(q) + T(phi1^2 phi2^4) Order of center |Z^F|: phi1^2 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 2 modulo 60: 1/384 q^2 ( q^4-13*q^3+60*q^2-116*q+80 ) q congruent 3 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) q congruent 4 modulo 60: 1/384 q^2 ( q^4-13*q^3+60*q^2-116*q+80 ) q congruent 5 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 7 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) q congruent 8 modulo 60: 1/384 q^2 ( q^4-13*q^3+60*q^2-116*q+80 ) q congruent 9 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 11 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) q congruent 13 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 16 modulo 60: 1/384 q^2 ( q^4-13*q^3+60*q^2-116*q+80 ) q congruent 17 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 19 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) q congruent 21 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 23 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) q congruent 25 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 27 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) q congruent 29 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 31 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) q congruent 32 modulo 60: 1/384 q^2 ( q^4-13*q^3+60*q^2-116*q+80 ) q congruent 37 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 41 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 43 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) q congruent 47 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) q congruent 49 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 53 modulo 60: 1/384 phi1^2 ( q^4-11*q^3+37*q^2-41*q+30 ) q congruent 59 modulo 60: 1/384 ( q^6-13*q^5+60*q^4-126*q^3+149*q^2-101*q-66 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 69, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 26 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 46 ], [ 5, 1, 2, 80 ], [ 6, 1, 2, 96 ], [ 7, 1, 2, 40 ], [ 8, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 40 ], [ 12, 1, 2, 70 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 48 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 120 ], [ 15, 1, 2, 152 ], [ 16, 1, 3, 176 ], [ 16, 1, 4, 24 ], [ 17, 1, 4, 240 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 112 ], [ 20, 1, 3, 112 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 48 ], [ 22, 1, 3, 72 ], [ 22, 1, 4, 120 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 18 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 36 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 60 ], [ 25, 1, 4, 24 ], [ 26, 1, 2, 32 ], [ 26, 1, 4, 48 ], [ 27, 1, 3, 32 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 48 ], [ 28, 1, 3, 72 ], [ 28, 1, 4, 72 ], [ 29, 1, 3, 160 ], [ 29, 1, 4, 144 ], [ 30, 1, 3, 144 ], [ 30, 1, 4, 96 ], [ 31, 1, 3, 184 ], [ 31, 1, 4, 168 ], [ 32, 1, 3, 224 ], [ 33, 1, 6, 48 ], [ 33, 1, 8, 144 ], [ 33, 1, 10, 96 ], [ 34, 1, 3, 128 ], [ 34, 1, 4, 96 ], [ 35, 1, 6, 144 ], [ 35, 1, 7, 96 ], [ 35, 1, 8, 144 ], [ 36, 1, 3, 96 ], [ 36, 1, 4, 48 ], [ 37, 1, 2, 48 ], [ 37, 1, 3, 96 ], [ 38, 1, 8, 192 ], [ 38, 1, 12, 288 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 48 ], [ 40, 1, 2, 40 ], [ 40, 1, 6, 36 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 96 ], [ 42, 1, 2, 128 ], [ 42, 1, 6, 96 ], [ 43, 1, 3, 32 ], [ 43, 1, 4, 192 ], [ 43, 1, 8, 48 ], [ 43, 1, 13, 96 ], [ 44, 1, 5, 96 ], [ 44, 1, 8, 96 ], [ 44, 1, 9, 48 ], [ 44, 1, 10, 48 ], [ 45, 1, 5, 192 ], [ 45, 1, 6, 96 ], [ 46, 1, 5, 256 ], [ 46, 1, 6, 192 ], [ 47, 1, 7, 144 ], [ 47, 1, 8, 144 ], [ 47, 1, 10, 96 ], [ 48, 1, 4, 96 ], [ 48, 1, 5, 192 ], [ 48, 1, 6, 96 ], [ 48, 1, 10, 192 ], [ 50, 1, 8, 64 ], [ 50, 1, 9, 192 ], [ 50, 1, 11, 192 ], [ 51, 1, 3, 48 ], [ 51, 1, 8, 288 ], [ 51, 1, 9, 48 ], [ 51, 1, 10, 80 ], [ 52, 1, 2, 96 ], [ 52, 1, 4, 96 ], [ 52, 1, 9, 96 ], [ 53, 1, 6, 96 ], [ 53, 1, 8, 192 ], [ 53, 1, 12, 192 ], [ 53, 1, 20, 96 ], [ 54, 1, 12, 192 ], [ 54, 1, 13, 192 ], [ 55, 1, 13, 192 ], [ 55, 1, 14, 96 ], [ 55, 1, 15, 96 ], [ 55, 1, 20, 192 ], [ 56, 1, 13, 192 ], [ 56, 1, 15, 192 ], [ 56, 1, 18, 192 ], [ 56, 1, 19, 192 ], [ 58, 1, 11, 128 ], [ 58, 1, 12, 384 ], [ 59, 1, 3, 192 ], [ 59, 1, 18, 192 ], [ 61, 1, 18, 192 ], [ 61, 1, 20, 192 ], [ 63, 1, 28, 384 ], [ 63, 1, 34, 384 ] ] k = 47: F-action on Pi is () [65,1,47] Dynkin type is A_2(q) + T(phi1^5 phi2) Order of center |Z^F|: phi1^5 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7175*q-7470 ) q congruent 2 modulo 60: 1/2880 q ( q^5-35*q^4+470*q^3-2980*q^2+8664*q-8640 ) q congruent 3 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9699*q^2-13485*q+4950 ) q congruent 4 modulo 60: 1/2880 q ( q^5-35*q^4+470*q^3-2980*q^2+8744*q-9440 ) q congruent 5 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7095*q-6750 ) q congruent 7 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9779*q^2-14285*q+5670 ) q congruent 8 modulo 60: 1/2880 q ( q^5-35*q^4+470*q^3-2980*q^2+8664*q-8640 ) q congruent 9 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7095*q-6750 ) q congruent 11 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9699*q^2-13485*q+4950 ) q congruent 13 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7175*q-7470 ) q congruent 16 modulo 60: 1/2880 q ( q^5-35*q^4+470*q^3-2980*q^2+8744*q-9440 ) q congruent 17 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7095*q-6750 ) q congruent 19 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9779*q^2-14285*q+5670 ) q congruent 21 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7095*q-6750 ) q congruent 23 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9699*q^2-13485*q+4950 ) q congruent 25 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7175*q-7470 ) q congruent 27 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9699*q^2-13485*q+4950 ) q congruent 29 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7095*q-6750 ) q congruent 31 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9779*q^2-14285*q+5670 ) q congruent 32 modulo 60: 1/2880 q ( q^5-35*q^4+470*q^3-2980*q^2+8664*q-8640 ) q congruent 37 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7175*q-7470 ) q congruent 41 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7095*q-6750 ) q congruent 43 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9779*q^2-14285*q+5670 ) q congruent 47 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9699*q^2-13485*q+4950 ) q congruent 49 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7175*q-7470 ) q congruent 53 modulo 60: 1/2880 phi1 ( q^5-34*q^4+436*q^3-2604*q^2+7095*q-6750 ) q congruent 59 modulo 60: 1/2880 ( q^6-35*q^5+470*q^4-3040*q^3+9699*q^2-13485*q+4950 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4, 77 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 62 ], [ 4, 1, 1, 150 ], [ 5, 1, 1, 264 ], [ 6, 1, 1, 312 ], [ 7, 1, 1, 132 ], [ 8, 1, 1, 60 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 30 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 140 ], [ 12, 1, 1, 330 ], [ 13, 1, 1, 360 ], [ 14, 1, 1, 660 ], [ 15, 1, 1, 732 ], [ 16, 1, 1, 840 ], [ 17, 1, 1, 840 ], [ 18, 1, 1, 420 ], [ 19, 1, 1, 600 ], [ 20, 1, 1, 840 ], [ 20, 1, 2, 120 ], [ 21, 1, 1, 240 ], [ 22, 1, 1, 540 ], [ 22, 1, 2, 84 ], [ 23, 1, 1, 90 ], [ 24, 1, 1, 210 ], [ 24, 1, 2, 30 ], [ 25, 1, 1, 540 ], [ 26, 1, 1, 240 ], [ 26, 1, 3, 24 ], [ 27, 1, 1, 240 ], [ 27, 1, 2, 40 ], [ 28, 1, 1, 540 ], [ 28, 1, 2, 180 ], [ 29, 1, 1, 1200 ], [ 29, 1, 2, 264 ], [ 30, 1, 1, 1080 ], [ 31, 1, 1, 1380 ], [ 31, 1, 2, 300 ], [ 32, 1, 1, 1200 ], [ 33, 1, 1, 720 ], [ 34, 1, 1, 960 ], [ 34, 1, 2, 240 ], [ 35, 1, 1, 1080 ], [ 35, 1, 3, 360 ], [ 36, 1, 1, 720 ], [ 36, 1, 2, 120 ], [ 37, 1, 1, 1440 ], [ 38, 1, 1, 1440 ], [ 38, 1, 5, 240 ], [ 39, 1, 1, 360 ], [ 39, 1, 4, 60 ], [ 40, 1, 1, 900 ], [ 41, 1, 1, 720 ], [ 41, 1, 6, 360 ], [ 42, 1, 1, 960 ], [ 42, 1, 4, 240 ], [ 43, 1, 1, 1440 ], [ 43, 1, 2, 240 ], [ 44, 1, 1, 720 ], [ 44, 1, 2, 360 ], [ 45, 1, 1, 1440 ], [ 45, 1, 2, 720 ], [ 46, 1, 1, 1920 ], [ 46, 1, 2, 480 ], [ 47, 1, 1, 1080 ], [ 47, 1, 2, 360 ], [ 48, 1, 1, 1440 ], [ 48, 1, 2, 720 ], [ 50, 1, 1, 1440 ], [ 50, 1, 2, 480 ], [ 50, 1, 4, 480 ], [ 51, 1, 1, 2160 ], [ 51, 1, 2, 600 ], [ 52, 1, 1, 720 ], [ 52, 1, 2, 720 ], [ 53, 1, 1, 1440 ], [ 53, 1, 3, 720 ], [ 54, 1, 1, 1440 ], [ 54, 1, 2, 1440 ], [ 55, 1, 1, 1440 ], [ 55, 1, 2, 720 ], [ 56, 1, 1, 1440 ], [ 56, 1, 2, 1440 ], [ 56, 1, 6, 1440 ], [ 58, 1, 1, 2880 ], [ 58, 1, 2, 960 ], [ 59, 1, 12, 1440 ], [ 61, 1, 1, 1440 ], [ 61, 1, 19, 1440 ], [ 63, 1, 33, 2880 ] ] k = 48: F-action on Pi is () [65,1,48] Dynkin type is A_2(q) + T(phi1^3 phi2^3) Order of center |Z^F|: phi1^3 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2+15*q+2 ) q congruent 2 modulo 60: 1/192 q^2 ( q^4-7*q^3+10*q^2+12*q-24 ) q congruent 3 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+11*q^2+5*q-6 ) q congruent 4 modulo 60: 1/192 q ( q^5-7*q^4+10*q^3+12*q^2-8*q-32 ) q congruent 5 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2-q+18 ) q congruent 7 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2+15*q-22 ) q congruent 8 modulo 60: 1/192 q^2 ( q^4-7*q^3+10*q^2+12*q-24 ) q congruent 9 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2-q+18 ) q congruent 11 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+11*q^2+5*q-6 ) q congruent 13 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2+15*q+2 ) q congruent 16 modulo 60: 1/192 q ( q^5-7*q^4+10*q^3+12*q^2-8*q-32 ) q congruent 17 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2-q+18 ) q congruent 19 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2+15*q-22 ) q congruent 21 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2-q+18 ) q congruent 23 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+11*q^2+5*q-6 ) q congruent 25 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2+15*q+2 ) q congruent 27 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+11*q^2+5*q-6 ) q congruent 29 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2-q+18 ) q congruent 31 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2+15*q-22 ) q congruent 32 modulo 60: 1/192 q^2 ( q^4-7*q^3+10*q^2+12*q-24 ) q congruent 37 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2+15*q+2 ) q congruent 41 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2-q+18 ) q congruent 43 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2+15*q-22 ) q congruent 47 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+11*q^2+5*q-6 ) q congruent 49 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2+15*q+2 ) q congruent 53 modulo 60: 1/192 phi1 ( q^5-6*q^4+4*q^3+16*q^2-q+18 ) q congruent 59 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+11*q^2+5*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7, 81 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 18 ], [ 4, 1, 2, 12 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 18 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 24 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], [ 16, 1, 1, 48 ], [ 16, 1, 2, 24 ], [ 16, 1, 4, 48 ], [ 17, 1, 1, 72 ], [ 17, 1, 2, 16 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 72 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 60 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 18 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 24 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 48 ], [ 26, 1, 3, 24 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 16 ], [ 28, 1, 1, 12 ], [ 28, 1, 2, 36 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 29, 1, 2, 72 ], [ 30, 1, 1, 24 ], [ 30, 1, 2, 48 ], [ 31, 1, 1, 12 ], [ 31, 1, 2, 84 ], [ 32, 1, 1, 48 ], [ 32, 1, 2, 48 ], [ 33, 1, 1, 48 ], [ 33, 1, 2, 48 ], [ 34, 1, 2, 48 ], [ 35, 1, 1, 24 ], [ 35, 1, 2, 48 ], [ 35, 1, 3, 72 ], [ 35, 1, 4, 48 ], [ 36, 1, 2, 24 ], [ 37, 1, 2, 48 ], [ 38, 1, 2, 32 ], [ 38, 1, 5, 144 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 48 ], [ 40, 1, 3, 72 ], [ 40, 1, 6, 48 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 48 ], [ 41, 1, 9, 48 ], [ 42, 1, 4, 48 ], [ 43, 1, 2, 48 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 96 ], [ 44, 1, 2, 24 ], [ 44, 1, 5, 48 ], [ 44, 1, 8, 48 ], [ 45, 1, 2, 48 ], [ 46, 1, 2, 96 ], [ 47, 1, 1, 24 ], [ 47, 1, 2, 72 ], [ 47, 1, 3, 48 ], [ 47, 1, 4, 48 ], [ 48, 1, 2, 48 ], [ 48, 1, 3, 96 ], [ 50, 1, 5, 96 ], [ 51, 1, 2, 24 ], [ 51, 1, 3, 96 ], [ 51, 1, 5, 144 ], [ 51, 1, 6, 48 ], [ 52, 1, 3, 48 ], [ 52, 1, 4, 48 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ], [ 53, 1, 3, 48 ], [ 53, 1, 4, 96 ], [ 53, 1, 9, 96 ], [ 54, 1, 5, 96 ], [ 55, 1, 2, 48 ], [ 55, 1, 5, 96 ], [ 55, 1, 8, 96 ], [ 56, 1, 5, 96 ], [ 56, 1, 7, 96 ], [ 56, 1, 10, 96 ], [ 58, 1, 4, 96 ], [ 58, 1, 9, 192 ], [ 59, 1, 13, 96 ], [ 59, 1, 22, 96 ], [ 61, 1, 12, 96 ], [ 61, 1, 17, 96 ], [ 63, 1, 32, 192 ] ] k = 49: F-action on Pi is (1,3) [65,1,49] Dynkin type is ^2A_2(q) + T(phi1 phi2^5) Order of center |Z^F|: phi1 phi2^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/2880 phi1 ( q^5-26*q^4+254*q^3-1186*q^2+2853*q-3240 ) q congruent 2 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1380*q^3+3264*q^2-3488*q+1280 ) q congruent 3 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4039*q^2-6453*q+5040 ) q congruent 4 modulo 60: 1/2880 q ( q^5-27*q^4+280*q^3-1380*q^2+3184*q-2688 ) q congruent 5 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4119*q^2-6893*q+5240 ) q congruent 7 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4039*q^2-6453*q+5040 ) q congruent 8 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1380*q^3+3264*q^2-3488*q+1280 ) q congruent 9 modulo 60: 1/2880 phi1 ( q^5-26*q^4+254*q^3-1186*q^2+2853*q-3240 ) q congruent 11 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4119*q^2-7253*q+7040 ) q congruent 13 modulo 60: 1/2880 phi1 ( q^5-26*q^4+254*q^3-1186*q^2+2853*q-3240 ) q congruent 16 modulo 60: 1/2880 q ( q^5-27*q^4+280*q^3-1380*q^2+3184*q-2688 ) q congruent 17 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4119*q^2-6893*q+5240 ) q congruent 19 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4039*q^2-6453*q+5040 ) q congruent 21 modulo 60: 1/2880 phi1 ( q^5-26*q^4+254*q^3-1186*q^2+2853*q-3240 ) q congruent 23 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4119*q^2-7253*q+7040 ) q congruent 25 modulo 60: 1/2880 phi1 ( q^5-26*q^4+254*q^3-1186*q^2+2853*q-3240 ) q congruent 27 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4039*q^2-6453*q+5040 ) q congruent 29 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4119*q^2-6893*q+5240 ) q congruent 31 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4039*q^2-6453*q+5040 ) q congruent 32 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1380*q^3+3264*q^2-3488*q+1280 ) q congruent 37 modulo 60: 1/2880 phi1 ( q^5-26*q^4+254*q^3-1186*q^2+2853*q-3240 ) q congruent 41 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4119*q^2-6893*q+5240 ) q congruent 43 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4039*q^2-6453*q+5040 ) q congruent 47 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4119*q^2-7253*q+7040 ) q congruent 49 modulo 60: 1/2880 phi1 ( q^5-26*q^4+254*q^3-1186*q^2+2853*q-3240 ) q congruent 53 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4119*q^2-6893*q+5240 ) q congruent 59 modulo 60: 1/2880 ( q^6-27*q^5+280*q^4-1440*q^3+4119*q^2-7253*q+7040 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 5, 78 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 62 ], [ 4, 1, 2, 150 ], [ 5, 1, 2, 264 ], [ 6, 1, 2, 312 ], [ 7, 1, 2, 132 ], [ 8, 1, 2, 60 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 30 ], [ 11, 1, 2, 140 ], [ 12, 1, 2, 330 ], [ 13, 1, 4, 360 ], [ 14, 1, 2, 660 ], [ 15, 1, 2, 732 ], [ 16, 1, 3, 840 ], [ 17, 1, 4, 840 ], [ 18, 1, 2, 420 ], [ 19, 1, 2, 600 ], [ 20, 1, 3, 120 ], [ 20, 1, 4, 840 ], [ 21, 1, 2, 240 ], [ 22, 1, 3, 84 ], [ 22, 1, 4, 540 ], [ 23, 1, 2, 90 ], [ 24, 1, 1, 30 ], [ 24, 1, 2, 210 ], [ 25, 1, 3, 540 ], [ 26, 1, 2, 24 ], [ 26, 1, 4, 240 ], [ 27, 1, 3, 40 ], [ 27, 1, 6, 240 ], [ 28, 1, 3, 180 ], [ 28, 1, 4, 540 ], [ 29, 1, 3, 264 ], [ 29, 1, 4, 1200 ], [ 30, 1, 3, 1080 ], [ 31, 1, 3, 300 ], [ 31, 1, 4, 1380 ], [ 32, 1, 3, 1200 ], [ 33, 1, 8, 720 ], [ 34, 1, 3, 240 ], [ 34, 1, 4, 960 ], [ 35, 1, 6, 360 ], [ 35, 1, 8, 1080 ], [ 36, 1, 3, 120 ], [ 36, 1, 4, 720 ], [ 37, 1, 3, 1440 ], [ 38, 1, 8, 240 ], [ 38, 1, 12, 1440 ], [ 39, 1, 3, 360 ], [ 39, 1, 4, 60 ], [ 40, 1, 6, 900 ], [ 41, 1, 6, 360 ], [ 41, 1, 9, 720 ], [ 42, 1, 2, 240 ], [ 42, 1, 6, 960 ], [ 43, 1, 4, 240 ], [ 43, 1, 13, 1440 ], [ 44, 1, 8, 360 ], [ 44, 1, 10, 720 ], [ 45, 1, 5, 720 ], [ 45, 1, 6, 1440 ], [ 46, 1, 5, 480 ], [ 46, 1, 6, 1920 ], [ 47, 1, 7, 360 ], [ 47, 1, 8, 1080 ], [ 48, 1, 5, 720 ], [ 48, 1, 6, 1440 ], [ 50, 1, 9, 480 ], [ 50, 1, 11, 480 ], [ 50, 1, 12, 1440 ], [ 51, 1, 8, 600 ], [ 51, 1, 9, 2160 ], [ 52, 1, 9, 720 ], [ 52, 1, 10, 720 ], [ 53, 1, 8, 720 ], [ 53, 1, 20, 1440 ], [ 54, 1, 12, 1440 ], [ 54, 1, 14, 1440 ], [ 55, 1, 13, 720 ], [ 55, 1, 15, 1440 ], [ 56, 1, 15, 1440 ], [ 56, 1, 18, 1440 ], [ 56, 1, 20, 1440 ], [ 58, 1, 12, 960 ], [ 58, 1, 15, 2880 ], [ 59, 1, 13, 1440 ], [ 61, 1, 20, 1440 ], [ 61, 1, 21, 1440 ], [ 63, 1, 36, 2880 ] ] k = 50: F-action on Pi is (1,3) [65,1,50] Dynkin type is ^2A_2(q) + T(phi1^3 phi2^3) Order of center |Z^F|: phi1^3 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 q phi1^2 ( q^3-5*q^2+q+11 ) q congruent 2 modulo 60: 1/192 q ( q^5-7*q^4+12*q^3+4*q^2-32 ) q congruent 3 modulo 60: 1/192 phi1 ( q^5-6*q^4+6*q^3+10*q^2-11*q+24 ) q congruent 4 modulo 60: 1/192 q^2 phi2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/192 phi1^2 ( q^4-5*q^3+q^2+11*q+16 ) q congruent 7 modulo 60: 1/192 phi1 ( q^5-6*q^4+6*q^3+10*q^2-11*q+24 ) q congruent 8 modulo 60: 1/192 q ( q^5-7*q^4+12*q^3+4*q^2-32 ) q congruent 9 modulo 60: 1/192 q phi1^2 ( q^3-5*q^2+q+11 ) q congruent 11 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+13*q^2-3*q+8 ) q congruent 13 modulo 60: 1/192 q phi1^2 ( q^3-5*q^2+q+11 ) q congruent 16 modulo 60: 1/192 q^2 phi2 ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/192 phi1^2 ( q^4-5*q^3+q^2+11*q+16 ) q congruent 19 modulo 60: 1/192 phi1 ( q^5-6*q^4+6*q^3+10*q^2-11*q+24 ) q congruent 21 modulo 60: 1/192 q phi1^2 ( q^3-5*q^2+q+11 ) q congruent 23 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+13*q^2-3*q+8 ) q congruent 25 modulo 60: 1/192 q phi1^2 ( q^3-5*q^2+q+11 ) q congruent 27 modulo 60: 1/192 phi1 ( q^5-6*q^4+6*q^3+10*q^2-11*q+24 ) q congruent 29 modulo 60: 1/192 phi1^2 ( q^4-5*q^3+q^2+11*q+16 ) q congruent 31 modulo 60: 1/192 phi1 ( q^5-6*q^4+6*q^3+10*q^2-11*q+24 ) q congruent 32 modulo 60: 1/192 q ( q^5-7*q^4+12*q^3+4*q^2-32 ) q congruent 37 modulo 60: 1/192 q phi1^2 ( q^3-5*q^2+q+11 ) q congruent 41 modulo 60: 1/192 phi1^2 ( q^4-5*q^3+q^2+11*q+16 ) q congruent 43 modulo 60: 1/192 phi1 ( q^5-6*q^4+6*q^3+10*q^2-11*q+24 ) q congruent 47 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+13*q^2-3*q+8 ) q congruent 49 modulo 60: 1/192 q phi1^2 ( q^3-5*q^2+q+11 ) q congruent 53 modulo 60: 1/192 phi1^2 ( q^4-5*q^3+q^2+11*q+16 ) q congruent 59 modulo 60: 1/192 phi1 phi2 ( q^4-7*q^3+13*q^2-3*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 7, 82 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 14 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 18 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 12 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 18 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], [ 16, 1, 2, 48 ], [ 16, 1, 3, 48 ], [ 16, 1, 4, 24 ], [ 17, 1, 3, 16 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], [ 20, 1, 3, 72 ], [ 20, 1, 4, 24 ], [ 22, 1, 3, 60 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 24 ], [ 26, 1, 2, 24 ], [ 27, 1, 2, 16 ], [ 27, 1, 3, 24 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 36 ], [ 28, 1, 4, 12 ], [ 29, 1, 3, 72 ], [ 30, 1, 3, 24 ], [ 30, 1, 4, 48 ], [ 31, 1, 3, 84 ], [ 31, 1, 4, 12 ], [ 32, 1, 2, 48 ], [ 32, 1, 3, 48 ], [ 33, 1, 6, 48 ], [ 33, 1, 8, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 72 ], [ 35, 1, 7, 48 ], [ 35, 1, 8, 24 ], [ 36, 1, 3, 24 ], [ 37, 1, 2, 48 ], [ 38, 1, 8, 144 ], [ 38, 1, 10, 32 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 72 ], [ 40, 1, 3, 48 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 48 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 48 ], [ 42, 1, 2, 48 ], [ 43, 1, 3, 96 ], [ 43, 1, 4, 48 ], [ 43, 1, 8, 48 ], [ 44, 1, 2, 48 ], [ 44, 1, 8, 24 ], [ 44, 1, 9, 48 ], [ 45, 1, 5, 48 ], [ 46, 1, 5, 96 ], [ 47, 1, 7, 72 ], [ 47, 1, 8, 24 ], [ 47, 1, 9, 48 ], [ 47, 1, 10, 48 ], [ 48, 1, 4, 96 ], [ 48, 1, 5, 48 ], [ 50, 1, 8, 96 ], [ 51, 1, 3, 48 ], [ 51, 1, 6, 96 ], [ 51, 1, 8, 24 ], [ 51, 1, 10, 144 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ], [ 52, 1, 3, 48 ], [ 52, 1, 4, 48 ], [ 53, 1, 6, 96 ], [ 53, 1, 7, 96 ], [ 53, 1, 8, 48 ], [ 54, 1, 13, 96 ], [ 55, 1, 13, 48 ], [ 55, 1, 14, 96 ], [ 55, 1, 17, 96 ], [ 56, 1, 13, 96 ], [ 56, 1, 14, 96 ], [ 56, 1, 19, 96 ], [ 58, 1, 4, 96 ], [ 58, 1, 11, 192 ], [ 59, 1, 12, 96 ], [ 59, 1, 22, 96 ], [ 61, 1, 18, 96 ], [ 61, 1, 22, 96 ], [ 63, 1, 35, 192 ] ] i = 66: Pi = [ 1 ] j = 1: Omega trivial k = 1: F-action on Pi is () [66,1,1] Dynkin type is A_1(q) + T(phi1^7) Order of center |Z^F|: phi1^7 Numbers of classes in class type: q congruent 1 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7184688*q^2+270957\ 46*q-46987451 ) q congruent 2 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84056*q^4+1008448*q^3-6668928*q^2+215285\ 76*q-23224320 ) q congruent 3 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+259908\ 66*q-35406315 ) q congruent 4 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84056*q^4+1008448*q^3-6695808*q^2+224066\ 56*q-29173760 ) q congruent 5 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+262176\ 66*q-38989755 ) q congruent 7 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7184688*q^2+268689\ 46*q-42242795 ) q congruent 8 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84056*q^4+1008448*q^3-6668928*q^2+215285\ 76*q-23224320 ) q congruent 9 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+262176\ 66*q-38989755 ) q congruent 11 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+259908\ 66*q-36567531 ) q congruent 13 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7184688*q^2+270957\ 46*q-45826235 ) q congruent 16 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84056*q^4+1008448*q^3-6695808*q^2+224066\ 56*q-30334976 ) q congruent 17 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+262176\ 66*q-38989755 ) q congruent 19 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7184688*q^2+268689\ 46*q-42242795 ) q congruent 21 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+262176\ 66*q-40150971 ) q congruent 23 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+259908\ 66*q-35406315 ) q congruent 25 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7184688*q^2+270957\ 46*q-45826235 ) q congruent 27 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+259908\ 66*q-35406315 ) q congruent 29 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+262176\ 66*q-38989755 ) q congruent 31 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7184688*q^2+268689\ 46*q-43404011 ) q congruent 32 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84056*q^4+1008448*q^3-6668928*q^2+215285\ 76*q-23224320 ) q congruent 37 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7184688*q^2+270957\ 46*q-45826235 ) q congruent 41 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+262176\ 66*q-40150971 ) q congruent 43 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7184688*q^2+268689\ 46*q-42242795 ) q congruent 47 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+259908\ 66*q-35406315 ) q congruent 49 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7184688*q^2+270957\ 46*q-45826235 ) q congruent 53 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+262176\ 66*q-38989755 ) q congruent 59 modulo 60: 1/2903040 ( q^7-98*q^6+3948*q^5-84371*q^4+1029553*q^3-7157808*q^2+259908\ 66*q-35406315 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 66 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 64 ], [ 3, 1, 1, 728 ], [ 4, 1, 1, 3276 ], [ 5, 1, 1, 8064 ], [ 6, 1, 1, 12768 ], [ 7, 1, 1, 2088 ], [ 8, 1, 1, 576 ], [ 9, 1, 1, 63 ], [ 10, 1, 1, 126 ], [ 11, 1, 1, 2072 ], [ 12, 1, 1, 11592 ], [ 13, 1, 1, 16632 ], [ 14, 1, 1, 32256 ], [ 15, 1, 1, 56448 ], [ 16, 1, 1, 110880 ], [ 17, 1, 1, 134400 ], [ 18, 1, 1, 12672 ], [ 19, 1, 1, 34272 ], [ 20, 1, 1, 65520 ], [ 21, 1, 1, 4032 ], [ 22, 1, 1, 24192 ], [ 23, 1, 1, 756 ], [ 24, 1, 1, 3906 ], [ 25, 1, 1, 22680 ], [ 26, 1, 1, 4032 ], [ 27, 1, 1, 4032 ], [ 28, 1, 1, 31752 ], [ 29, 1, 1, 104832 ], [ 30, 1, 1, 145152 ], [ 31, 1, 1, 201600 ], [ 32, 1, 1, 322560 ], [ 33, 1, 1, 423360 ], [ 34, 1, 1, 64512 ], [ 35, 1, 1, 272160 ], [ 36, 1, 1, 24192 ], [ 37, 1, 1, 120960 ], [ 38, 1, 1, 241920 ], [ 39, 1, 1, 7560 ], [ 40, 1, 1, 75600 ], [ 41, 1, 1, 105840 ], [ 42, 1, 1, 64512 ], [ 43, 1, 1, 120960 ], [ 44, 1, 1, 60480 ], [ 45, 1, 1, 266112 ], [ 46, 1, 1, 564480 ], [ 47, 1, 1, 725760 ], [ 48, 1, 1, 483840 ], [ 49, 1, 1, 907200 ], [ 50, 1, 1, 120960 ], [ 51, 1, 1, 362880 ], [ 52, 1, 1, 196560 ], [ 53, 1, 1, 483840 ], [ 54, 1, 1, 483840 ], [ 55, 1, 1, 1209600 ], [ 56, 1, 1, 846720 ], [ 57, 1, 1, 1451520 ], [ 58, 1, 1, 967680 ], [ 59, 1, 1, 362880 ], [ 60, 1, 1, 1451520 ], [ 61, 1, 1, 1935360 ], [ 62, 1, 1, 2177280 ], [ 63, 1, 1, 1451520 ], [ 64, 1, 1, 2903040 ], [ 65, 1, 1, 2903040 ] ] k = 2: F-action on Pi is () [66,1,2] Dynkin type is A_1(q) + T(phi1 phi7) Order of center |Z^F|: phi1 phi7 Numbers of classes in class type: q congruent 1 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 2 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 3 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 4 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 5 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 7 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 8 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 9 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 11 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 13 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 16 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 17 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 19 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 21 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 23 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 25 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 27 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 29 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 31 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 32 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 37 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 41 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 43 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 47 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 49 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 53 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 59 modulo 60: 1/14 q phi1 phi2 phi3 phi6 Fusion of maximal tori of C^F in those of G^F: [ 41, 103 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 18, 1, 1, 2 ] ] k = 3: F-action on Pi is () [66,1,3] Dynkin type is A_1(q) + T(phi2 phi14) Order of center |Z^F|: phi2 phi14 Numbers of classes in class type: q congruent 1 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 2 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 3 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 4 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 5 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 7 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 8 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 9 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 11 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 13 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 16 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 17 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 19 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 21 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 23 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 25 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 27 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 29 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 31 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 32 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 37 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 41 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 43 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 47 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 49 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 53 modulo 60: 1/14 q phi1 phi2 phi3 phi6 q congruent 59 modulo 60: 1/14 q phi1 phi2 phi3 phi6 Fusion of maximal tori of C^F in those of G^F: [ 104, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 18, 1, 2, 2 ] ] k = 4: F-action on Pi is () [66,1,4] Dynkin type is A_1(q) + T(phi1^3 phi5) Order of center |Z^F|: phi1^3 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/60 phi1 ( q^6-7*q^5+11*q^4+5*q^3-2*q^2-24 ) q congruent 2 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 4 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 5 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 7 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 8 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 9 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 11 modulo 60: 1/60 phi1 ( q^6-7*q^5+11*q^4+5*q^3-2*q^2-24 ) q congruent 13 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 16 modulo 60: 1/60 phi1 ( q^6-7*q^5+11*q^4+5*q^3-2*q^2-24 ) q congruent 17 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 19 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 21 modulo 60: 1/60 phi1 ( q^6-7*q^5+11*q^4+5*q^3-2*q^2-24 ) q congruent 23 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 25 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 27 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 29 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 31 modulo 60: 1/60 phi1 ( q^6-7*q^5+11*q^4+5*q^3-2*q^2-24 ) q congruent 32 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 37 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 41 modulo 60: 1/60 phi1 ( q^6-7*q^5+11*q^4+5*q^3-2*q^2-24 ) q congruent 43 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 47 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 49 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 53 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) q congruent 59 modulo 60: 1/60 q phi2 phi4 ( q^3-9*q^2+26*q-24 ) Fusion of maximal tori of C^F in those of G^F: [ 23, 93 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 6 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 12 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 15, 1, 1, 8 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 12 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 28, 1, 1, 12 ], [ 29, 1, 1, 12 ], [ 30, 1, 1, 12 ], [ 34, 1, 1, 12 ], [ 36, 1, 1, 12 ], [ 42, 1, 1, 12 ], [ 45, 1, 1, 12 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 40 ], [ 63, 1, 2, 30 ], [ 64, 1, 2, 60 ], [ 65, 1, 2, 60 ] ] k = 5: F-action on Pi is () [66,1,5] Dynkin type is A_1(q) + T(phi1 phi3 phi5) Order of center |Z^F|: phi1 phi3 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 2 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 3 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 4 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 5 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 7 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 8 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 9 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 11 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 13 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 16 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 17 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 19 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 21 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 23 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 25 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 27 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 29 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 31 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 32 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 37 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 41 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 43 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 47 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 49 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 53 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 q congruent 59 modulo 60: 1/30 q^2 phi1 phi2^2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 62, 111 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 15, 1, 1, 2 ], [ 27, 1, 5, 6 ], [ 42, 1, 3, 6 ], [ 45, 1, 3, 6 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 10 ] ] k = 6: F-action on Pi is () [66,1,6] Dynkin type is A_1(q) + T(phi2 phi6 phi10) Order of center |Z^F|: phi2 phi6 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 2 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 3 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 4 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 5 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 7 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 8 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 9 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 11 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 13 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 16 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 17 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 19 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 21 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 23 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 25 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 27 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 29 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 31 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 32 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 37 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 41 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 43 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 47 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 49 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 53 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 q congruent 59 modulo 60: 1/30 q^2 phi1^2 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 112, 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 15, 1, 2, 2 ], [ 27, 1, 4, 6 ], [ 42, 1, 5, 6 ], [ 45, 1, 4, 6 ], [ 54, 1, 8, 10 ], [ 61, 1, 3, 10 ] ] k = 7: F-action on Pi is () [66,1,7] Dynkin type is A_1(q) + T(phi1^2 phi2 phi5) Order of center |Z^F|: phi1^2 phi2 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 17 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 93, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 15, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 28, 1, 2, 4 ], [ 29, 1, 2, 4 ], [ 30, 1, 1, 4 ], [ 34, 1, 2, 4 ], [ 36, 1, 2, 4 ], [ 42, 1, 4, 4 ], [ 45, 1, 2, 4 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 20 ], [ 63, 1, 2, 10 ], [ 64, 1, 2, 20 ], [ 65, 1, 3, 20 ] ] k = 8: F-action on Pi is () [66,1,8] Dynkin type is A_1(q) + T(phi1 phi2^2 phi10) Order of center |Z^F|: phi1 phi2^2 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 17 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/20 q^2 phi1 phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 51, 94 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 28, 1, 3, 4 ], [ 29, 1, 3, 4 ], [ 30, 1, 3, 4 ], [ 34, 1, 3, 4 ], [ 36, 1, 3, 4 ], [ 42, 1, 2, 4 ], [ 45, 1, 5, 4 ], [ 54, 1, 8, 10 ], [ 61, 1, 3, 20 ], [ 63, 1, 3, 10 ], [ 64, 1, 5, 20 ], [ 65, 1, 5, 20 ] ] k = 9: F-action on Pi is () [66,1,9] Dynkin type is A_1(q) + T(phi2^3 phi10) Order of center |Z^F|: phi2^3 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/60 phi2 ( q^6-5*q^5+11*q^4-17*q^3+22*q^2-24*q+24 ) q congruent 5 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/60 phi2 ( q^6-5*q^5+11*q^4-17*q^3+22*q^2-24*q+24 ) q congruent 11 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 17 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/60 phi2 ( q^6-5*q^5+11*q^4-17*q^3+22*q^2-24*q+24 ) q congruent 21 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/60 phi2 ( q^6-5*q^5+11*q^4-17*q^3+22*q^2-24*q+24 ) q congruent 31 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/60 phi2 ( q^6-5*q^5+11*q^4-17*q^3+22*q^2-24*q+24 ) q congruent 53 modulo 60: 1/60 q^2 phi1^2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/60 phi2 ( q^6-5*q^5+11*q^4-17*q^3+22*q^2-24*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 94, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 6 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 14, 1, 2, 6 ], [ 15, 1, 2, 8 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 21, 1, 2, 12 ], [ 22, 1, 4, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 28, 1, 4, 12 ], [ 29, 1, 4, 12 ], [ 30, 1, 3, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 4, 12 ], [ 42, 1, 6, 12 ], [ 45, 1, 6, 12 ], [ 54, 1, 8, 10 ], [ 61, 1, 3, 40 ], [ 63, 1, 3, 30 ], [ 64, 1, 5, 60 ], [ 65, 1, 4, 60 ] ] k = 10: F-action on Pi is () [66,1,10] Dynkin type is A_1(q) + T(phi1 phi3^3) Order of center |Z^F|: phi1 phi3^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/1296 phi1^2 phi2 ( q^4+2*q^3-9*q^2-22*q-8 ) q congruent 2 modulo 60: 1/1296 q phi2 ( q^5-12*q^3+7*q^2+36*q-36 ) q congruent 3 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 4 modulo 60: 1/1296 phi1 ( q^6+2*q^5-10*q^4-15*q^3+28*q^2+4*q-64 ) q congruent 5 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 7 modulo 60: 1/1296 phi1^2 phi2 ( q^4+2*q^3-9*q^2-22*q-8 ) q congruent 8 modulo 60: 1/1296 q phi2 ( q^5-12*q^3+7*q^2+36*q-36 ) q congruent 9 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 11 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 13 modulo 60: 1/1296 phi1^2 phi2 ( q^4+2*q^3-9*q^2-22*q-8 ) q congruent 16 modulo 60: 1/1296 phi1 ( q^6+2*q^5-10*q^4-15*q^3+28*q^2+4*q-64 ) q congruent 17 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 19 modulo 60: 1/1296 phi1^2 phi2 ( q^4+2*q^3-9*q^2-22*q-8 ) q congruent 21 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 23 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 25 modulo 60: 1/1296 phi1^2 phi2 ( q^4+2*q^3-9*q^2-22*q-8 ) q congruent 27 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 29 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 31 modulo 60: 1/1296 phi1^2 phi2 ( q^4+2*q^3-9*q^2-22*q-8 ) q congruent 32 modulo 60: 1/1296 q phi2 ( q^5-12*q^3+7*q^2+36*q-36 ) q congruent 37 modulo 60: 1/1296 phi1^2 phi2 ( q^4+2*q^3-9*q^2-22*q-8 ) q congruent 41 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 43 modulo 60: 1/1296 phi1^2 phi2 ( q^4+2*q^3-9*q^2-22*q-8 ) q congruent 47 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 49 modulo 60: 1/1296 phi1^2 phi2 ( q^4+2*q^3-9*q^2-22*q-8 ) q congruent 53 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) q congruent 59 modulo 60: 1/1296 q phi2^3 ( q^3-2*q^2-9*q+18 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 79 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 26 ], [ 6, 1, 1, 24 ], [ 11, 1, 1, 2 ], [ 17, 1, 1, 48 ], [ 27, 1, 5, 72 ], [ 33, 1, 3, 216 ], [ 38, 1, 3, 432 ], [ 40, 1, 5, 270 ], [ 42, 1, 3, 72 ], [ 46, 1, 3, 144 ], [ 52, 1, 6, 54 ], [ 58, 1, 8, 864 ], [ 59, 1, 9, 648 ], [ 60, 1, 4, 648 ], [ 61, 1, 5, 432 ], [ 65, 1, 6, 1296 ] ] k = 11: F-action on Pi is () [66,1,11] Dynkin type is A_1(q) + T(phi1 phi9) Order of center |Z^F|: phi1 phi9 Numbers of classes in class type: q congruent 1 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 2 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 3 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 4 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 5 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 7 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 8 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 9 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 11 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 13 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 16 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 17 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 19 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 21 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 23 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 25 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 27 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 29 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 31 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 32 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 37 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 41 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 43 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 47 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 49 modulo 60: 1/18 phi1 phi3 ( q^4-2*q^3+2*q-4 ) q congruent 53 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) q congruent 59 modulo 60: 1/18 q^3 phi2 phi6 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 46, 105 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 5, 6 ], [ 65, 1, 7, 18 ] ] k = 12: F-action on Pi is () [66,1,12] Dynkin type is A_1(q) + T(phi1^3 phi3^2) Order of center |Z^F|: phi1^3 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/216 phi1 phi2 ( q^5-5*q^4+4*q^3-4*q^2+44*q-22 ) q congruent 2 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-5*q^2+24*q-36 ) q congruent 3 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 4 modulo 60: 1/216 phi1 ( q^6-4*q^5-q^4+3*q^3+22*q^2+16*q+8 ) q congruent 5 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 7 modulo 60: 1/216 phi1 phi2 ( q^5-5*q^4+4*q^3-4*q^2+44*q-22 ) q congruent 8 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-5*q^2+24*q-36 ) q congruent 9 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 11 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 13 modulo 60: 1/216 phi1 phi2 ( q^5-5*q^4+4*q^3-4*q^2+44*q-22 ) q congruent 16 modulo 60: 1/216 phi1 ( q^6-4*q^5-q^4+3*q^3+22*q^2+16*q+8 ) q congruent 17 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 19 modulo 60: 1/216 phi1 phi2 ( q^5-5*q^4+4*q^3-4*q^2+44*q-22 ) q congruent 21 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 23 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 25 modulo 60: 1/216 phi1 phi2 ( q^5-5*q^4+4*q^3-4*q^2+44*q-22 ) q congruent 27 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 29 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 31 modulo 60: 1/216 phi1 phi2 ( q^5-5*q^4+4*q^3-4*q^2+44*q-22 ) q congruent 32 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-5*q^2+24*q-36 ) q congruent 37 modulo 60: 1/216 phi1 phi2 ( q^5-5*q^4+4*q^3-4*q^2+44*q-22 ) q congruent 41 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 43 modulo 60: 1/216 phi1 phi2 ( q^5-5*q^4+4*q^3-4*q^2+44*q-22 ) q congruent 47 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 49 modulo 60: 1/216 phi1 phi2 ( q^5-5*q^4+4*q^3-4*q^2+44*q-22 ) q congruent 53 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) q congruent 59 modulo 60: 1/216 q phi2 ( q^5-6*q^4+9*q^3-8*q^2+48*q-72 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 83 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 48 ], [ 17, 1, 5, 36 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 20, 1, 1, 24 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 36 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 27, 1, 5, 12 ], [ 29, 1, 1, 24 ], [ 31, 1, 1, 24 ], [ 32, 1, 1, 24 ], [ 33, 1, 3, 72 ], [ 34, 1, 1, 12 ], [ 38, 1, 1, 72 ], [ 38, 1, 3, 72 ], [ 40, 1, 5, 36 ], [ 42, 1, 1, 12 ], [ 42, 1, 3, 48 ], [ 44, 1, 3, 36 ], [ 45, 1, 3, 72 ], [ 46, 1, 1, 24 ], [ 46, 1, 3, 96 ], [ 47, 1, 5, 108 ], [ 49, 1, 3, 108 ], [ 50, 1, 3, 72 ], [ 52, 1, 6, 72 ], [ 53, 1, 16, 72 ], [ 54, 1, 3, 72 ], [ 55, 1, 3, 72 ], [ 56, 1, 3, 72 ], [ 57, 1, 12, 108 ], [ 58, 1, 3, 144 ], [ 58, 1, 8, 72 ], [ 59, 1, 7, 108 ], [ 60, 1, 3, 108 ], [ 61, 1, 4, 72 ], [ 61, 1, 5, 144 ], [ 64, 1, 7, 216 ], [ 65, 1, 8, 216 ] ] k = 13: F-action on Pi is () [66,1,13] Dynkin type is A_1(q) + T(phi1^5 phi3) Order of center |Z^F|: phi1^5 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1263*q^3+1816*q^2+1795*q-4480 ) q congruent 2 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1880*q^2+4764*q-4320 ) q congruent 3 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 4 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1248*q^3+1636*q^2+2080*q-3520 ) q congruent 5 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 7 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1263*q^3+1816*q^2+1795*q-4480 ) q congruent 8 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1880*q^2+4764*q-4320 ) q congruent 9 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 11 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 13 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1263*q^3+1816*q^2+1795*q-4480 ) q congruent 16 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1248*q^3+1636*q^2+2080*q-3520 ) q congruent 17 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 19 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1263*q^3+1816*q^2+1795*q-4480 ) q congruent 21 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 23 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 25 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1263*q^3+1816*q^2+1795*q-4480 ) q congruent 27 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 29 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 31 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1263*q^3+1816*q^2+1795*q-4480 ) q congruent 32 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1880*q^2+4764*q-4320 ) q congruent 37 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1263*q^3+1816*q^2+1795*q-4480 ) q congruent 41 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 43 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1263*q^3+1816*q^2+1795*q-4480 ) q congruent 47 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 49 modulo 60: 1/4320 phi1 ( q^6-28*q^5+287*q^4-1263*q^3+1816*q^2+1795*q-4480 ) q congruent 53 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 59 modulo 60: 1/4320 q phi2 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 77 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 62 ], [ 4, 1, 1, 150 ], [ 5, 1, 1, 264 ], [ 6, 1, 1, 312 ], [ 7, 1, 1, 132 ], [ 8, 1, 1, 60 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 30 ], [ 11, 1, 1, 140 ], [ 12, 1, 1, 330 ], [ 13, 1, 1, 360 ], [ 14, 1, 1, 660 ], [ 15, 1, 1, 732 ], [ 16, 1, 1, 840 ], [ 17, 1, 1, 840 ], [ 18, 1, 1, 420 ], [ 19, 1, 1, 600 ], [ 20, 1, 1, 840 ], [ 21, 1, 1, 240 ], [ 22, 1, 1, 540 ], [ 23, 1, 1, 90 ], [ 24, 1, 1, 210 ], [ 25, 1, 1, 540 ], [ 26, 1, 1, 240 ], [ 27, 1, 1, 240 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 540 ], [ 29, 1, 1, 1200 ], [ 30, 1, 1, 1080 ], [ 31, 1, 1, 1380 ], [ 32, 1, 1, 1200 ], [ 33, 1, 1, 720 ], [ 34, 1, 1, 960 ], [ 35, 1, 1, 1080 ], [ 36, 1, 1, 720 ], [ 37, 1, 1, 1440 ], [ 38, 1, 1, 1440 ], [ 38, 1, 3, 360 ], [ 39, 1, 1, 360 ], [ 40, 1, 1, 900 ], [ 41, 1, 1, 720 ], [ 42, 1, 1, 960 ], [ 42, 1, 3, 96 ], [ 43, 1, 1, 1440 ], [ 44, 1, 1, 720 ], [ 44, 1, 3, 90 ], [ 45, 1, 1, 1440 ], [ 45, 1, 3, 396 ], [ 46, 1, 1, 1920 ], [ 46, 1, 3, 840 ], [ 47, 1, 1, 1080 ], [ 48, 1, 1, 1440 ], [ 50, 1, 1, 1440 ], [ 50, 1, 3, 180 ], [ 51, 1, 1, 2160 ], [ 52, 1, 1, 720 ], [ 53, 1, 1, 1440 ], [ 53, 1, 16, 720 ], [ 54, 1, 1, 1440 ], [ 54, 1, 3, 720 ], [ 55, 1, 1, 1440 ], [ 55, 1, 3, 1800 ], [ 56, 1, 1, 1440 ], [ 56, 1, 3, 1260 ], [ 58, 1, 1, 2880 ], [ 58, 1, 3, 1440 ], [ 59, 1, 4, 540 ], [ 60, 1, 2, 2160 ], [ 61, 1, 1, 1440 ], [ 61, 1, 4, 2880 ], [ 62, 1, 2, 3240 ], [ 63, 1, 4, 2160 ], [ 64, 1, 6, 4320 ], [ 65, 1, 9, 4320 ] ] k = 14: F-action on Pi is () [66,1,14] Dynkin type is A_1(q) + T(phi1 phi3 phi6^2) Order of center |Z^F|: phi1 phi3 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+26 ) q congruent 2 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-q^3+12*q-16 ) q congruent 3 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+18 ) q congruent 4 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q^2+20 ) q congruent 5 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-2*q^3+3*q^2+14*q-24 ) q congruent 7 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+26 ) q congruent 8 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-q^3+12*q-16 ) q congruent 9 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+18 ) q congruent 11 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-2*q^3+3*q^2+14*q-24 ) q congruent 13 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+26 ) q congruent 16 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q^2+20 ) q congruent 17 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-2*q^3+3*q^2+14*q-24 ) q congruent 19 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+26 ) q congruent 21 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+18 ) q congruent 23 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-2*q^3+3*q^2+14*q-24 ) q congruent 25 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+26 ) q congruent 27 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+18 ) q congruent 29 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-2*q^3+3*q^2+14*q-24 ) q congruent 31 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+26 ) q congruent 32 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-q^3+12*q-16 ) q congruent 37 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+26 ) q congruent 41 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-2*q^3+3*q^2+14*q-24 ) q congruent 43 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+26 ) q congruent 47 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-2*q^3+3*q^2+14*q-24 ) q congruent 49 modulo 60: 1/144 q phi1 ( q^5-2*q^4-2*q^3+q+26 ) q congruent 53 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-2*q^3+3*q^2+14*q-24 ) q congruent 59 modulo 60: 1/144 phi2 ( q^6-4*q^5+4*q^4-2*q^3+3*q^2+14*q-24 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 11, 1, 1, 2 ], [ 17, 1, 3, 16 ], [ 27, 1, 4, 24 ], [ 33, 1, 7, 24 ], [ 38, 1, 4, 48 ], [ 40, 1, 4, 24 ], [ 40, 1, 5, 6 ], [ 42, 1, 5, 24 ], [ 46, 1, 10, 48 ], [ 52, 1, 6, 6 ], [ 58, 1, 6, 48 ], [ 59, 1, 10, 72 ], [ 60, 1, 15, 72 ], [ 61, 1, 10, 48 ], [ 65, 1, 11, 144 ] ] k = 15: F-action on Pi is () [66,1,15] Dynkin type is A_1(q) + T(phi2 phi6 phi12) Order of center |Z^F|: phi2 phi6 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 2 modulo 60: 1/24 q^3 phi1 phi2 phi6 q congruent 3 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 4 modulo 60: 1/24 q^3 phi1 phi2 phi6 q congruent 5 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 7 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 8 modulo 60: 1/24 q^3 phi1 phi2 phi6 q congruent 9 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 11 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 13 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 16 modulo 60: 1/24 q^3 phi1 phi2 phi6 q congruent 17 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 19 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 21 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 23 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 25 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 27 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 29 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 31 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 32 modulo 60: 1/24 q^3 phi1 phi2 phi6 q congruent 37 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 41 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 43 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 47 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 49 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 53 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 q congruent 59 modulo 60: 1/24 q^2 phi1^2 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 102, 58 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 40, 1, 4, 6 ], [ 52, 1, 7, 6 ], [ 59, 1, 11, 12 ], [ 60, 1, 16, 12 ], [ 65, 1, 13, 24 ] ] k = 16: F-action on Pi is () [66,1,16] Dynkin type is A_1(q) + T(phi1 phi3 phi12) Order of center |Z^F|: phi1 phi3 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 2 modulo 60: 1/24 q^2 phi1 phi2 phi3 ( q-2 ) q congruent 3 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 4 modulo 60: 1/24 q^2 phi1 phi2 phi3 ( q-2 ) q congruent 5 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 7 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 8 modulo 60: 1/24 q^2 phi1 phi2 phi3 ( q-2 ) q congruent 9 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 11 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 13 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 16 modulo 60: 1/24 q^2 phi1 phi2 phi3 ( q-2 ) q congruent 17 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 19 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 21 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 23 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 25 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 27 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 29 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 31 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 32 modulo 60: 1/24 q^2 phi1 phi2 phi3 ( q-2 ) q congruent 37 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 41 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 43 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 47 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 49 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 53 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) q congruent 59 modulo 60: 1/24 q^2 phi1 phi2 ( q^3-q^2-q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 57, 101 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 6 ], [ 59, 1, 11, 12 ], [ 60, 1, 16, 12 ], [ 65, 1, 12, 24 ] ] k = 17: F-action on Pi is () [66,1,17] Dynkin type is A_1(q) + T(phi2 phi3^2 phi6) Order of center |Z^F|: phi2 phi3^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 phi1^3 ( q^4+4*q^3+7*q^2+10*q+8 ) q congruent 2 modulo 60: 1/144 q phi2 ( q^5-2*q^3+3*q^2-6*q+8 ) q congruent 3 modulo 60: 1/144 q phi1 phi2 ( q^4+q^3-q^2+q-6 ) q congruent 4 modulo 60: 1/144 q phi1 ( q^5+2*q^4+q^2-2*q-8 ) q congruent 5 modulo 60: 1/144 q phi2 ( q^5-2*q^3+2*q^2-7*q+14 ) q congruent 7 modulo 60: 1/144 phi1^3 ( q^4+4*q^3+7*q^2+10*q+8 ) q congruent 8 modulo 60: 1/144 q phi2 ( q^5-2*q^3+3*q^2-6*q+8 ) q congruent 9 modulo 60: 1/144 q phi1 phi2 ( q^4+q^3-q^2+q-6 ) q congruent 11 modulo 60: 1/144 q phi2 ( q^5-2*q^3+2*q^2-7*q+14 ) q congruent 13 modulo 60: 1/144 phi1^3 ( q^4+4*q^3+7*q^2+10*q+8 ) q congruent 16 modulo 60: 1/144 q phi1 ( q^5+2*q^4+q^2-2*q-8 ) q congruent 17 modulo 60: 1/144 q phi2 ( q^5-2*q^3+2*q^2-7*q+14 ) q congruent 19 modulo 60: 1/144 phi1^3 ( q^4+4*q^3+7*q^2+10*q+8 ) q congruent 21 modulo 60: 1/144 q phi1 phi2 ( q^4+q^3-q^2+q-6 ) q congruent 23 modulo 60: 1/144 q phi2 ( q^5-2*q^3+2*q^2-7*q+14 ) q congruent 25 modulo 60: 1/144 phi1^3 ( q^4+4*q^3+7*q^2+10*q+8 ) q congruent 27 modulo 60: 1/144 q phi1 phi2 ( q^4+q^3-q^2+q-6 ) q congruent 29 modulo 60: 1/144 q phi2 ( q^5-2*q^3+2*q^2-7*q+14 ) q congruent 31 modulo 60: 1/144 phi1^3 ( q^4+4*q^3+7*q^2+10*q+8 ) q congruent 32 modulo 60: 1/144 q phi2 ( q^5-2*q^3+3*q^2-6*q+8 ) q congruent 37 modulo 60: 1/144 phi1^3 ( q^4+4*q^3+7*q^2+10*q+8 ) q congruent 41 modulo 60: 1/144 q phi2 ( q^5-2*q^3+2*q^2-7*q+14 ) q congruent 43 modulo 60: 1/144 phi1^3 ( q^4+4*q^3+7*q^2+10*q+8 ) q congruent 47 modulo 60: 1/144 q phi2 ( q^5-2*q^3+2*q^2-7*q+14 ) q congruent 49 modulo 60: 1/144 phi1^3 ( q^4+4*q^3+7*q^2+10*q+8 ) q congruent 53 modulo 60: 1/144 q phi2 ( q^5-2*q^3+2*q^2-7*q+14 ) q congruent 59 modulo 60: 1/144 q phi2 ( q^5-2*q^3+2*q^2-7*q+14 ) Fusion of maximal tori of C^F in those of G^F: [ 85, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 8 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 16 ], [ 27, 1, 5, 24 ], [ 33, 1, 3, 24 ], [ 38, 1, 9, 48 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 24 ], [ 42, 1, 3, 24 ], [ 46, 1, 9, 48 ], [ 52, 1, 7, 6 ], [ 58, 1, 6, 48 ], [ 59, 1, 9, 72 ], [ 60, 1, 4, 72 ], [ 61, 1, 11, 48 ], [ 65, 1, 14, 144 ] ] k = 18: F-action on Pi is () [66,1,18] Dynkin type is A_1(q) + T(phi2 phi6^3) Order of center |Z^F|: phi2 phi6^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 2 modulo 60: 1/1296 phi2 ( q^6-4*q^5-2*q^4+19*q^3-10*q^2-32*q+48 ) q congruent 3 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 4 modulo 60: 1/1296 q^2 phi1 ( q^4-2*q^3-8*q^2+9*q+18 ) q congruent 5 modulo 60: 1/1296 phi2^2 ( q^5-5*q^4+3*q^3+7*q^2+10*q-24 ) q congruent 7 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 8 modulo 60: 1/1296 phi2 ( q^6-4*q^5-2*q^4+19*q^3-10*q^2-32*q+48 ) q congruent 9 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 11 modulo 60: 1/1296 phi2^2 ( q^5-5*q^4+3*q^3+7*q^2+10*q-24 ) q congruent 13 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 16 modulo 60: 1/1296 q^2 phi1 ( q^4-2*q^3-8*q^2+9*q+18 ) q congruent 17 modulo 60: 1/1296 phi2^2 ( q^5-5*q^4+3*q^3+7*q^2+10*q-24 ) q congruent 19 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 21 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 23 modulo 60: 1/1296 phi2^2 ( q^5-5*q^4+3*q^3+7*q^2+10*q-24 ) q congruent 25 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 27 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 29 modulo 60: 1/1296 phi2^2 ( q^5-5*q^4+3*q^3+7*q^2+10*q-24 ) q congruent 31 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 32 modulo 60: 1/1296 phi2 ( q^6-4*q^5-2*q^4+19*q^3-10*q^2-32*q+48 ) q congruent 37 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 41 modulo 60: 1/1296 phi2^2 ( q^5-5*q^4+3*q^3+7*q^2+10*q-24 ) q congruent 43 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 47 modulo 60: 1/1296 phi2^2 ( q^5-5*q^4+3*q^3+7*q^2+10*q-24 ) q congruent 49 modulo 60: 1/1296 q phi1 ( q^5-2*q^4-8*q^3+27*q+54 ) q congruent 53 modulo 60: 1/1296 phi2^2 ( q^5-5*q^4+3*q^3+7*q^2+10*q-24 ) q congruent 59 modulo 60: 1/1296 phi2^2 ( q^5-5*q^4+3*q^3+7*q^2+10*q-24 ) Fusion of maximal tori of C^F in those of G^F: [ 80, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 26 ], [ 6, 1, 2, 24 ], [ 11, 1, 2, 2 ], [ 17, 1, 4, 48 ], [ 27, 1, 4, 72 ], [ 33, 1, 7, 216 ], [ 38, 1, 11, 432 ], [ 40, 1, 4, 270 ], [ 42, 1, 5, 72 ], [ 46, 1, 4, 144 ], [ 52, 1, 7, 54 ], [ 58, 1, 13, 864 ], [ 59, 1, 10, 648 ], [ 60, 1, 15, 648 ], [ 61, 1, 9, 432 ], [ 65, 1, 10, 1296 ] ] k = 19: F-action on Pi is () [66,1,19] Dynkin type is A_1(q) + T(phi2 phi18) Order of center |Z^F|: phi2 phi18 Numbers of classes in class type: q congruent 1 modulo 60: 1/18 q^4 phi1 phi3 q congruent 2 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 3 modulo 60: 1/18 q^4 phi1 phi3 q congruent 4 modulo 60: 1/18 q^4 phi1 phi3 q congruent 5 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 7 modulo 60: 1/18 q^4 phi1 phi3 q congruent 8 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 9 modulo 60: 1/18 q^4 phi1 phi3 q congruent 11 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 13 modulo 60: 1/18 q^4 phi1 phi3 q congruent 16 modulo 60: 1/18 q^4 phi1 phi3 q congruent 17 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 19 modulo 60: 1/18 q^4 phi1 phi3 q congruent 21 modulo 60: 1/18 q^4 phi1 phi3 q congruent 23 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 25 modulo 60: 1/18 q^4 phi1 phi3 q congruent 27 modulo 60: 1/18 q^4 phi1 phi3 q congruent 29 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 31 modulo 60: 1/18 q^4 phi1 phi3 q congruent 32 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 37 modulo 60: 1/18 q^4 phi1 phi3 q congruent 41 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 43 modulo 60: 1/18 q^4 phi1 phi3 q congruent 47 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 49 modulo 60: 1/18 q^4 phi1 phi3 q congruent 53 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) q congruent 59 modulo 60: 1/18 q phi2 phi6 ( q^3-2 ) Fusion of maximal tori of C^F in those of G^F: [ 106, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 6, 6 ], [ 65, 1, 15, 18 ] ] k = 20: F-action on Pi is () [66,1,20] Dynkin type is A_1(q) + T(phi1 phi2^2 phi3 phi6) Order of center |Z^F|: phi1 phi2^2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 2 modulo 60: 1/24 q phi2 ( q^5-2*q^4+3*q^3-5*q^2+6*q-4 ) q congruent 3 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 4 modulo 60: 1/24 q^3 phi1 ( q^3+q-1 ) q congruent 5 modulo 60: 1/24 phi1^2 phi2 ( q^4+2*q^2-2*q+2 ) q congruent 7 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 8 modulo 60: 1/24 q phi2 ( q^5-2*q^4+3*q^3-5*q^2+6*q-4 ) q congruent 9 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 11 modulo 60: 1/24 phi1^2 phi2 ( q^4+2*q^2-2*q+2 ) q congruent 13 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 16 modulo 60: 1/24 q^3 phi1 ( q^3+q-1 ) q congruent 17 modulo 60: 1/24 phi1^2 phi2 ( q^4+2*q^2-2*q+2 ) q congruent 19 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 21 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 23 modulo 60: 1/24 phi1^2 phi2 ( q^4+2*q^2-2*q+2 ) q congruent 25 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 27 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 29 modulo 60: 1/24 phi1^2 phi2 ( q^4+2*q^2-2*q+2 ) q congruent 31 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 32 modulo 60: 1/24 q phi2 ( q^5-2*q^4+3*q^3-5*q^2+6*q-4 ) q congruent 37 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 41 modulo 60: 1/24 phi1^2 phi2 ( q^4+2*q^2-2*q+2 ) q congruent 43 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 47 modulo 60: 1/24 phi1^2 phi2 ( q^4+2*q^2-2*q+2 ) q congruent 49 modulo 60: 1/24 q^3 phi1^2 ( q^2+q+2 ) q congruent 53 modulo 60: 1/24 phi1^2 phi2 ( q^4+2*q^2-2*q+2 ) q congruent 59 modulo 60: 1/24 phi1^2 phi2 ( q^4+2*q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 40, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 6, 12 ], [ 18, 1, 2, 4 ], [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ], [ 20, 1, 7, 8 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 32, 1, 4, 4 ], [ 33, 1, 3, 6 ], [ 33, 1, 7, 6 ], [ 34, 1, 4, 4 ], [ 38, 1, 10, 8 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 4, 4 ], [ 46, 1, 8, 8 ], [ 47, 1, 12, 12 ], [ 49, 1, 3, 6 ], [ 49, 1, 6, 6 ], [ 52, 1, 6, 6 ], [ 52, 1, 7, 6 ], [ 57, 1, 15, 12 ], [ 58, 1, 6, 12 ], [ 59, 1, 14, 12 ], [ 60, 1, 12, 12 ], [ 61, 1, 10, 12 ], [ 61, 1, 11, 12 ], [ 64, 1, 25, 12 ], [ 65, 1, 21, 24 ] ] k = 21: F-action on Pi is () [66,1,21] Dynkin type is A_1(q) + T(phi1^2 phi2 phi3 phi6) Order of center |Z^F|: phi1^2 phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 ( q^6-4*q^5+3*q^4-6*q^3+16*q^2+6*q-4 ) q congruent 2 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-21*q^3+36*q^2-40*q+24 ) q congruent 3 modulo 60: 1/72 q phi1 ( q^5-4*q^4+3*q^3-6*q^2+16*q+6 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^5-4*q^4+3*q^3-5*q^2+10*q+4 ) q congruent 5 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-22*q^3+44*q^2-52*q+30 ) q congruent 7 modulo 60: 1/72 phi1 ( q^6-4*q^5+3*q^4-6*q^3+16*q^2+6*q-4 ) q congruent 8 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-21*q^3+36*q^2-40*q+24 ) q congruent 9 modulo 60: 1/72 q phi1 ( q^5-4*q^4+3*q^3-6*q^2+16*q+6 ) q congruent 11 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-22*q^3+44*q^2-52*q+30 ) q congruent 13 modulo 60: 1/72 phi1 ( q^6-4*q^5+3*q^4-6*q^3+16*q^2+6*q-4 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^5-4*q^4+3*q^3-5*q^2+10*q+4 ) q congruent 17 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-22*q^3+44*q^2-52*q+30 ) q congruent 19 modulo 60: 1/72 phi1 ( q^6-4*q^5+3*q^4-6*q^3+16*q^2+6*q-4 ) q congruent 21 modulo 60: 1/72 q phi1 ( q^5-4*q^4+3*q^3-6*q^2+16*q+6 ) q congruent 23 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-22*q^3+44*q^2-52*q+30 ) q congruent 25 modulo 60: 1/72 phi1 ( q^6-4*q^5+3*q^4-6*q^3+16*q^2+6*q-4 ) q congruent 27 modulo 60: 1/72 q phi1 ( q^5-4*q^4+3*q^3-6*q^2+16*q+6 ) q congruent 29 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-22*q^3+44*q^2-52*q+30 ) q congruent 31 modulo 60: 1/72 phi1 ( q^6-4*q^5+3*q^4-6*q^3+16*q^2+6*q-4 ) q congruent 32 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-21*q^3+36*q^2-40*q+24 ) q congruent 37 modulo 60: 1/72 phi1 ( q^6-4*q^5+3*q^4-6*q^3+16*q^2+6*q-4 ) q congruent 41 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-22*q^3+44*q^2-52*q+30 ) q congruent 43 modulo 60: 1/72 phi1 ( q^6-4*q^5+3*q^4-6*q^3+16*q^2+6*q-4 ) q congruent 47 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-22*q^3+44*q^2-52*q+30 ) q congruent 49 modulo 60: 1/72 phi1 ( q^6-4*q^5+3*q^4-6*q^3+16*q^2+6*q-4 ) q congruent 53 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-22*q^3+44*q^2-52*q+30 ) q congruent 59 modulo 60: 1/72 phi2 ( q^6-6*q^5+13*q^4-22*q^3+44*q^2-52*q+30 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 12 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 8, 24 ], [ 22, 1, 3, 12 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 32, 1, 4, 12 ], [ 33, 1, 3, 6 ], [ 33, 1, 7, 18 ], [ 34, 1, 3, 12 ], [ 38, 1, 7, 24 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 1, 12 ], [ 46, 1, 7, 24 ], [ 47, 1, 11, 36 ], [ 49, 1, 3, 18 ], [ 49, 1, 6, 18 ], [ 52, 1, 6, 18 ], [ 52, 1, 7, 6 ], [ 57, 1, 14, 36 ], [ 58, 1, 6, 12 ], [ 59, 1, 7, 36 ], [ 60, 1, 3, 36 ], [ 61, 1, 10, 36 ], [ 61, 1, 11, 12 ], [ 64, 1, 25, 36 ], [ 65, 1, 19, 72 ] ] k = 22: F-action on Pi is () [66,1,22] Dynkin type is A_1(q) + T(phi1^2 phi2 phi3^2) Order of center |Z^F|: phi1^2 phi2 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1 ( q^6-3*q^4-8*q^3+4*q-6 ) q congruent 2 modulo 60: 1/72 q^2 phi2 ( q^4-2*q^3-q^2-q+6 ) q congruent 3 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^5-3*q^3-5*q^2+4 ) q congruent 5 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 7 modulo 60: 1/72 phi1 ( q^6-3*q^4-8*q^3+4*q-6 ) q congruent 8 modulo 60: 1/72 q^2 phi2 ( q^4-2*q^3-q^2-q+6 ) q congruent 9 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 11 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 13 modulo 60: 1/72 phi1 ( q^6-3*q^4-8*q^3+4*q-6 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^5-3*q^3-5*q^2+4 ) q congruent 17 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 19 modulo 60: 1/72 phi1 ( q^6-3*q^4-8*q^3+4*q-6 ) q congruent 21 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 23 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 25 modulo 60: 1/72 phi1 ( q^6-3*q^4-8*q^3+4*q-6 ) q congruent 27 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 29 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 31 modulo 60: 1/72 phi1 ( q^6-3*q^4-8*q^3+4*q-6 ) q congruent 32 modulo 60: 1/72 q^2 phi2 ( q^4-2*q^3-q^2-q+6 ) q congruent 37 modulo 60: 1/72 phi1 ( q^6-3*q^4-8*q^3+4*q-6 ) q congruent 41 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 43 modulo 60: 1/72 phi1 ( q^6-3*q^4-8*q^3+4*q-6 ) q congruent 47 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 49 modulo 60: 1/72 phi1 ( q^6-3*q^4-8*q^3+4*q-6 ) q congruent 53 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) q congruent 59 modulo 60: 1/72 q phi1 phi2 ( q^4-q^3-2*q^2-6*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 83, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 12 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 27, 1, 5, 12 ], [ 29, 1, 2, 8 ], [ 31, 1, 2, 8 ], [ 32, 1, 1, 8 ], [ 33, 1, 3, 36 ], [ 34, 1, 2, 4 ], [ 38, 1, 3, 72 ], [ 38, 1, 5, 24 ], [ 40, 1, 5, 36 ], [ 42, 1, 3, 24 ], [ 42, 1, 4, 4 ], [ 44, 1, 3, 12 ], [ 45, 1, 3, 24 ], [ 46, 1, 2, 8 ], [ 46, 1, 3, 48 ], [ 47, 1, 6, 36 ], [ 49, 1, 3, 36 ], [ 50, 1, 6, 24 ], [ 52, 1, 6, 36 ], [ 53, 1, 16, 24 ], [ 54, 1, 7, 24 ], [ 55, 1, 3, 24 ], [ 56, 1, 8, 24 ], [ 57, 1, 13, 36 ], [ 58, 1, 7, 48 ], [ 58, 1, 8, 72 ], [ 59, 1, 14, 36 ], [ 60, 1, 12, 36 ], [ 61, 1, 5, 72 ], [ 61, 1, 7, 24 ], [ 64, 1, 7, 72 ], [ 65, 1, 17, 72 ] ] k = 23: F-action on Pi is () [66,1,23] Dynkin type is A_1(q) + T(phi1 phi2^2 phi6^2) Order of center |Z^F|: phi1 phi2^2 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 2 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-5*q^3+12*q^2-20*q+16 ) q congruent 3 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 4 modulo 60: 1/72 q^2 phi1 ( q^4-2*q^3-q^2-q+6 ) q congruent 5 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-8*q^3+24*q^2-32*q+22 ) q congruent 7 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 8 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-5*q^3+12*q^2-20*q+16 ) q congruent 9 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 11 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-8*q^3+24*q^2-32*q+22 ) q congruent 13 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 16 modulo 60: 1/72 q^2 phi1 ( q^4-2*q^3-q^2-q+6 ) q congruent 17 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-8*q^3+24*q^2-32*q+22 ) q congruent 19 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 21 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 23 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-8*q^3+24*q^2-32*q+22 ) q congruent 25 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 27 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 29 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-8*q^3+24*q^2-32*q+22 ) q congruent 31 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 32 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-5*q^3+12*q^2-20*q+16 ) q congruent 37 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 41 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-8*q^3+24*q^2-32*q+22 ) q congruent 43 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 47 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-8*q^3+24*q^2-32*q+22 ) q congruent 49 modulo 60: 1/72 q phi1 ( q^5-2*q^4-q^3-4*q^2+12*q+6 ) q congruent 53 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-8*q^3+24*q^2-32*q+22 ) q congruent 59 modulo 60: 1/72 phi2 ( q^6-4*q^5+5*q^4-8*q^3+24*q^2-32*q+22 ) Fusion of maximal tori of C^F in those of G^F: [ 38, 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 12 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 27, 1, 4, 12 ], [ 29, 1, 3, 8 ], [ 31, 1, 3, 8 ], [ 32, 1, 3, 8 ], [ 33, 1, 7, 36 ], [ 34, 1, 3, 4 ], [ 38, 1, 8, 24 ], [ 38, 1, 11, 72 ], [ 40, 1, 4, 36 ], [ 42, 1, 2, 4 ], [ 42, 1, 5, 24 ], [ 44, 1, 7, 12 ], [ 45, 1, 4, 24 ], [ 46, 1, 4, 48 ], [ 46, 1, 5, 8 ], [ 47, 1, 11, 36 ], [ 49, 1, 6, 36 ], [ 50, 1, 7, 24 ], [ 52, 1, 7, 36 ], [ 53, 1, 18, 24 ], [ 54, 1, 11, 24 ], [ 55, 1, 12, 24 ], [ 56, 1, 12, 24 ], [ 57, 1, 14, 36 ], [ 58, 1, 10, 48 ], [ 58, 1, 13, 72 ], [ 59, 1, 15, 36 ], [ 60, 1, 13, 36 ], [ 61, 1, 8, 24 ], [ 61, 1, 9, 72 ], [ 64, 1, 23, 72 ], [ 65, 1, 16, 72 ] ] k = 24: F-action on Pi is () [66,1,24] Dynkin type is A_1(q) + T(phi1 phi2^2 phi3 phi6) Order of center |Z^F|: phi1 phi2^2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 phi1^2 phi2 ( q^4-2*q^3+2*q^2-8*q+6 ) q congruent 2 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-13*q^3+18*q^2-12*q+8 ) q congruent 3 modulo 60: 1/72 q phi1 ( q^5-2*q^4+q^3-6*q^2+4*q+6 ) q congruent 4 modulo 60: 1/72 q phi1 ( q^5-2*q^4+q^3-5*q^2+8 ) q congruent 5 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-14*q^3+24*q^2-22*q+12 ) q congruent 7 modulo 60: 1/72 phi1^2 phi2 ( q^4-2*q^3+2*q^2-8*q+6 ) q congruent 8 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-13*q^3+18*q^2-12*q+8 ) q congruent 9 modulo 60: 1/72 q phi1 ( q^5-2*q^4+q^3-6*q^2+4*q+6 ) q congruent 11 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-14*q^3+24*q^2-22*q+12 ) q congruent 13 modulo 60: 1/72 phi1^2 phi2 ( q^4-2*q^3+2*q^2-8*q+6 ) q congruent 16 modulo 60: 1/72 q phi1 ( q^5-2*q^4+q^3-5*q^2+8 ) q congruent 17 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-14*q^3+24*q^2-22*q+12 ) q congruent 19 modulo 60: 1/72 phi1^2 phi2 ( q^4-2*q^3+2*q^2-8*q+6 ) q congruent 21 modulo 60: 1/72 q phi1 ( q^5-2*q^4+q^3-6*q^2+4*q+6 ) q congruent 23 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-14*q^3+24*q^2-22*q+12 ) q congruent 25 modulo 60: 1/72 phi1^2 phi2 ( q^4-2*q^3+2*q^2-8*q+6 ) q congruent 27 modulo 60: 1/72 q phi1 ( q^5-2*q^4+q^3-6*q^2+4*q+6 ) q congruent 29 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-14*q^3+24*q^2-22*q+12 ) q congruent 31 modulo 60: 1/72 phi1^2 phi2 ( q^4-2*q^3+2*q^2-8*q+6 ) q congruent 32 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-13*q^3+18*q^2-12*q+8 ) q congruent 37 modulo 60: 1/72 phi1^2 phi2 ( q^4-2*q^3+2*q^2-8*q+6 ) q congruent 41 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-14*q^3+24*q^2-22*q+12 ) q congruent 43 modulo 60: 1/72 phi1^2 phi2 ( q^4-2*q^3+2*q^2-8*q+6 ) q congruent 47 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-14*q^3+24*q^2-22*q+12 ) q congruent 49 modulo 60: 1/72 phi1^2 phi2 ( q^4-2*q^3+2*q^2-8*q+6 ) q congruent 53 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-14*q^3+24*q^2-22*q+12 ) q congruent 59 modulo 60: 1/72 phi2 ( q^6-4*q^5+7*q^4-14*q^3+24*q^2-22*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 6 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 17, 1, 3, 4 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 5, 24 ], [ 22, 1, 2, 12 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 32, 1, 4, 12 ], [ 33, 1, 3, 18 ], [ 33, 1, 7, 6 ], [ 34, 1, 2, 12 ], [ 38, 1, 6, 24 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 6, 12 ], [ 46, 1, 12, 24 ], [ 47, 1, 6, 36 ], [ 49, 1, 3, 18 ], [ 49, 1, 6, 18 ], [ 52, 1, 6, 6 ], [ 52, 1, 7, 18 ], [ 57, 1, 13, 36 ], [ 58, 1, 6, 12 ], [ 59, 1, 8, 36 ], [ 60, 1, 14, 36 ], [ 61, 1, 10, 12 ], [ 61, 1, 11, 36 ], [ 64, 1, 25, 36 ], [ 65, 1, 22, 72 ] ] k = 25: F-action on Pi is () [66,1,25] Dynkin type is A_1(q) + T(phi1^2 phi2 phi3 phi6) Order of center |Z^F|: phi1^2 phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 phi1 ( q^6-2*q^5-q^4-2*q^3+4*q^2+10*q-2 ) q congruent 2 modulo 60: 1/24 q phi2 ( q^5-4*q^4+5*q^3-5*q^2+8*q-4 ) q congruent 3 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 4 modulo 60: 1/24 q phi1 ( q^5-2*q^4-q^3-q^2+2*q+8 ) q congruent 5 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 7 modulo 60: 1/24 phi1 ( q^6-2*q^5-q^4-2*q^3+4*q^2+10*q-2 ) q congruent 8 modulo 60: 1/24 q phi2 ( q^5-4*q^4+5*q^3-5*q^2+8*q-4 ) q congruent 9 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 11 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 13 modulo 60: 1/24 phi1 ( q^6-2*q^5-q^4-2*q^3+4*q^2+10*q-2 ) q congruent 16 modulo 60: 1/24 q phi1 ( q^5-2*q^4-q^3-q^2+2*q+8 ) q congruent 17 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 19 modulo 60: 1/24 phi1 ( q^6-2*q^5-q^4-2*q^3+4*q^2+10*q-2 ) q congruent 21 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 23 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 25 modulo 60: 1/24 phi1 ( q^6-2*q^5-q^4-2*q^3+4*q^2+10*q-2 ) q congruent 27 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 29 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 31 modulo 60: 1/24 phi1 ( q^6-2*q^5-q^4-2*q^3+4*q^2+10*q-2 ) q congruent 32 modulo 60: 1/24 q phi2 ( q^5-4*q^4+5*q^3-5*q^2+8*q-4 ) q congruent 37 modulo 60: 1/24 phi1 ( q^6-2*q^5-q^4-2*q^3+4*q^2+10*q-2 ) q congruent 41 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 43 modulo 60: 1/24 phi1 ( q^6-2*q^5-q^4-2*q^3+4*q^2+10*q-2 ) q congruent 47 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 49 modulo 60: 1/24 phi1 ( q^6-2*q^5-q^4-2*q^3+4*q^2+10*q-2 ) q congruent 53 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) q congruent 59 modulo 60: 1/24 q phi1 phi2 ( q^4-3*q^3+2*q^2-4*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 87, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 5, 12 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ], [ 20, 1, 6, 8 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 32, 1, 4, 4 ], [ 33, 1, 3, 6 ], [ 33, 1, 7, 6 ], [ 34, 1, 1, 4 ], [ 38, 1, 2, 8 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 2, 4 ], [ 46, 1, 11, 8 ], [ 47, 1, 5, 12 ], [ 49, 1, 3, 6 ], [ 49, 1, 6, 6 ], [ 52, 1, 6, 6 ], [ 52, 1, 7, 6 ], [ 57, 1, 12, 12 ], [ 58, 1, 6, 12 ], [ 59, 1, 15, 12 ], [ 60, 1, 13, 12 ], [ 61, 1, 10, 12 ], [ 61, 1, 11, 12 ], [ 64, 1, 25, 12 ], [ 65, 1, 20, 24 ] ] k = 26: F-action on Pi is () [66,1,26] Dynkin type is A_1(q) + T(phi2^3 phi6^2) Order of center |Z^F|: phi2^3 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 2 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-17*q^3+26*q^2-20*q+24 ) q congruent 3 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 4 modulo 60: 1/216 q^3 phi1 ( q^3-2*q^2+q-9 ) q congruent 5 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-20*q^3+44*q^2-50*q+54 ) q congruent 7 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 8 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-17*q^3+26*q^2-20*q+24 ) q congruent 9 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 11 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-20*q^3+44*q^2-50*q+54 ) q congruent 13 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 16 modulo 60: 1/216 q^3 phi1 ( q^3-2*q^2+q-9 ) q congruent 17 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-20*q^3+44*q^2-50*q+54 ) q congruent 19 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 21 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 23 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-20*q^3+44*q^2-50*q+54 ) q congruent 25 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 27 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 29 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-20*q^3+44*q^2-50*q+54 ) q congruent 31 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 32 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-17*q^3+26*q^2-20*q+24 ) q congruent 37 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 41 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-20*q^3+44*q^2-50*q+54 ) q congruent 43 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 47 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-20*q^3+44*q^2-50*q+54 ) q congruent 49 modulo 60: 1/216 q^2 phi1^2 ( q^3-q^2-12 ) q congruent 53 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-20*q^3+44*q^2-50*q+54 ) q congruent 59 modulo 60: 1/216 phi2 ( q^6-4*q^5+7*q^4-20*q^3+44*q^2-50*q+54 ) Fusion of maximal tori of C^F in those of G^F: [ 84, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 12 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 24 ], [ 16, 1, 3, 24 ], [ 17, 1, 4, 48 ], [ 17, 1, 6, 36 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 20, 1, 4, 24 ], [ 21, 1, 2, 12 ], [ 22, 1, 4, 36 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 29, 1, 4, 24 ], [ 31, 1, 4, 24 ], [ 32, 1, 3, 24 ], [ 33, 1, 7, 72 ], [ 34, 1, 4, 12 ], [ 38, 1, 11, 72 ], [ 38, 1, 12, 72 ], [ 40, 1, 4, 36 ], [ 42, 1, 5, 48 ], [ 42, 1, 6, 12 ], [ 44, 1, 7, 36 ], [ 45, 1, 4, 72 ], [ 46, 1, 4, 96 ], [ 46, 1, 6, 24 ], [ 47, 1, 12, 108 ], [ 49, 1, 6, 108 ], [ 50, 1, 10, 72 ], [ 52, 1, 7, 72 ], [ 53, 1, 18, 72 ], [ 54, 1, 10, 72 ], [ 55, 1, 12, 72 ], [ 56, 1, 17, 72 ], [ 57, 1, 15, 108 ], [ 58, 1, 13, 72 ], [ 58, 1, 14, 144 ], [ 59, 1, 8, 108 ], [ 60, 1, 14, 108 ], [ 61, 1, 6, 72 ], [ 61, 1, 9, 144 ], [ 64, 1, 23, 216 ], [ 65, 1, 18, 216 ] ] k = 27: F-action on Pi is () [66,1,27] Dynkin type is A_1(q) + T(phi1^3 phi2^2 phi3) Order of center |Z^F|: phi1^3 phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 2 modulo 60: 1/96 q^2 phi1 phi2 ( q^3-5*q^2+4*q+4 ) q congruent 3 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 4 modulo 60: 1/96 q^2 phi1 phi2 ( q^3-5*q^2+4*q+4 ) q congruent 5 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 7 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 8 modulo 60: 1/96 q^2 phi1 phi2 ( q^3-5*q^2+4*q+4 ) q congruent 9 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 11 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 13 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 16 modulo 60: 1/96 q^2 phi1 phi2 ( q^3-5*q^2+4*q+4 ) q congruent 17 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 19 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 21 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 23 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 25 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 27 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 29 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 31 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 32 modulo 60: 1/96 q^2 phi1 phi2 ( q^3-5*q^2+4*q+4 ) q congruent 37 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 41 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 43 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 47 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 49 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 53 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 59 modulo 60: 1/96 q phi1 phi2 ( q^4-5*q^3+4*q^2+5*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 30, 81 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 4, 1, 1, 18 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 18 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 8 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], [ 16, 1, 1, 48 ], [ 16, 1, 2, 8 ], [ 17, 1, 1, 72 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 48 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 40 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 12 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 8 ], [ 29, 1, 2, 48 ], [ 30, 1, 1, 24 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 12 ], [ 31, 1, 2, 56 ], [ 32, 1, 1, 48 ], [ 33, 1, 1, 48 ], [ 33, 1, 2, 16 ], [ 34, 1, 2, 32 ], [ 35, 1, 1, 24 ], [ 35, 1, 2, 16 ], [ 35, 1, 3, 48 ], [ 36, 1, 2, 16 ], [ 37, 1, 2, 16 ], [ 38, 1, 3, 72 ], [ 38, 1, 5, 96 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 40, 1, 1, 12 ], [ 40, 1, 3, 24 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 3, 24 ], [ 42, 1, 4, 32 ], [ 43, 1, 2, 32 ], [ 43, 1, 8, 16 ], [ 43, 1, 12, 32 ], [ 44, 1, 2, 16 ], [ 44, 1, 3, 18 ], [ 44, 1, 5, 16 ], [ 45, 1, 2, 32 ], [ 45, 1, 3, 36 ], [ 46, 1, 2, 64 ], [ 46, 1, 3, 72 ], [ 47, 1, 1, 24 ], [ 47, 1, 2, 48 ], [ 47, 1, 3, 16 ], [ 48, 1, 2, 32 ], [ 48, 1, 3, 32 ], [ 50, 1, 3, 12 ], [ 50, 1, 5, 32 ], [ 50, 1, 6, 24 ], [ 51, 1, 2, 16 ], [ 51, 1, 5, 48 ], [ 51, 1, 6, 16 ], [ 52, 1, 3, 16 ], [ 52, 1, 9, 16 ], [ 53, 1, 3, 32 ], [ 53, 1, 9, 32 ], [ 53, 1, 16, 72 ], [ 53, 1, 17, 24 ], [ 54, 1, 5, 32 ], [ 54, 1, 7, 48 ], [ 55, 1, 2, 32 ], [ 55, 1, 3, 72 ], [ 55, 1, 5, 32 ], [ 56, 1, 3, 36 ], [ 56, 1, 5, 32 ], [ 56, 1, 7, 32 ], [ 56, 1, 8, 72 ], [ 58, 1, 7, 96 ], [ 58, 1, 9, 64 ], [ 59, 1, 4, 36 ], [ 59, 1, 19, 24 ], [ 60, 1, 2, 144 ], [ 60, 1, 11, 48 ], [ 61, 1, 7, 96 ], [ 61, 1, 12, 32 ], [ 62, 1, 2, 72 ], [ 62, 1, 5, 144 ], [ 62, 1, 10, 48 ], [ 63, 1, 5, 48 ], [ 63, 1, 10, 48 ], [ 63, 1, 13, 48 ], [ 64, 1, 8, 96 ], [ 64, 1, 19, 96 ], [ 65, 1, 23, 96 ] ] k = 28: F-action on Pi is () [66,1,28] Dynkin type is A_1(q) + T(phi1^2 phi2 phi3 phi4) Order of center |Z^F|: phi1^2 phi2 phi3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 2 modulo 60: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 3 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 4 modulo 60: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 5 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 7 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 8 modulo 60: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 9 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 11 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 13 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 16 modulo 60: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 17 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 19 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 21 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 23 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 25 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 27 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 29 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 31 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 32 modulo 60: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 37 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 41 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 43 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 47 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 49 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 53 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 59 modulo 60: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 97, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 28, 1, 3, 4 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 33, 1, 2, 8 ], [ 35, 1, 2, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 8, 8 ], [ 42, 1, 3, 12 ], [ 43, 1, 9, 8 ], [ 44, 1, 3, 6 ], [ 44, 1, 4, 8 ], [ 45, 1, 3, 12 ], [ 47, 1, 3, 8 ], [ 50, 1, 3, 12 ], [ 51, 1, 7, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 11, 16 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 12 ], [ 54, 1, 4, 16 ], [ 55, 1, 4, 16 ], [ 56, 1, 3, 12 ], [ 56, 1, 4, 16 ], [ 59, 1, 19, 12 ], [ 60, 1, 11, 24 ], [ 61, 1, 13, 16 ], [ 62, 1, 10, 24 ], [ 63, 1, 7, 24 ], [ 64, 1, 10, 48 ] ] k = 29: F-action on Pi is () [66,1,29] Dynkin type is A_1(q) + T(phi1 phi2^2 phi4 phi6) Order of center |Z^F|: phi1 phi2^2 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 2 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 3 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 4 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 5 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 7 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 8 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 9 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 11 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 13 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 16 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 17 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 19 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 21 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 23 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 25 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 27 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 29 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 31 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 32 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 37 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 41 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 43 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 47 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 49 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 53 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 59 modulo 60: 1/48 q phi1^2 phi2^2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 60, 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 4, 8 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 28, 1, 2, 4 ], [ 30, 1, 4, 8 ], [ 31, 1, 4, 4 ], [ 33, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 8, 8 ], [ 42, 1, 5, 12 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 47, 1, 10, 8 ], [ 50, 1, 10, 12 ], [ 51, 1, 4, 8 ], [ 52, 1, 5, 8 ], [ 53, 1, 13, 16 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 12 ], [ 54, 1, 9, 16 ], [ 55, 1, 11, 16 ], [ 56, 1, 16, 16 ], [ 56, 1, 17, 12 ], [ 59, 1, 20, 12 ], [ 60, 1, 10, 24 ], [ 61, 1, 16, 16 ], [ 62, 1, 9, 24 ], [ 63, 1, 6, 24 ], [ 64, 1, 11, 48 ] ] k = 30: F-action on Pi is () [66,1,30] Dynkin type is A_1(q) + T(phi1^2 phi2 phi4 phi6) Order of center |Z^F|: phi1^2 phi2 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 2 modulo 60: 1/48 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 4 modulo 60: 1/48 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 7 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 8 modulo 60: 1/48 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 11 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 13 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 16 modulo 60: 1/48 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 17 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 19 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 21 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 23 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 25 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 27 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 29 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 31 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 32 modulo 60: 1/48 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 41 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 43 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 47 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 49 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 53 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 59 modulo 60: 1/48 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 96, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 28, 1, 1, 4 ], [ 31, 1, 3, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 35, 1, 5, 8 ], [ 38, 1, 4, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 8, 8 ], [ 42, 1, 5, 12 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 44, 1, 7, 6 ], [ 46, 1, 10, 24 ], [ 47, 1, 9, 8 ], [ 50, 1, 7, 12 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 16 ], [ 52, 1, 8, 8 ], [ 53, 1, 13, 16 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 12 ], [ 55, 1, 7, 24 ], [ 55, 1, 11, 16 ], [ 56, 1, 11, 16 ], [ 56, 1, 12, 12 ], [ 58, 1, 5, 16 ], [ 59, 1, 20, 12 ], [ 60, 1, 10, 24 ], [ 61, 1, 14, 16 ], [ 62, 1, 8, 24 ], [ 63, 1, 6, 24 ], [ 64, 1, 11, 48 ], [ 65, 1, 25, 48 ] ] k = 31: F-action on Pi is () [66,1,31] Dynkin type is A_1(q) + T(phi1 phi2^2 phi3 phi4) Order of center |Z^F|: phi1 phi2^2 phi3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 2 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 3 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 4 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 5 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 7 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 8 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 9 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 11 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 13 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 16 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 17 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 19 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 21 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 23 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 25 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 27 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 29 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 31 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 32 modulo 60: 1/48 q^4 phi1^2 phi2 q congruent 37 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 41 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 43 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 47 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 49 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 53 modulo 60: 1/48 q phi1^2 phi2^2 phi6 q congruent 59 modulo 60: 1/48 q phi1^2 phi2^2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 59, 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 28, 1, 4, 4 ], [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 38, 1, 9, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 8, 8 ], [ 42, 1, 3, 12 ], [ 43, 1, 9, 8 ], [ 44, 1, 3, 6 ], [ 44, 1, 4, 8 ], [ 46, 1, 9, 24 ], [ 47, 1, 4, 8 ], [ 50, 1, 6, 12 ], [ 51, 1, 4, 16 ], [ 51, 1, 7, 8 ], [ 52, 1, 5, 8 ], [ 53, 1, 11, 16 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 12 ], [ 55, 1, 4, 16 ], [ 55, 1, 18, 24 ], [ 56, 1, 8, 12 ], [ 56, 1, 9, 16 ], [ 58, 1, 5, 16 ], [ 59, 1, 19, 12 ], [ 60, 1, 11, 24 ], [ 61, 1, 15, 16 ], [ 62, 1, 11, 24 ], [ 63, 1, 7, 24 ], [ 64, 1, 10, 48 ], [ 65, 1, 24, 48 ] ] k = 32: F-action on Pi is () [66,1,32] Dynkin type is A_1(q) + T(phi1^2 phi2^3 phi6) Order of center |Z^F|: phi1^2 phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 2 modulo 60: 1/96 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 4 modulo 60: 1/96 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 7 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 8 modulo 60: 1/96 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 11 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 13 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 16 modulo 60: 1/96 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 17 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 19 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 21 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 23 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 25 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 27 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 29 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 31 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 32 modulo 60: 1/96 q^3 phi1 phi2 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 41 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 43 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 47 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 49 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 53 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 59 modulo 60: 1/96 q phi1^2 phi2 ( q^3-4*q^2+2*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 82, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 14 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 18 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 18 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], [ 16, 1, 3, 48 ], [ 16, 1, 4, 8 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 24 ], [ 22, 1, 3, 40 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 16 ], [ 27, 1, 3, 16 ], [ 27, 1, 4, 6 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 12 ], [ 29, 1, 3, 48 ], [ 30, 1, 3, 24 ], [ 30, 1, 4, 16 ], [ 31, 1, 3, 56 ], [ 31, 1, 4, 12 ], [ 32, 1, 3, 48 ], [ 33, 1, 6, 16 ], [ 33, 1, 8, 48 ], [ 34, 1, 3, 32 ], [ 35, 1, 6, 48 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 24 ], [ 36, 1, 3, 16 ], [ 37, 1, 2, 16 ], [ 38, 1, 8, 96 ], [ 38, 1, 11, 72 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 4, 8 ], [ 40, 1, 2, 24 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 42, 1, 2, 32 ], [ 42, 1, 5, 24 ], [ 43, 1, 3, 32 ], [ 43, 1, 4, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 7, 18 ], [ 44, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 45, 1, 4, 36 ], [ 45, 1, 5, 32 ], [ 46, 1, 4, 72 ], [ 46, 1, 5, 64 ], [ 47, 1, 7, 48 ], [ 47, 1, 8, 24 ], [ 47, 1, 10, 16 ], [ 48, 1, 4, 32 ], [ 48, 1, 5, 32 ], [ 50, 1, 7, 24 ], [ 50, 1, 8, 32 ], [ 50, 1, 10, 12 ], [ 51, 1, 3, 16 ], [ 51, 1, 8, 16 ], [ 51, 1, 10, 48 ], [ 52, 1, 2, 16 ], [ 52, 1, 4, 16 ], [ 53, 1, 6, 32 ], [ 53, 1, 8, 32 ], [ 53, 1, 15, 24 ], [ 53, 1, 18, 72 ], [ 54, 1, 11, 48 ], [ 54, 1, 13, 32 ], [ 55, 1, 12, 72 ], [ 55, 1, 13, 32 ], [ 55, 1, 14, 32 ], [ 56, 1, 12, 72 ], [ 56, 1, 13, 32 ], [ 56, 1, 17, 36 ], [ 56, 1, 19, 32 ], [ 58, 1, 10, 96 ], [ 58, 1, 11, 64 ], [ 59, 1, 5, 36 ], [ 59, 1, 20, 24 ], [ 60, 1, 8, 144 ], [ 60, 1, 10, 48 ], [ 61, 1, 8, 96 ], [ 61, 1, 18, 32 ], [ 62, 1, 6, 144 ], [ 62, 1, 7, 72 ], [ 62, 1, 9, 48 ], [ 63, 1, 8, 48 ], [ 63, 1, 11, 48 ], [ 63, 1, 12, 48 ], [ 64, 1, 16, 96 ], [ 64, 1, 22, 96 ], [ 65, 1, 26, 96 ] ] k = 33: F-action on Pi is () [66,1,33] Dynkin type is A_1(q) + T(phi2^5 phi6) Order of center |Z^F|: phi2^5 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 2 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-782*q^3+1736*q^2-2240*q+1440 ) q congruent 3 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 4 modulo 60: 1/4320 q^2 phi1 ( q^4-20*q^3+145*q^2-450*q+504 ) q congruent 5 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-797*q^3+1916*q^2-2885*q+2400 ) q congruent 7 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 8 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-782*q^3+1736*q^2-2240*q+1440 ) q congruent 9 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 11 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-797*q^3+1916*q^2-2885*q+2400 ) q congruent 13 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 16 modulo 60: 1/4320 q^2 phi1 ( q^4-20*q^3+145*q^2-450*q+504 ) q congruent 17 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-797*q^3+1916*q^2-2885*q+2400 ) q congruent 19 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 21 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 23 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-797*q^3+1916*q^2-2885*q+2400 ) q congruent 25 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 27 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 29 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-797*q^3+1916*q^2-2885*q+2400 ) q congruent 31 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 32 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-782*q^3+1736*q^2-2240*q+1440 ) q congruent 37 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 41 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-797*q^3+1916*q^2-2885*q+2400 ) q congruent 43 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 47 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-797*q^3+1916*q^2-2885*q+2400 ) q congruent 49 modulo 60: 1/4320 q phi1^2 ( q^4-19*q^3+126*q^2-339*q+315 ) q congruent 53 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-797*q^3+1916*q^2-2885*q+2400 ) q congruent 59 modulo 60: 1/4320 phi2 ( q^6-22*q^5+187*q^4-797*q^3+1916*q^2-2885*q+2400 ) Fusion of maximal tori of C^F in those of G^F: [ 78, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 62 ], [ 4, 1, 2, 150 ], [ 5, 1, 2, 264 ], [ 6, 1, 2, 312 ], [ 7, 1, 2, 132 ], [ 8, 1, 2, 60 ], [ 9, 1, 1, 15 ], [ 10, 1, 2, 30 ], [ 11, 1, 2, 140 ], [ 12, 1, 2, 330 ], [ 13, 1, 4, 360 ], [ 14, 1, 2, 660 ], [ 15, 1, 2, 732 ], [ 16, 1, 3, 840 ], [ 17, 1, 4, 840 ], [ 18, 1, 2, 420 ], [ 19, 1, 2, 600 ], [ 20, 1, 4, 840 ], [ 21, 1, 2, 240 ], [ 22, 1, 4, 540 ], [ 23, 1, 2, 90 ], [ 24, 1, 2, 210 ], [ 25, 1, 3, 540 ], [ 26, 1, 4, 240 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 240 ], [ 28, 1, 4, 540 ], [ 29, 1, 4, 1200 ], [ 30, 1, 3, 1080 ], [ 31, 1, 4, 1380 ], [ 32, 1, 3, 1200 ], [ 33, 1, 8, 720 ], [ 34, 1, 4, 960 ], [ 35, 1, 8, 1080 ], [ 36, 1, 4, 720 ], [ 37, 1, 3, 1440 ], [ 38, 1, 11, 360 ], [ 38, 1, 12, 1440 ], [ 39, 1, 3, 360 ], [ 40, 1, 6, 900 ], [ 41, 1, 9, 720 ], [ 42, 1, 5, 96 ], [ 42, 1, 6, 960 ], [ 43, 1, 13, 1440 ], [ 44, 1, 7, 90 ], [ 44, 1, 10, 720 ], [ 45, 1, 4, 396 ], [ 45, 1, 6, 1440 ], [ 46, 1, 4, 840 ], [ 46, 1, 6, 1920 ], [ 47, 1, 8, 1080 ], [ 48, 1, 6, 1440 ], [ 50, 1, 10, 180 ], [ 50, 1, 12, 1440 ], [ 51, 1, 9, 2160 ], [ 52, 1, 10, 720 ], [ 53, 1, 18, 720 ], [ 53, 1, 20, 1440 ], [ 54, 1, 10, 720 ], [ 54, 1, 14, 1440 ], [ 55, 1, 12, 1800 ], [ 55, 1, 15, 1440 ], [ 56, 1, 17, 1260 ], [ 56, 1, 20, 1440 ], [ 58, 1, 14, 1440 ], [ 58, 1, 15, 2880 ], [ 59, 1, 5, 540 ], [ 60, 1, 8, 2160 ], [ 61, 1, 6, 2880 ], [ 61, 1, 21, 1440 ], [ 62, 1, 7, 3240 ], [ 63, 1, 9, 2160 ], [ 64, 1, 15, 4320 ], [ 65, 1, 27, 4320 ] ] k = 34: F-action on Pi is () [66,1,34] Dynkin type is A_1(q) + T(phi1^4 phi2 phi3) Order of center |Z^F|: phi1^4 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 phi1 ( q^6-12*q^5+45*q^4-41*q^3-54*q^2+61*q-48 ) q congruent 2 modulo 60: 1/288 q^2 phi2 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 3 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 4 modulo 60: 1/288 q phi1 ( q^5-12*q^4+45*q^3-38*q^2-72*q+64 ) q congruent 5 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 7 modulo 60: 1/288 phi1 ( q^6-12*q^5+45*q^4-41*q^3-54*q^2+61*q-48 ) q congruent 8 modulo 60: 1/288 q^2 phi2 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 9 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 11 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 13 modulo 60: 1/288 phi1 ( q^6-12*q^5+45*q^4-41*q^3-54*q^2+61*q-48 ) q congruent 16 modulo 60: 1/288 q phi1 ( q^5-12*q^4+45*q^3-38*q^2-72*q+64 ) q congruent 17 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 19 modulo 60: 1/288 phi1 ( q^6-12*q^5+45*q^4-41*q^3-54*q^2+61*q-48 ) q congruent 21 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 23 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 25 modulo 60: 1/288 phi1 ( q^6-12*q^5+45*q^4-41*q^3-54*q^2+61*q-48 ) q congruent 27 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 29 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 31 modulo 60: 1/288 phi1 ( q^6-12*q^5+45*q^4-41*q^3-54*q^2+61*q-48 ) q congruent 32 modulo 60: 1/288 q^2 phi2 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 37 modulo 60: 1/288 phi1 ( q^6-12*q^5+45*q^4-41*q^3-54*q^2+61*q-48 ) q congruent 41 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 43 modulo 60: 1/288 phi1 ( q^6-12*q^5+45*q^4-41*q^3-54*q^2+61*q-48 ) q congruent 47 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 49 modulo 60: 1/288 phi1 ( q^6-12*q^5+45*q^4-41*q^3-54*q^2+61*q-48 ) q congruent 53 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 59 modulo 60: 1/288 q phi1 phi2 ( q^4-13*q^3+58*q^2-99*q+45 ) Fusion of maximal tori of C^F in those of G^F: [ 77, 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 26 ], [ 4, 1, 1, 46 ], [ 5, 1, 1, 80 ], [ 6, 1, 1, 96 ], [ 7, 1, 1, 40 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 40 ], [ 12, 1, 1, 70 ], [ 13, 1, 1, 72 ], [ 14, 1, 1, 120 ], [ 15, 1, 1, 152 ], [ 16, 1, 1, 176 ], [ 17, 1, 1, 240 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 112 ], [ 20, 1, 1, 144 ], [ 20, 1, 2, 56 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 120 ], [ 22, 1, 2, 36 ], [ 23, 1, 1, 18 ], [ 24, 1, 1, 36 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 60 ], [ 26, 1, 1, 48 ], [ 26, 1, 3, 16 ], [ 27, 1, 1, 48 ], [ 27, 1, 2, 16 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 72 ], [ 28, 1, 2, 36 ], [ 29, 1, 1, 144 ], [ 29, 1, 2, 80 ], [ 30, 1, 1, 144 ], [ 31, 1, 1, 168 ], [ 31, 1, 2, 92 ], [ 32, 1, 1, 224 ], [ 33, 1, 1, 144 ], [ 34, 1, 1, 96 ], [ 34, 1, 2, 64 ], [ 35, 1, 1, 144 ], [ 35, 1, 3, 72 ], [ 36, 1, 1, 48 ], [ 36, 1, 2, 48 ], [ 37, 1, 1, 96 ], [ 38, 1, 1, 288 ], [ 38, 1, 3, 144 ], [ 38, 1, 5, 96 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 24 ], [ 40, 1, 1, 36 ], [ 41, 1, 1, 48 ], [ 41, 1, 6, 48 ], [ 42, 1, 1, 96 ], [ 42, 1, 3, 48 ], [ 42, 1, 4, 64 ], [ 43, 1, 1, 96 ], [ 43, 1, 2, 96 ], [ 44, 1, 1, 48 ], [ 44, 1, 2, 48 ], [ 44, 1, 3, 42 ], [ 45, 1, 1, 96 ], [ 45, 1, 2, 96 ], [ 45, 1, 3, 120 ], [ 46, 1, 1, 192 ], [ 46, 1, 2, 128 ], [ 46, 1, 3, 240 ], [ 47, 1, 1, 144 ], [ 47, 1, 2, 72 ], [ 48, 1, 1, 96 ], [ 48, 1, 2, 96 ], [ 50, 1, 2, 96 ], [ 50, 1, 3, 72 ], [ 50, 1, 4, 96 ], [ 50, 1, 6, 12 ], [ 51, 1, 1, 48 ], [ 51, 1, 2, 144 ], [ 52, 1, 2, 48 ], [ 53, 1, 1, 96 ], [ 53, 1, 3, 96 ], [ 53, 1, 16, 192 ], [ 54, 1, 2, 96 ], [ 54, 1, 3, 144 ], [ 54, 1, 7, 48 ], [ 55, 1, 1, 96 ], [ 55, 1, 2, 96 ], [ 55, 1, 3, 336 ], [ 56, 1, 2, 96 ], [ 56, 1, 3, 216 ], [ 56, 1, 6, 96 ], [ 56, 1, 8, 84 ], [ 58, 1, 2, 192 ], [ 58, 1, 3, 288 ], [ 58, 1, 7, 96 ], [ 59, 1, 4, 108 ], [ 60, 1, 2, 432 ], [ 61, 1, 4, 288 ], [ 61, 1, 7, 192 ], [ 61, 1, 19, 96 ], [ 62, 1, 2, 432 ], [ 62, 1, 5, 216 ], [ 63, 1, 4, 144 ], [ 63, 1, 10, 144 ], [ 64, 1, 6, 288 ], [ 64, 1, 19, 288 ], [ 65, 1, 28, 288 ] ] k = 35: F-action on Pi is () [66,1,35] Dynkin type is A_1(q) + T(phi1^2 phi2^3 phi3) Order of center |Z^F|: phi1^2 phi2^3 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 phi1^2 ( q^5-3*q^4-6*q^3+9*q^2+19*q+16 ) q congruent 2 modulo 60: 1/288 q phi2 ( q^5-6*q^4+7*q^3+6*q^2-16 ) q congruent 3 modulo 60: 1/288 q phi1 phi2 ( q^4-5*q^3+2*q^2+13*q-3 ) q congruent 4 modulo 60: 1/288 q phi1 ( q^5-4*q^4-3*q^3+10*q^2+16*q+16 ) q congruent 5 modulo 60: 1/288 q phi2^2 ( q^4-7*q^3+14*q^2-3*q-13 ) q congruent 7 modulo 60: 1/288 phi1^2 ( q^5-3*q^4-6*q^3+9*q^2+19*q+16 ) q congruent 8 modulo 60: 1/288 q phi2 ( q^5-6*q^4+7*q^3+6*q^2-16 ) q congruent 9 modulo 60: 1/288 q phi1 phi2 ( q^4-5*q^3+2*q^2+13*q-3 ) q congruent 11 modulo 60: 1/288 q phi2^2 ( q^4-7*q^3+14*q^2-3*q-13 ) q congruent 13 modulo 60: 1/288 phi1^2 ( q^5-3*q^4-6*q^3+9*q^2+19*q+16 ) q congruent 16 modulo 60: 1/288 q phi1 ( q^5-4*q^4-3*q^3+10*q^2+16*q+16 ) q congruent 17 modulo 60: 1/288 q phi2^2 ( q^4-7*q^3+14*q^2-3*q-13 ) q congruent 19 modulo 60: 1/288 phi1^2 ( q^5-3*q^4-6*q^3+9*q^2+19*q+16 ) q congruent 21 modulo 60: 1/288 q phi1 phi2 ( q^4-5*q^3+2*q^2+13*q-3 ) q congruent 23 modulo 60: 1/288 q phi2^2 ( q^4-7*q^3+14*q^2-3*q-13 ) q congruent 25 modulo 60: 1/288 phi1^2 ( q^5-3*q^4-6*q^3+9*q^2+19*q+16 ) q congruent 27 modulo 60: 1/288 q phi1 phi2 ( q^4-5*q^3+2*q^2+13*q-3 ) q congruent 29 modulo 60: 1/288 q phi2^2 ( q^4-7*q^3+14*q^2-3*q-13 ) q congruent 31 modulo 60: 1/288 phi1^2 ( q^5-3*q^4-6*q^3+9*q^2+19*q+16 ) q congruent 32 modulo 60: 1/288 q phi2 ( q^5-6*q^4+7*q^3+6*q^2-16 ) q congruent 37 modulo 60: 1/288 phi1^2 ( q^5-3*q^4-6*q^3+9*q^2+19*q+16 ) q congruent 41 modulo 60: 1/288 q phi2^2 ( q^4-7*q^3+14*q^2-3*q-13 ) q congruent 43 modulo 60: 1/288 phi1^2 ( q^5-3*q^4-6*q^3+9*q^2+19*q+16 ) q congruent 47 modulo 60: 1/288 q phi2^2 ( q^4-7*q^3+14*q^2-3*q-13 ) q congruent 49 modulo 60: 1/288 phi1^2 ( q^5-3*q^4-6*q^3+9*q^2+19*q+16 ) q congruent 53 modulo 60: 1/288 q phi2^2 ( q^4-7*q^3+14*q^2-3*q-13 ) q congruent 59 modulo 60: 1/288 q phi2^2 ( q^4-7*q^3+14*q^2-3*q-13 ) Fusion of maximal tori of C^F in those of G^F: [ 81, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 18 ], [ 4, 1, 2, 12 ], [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 6 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 24 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 24 ], [ 16, 1, 4, 48 ], [ 17, 1, 2, 16 ], [ 20, 1, 2, 72 ], [ 22, 1, 2, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 18 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 24 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 48 ], [ 27, 1, 5, 6 ], [ 28, 1, 2, 36 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 36 ], [ 32, 1, 2, 48 ], [ 33, 1, 1, 48 ], [ 33, 1, 2, 48 ], [ 35, 1, 3, 72 ], [ 35, 1, 4, 48 ], [ 37, 1, 2, 48 ], [ 38, 1, 9, 48 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 24 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 48 ], [ 40, 1, 3, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 4, 48 ], [ 41, 1, 9, 48 ], [ 42, 1, 3, 24 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 96 ], [ 44, 1, 3, 18 ], [ 44, 1, 5, 48 ], [ 46, 1, 9, 48 ], [ 47, 1, 2, 72 ], [ 47, 1, 4, 48 ], [ 48, 1, 3, 96 ], [ 50, 1, 6, 36 ], [ 51, 1, 3, 96 ], [ 51, 1, 5, 48 ], [ 51, 1, 6, 48 ], [ 52, 1, 4, 48 ], [ 52, 1, 10, 48 ], [ 53, 1, 9, 96 ], [ 53, 1, 16, 72 ], [ 53, 1, 17, 72 ], [ 55, 1, 5, 96 ], [ 55, 1, 18, 144 ], [ 56, 1, 8, 108 ], [ 56, 1, 10, 96 ], [ 58, 1, 4, 96 ], [ 59, 1, 4, 36 ], [ 59, 1, 19, 72 ], [ 60, 1, 2, 144 ], [ 60, 1, 11, 144 ], [ 61, 1, 17, 96 ], [ 62, 1, 5, 216 ], [ 62, 1, 11, 144 ], [ 63, 1, 5, 144 ], [ 63, 1, 13, 144 ], [ 64, 1, 8, 288 ], [ 65, 1, 30, 288 ] ] k = 36: F-action on Pi is () [66,1,36] Dynkin type is A_1(q) + T(phi1^3 phi2^2 phi6) Order of center |Z^F|: phi1^3 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-145 ) q congruent 2 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+20*q^3-108*q^2+48*q+32 ) q congruent 3 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-129 ) q congruent 4 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+52*q^2-36*q-112 ) q congruent 5 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+25*q^3-138*q^2+65*q+48 ) q congruent 7 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-145 ) q congruent 8 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+20*q^3-108*q^2+48*q+32 ) q congruent 9 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-129 ) q congruent 11 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+25*q^3-138*q^2+65*q+48 ) q congruent 13 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-145 ) q congruent 16 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+52*q^2-36*q-112 ) q congruent 17 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+25*q^3-138*q^2+65*q+48 ) q congruent 19 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-145 ) q congruent 21 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-129 ) q congruent 23 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+25*q^3-138*q^2+65*q+48 ) q congruent 25 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-145 ) q congruent 27 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-129 ) q congruent 29 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+25*q^3-138*q^2+65*q+48 ) q congruent 31 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-145 ) q congruent 32 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+20*q^3-108*q^2+48*q+32 ) q congruent 37 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-145 ) q congruent 41 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+25*q^3-138*q^2+65*q+48 ) q congruent 43 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-145 ) q congruent 47 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+25*q^3-138*q^2+65*q+48 ) q congruent 49 modulo 60: 1/288 q phi1 ( q^5-8*q^4+7*q^3+57*q^2-56*q-145 ) q congruent 53 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+25*q^3-138*q^2+65*q+48 ) q congruent 59 modulo 60: 1/288 phi2 ( q^6-10*q^5+25*q^4+25*q^3-138*q^2+65*q+48 ) Fusion of maximal tori of C^F in those of G^F: [ 28, 82 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 18 ], [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 6 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 24 ], [ 16, 1, 2, 48 ], [ 16, 1, 3, 24 ], [ 16, 1, 4, 24 ], [ 17, 1, 3, 16 ], [ 20, 1, 3, 72 ], [ 22, 1, 3, 12 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 24 ], [ 27, 1, 4, 6 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 36 ], [ 31, 1, 3, 36 ], [ 32, 1, 2, 48 ], [ 33, 1, 6, 48 ], [ 33, 1, 8, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 72 ], [ 37, 1, 2, 48 ], [ 38, 1, 4, 48 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 24 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 24 ], [ 40, 1, 3, 48 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 48 ], [ 41, 1, 4, 48 ], [ 42, 1, 5, 24 ], [ 43, 1, 3, 96 ], [ 43, 1, 8, 48 ], [ 44, 1, 7, 18 ], [ 44, 1, 9, 48 ], [ 46, 1, 10, 48 ], [ 47, 1, 7, 72 ], [ 47, 1, 9, 48 ], [ 48, 1, 4, 96 ], [ 50, 1, 7, 36 ], [ 51, 1, 3, 48 ], [ 51, 1, 6, 96 ], [ 51, 1, 10, 48 ], [ 52, 1, 1, 48 ], [ 52, 1, 3, 48 ], [ 53, 1, 6, 96 ], [ 53, 1, 15, 72 ], [ 53, 1, 18, 72 ], [ 55, 1, 7, 144 ], [ 55, 1, 14, 96 ], [ 56, 1, 12, 108 ], [ 56, 1, 14, 96 ], [ 58, 1, 4, 96 ], [ 59, 1, 5, 36 ], [ 59, 1, 20, 72 ], [ 60, 1, 8, 144 ], [ 60, 1, 10, 144 ], [ 61, 1, 22, 96 ], [ 62, 1, 6, 216 ], [ 62, 1, 8, 144 ], [ 63, 1, 8, 144 ], [ 63, 1, 12, 144 ], [ 64, 1, 16, 288 ], [ 65, 1, 31, 288 ] ] k = 37: F-action on Pi is () [66,1,37] Dynkin type is A_1(q) + T(phi1 phi2^4 phi6) Order of center |Z^F|: phi1 phi2^4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 2 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-92*q^3+132*q^2-128*q+64 ) q congruent 3 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 4 modulo 60: 1/288 q^2 phi1^2 ( q^3-7*q^2+16*q-12 ) q congruent 5 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-95*q^3+150*q^2-167*q+112 ) q congruent 7 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 8 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-92*q^3+132*q^2-128*q+64 ) q congruent 9 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 11 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-95*q^3+150*q^2-167*q+112 ) q congruent 13 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 16 modulo 60: 1/288 q^2 phi1^2 ( q^3-7*q^2+16*q-12 ) q congruent 17 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-95*q^3+150*q^2-167*q+112 ) q congruent 19 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 21 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 23 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-95*q^3+150*q^2-167*q+112 ) q congruent 25 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 27 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 29 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-95*q^3+150*q^2-167*q+112 ) q congruent 31 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 32 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-92*q^3+132*q^2-128*q+64 ) q congruent 37 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 41 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-95*q^3+150*q^2-167*q+112 ) q congruent 43 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 47 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-95*q^3+150*q^2-167*q+112 ) q congruent 49 modulo 60: 1/288 q phi1^2 phi6 ( q^2-6*q+9 ) q congruent 53 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-95*q^3+150*q^2-167*q+112 ) q congruent 59 modulo 60: 1/288 phi2 ( q^6-10*q^5+41*q^4-95*q^3+150*q^2-167*q+112 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 78 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 26 ], [ 4, 1, 2, 46 ], [ 5, 1, 2, 80 ], [ 6, 1, 2, 96 ], [ 7, 1, 2, 40 ], [ 8, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 40 ], [ 12, 1, 2, 70 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 120 ], [ 15, 1, 2, 152 ], [ 16, 1, 3, 176 ], [ 17, 1, 4, 240 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 112 ], [ 20, 1, 3, 56 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 48 ], [ 22, 1, 3, 36 ], [ 22, 1, 4, 120 ], [ 23, 1, 2, 18 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 60 ], [ 26, 1, 2, 16 ], [ 26, 1, 4, 48 ], [ 27, 1, 3, 16 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 48 ], [ 28, 1, 3, 36 ], [ 28, 1, 4, 72 ], [ 29, 1, 3, 80 ], [ 29, 1, 4, 144 ], [ 30, 1, 3, 144 ], [ 31, 1, 3, 92 ], [ 31, 1, 4, 168 ], [ 32, 1, 3, 224 ], [ 33, 1, 8, 144 ], [ 34, 1, 3, 64 ], [ 34, 1, 4, 96 ], [ 35, 1, 6, 72 ], [ 35, 1, 8, 144 ], [ 36, 1, 3, 48 ], [ 36, 1, 4, 48 ], [ 37, 1, 3, 96 ], [ 38, 1, 8, 96 ], [ 38, 1, 11, 144 ], [ 38, 1, 12, 288 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 24 ], [ 40, 1, 6, 36 ], [ 41, 1, 6, 48 ], [ 41, 1, 9, 48 ], [ 42, 1, 2, 64 ], [ 42, 1, 5, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 4, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 7, 42 ], [ 44, 1, 8, 48 ], [ 44, 1, 10, 48 ], [ 45, 1, 4, 120 ], [ 45, 1, 5, 96 ], [ 45, 1, 6, 96 ], [ 46, 1, 4, 240 ], [ 46, 1, 5, 128 ], [ 46, 1, 6, 192 ], [ 47, 1, 7, 72 ], [ 47, 1, 8, 144 ], [ 48, 1, 5, 96 ], [ 48, 1, 6, 96 ], [ 50, 1, 7, 12 ], [ 50, 1, 9, 96 ], [ 50, 1, 10, 72 ], [ 50, 1, 11, 96 ], [ 51, 1, 8, 144 ], [ 51, 1, 9, 48 ], [ 52, 1, 9, 48 ], [ 53, 1, 8, 96 ], [ 53, 1, 18, 192 ], [ 53, 1, 20, 96 ], [ 54, 1, 10, 144 ], [ 54, 1, 11, 48 ], [ 54, 1, 12, 96 ], [ 55, 1, 12, 336 ], [ 55, 1, 13, 96 ], [ 55, 1, 15, 96 ], [ 56, 1, 12, 84 ], [ 56, 1, 15, 96 ], [ 56, 1, 17, 216 ], [ 56, 1, 18, 96 ], [ 58, 1, 10, 96 ], [ 58, 1, 12, 192 ], [ 58, 1, 14, 288 ], [ 59, 1, 5, 108 ], [ 60, 1, 8, 432 ], [ 61, 1, 6, 288 ], [ 61, 1, 8, 192 ], [ 61, 1, 20, 96 ], [ 62, 1, 6, 216 ], [ 62, 1, 7, 432 ], [ 63, 1, 9, 144 ], [ 63, 1, 11, 144 ], [ 64, 1, 15, 288 ], [ 64, 1, 22, 288 ], [ 65, 1, 29, 288 ] ] k = 38: F-action on Pi is () [66,1,38] Dynkin type is A_1(q) + T(phi1^3 phi2^4) Order of center |Z^F|: phi1^3 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/9216 phi1 ( q^6-17*q^5+91*q^4-120*q^3-215*q^2+89*q-213 ) q congruent 2 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-216*q^4-64*q^3+384*q^2+512*q-1024 ) q congruent 3 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-211*q^4-95*q^3+560*q^2-606*q+1125 ) q congruent 4 modulo 60: 1/9216 q ( q^6-18*q^5+108*q^4-216*q^3-64*q^2+128*q+1024 ) q congruent 5 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-211*q^4-95*q^3+560*q^2-814*q-555 ) q congruent 7 modulo 60: 1/9216 phi2 ( q^6-19*q^5+127*q^4-338*q^3+243*q^2+61*q+357 ) q congruent 8 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-216*q^4-64*q^3+384*q^2+512*q-1024 ) q congruent 9 modulo 60: 1/9216 phi1 ( q^6-17*q^5+91*q^4-120*q^3-215*q^2+345*q-981 ) q congruent 11 modulo 60: 1/9216 phi2^2 ( q^5-20*q^4+147*q^3-485*q^2+728*q-411 ) q congruent 13 modulo 60: 1/9216 phi1 ( q^6-17*q^5+91*q^4-120*q^3-215*q^2+89*q-213 ) q congruent 16 modulo 60: 1/9216 q ( q^6-18*q^5+108*q^4-216*q^3-64*q^2+128*q+1024 ) q congruent 17 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-211*q^4-95*q^3+560*q^2-814*q-555 ) q congruent 19 modulo 60: 1/9216 phi2 ( q^6-19*q^5+127*q^4-338*q^3+243*q^2+61*q+357 ) q congruent 21 modulo 60: 1/9216 phi1 ( q^6-17*q^5+91*q^4-120*q^3-215*q^2+345*q-981 ) q congruent 23 modulo 60: 1/9216 phi2^2 ( q^5-20*q^4+147*q^3-485*q^2+728*q-411 ) q congruent 25 modulo 60: 1/9216 phi1 ( q^6-17*q^5+91*q^4-120*q^3-215*q^2+89*q-213 ) q congruent 27 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-211*q^4-95*q^3+560*q^2-606*q+1125 ) q congruent 29 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-211*q^4-95*q^3+560*q^2-814*q-555 ) q congruent 31 modulo 60: 1/9216 phi2 ( q^6-19*q^5+127*q^4-338*q^3+243*q^2+61*q+357 ) q congruent 32 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-216*q^4-64*q^3+384*q^2+512*q-1024 ) q congruent 37 modulo 60: 1/9216 phi1 ( q^6-17*q^5+91*q^4-120*q^3-215*q^2+89*q-213 ) q congruent 41 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-211*q^4-95*q^3+560*q^2-814*q-555 ) q congruent 43 modulo 60: 1/9216 phi2 ( q^6-19*q^5+127*q^4-338*q^3+243*q^2+61*q+357 ) q congruent 47 modulo 60: 1/9216 phi2^2 ( q^5-20*q^4+147*q^3-485*q^2+728*q-411 ) q congruent 49 modulo 60: 1/9216 phi1 ( q^6-17*q^5+91*q^4-120*q^3-215*q^2+89*q-213 ) q congruent 53 modulo 60: 1/9216 ( q^7-18*q^6+108*q^5-211*q^4-95*q^3+560*q^2-814*q-555 ) q congruent 59 modulo 60: 1/9216 phi2^2 ( q^5-20*q^4+147*q^3-485*q^2+728*q-411 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 84 ], [ 4, 1, 2, 72 ], [ 6, 1, 1, 96 ], [ 6, 1, 2, 128 ], [ 7, 1, 1, 24 ], [ 7, 1, 2, 96 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 24 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 96 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 96 ], [ 13, 1, 1, 168 ], [ 13, 1, 2, 288 ], [ 13, 1, 3, 96 ], [ 13, 1, 4, 240 ], [ 16, 1, 1, 288 ], [ 16, 1, 2, 192 ], [ 16, 1, 3, 384 ], [ 16, 1, 4, 384 ], [ 17, 1, 2, 768 ], [ 17, 1, 3, 256 ], [ 19, 1, 1, 96 ], [ 19, 1, 2, 384 ], [ 20, 1, 1, 144 ], [ 20, 1, 2, 576 ], [ 20, 1, 3, 288 ], [ 20, 1, 4, 576 ], [ 20, 1, 5, 384 ], [ 22, 1, 2, 192 ], [ 22, 1, 3, 192 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 24 ], [ 24, 1, 1, 90 ], [ 24, 1, 2, 168 ], [ 25, 1, 1, 168 ], [ 25, 1, 2, 192 ], [ 25, 1, 3, 336 ], [ 25, 1, 4, 384 ], [ 26, 1, 4, 192 ], [ 27, 1, 6, 192 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 288 ], [ 28, 1, 3, 144 ], [ 28, 1, 4, 288 ], [ 31, 1, 2, 576 ], [ 31, 1, 3, 576 ], [ 32, 1, 2, 768 ], [ 32, 1, 4, 768 ], [ 33, 1, 1, 576 ], [ 33, 1, 2, 1152 ], [ 33, 1, 6, 768 ], [ 33, 1, 8, 768 ], [ 34, 1, 2, 192 ], [ 34, 1, 3, 576 ], [ 35, 1, 1, 288 ], [ 35, 1, 2, 576 ], [ 35, 1, 3, 1152 ], [ 35, 1, 4, 1152 ], [ 35, 1, 5, 192 ], [ 35, 1, 6, 1152 ], [ 35, 1, 7, 1152 ], [ 35, 1, 8, 1152 ], [ 37, 1, 2, 192 ], [ 38, 1, 6, 1536 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 96 ], [ 39, 1, 3, 144 ], [ 39, 1, 4, 144 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 384 ], [ 40, 1, 3, 192 ], [ 40, 1, 6, 192 ], [ 41, 1, 1, 336 ], [ 41, 1, 2, 576 ], [ 41, 1, 4, 768 ], [ 41, 1, 6, 864 ], [ 41, 1, 9, 864 ], [ 41, 1, 10, 1152 ], [ 42, 1, 6, 768 ], [ 43, 1, 3, 384 ], [ 43, 1, 8, 768 ], [ 43, 1, 12, 1152 ], [ 43, 1, 13, 1152 ], [ 44, 1, 5, 576 ], [ 44, 1, 9, 192 ], [ 44, 1, 10, 576 ], [ 46, 1, 12, 1536 ], [ 47, 1, 2, 1152 ], [ 47, 1, 4, 2304 ], [ 47, 1, 7, 1152 ], [ 47, 1, 9, 768 ], [ 48, 1, 2, 576 ], [ 48, 1, 3, 1152 ], [ 48, 1, 4, 384 ], [ 48, 1, 5, 1728 ], [ 49, 1, 1, 576 ], [ 49, 1, 2, 1152 ], [ 49, 1, 5, 3456 ], [ 49, 1, 8, 2304 ], [ 49, 1, 9, 2304 ], [ 49, 1, 10, 2304 ], [ 49, 1, 14, 2304 ], [ 50, 1, 9, 1152 ], [ 51, 1, 3, 768 ], [ 51, 1, 5, 1152 ], [ 51, 1, 6, 384 ], [ 51, 1, 10, 768 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 576 ], [ 52, 1, 3, 192 ], [ 52, 1, 4, 1152 ], [ 52, 1, 9, 864 ], [ 52, 1, 10, 576 ], [ 53, 1, 6, 1536 ], [ 53, 1, 9, 2304 ], [ 53, 1, 12, 2304 ], [ 53, 1, 19, 2304 ], [ 53, 1, 20, 2304 ], [ 55, 1, 5, 2304 ], [ 55, 1, 10, 4608 ], [ 55, 1, 14, 1536 ], [ 56, 1, 5, 1152 ], [ 56, 1, 10, 2304 ], [ 56, 1, 14, 384 ], [ 56, 1, 15, 3456 ], [ 56, 1, 19, 2304 ], [ 57, 1, 2, 1152 ], [ 57, 1, 4, 2304 ], [ 57, 1, 5, 2304 ], [ 57, 1, 6, 3456 ], [ 58, 1, 4, 1536 ], [ 59, 1, 2, 1152 ], [ 59, 1, 3, 1152 ], [ 59, 1, 18, 2304 ], [ 60, 1, 17, 4608 ], [ 60, 1, 27, 4608 ], [ 60, 1, 43, 4608 ], [ 61, 1, 17, 4608 ], [ 61, 1, 22, 1536 ], [ 62, 1, 24, 6912 ], [ 62, 1, 31, 4608 ], [ 62, 1, 32, 2304 ], [ 62, 1, 44, 4608 ], [ 63, 1, 14, 4608 ], [ 63, 1, 28, 4608 ], [ 64, 1, 27, 9216 ], [ 64, 1, 64, 4608 ], [ 65, 1, 32, 9216 ] ] k = 39: F-action on Pi is () [66,1,39] Dynkin type is A_1(q) + T(phi1 phi2^2 phi4^2) Order of center |Z^F|: phi1 phi2^2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 2 modulo 60: 1/256 q^4 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 4 modulo 60: 1/256 q^4 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 7 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 8 modulo 60: 1/256 q^4 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 11 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 13 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 16 modulo 60: 1/256 q^4 ( q^3-2*q^2-4*q+8 ) q congruent 17 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 19 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 21 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 23 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 25 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 27 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 29 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 31 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 32 modulo 60: 1/256 q^4 ( q^3-2*q^2-4*q+8 ) q congruent 37 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 41 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 43 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 47 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 49 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 53 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 59 modulo 60: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 8 ], [ 20, 1, 1, 16 ], [ 20, 1, 5, 32 ], [ 20, 1, 7, 32 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 28, 1, 3, 8 ], [ 35, 1, 2, 32 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 32 ], [ 41, 1, 8, 96 ], [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], [ 43, 1, 9, 32 ], [ 44, 1, 4, 32 ], [ 48, 1, 9, 64 ], [ 49, 1, 4, 192 ], [ 49, 1, 7, 96 ], [ 49, 1, 13, 128 ], [ 49, 1, 14, 64 ], [ 49, 1, 15, 64 ], [ 52, 1, 5, 96 ], [ 52, 1, 8, 48 ], [ 52, 1, 9, 16 ], [ 53, 1, 11, 64 ], [ 53, 1, 14, 64 ], [ 56, 1, 4, 64 ], [ 57, 1, 7, 128 ], [ 57, 1, 8, 128 ], [ 59, 1, 6, 96 ], [ 59, 1, 21, 64 ], [ 59, 1, 24, 64 ], [ 60, 1, 18, 384 ], [ 60, 1, 30, 128 ], [ 60, 1, 33, 128 ], [ 62, 1, 25, 384 ], [ 62, 1, 26, 192 ], [ 62, 1, 36, 128 ], [ 62, 1, 38, 128 ], [ 63, 1, 15, 128 ], [ 64, 1, 33, 256 ], [ 64, 1, 35, 256 ] ] k = 40: F-action on Pi is () [66,1,40] Dynkin type is A_1(q) + T(phi1 phi4 phi8) Order of center |Z^F|: phi1 phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 2 modulo 60: 1/32 q^6 ( q-2 ) q congruent 3 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 4 modulo 60: 1/32 q^6 ( q-2 ) q congruent 5 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 7 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 8 modulo 60: 1/32 q^6 ( q-2 ) q congruent 9 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 11 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 13 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 16 modulo 60: 1/32 q^6 ( q-2 ) q congruent 17 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 19 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 21 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 23 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 25 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 27 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 29 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 31 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 32 modulo 60: 1/32 q^6 ( q-2 ) q congruent 37 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 41 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 43 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 47 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 49 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 53 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 59 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 44, 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 20, 1, 6, 8 ], [ 20, 1, 8, 8 ], [ 24, 1, 1, 2 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 49, 1, 17, 16 ], [ 52, 1, 8, 8 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 62, 1, 28, 16 ], [ 64, 1, 34, 32 ] ] k = 41: F-action on Pi is () [66,1,41] Dynkin type is A_1(q) + T(phi2 phi4 phi8) Order of center |Z^F|: phi2 phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 2 modulo 60: 1/32 q^7 q congruent 3 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 4 modulo 60: 1/32 q^7 q congruent 5 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 7 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 8 modulo 60: 1/32 q^7 q congruent 9 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 11 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 13 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 16 modulo 60: 1/32 q^7 q congruent 17 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 19 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 21 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 23 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 25 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 27 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 29 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 31 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 32 modulo 60: 1/32 q^7 q congruent 37 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 41 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 43 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 47 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 49 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 53 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 q congruent 59 modulo 60: 1/32 phi1 phi2^2 phi4 phi6 Fusion of maximal tori of C^F in those of G^F: [ 91, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 20, 1, 5, 8 ], [ 20, 1, 7, 8 ], [ 24, 1, 2, 2 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 49, 1, 13, 16 ], [ 52, 1, 5, 8 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 62, 1, 27, 16 ], [ 64, 1, 34, 32 ] ] k = 42: F-action on Pi is () [66,1,42] Dynkin type is A_1(q) + T(phi1^3 phi4^2) Order of center |Z^F|: phi1^3 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 2 modulo 60: 1/768 q^2 ( q^5-10*q^4+28*q^3+8*q^2-128*q+128 ) q congruent 3 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 4 modulo 60: 1/768 q^2 ( q^5-10*q^4+28*q^3+8*q^2-128*q+128 ) q congruent 5 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 7 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 8 modulo 60: 1/768 q^2 ( q^5-10*q^4+28*q^3+8*q^2-128*q+128 ) q congruent 9 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 11 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 13 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 16 modulo 60: 1/768 q^2 ( q^5-10*q^4+28*q^3+8*q^2-128*q+128 ) q congruent 17 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 19 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 21 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 23 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 25 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 27 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 29 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 31 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 32 modulo 60: 1/768 q^2 ( q^5-10*q^4+28*q^3+8*q^2-128*q+128 ) q congruent 37 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 41 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 43 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 47 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 49 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 53 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) q congruent 59 modulo 60: 1/768 phi1 phi2 ( q^5-10*q^4+29*q^3+3*q^2-150*q+207 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 48 ], [ 16, 1, 2, 96 ], [ 20, 1, 3, 48 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 48 ], [ 28, 1, 1, 24 ], [ 33, 1, 4, 192 ], [ 35, 1, 5, 96 ], [ 39, 1, 1, 24 ], [ 39, 1, 5, 24 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 3, 96 ], [ 41, 1, 5, 48 ], [ 41, 1, 8, 96 ], [ 43, 1, 9, 96 ], [ 44, 1, 6, 96 ], [ 48, 1, 8, 192 ], [ 49, 1, 7, 288 ], [ 49, 1, 11, 192 ], [ 51, 1, 7, 192 ], [ 52, 1, 1, 48 ], [ 52, 1, 8, 144 ], [ 53, 1, 10, 192 ], [ 53, 1, 13, 192 ], [ 55, 1, 6, 384 ], [ 56, 1, 11, 192 ], [ 57, 1, 11, 384 ], [ 59, 1, 6, 96 ], [ 59, 1, 23, 192 ], [ 60, 1, 18, 384 ], [ 60, 1, 31, 384 ], [ 62, 1, 26, 576 ], [ 62, 1, 33, 384 ], [ 63, 1, 16, 384 ], [ 64, 1, 28, 768 ], [ 65, 1, 33, 768 ] ] k = 43: F-action on Pi is () [66,1,43] Dynkin type is A_1(q) + T(phi1^2 phi2 phi8) Order of center |Z^F|: phi1^2 phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 2 modulo 60: 1/32 q^4 ( q^3-4*q^2+8 ) q congruent 3 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 4 modulo 60: 1/32 q^4 ( q^3-4*q^2+8 ) q congruent 5 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 7 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 8 modulo 60: 1/32 q^4 ( q^3-4*q^2+8 ) q congruent 9 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 11 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 13 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 16 modulo 60: 1/32 q^4 ( q^3-4*q^2+8 ) q congruent 17 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 19 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 21 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 23 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 25 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 27 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 29 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 31 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 32 modulo 60: 1/32 q^4 ( q^3-4*q^2+8 ) q congruent 37 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 41 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 43 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 47 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 49 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 53 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) q congruent 59 modulo 60: 1/32 phi1 phi2 phi4 ( q^3-4*q^2+9 ) Fusion of maximal tori of C^F in those of G^F: [ 89, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 28, 1, 1, 4 ], [ 28, 1, 3, 4 ], [ 33, 1, 5, 16 ], [ 39, 1, 2, 4 ], [ 40, 1, 3, 8 ], [ 41, 1, 4, 8 ], [ 49, 1, 12, 16 ], [ 52, 1, 3, 8 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 62, 1, 28, 16 ], [ 63, 1, 17, 16 ], [ 63, 1, 18, 16 ], [ 64, 1, 31, 32 ], [ 65, 1, 34, 32 ] ] k = 44: F-action on Pi is () [66,1,44] Dynkin type is A_1(q) + T(phi1 phi2^2 phi8) Order of center |Z^F|: phi1 phi2^2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 2 modulo 60: 1/32 q^6 ( q-2 ) q congruent 3 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 4 modulo 60: 1/32 q^6 ( q-2 ) q congruent 5 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 7 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 8 modulo 60: 1/32 q^6 ( q-2 ) q congruent 9 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 11 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 13 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 16 modulo 60: 1/32 q^6 ( q-2 ) q congruent 17 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 19 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 21 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 23 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 25 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 27 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 29 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 31 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 32 modulo 60: 1/32 q^6 ( q-2 ) q congruent 37 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 41 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 43 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 47 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 49 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 53 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 59 modulo 60: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 43, 90 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 9, 16 ], [ 39, 1, 2, 4 ], [ 40, 1, 2, 8 ], [ 41, 1, 4, 8 ], [ 49, 1, 16, 16 ], [ 52, 1, 4, 8 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 62, 1, 27, 16 ], [ 63, 1, 17, 16 ], [ 63, 1, 18, 16 ], [ 64, 1, 31, 32 ], [ 65, 1, 35, 32 ] ] k = 45: F-action on Pi is () [66,1,45] Dynkin type is A_1(q) + T(phi2^3 phi4^2) Order of center |Z^F|: phi2^3 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 2 modulo 60: 1/768 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 3 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 4 modulo 60: 1/768 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 5 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 7 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 8 modulo 60: 1/768 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 9 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 11 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 13 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 16 modulo 60: 1/768 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 17 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 19 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 21 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 23 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 25 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 27 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 29 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 31 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 32 modulo 60: 1/768 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 37 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 41 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 43 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 47 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 49 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 53 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 59 modulo 60: 1/768 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 74, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 2, 48 ], [ 13, 1, 4, 24 ], [ 16, 1, 4, 96 ], [ 20, 1, 2, 48 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 48 ], [ 28, 1, 4, 24 ], [ 33, 1, 10, 192 ], [ 35, 1, 4, 96 ], [ 39, 1, 3, 24 ], [ 39, 1, 5, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 5, 48 ], [ 41, 1, 8, 96 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 96 ], [ 43, 1, 9, 96 ], [ 44, 1, 4, 96 ], [ 48, 1, 9, 192 ], [ 49, 1, 4, 288 ], [ 49, 1, 19, 192 ], [ 51, 1, 4, 192 ], [ 52, 1, 5, 144 ], [ 52, 1, 10, 48 ], [ 53, 1, 11, 192 ], [ 53, 1, 14, 192 ], [ 55, 1, 19, 384 ], [ 56, 1, 9, 192 ], [ 57, 1, 8, 384 ], [ 59, 1, 6, 96 ], [ 59, 1, 24, 192 ], [ 60, 1, 18, 384 ], [ 60, 1, 30, 384 ], [ 62, 1, 25, 576 ], [ 62, 1, 35, 384 ], [ 63, 1, 15, 384 ], [ 64, 1, 33, 768 ], [ 65, 1, 36, 768 ] ] k = 46: F-action on Pi is () [66,1,46] Dynkin type is A_1(q) + T(phi1^2 phi2 phi4^2) Order of center |Z^F|: phi1^2 phi2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 2 modulo 60: 1/256 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 3 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 4 modulo 60: 1/256 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 5 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 7 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 8 modulo 60: 1/256 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 9 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 11 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 13 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 16 modulo 60: 1/256 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 17 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 19 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 21 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 23 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 25 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 27 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 29 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 31 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 32 modulo 60: 1/256 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 37 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 41 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 43 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 47 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 49 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 53 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 59 modulo 60: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 73, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 16 ], [ 20, 1, 4, 16 ], [ 20, 1, 6, 32 ], [ 20, 1, 8, 32 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 28, 1, 2, 8 ], [ 35, 1, 7, 32 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 39, 1, 5, 24 ], [ 41, 1, 1, 16 ], [ 41, 1, 3, 32 ], [ 41, 1, 5, 48 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 32 ], [ 41, 1, 8, 96 ], [ 43, 1, 9, 32 ], [ 44, 1, 6, 32 ], [ 48, 1, 8, 64 ], [ 49, 1, 4, 96 ], [ 49, 1, 7, 192 ], [ 49, 1, 17, 128 ], [ 49, 1, 18, 64 ], [ 49, 1, 20, 64 ], [ 52, 1, 2, 16 ], [ 52, 1, 5, 48 ], [ 52, 1, 8, 96 ], [ 53, 1, 10, 64 ], [ 53, 1, 13, 64 ], [ 56, 1, 16, 64 ], [ 57, 1, 7, 128 ], [ 57, 1, 11, 128 ], [ 59, 1, 6, 96 ], [ 59, 1, 21, 64 ], [ 59, 1, 23, 64 ], [ 60, 1, 18, 384 ], [ 60, 1, 31, 128 ], [ 60, 1, 33, 128 ], [ 62, 1, 25, 192 ], [ 62, 1, 26, 384 ], [ 62, 1, 34, 128 ], [ 62, 1, 40, 128 ], [ 63, 1, 16, 128 ], [ 64, 1, 28, 256 ], [ 64, 1, 35, 256 ] ] k = 47: F-action on Pi is () [66,1,47] Dynkin type is A_1(q) + T(phi1^5 phi2^2) Order of center |Z^F|: phi1^5 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 2 modulo 60: 1/3072 q ( q^6-26*q^5+252*q^4-1080*q^3+1664*q^2+896*q-3072 ) q congruent 3 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) q congruent 4 modulo 60: 1/3072 q ( q^6-26*q^5+252*q^4-1080*q^3+1664*q^2+896*q-3072 ) q congruent 5 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 7 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) q congruent 8 modulo 60: 1/3072 q ( q^6-26*q^5+252*q^4-1080*q^3+1664*q^2+896*q-3072 ) q congruent 9 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 11 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) q congruent 13 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 16 modulo 60: 1/3072 q ( q^6-26*q^5+252*q^4-1080*q^3+1664*q^2+896*q-3072 ) q congruent 17 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 19 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) q congruent 21 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 23 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) q congruent 25 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 27 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) q congruent 29 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 31 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) q congruent 32 modulo 60: 1/3072 q ( q^6-26*q^5+252*q^4-1080*q^3+1664*q^2+896*q-3072 ) q congruent 37 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 41 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 43 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) q congruent 47 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) q congruent 49 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 53 modulo 60: 1/3072 phi1 ( q^6-25*q^5+227*q^4-864*q^3+977*q^2+969*q-645 ) q congruent 59 modulo 60: 1/3072 ( q^7-26*q^6+252*q^5-1091*q^4+1841*q^3-8*q^2-1470*q-1323 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 68 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 80 ], [ 4, 1, 1, 216 ], [ 4, 1, 2, 28 ], [ 5, 1, 1, 384 ], [ 6, 1, 1, 512 ], [ 7, 1, 1, 144 ], [ 8, 1, 1, 64 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 26 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 144 ], [ 12, 1, 1, 432 ], [ 13, 1, 1, 528 ], [ 13, 1, 2, 32 ], [ 13, 1, 3, 96 ], [ 13, 1, 4, 56 ], [ 14, 1, 1, 768 ], [ 15, 1, 1, 1152 ], [ 16, 1, 1, 1920 ], [ 16, 1, 2, 320 ], [ 17, 1, 1, 2304 ], [ 18, 1, 1, 384 ], [ 19, 1, 1, 768 ], [ 20, 1, 1, 1248 ], [ 20, 1, 2, 576 ], [ 20, 1, 3, 240 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 640 ], [ 22, 1, 2, 256 ], [ 23, 1, 1, 72 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 198 ], [ 24, 1, 2, 60 ], [ 25, 1, 1, 624 ], [ 25, 1, 2, 128 ], [ 25, 1, 3, 56 ], [ 25, 1, 4, 64 ], [ 26, 1, 1, 192 ], [ 26, 1, 3, 64 ], [ 27, 1, 1, 192 ], [ 27, 1, 2, 64 ], [ 28, 1, 1, 624 ], [ 28, 1, 2, 288 ], [ 28, 1, 3, 104 ], [ 29, 1, 1, 1152 ], [ 29, 1, 2, 768 ], [ 30, 1, 1, 1536 ], [ 30, 1, 2, 256 ], [ 31, 1, 1, 1920 ], [ 31, 1, 2, 1280 ], [ 32, 1, 1, 3072 ], [ 33, 1, 1, 4224 ], [ 33, 1, 2, 640 ], [ 33, 1, 4, 768 ], [ 34, 1, 1, 768 ], [ 34, 1, 2, 512 ], [ 35, 1, 1, 2688 ], [ 35, 1, 2, 448 ], [ 35, 1, 3, 1536 ], [ 35, 1, 5, 576 ], [ 35, 1, 6, 480 ], [ 36, 1, 1, 384 ], [ 36, 1, 2, 256 ], [ 37, 1, 1, 1152 ], [ 37, 1, 2, 256 ], [ 38, 1, 1, 2304 ], [ 38, 1, 5, 1536 ], [ 39, 1, 1, 240 ], [ 39, 1, 2, 32 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 104 ], [ 40, 1, 1, 1056 ], [ 40, 1, 3, 192 ], [ 41, 1, 1, 1440 ], [ 41, 1, 2, 192 ], [ 41, 1, 3, 384 ], [ 41, 1, 4, 256 ], [ 41, 1, 6, 688 ], [ 41, 1, 9, 112 ], [ 42, 1, 1, 768 ], [ 42, 1, 4, 512 ], [ 43, 1, 1, 1152 ], [ 43, 1, 2, 896 ], [ 43, 1, 3, 384 ], [ 43, 1, 8, 256 ], [ 43, 1, 12, 128 ], [ 44, 1, 1, 576 ], [ 44, 1, 2, 448 ], [ 44, 1, 5, 64 ], [ 44, 1, 9, 192 ], [ 45, 1, 1, 1152 ], [ 45, 1, 2, 1280 ], [ 46, 1, 1, 2304 ], [ 46, 1, 2, 2560 ], [ 47, 1, 1, 3840 ], [ 47, 1, 2, 3072 ], [ 47, 1, 3, 1024 ], [ 48, 1, 1, 2304 ], [ 48, 1, 2, 2048 ], [ 48, 1, 3, 512 ], [ 48, 1, 4, 768 ], [ 48, 1, 7, 768 ], [ 49, 1, 1, 5760 ], [ 49, 1, 2, 1152 ], [ 49, 1, 5, 960 ], [ 49, 1, 9, 3840 ], [ 49, 1, 11, 768 ], [ 50, 1, 1, 384 ], [ 50, 1, 2, 768 ], [ 50, 1, 4, 768 ], [ 50, 1, 5, 128 ], [ 51, 1, 1, 1152 ], [ 51, 1, 2, 1792 ], [ 51, 1, 5, 384 ], [ 51, 1, 6, 640 ], [ 52, 1, 1, 1440 ], [ 52, 1, 2, 960 ], [ 52, 1, 3, 448 ], [ 52, 1, 9, 208 ], [ 53, 1, 1, 2304 ], [ 53, 1, 2, 768 ], [ 53, 1, 3, 2048 ], [ 53, 1, 5, 768 ], [ 53, 1, 6, 768 ], [ 53, 1, 9, 512 ], [ 54, 1, 2, 1536 ], [ 54, 1, 5, 512 ], [ 55, 1, 1, 2304 ], [ 55, 1, 2, 3584 ], [ 55, 1, 5, 1280 ], [ 55, 1, 9, 1536 ], [ 56, 1, 1, 1152 ], [ 56, 1, 2, 2304 ], [ 56, 1, 5, 896 ], [ 56, 1, 6, 2304 ], [ 56, 1, 7, 896 ], [ 56, 1, 14, 1152 ], [ 57, 1, 1, 4608 ], [ 57, 1, 2, 4608 ], [ 57, 1, 3, 1536 ], [ 57, 1, 5, 1536 ], [ 58, 1, 2, 3072 ], [ 58, 1, 9, 1024 ], [ 59, 1, 1, 1152 ], [ 59, 1, 3, 384 ], [ 59, 1, 12, 1152 ], [ 59, 1, 17, 768 ], [ 60, 1, 1, 4608 ], [ 60, 1, 27, 1536 ], [ 60, 1, 40, 4608 ], [ 60, 1, 44, 1536 ], [ 61, 1, 12, 2048 ], [ 61, 1, 19, 3072 ], [ 62, 1, 1, 2304 ], [ 62, 1, 30, 4608 ], [ 62, 1, 32, 2304 ], [ 62, 1, 41, 4608 ], [ 62, 1, 46, 2304 ], [ 62, 1, 47, 1536 ], [ 63, 1, 20, 1536 ], [ 63, 1, 21, 1536 ], [ 63, 1, 29, 1536 ], [ 63, 1, 33, 1536 ], [ 64, 1, 37, 3072 ], [ 64, 1, 51, 3072 ], [ 64, 1, 53, 3072 ], [ 65, 1, 39, 3072 ] ] k = 48: F-action on Pi is () [66,1,48] Dynkin type is A_1(q) + T(phi1^2 phi2^3 phi4) Order of center |Z^F|: phi1^2 phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 2 modulo 60: 1/384 q^4 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 4 modulo 60: 1/384 q^4 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 7 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 8 modulo 60: 1/384 q^4 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 11 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 13 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 16 modulo 60: 1/384 q^4 ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 19 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 21 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 23 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 25 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 27 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 29 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 31 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 32 modulo 60: 1/384 q^4 ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 41 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 43 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 47 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 49 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 53 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) q congruent 59 modulo 60: 1/384 phi1^2 phi2 ( q^4-7*q^3+14*q^2-9*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 72, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 14 ], [ 4, 1, 2, 10 ], [ 6, 1, 1, 24 ], [ 6, 1, 2, 16 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 12 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 24 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 36 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 24 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 96 ], [ 17, 1, 3, 32 ], [ 19, 1, 1, 24 ], [ 19, 1, 2, 48 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 48 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 48 ], [ 20, 1, 5, 96 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 36 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 36 ], [ 25, 1, 4, 48 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 48 ], [ 31, 1, 3, 16 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 96 ], [ 33, 1, 2, 48 ], [ 33, 1, 6, 32 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 1, 24 ], [ 35, 1, 2, 72 ], [ 35, 1, 3, 48 ], [ 35, 1, 4, 48 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 48 ], [ 35, 1, 8, 48 ], [ 38, 1, 6, 192 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 16 ], [ 40, 1, 3, 24 ], [ 41, 1, 2, 24 ], [ 41, 1, 4, 48 ], [ 41, 1, 5, 24 ], [ 41, 1, 6, 48 ], [ 41, 1, 8, 32 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 96 ], [ 42, 1, 6, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 9, 32 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 4, 24 ], [ 44, 1, 5, 48 ], [ 44, 1, 6, 8 ], [ 44, 1, 10, 48 ], [ 46, 1, 12, 192 ], [ 47, 1, 4, 96 ], [ 47, 1, 9, 32 ], [ 48, 1, 2, 48 ], [ 48, 1, 5, 48 ], [ 49, 1, 2, 48 ], [ 49, 1, 4, 96 ], [ 49, 1, 7, 48 ], [ 49, 1, 8, 96 ], [ 49, 1, 14, 192 ], [ 50, 1, 9, 96 ], [ 51, 1, 4, 32 ], [ 51, 1, 5, 96 ], [ 51, 1, 7, 16 ], [ 52, 1, 3, 24 ], [ 52, 1, 4, 48 ], [ 52, 1, 5, 48 ], [ 52, 1, 8, 8 ], [ 52, 1, 9, 48 ], [ 53, 1, 9, 96 ], [ 53, 1, 11, 96 ], [ 53, 1, 12, 96 ], [ 53, 1, 13, 64 ], [ 53, 1, 14, 96 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 96 ], [ 55, 1, 4, 96 ], [ 55, 1, 10, 192 ], [ 55, 1, 11, 64 ], [ 56, 1, 4, 48 ], [ 56, 1, 5, 96 ], [ 56, 1, 9, 96 ], [ 56, 1, 11, 16 ], [ 56, 1, 15, 96 ], [ 56, 1, 16, 96 ], [ 57, 1, 4, 96 ], [ 57, 1, 7, 96 ], [ 58, 1, 5, 64 ], [ 59, 1, 16, 48 ], [ 59, 1, 18, 96 ], [ 59, 1, 24, 96 ], [ 60, 1, 28, 192 ], [ 60, 1, 30, 192 ], [ 60, 1, 43, 192 ], [ 61, 1, 14, 64 ], [ 61, 1, 15, 192 ], [ 62, 1, 36, 192 ], [ 62, 1, 37, 96 ], [ 62, 1, 39, 192 ], [ 62, 1, 44, 192 ], [ 63, 1, 22, 192 ], [ 63, 1, 25, 192 ], [ 64, 1, 42, 384 ], [ 64, 1, 56, 192 ], [ 65, 1, 41, 384 ] ] k = 49: F-action on Pi is () [66,1,49] Dynkin type is A_1(q) + T(phi1^4 phi2 phi4) Order of center |Z^F|: phi1^4 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 2 modulo 60: 1/384 q^2 ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 ) q congruent 3 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 4 modulo 60: 1/384 q^2 ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 ) q congruent 5 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 7 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 8 modulo 60: 1/384 q^2 ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 ) q congruent 9 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 11 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 13 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 16 modulo 60: 1/384 q^2 ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 ) q congruent 17 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 19 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 21 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 23 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 25 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 27 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 29 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 31 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 32 modulo 60: 1/384 q^2 ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 ) q congruent 37 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 41 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 43 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 47 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 49 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 53 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) q congruent 59 modulo 60: 1/384 phi1 phi2 ( q^5-16*q^4+85*q^3-143*q^2-110*q+375 ) Fusion of maximal tori of C^F in those of G^F: [ 70, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 20 ], [ 4, 1, 1, 34 ], [ 4, 1, 2, 14 ], [ 5, 1, 1, 32 ], [ 6, 1, 1, 40 ], [ 7, 1, 1, 28 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 14 ], [ 11, 1, 1, 36 ], [ 12, 1, 1, 68 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 36 ], [ 13, 1, 4, 16 ], [ 14, 1, 1, 64 ], [ 15, 1, 1, 64 ], [ 16, 1, 1, 40 ], [ 16, 1, 2, 88 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 72 ], [ 20, 1, 1, 56 ], [ 20, 1, 3, 72 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 64 ], [ 23, 1, 1, 30 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 50 ], [ 25, 1, 1, 84 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 84 ], [ 28, 1, 3, 28 ], [ 29, 1, 1, 96 ], [ 30, 1, 1, 96 ], [ 30, 1, 2, 32 ], [ 31, 1, 1, 64 ], [ 33, 1, 2, 80 ], [ 33, 1, 4, 192 ], [ 34, 1, 1, 96 ], [ 35, 1, 1, 72 ], [ 35, 1, 2, 56 ], [ 35, 1, 5, 120 ], [ 35, 1, 6, 72 ], [ 36, 1, 1, 96 ], [ 37, 1, 1, 96 ], [ 37, 1, 2, 48 ], [ 39, 1, 1, 72 ], [ 39, 1, 2, 12 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 144 ], [ 40, 1, 3, 40 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 24 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 5, 24 ], [ 41, 1, 8, 32 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 43, 1, 3, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 9, 32 ], [ 44, 1, 1, 48 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 24 ], [ 44, 1, 9, 48 ], [ 45, 1, 1, 96 ], [ 47, 1, 3, 128 ], [ 48, 1, 1, 96 ], [ 48, 1, 4, 96 ], [ 48, 1, 7, 96 ], [ 48, 1, 8, 96 ], [ 49, 1, 2, 144 ], [ 49, 1, 7, 144 ], [ 49, 1, 11, 192 ], [ 50, 1, 1, 96 ], [ 51, 1, 1, 96 ], [ 51, 1, 6, 96 ], [ 51, 1, 7, 80 ], [ 52, 1, 1, 144 ], [ 52, 1, 3, 72 ], [ 52, 1, 8, 56 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 96 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 96 ], [ 53, 1, 10, 96 ], [ 53, 1, 11, 64 ], [ 53, 1, 13, 96 ], [ 54, 1, 4, 64 ], [ 55, 1, 4, 160 ], [ 55, 1, 6, 192 ], [ 55, 1, 9, 192 ], [ 56, 1, 1, 96 ], [ 56, 1, 4, 112 ], [ 56, 1, 11, 144 ], [ 56, 1, 14, 96 ], [ 57, 1, 3, 192 ], [ 57, 1, 11, 192 ], [ 59, 1, 16, 48 ], [ 59, 1, 17, 96 ], [ 59, 1, 23, 96 ], [ 60, 1, 28, 192 ], [ 60, 1, 31, 192 ], [ 60, 1, 44, 192 ], [ 61, 1, 13, 256 ], [ 62, 1, 33, 192 ], [ 62, 1, 37, 288 ], [ 62, 1, 47, 192 ], [ 63, 1, 23, 192 ], [ 63, 1, 24, 192 ], [ 63, 1, 31, 192 ], [ 64, 1, 43, 384 ], [ 64, 1, 54, 384 ], [ 65, 1, 40, 384 ] ] k = 50: F-action on Pi is () [66,1,50] Dynkin type is A_1(q) + T(phi1^3 phi2^2 phi4) Order of center |Z^F|: phi1^3 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 2 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 3 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 4 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 5 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 7 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 8 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 9 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 11 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 13 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 16 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 17 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 19 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 21 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 23 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 25 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 27 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 29 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 31 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 32 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 37 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 41 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 43 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 47 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 49 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 53 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 59 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 14 ], [ 6, 1, 1, 16 ], [ 6, 1, 2, 24 ], [ 7, 1, 1, 24 ], [ 7, 1, 2, 12 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 24 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 36 ], [ 13, 1, 4, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 24 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 32 ], [ 17, 1, 3, 96 ], [ 19, 1, 1, 48 ], [ 19, 1, 2, 24 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 24 ], [ 20, 1, 8, 96 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 48 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 36 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 36 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 12 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 4 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 48 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 96 ], [ 33, 1, 2, 32 ], [ 33, 1, 6, 48 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 2, 48 ], [ 35, 1, 3, 24 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 48 ], [ 35, 1, 7, 72 ], [ 35, 1, 8, 24 ], [ 38, 1, 7, 192 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 12 ], [ 39, 1, 4, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 24 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 24 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 5, 24 ], [ 41, 1, 6, 48 ], [ 41, 1, 8, 32 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 43, 1, 3, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 9, 32 ], [ 44, 1, 1, 48 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 24 ], [ 44, 1, 9, 48 ], [ 46, 1, 7, 192 ], [ 47, 1, 4, 32 ], [ 47, 1, 9, 96 ], [ 48, 1, 2, 48 ], [ 48, 1, 5, 48 ], [ 49, 1, 2, 96 ], [ 49, 1, 4, 48 ], [ 49, 1, 7, 96 ], [ 49, 1, 8, 48 ], [ 49, 1, 20, 192 ], [ 50, 1, 4, 96 ], [ 51, 1, 4, 16 ], [ 51, 1, 7, 32 ], [ 51, 1, 10, 96 ], [ 52, 1, 2, 48 ], [ 52, 1, 3, 48 ], [ 52, 1, 4, 24 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 48 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 96 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 96 ], [ 53, 1, 10, 96 ], [ 53, 1, 11, 64 ], [ 53, 1, 13, 96 ], [ 55, 1, 4, 64 ], [ 55, 1, 11, 96 ], [ 55, 1, 16, 192 ], [ 56, 1, 4, 96 ], [ 56, 1, 6, 96 ], [ 56, 1, 9, 16 ], [ 56, 1, 11, 96 ], [ 56, 1, 16, 48 ], [ 56, 1, 19, 96 ], [ 57, 1, 4, 96 ], [ 57, 1, 7, 96 ], [ 58, 1, 5, 64 ], [ 59, 1, 16, 48 ], [ 59, 1, 17, 96 ], [ 59, 1, 23, 96 ], [ 60, 1, 28, 192 ], [ 60, 1, 31, 192 ], [ 60, 1, 44, 192 ], [ 61, 1, 14, 192 ], [ 61, 1, 15, 64 ], [ 62, 1, 34, 192 ], [ 62, 1, 37, 192 ], [ 62, 1, 39, 96 ], [ 62, 1, 45, 192 ], [ 63, 1, 23, 192 ], [ 63, 1, 24, 192 ], [ 64, 1, 43, 384 ], [ 64, 1, 56, 192 ], [ 65, 1, 43, 384 ] ] k = 51: F-action on Pi is () [66,1,51] Dynkin type is A_1(q) + T(phi1 phi2^4 phi4) Order of center |Z^F|: phi1 phi2^4 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 2 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 3 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 4 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 5 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 7 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 8 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 9 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 11 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 13 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 16 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 17 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 19 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 21 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 23 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 25 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 27 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 29 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 31 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 32 modulo 60: 1/384 q^4 ( q^3-10*q^2+32*q-32 ) q congruent 37 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 41 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 43 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 47 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 49 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 53 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) q congruent 59 modulo 60: 1/384 phi1^2 phi2 ( q^4-9*q^3+24*q^2-17*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 20 ], [ 4, 1, 1, 14 ], [ 4, 1, 2, 34 ], [ 5, 1, 2, 32 ], [ 6, 1, 2, 40 ], [ 7, 1, 2, 28 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 14 ], [ 11, 1, 2, 36 ], [ 12, 1, 2, 68 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 36 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 64 ], [ 15, 1, 2, 64 ], [ 16, 1, 3, 40 ], [ 16, 1, 4, 88 ], [ 18, 1, 2, 64 ], [ 19, 1, 2, 72 ], [ 20, 1, 2, 72 ], [ 20, 1, 4, 56 ], [ 21, 1, 2, 48 ], [ 22, 1, 4, 64 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 30 ], [ 24, 1, 2, 50 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 84 ], [ 25, 1, 4, 48 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 28 ], [ 28, 1, 4, 84 ], [ 29, 1, 4, 96 ], [ 30, 1, 3, 96 ], [ 30, 1, 4, 32 ], [ 31, 1, 4, 64 ], [ 33, 1, 6, 80 ], [ 33, 1, 10, 192 ], [ 34, 1, 4, 96 ], [ 35, 1, 3, 72 ], [ 35, 1, 4, 120 ], [ 35, 1, 7, 56 ], [ 35, 1, 8, 72 ], [ 36, 1, 4, 96 ], [ 37, 1, 2, 48 ], [ 37, 1, 3, 96 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 72 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 40 ], [ 40, 1, 6, 144 ], [ 41, 1, 2, 24 ], [ 41, 1, 4, 48 ], [ 41, 1, 5, 24 ], [ 41, 1, 8, 32 ], [ 41, 1, 9, 144 ], [ 41, 1, 10, 96 ], [ 42, 1, 6, 96 ], [ 43, 1, 8, 48 ], [ 43, 1, 9, 32 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 4, 24 ], [ 44, 1, 5, 48 ], [ 44, 1, 6, 8 ], [ 44, 1, 10, 48 ], [ 45, 1, 6, 96 ], [ 47, 1, 10, 128 ], [ 48, 1, 3, 96 ], [ 48, 1, 6, 96 ], [ 48, 1, 9, 96 ], [ 48, 1, 10, 96 ], [ 49, 1, 4, 144 ], [ 49, 1, 8, 144 ], [ 49, 1, 19, 192 ], [ 50, 1, 12, 96 ], [ 51, 1, 3, 96 ], [ 51, 1, 4, 80 ], [ 51, 1, 9, 96 ], [ 52, 1, 4, 72 ], [ 52, 1, 5, 56 ], [ 52, 1, 10, 144 ], [ 53, 1, 9, 96 ], [ 53, 1, 11, 96 ], [ 53, 1, 12, 96 ], [ 53, 1, 13, 64 ], [ 53, 1, 14, 96 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 96 ], [ 54, 1, 9, 64 ], [ 55, 1, 11, 160 ], [ 55, 1, 19, 192 ], [ 55, 1, 20, 192 ], [ 56, 1, 9, 144 ], [ 56, 1, 10, 96 ], [ 56, 1, 16, 112 ], [ 56, 1, 20, 96 ], [ 57, 1, 8, 192 ], [ 57, 1, 9, 192 ], [ 59, 1, 16, 48 ], [ 59, 1, 18, 96 ], [ 59, 1, 24, 96 ], [ 60, 1, 28, 192 ], [ 60, 1, 30, 192 ], [ 60, 1, 43, 192 ], [ 61, 1, 16, 256 ], [ 62, 1, 35, 192 ], [ 62, 1, 39, 288 ], [ 62, 1, 48, 192 ], [ 63, 1, 22, 192 ], [ 63, 1, 25, 192 ], [ 63, 1, 30, 192 ], [ 64, 1, 42, 384 ], [ 64, 1, 55, 384 ], [ 65, 1, 42, 384 ] ] k = 52: F-action on Pi is () [66,1,52] Dynkin type is A_1(q) + T(phi1^3 phi2^2 phi4) Order of center |Z^F|: phi1^3 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 2 modulo 60: 1/64 q^3 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 3 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 4 modulo 60: 1/64 q^3 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 5 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 7 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 8 modulo 60: 1/64 q^3 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 9 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 11 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 13 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 16 modulo 60: 1/64 q^3 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 17 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 19 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 21 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 23 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 25 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 27 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 29 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 31 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 32 modulo 60: 1/64 q^3 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 37 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 41 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 43 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 47 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 49 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 53 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) q congruent 59 modulo 60: 1/64 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-14*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 8 ], [ 7, 1, 2, 4 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 8 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 16 ], [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 19, 1, 2, 8 ], [ 20, 1, 1, 16 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 8 ], [ 20, 1, 6, 16 ], [ 21, 1, 1, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 8 ], [ 28, 1, 2, 12 ], [ 28, 1, 3, 8 ], [ 28, 1, 4, 4 ], [ 29, 1, 2, 16 ], [ 30, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 16 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 32, 1, 2, 16 ], [ 32, 1, 4, 16 ], [ 33, 1, 2, 32 ], [ 33, 1, 5, 32 ], [ 33, 1, 6, 16 ], [ 34, 1, 1, 16 ], [ 34, 1, 2, 8 ], [ 34, 1, 3, 8 ], [ 35, 1, 1, 16 ], [ 35, 1, 2, 16 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 16 ], [ 35, 1, 6, 16 ], [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 36, 1, 2, 16 ], [ 37, 1, 1, 16 ], [ 37, 1, 2, 8 ], [ 38, 1, 2, 32 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 16 ], [ 41, 1, 8, 16 ], [ 42, 1, 2, 16 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 44, 1, 8, 8 ], [ 45, 1, 2, 16 ], [ 46, 1, 11, 32 ], [ 47, 1, 3, 32 ], [ 47, 1, 4, 16 ], [ 47, 1, 9, 16 ], [ 48, 1, 1, 16 ], [ 48, 1, 2, 8 ], [ 48, 1, 4, 16 ], [ 48, 1, 5, 8 ], [ 48, 1, 7, 16 ], [ 48, 1, 8, 16 ], [ 49, 1, 2, 32 ], [ 49, 1, 4, 16 ], [ 49, 1, 7, 32 ], [ 49, 1, 8, 16 ], [ 49, 1, 12, 32 ], [ 49, 1, 18, 32 ], [ 50, 1, 2, 16 ], [ 50, 1, 8, 16 ], [ 51, 1, 2, 16 ], [ 51, 1, 4, 16 ], [ 51, 1, 7, 32 ], [ 52, 1, 2, 16 ], [ 52, 1, 3, 16 ], [ 52, 1, 4, 8 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 16 ], [ 53, 1, 3, 16 ], [ 53, 1, 4, 16 ], [ 53, 1, 7, 16 ], [ 53, 1, 8, 16 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 54, 1, 4, 32 ], [ 55, 1, 4, 64 ], [ 55, 1, 8, 32 ], [ 55, 1, 11, 32 ], [ 56, 1, 2, 16 ], [ 56, 1, 4, 32 ], [ 56, 1, 9, 16 ], [ 56, 1, 11, 32 ], [ 56, 1, 13, 16 ], [ 56, 1, 16, 16 ], [ 57, 1, 3, 32 ], [ 57, 1, 4, 16 ], [ 57, 1, 7, 16 ], [ 57, 1, 11, 32 ], [ 58, 1, 5, 32 ], [ 59, 1, 16, 16 ], [ 59, 1, 21, 16 ], [ 59, 1, 22, 16 ], [ 60, 1, 28, 64 ], [ 60, 1, 33, 32 ], [ 60, 1, 45, 32 ], [ 61, 1, 13, 64 ], [ 61, 1, 14, 32 ], [ 61, 1, 15, 32 ], [ 62, 1, 37, 64 ], [ 62, 1, 39, 32 ], [ 62, 1, 40, 32 ], [ 62, 1, 50, 32 ], [ 63, 1, 26, 32 ], [ 63, 1, 27, 32 ], [ 63, 1, 31, 32 ], [ 64, 1, 46, 64 ], [ 64, 1, 54, 64 ], [ 64, 1, 56, 32 ], [ 65, 1, 45, 64 ] ] k = 53: F-action on Pi is () [66,1,53] Dynkin type is A_1(q) + T(phi1^2 phi2^3 phi4) Order of center |Z^F|: phi1^2 phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 2 modulo 60: 1/64 q^5 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 4 modulo 60: 1/64 q^5 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 7 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 8 modulo 60: 1/64 q^5 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 11 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 13 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 16 modulo 60: 1/64 q^5 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 19 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 21 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 23 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 25 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 27 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 29 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 31 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 32 modulo 60: 1/64 q^5 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 41 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 43 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 47 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 49 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 53 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) q congruent 59 modulo 60: 1/64 phi1^2 phi2 ( q^4-3*q^3+2*q^2-q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 76, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 10 ], [ 5, 1, 2, 16 ], [ 6, 1, 1, 8 ], [ 6, 1, 2, 16 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 1, 8 ], [ 19, 1, 2, 16 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 16 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 16 ], [ 20, 1, 7, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 8 ], [ 22, 1, 4, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 8 ], [ 29, 1, 3, 16 ], [ 30, 1, 3, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 31, 1, 4, 16 ], [ 32, 1, 2, 16 ], [ 32, 1, 4, 16 ], [ 33, 1, 2, 16 ], [ 33, 1, 6, 32 ], [ 33, 1, 9, 32 ], [ 34, 1, 2, 8 ], [ 34, 1, 3, 8 ], [ 34, 1, 4, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 16 ], [ 36, 1, 3, 16 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 16 ], [ 38, 1, 10, 32 ], [ 39, 1, 2, 4 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 16 ], [ 40, 1, 3, 8 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 7, 16 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 2, 16 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], [ 44, 1, 8, 8 ], [ 45, 1, 5, 16 ], [ 46, 1, 8, 32 ], [ 47, 1, 4, 16 ], [ 47, 1, 9, 16 ], [ 47, 1, 10, 32 ], [ 48, 1, 2, 8 ], [ 48, 1, 3, 16 ], [ 48, 1, 5, 8 ], [ 48, 1, 6, 16 ], [ 48, 1, 9, 16 ], [ 48, 1, 10, 16 ], [ 49, 1, 2, 16 ], [ 49, 1, 4, 32 ], [ 49, 1, 7, 16 ], [ 49, 1, 8, 32 ], [ 49, 1, 15, 32 ], [ 49, 1, 16, 32 ], [ 50, 1, 5, 16 ], [ 50, 1, 11, 16 ], [ 51, 1, 4, 32 ], [ 51, 1, 7, 16 ], [ 51, 1, 8, 16 ], [ 52, 1, 3, 8 ], [ 52, 1, 4, 16 ], [ 52, 1, 5, 16 ], [ 52, 1, 8, 8 ], [ 52, 1, 9, 16 ], [ 53, 1, 3, 16 ], [ 53, 1, 4, 16 ], [ 53, 1, 7, 16 ], [ 53, 1, 8, 16 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 54, 1, 9, 32 ], [ 55, 1, 4, 32 ], [ 55, 1, 11, 64 ], [ 55, 1, 17, 32 ], [ 56, 1, 4, 16 ], [ 56, 1, 7, 16 ], [ 56, 1, 9, 32 ], [ 56, 1, 11, 16 ], [ 56, 1, 16, 32 ], [ 56, 1, 18, 16 ], [ 57, 1, 4, 16 ], [ 57, 1, 7, 16 ], [ 57, 1, 8, 32 ], [ 57, 1, 9, 32 ], [ 58, 1, 5, 32 ], [ 59, 1, 16, 16 ], [ 59, 1, 21, 16 ], [ 59, 1, 22, 16 ], [ 60, 1, 28, 64 ], [ 60, 1, 33, 32 ], [ 60, 1, 45, 32 ], [ 61, 1, 14, 32 ], [ 61, 1, 15, 32 ], [ 61, 1, 16, 64 ], [ 62, 1, 37, 32 ], [ 62, 1, 38, 32 ], [ 62, 1, 39, 64 ], [ 62, 1, 49, 32 ], [ 63, 1, 26, 32 ], [ 63, 1, 27, 32 ], [ 63, 1, 30, 32 ], [ 64, 1, 46, 64 ], [ 64, 1, 55, 64 ], [ 64, 1, 56, 32 ], [ 65, 1, 44, 64 ] ] k = 54: F-action on Pi is () [66,1,54] Dynkin type is A_1(q) + T(phi1 phi2^6) Order of center |Z^F|: phi1 phi2^6 Numbers of classes in class type: q congruent 1 modulo 60: 1/46080 phi1 ( q^6-41*q^5+659*q^4-5296*q^3+22833*q^2-53655*q+60075 ) q congruent 2 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5880*q^4+25984*q^3-57728*q^2+58880*q-20480 \ ) q congruent 3 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-76488*q^2+120210*q-91035\ ) q congruent 4 modulo 60: 1/46080 q ( q^6-42*q^5+700*q^4-5880*q^3+25984*q^2-56448*q+46080 ) q congruent 5 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-77768*q^2+126530*q-92075\ ) q congruent 7 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-76488*q^2+120210*q-91035\ ) q congruent 8 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5880*q^4+25984*q^3-57728*q^2+58880*q-20480 \ ) q congruent 9 modulo 60: 1/46080 phi1 ( q^6-41*q^5+659*q^4-5296*q^3+22833*q^2-53655*q+60075 ) q congruent 11 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-77768*q^2+133010*q-12303\ 5 ) q congruent 13 modulo 60: 1/46080 phi1 ( q^6-41*q^5+659*q^4-5296*q^3+22833*q^2-53655*q+60075 ) q congruent 16 modulo 60: 1/46080 q ( q^6-42*q^5+700*q^4-5880*q^3+25984*q^2-56448*q+46080 ) q congruent 17 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-77768*q^2+126530*q-92075\ ) q congruent 19 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-76488*q^2+120210*q-91035\ ) q congruent 21 modulo 60: 1/46080 phi1 ( q^6-41*q^5+659*q^4-5296*q^3+22833*q^2-53655*q+60075 ) q congruent 23 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-77768*q^2+133010*q-12303\ 5 ) q congruent 25 modulo 60: 1/46080 phi1 ( q^6-41*q^5+659*q^4-5296*q^3+22833*q^2-53655*q+60075 ) q congruent 27 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-76488*q^2+120210*q-91035\ ) q congruent 29 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-77768*q^2+126530*q-92075\ ) q congruent 31 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-76488*q^2+120210*q-91035\ ) q congruent 32 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5880*q^4+25984*q^3-57728*q^2+58880*q-20480 \ ) q congruent 37 modulo 60: 1/46080 phi1 ( q^6-41*q^5+659*q^4-5296*q^3+22833*q^2-53655*q+60075 ) q congruent 41 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-77768*q^2+126530*q-92075\ ) q congruent 43 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-76488*q^2+120210*q-91035\ ) q congruent 47 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-77768*q^2+133010*q-12303\ 5 ) q congruent 49 modulo 60: 1/46080 phi1 ( q^6-41*q^5+659*q^4-5296*q^3+22833*q^2-53655*q+60075 ) q congruent 53 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-77768*q^2+126530*q-92075\ ) q congruent 59 modulo 60: 1/46080 ( q^7-42*q^6+700*q^5-5955*q^4+28129*q^3-77768*q^2+133010*q-12303\ 5 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 67 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 32 ], [ 3, 1, 2, 224 ], [ 4, 1, 2, 772 ], [ 5, 1, 2, 1664 ], [ 6, 1, 2, 2304 ], [ 7, 1, 2, 544 ], [ 8, 1, 2, 192 ], [ 9, 1, 1, 31 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 60 ], [ 11, 1, 2, 544 ], [ 12, 1, 2, 2080 ], [ 13, 1, 4, 2664 ], [ 14, 1, 2, 4992 ], [ 15, 1, 2, 7424 ], [ 16, 1, 3, 12800 ], [ 17, 1, 4, 15360 ], [ 18, 1, 2, 2304 ], [ 19, 1, 2, 4864 ], [ 20, 1, 3, 1040 ], [ 20, 1, 4, 8640 ], [ 21, 1, 2, 960 ], [ 22, 1, 3, 384 ], [ 22, 1, 4, 3840 ], [ 23, 1, 2, 252 ], [ 24, 1, 1, 62 ], [ 24, 1, 2, 900 ], [ 25, 1, 3, 3720 ], [ 26, 1, 2, 64 ], [ 26, 1, 4, 960 ], [ 27, 1, 3, 64 ], [ 27, 1, 6, 960 ], [ 28, 1, 3, 504 ], [ 28, 1, 4, 4320 ], [ 29, 1, 3, 1664 ], [ 29, 1, 4, 11520 ], [ 30, 1, 3, 13824 ], [ 31, 1, 3, 3200 ], [ 31, 1, 4, 19200 ], [ 32, 1, 3, 28160 ], [ 33, 1, 8, 34560 ], [ 34, 1, 3, 1024 ], [ 34, 1, 4, 7680 ], [ 35, 1, 6, 4320 ], [ 35, 1, 8, 23040 ], [ 36, 1, 3, 384 ], [ 36, 1, 4, 3840 ], [ 37, 1, 3, 13440 ], [ 38, 1, 8, 3840 ], [ 38, 1, 12, 23040 ], [ 39, 1, 3, 1560 ], [ 39, 1, 4, 120 ], [ 40, 1, 6, 8640 ], [ 41, 1, 6, 1680 ], [ 41, 1, 9, 10320 ], [ 42, 1, 2, 1024 ], [ 42, 1, 6, 7680 ], [ 43, 1, 4, 1920 ], [ 43, 1, 13, 13440 ], [ 44, 1, 8, 960 ], [ 44, 1, 10, 6720 ], [ 45, 1, 5, 4224 ], [ 45, 1, 6, 19200 ], [ 46, 1, 5, 8960 ], [ 46, 1, 6, 38400 ], [ 47, 1, 7, 11520 ], [ 47, 1, 8, 46080 ], [ 48, 1, 5, 7680 ], [ 48, 1, 6, 30720 ], [ 49, 1, 5, 14400 ], [ 49, 1, 10, 57600 ], [ 50, 1, 9, 1920 ], [ 50, 1, 11, 1920 ], [ 50, 1, 12, 11520 ], [ 51, 1, 8, 5760 ], [ 51, 1, 9, 26880 ], [ 52, 1, 9, 3120 ], [ 52, 1, 10, 14400 ], [ 53, 1, 8, 7680 ], [ 53, 1, 20, 30720 ], [ 54, 1, 12, 7680 ], [ 54, 1, 14, 23040 ], [ 55, 1, 13, 19200 ], [ 55, 1, 15, 53760 ], [ 56, 1, 15, 13440 ], [ 56, 1, 18, 13440 ], [ 56, 1, 20, 34560 ], [ 57, 1, 6, 23040 ], [ 57, 1, 10, 69120 ], [ 58, 1, 12, 15360 ], [ 58, 1, 15, 46080 ], [ 59, 1, 2, 17280 ], [ 59, 1, 13, 5760 ], [ 60, 1, 17, 69120 ], [ 60, 1, 41, 23040 ], [ 61, 1, 20, 30720 ], [ 61, 1, 21, 46080 ], [ 62, 1, 24, 34560 ], [ 62, 1, 29, 69120 ], [ 62, 1, 43, 34560 ], [ 63, 1, 19, 23040 ], [ 63, 1, 36, 23040 ], [ 64, 1, 47, 46080 ], [ 64, 1, 52, 46080 ], [ 65, 1, 49, 46080 ] ] k = 55: F-action on Pi is () [66,1,55] Dynkin type is A_1(q) + T(phi1^2 phi2^5) Order of center |Z^F|: phi1^2 phi2^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 2 modulo 60: 1/3072 q^2 ( q^5-20*q^4+152*q^3-544*q^2+912*q-576 ) q congruent 3 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) q congruent 4 modulo 60: 1/3072 q^2 ( q^5-20*q^4+152*q^3-544*q^2+912*q-576 ) q congruent 5 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 7 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) q congruent 8 modulo 60: 1/3072 q^2 ( q^5-20*q^4+152*q^3-544*q^2+912*q-576 ) q congruent 9 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 11 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) q congruent 13 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 16 modulo 60: 1/3072 q^2 ( q^5-20*q^4+152*q^3-544*q^2+912*q-576 ) q congruent 17 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 19 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) q congruent 21 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 23 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) q congruent 25 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 27 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) q congruent 29 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 31 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) q congruent 32 modulo 60: 1/3072 q^2 ( q^5-20*q^4+152*q^3-544*q^2+912*q-576 ) q congruent 37 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 41 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 43 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) q congruent 47 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) q congruent 49 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 53 modulo 60: 1/3072 phi1^2 ( q^5-18*q^4+115*q^3-307*q^2+336*q-255 ) q congruent 59 modulo 60: 1/3072 ( q^7-20*q^6+152*q^5-555*q^4+1065*q^3-1234*q^2+702*q+657 ) Fusion of maximal tori of C^F in those of G^F: [ 69, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 80 ], [ 4, 1, 1, 28 ], [ 4, 1, 2, 216 ], [ 5, 1, 2, 384 ], [ 6, 1, 2, 512 ], [ 7, 1, 2, 144 ], [ 8, 1, 2, 64 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 26 ], [ 11, 1, 2, 144 ], [ 12, 1, 2, 432 ], [ 13, 1, 1, 56 ], [ 13, 1, 2, 96 ], [ 13, 1, 3, 32 ], [ 13, 1, 4, 528 ], [ 14, 1, 2, 768 ], [ 15, 1, 2, 1152 ], [ 16, 1, 3, 1920 ], [ 16, 1, 4, 320 ], [ 17, 1, 4, 2304 ], [ 18, 1, 2, 384 ], [ 19, 1, 2, 768 ], [ 20, 1, 2, 240 ], [ 20, 1, 3, 576 ], [ 20, 1, 4, 1248 ], [ 21, 1, 2, 192 ], [ 22, 1, 3, 256 ], [ 22, 1, 4, 640 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 72 ], [ 24, 1, 1, 60 ], [ 24, 1, 2, 198 ], [ 25, 1, 1, 56 ], [ 25, 1, 2, 64 ], [ 25, 1, 3, 624 ], [ 25, 1, 4, 128 ], [ 26, 1, 2, 64 ], [ 26, 1, 4, 192 ], [ 27, 1, 3, 64 ], [ 27, 1, 6, 192 ], [ 28, 1, 2, 104 ], [ 28, 1, 3, 288 ], [ 28, 1, 4, 624 ], [ 29, 1, 3, 768 ], [ 29, 1, 4, 1152 ], [ 30, 1, 3, 1536 ], [ 30, 1, 4, 256 ], [ 31, 1, 3, 1280 ], [ 31, 1, 4, 1920 ], [ 32, 1, 3, 3072 ], [ 33, 1, 6, 640 ], [ 33, 1, 8, 4224 ], [ 33, 1, 10, 768 ], [ 34, 1, 3, 512 ], [ 34, 1, 4, 768 ], [ 35, 1, 3, 480 ], [ 35, 1, 4, 576 ], [ 35, 1, 6, 1536 ], [ 35, 1, 7, 448 ], [ 35, 1, 8, 2688 ], [ 36, 1, 3, 256 ], [ 36, 1, 4, 384 ], [ 37, 1, 2, 256 ], [ 37, 1, 3, 1152 ], [ 38, 1, 8, 1536 ], [ 38, 1, 12, 2304 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 32 ], [ 39, 1, 3, 240 ], [ 39, 1, 4, 104 ], [ 40, 1, 2, 192 ], [ 40, 1, 6, 1056 ], [ 41, 1, 1, 112 ], [ 41, 1, 2, 192 ], [ 41, 1, 4, 256 ], [ 41, 1, 6, 688 ], [ 41, 1, 9, 1440 ], [ 41, 1, 10, 384 ], [ 42, 1, 2, 512 ], [ 42, 1, 6, 768 ], [ 43, 1, 3, 128 ], [ 43, 1, 4, 896 ], [ 43, 1, 8, 256 ], [ 43, 1, 12, 384 ], [ 43, 1, 13, 1152 ], [ 44, 1, 5, 192 ], [ 44, 1, 8, 448 ], [ 44, 1, 9, 64 ], [ 44, 1, 10, 576 ], [ 45, 1, 5, 1280 ], [ 45, 1, 6, 1152 ], [ 46, 1, 5, 2560 ], [ 46, 1, 6, 2304 ], [ 47, 1, 7, 3072 ], [ 47, 1, 8, 3840 ], [ 47, 1, 10, 1024 ], [ 48, 1, 3, 768 ], [ 48, 1, 4, 512 ], [ 48, 1, 5, 2048 ], [ 48, 1, 6, 2304 ], [ 48, 1, 10, 768 ], [ 49, 1, 5, 3840 ], [ 49, 1, 8, 1152 ], [ 49, 1, 9, 960 ], [ 49, 1, 10, 5760 ], [ 49, 1, 19, 768 ], [ 50, 1, 8, 128 ], [ 50, 1, 9, 768 ], [ 50, 1, 11, 768 ], [ 50, 1, 12, 384 ], [ 51, 1, 3, 640 ], [ 51, 1, 8, 1792 ], [ 51, 1, 9, 1152 ], [ 51, 1, 10, 384 ], [ 52, 1, 2, 208 ], [ 52, 1, 4, 448 ], [ 52, 1, 9, 960 ], [ 52, 1, 10, 1440 ], [ 53, 1, 6, 512 ], [ 53, 1, 8, 2048 ], [ 53, 1, 9, 768 ], [ 53, 1, 12, 768 ], [ 53, 1, 19, 768 ], [ 53, 1, 20, 2304 ], [ 54, 1, 12, 1536 ], [ 54, 1, 13, 512 ], [ 55, 1, 13, 3584 ], [ 55, 1, 14, 1280 ], [ 55, 1, 15, 2304 ], [ 55, 1, 20, 1536 ], [ 56, 1, 10, 1152 ], [ 56, 1, 13, 896 ], [ 56, 1, 15, 2304 ], [ 56, 1, 18, 2304 ], [ 56, 1, 19, 896 ], [ 56, 1, 20, 1152 ], [ 57, 1, 5, 1536 ], [ 57, 1, 6, 4608 ], [ 57, 1, 9, 1536 ], [ 57, 1, 10, 4608 ], [ 58, 1, 11, 1024 ], [ 58, 1, 12, 3072 ], [ 59, 1, 2, 1152 ], [ 59, 1, 3, 384 ], [ 59, 1, 13, 1152 ], [ 59, 1, 18, 768 ], [ 60, 1, 17, 4608 ], [ 60, 1, 27, 1536 ], [ 60, 1, 41, 4608 ], [ 60, 1, 43, 1536 ], [ 61, 1, 18, 2048 ], [ 61, 1, 20, 3072 ], [ 62, 1, 24, 4608 ], [ 62, 1, 29, 2304 ], [ 62, 1, 31, 2304 ], [ 62, 1, 42, 2304 ], [ 62, 1, 43, 4608 ], [ 62, 1, 48, 1536 ], [ 63, 1, 14, 1536 ], [ 63, 1, 28, 1536 ], [ 63, 1, 34, 1536 ], [ 63, 1, 36, 1536 ], [ 64, 1, 27, 3072 ], [ 64, 1, 52, 3072 ], [ 64, 1, 58, 3072 ], [ 65, 1, 46, 3072 ] ] k = 56: F-action on Pi is () [66,1,56] Dynkin type is A_1(q) + T(phi1^4 phi2^3) Order of center |Z^F|: phi1^4 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/9216 phi1 ( q^6-19*q^5+117*q^4-198*q^3-365*q^2+945*q+287 ) q congruent 2 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-320*q^4-48*q^3+320*q^2+2048*q-3072 ) q congruent 3 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1310*q^2-1890*q+3249 ) q congruent 4 modulo 60: 1/9216 q ( q^6-20*q^5+136*q^4-320*q^3-48*q^2+576*q+512 ) q congruent 5 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1054*q^2+878*q-3615 ) q congruent 7 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1310*q^2-1378*q+2737 ) q congruent 8 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-320*q^4-48*q^3+320*q^2+2048*q-3072 ) q congruent 9 modulo 60: 1/9216 phi1 ( q^6-19*q^5+117*q^4-198*q^3-365*q^2+945*q-225 ) q congruent 11 modulo 60: 1/9216 phi2 ( q^6-21*q^5+157*q^4-472*q^3+305*q^2+749*q-591 ) q congruent 13 modulo 60: 1/9216 phi1 ( q^6-19*q^5+117*q^4-198*q^3-365*q^2+945*q+287 ) q congruent 16 modulo 60: 1/9216 q ( q^6-20*q^5+136*q^4-320*q^3-48*q^2+576*q+512 ) q congruent 17 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1054*q^2+878*q-3615 ) q congruent 19 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1310*q^2-1378*q+2737 ) q congruent 21 modulo 60: 1/9216 phi1 ( q^6-19*q^5+117*q^4-198*q^3-365*q^2+945*q-225 ) q congruent 23 modulo 60: 1/9216 phi2 ( q^6-21*q^5+157*q^4-472*q^3+305*q^2+749*q-591 ) q congruent 25 modulo 60: 1/9216 phi1 ( q^6-19*q^5+117*q^4-198*q^3-365*q^2+945*q+287 ) q congruent 27 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1310*q^2-1890*q+3249 ) q congruent 29 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1054*q^2+878*q-3615 ) q congruent 31 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1310*q^2-1378*q+2737 ) q congruent 32 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-320*q^4-48*q^3+320*q^2+2048*q-3072 ) q congruent 37 modulo 60: 1/9216 phi1 ( q^6-19*q^5+117*q^4-198*q^3-365*q^2+945*q+287 ) q congruent 41 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1054*q^2+878*q-3615 ) q congruent 43 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1310*q^2-1378*q+2737 ) q congruent 47 modulo 60: 1/9216 phi2 ( q^6-21*q^5+157*q^4-472*q^3+305*q^2+749*q-591 ) q congruent 49 modulo 60: 1/9216 phi1 ( q^6-19*q^5+117*q^4-198*q^3-365*q^2+945*q+287 ) q congruent 53 modulo 60: 1/9216 ( q^7-20*q^6+136*q^5-315*q^4-167*q^3+1054*q^2+878*q-3615 ) q congruent 59 modulo 60: 1/9216 phi2 ( q^6-21*q^5+157*q^4-472*q^3+305*q^2+749*q-591 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 32 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 72 ], [ 4, 1, 2, 84 ], [ 6, 1, 1, 128 ], [ 6, 1, 2, 96 ], [ 7, 1, 1, 96 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 24 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 96 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 96 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 240 ], [ 13, 1, 2, 96 ], [ 13, 1, 3, 288 ], [ 13, 1, 4, 168 ], [ 16, 1, 1, 384 ], [ 16, 1, 2, 384 ], [ 16, 1, 3, 288 ], [ 16, 1, 4, 192 ], [ 17, 1, 2, 256 ], [ 17, 1, 3, 768 ], [ 19, 1, 1, 384 ], [ 19, 1, 2, 96 ], [ 20, 1, 1, 576 ], [ 20, 1, 2, 288 ], [ 20, 1, 3, 576 ], [ 20, 1, 4, 144 ], [ 20, 1, 8, 384 ], [ 22, 1, 2, 192 ], [ 22, 1, 3, 192 ], [ 23, 1, 1, 24 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 168 ], [ 24, 1, 2, 90 ], [ 25, 1, 1, 336 ], [ 25, 1, 2, 384 ], [ 25, 1, 3, 168 ], [ 25, 1, 4, 192 ], [ 26, 1, 1, 192 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 28, 1, 2, 144 ], [ 28, 1, 3, 288 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 576 ], [ 31, 1, 3, 576 ], [ 32, 1, 2, 768 ], [ 32, 1, 4, 768 ], [ 33, 1, 1, 768 ], [ 33, 1, 2, 768 ], [ 33, 1, 6, 1152 ], [ 33, 1, 8, 576 ], [ 34, 1, 2, 576 ], [ 34, 1, 3, 192 ], [ 35, 1, 1, 1152 ], [ 35, 1, 2, 1152 ], [ 35, 1, 3, 1152 ], [ 35, 1, 4, 192 ], [ 35, 1, 5, 1152 ], [ 35, 1, 6, 1152 ], [ 35, 1, 7, 576 ], [ 35, 1, 8, 288 ], [ 37, 1, 2, 192 ], [ 38, 1, 7, 1536 ], [ 39, 1, 1, 144 ], [ 39, 1, 2, 96 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 144 ], [ 40, 1, 1, 192 ], [ 40, 1, 2, 192 ], [ 40, 1, 3, 384 ], [ 40, 1, 6, 48 ], [ 41, 1, 1, 864 ], [ 41, 1, 2, 576 ], [ 41, 1, 3, 1152 ], [ 41, 1, 4, 768 ], [ 41, 1, 6, 864 ], [ 41, 1, 9, 336 ], [ 42, 1, 1, 768 ], [ 43, 1, 1, 1152 ], [ 43, 1, 3, 1152 ], [ 43, 1, 8, 768 ], [ 43, 1, 12, 384 ], [ 44, 1, 1, 576 ], [ 44, 1, 5, 192 ], [ 44, 1, 9, 576 ], [ 46, 1, 7, 1536 ], [ 47, 1, 2, 1152 ], [ 47, 1, 4, 768 ], [ 47, 1, 7, 1152 ], [ 47, 1, 9, 2304 ], [ 48, 1, 2, 1728 ], [ 48, 1, 3, 384 ], [ 48, 1, 4, 1152 ], [ 48, 1, 5, 576 ], [ 49, 1, 1, 2304 ], [ 49, 1, 2, 2304 ], [ 49, 1, 5, 2304 ], [ 49, 1, 8, 1152 ], [ 49, 1, 9, 3456 ], [ 49, 1, 10, 576 ], [ 49, 1, 20, 2304 ], [ 50, 1, 4, 1152 ], [ 51, 1, 3, 384 ], [ 51, 1, 5, 768 ], [ 51, 1, 6, 768 ], [ 51, 1, 10, 1152 ], [ 52, 1, 1, 576 ], [ 52, 1, 2, 864 ], [ 52, 1, 3, 1152 ], [ 52, 1, 4, 192 ], [ 52, 1, 9, 576 ], [ 52, 1, 10, 48 ], [ 53, 1, 1, 2304 ], [ 53, 1, 2, 2304 ], [ 53, 1, 5, 2304 ], [ 53, 1, 6, 2304 ], [ 53, 1, 9, 1536 ], [ 55, 1, 5, 1536 ], [ 55, 1, 14, 2304 ], [ 55, 1, 16, 4608 ], [ 56, 1, 5, 2304 ], [ 56, 1, 6, 3456 ], [ 56, 1, 10, 384 ], [ 56, 1, 14, 2304 ], [ 56, 1, 19, 1152 ], [ 57, 1, 2, 3456 ], [ 57, 1, 4, 2304 ], [ 57, 1, 5, 2304 ], [ 57, 1, 6, 1152 ], [ 58, 1, 4, 1536 ], [ 59, 1, 1, 1152 ], [ 59, 1, 3, 1152 ], [ 59, 1, 17, 2304 ], [ 60, 1, 1, 4608 ], [ 60, 1, 27, 4608 ], [ 60, 1, 44, 4608 ], [ 61, 1, 17, 1536 ], [ 61, 1, 22, 4608 ], [ 62, 1, 30, 6912 ], [ 62, 1, 31, 2304 ], [ 62, 1, 32, 4608 ], [ 62, 1, 45, 4608 ], [ 63, 1, 20, 4608 ], [ 63, 1, 21, 4608 ], [ 64, 1, 37, 9216 ], [ 64, 1, 64, 4608 ], [ 65, 1, 37, 9216 ] ] k = 57: F-action on Pi is () [66,1,57] Dynkin type is A_1(q) + T(phi2^7) Order of center |Z^F|: phi2^7 Numbers of classes in class type: q congruent 1 modulo 60: 1/2903040 phi1 ( q^6-83*q^5+2773*q^4-47718*q^3+449667*q^2-2262735*q+5049\ 135 ) q congruent 2 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50176*q^4+478800*q^3-2369472*q^2+5332480\ *q-4300800 ) q congruent 3 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2712402*q^2+7538670\ *q-8178975 ) q congruent 4 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50176*q^4+478800*q^3-2342592*q^2+4561920\ *q-1161216 ) q congruent 5 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2739282*q^2+8082430\ *q-10236975 ) q congruent 7 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2712402*q^2+7538670\ *q-8178975 ) q congruent 8 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50176*q^4+478800*q^3-2369472*q^2+5332480\ *q-4300800 ) q congruent 9 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2712402*q^2+7311870\ *q-6210351 ) q congruent 11 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2739282*q^2+8309230\ *q-13366815 ) q congruent 13 modulo 60: 1/2903040 phi1 ( q^6-83*q^5+2773*q^4-47718*q^3+449667*q^2-2262735*q+5049\ 135 ) q congruent 16 modulo 60: 1/2903040 q ( q^6-84*q^5+2856*q^4-50176*q^3+478800*q^2-2342592*q+4561920\ ) q congruent 17 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2739282*q^2+8082430\ *q-10236975 ) q congruent 19 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2712402*q^2+7538670\ *q-9340191 ) q congruent 21 modulo 60: 1/2903040 phi1 ( q^6-83*q^5+2773*q^4-47718*q^3+449667*q^2-2262735*q+5049\ 135 ) q congruent 23 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2739282*q^2+8309230\ *q-13366815 ) q congruent 25 modulo 60: 1/2903040 phi1 ( q^6-83*q^5+2773*q^4-47718*q^3+449667*q^2-2262735*q+5049\ 135 ) q congruent 27 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2712402*q^2+7538670\ *q-8178975 ) q congruent 29 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2739282*q^2+8082430\ *q-11398191 ) q congruent 31 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2712402*q^2+7538670\ *q-8178975 ) q congruent 32 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50176*q^4+478800*q^3-2369472*q^2+5332480\ *q-4300800 ) q congruent 37 modulo 60: 1/2903040 phi1 ( q^6-83*q^5+2773*q^4-47718*q^3+449667*q^2-2262735*q+5049\ 135 ) q congruent 41 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2739282*q^2+8082430\ *q-10236975 ) q congruent 43 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2712402*q^2+7538670\ *q-8178975 ) q congruent 47 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2739282*q^2+8309230\ *q-13366815 ) q congruent 49 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2712402*q^2+7311870\ *q-6210351 ) q congruent 53 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2739282*q^2+8082430\ *q-10236975 ) q congruent 59 modulo 60: 1/2903040 ( q^7-84*q^6+2856*q^5-50491*q^4+497385*q^3-2739282*q^2+8309230\ *q-14528031 ) Fusion of maximal tori of C^F in those of G^F: [ 67, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 64 ], [ 3, 1, 2, 728 ], [ 4, 1, 2, 3276 ], [ 5, 1, 2, 8064 ], [ 6, 1, 2, 12768 ], [ 7, 1, 2, 2088 ], [ 8, 1, 2, 576 ], [ 9, 1, 1, 63 ], [ 10, 1, 2, 126 ], [ 11, 1, 2, 2072 ], [ 12, 1, 2, 11592 ], [ 13, 1, 4, 16632 ], [ 14, 1, 2, 32256 ], [ 15, 1, 2, 56448 ], [ 16, 1, 3, 110880 ], [ 17, 1, 4, 134400 ], [ 18, 1, 2, 12672 ], [ 19, 1, 2, 34272 ], [ 20, 1, 4, 65520 ], [ 21, 1, 2, 4032 ], [ 22, 1, 4, 24192 ], [ 23, 1, 2, 756 ], [ 24, 1, 2, 3906 ], [ 25, 1, 3, 22680 ], [ 26, 1, 4, 4032 ], [ 27, 1, 6, 4032 ], [ 28, 1, 4, 31752 ], [ 29, 1, 4, 104832 ], [ 30, 1, 3, 145152 ], [ 31, 1, 4, 201600 ], [ 32, 1, 3, 322560 ], [ 33, 1, 8, 423360 ], [ 34, 1, 4, 64512 ], [ 35, 1, 8, 272160 ], [ 36, 1, 4, 24192 ], [ 37, 1, 3, 120960 ], [ 38, 1, 12, 241920 ], [ 39, 1, 3, 7560 ], [ 40, 1, 6, 75600 ], [ 41, 1, 9, 105840 ], [ 42, 1, 6, 64512 ], [ 43, 1, 13, 120960 ], [ 44, 1, 10, 60480 ], [ 45, 1, 6, 266112 ], [ 46, 1, 6, 564480 ], [ 47, 1, 8, 725760 ], [ 48, 1, 6, 483840 ], [ 49, 1, 10, 907200 ], [ 50, 1, 12, 120960 ], [ 51, 1, 9, 362880 ], [ 52, 1, 10, 196560 ], [ 53, 1, 20, 483840 ], [ 54, 1, 14, 483840 ], [ 55, 1, 15, 1209600 ], [ 56, 1, 20, 846720 ], [ 57, 1, 10, 1451520 ], [ 58, 1, 15, 967680 ], [ 59, 1, 2, 362880 ], [ 60, 1, 17, 1451520 ], [ 61, 1, 21, 1935360 ], [ 62, 1, 29, 2177280 ], [ 63, 1, 19, 1451520 ], [ 64, 1, 47, 2903040 ], [ 65, 1, 38, 2903040 ] ] k = 58: F-action on Pi is () [66,1,58] Dynkin type is A_1(q) + T(phi1^6 phi2) Order of center |Z^F|: phi1^6 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-142415*q+144495 ) q congruent 2 modulo 60: 1/46080 q ( q^6-52*q^5+1080*q^4-11360*q^3+62864*q^2-168768*q+161280 ) q congruent 3 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-196098*q^2+267630*q-10\ 3455 ) q congruent 4 modulo 60: 1/46080 q ( q^6-52*q^5+1080*q^4-11360*q^3+62864*q^2-170048*q+174080 ) q congruent 5 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-141135*q+132975 ) q congruent 7 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-197378*q^2+280430*q-11\ 4975 ) q congruent 8 modulo 60: 1/46080 q ( q^6-52*q^5+1080*q^4-11360*q^3+62864*q^2-168768*q+161280 ) q congruent 9 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-141135*q+132975 ) q congruent 11 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-196098*q^2+267630*q-10\ 3455 ) q congruent 13 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-142415*q+144495 ) q congruent 16 modulo 60: 1/46080 q ( q^6-52*q^5+1080*q^4-11360*q^3+62864*q^2-170048*q+174080 ) q congruent 17 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-141135*q+132975 ) q congruent 19 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-197378*q^2+280430*q-11\ 4975 ) q congruent 21 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-141135*q+132975 ) q congruent 23 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-196098*q^2+267630*q-10\ 3455 ) q congruent 25 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-142415*q+144495 ) q congruent 27 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-196098*q^2+267630*q-10\ 3455 ) q congruent 29 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-141135*q+132975 ) q congruent 31 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-197378*q^2+280430*q-11\ 4975 ) q congruent 32 modulo 60: 1/46080 q ( q^6-52*q^5+1080*q^4-11360*q^3+62864*q^2-168768*q+161280 ) q congruent 37 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-142415*q+144495 ) q congruent 41 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-141135*q+132975 ) q congruent 43 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-197378*q^2+280430*q-11\ 4975 ) q congruent 47 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-196098*q^2+267630*q-10\ 3455 ) q congruent 49 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-142415*q+144495 ) q congruent 53 modulo 60: 1/46080 phi1 ( q^6-51*q^5+1029*q^4-10406*q^3+54963*q^2-141135*q+132975 ) q congruent 59 modulo 60: 1/46080 ( q^7-52*q^6+1080*q^5-11435*q^4+65369*q^3-196098*q^2+267630*q-10\ 3455 ) Fusion of maximal tori of C^F in those of G^F: [ 66, 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 32 ], [ 3, 1, 1, 224 ], [ 4, 1, 1, 772 ], [ 5, 1, 1, 1664 ], [ 6, 1, 1, 2304 ], [ 7, 1, 1, 544 ], [ 8, 1, 1, 192 ], [ 9, 1, 1, 31 ], [ 10, 1, 1, 60 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 544 ], [ 12, 1, 1, 2080 ], [ 13, 1, 1, 2664 ], [ 14, 1, 1, 4992 ], [ 15, 1, 1, 7424 ], [ 16, 1, 1, 12800 ], [ 17, 1, 1, 15360 ], [ 18, 1, 1, 2304 ], [ 19, 1, 1, 4864 ], [ 20, 1, 1, 8640 ], [ 20, 1, 2, 1040 ], [ 21, 1, 1, 960 ], [ 22, 1, 1, 3840 ], [ 22, 1, 2, 384 ], [ 23, 1, 1, 252 ], [ 24, 1, 1, 900 ], [ 24, 1, 2, 62 ], [ 25, 1, 1, 3720 ], [ 26, 1, 1, 960 ], [ 26, 1, 3, 64 ], [ 27, 1, 1, 960 ], [ 27, 1, 2, 64 ], [ 28, 1, 1, 4320 ], [ 28, 1, 2, 504 ], [ 29, 1, 1, 11520 ], [ 29, 1, 2, 1664 ], [ 30, 1, 1, 13824 ], [ 31, 1, 1, 19200 ], [ 31, 1, 2, 3200 ], [ 32, 1, 1, 28160 ], [ 33, 1, 1, 34560 ], [ 34, 1, 1, 7680 ], [ 34, 1, 2, 1024 ], [ 35, 1, 1, 23040 ], [ 35, 1, 3, 4320 ], [ 36, 1, 1, 3840 ], [ 36, 1, 2, 384 ], [ 37, 1, 1, 13440 ], [ 38, 1, 1, 23040 ], [ 38, 1, 5, 3840 ], [ 39, 1, 1, 1560 ], [ 39, 1, 4, 120 ], [ 40, 1, 1, 8640 ], [ 41, 1, 1, 10320 ], [ 41, 1, 6, 1680 ], [ 42, 1, 1, 7680 ], [ 42, 1, 4, 1024 ], [ 43, 1, 1, 13440 ], [ 43, 1, 2, 1920 ], [ 44, 1, 1, 6720 ], [ 44, 1, 2, 960 ], [ 45, 1, 1, 19200 ], [ 45, 1, 2, 4224 ], [ 46, 1, 1, 38400 ], [ 46, 1, 2, 8960 ], [ 47, 1, 1, 46080 ], [ 47, 1, 2, 11520 ], [ 48, 1, 1, 30720 ], [ 48, 1, 2, 7680 ], [ 49, 1, 1, 57600 ], [ 49, 1, 9, 14400 ], [ 50, 1, 1, 11520 ], [ 50, 1, 2, 1920 ], [ 50, 1, 4, 1920 ], [ 51, 1, 1, 26880 ], [ 51, 1, 2, 5760 ], [ 52, 1, 1, 14400 ], [ 52, 1, 2, 3120 ], [ 53, 1, 1, 30720 ], [ 53, 1, 3, 7680 ], [ 54, 1, 1, 23040 ], [ 54, 1, 2, 7680 ], [ 55, 1, 1, 53760 ], [ 55, 1, 2, 19200 ], [ 56, 1, 1, 34560 ], [ 56, 1, 2, 13440 ], [ 56, 1, 6, 13440 ], [ 57, 1, 1, 69120 ], [ 57, 1, 2, 23040 ], [ 58, 1, 1, 46080 ], [ 58, 1, 2, 15360 ], [ 59, 1, 1, 17280 ], [ 59, 1, 12, 5760 ], [ 60, 1, 1, 69120 ], [ 60, 1, 40, 23040 ], [ 61, 1, 1, 46080 ], [ 61, 1, 19, 30720 ], [ 62, 1, 1, 69120 ], [ 62, 1, 30, 34560 ], [ 62, 1, 41, 34560 ], [ 63, 1, 1, 23040 ], [ 63, 1, 33, 23040 ], [ 64, 1, 1, 46080 ], [ 64, 1, 51, 46080 ], [ 65, 1, 47, 46080 ] ] k = 59: F-action on Pi is () [66,1,59] Dynkin type is A_1(q) + T(phi1^4 phi2^3) Order of center |Z^F|: phi1^4 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-143*q-41 ) q congruent 2 modulo 60: 1/768 q ( q^6-12*q^5+40*q^4-144*q^2+64*q+128 ) q congruent 3 modulo 60: 1/768 phi1 phi2 ( q^5-12*q^4+41*q^3-7*q^2-118*q+39 ) q congruent 4 modulo 60: 1/768 q ( q^6-12*q^5+40*q^4-144*q^2+256 ) q congruent 5 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-79*q-105 ) q congruent 7 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-143*q+103 ) q congruent 8 modulo 60: 1/768 q ( q^6-12*q^5+40*q^4-144*q^2+64*q+128 ) q congruent 9 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-79*q-105 ) q congruent 11 modulo 60: 1/768 phi1 phi2 ( q^5-12*q^4+41*q^3-7*q^2-118*q+39 ) q congruent 13 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-143*q-41 ) q congruent 16 modulo 60: 1/768 q ( q^6-12*q^5+40*q^4-144*q^2+256 ) q congruent 17 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-79*q-105 ) q congruent 19 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-143*q+103 ) q congruent 21 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-79*q-105 ) q congruent 23 modulo 60: 1/768 phi1 phi2 ( q^5-12*q^4+41*q^3-7*q^2-118*q+39 ) q congruent 25 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-143*q-41 ) q congruent 27 modulo 60: 1/768 phi1 phi2 ( q^5-12*q^4+41*q^3-7*q^2-118*q+39 ) q congruent 29 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-79*q-105 ) q congruent 31 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-143*q+103 ) q congruent 32 modulo 60: 1/768 q ( q^6-12*q^5+40*q^4-144*q^2+64*q+128 ) q congruent 37 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-143*q-41 ) q congruent 41 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-79*q-105 ) q congruent 43 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-143*q+103 ) q congruent 47 modulo 60: 1/768 phi1 phi2 ( q^5-12*q^4+41*q^3-7*q^2-118*q+39 ) q congruent 49 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-143*q-41 ) q congruent 53 modulo 60: 1/768 phi1 ( q^6-11*q^5+29*q^4+34*q^3-125*q^2-79*q-105 ) q congruent 59 modulo 60: 1/768 phi1 phi2 ( q^5-12*q^4+41*q^3-7*q^2-118*q+39 ) Fusion of maximal tori of C^F in those of G^F: [ 68, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 32 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 72 ], [ 4, 1, 2, 36 ], [ 5, 1, 1, 96 ], [ 6, 1, 1, 128 ], [ 6, 1, 2, 32 ], [ 7, 1, 1, 32 ], [ 7, 1, 2, 8 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 8 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 32 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 96 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 144 ], [ 13, 1, 2, 48 ], [ 13, 1, 3, 48 ], [ 13, 1, 4, 72 ], [ 14, 1, 1, 96 ], [ 15, 1, 1, 192 ], [ 16, 1, 1, 384 ], [ 16, 1, 2, 192 ], [ 16, 1, 3, 96 ], [ 16, 1, 4, 96 ], [ 17, 1, 1, 384 ], [ 17, 1, 2, 64 ], [ 17, 1, 3, 64 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 128 ], [ 19, 1, 2, 32 ], [ 20, 1, 1, 192 ], [ 20, 1, 2, 288 ], [ 20, 1, 3, 192 ], [ 20, 1, 4, 48 ], [ 20, 1, 6, 32 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 64 ], [ 22, 1, 2, 144 ], [ 22, 1, 3, 48 ], [ 23, 1, 1, 24 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 56 ], [ 24, 1, 2, 42 ], [ 25, 1, 1, 144 ], [ 25, 1, 2, 96 ], [ 25, 1, 3, 72 ], [ 25, 1, 4, 96 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 48 ], [ 27, 1, 2, 48 ], [ 27, 1, 3, 16 ], [ 28, 1, 1, 96 ], [ 28, 1, 2, 144 ], [ 28, 1, 3, 96 ], [ 28, 1, 4, 24 ], [ 29, 1, 2, 288 ], [ 30, 1, 1, 192 ], [ 30, 1, 2, 192 ], [ 31, 1, 1, 192 ], [ 31, 1, 2, 432 ], [ 31, 1, 3, 144 ], [ 32, 1, 1, 384 ], [ 32, 1, 2, 192 ], [ 32, 1, 4, 64 ], [ 33, 1, 1, 768 ], [ 33, 1, 2, 384 ], [ 33, 1, 6, 192 ], [ 33, 1, 8, 192 ], [ 34, 1, 1, 64 ], [ 34, 1, 2, 144 ], [ 34, 1, 3, 48 ], [ 35, 1, 1, 384 ], [ 35, 1, 2, 192 ], [ 35, 1, 3, 576 ], [ 35, 1, 4, 96 ], [ 35, 1, 5, 192 ], [ 35, 1, 6, 384 ], [ 35, 1, 7, 96 ], [ 35, 1, 8, 96 ], [ 36, 1, 2, 96 ], [ 37, 1, 1, 96 ], [ 37, 1, 2, 240 ], [ 38, 1, 2, 128 ], [ 38, 1, 5, 576 ], [ 39, 1, 1, 48 ], [ 39, 1, 2, 48 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 48 ], [ 40, 1, 1, 192 ], [ 40, 1, 2, 96 ], [ 40, 1, 3, 192 ], [ 40, 1, 6, 48 ], [ 41, 1, 1, 288 ], [ 41, 1, 2, 96 ], [ 41, 1, 4, 192 ], [ 41, 1, 6, 288 ], [ 41, 1, 7, 96 ], [ 41, 1, 9, 144 ], [ 42, 1, 2, 64 ], [ 42, 1, 4, 192 ], [ 43, 1, 2, 288 ], [ 43, 1, 3, 192 ], [ 43, 1, 4, 96 ], [ 43, 1, 8, 192 ], [ 43, 1, 12, 192 ], [ 44, 1, 2, 144 ], [ 44, 1, 5, 96 ], [ 44, 1, 8, 48 ], [ 44, 1, 9, 96 ], [ 45, 1, 2, 288 ], [ 46, 1, 2, 576 ], [ 46, 1, 11, 128 ], [ 47, 1, 1, 384 ], [ 47, 1, 2, 864 ], [ 47, 1, 3, 384 ], [ 47, 1, 4, 192 ], [ 47, 1, 7, 288 ], [ 47, 1, 9, 192 ], [ 48, 1, 1, 192 ], [ 48, 1, 2, 432 ], [ 48, 1, 3, 480 ], [ 48, 1, 4, 480 ], [ 48, 1, 5, 144 ], [ 48, 1, 7, 192 ], [ 49, 1, 1, 768 ], [ 49, 1, 2, 384 ], [ 49, 1, 5, 768 ], [ 49, 1, 8, 192 ], [ 49, 1, 9, 1152 ], [ 49, 1, 10, 192 ], [ 49, 1, 18, 192 ], [ 50, 1, 2, 96 ], [ 50, 1, 5, 192 ], [ 50, 1, 8, 96 ], [ 51, 1, 2, 288 ], [ 51, 1, 3, 192 ], [ 51, 1, 5, 384 ], [ 51, 1, 6, 384 ], [ 51, 1, 10, 192 ], [ 52, 1, 1, 192 ], [ 52, 1, 2, 288 ], [ 52, 1, 3, 192 ], [ 52, 1, 4, 96 ], [ 52, 1, 9, 192 ], [ 52, 1, 10, 48 ], [ 53, 1, 3, 576 ], [ 53, 1, 4, 192 ], [ 53, 1, 6, 384 ], [ 53, 1, 7, 192 ], [ 53, 1, 8, 192 ], [ 53, 1, 9, 384 ], [ 54, 1, 5, 384 ], [ 55, 1, 2, 576 ], [ 55, 1, 5, 768 ], [ 55, 1, 8, 384 ], [ 55, 1, 14, 384 ], [ 56, 1, 2, 288 ], [ 56, 1, 5, 384 ], [ 56, 1, 7, 576 ], [ 56, 1, 10, 192 ], [ 56, 1, 13, 288 ], [ 56, 1, 14, 384 ], [ 56, 1, 19, 192 ], [ 57, 1, 1, 384 ], [ 57, 1, 2, 864 ], [ 57, 1, 3, 384 ], [ 57, 1, 4, 192 ], [ 57, 1, 5, 960 ], [ 57, 1, 6, 288 ], [ 58, 1, 4, 384 ], [ 58, 1, 9, 768 ], [ 59, 1, 3, 192 ], [ 59, 1, 12, 288 ], [ 59, 1, 13, 96 ], [ 59, 1, 22, 192 ], [ 60, 1, 27, 768 ], [ 60, 1, 40, 1152 ], [ 60, 1, 41, 384 ], [ 60, 1, 45, 384 ], [ 61, 1, 12, 768 ], [ 61, 1, 17, 384 ], [ 61, 1, 22, 384 ], [ 62, 1, 31, 384 ], [ 62, 1, 32, 768 ], [ 62, 1, 41, 576 ], [ 62, 1, 42, 576 ], [ 62, 1, 46, 1152 ], [ 62, 1, 50, 384 ], [ 63, 1, 29, 384 ], [ 63, 1, 32, 384 ], [ 63, 1, 35, 384 ], [ 64, 1, 53, 768 ], [ 64, 1, 60, 768 ], [ 64, 1, 64, 384 ], [ 65, 1, 48, 768 ] ] k = 60: F-action on Pi is () [66,1,60] Dynkin type is A_1(q) + T(phi1^3 phi2^4) Order of center |Z^F|: phi1^3 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-3 ) q congruent 2 modulo 60: 1/768 q ( q^6-10*q^5+28*q^4-8*q^3-32*q^2-64*q+128 ) q congruent 3 modulo 60: 1/768 ( q^7-10*q^6+28*q^5-3*q^4-55*q^3+48*q^2-150*q+45 ) q congruent 4 modulo 60: 1/768 q^3 ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 5 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-67 ) q congruent 7 modulo 60: 1/768 ( q^7-10*q^6+28*q^5-3*q^4-55*q^3+48*q^2-150*q+45 ) q congruent 8 modulo 60: 1/768 q ( q^6-10*q^5+28*q^4-8*q^3-32*q^2-64*q+128 ) q congruent 9 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-3 ) q congruent 11 modulo 60: 1/768 phi2 ( q^6-11*q^5+39*q^4-42*q^3-13*q^2-3*q-19 ) q congruent 13 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-3 ) q congruent 16 modulo 60: 1/768 q^3 ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 17 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-67 ) q congruent 19 modulo 60: 1/768 ( q^7-10*q^6+28*q^5-3*q^4-55*q^3+48*q^2-150*q+45 ) q congruent 21 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-3 ) q congruent 23 modulo 60: 1/768 phi2 ( q^6-11*q^5+39*q^4-42*q^3-13*q^2-3*q-19 ) q congruent 25 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-3 ) q congruent 27 modulo 60: 1/768 ( q^7-10*q^6+28*q^5-3*q^4-55*q^3+48*q^2-150*q+45 ) q congruent 29 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-67 ) q congruent 31 modulo 60: 1/768 ( q^7-10*q^6+28*q^5-3*q^4-55*q^3+48*q^2-150*q+45 ) q congruent 32 modulo 60: 1/768 q ( q^6-10*q^5+28*q^4-8*q^3-32*q^2-64*q+128 ) q congruent 37 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-3 ) q congruent 41 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-67 ) q congruent 43 modulo 60: 1/768 ( q^7-10*q^6+28*q^5-3*q^4-55*q^3+48*q^2-150*q+45 ) q congruent 47 modulo 60: 1/768 phi2 ( q^6-11*q^5+39*q^4-42*q^3-13*q^2-3*q-19 ) q congruent 49 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-3 ) q congruent 53 modulo 60: 1/768 phi1^2 ( q^5-8*q^4+11*q^3+27*q^2-12*q-67 ) q congruent 59 modulo 60: 1/768 phi2 ( q^6-11*q^5+39*q^4-42*q^3-13*q^2-3*q-19 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 36 ], [ 4, 1, 2, 72 ], [ 5, 1, 2, 96 ], [ 6, 1, 1, 32 ], [ 6, 1, 2, 128 ], [ 7, 1, 1, 8 ], [ 7, 1, 2, 32 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 8 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 32 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 96 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 48 ], [ 13, 1, 3, 48 ], [ 13, 1, 4, 144 ], [ 14, 1, 2, 96 ], [ 15, 1, 2, 192 ], [ 16, 1, 1, 96 ], [ 16, 1, 2, 96 ], [ 16, 1, 3, 384 ], [ 16, 1, 4, 192 ], [ 17, 1, 2, 64 ], [ 17, 1, 3, 64 ], [ 17, 1, 4, 384 ], [ 18, 1, 2, 64 ], [ 19, 1, 1, 32 ], [ 19, 1, 2, 128 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 192 ], [ 20, 1, 3, 288 ], [ 20, 1, 4, 192 ], [ 20, 1, 7, 32 ], [ 21, 1, 2, 16 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 144 ], [ 22, 1, 4, 64 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 24 ], [ 24, 1, 1, 42 ], [ 24, 1, 2, 56 ], [ 25, 1, 1, 72 ], [ 25, 1, 2, 96 ], [ 25, 1, 3, 144 ], [ 25, 1, 4, 96 ], [ 26, 1, 2, 48 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 27, 1, 3, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 96 ], [ 28, 1, 3, 144 ], [ 28, 1, 4, 96 ], [ 29, 1, 3, 288 ], [ 30, 1, 3, 192 ], [ 30, 1, 4, 192 ], [ 31, 1, 2, 144 ], [ 31, 1, 3, 432 ], [ 31, 1, 4, 192 ], [ 32, 1, 2, 192 ], [ 32, 1, 3, 384 ], [ 32, 1, 4, 64 ], [ 33, 1, 1, 192 ], [ 33, 1, 2, 192 ], [ 33, 1, 6, 384 ], [ 33, 1, 8, 768 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 144 ], [ 34, 1, 4, 64 ], [ 35, 1, 1, 96 ], [ 35, 1, 2, 96 ], [ 35, 1, 3, 384 ], [ 35, 1, 4, 192 ], [ 35, 1, 5, 96 ], [ 35, 1, 6, 576 ], [ 35, 1, 7, 192 ], [ 35, 1, 8, 384 ], [ 36, 1, 3, 96 ], [ 37, 1, 2, 240 ], [ 37, 1, 3, 96 ], [ 38, 1, 8, 576 ], [ 38, 1, 10, 128 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 48 ], [ 39, 1, 3, 48 ], [ 39, 1, 4, 48 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 192 ], [ 40, 1, 3, 96 ], [ 40, 1, 6, 192 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 96 ], [ 41, 1, 4, 192 ], [ 41, 1, 6, 288 ], [ 41, 1, 7, 96 ], [ 41, 1, 9, 288 ], [ 42, 1, 2, 192 ], [ 42, 1, 4, 64 ], [ 43, 1, 2, 96 ], [ 43, 1, 3, 192 ], [ 43, 1, 4, 288 ], [ 43, 1, 8, 192 ], [ 43, 1, 12, 192 ], [ 44, 1, 2, 48 ], [ 44, 1, 5, 96 ], [ 44, 1, 8, 144 ], [ 44, 1, 9, 96 ], [ 45, 1, 5, 288 ], [ 46, 1, 5, 576 ], [ 46, 1, 8, 128 ], [ 47, 1, 2, 288 ], [ 47, 1, 4, 192 ], [ 47, 1, 7, 864 ], [ 47, 1, 8, 384 ], [ 47, 1, 9, 192 ], [ 47, 1, 10, 384 ], [ 48, 1, 2, 144 ], [ 48, 1, 3, 480 ], [ 48, 1, 4, 480 ], [ 48, 1, 5, 432 ], [ 48, 1, 6, 192 ], [ 48, 1, 10, 192 ], [ 49, 1, 1, 192 ], [ 49, 1, 2, 192 ], [ 49, 1, 5, 1152 ], [ 49, 1, 8, 384 ], [ 49, 1, 9, 768 ], [ 49, 1, 10, 768 ], [ 49, 1, 15, 192 ], [ 50, 1, 5, 96 ], [ 50, 1, 8, 192 ], [ 50, 1, 11, 96 ], [ 51, 1, 3, 384 ], [ 51, 1, 5, 192 ], [ 51, 1, 6, 192 ], [ 51, 1, 8, 288 ], [ 51, 1, 10, 384 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 192 ], [ 52, 1, 3, 96 ], [ 52, 1, 4, 192 ], [ 52, 1, 9, 288 ], [ 52, 1, 10, 192 ], [ 53, 1, 3, 192 ], [ 53, 1, 4, 192 ], [ 53, 1, 6, 384 ], [ 53, 1, 7, 192 ], [ 53, 1, 8, 576 ], [ 53, 1, 9, 384 ], [ 54, 1, 13, 384 ], [ 55, 1, 5, 384 ], [ 55, 1, 13, 576 ], [ 55, 1, 14, 768 ], [ 55, 1, 17, 384 ], [ 56, 1, 5, 192 ], [ 56, 1, 7, 288 ], [ 56, 1, 10, 384 ], [ 56, 1, 13, 576 ], [ 56, 1, 14, 192 ], [ 56, 1, 18, 288 ], [ 56, 1, 19, 384 ], [ 57, 1, 2, 288 ], [ 57, 1, 4, 192 ], [ 57, 1, 5, 960 ], [ 57, 1, 6, 864 ], [ 57, 1, 9, 384 ], [ 57, 1, 10, 384 ], [ 58, 1, 4, 384 ], [ 58, 1, 11, 768 ], [ 59, 1, 3, 192 ], [ 59, 1, 12, 96 ], [ 59, 1, 13, 288 ], [ 59, 1, 22, 192 ], [ 60, 1, 27, 768 ], [ 60, 1, 40, 384 ], [ 60, 1, 41, 1152 ], [ 60, 1, 45, 384 ], [ 61, 1, 17, 384 ], [ 61, 1, 18, 768 ], [ 61, 1, 22, 384 ], [ 62, 1, 31, 768 ], [ 62, 1, 32, 384 ], [ 62, 1, 42, 1152 ], [ 62, 1, 43, 576 ], [ 62, 1, 46, 576 ], [ 62, 1, 49, 384 ], [ 63, 1, 32, 384 ], [ 63, 1, 34, 384 ], [ 63, 1, 35, 384 ], [ 64, 1, 58, 768 ], [ 64, 1, 60, 768 ], [ 64, 1, 64, 384 ], [ 65, 1, 50, 768 ] ] i = 67: Pi = [ ] j = 1: Omega trivial k = 1: F-action on Pi is () [67,1,1] Dynkin type is A_0(q) + T(phi1^8) Order of center |Z^F|: phi1^8 Numbers of classes in class type: q congruent 1 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35845616*q^2-818120000*q+1313187309 ) q congruent 2 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3530128*q^4-36922368*q^3+2\ 21596416*q^2-669081600*q+696729600 ) q congruent 3 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-789739200*q+1024044525 ) q congruent 4 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3530128*q^4-36922368*q^3+2\ 22313216*q^2-692019200*q+851558400 ) q congruent 5 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-795182400*q+1111135725 ) q congruent 7 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35845616*q^2-812676800*q+1198226925 ) q congruent 8 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3530128*q^4-36922368*q^3+2\ 21596416*q^2-669081600*q+696729600 ) q congruent 9 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-795182400*q+1111135725 ) q congruent 11 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-789739200*q+1051913709 ) q congruent 13 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35845616*q^2-818120000*q+1285318125 ) q congruent 16 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3530128*q^4-36922368*q^3+2\ 22313216*q^2-692019200*q+879427584 ) q congruent 17 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-795182400*q+1111135725 ) q congruent 19 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35845616*q^2-812676800*q+1198226925 ) q congruent 21 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-795182400*q+1139004909 ) q congruent 23 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-789739200*q+1024044525 ) q congruent 25 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35845616*q^2-818120000*q+1285318125 ) q congruent 27 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-789739200*q+1024044525 ) q congruent 29 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-795182400*q+1111135725 ) q congruent 31 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35845616*q^2-812676800*q+1226096109 ) q congruent 32 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3530128*q^4-36922368*q^3+2\ 21596416*q^2-669081600*q+696729600 ) q congruent 37 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35845616*q^2-818120000*q+1285318125 ) q congruent 41 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-795182400*q+1139004909 ) q congruent 43 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35845616*q^2-812676800*q+1198226925 ) q congruent 47 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-789739200*q+1024044525 ) q congruent 49 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35845616*q^2-818120000*q+1285318125 ) q congruent 53 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-795182400*q+1111135725 ) q congruent 59 modulo 60: 1/696729600 ( q^8-128*q^7+6888*q^6-202496*q^5+3539578*q^4-37527168*q^3+2\ 35128816*q^2-789739200*q+1024044525 ) Fusion of maximal tori of C^F in those of G^F: [ 1 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 120 ], [ 3, 1, 1, 2240 ], [ 4, 1, 1, 15120 ], [ 5, 1, 1, 48384 ], [ 6, 1, 1, 80640 ], [ 7, 1, 1, 8640 ], [ 8, 1, 1, 1920 ], [ 9, 1, 1, 135 ], [ 10, 1, 1, 240 ], [ 11, 1, 1, 6720 ], [ 12, 1, 1, 60480 ], [ 13, 1, 1, 90720 ], [ 14, 1, 1, 241920 ], [ 15, 1, 1, 483840 ], [ 16, 1, 1, 1209600 ], [ 17, 1, 1, 1612800 ], [ 18, 1, 1, 69120 ], [ 19, 1, 1, 241920 ], [ 20, 1, 1, 604800 ], [ 21, 1, 1, 17280 ], [ 22, 1, 1, 161280 ], [ 23, 1, 1, 2160 ], [ 24, 1, 1, 15120 ], [ 25, 1, 1, 151200 ], [ 26, 1, 1, 17280 ], [ 27, 1, 1, 13440 ], [ 28, 1, 1, 181440 ], [ 29, 1, 1, 967680 ], [ 30, 1, 1, 1451520 ], [ 31, 1, 1, 2419200 ], [ 32, 1, 1, 4838400 ], [ 33, 1, 1, 7257600 ], [ 34, 1, 1, 483840 ], [ 35, 1, 1, 3628800 ], [ 36, 1, 1, 138240 ], [ 37, 1, 1, 1209600 ], [ 38, 1, 1, 3225600 ], [ 39, 1, 1, 30240 ], [ 40, 1, 1, 604800 ], [ 41, 1, 1, 907200 ], [ 42, 1, 1, 483840 ], [ 43, 1, 1, 1209600 ], [ 44, 1, 1, 362880 ], [ 45, 1, 1, 2903040 ], [ 46, 1, 1, 9676800 ], [ 47, 1, 1, 14515200 ], [ 48, 1, 1, 7257600 ], [ 49, 1, 1, 21772800 ], [ 50, 1, 1, 967680 ], [ 51, 1, 1, 4838400 ], [ 52, 1, 1, 1814400 ], [ 53, 1, 1, 7257600 ], [ 54, 1, 1, 5806080 ], [ 55, 1, 1, 29030400 ], [ 56, 1, 1, 14515200 ], [ 57, 1, 1, 43545600 ], [ 58, 1, 1, 19353600 ], [ 59, 1, 1, 3628800 ], [ 60, 1, 1, 43545600 ], [ 61, 1, 1, 58060800 ], [ 62, 1, 1, 87091200 ], [ 63, 1, 1, 29030400 ], [ 64, 1, 1, 174182400 ], [ 65, 1, 1, 116121600 ], [ 66, 1, 1, 348364800 ] ] k = 2: F-action on Pi is () [67,1,2] Dynkin type is A_0(q) + T(phi2^8) Order of center |Z^F|: phi2^8 Numbers of classes in class type: q congruent 1 modulo 60: 1/696729600 phi1 ( q^7-111*q^6+5097*q^5-125047*q^4+1768131*q^3-14510061*\ q^2+65774835*q-135442125 ) q congruent 2 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1883728*q^4-15748992*q^3+7\ 0871296*q^2-147804160*q+111820800 ) q congruent 3 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 0284896*q^2-206660160*q+211646925 ) q congruent 4 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1883728*q^4-15748992*q^3+7\ 0154496*q^2-127733760*q+27869184 ) q congruent 5 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 1001696*q^2-221287360*q+266616525 ) q congruent 7 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 0284896*q^2-206660160*q+211646925 ) q congruent 8 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1883728*q^4-15748992*q^3+7\ 0871296*q^2-147804160*q+111820800 ) q congruent 9 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 0284896*q^2-201216960*q+163311309 ) q congruent 11 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 1001696*q^2-226730560*q+342821325 ) q congruent 13 modulo 60: 1/696729600 phi1 ( q^7-111*q^6+5097*q^5-125047*q^4+1768131*q^3-14510061*\ q^2+65774835*q-135442125 ) q congruent 16 modulo 60: 1/696729600 q ( q^7-112*q^6+5208*q^5-130144*q^4+1883728*q^3-15748992*q^2\ +70154496*q-127733760 ) q congruent 17 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 1001696*q^2-221287360*q+266616525 ) q congruent 19 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 0284896*q^2-206660160*q+239516109 ) q congruent 21 modulo 60: 1/696729600 phi1 ( q^7-111*q^6+5097*q^5-125047*q^4+1768131*q^3-14510061*\ q^2+65774835*q-135442125 ) q congruent 23 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 1001696*q^2-226730560*q+342821325 ) q congruent 25 modulo 60: 1/696729600 phi1 ( q^7-111*q^6+5097*q^5-125047*q^4+1768131*q^3-14510061*\ q^2+65774835*q-135442125 ) q congruent 27 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 0284896*q^2-206660160*q+211646925 ) q congruent 29 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 1001696*q^2-221287360*q+294485709 ) q congruent 31 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 0284896*q^2-206660160*q+211646925 ) q congruent 32 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1883728*q^4-15748992*q^3+7\ 0871296*q^2-147804160*q+111820800 ) q congruent 37 modulo 60: 1/696729600 phi1 ( q^7-111*q^6+5097*q^5-125047*q^4+1768131*q^3-14510061*\ q^2+65774835*q-135442125 ) q congruent 41 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 1001696*q^2-221287360*q+266616525 ) q congruent 43 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 0284896*q^2-206660160*q+211646925 ) q congruent 47 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 1001696*q^2-226730560*q+342821325 ) q congruent 49 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 0284896*q^2-201216960*q+163311309 ) q congruent 53 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 1001696*q^2-221287360*q+266616525 ) q congruent 59 modulo 60: 1/696729600 ( q^8-112*q^7+5208*q^6-130144*q^5+1893178*q^4-16278192*q^3+8\ 1001696*q^2-226730560*q+370690509 ) Fusion of maximal tori of C^F in those of G^F: [ 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 120 ], [ 3, 1, 2, 2240 ], [ 4, 1, 2, 15120 ], [ 5, 1, 2, 48384 ], [ 6, 1, 2, 80640 ], [ 7, 1, 2, 8640 ], [ 8, 1, 2, 1920 ], [ 9, 1, 1, 135 ], [ 10, 1, 2, 240 ], [ 11, 1, 2, 6720 ], [ 12, 1, 2, 60480 ], [ 13, 1, 4, 90720 ], [ 14, 1, 2, 241920 ], [ 15, 1, 2, 483840 ], [ 16, 1, 3, 1209600 ], [ 17, 1, 4, 1612800 ], [ 18, 1, 2, 69120 ], [ 19, 1, 2, 241920 ], [ 20, 1, 4, 604800 ], [ 21, 1, 2, 17280 ], [ 22, 1, 4, 161280 ], [ 23, 1, 2, 2160 ], [ 24, 1, 2, 15120 ], [ 25, 1, 3, 151200 ], [ 26, 1, 4, 17280 ], [ 27, 1, 6, 13440 ], [ 28, 1, 4, 181440 ], [ 29, 1, 4, 967680 ], [ 30, 1, 3, 1451520 ], [ 31, 1, 4, 2419200 ], [ 32, 1, 3, 4838400 ], [ 33, 1, 8, 7257600 ], [ 34, 1, 4, 483840 ], [ 35, 1, 8, 3628800 ], [ 36, 1, 4, 138240 ], [ 37, 1, 3, 1209600 ], [ 38, 1, 12, 3225600 ], [ 39, 1, 3, 30240 ], [ 40, 1, 6, 604800 ], [ 41, 1, 9, 907200 ], [ 42, 1, 6, 483840 ], [ 43, 1, 13, 1209600 ], [ 44, 1, 10, 362880 ], [ 45, 1, 6, 2903040 ], [ 46, 1, 6, 9676800 ], [ 47, 1, 8, 14515200 ], [ 48, 1, 6, 7257600 ], [ 49, 1, 10, 21772800 ], [ 50, 1, 12, 967680 ], [ 51, 1, 9, 4838400 ], [ 52, 1, 10, 1814400 ], [ 53, 1, 20, 7257600 ], [ 54, 1, 14, 5806080 ], [ 55, 1, 15, 29030400 ], [ 56, 1, 20, 14515200 ], [ 57, 1, 10, 43545600 ], [ 58, 1, 15, 19353600 ], [ 59, 1, 2, 3628800 ], [ 60, 1, 17, 43545600 ], [ 61, 1, 21, 58060800 ], [ 62, 1, 29, 87091200 ], [ 63, 1, 19, 29030400 ], [ 64, 1, 47, 174182400 ], [ 65, 1, 38, 116121600 ], [ 66, 1, 57, 348364800 ] ] k = 3: F-action on Pi is () [67,1,3] Dynkin type is A_0(q) + T(phi1^4 phi2^4) Order of center |Z^F|: phi1^4 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/221184 phi1 ( q^7-23*q^6+169*q^5-263*q^4-1581*q^3+3867*q^2+3875*q+3171\ ) q congruent 2 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1360*q^4+5952*q^3+1280*q^2-25600*q\ +24576 ) q congruent 3 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3-2040*q^2+7488*q-\ 33507 ) q congruent 4 modulo 60: 1/221184 q ( q^7-24*q^6+192*q^5-432*q^4-1360*q^3+5952*q^2+1280*q-17408 ) q congruent 5 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3+8*q^2-8896*q+214\ 05 ) q congruent 7 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3+8*q^2-704*q-2736\ 3 ) q congruent 8 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1360*q^4+5952*q^3+1280*q^2-25600*q\ +24576 ) q congruent 9 modulo 60: 1/221184 phi1 ( q^7-23*q^6+169*q^5-263*q^4-1581*q^3+3867*q^2+1827*q+9315\ ) q congruent 11 modulo 60: 1/221184 phi2 ( q^7-25*q^6+217*q^5-649*q^4-669*q^3+6117*q^2-6109*q-2787 \ ) q congruent 13 modulo 60: 1/221184 phi1 ( q^7-23*q^6+169*q^5-263*q^4-1581*q^3+3867*q^2+3875*q+3171\ ) q congruent 16 modulo 60: 1/221184 q ( q^7-24*q^6+192*q^5-432*q^4-1360*q^3+5952*q^2+1280*q-17408 ) q congruent 17 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3+8*q^2-8896*q+214\ 05 ) q congruent 19 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3+8*q^2-704*q-2736\ 3 ) q congruent 21 modulo 60: 1/221184 phi1 ( q^7-23*q^6+169*q^5-263*q^4-1581*q^3+3867*q^2+1827*q+9315\ ) q congruent 23 modulo 60: 1/221184 phi2 ( q^7-25*q^6+217*q^5-649*q^4-669*q^3+6117*q^2-6109*q-2787 \ ) q congruent 25 modulo 60: 1/221184 phi1 ( q^7-23*q^6+169*q^5-263*q^4-1581*q^3+3867*q^2+3875*q+3171\ ) q congruent 27 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3-2040*q^2+7488*q-\ 33507 ) q congruent 29 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3+8*q^2-8896*q+214\ 05 ) q congruent 31 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3+8*q^2-704*q-2736\ 3 ) q congruent 32 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1360*q^4+5952*q^3+1280*q^2-25600*q\ +24576 ) q congruent 37 modulo 60: 1/221184 phi1 ( q^7-23*q^6+169*q^5-263*q^4-1581*q^3+3867*q^2+3875*q+3171\ ) q congruent 41 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3+8*q^2-8896*q+214\ 05 ) q congruent 43 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3+8*q^2-704*q-2736\ 3 ) q congruent 47 modulo 60: 1/221184 phi2 ( q^7-25*q^6+217*q^5-649*q^4-669*q^3+6117*q^2-6109*q-2787 \ ) q congruent 49 modulo 60: 1/221184 phi1 ( q^7-23*q^6+169*q^5-263*q^4-1581*q^3+3867*q^2+3875*q+3171\ ) q congruent 53 modulo 60: 1/221184 ( q^8-24*q^7+192*q^6-432*q^5-1318*q^4+5448*q^3+8*q^2-8896*q+214\ 05 ) q congruent 59 modulo 60: 1/221184 phi2 ( q^7-25*q^6+217*q^5-649*q^4-669*q^3+6117*q^2-6109*q-2787 \ ) Fusion of maximal tori of C^F in those of G^F: [ 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 24 ], [ 3, 1, 1, 32 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 168 ], [ 4, 1, 2, 168 ], [ 6, 1, 1, 384 ], [ 6, 1, 2, 384 ], [ 7, 1, 1, 288 ], [ 7, 1, 2, 288 ], [ 9, 1, 1, 39 ], [ 10, 1, 1, 24 ], [ 10, 1, 2, 24 ], [ 11, 1, 1, 96 ], [ 11, 1, 2, 96 ], [ 12, 1, 1, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 1, 432 ], [ 13, 1, 2, 576 ], [ 13, 1, 3, 576 ], [ 13, 1, 4, 432 ], [ 16, 1, 1, 1152 ], [ 16, 1, 2, 768 ], [ 16, 1, 3, 1152 ], [ 16, 1, 4, 768 ], [ 17, 1, 2, 3072 ], [ 17, 1, 3, 3072 ], [ 19, 1, 1, 1152 ], [ 19, 1, 2, 1152 ], [ 20, 1, 1, 1728 ], [ 20, 1, 2, 1152 ], [ 20, 1, 3, 1152 ], [ 20, 1, 4, 1728 ], [ 20, 1, 5, 4608 ], [ 20, 1, 8, 4608 ], [ 22, 1, 2, 768 ], [ 22, 1, 3, 768 ], [ 23, 1, 1, 24 ], [ 23, 1, 2, 24 ], [ 24, 1, 1, 360 ], [ 24, 1, 2, 360 ], [ 25, 1, 1, 912 ], [ 25, 1, 2, 768 ], [ 25, 1, 3, 912 ], [ 25, 1, 4, 768 ], [ 26, 1, 1, 576 ], [ 26, 1, 4, 576 ], [ 27, 1, 1, 192 ], [ 27, 1, 6, 192 ], [ 28, 1, 1, 288 ], [ 28, 1, 2, 576 ], [ 28, 1, 3, 576 ], [ 28, 1, 4, 288 ], [ 31, 1, 2, 2304 ], [ 31, 1, 3, 2304 ], [ 32, 1, 2, 3072 ], [ 32, 1, 4, 9216 ], [ 33, 1, 1, 2304 ], [ 33, 1, 2, 4608 ], [ 33, 1, 6, 4608 ], [ 33, 1, 8, 2304 ], [ 34, 1, 2, 2304 ], [ 34, 1, 3, 2304 ], [ 35, 1, 1, 3456 ], [ 35, 1, 2, 6912 ], [ 35, 1, 3, 4608 ], [ 35, 1, 4, 2304 ], [ 35, 1, 5, 2304 ], [ 35, 1, 6, 4608 ], [ 35, 1, 7, 6912 ], [ 35, 1, 8, 3456 ], [ 37, 1, 2, 384 ], [ 38, 1, 6, 6144 ], [ 38, 1, 7, 6144 ], [ 39, 1, 1, 144 ], [ 39, 1, 2, 192 ], [ 39, 1, 3, 144 ], [ 39, 1, 4, 576 ], [ 40, 1, 1, 192 ], [ 40, 1, 2, 768 ], [ 40, 1, 3, 768 ], [ 40, 1, 6, 192 ], [ 41, 1, 1, 2016 ], [ 41, 1, 2, 3456 ], [ 41, 1, 3, 2304 ], [ 41, 1, 4, 2304 ], [ 41, 1, 6, 3456 ], [ 41, 1, 9, 2016 ], [ 41, 1, 10, 2304 ], [ 42, 1, 1, 2304 ], [ 42, 1, 6, 2304 ], [ 43, 1, 1, 3456 ], [ 43, 1, 3, 2304 ], [ 43, 1, 5, 9216 ], [ 43, 1, 8, 3840 ], [ 43, 1, 12, 2304 ], [ 43, 1, 13, 3456 ], [ 44, 1, 1, 576 ], [ 44, 1, 5, 1152 ], [ 44, 1, 9, 1152 ], [ 44, 1, 10, 576 ], [ 46, 1, 7, 18432 ], [ 46, 1, 12, 18432 ], [ 47, 1, 2, 4608 ], [ 47, 1, 4, 9216 ], [ 47, 1, 7, 4608 ], [ 47, 1, 9, 9216 ], [ 48, 1, 2, 6912 ], [ 48, 1, 3, 2304 ], [ 48, 1, 4, 2304 ], [ 48, 1, 5, 6912 ], [ 49, 1, 1, 6912 ], [ 49, 1, 2, 13824 ], [ 49, 1, 5, 13824 ], [ 49, 1, 8, 13824 ], [ 49, 1, 9, 13824 ], [ 49, 1, 10, 6912 ], [ 49, 1, 14, 27648 ], [ 49, 1, 20, 27648 ], [ 50, 1, 4, 4608 ], [ 50, 1, 9, 4608 ], [ 51, 1, 3, 1536 ], [ 51, 1, 5, 4608 ], [ 51, 1, 6, 1536 ], [ 51, 1, 10, 4608 ], [ 52, 1, 1, 576 ], [ 52, 1, 2, 3456 ], [ 52, 1, 3, 2304 ], [ 52, 1, 4, 2304 ], [ 52, 1, 9, 3456 ], [ 52, 1, 10, 576 ], [ 53, 1, 1, 6912 ], [ 53, 1, 2, 13824 ], [ 53, 1, 5, 4608 ], [ 53, 1, 6, 9216 ], [ 53, 1, 9, 9216 ], [ 53, 1, 12, 13824 ], [ 53, 1, 19, 4608 ], [ 53, 1, 20, 6912 ], [ 55, 1, 5, 9216 ], [ 55, 1, 10, 18432 ], [ 55, 1, 14, 9216 ], [ 55, 1, 16, 18432 ], [ 56, 1, 5, 13824 ], [ 56, 1, 6, 13824 ], [ 56, 1, 10, 4608 ], [ 56, 1, 14, 4608 ], [ 56, 1, 15, 13824 ], [ 56, 1, 19, 13824 ], [ 57, 1, 2, 13824 ], [ 57, 1, 4, 27648 ], [ 57, 1, 5, 13824 ], [ 57, 1, 6, 13824 ], [ 58, 1, 4, 6144 ], [ 58, 1, 25, 36864 ], [ 59, 1, 1, 1152 ], [ 59, 1, 2, 1152 ], [ 59, 1, 3, 6912 ], [ 59, 1, 17, 4608 ], [ 59, 1, 18, 4608 ], [ 60, 1, 1, 13824 ], [ 60, 1, 17, 13824 ], [ 60, 1, 27, 27648 ], [ 60, 1, 34, 55296 ], [ 60, 1, 43, 27648 ], [ 60, 1, 44, 27648 ], [ 61, 1, 17, 18432 ], [ 61, 1, 22, 18432 ], [ 62, 1, 24, 27648 ], [ 62, 1, 30, 27648 ], [ 62, 1, 31, 27648 ], [ 62, 1, 32, 27648 ], [ 62, 1, 44, 55296 ], [ 62, 1, 45, 55296 ], [ 63, 1, 14, 9216 ], [ 63, 1, 20, 9216 ], [ 63, 1, 21, 27648 ], [ 63, 1, 28, 27648 ], [ 64, 1, 27, 55296 ], [ 64, 1, 37, 55296 ], [ 64, 1, 61, 110592 ], [ 64, 1, 64, 55296 ], [ 65, 1, 32, 36864 ], [ 65, 1, 37, 36864 ], [ 66, 1, 38, 110592 ], [ 66, 1, 56, 110592 ] ] k = 4: F-action on Pi is () [67,1,4] Dynkin type is A_0(q) + T(phi1^6 phi2^2) Order of center |Z^F|: phi1^6 phi2^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 2 modulo 60: 1/184320 q ( q^7-36*q^6+508*q^5-3480*q^4+11104*q^3-8544*q^2-29568*q+4608\ 0 ) q congruent 3 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) q congruent 4 modulo 60: 1/184320 q ( q^7-36*q^6+508*q^5-3480*q^4+11104*q^3-8544*q^2-29568*q+4608\ 0 ) q congruent 5 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 7 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) q congruent 8 modulo 60: 1/184320 q ( q^7-36*q^6+508*q^5-3480*q^4+11104*q^3-8544*q^2-29568*q+4608\ 0 ) q congruent 9 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 11 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) q congruent 13 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 16 modulo 60: 1/184320 q ( q^7-36*q^6+508*q^5-3480*q^4+11104*q^3-8544*q^2-29568*q+4608\ 0 ) q congruent 17 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 19 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) q congruent 21 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 23 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) q congruent 25 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 27 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) q congruent 29 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 31 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) q congruent 32 modulo 60: 1/184320 q ( q^7-36*q^6+508*q^5-3480*q^4+11104*q^3-8544*q^2-29568*q+4608\ 0 ) q congruent 37 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 41 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 43 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) q congruent 47 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) q congruent 49 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 53 modulo 60: 1/184320 phi1 ( q^7-35*q^6+473*q^5-3007*q^4+8187*q^3-1977*q^2-22005*q+60\ 75 ) q congruent 59 modulo 60: 1/184320 phi2 ( q^7-37*q^6+545*q^5-4025*q^4+15219*q^3-25383*q^2+5355*q+1\ 9845 ) Fusion of maximal tori of C^F in those of G^F: [ 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 32 ], [ 3, 1, 1, 224 ], [ 4, 1, 1, 772 ], [ 4, 1, 2, 60 ], [ 5, 1, 1, 1664 ], [ 6, 1, 1, 2304 ], [ 7, 1, 1, 544 ], [ 8, 1, 1, 192 ], [ 9, 1, 1, 31 ], [ 10, 1, 1, 60 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 544 ], [ 12, 1, 1, 2080 ], [ 13, 1, 1, 2664 ], [ 13, 1, 2, 48 ], [ 13, 1, 3, 240 ], [ 13, 1, 4, 120 ], [ 14, 1, 1, 4992 ], [ 15, 1, 1, 7424 ], [ 16, 1, 1, 12800 ], [ 16, 1, 2, 1920 ], [ 17, 1, 1, 15360 ], [ 18, 1, 1, 2304 ], [ 19, 1, 1, 4864 ], [ 20, 1, 1, 8640 ], [ 20, 1, 2, 2080 ], [ 20, 1, 3, 1440 ], [ 21, 1, 1, 960 ], [ 22, 1, 1, 3840 ], [ 22, 1, 2, 768 ], [ 23, 1, 1, 252 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 900 ], [ 24, 1, 2, 124 ], [ 25, 1, 1, 3720 ], [ 25, 1, 2, 480 ], [ 25, 1, 3, 120 ], [ 25, 1, 4, 160 ], [ 26, 1, 1, 960 ], [ 26, 1, 3, 128 ], [ 27, 1, 1, 960 ], [ 27, 1, 2, 128 ], [ 28, 1, 1, 4320 ], [ 28, 1, 2, 1008 ], [ 28, 1, 3, 240 ], [ 29, 1, 1, 11520 ], [ 29, 1, 2, 3328 ], [ 30, 1, 1, 13824 ], [ 30, 1, 2, 768 ], [ 31, 1, 1, 19200 ], [ 31, 1, 2, 6400 ], [ 32, 1, 1, 28160 ], [ 33, 1, 1, 34560 ], [ 33, 1, 2, 3840 ], [ 33, 1, 4, 7680 ], [ 34, 1, 1, 7680 ], [ 34, 1, 2, 2048 ], [ 35, 1, 1, 23040 ], [ 35, 1, 2, 1920 ], [ 35, 1, 3, 8640 ], [ 35, 1, 5, 5760 ], [ 35, 1, 6, 2880 ], [ 36, 1, 1, 3840 ], [ 36, 1, 2, 768 ], [ 37, 1, 1, 13440 ], [ 37, 1, 2, 960 ], [ 38, 1, 1, 23040 ], [ 38, 1, 5, 7680 ], [ 39, 1, 1, 1560 ], [ 39, 1, 2, 48 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 240 ], [ 40, 1, 1, 8640 ], [ 40, 1, 3, 640 ], [ 41, 1, 1, 10320 ], [ 41, 1, 2, 480 ], [ 41, 1, 3, 1920 ], [ 41, 1, 4, 960 ], [ 41, 1, 6, 3360 ], [ 41, 1, 9, 240 ], [ 42, 1, 1, 7680 ], [ 42, 1, 4, 2048 ], [ 43, 1, 1, 13440 ], [ 43, 1, 2, 3840 ], [ 43, 1, 3, 2880 ], [ 43, 1, 8, 960 ], [ 43, 1, 12, 320 ], [ 44, 1, 1, 6720 ], [ 44, 1, 2, 1920 ], [ 44, 1, 5, 96 ], [ 44, 1, 9, 480 ], [ 45, 1, 1, 19200 ], [ 45, 1, 2, 8448 ], [ 46, 1, 1, 38400 ], [ 46, 1, 2, 17920 ], [ 47, 1, 1, 46080 ], [ 47, 1, 2, 23040 ], [ 47, 1, 3, 7680 ], [ 48, 1, 1, 30720 ], [ 48, 1, 2, 15360 ], [ 48, 1, 3, 1920 ], [ 48, 1, 4, 5760 ], [ 48, 1, 7, 3840 ], [ 49, 1, 1, 57600 ], [ 49, 1, 2, 11520 ], [ 49, 1, 5, 5760 ], [ 49, 1, 9, 28800 ], [ 49, 1, 11, 23040 ], [ 50, 1, 1, 11520 ], [ 50, 1, 2, 3840 ], [ 50, 1, 4, 3840 ], [ 50, 1, 5, 256 ], [ 51, 1, 1, 26880 ], [ 51, 1, 2, 11520 ], [ 51, 1, 5, 1280 ], [ 51, 1, 6, 3840 ], [ 52, 1, 1, 14400 ], [ 52, 1, 2, 6240 ], [ 52, 1, 3, 1920 ], [ 52, 1, 9, 480 ], [ 53, 1, 1, 30720 ], [ 53, 1, 2, 3840 ], [ 53, 1, 3, 15360 ], [ 53, 1, 5, 11520 ], [ 53, 1, 6, 5760 ], [ 53, 1, 9, 1920 ], [ 54, 1, 1, 23040 ], [ 54, 1, 2, 15360 ], [ 54, 1, 5, 1536 ], [ 55, 1, 1, 53760 ], [ 55, 1, 2, 38400 ], [ 55, 1, 5, 7680 ], [ 55, 1, 9, 15360 ], [ 56, 1, 1, 34560 ], [ 56, 1, 2, 26880 ], [ 56, 1, 5, 3840 ], [ 56, 1, 6, 26880 ], [ 56, 1, 7, 3840 ], [ 56, 1, 14, 11520 ], [ 57, 1, 1, 69120 ], [ 57, 1, 2, 46080 ], [ 57, 1, 3, 23040 ], [ 57, 1, 5, 11520 ], [ 58, 1, 1, 46080 ], [ 58, 1, 2, 30720 ], [ 58, 1, 9, 5120 ], [ 59, 1, 1, 17280 ], [ 59, 1, 3, 960 ], [ 59, 1, 12, 11520 ], [ 59, 1, 17, 3840 ], [ 60, 1, 1, 69120 ], [ 60, 1, 22, 46080 ], [ 60, 1, 27, 11520 ], [ 60, 1, 40, 46080 ], [ 60, 1, 44, 23040 ], [ 61, 1, 1, 46080 ], [ 61, 1, 12, 15360 ], [ 61, 1, 19, 61440 ], [ 62, 1, 1, 69120 ], [ 62, 1, 30, 69120 ], [ 62, 1, 32, 23040 ], [ 62, 1, 41, 69120 ], [ 62, 1, 46, 23040 ], [ 62, 1, 47, 46080 ], [ 63, 1, 1, 23040 ], [ 63, 1, 20, 23040 ], [ 63, 1, 21, 7680 ], [ 63, 1, 29, 7680 ], [ 63, 1, 33, 46080 ], [ 64, 1, 1, 46080 ], [ 64, 1, 37, 46080 ], [ 64, 1, 49, 92160 ], [ 64, 1, 51, 92160 ], [ 64, 1, 53, 46080 ], [ 65, 1, 39, 30720 ], [ 65, 1, 47, 92160 ], [ 66, 1, 47, 92160 ], [ 66, 1, 58, 92160 ] ] k = 5: F-action on Pi is () [67,1,5] Dynkin type is A_0(q) + T(phi1^2 phi2^6) Order of center |Z^F|: phi1^2 phi2^6 Numbers of classes in class type: q congruent 1 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 2 modulo 60: 1/184320 q ( q^7-28*q^6+308*q^5-1672*q^4+4544*q^3-5152*q^2-128*q+3072 ) q congruent 3 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) q congruent 4 modulo 60: 1/184320 q ( q^7-28*q^6+308*q^5-1672*q^4+4544*q^3-5152*q^2-128*q+3072 ) q congruent 5 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 7 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) q congruent 8 modulo 60: 1/184320 q ( q^7-28*q^6+308*q^5-1672*q^4+4544*q^3-5152*q^2-128*q+3072 ) q congruent 9 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 11 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) q congruent 13 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 16 modulo 60: 1/184320 q ( q^7-28*q^6+308*q^5-1672*q^4+4544*q^3-5152*q^2-128*q+3072 ) q congruent 17 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 19 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) q congruent 21 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 23 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) q congruent 25 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 27 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) q congruent 29 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 31 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) q congruent 32 modulo 60: 1/184320 q ( q^7-28*q^6+308*q^5-1672*q^4+4544*q^3-5152*q^2-128*q+3072 ) q congruent 37 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 41 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 43 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) q congruent 47 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) q congruent 49 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 53 modulo 60: 1/184320 phi1 ( q^7-27*q^6+281*q^5-1391*q^4+3243*q^3-3169*q^2+1563*q+103\ 5 ) q congruent 59 modulo 60: 1/184320 phi2 ( q^7-29*q^6+337*q^5-2009*q^4+6643*q^3-13055*q^2+17787*q-1\ 5435 ) Fusion of maximal tori of C^F in those of G^F: [ 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 32 ], [ 3, 1, 2, 224 ], [ 4, 1, 1, 60 ], [ 4, 1, 2, 772 ], [ 5, 1, 2, 1664 ], [ 6, 1, 2, 2304 ], [ 7, 1, 2, 544 ], [ 8, 1, 2, 192 ], [ 9, 1, 1, 31 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 60 ], [ 11, 1, 2, 544 ], [ 12, 1, 2, 2080 ], [ 13, 1, 1, 120 ], [ 13, 1, 2, 240 ], [ 13, 1, 3, 48 ], [ 13, 1, 4, 2664 ], [ 14, 1, 2, 4992 ], [ 15, 1, 2, 7424 ], [ 16, 1, 3, 12800 ], [ 16, 1, 4, 1920 ], [ 17, 1, 4, 15360 ], [ 18, 1, 2, 2304 ], [ 19, 1, 2, 4864 ], [ 20, 1, 2, 1440 ], [ 20, 1, 3, 2080 ], [ 20, 1, 4, 8640 ], [ 21, 1, 2, 960 ], [ 22, 1, 3, 768 ], [ 22, 1, 4, 3840 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 252 ], [ 24, 1, 1, 124 ], [ 24, 1, 2, 900 ], [ 25, 1, 1, 120 ], [ 25, 1, 2, 160 ], [ 25, 1, 3, 3720 ], [ 25, 1, 4, 480 ], [ 26, 1, 2, 128 ], [ 26, 1, 4, 960 ], [ 27, 1, 3, 128 ], [ 27, 1, 6, 960 ], [ 28, 1, 2, 240 ], [ 28, 1, 3, 1008 ], [ 28, 1, 4, 4320 ], [ 29, 1, 3, 3328 ], [ 29, 1, 4, 11520 ], [ 30, 1, 3, 13824 ], [ 30, 1, 4, 768 ], [ 31, 1, 3, 6400 ], [ 31, 1, 4, 19200 ], [ 32, 1, 3, 28160 ], [ 33, 1, 6, 3840 ], [ 33, 1, 8, 34560 ], [ 33, 1, 10, 7680 ], [ 34, 1, 3, 2048 ], [ 34, 1, 4, 7680 ], [ 35, 1, 3, 2880 ], [ 35, 1, 4, 5760 ], [ 35, 1, 6, 8640 ], [ 35, 1, 7, 1920 ], [ 35, 1, 8, 23040 ], [ 36, 1, 3, 768 ], [ 36, 1, 4, 3840 ], [ 37, 1, 2, 960 ], [ 37, 1, 3, 13440 ], [ 38, 1, 8, 7680 ], [ 38, 1, 12, 23040 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 48 ], [ 39, 1, 3, 1560 ], [ 39, 1, 4, 240 ], [ 40, 1, 2, 640 ], [ 40, 1, 6, 8640 ], [ 41, 1, 1, 240 ], [ 41, 1, 2, 480 ], [ 41, 1, 4, 960 ], [ 41, 1, 6, 3360 ], [ 41, 1, 9, 10320 ], [ 41, 1, 10, 1920 ], [ 42, 1, 2, 2048 ], [ 42, 1, 6, 7680 ], [ 43, 1, 3, 320 ], [ 43, 1, 4, 3840 ], [ 43, 1, 8, 960 ], [ 43, 1, 12, 2880 ], [ 43, 1, 13, 13440 ], [ 44, 1, 5, 480 ], [ 44, 1, 8, 1920 ], [ 44, 1, 9, 96 ], [ 44, 1, 10, 6720 ], [ 45, 1, 5, 8448 ], [ 45, 1, 6, 19200 ], [ 46, 1, 5, 17920 ], [ 46, 1, 6, 38400 ], [ 47, 1, 7, 23040 ], [ 47, 1, 8, 46080 ], [ 47, 1, 10, 7680 ], [ 48, 1, 3, 5760 ], [ 48, 1, 4, 1920 ], [ 48, 1, 5, 15360 ], [ 48, 1, 6, 30720 ], [ 48, 1, 10, 3840 ], [ 49, 1, 5, 28800 ], [ 49, 1, 8, 11520 ], [ 49, 1, 9, 5760 ], [ 49, 1, 10, 57600 ], [ 49, 1, 19, 23040 ], [ 50, 1, 8, 256 ], [ 50, 1, 9, 3840 ], [ 50, 1, 11, 3840 ], [ 50, 1, 12, 11520 ], [ 51, 1, 3, 3840 ], [ 51, 1, 8, 11520 ], [ 51, 1, 9, 26880 ], [ 51, 1, 10, 1280 ], [ 52, 1, 2, 480 ], [ 52, 1, 4, 1920 ], [ 52, 1, 9, 6240 ], [ 52, 1, 10, 14400 ], [ 53, 1, 6, 1920 ], [ 53, 1, 8, 15360 ], [ 53, 1, 9, 5760 ], [ 53, 1, 12, 3840 ], [ 53, 1, 19, 11520 ], [ 53, 1, 20, 30720 ], [ 54, 1, 12, 15360 ], [ 54, 1, 13, 1536 ], [ 54, 1, 14, 23040 ], [ 55, 1, 13, 38400 ], [ 55, 1, 14, 7680 ], [ 55, 1, 15, 53760 ], [ 55, 1, 20, 15360 ], [ 56, 1, 10, 11520 ], [ 56, 1, 13, 3840 ], [ 56, 1, 15, 26880 ], [ 56, 1, 18, 26880 ], [ 56, 1, 19, 3840 ], [ 56, 1, 20, 34560 ], [ 57, 1, 5, 11520 ], [ 57, 1, 6, 46080 ], [ 57, 1, 9, 23040 ], [ 57, 1, 10, 69120 ], [ 58, 1, 11, 5120 ], [ 58, 1, 12, 30720 ], [ 58, 1, 15, 46080 ], [ 59, 1, 2, 17280 ], [ 59, 1, 3, 960 ], [ 59, 1, 13, 11520 ], [ 59, 1, 18, 3840 ], [ 60, 1, 17, 69120 ], [ 60, 1, 26, 46080 ], [ 60, 1, 27, 11520 ], [ 60, 1, 41, 46080 ], [ 60, 1, 43, 23040 ], [ 61, 1, 18, 15360 ], [ 61, 1, 20, 61440 ], [ 61, 1, 21, 46080 ], [ 62, 1, 24, 69120 ], [ 62, 1, 29, 69120 ], [ 62, 1, 31, 23040 ], [ 62, 1, 42, 23040 ], [ 62, 1, 43, 69120 ], [ 62, 1, 48, 46080 ], [ 63, 1, 14, 23040 ], [ 63, 1, 19, 23040 ], [ 63, 1, 28, 7680 ], [ 63, 1, 34, 7680 ], [ 63, 1, 36, 46080 ], [ 64, 1, 27, 46080 ], [ 64, 1, 47, 46080 ], [ 64, 1, 50, 92160 ], [ 64, 1, 52, 92160 ], [ 64, 1, 58, 46080 ], [ 65, 1, 46, 30720 ], [ 65, 1, 49, 92160 ], [ 66, 1, 54, 92160 ], [ 66, 1, 55, 92160 ] ] k = 6: F-action on Pi is () [67,1,6] Dynkin type is A_0(q) + T(phi4^4) Order of center |Z^F|: phi4^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 2 modulo 60: 1/46080 ( q^8-56*q^6+976*q^4-5376*q^2+9216 ) q congruent 3 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 4 modulo 60: 1/46080 q^2 ( q^6-56*q^4+976*q^2-5376 ) q congruent 5 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 7 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 8 modulo 60: 1/46080 ( q^8-56*q^6+976*q^4-5376*q^2+9216 ) q congruent 9 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 11 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 13 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 16 modulo 60: 1/46080 q^2 ( q^6-56*q^4+976*q^2-5376 ) q congruent 17 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 19 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 21 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 23 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 25 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 27 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 29 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 31 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 32 modulo 60: 1/46080 ( q^8-56*q^6+976*q^4-5376*q^2+9216 ) q congruent 37 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 41 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 43 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 47 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 49 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) q congruent 53 modulo 60: 1/46080 ( q^8-56*q^6+1066*q^4-7536*q^2+15741 ) q congruent 59 modulo 60: 1/46080 phi1 phi2 ( q^6-55*q^4+1011*q^2-6525 ) Fusion of maximal tori of C^F in those of G^F: [ 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 384 ], [ 5, 1, 4, 384 ], [ 9, 1, 1, 15 ], [ 32, 1, 5, 3840 ], [ 37, 1, 5, 1920 ], [ 39, 1, 5, 240 ], [ 41, 1, 5, 1440 ], [ 43, 1, 10, 1920 ], [ 57, 1, 18, 11520 ], [ 58, 1, 21, 7680 ], [ 59, 1, 6, 2880 ], [ 60, 1, 20, 11520 ], [ 64, 1, 48, 23040 ] ] k = 7: F-action on Pi is () [67,1,7] Dynkin type is A_0(q) + T(phi1^4 phi2^4) Order of center |Z^F|: phi1^4 phi2^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 2 modulo 60: 1/6144 q ( q^7-8*q^6+112*q^4-96*q^3-512*q^2+320*q+768 ) q congruent 3 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) q congruent 4 modulo 60: 1/6144 q ( q^7-8*q^6+112*q^4-96*q^3-512*q^2+320*q+768 ) q congruent 5 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 7 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) q congruent 8 modulo 60: 1/6144 q ( q^7-8*q^6+112*q^4-96*q^3-512*q^2+320*q+768 ) q congruent 9 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 11 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) q congruent 13 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 16 modulo 60: 1/6144 q ( q^7-8*q^6+112*q^4-96*q^3-512*q^2+320*q+768 ) q congruent 17 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 19 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) q congruent 21 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 23 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) q congruent 25 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 27 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) q congruent 29 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 31 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) q congruent 32 modulo 60: 1/6144 q ( q^7-8*q^6+112*q^4-96*q^3-512*q^2+320*q+768 ) q congruent 37 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 41 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 43 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) q congruent 47 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) q congruent 49 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 53 modulo 60: 1/6144 phi1^2 ( q^6-6*q^5-13*q^4+92*q^3+79*q^2-358*q-435 ) q congruent 59 modulo 60: 1/6144 phi2 ( q^7-9*q^6+9*q^5+103*q^4-221*q^3-203*q^2+563*q-51 ) Fusion of maximal tori of C^F in those of G^F: [ 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 32 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 72 ], [ 4, 1, 2, 72 ], [ 5, 1, 1, 96 ], [ 5, 1, 2, 96 ], [ 6, 1, 1, 128 ], [ 6, 1, 2, 128 ], [ 7, 1, 1, 32 ], [ 7, 1, 2, 32 ], [ 8, 1, 1, 16 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 8 ], [ 10, 1, 2, 8 ], [ 11, 1, 1, 32 ], [ 11, 1, 2, 32 ], [ 12, 1, 1, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 1, 144 ], [ 13, 1, 2, 96 ], [ 13, 1, 3, 96 ], [ 13, 1, 4, 144 ], [ 14, 1, 1, 96 ], [ 14, 1, 2, 96 ], [ 15, 1, 1, 192 ], [ 15, 1, 2, 192 ], [ 16, 1, 1, 384 ], [ 16, 1, 2, 384 ], [ 16, 1, 3, 384 ], [ 16, 1, 4, 384 ], [ 17, 1, 1, 384 ], [ 17, 1, 2, 256 ], [ 17, 1, 3, 256 ], [ 17, 1, 4, 384 ], [ 18, 1, 1, 64 ], [ 18, 1, 2, 64 ], [ 19, 1, 1, 128 ], [ 19, 1, 2, 128 ], [ 20, 1, 1, 192 ], [ 20, 1, 2, 384 ], [ 20, 1, 3, 384 ], [ 20, 1, 4, 192 ], [ 20, 1, 6, 128 ], [ 20, 1, 7, 128 ], [ 21, 1, 1, 16 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 64 ], [ 22, 1, 2, 192 ], [ 22, 1, 3, 192 ], [ 22, 1, 4, 64 ], [ 23, 1, 1, 24 ], [ 23, 1, 2, 24 ], [ 24, 1, 1, 56 ], [ 24, 1, 2, 56 ], [ 25, 1, 1, 144 ], [ 25, 1, 2, 192 ], [ 25, 1, 3, 144 ], [ 25, 1, 4, 192 ], [ 26, 1, 2, 64 ], [ 26, 1, 3, 64 ], [ 27, 1, 2, 64 ], [ 27, 1, 3, 64 ], [ 28, 1, 1, 96 ], [ 28, 1, 2, 192 ], [ 28, 1, 3, 192 ], [ 28, 1, 4, 96 ], [ 29, 1, 2, 384 ], [ 29, 1, 3, 384 ], [ 30, 1, 1, 192 ], [ 30, 1, 2, 384 ], [ 30, 1, 3, 192 ], [ 30, 1, 4, 384 ], [ 31, 1, 1, 192 ], [ 31, 1, 2, 576 ], [ 31, 1, 3, 576 ], [ 31, 1, 4, 192 ], [ 32, 1, 1, 384 ], [ 32, 1, 2, 768 ], [ 32, 1, 3, 384 ], [ 32, 1, 4, 256 ], [ 33, 1, 1, 768 ], [ 33, 1, 2, 768 ], [ 33, 1, 6, 768 ], [ 33, 1, 8, 768 ], [ 34, 1, 1, 64 ], [ 34, 1, 2, 192 ], [ 34, 1, 3, 192 ], [ 34, 1, 4, 64 ], [ 35, 1, 1, 384 ], [ 35, 1, 2, 384 ], [ 35, 1, 3, 768 ], [ 35, 1, 4, 384 ], [ 35, 1, 5, 384 ], [ 35, 1, 6, 768 ], [ 35, 1, 7, 384 ], [ 35, 1, 8, 384 ], [ 36, 1, 2, 128 ], [ 36, 1, 3, 128 ], [ 37, 1, 1, 96 ], [ 37, 1, 2, 480 ], [ 37, 1, 3, 96 ], [ 37, 1, 4, 256 ], [ 38, 1, 2, 512 ], [ 38, 1, 5, 768 ], [ 38, 1, 8, 768 ], [ 38, 1, 10, 512 ], [ 39, 1, 1, 48 ], [ 39, 1, 2, 96 ], [ 39, 1, 3, 48 ], [ 39, 1, 4, 64 ], [ 40, 1, 1, 192 ], [ 40, 1, 2, 384 ], [ 40, 1, 3, 384 ], [ 40, 1, 6, 192 ], [ 41, 1, 1, 288 ], [ 41, 1, 2, 192 ], [ 41, 1, 4, 384 ], [ 41, 1, 6, 384 ], [ 41, 1, 7, 384 ], [ 41, 1, 9, 288 ], [ 42, 1, 2, 256 ], [ 42, 1, 4, 256 ], [ 43, 1, 2, 384 ], [ 43, 1, 3, 384 ], [ 43, 1, 4, 384 ], [ 43, 1, 7, 256 ], [ 43, 1, 8, 384 ], [ 43, 1, 12, 384 ], [ 44, 1, 2, 192 ], [ 44, 1, 5, 192 ], [ 44, 1, 8, 192 ], [ 44, 1, 9, 192 ], [ 45, 1, 2, 384 ], [ 45, 1, 5, 384 ], [ 46, 1, 2, 768 ], [ 46, 1, 5, 768 ], [ 46, 1, 8, 512 ], [ 46, 1, 11, 512 ], [ 47, 1, 1, 384 ], [ 47, 1, 2, 1152 ], [ 47, 1, 3, 768 ], [ 47, 1, 4, 768 ], [ 47, 1, 7, 1152 ], [ 47, 1, 8, 384 ], [ 47, 1, 9, 768 ], [ 47, 1, 10, 768 ], [ 48, 1, 1, 192 ], [ 48, 1, 2, 576 ], [ 48, 1, 3, 960 ], [ 48, 1, 4, 960 ], [ 48, 1, 5, 576 ], [ 48, 1, 6, 192 ], [ 48, 1, 7, 384 ], [ 48, 1, 10, 384 ], [ 49, 1, 1, 768 ], [ 49, 1, 2, 768 ], [ 49, 1, 5, 1536 ], [ 49, 1, 8, 768 ], [ 49, 1, 9, 1536 ], [ 49, 1, 10, 768 ], [ 49, 1, 15, 768 ], [ 49, 1, 18, 768 ], [ 50, 1, 2, 128 ], [ 50, 1, 5, 384 ], [ 50, 1, 8, 384 ], [ 50, 1, 11, 128 ], [ 51, 1, 2, 384 ], [ 51, 1, 3, 768 ], [ 51, 1, 5, 768 ], [ 51, 1, 6, 768 ], [ 51, 1, 8, 384 ], [ 51, 1, 10, 768 ], [ 52, 1, 1, 192 ], [ 52, 1, 2, 384 ], [ 52, 1, 3, 384 ], [ 52, 1, 4, 384 ], [ 52, 1, 9, 384 ], [ 52, 1, 10, 192 ], [ 53, 1, 3, 768 ], [ 53, 1, 4, 768 ], [ 53, 1, 6, 768 ], [ 53, 1, 7, 768 ], [ 53, 1, 8, 768 ], [ 53, 1, 9, 768 ], [ 54, 1, 5, 768 ], [ 54, 1, 13, 768 ], [ 55, 1, 2, 768 ], [ 55, 1, 5, 1536 ], [ 55, 1, 8, 1536 ], [ 55, 1, 13, 768 ], [ 55, 1, 14, 1536 ], [ 55, 1, 17, 1536 ], [ 56, 1, 2, 384 ], [ 56, 1, 5, 768 ], [ 56, 1, 7, 1152 ], [ 56, 1, 10, 768 ], [ 56, 1, 13, 1152 ], [ 56, 1, 14, 768 ], [ 56, 1, 18, 384 ], [ 56, 1, 19, 768 ], [ 57, 1, 1, 384 ], [ 57, 1, 2, 1152 ], [ 57, 1, 3, 768 ], [ 57, 1, 4, 768 ], [ 57, 1, 5, 1920 ], [ 57, 1, 6, 1152 ], [ 57, 1, 9, 768 ], [ 57, 1, 10, 384 ], [ 57, 1, 16, 1536 ], [ 58, 1, 4, 1536 ], [ 58, 1, 9, 1536 ], [ 58, 1, 11, 1536 ], [ 58, 1, 17, 1024 ], [ 59, 1, 3, 384 ], [ 59, 1, 12, 384 ], [ 59, 1, 13, 384 ], [ 59, 1, 22, 768 ], [ 60, 1, 27, 1536 ], [ 60, 1, 38, 1536 ], [ 60, 1, 40, 1536 ], [ 60, 1, 41, 1536 ], [ 60, 1, 45, 1536 ], [ 61, 1, 12, 1536 ], [ 61, 1, 17, 1536 ], [ 61, 1, 18, 1536 ], [ 61, 1, 22, 1536 ], [ 62, 1, 31, 1536 ], [ 62, 1, 32, 1536 ], [ 62, 1, 41, 768 ], [ 62, 1, 42, 2304 ], [ 62, 1, 43, 768 ], [ 62, 1, 46, 2304 ], [ 62, 1, 49, 1536 ], [ 62, 1, 50, 1536 ], [ 63, 1, 29, 768 ], [ 63, 1, 32, 1536 ], [ 63, 1, 34, 768 ], [ 63, 1, 35, 1536 ], [ 64, 1, 53, 1536 ], [ 64, 1, 58, 1536 ], [ 64, 1, 60, 3072 ], [ 64, 1, 64, 1536 ], [ 64, 1, 65, 3072 ], [ 65, 1, 48, 3072 ], [ 65, 1, 50, 3072 ], [ 66, 1, 59, 3072 ], [ 66, 1, 60, 3072 ] ] k = 8: F-action on Pi is () [67,1,8] Dynkin type is A_0(q) + T(phi1^6 phi3) Order of center |Z^F|: phi1^6 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16747*q^3-19172*q^2-24955*q+\ 47040 ) q congruent 2 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27324*q^2-61488*q+51840 ) q congruent 3 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 4 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16612*q^3-17552*q^2-27520*q+\ 38400 ) q congruent 5 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 7 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16747*q^3-19172*q^2-24955*q+\ 47040 ) q congruent 8 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27324*q^2-61488*q+51840 ) q congruent 9 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 11 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 13 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16747*q^3-19172*q^2-24955*q+\ 47040 ) q congruent 16 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16612*q^3-17552*q^2-27520*q+\ 38400 ) q congruent 17 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 19 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16747*q^3-19172*q^2-24955*q+\ 47040 ) q congruent 21 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 23 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 25 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16747*q^3-19172*q^2-24955*q+\ 47040 ) q congruent 27 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 29 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 31 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16747*q^3-19172*q^2-24955*q+\ 47040 ) q congruent 32 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27324*q^2-61488*q+51840 ) q congruent 37 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16747*q^3-19172*q^2-24955*q+\ 47040 ) q congruent 41 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 43 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16747*q^3-19172*q^2-24955*q+\ 47040 ) q congruent 47 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 49 modulo 60: 1/311040 phi1 ( q^7-40*q^6+623*q^5-4692*q^4+16747*q^3-19172*q^2-24955*q+\ 47040 ) q congruent 53 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 59 modulo 60: 1/311040 q phi2 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) Fusion of maximal tori of C^F in those of G^F: [ 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 36 ], [ 3, 1, 1, 242 ], [ 4, 1, 1, 594 ], [ 5, 1, 1, 864 ], [ 6, 1, 1, 1512 ], [ 7, 1, 1, 432 ], [ 8, 1, 1, 144 ], [ 9, 1, 1, 27 ], [ 10, 1, 1, 72 ], [ 11, 1, 1, 720 ], [ 12, 1, 1, 2214 ], [ 13, 1, 1, 3240 ], [ 14, 1, 1, 3024 ], [ 15, 1, 1, 4752 ], [ 16, 1, 1, 5400 ], [ 17, 1, 1, 4320 ], [ 18, 1, 1, 2160 ], [ 19, 1, 1, 4320 ], [ 20, 1, 1, 4320 ], [ 21, 1, 1, 864 ], [ 22, 1, 1, 3024 ], [ 23, 1, 1, 270 ], [ 24, 1, 1, 1080 ], [ 25, 1, 1, 2700 ], [ 26, 1, 1, 864 ], [ 27, 1, 1, 1440 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 6480 ], [ 29, 1, 1, 9504 ], [ 30, 1, 1, 12960 ], [ 31, 1, 1, 10800 ], [ 32, 1, 1, 8640 ], [ 33, 1, 1, 6480 ], [ 34, 1, 1, 8640 ], [ 35, 1, 1, 12960 ], [ 36, 1, 1, 4320 ], [ 37, 1, 1, 8640 ], [ 38, 1, 1, 8640 ], [ 38, 1, 3, 1440 ], [ 39, 1, 1, 2160 ], [ 40, 1, 1, 9180 ], [ 41, 1, 1, 12960 ], [ 42, 1, 1, 8640 ], [ 42, 1, 3, 216 ], [ 43, 1, 1, 8640 ], [ 44, 1, 1, 12960 ], [ 44, 1, 3, 162 ], [ 45, 1, 1, 25920 ], [ 45, 1, 3, 1296 ], [ 46, 1, 1, 17280 ], [ 46, 1, 3, 4320 ], [ 47, 1, 1, 12960 ], [ 48, 1, 1, 25920 ], [ 50, 1, 1, 17280 ], [ 50, 1, 3, 432 ], [ 51, 1, 1, 21600 ], [ 52, 1, 1, 25920 ], [ 53, 1, 1, 25920 ], [ 53, 1, 16, 3240 ], [ 54, 1, 1, 51840 ], [ 54, 1, 3, 2592 ], [ 55, 1, 1, 25920 ], [ 55, 1, 3, 12960 ], [ 56, 1, 1, 51840 ], [ 56, 1, 3, 6480 ], [ 58, 1, 1, 34560 ], [ 58, 1, 3, 8640 ], [ 59, 1, 1, 51840 ], [ 59, 1, 4, 1620 ], [ 60, 1, 2, 19440 ], [ 61, 1, 1, 51840 ], [ 61, 1, 4, 25920 ], [ 62, 1, 2, 38880 ], [ 63, 1, 1, 103680 ], [ 63, 1, 4, 12960 ], [ 64, 1, 6, 77760 ], [ 65, 1, 1, 103680 ], [ 65, 1, 9, 51840 ], [ 66, 1, 13, 155520 ] ] k = 9: F-action on Pi is () [67,1,9] Dynkin type is A_0(q) + T(phi2^6 phi6) Order of center |Z^F|: phi2^6 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 2 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9556*q^3-19600*q^2+24320*q-1\ 5360 ) q congruent 3 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 4 modulo 60: 1/311040 q^2 phi1 ( q^5-30*q^4+345*q^3-1900*q^2+5004*q-5040 ) q congruent 5 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9691*q^3-21220*q^2+30125*q-2\ 4000 ) q congruent 7 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 8 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9556*q^3-19600*q^2+24320*q-1\ 5360 ) q congruent 9 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 11 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9691*q^3-21220*q^2+30125*q-2\ 4000 ) q congruent 13 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 16 modulo 60: 1/311040 q^2 phi1 ( q^5-30*q^4+345*q^3-1900*q^2+5004*q-5040 ) q congruent 17 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9691*q^3-21220*q^2+30125*q-2\ 4000 ) q congruent 19 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 21 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 23 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9691*q^3-21220*q^2+30125*q-2\ 4000 ) q congruent 25 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 27 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 29 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9691*q^3-21220*q^2+30125*q-2\ 4000 ) q congruent 31 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 32 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9556*q^3-19600*q^2+24320*q-1\ 5360 ) q congruent 37 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 41 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9691*q^3-21220*q^2+30125*q-2\ 4000 ) q congruent 43 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 47 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9691*q^3-21220*q^2+30125*q-2\ 4000 ) q congruent 49 modulo 60: 1/311040 q phi1^2 ( q^5-29*q^4+316*q^3-1584*q^2+3555*q-2835 ) q congruent 53 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9691*q^3-21220*q^2+30125*q-2\ 4000 ) q congruent 59 modulo 60: 1/311040 phi2 ( q^7-32*q^6+407*q^5-2652*q^4+9691*q^3-21220*q^2+30125*q-2\ 4000 ) Fusion of maximal tori of C^F in those of G^F: [ 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 36 ], [ 3, 1, 2, 242 ], [ 4, 1, 2, 594 ], [ 5, 1, 2, 864 ], [ 6, 1, 2, 1512 ], [ 7, 1, 2, 432 ], [ 8, 1, 2, 144 ], [ 9, 1, 1, 27 ], [ 10, 1, 2, 72 ], [ 11, 1, 2, 720 ], [ 12, 1, 2, 2214 ], [ 13, 1, 4, 3240 ], [ 14, 1, 2, 3024 ], [ 15, 1, 2, 4752 ], [ 16, 1, 3, 5400 ], [ 17, 1, 4, 4320 ], [ 18, 1, 2, 2160 ], [ 19, 1, 2, 4320 ], [ 20, 1, 4, 4320 ], [ 21, 1, 2, 864 ], [ 22, 1, 4, 3024 ], [ 23, 1, 2, 270 ], [ 24, 1, 2, 1080 ], [ 25, 1, 3, 2700 ], [ 26, 1, 4, 864 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 1440 ], [ 28, 1, 4, 6480 ], [ 29, 1, 4, 9504 ], [ 30, 1, 3, 12960 ], [ 31, 1, 4, 10800 ], [ 32, 1, 3, 8640 ], [ 33, 1, 8, 6480 ], [ 34, 1, 4, 8640 ], [ 35, 1, 8, 12960 ], [ 36, 1, 4, 4320 ], [ 37, 1, 3, 8640 ], [ 38, 1, 11, 1440 ], [ 38, 1, 12, 8640 ], [ 39, 1, 3, 2160 ], [ 40, 1, 6, 9180 ], [ 41, 1, 9, 12960 ], [ 42, 1, 5, 216 ], [ 42, 1, 6, 8640 ], [ 43, 1, 13, 8640 ], [ 44, 1, 7, 162 ], [ 44, 1, 10, 12960 ], [ 45, 1, 4, 1296 ], [ 45, 1, 6, 25920 ], [ 46, 1, 4, 4320 ], [ 46, 1, 6, 17280 ], [ 47, 1, 8, 12960 ], [ 48, 1, 6, 25920 ], [ 50, 1, 10, 432 ], [ 50, 1, 12, 17280 ], [ 51, 1, 9, 21600 ], [ 52, 1, 10, 25920 ], [ 53, 1, 18, 3240 ], [ 53, 1, 20, 25920 ], [ 54, 1, 10, 2592 ], [ 54, 1, 14, 51840 ], [ 55, 1, 12, 12960 ], [ 55, 1, 15, 25920 ], [ 56, 1, 17, 6480 ], [ 56, 1, 20, 51840 ], [ 58, 1, 14, 8640 ], [ 58, 1, 15, 34560 ], [ 59, 1, 2, 51840 ], [ 59, 1, 5, 1620 ], [ 60, 1, 8, 19440 ], [ 61, 1, 6, 25920 ], [ 61, 1, 21, 51840 ], [ 62, 1, 7, 38880 ], [ 63, 1, 9, 12960 ], [ 63, 1, 19, 103680 ], [ 64, 1, 15, 77760 ], [ 65, 1, 27, 51840 ], [ 65, 1, 38, 103680 ], [ 66, 1, 33, 155520 ] ] k = 10: F-action on Pi is () [67,1,10] Dynkin type is A_0(q) + T(phi3^4) Order of center |Z^F|: phi3^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 2 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 3 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 4 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 5 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 7 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 8 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 9 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 11 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 13 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 16 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 17 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 19 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 21 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 23 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 25 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 27 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 29 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 31 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 32 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 37 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 41 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 43 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 47 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 49 modulo 60: 1/155520 phi1 ( q^7+5*q^6-25*q^5-129*q^4+160*q^3+916*q^2-304*q-1920 ) q congruent 53 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) q congruent 59 modulo 60: 1/155520 q phi2 ( q^6+3*q^5-33*q^4-71*q^3+360*q^2+396*q-1296 ) Fusion of maximal tori of C^F in those of G^F: [ 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 80 ], [ 27, 1, 5, 240 ], [ 38, 1, 3, 5760 ], [ 40, 1, 5, 2160 ], [ 58, 1, 8, 17280 ], [ 59, 1, 9, 6480 ], [ 65, 1, 6, 51840 ] ] k = 11: F-action on Pi is () [67,1,11] Dynkin type is A_0(q) + T(phi6^4) Order of center |Z^F|: phi6^4 Numbers of classes in class type: q congruent 1 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 2 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 3 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 4 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 5 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 7 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 8 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 9 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 11 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 13 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 16 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 17 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 19 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 21 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 23 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 25 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 27 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 29 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 31 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 32 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 37 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 41 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 43 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 47 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 49 modulo 60: 1/155520 q phi1 ( q^6-3*q^5-33*q^4+71*q^3+360*q^2-396*q-1296 ) q congruent 53 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) q congruent 59 modulo 60: 1/155520 phi2 ( q^7-5*q^6-25*q^5+129*q^4+160*q^3-916*q^2-304*q+1920 ) Fusion of maximal tori of C^F in those of G^F: [ 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 80 ], [ 27, 1, 4, 240 ], [ 38, 1, 11, 5760 ], [ 40, 1, 4, 2160 ], [ 58, 1, 13, 17280 ], [ 59, 1, 10, 6480 ], [ 65, 1, 10, 51840 ] ] k = 12: F-action on Pi is () [67,1,12] Dynkin type is A_0(q) + T(phi1^2 phi3^3) Order of center |Z^F|: phi1^2 phi3^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+73*q^3+241*q^2+290*q+72 ) q congruent 2 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+42*q^2+72*q-216 ) q congruent 3 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 4 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+46*q^3+160*q^2+344*q+288 ) q congruent 5 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 7 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+73*q^3+241*q^2+290*q+72 ) q congruent 8 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+42*q^2+72*q-216 ) q congruent 9 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 11 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 13 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+73*q^3+241*q^2+290*q+72 ) q congruent 16 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+46*q^3+160*q^2+344*q+288 ) q congruent 17 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 19 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+73*q^3+241*q^2+290*q+72 ) q congruent 21 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 23 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 25 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+73*q^3+241*q^2+290*q+72 ) q congruent 27 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 29 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 31 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+73*q^3+241*q^2+290*q+72 ) q congruent 32 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+42*q^2+72*q-216 ) q congruent 37 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+73*q^3+241*q^2+290*q+72 ) q congruent 41 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 43 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+73*q^3+241*q^2+290*q+72 ) q congruent 47 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 49 modulo 60: 1/7776 phi1 ( q^7-q^6-16*q^5-12*q^4+73*q^3+241*q^2+290*q+72 ) q congruent 53 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) q congruent 59 modulo 60: 1/7776 q phi2 ( q^6-3*q^5-12*q^4+16*q^3+69*q^2+99*q-378 ) Fusion of maximal tori of C^F in those of G^F: [ 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 26 ], [ 6, 1, 1, 72 ], [ 8, 1, 1, 48 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 1, 144 ], [ 22, 1, 1, 144 ], [ 27, 1, 1, 12 ], [ 27, 1, 5, 72 ], [ 33, 1, 3, 648 ], [ 38, 1, 1, 288 ], [ 38, 1, 3, 432 ], [ 38, 1, 14, 1296 ], [ 40, 1, 5, 270 ], [ 42, 1, 3, 216 ], [ 46, 1, 3, 432 ], [ 47, 1, 5, 1296 ], [ 50, 1, 3, 432 ], [ 52, 1, 6, 162 ], [ 58, 1, 3, 864 ], [ 58, 1, 8, 864 ], [ 59, 1, 7, 324 ], [ 59, 1, 9, 648 ], [ 60, 1, 4, 1944 ], [ 61, 1, 5, 1296 ], [ 62, 1, 3, 3888 ], [ 65, 1, 6, 1296 ], [ 65, 1, 8, 2592 ], [ 66, 1, 10, 3888 ] ] k = 13: F-action on Pi is () [67,1,13] Dynkin type is A_0(q) + T(phi2^2 phi6^3) Order of center |Z^F|: phi2^2 phi6^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 2 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+52*q^3+56*q^2+128*q-672 ) q congruent 3 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 4 modulo 60: 1/7776 q^2 phi1 ( q^5-3*q^4-6*q^3-10*q^2+36*q+144 ) q congruent 5 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+79*q^3-25*q^2+74*q-456 ) q congruent 7 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 8 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+52*q^3+56*q^2+128*q-672 ) q congruent 9 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 11 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+79*q^3-25*q^2+74*q-456 ) q congruent 13 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 16 modulo 60: 1/7776 q^2 phi1 ( q^5-3*q^4-6*q^3-10*q^2+36*q+144 ) q congruent 17 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+79*q^3-25*q^2+74*q-456 ) q congruent 19 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 21 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 23 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+79*q^3-25*q^2+74*q-456 ) q congruent 25 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 27 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 29 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+79*q^3-25*q^2+74*q-456 ) q congruent 31 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 32 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+52*q^3+56*q^2+128*q-672 ) q congruent 37 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 41 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+79*q^3-25*q^2+74*q-456 ) q congruent 43 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 47 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+79*q^3-25*q^2+74*q-456 ) q congruent 49 modulo 60: 1/7776 q phi1^2 ( q^5-2*q^4-8*q^3-18*q^2+45*q+162 ) q congruent 53 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+79*q^3-25*q^2+74*q-456 ) q congruent 59 modulo 60: 1/7776 phi2 ( q^7-5*q^6+2*q^5-6*q^4+79*q^3-25*q^2+74*q-456 ) Fusion of maximal tori of C^F in those of G^F: [ 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 26 ], [ 6, 1, 2, 72 ], [ 8, 1, 2, 48 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 4, 144 ], [ 22, 1, 4, 144 ], [ 27, 1, 4, 72 ], [ 27, 1, 6, 12 ], [ 33, 1, 7, 648 ], [ 38, 1, 11, 432 ], [ 38, 1, 12, 288 ], [ 38, 1, 17, 1296 ], [ 40, 1, 4, 270 ], [ 42, 1, 5, 216 ], [ 46, 1, 4, 432 ], [ 47, 1, 12, 1296 ], [ 50, 1, 10, 432 ], [ 52, 1, 7, 162 ], [ 58, 1, 13, 864 ], [ 58, 1, 14, 864 ], [ 59, 1, 8, 324 ], [ 59, 1, 10, 648 ], [ 60, 1, 15, 1944 ], [ 61, 1, 9, 1296 ], [ 62, 1, 16, 3888 ], [ 65, 1, 10, 1296 ], [ 65, 1, 18, 2592 ], [ 66, 1, 18, 3888 ] ] k = 14: F-action on Pi is () [67,1,14] Dynkin type is A_0(q) + T(phi1^4 phi3^2) Order of center |Z^F|: phi1^4 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+76*q^3-146*q^2-124*q-24 ) q congruent 2 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+102*q^2-252*q+216 ) q congruent 3 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 4 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+58*q^3-92*q^2-88*q-96 ) q congruent 5 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 7 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+76*q^3-146*q^2-124*q-24 ) q congruent 8 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+102*q^2-252*q+216 ) q congruent 9 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 11 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 13 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+76*q^3-146*q^2-124*q-24 ) q congruent 16 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+58*q^3-92*q^2-88*q-96 ) q congruent 17 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 19 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+76*q^3-146*q^2-124*q-24 ) q congruent 21 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 23 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 25 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+76*q^3-146*q^2-124*q-24 ) q congruent 27 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 29 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 31 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+76*q^3-146*q^2-124*q-24 ) q congruent 32 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+102*q^2-252*q+216 ) q congruent 37 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+76*q^3-146*q^2-124*q-24 ) q congruent 41 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 43 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+76*q^3-146*q^2-124*q-24 ) q congruent 47 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 49 modulo 60: 1/2592 phi1 ( q^7-7*q^6+11*q^5-3*q^4+76*q^3-146*q^2-124*q-24 ) q congruent 53 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) q congruent 59 modulo 60: 1/2592 q phi2 ( q^6-9*q^5+27*q^4-41*q^3+120*q^2-342*q+324 ) Fusion of maximal tori of C^F in those of G^F: [ 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], [ 5, 1, 1, 72 ], [ 6, 1, 1, 36 ], [ 7, 1, 1, 36 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 9 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 36 ], [ 14, 1, 1, 144 ], [ 15, 1, 1, 72 ], [ 16, 1, 1, 72 ], [ 17, 1, 1, 72 ], [ 17, 1, 5, 216 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 36 ], [ 20, 1, 1, 144 ], [ 21, 1, 1, 72 ], [ 22, 1, 1, 72 ], [ 23, 1, 1, 36 ], [ 24, 1, 1, 36 ], [ 25, 1, 1, 144 ], [ 26, 1, 1, 72 ], [ 27, 1, 1, 24 ], [ 27, 1, 5, 12 ], [ 29, 1, 1, 144 ], [ 31, 1, 1, 144 ], [ 32, 1, 1, 72 ], [ 33, 1, 3, 108 ], [ 34, 1, 1, 72 ], [ 36, 1, 1, 144 ], [ 37, 1, 1, 288 ], [ 38, 1, 1, 144 ], [ 38, 1, 3, 72 ], [ 38, 1, 13, 432 ], [ 39, 1, 1, 72 ], [ 40, 1, 1, 144 ], [ 40, 1, 5, 36 ], [ 42, 1, 1, 72 ], [ 42, 1, 3, 72 ], [ 43, 1, 1, 288 ], [ 44, 1, 3, 108 ], [ 45, 1, 3, 216 ], [ 46, 1, 1, 144 ], [ 46, 1, 3, 144 ], [ 47, 1, 5, 216 ], [ 49, 1, 3, 324 ], [ 50, 1, 1, 144 ], [ 50, 1, 3, 144 ], [ 51, 1, 1, 288 ], [ 52, 1, 6, 108 ], [ 53, 1, 16, 216 ], [ 54, 1, 3, 432 ], [ 55, 1, 3, 216 ], [ 56, 1, 3, 432 ], [ 57, 1, 12, 648 ], [ 58, 1, 1, 288 ], [ 58, 1, 3, 288 ], [ 58, 1, 8, 72 ], [ 59, 1, 4, 432 ], [ 59, 1, 7, 216 ], [ 60, 1, 3, 648 ], [ 61, 1, 4, 432 ], [ 61, 1, 5, 216 ], [ 62, 1, 4, 1296 ], [ 63, 1, 4, 864 ], [ 64, 1, 7, 648 ], [ 65, 1, 8, 432 ], [ 65, 1, 9, 864 ], [ 66, 1, 12, 1296 ] ] k = 15: F-action on Pi is () [67,1,15] Dynkin type is A_0(q) + T(phi2^4 phi6^2) Order of center |Z^F|: phi2^4 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 2 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+70*q^3-88*q^2+128*q-96 ) q congruent 3 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 4 modulo 60: 1/2592 q^3 phi1^2 ( q^3-2*q^2+q-18 ) q congruent 5 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+88*q^3-142*q^2+200*q-168 ) q congruent 7 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 8 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+70*q^3-88*q^2+128*q-96 ) q congruent 9 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 11 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+88*q^3-142*q^2+200*q-168 ) q congruent 13 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 16 modulo 60: 1/2592 q^3 phi1^2 ( q^3-2*q^2+q-18 ) q congruent 17 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+88*q^3-142*q^2+200*q-168 ) q congruent 19 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 21 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 23 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+88*q^3-142*q^2+200*q-168 ) q congruent 25 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 27 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 29 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+88*q^3-142*q^2+200*q-168 ) q congruent 31 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 32 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+70*q^3-88*q^2+128*q-96 ) q congruent 37 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 41 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+88*q^3-142*q^2+200*q-168 ) q congruent 43 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 47 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+88*q^3-142*q^2+200*q-168 ) q congruent 49 modulo 60: 1/2592 q^2 phi1^3 ( q^3-q^2-18 ) q congruent 53 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+88*q^3-142*q^2+200*q-168 ) q congruent 59 modulo 60: 1/2592 phi2 ( q^7-5*q^6+11*q^5-33*q^4+88*q^3-142*q^2+200*q-168 ) Fusion of maximal tori of C^F in those of G^F: [ 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 36 ], [ 5, 1, 2, 72 ], [ 6, 1, 2, 36 ], [ 7, 1, 2, 36 ], [ 8, 1, 2, 24 ], [ 9, 1, 1, 9 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 36 ], [ 14, 1, 2, 144 ], [ 15, 1, 2, 72 ], [ 16, 1, 3, 72 ], [ 17, 1, 4, 72 ], [ 17, 1, 6, 216 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 36 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 72 ], [ 22, 1, 4, 72 ], [ 23, 1, 2, 36 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 144 ], [ 26, 1, 4, 72 ], [ 27, 1, 4, 12 ], [ 27, 1, 6, 24 ], [ 29, 1, 4, 144 ], [ 31, 1, 4, 144 ], [ 32, 1, 3, 72 ], [ 33, 1, 7, 108 ], [ 34, 1, 4, 72 ], [ 36, 1, 4, 144 ], [ 37, 1, 3, 288 ], [ 38, 1, 11, 72 ], [ 38, 1, 12, 144 ], [ 38, 1, 18, 432 ], [ 39, 1, 3, 72 ], [ 40, 1, 4, 36 ], [ 40, 1, 6, 144 ], [ 42, 1, 5, 72 ], [ 42, 1, 6, 72 ], [ 43, 1, 13, 288 ], [ 44, 1, 7, 108 ], [ 45, 1, 4, 216 ], [ 46, 1, 4, 144 ], [ 46, 1, 6, 144 ], [ 47, 1, 12, 216 ], [ 49, 1, 6, 324 ], [ 50, 1, 10, 144 ], [ 50, 1, 12, 144 ], [ 51, 1, 9, 288 ], [ 52, 1, 7, 108 ], [ 53, 1, 18, 216 ], [ 54, 1, 10, 432 ], [ 55, 1, 12, 216 ], [ 56, 1, 17, 432 ], [ 57, 1, 15, 648 ], [ 58, 1, 13, 72 ], [ 58, 1, 14, 288 ], [ 58, 1, 15, 288 ], [ 59, 1, 5, 432 ], [ 59, 1, 8, 216 ], [ 60, 1, 14, 648 ], [ 61, 1, 6, 432 ], [ 61, 1, 9, 216 ], [ 62, 1, 21, 1296 ], [ 63, 1, 9, 864 ], [ 64, 1, 23, 648 ], [ 65, 1, 18, 432 ], [ 65, 1, 27, 864 ], [ 66, 1, 26, 1296 ] ] k = 16: F-action on Pi is () [67,1,16] Dynkin type is A_0(q) + T(phi1^4 phi4^2) Order of center |Z^F|: phi1^4 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 2 modulo 60: 1/18432 q^2 ( q^6-16*q^5+88*q^4-160*q^3-176*q^2+896*q-768 ) q congruent 3 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 4 modulo 60: 1/18432 q^2 ( q^6-16*q^5+88*q^4-160*q^3-176*q^2+896*q-768 ) q congruent 5 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 7 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 8 modulo 60: 1/18432 q^2 ( q^6-16*q^5+88*q^4-160*q^3-176*q^2+896*q-768 ) q congruent 9 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 11 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 13 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 16 modulo 60: 1/18432 q^2 ( q^6-16*q^5+88*q^4-160*q^3-176*q^2+896*q-768 ) q congruent 17 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 19 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 21 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 23 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 25 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 27 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 29 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 31 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 32 modulo 60: 1/18432 q^2 ( q^6-16*q^5+88*q^4-160*q^3-176*q^2+896*q-768 ) q congruent 37 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 41 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 43 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 47 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 49 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 53 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) q congruent 59 modulo 60: 1/18432 phi1 phi2 ( q^6-16*q^5+89*q^4-176*q^3-117*q^2+960*q-1125 ) Fusion of maximal tori of C^F in those of G^F: [ 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 48 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 144 ], [ 13, 1, 3, 96 ], [ 16, 1, 2, 384 ], [ 20, 1, 3, 576 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 25, 1, 2, 288 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 33, 1, 4, 768 ], [ 35, 1, 5, 1152 ], [ 39, 1, 1, 144 ], [ 39, 1, 5, 24 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 288 ], [ 41, 1, 3, 576 ], [ 41, 1, 5, 48 ], [ 41, 1, 8, 288 ], [ 43, 1, 3, 1152 ], [ 43, 1, 9, 192 ], [ 44, 1, 1, 576 ], [ 44, 1, 6, 192 ], [ 48, 1, 8, 384 ], [ 49, 1, 7, 1152 ], [ 49, 1, 11, 2304 ], [ 51, 1, 7, 768 ], [ 52, 1, 1, 576 ], [ 52, 1, 8, 576 ], [ 53, 1, 5, 2304 ], [ 53, 1, 10, 384 ], [ 53, 1, 13, 1152 ], [ 55, 1, 6, 1536 ], [ 56, 1, 11, 2304 ], [ 57, 1, 11, 2304 ], [ 59, 1, 1, 1152 ], [ 59, 1, 6, 96 ], [ 59, 1, 23, 1152 ], [ 60, 1, 18, 1152 ], [ 60, 1, 22, 4608 ], [ 60, 1, 31, 2304 ], [ 62, 1, 26, 2304 ], [ 62, 1, 33, 4608 ], [ 63, 1, 16, 768 ], [ 63, 1, 24, 4608 ], [ 64, 1, 28, 4608 ], [ 64, 1, 38, 9216 ], [ 65, 1, 33, 3072 ], [ 66, 1, 42, 9216 ] ] k = 17: F-action on Pi is () [67,1,17] Dynkin type is A_0(q) + T(phi2^4 phi4^2) Order of center |Z^F|: phi2^4 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 2 modulo 60: 1/18432 q^3 ( q^5-8*q^4+16*q^3+16*q^2-80*q+64 ) q congruent 3 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 4 modulo 60: 1/18432 q^3 ( q^5-8*q^4+16*q^3+16*q^2-80*q+64 ) q congruent 5 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 7 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 8 modulo 60: 1/18432 q^3 ( q^5-8*q^4+16*q^3+16*q^2-80*q+64 ) q congruent 9 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 11 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 13 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 16 modulo 60: 1/18432 q^3 ( q^5-8*q^4+16*q^3+16*q^2-80*q+64 ) q congruent 17 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 19 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 21 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 23 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 25 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 27 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 29 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 31 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 32 modulo 60: 1/18432 q^3 ( q^5-8*q^4+16*q^3+16*q^2-80*q+64 ) q congruent 37 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 41 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 43 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 47 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 49 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 53 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) q congruent 59 modulo 60: 1/18432 phi1^2 phi2 ( q^5-7*q^4+10*q^3+18*q^2-75*q+117 ) Fusion of maximal tori of C^F in those of G^F: [ 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 48 ], [ 4, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 2, 96 ], [ 13, 1, 4, 144 ], [ 16, 1, 4, 384 ], [ 20, 1, 2, 576 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 72 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 288 ], [ 27, 1, 6, 192 ], [ 28, 1, 4, 288 ], [ 33, 1, 10, 768 ], [ 35, 1, 4, 1152 ], [ 39, 1, 3, 144 ], [ 39, 1, 5, 24 ], [ 40, 1, 6, 192 ], [ 41, 1, 5, 48 ], [ 41, 1, 8, 288 ], [ 41, 1, 9, 288 ], [ 41, 1, 10, 576 ], [ 43, 1, 9, 192 ], [ 43, 1, 12, 1152 ], [ 44, 1, 4, 192 ], [ 44, 1, 10, 576 ], [ 48, 1, 9, 384 ], [ 49, 1, 4, 1152 ], [ 49, 1, 19, 2304 ], [ 51, 1, 4, 768 ], [ 52, 1, 5, 576 ], [ 52, 1, 10, 576 ], [ 53, 1, 11, 1152 ], [ 53, 1, 14, 384 ], [ 53, 1, 19, 2304 ], [ 55, 1, 19, 1536 ], [ 56, 1, 9, 2304 ], [ 57, 1, 8, 2304 ], [ 59, 1, 2, 1152 ], [ 59, 1, 6, 96 ], [ 59, 1, 24, 1152 ], [ 60, 1, 18, 1152 ], [ 60, 1, 26, 4608 ], [ 60, 1, 30, 2304 ], [ 62, 1, 25, 2304 ], [ 62, 1, 35, 4608 ], [ 63, 1, 15, 768 ], [ 63, 1, 22, 4608 ], [ 64, 1, 33, 4608 ], [ 64, 1, 39, 9216 ], [ 65, 1, 36, 3072 ], [ 66, 1, 45, 9216 ] ] k = 18: F-action on Pi is () [67,1,18] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi4^2) Order of center |Z^F|: phi1^2 phi2^2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 2 modulo 60: 1/1024 q^3 ( q^5-4*q^4-4*q^3+24*q^2-32 ) q congruent 3 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 4 modulo 60: 1/1024 q^3 ( q^5-4*q^4-4*q^3+24*q^2-32 ) q congruent 5 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 7 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 8 modulo 60: 1/1024 q^3 ( q^5-4*q^4-4*q^3+24*q^2-32 ) q congruent 9 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 11 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 13 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 16 modulo 60: 1/1024 q^3 ( q^5-4*q^4-4*q^3+24*q^2-32 ) q congruent 17 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 19 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 21 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 23 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 25 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 27 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 29 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 31 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 32 modulo 60: 1/1024 q^3 ( q^5-4*q^4-4*q^3+24*q^2-32 ) q congruent 37 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 41 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 43 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 47 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 49 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 53 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) q congruent 59 modulo 60: 1/1024 phi1 phi2^2 ( q^5-5*q^4+2*q^3+18*q^2-35*q+51 ) Fusion of maximal tori of C^F in those of G^F: [ 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ], [ 9, 1, 1, 11 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 32 ], [ 13, 1, 3, 32 ], [ 13, 1, 4, 8 ], [ 20, 1, 1, 32 ], [ 20, 1, 4, 32 ], [ 20, 1, 5, 64 ], [ 20, 1, 6, 64 ], [ 20, 1, 7, 64 ], [ 20, 1, 8, 64 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 40 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 40 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 32 ], [ 26, 1, 4, 32 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 35, 1, 2, 64 ], [ 35, 1, 7, 64 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 39, 1, 5, 24 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 96 ], [ 41, 1, 3, 32 ], [ 41, 1, 5, 112 ], [ 41, 1, 6, 32 ], [ 41, 1, 7, 64 ], [ 41, 1, 8, 96 ], [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], [ 43, 1, 1, 64 ], [ 43, 1, 5, 128 ], [ 43, 1, 7, 128 ], [ 43, 1, 8, 64 ], [ 43, 1, 9, 64 ], [ 43, 1, 10, 128 ], [ 43, 1, 13, 64 ], [ 44, 1, 4, 32 ], [ 44, 1, 5, 32 ], [ 44, 1, 6, 32 ], [ 44, 1, 9, 32 ], [ 48, 1, 8, 64 ], [ 48, 1, 9, 64 ], [ 49, 1, 4, 192 ], [ 49, 1, 7, 192 ], [ 49, 1, 13, 256 ], [ 49, 1, 14, 128 ], [ 49, 1, 15, 128 ], [ 49, 1, 17, 256 ], [ 49, 1, 18, 128 ], [ 49, 1, 20, 128 ], [ 52, 1, 2, 32 ], [ 52, 1, 5, 96 ], [ 52, 1, 8, 96 ], [ 52, 1, 9, 32 ], [ 53, 1, 2, 128 ], [ 53, 1, 10, 192 ], [ 53, 1, 11, 64 ], [ 53, 1, 12, 128 ], [ 53, 1, 13, 64 ], [ 53, 1, 14, 192 ], [ 56, 1, 4, 128 ], [ 56, 1, 16, 128 ], [ 57, 1, 7, 256 ], [ 57, 1, 8, 128 ], [ 57, 1, 11, 128 ], [ 57, 1, 17, 256 ], [ 59, 1, 3, 64 ], [ 59, 1, 6, 96 ], [ 59, 1, 16, 128 ], [ 59, 1, 21, 128 ], [ 59, 1, 23, 64 ], [ 59, 1, 24, 64 ], [ 60, 1, 18, 384 ], [ 60, 1, 20, 256 ], [ 60, 1, 29, 512 ], [ 60, 1, 30, 128 ], [ 60, 1, 31, 128 ], [ 60, 1, 33, 256 ], [ 60, 1, 34, 256 ], [ 60, 1, 37, 512 ], [ 60, 1, 38, 256 ], [ 62, 1, 25, 384 ], [ 62, 1, 26, 384 ], [ 62, 1, 34, 256 ], [ 62, 1, 36, 256 ], [ 62, 1, 38, 256 ], [ 62, 1, 40, 256 ], [ 63, 1, 15, 128 ], [ 63, 1, 16, 128 ], [ 63, 1, 23, 256 ], [ 63, 1, 25, 256 ], [ 64, 1, 28, 256 ], [ 64, 1, 33, 256 ], [ 64, 1, 35, 512 ], [ 64, 1, 36, 512 ], [ 64, 1, 40, 512 ], [ 64, 1, 41, 512 ], [ 66, 1, 39, 512 ], [ 66, 1, 46, 512 ] ] k = 19: F-action on Pi is () [67,1,19] Dynkin type is A_0(q) + T(phi1^4 phi2^2 phi4) Order of center |Z^F|: phi1^4 phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 2 modulo 60: 1/768 q^3 ( q^5-10*q^4+30*q^3-8*q^2-88*q+96 ) q congruent 3 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 4 modulo 60: 1/768 q^3 ( q^5-10*q^4+30*q^3-8*q^2-88*q+96 ) q congruent 5 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 7 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 8 modulo 60: 1/768 q^3 ( q^5-10*q^4+30*q^3-8*q^2-88*q+96 ) q congruent 9 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 11 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 13 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 16 modulo 60: 1/768 q^3 ( q^5-10*q^4+30*q^3-8*q^2-88*q+96 ) q congruent 17 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 19 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 21 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 23 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 25 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 27 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 29 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 31 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 32 modulo 60: 1/768 q^3 ( q^5-10*q^4+30*q^3-8*q^2-88*q+96 ) q congruent 37 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 41 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 43 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 47 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 49 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 53 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) q congruent 59 modulo 60: 1/768 phi1 phi2 ( q^6-10*q^5+31*q^4-18*q^3-63*q^2+108*q-81 ) Fusion of maximal tori of C^F in those of G^F: [ 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 20 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 34 ], [ 4, 1, 2, 14 ], [ 5, 1, 1, 32 ], [ 6, 1, 1, 40 ], [ 6, 1, 2, 24 ], [ 7, 1, 1, 28 ], [ 7, 1, 2, 12 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 14 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 36 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 68 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 36 ], [ 13, 1, 4, 16 ], [ 14, 1, 1, 64 ], [ 15, 1, 1, 64 ], [ 16, 1, 1, 40 ], [ 16, 1, 2, 88 ], [ 16, 1, 3, 24 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 32 ], [ 17, 1, 3, 96 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 72 ], [ 19, 1, 2, 24 ], [ 20, 1, 1, 56 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 72 ], [ 20, 1, 4, 24 ], [ 20, 1, 6, 96 ], [ 20, 1, 8, 96 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 64 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 48 ], [ 23, 1, 1, 30 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 50 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 84 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 8 ], [ 27, 1, 1, 48 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 84 ], [ 28, 1, 2, 60 ], [ 28, 1, 3, 28 ], [ 28, 1, 4, 4 ], [ 29, 1, 1, 96 ], [ 29, 1, 2, 32 ], [ 30, 1, 1, 96 ], [ 30, 1, 2, 32 ], [ 31, 1, 1, 64 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 48 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 96 ], [ 33, 1, 2, 80 ], [ 33, 1, 4, 192 ], [ 33, 1, 5, 64 ], [ 33, 1, 6, 48 ], [ 34, 1, 1, 96 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 1, 72 ], [ 35, 1, 2, 56 ], [ 35, 1, 3, 24 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 120 ], [ 35, 1, 6, 72 ], [ 35, 1, 7, 72 ], [ 35, 1, 8, 24 ], [ 36, 1, 1, 96 ], [ 36, 1, 2, 32 ], [ 37, 1, 1, 96 ], [ 37, 1, 2, 48 ], [ 38, 1, 2, 64 ], [ 38, 1, 7, 192 ], [ 39, 1, 1, 72 ], [ 39, 1, 2, 12 ], [ 39, 1, 4, 28 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 144 ], [ 40, 1, 2, 24 ], [ 40, 1, 3, 40 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 24 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 5, 24 ], [ 41, 1, 6, 72 ], [ 41, 1, 7, 32 ], [ 41, 1, 8, 32 ], [ 42, 1, 1, 96 ], [ 42, 1, 2, 48 ], [ 42, 1, 4, 48 ], [ 43, 1, 1, 96 ], [ 43, 1, 2, 16 ], [ 43, 1, 3, 96 ], [ 43, 1, 4, 48 ], [ 43, 1, 6, 192 ], [ 43, 1, 8, 48 ], [ 43, 1, 9, 32 ], [ 44, 1, 1, 48 ], [ 44, 1, 2, 120 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 24 ], [ 44, 1, 8, 8 ], [ 44, 1, 9, 48 ], [ 45, 1, 1, 96 ], [ 45, 1, 2, 96 ], [ 46, 1, 7, 192 ], [ 46, 1, 11, 192 ], [ 47, 1, 3, 128 ], [ 47, 1, 4, 32 ], [ 47, 1, 9, 96 ], [ 48, 1, 1, 96 ], [ 48, 1, 2, 48 ], [ 48, 1, 4, 96 ], [ 48, 1, 5, 48 ], [ 48, 1, 7, 96 ], [ 48, 1, 8, 96 ], [ 49, 1, 2, 144 ], [ 49, 1, 4, 48 ], [ 49, 1, 7, 144 ], [ 49, 1, 8, 48 ], [ 49, 1, 11, 192 ], [ 49, 1, 12, 192 ], [ 49, 1, 18, 192 ], [ 49, 1, 20, 192 ], [ 50, 1, 1, 96 ], [ 50, 1, 2, 96 ], [ 50, 1, 4, 96 ], [ 50, 1, 8, 96 ], [ 51, 1, 1, 96 ], [ 51, 1, 2, 32 ], [ 51, 1, 4, 16 ], [ 51, 1, 6, 96 ], [ 51, 1, 7, 80 ], [ 51, 1, 10, 96 ], [ 52, 1, 1, 144 ], [ 52, 1, 2, 144 ], [ 52, 1, 3, 72 ], [ 52, 1, 4, 24 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 56 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 96 ], [ 53, 1, 3, 48 ], [ 53, 1, 4, 16 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 96 ], [ 53, 1, 7, 144 ], [ 53, 1, 8, 48 ], [ 53, 1, 10, 96 ], [ 53, 1, 11, 64 ], [ 53, 1, 13, 96 ], [ 54, 1, 2, 192 ], [ 54, 1, 4, 64 ], [ 55, 1, 4, 160 ], [ 55, 1, 6, 192 ], [ 55, 1, 8, 64 ], [ 55, 1, 9, 192 ], [ 55, 1, 11, 96 ], [ 55, 1, 16, 192 ], [ 56, 1, 1, 96 ], [ 56, 1, 2, 96 ], [ 56, 1, 4, 112 ], [ 56, 1, 6, 96 ], [ 56, 1, 9, 16 ], [ 56, 1, 11, 144 ], [ 56, 1, 13, 96 ], [ 56, 1, 14, 96 ], [ 56, 1, 16, 48 ], [ 56, 1, 19, 96 ], [ 57, 1, 3, 192 ], [ 57, 1, 4, 96 ], [ 57, 1, 7, 96 ], [ 57, 1, 11, 192 ], [ 58, 1, 5, 64 ], [ 58, 1, 16, 384 ], [ 59, 1, 12, 288 ], [ 59, 1, 16, 48 ], [ 59, 1, 17, 96 ], [ 59, 1, 21, 16 ], [ 59, 1, 22, 48 ], [ 59, 1, 23, 96 ], [ 60, 1, 23, 384 ], [ 60, 1, 28, 192 ], [ 60, 1, 31, 192 ], [ 60, 1, 33, 96 ], [ 60, 1, 42, 384 ], [ 60, 1, 44, 192 ], [ 60, 1, 45, 96 ], [ 61, 1, 13, 256 ], [ 61, 1, 14, 192 ], [ 61, 1, 15, 64 ], [ 62, 1, 33, 192 ], [ 62, 1, 34, 192 ], [ 62, 1, 37, 288 ], [ 62, 1, 39, 96 ], [ 62, 1, 40, 192 ], [ 62, 1, 45, 192 ], [ 62, 1, 47, 192 ], [ 62, 1, 50, 192 ], [ 63, 1, 23, 192 ], [ 63, 1, 24, 192 ], [ 63, 1, 26, 96 ], [ 63, 1, 27, 32 ], [ 63, 1, 31, 192 ], [ 63, 1, 33, 192 ], [ 63, 1, 35, 192 ], [ 64, 1, 43, 384 ], [ 64, 1, 45, 384 ], [ 64, 1, 46, 192 ], [ 64, 1, 54, 384 ], [ 64, 1, 56, 192 ], [ 64, 1, 62, 384 ], [ 65, 1, 40, 384 ], [ 65, 1, 43, 384 ], [ 65, 1, 45, 128 ], [ 66, 1, 49, 384 ], [ 66, 1, 50, 384 ], [ 66, 1, 52, 384 ] ] k = 20: F-action on Pi is () [67,1,20] Dynkin type is A_0(q) + T(phi1^2 phi2^4 phi4) Order of center |Z^F|: phi1^2 phi2^4 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 2 modulo 60: 1/768 q^4 ( q^4-6*q^3+10*q^2-8 ) q congruent 3 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 4 modulo 60: 1/768 q^4 ( q^4-6*q^3+10*q^2-8 ) q congruent 5 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 7 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 8 modulo 60: 1/768 q^4 ( q^4-6*q^3+10*q^2-8 ) q congruent 9 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 11 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 13 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 16 modulo 60: 1/768 q^4 ( q^4-6*q^3+10*q^2-8 ) q congruent 17 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 19 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 21 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 23 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 25 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 27 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 29 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 31 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 32 modulo 60: 1/768 q^4 ( q^4-6*q^3+10*q^2-8 ) q congruent 37 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 41 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 43 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 47 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 49 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 53 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) q congruent 59 modulo 60: 1/768 phi1^2 phi2^2 ( q^4-6*q^3+12*q^2-12*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 20 ], [ 4, 1, 1, 14 ], [ 4, 1, 2, 34 ], [ 5, 1, 2, 32 ], [ 6, 1, 1, 24 ], [ 6, 1, 2, 40 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 28 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 14 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 36 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 68 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 36 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 64 ], [ 15, 1, 2, 64 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 40 ], [ 16, 1, 4, 88 ], [ 17, 1, 2, 96 ], [ 17, 1, 3, 32 ], [ 18, 1, 2, 64 ], [ 19, 1, 1, 24 ], [ 19, 1, 2, 72 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 72 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 56 ], [ 20, 1, 5, 96 ], [ 20, 1, 7, 96 ], [ 21, 1, 2, 48 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 64 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 30 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 50 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 84 ], [ 25, 1, 4, 48 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 48 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 24 ], [ 27, 1, 6, 48 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 28 ], [ 28, 1, 3, 60 ], [ 28, 1, 4, 84 ], [ 29, 1, 3, 32 ], [ 29, 1, 4, 96 ], [ 30, 1, 3, 96 ], [ 30, 1, 4, 32 ], [ 31, 1, 2, 48 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 64 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 96 ], [ 33, 1, 2, 48 ], [ 33, 1, 6, 80 ], [ 33, 1, 9, 64 ], [ 33, 1, 10, 192 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 34, 1, 4, 96 ], [ 35, 1, 1, 24 ], [ 35, 1, 2, 72 ], [ 35, 1, 3, 72 ], [ 35, 1, 4, 120 ], [ 35, 1, 5, 8 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 56 ], [ 35, 1, 8, 72 ], [ 36, 1, 3, 32 ], [ 36, 1, 4, 96 ], [ 37, 1, 2, 48 ], [ 37, 1, 3, 96 ], [ 38, 1, 6, 192 ], [ 38, 1, 10, 64 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 72 ], [ 39, 1, 4, 28 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 40 ], [ 40, 1, 3, 24 ], [ 40, 1, 6, 144 ], [ 41, 1, 2, 24 ], [ 41, 1, 4, 48 ], [ 41, 1, 5, 24 ], [ 41, 1, 6, 72 ], [ 41, 1, 7, 32 ], [ 41, 1, 8, 32 ], [ 41, 1, 9, 144 ], [ 41, 1, 10, 96 ], [ 42, 1, 2, 48 ], [ 42, 1, 4, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 2, 48 ], [ 43, 1, 4, 16 ], [ 43, 1, 8, 48 ], [ 43, 1, 9, 32 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 96 ], [ 43, 1, 14, 192 ], [ 44, 1, 2, 8 ], [ 44, 1, 4, 24 ], [ 44, 1, 5, 48 ], [ 44, 1, 6, 8 ], [ 44, 1, 8, 120 ], [ 44, 1, 10, 48 ], [ 45, 1, 5, 96 ], [ 45, 1, 6, 96 ], [ 46, 1, 8, 192 ], [ 46, 1, 12, 192 ], [ 47, 1, 4, 96 ], [ 47, 1, 9, 32 ], [ 47, 1, 10, 128 ], [ 48, 1, 2, 48 ], [ 48, 1, 3, 96 ], [ 48, 1, 5, 48 ], [ 48, 1, 6, 96 ], [ 48, 1, 9, 96 ], [ 48, 1, 10, 96 ], [ 49, 1, 2, 48 ], [ 49, 1, 4, 144 ], [ 49, 1, 7, 48 ], [ 49, 1, 8, 144 ], [ 49, 1, 14, 192 ], [ 49, 1, 15, 192 ], [ 49, 1, 16, 192 ], [ 49, 1, 19, 192 ], [ 50, 1, 5, 96 ], [ 50, 1, 9, 96 ], [ 50, 1, 11, 96 ], [ 50, 1, 12, 96 ], [ 51, 1, 3, 96 ], [ 51, 1, 4, 80 ], [ 51, 1, 5, 96 ], [ 51, 1, 7, 16 ], [ 51, 1, 8, 32 ], [ 51, 1, 9, 96 ], [ 52, 1, 3, 24 ], [ 52, 1, 4, 72 ], [ 52, 1, 5, 56 ], [ 52, 1, 8, 8 ], [ 52, 1, 9, 144 ], [ 52, 1, 10, 144 ], [ 53, 1, 3, 48 ], [ 53, 1, 4, 144 ], [ 53, 1, 7, 16 ], [ 53, 1, 8, 48 ], [ 53, 1, 9, 96 ], [ 53, 1, 11, 96 ], [ 53, 1, 12, 96 ], [ 53, 1, 13, 64 ], [ 53, 1, 14, 96 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 96 ], [ 54, 1, 9, 64 ], [ 54, 1, 12, 192 ], [ 55, 1, 4, 96 ], [ 55, 1, 10, 192 ], [ 55, 1, 11, 160 ], [ 55, 1, 17, 64 ], [ 55, 1, 19, 192 ], [ 55, 1, 20, 192 ], [ 56, 1, 4, 48 ], [ 56, 1, 5, 96 ], [ 56, 1, 7, 96 ], [ 56, 1, 9, 144 ], [ 56, 1, 10, 96 ], [ 56, 1, 11, 16 ], [ 56, 1, 15, 96 ], [ 56, 1, 16, 112 ], [ 56, 1, 18, 96 ], [ 56, 1, 20, 96 ], [ 57, 1, 4, 96 ], [ 57, 1, 7, 96 ], [ 57, 1, 8, 192 ], [ 57, 1, 9, 192 ], [ 58, 1, 5, 64 ], [ 58, 1, 26, 384 ], [ 59, 1, 13, 288 ], [ 59, 1, 16, 48 ], [ 59, 1, 18, 96 ], [ 59, 1, 21, 16 ], [ 59, 1, 22, 48 ], [ 59, 1, 24, 96 ], [ 60, 1, 24, 384 ], [ 60, 1, 28, 192 ], [ 60, 1, 30, 192 ], [ 60, 1, 33, 96 ], [ 60, 1, 39, 384 ], [ 60, 1, 43, 192 ], [ 60, 1, 45, 96 ], [ 61, 1, 14, 64 ], [ 61, 1, 15, 192 ], [ 61, 1, 16, 256 ], [ 62, 1, 35, 192 ], [ 62, 1, 36, 192 ], [ 62, 1, 37, 96 ], [ 62, 1, 38, 192 ], [ 62, 1, 39, 288 ], [ 62, 1, 44, 192 ], [ 62, 1, 48, 192 ], [ 62, 1, 49, 192 ], [ 63, 1, 22, 192 ], [ 63, 1, 25, 192 ], [ 63, 1, 26, 32 ], [ 63, 1, 27, 96 ], [ 63, 1, 30, 192 ], [ 63, 1, 32, 192 ], [ 63, 1, 36, 192 ], [ 64, 1, 42, 384 ], [ 64, 1, 44, 384 ], [ 64, 1, 46, 192 ], [ 64, 1, 55, 384 ], [ 64, 1, 56, 192 ], [ 64, 1, 63, 384 ], [ 65, 1, 41, 384 ], [ 65, 1, 42, 384 ], [ 65, 1, 44, 128 ], [ 66, 1, 48, 384 ], [ 66, 1, 51, 384 ], [ 66, 1, 53, 384 ] ] k = 21: F-action on Pi is () [67,1,21] Dynkin type is A_0(q) + T(phi8^2) Order of center |Z^F|: phi8^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 2 modulo 60: 1/192 q^4 ( q^4-16 ) q congruent 3 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 4 modulo 60: 1/192 q^4 ( q^4-16 ) q congruent 5 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 7 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 8 modulo 60: 1/192 q^4 ( q^4-16 ) q congruent 9 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 11 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 13 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 16 modulo 60: 1/192 q^4 ( q^4-16 ) q congruent 17 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 19 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 21 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 23 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 25 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 27 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 29 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 31 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 32 modulo 60: 1/192 q^4 ( q^4-16 ) q congruent 37 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 41 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 43 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 47 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 49 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 53 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) q congruent 59 modulo 60: 1/192 phi1 phi2 phi4 ( q^4-21 ) Fusion of maximal tori of C^F in those of G^F: [ 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 9, 1, 1, 3 ], [ 57, 1, 19, 96 ], [ 59, 1, 25, 48 ], [ 60, 1, 21, 96 ] ] k = 22: F-action on Pi is () [67,1,22] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi4^2) Order of center |Z^F|: phi1^2 phi2^2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 2 modulo 60: 1/128 q^2 ( q^6-4*q^4-4*q^2+16 ) q congruent 3 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 4 modulo 60: 1/128 q^2 ( q^6-4*q^4-4*q^2+16 ) q congruent 5 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 7 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 8 modulo 60: 1/128 q^2 ( q^6-4*q^4-4*q^2+16 ) q congruent 9 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 11 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 13 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 16 modulo 60: 1/128 q^2 ( q^6-4*q^4-4*q^2+16 ) q congruent 17 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 19 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 21 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 23 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 25 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 27 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 29 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 31 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 32 modulo 60: 1/128 q^2 ( q^6-4*q^4-4*q^2+16 ) q congruent 37 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 41 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 43 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 47 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 49 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 53 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) q congruent 59 modulo 60: 1/128 phi1^2 phi2^2 ( q^4-2*q^2-7 ) Fusion of maximal tori of C^F in those of G^F: [ 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 8 ], [ 5, 1, 2, 8 ], [ 5, 1, 3, 16 ], [ 5, 1, 4, 16 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 8 ], [ 13, 1, 3, 8 ], [ 14, 1, 1, 8 ], [ 14, 1, 2, 8 ], [ 21, 1, 1, 4 ], [ 21, 1, 2, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 8 ], [ 30, 1, 2, 16 ], [ 30, 1, 4, 16 ], [ 32, 1, 5, 32 ], [ 37, 1, 1, 8 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 8 ], [ 37, 1, 4, 16 ], [ 37, 1, 5, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 5, 8 ], [ 41, 1, 2, 16 ], [ 41, 1, 5, 16 ], [ 43, 1, 11, 32 ], [ 44, 1, 4, 16 ], [ 44, 1, 6, 16 ], [ 48, 1, 7, 16 ], [ 48, 1, 8, 16 ], [ 48, 1, 9, 16 ], [ 48, 1, 10, 16 ], [ 54, 1, 4, 32 ], [ 54, 1, 9, 32 ], [ 57, 1, 16, 32 ], [ 57, 1, 17, 32 ], [ 57, 1, 18, 32 ], [ 57, 1, 20, 64 ], [ 58, 1, 19, 64 ], [ 59, 1, 16, 32 ], [ 60, 1, 32, 64 ], [ 63, 1, 30, 32 ], [ 63, 1, 31, 32 ], [ 64, 1, 57, 64 ], [ 64, 1, 59, 64 ] ] k = 23: F-action on Pi is () [67,1,23] Dynkin type is A_0(q) + T(phi1^4 phi5) Order of center |Z^F|: phi1^4 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/1200 phi1 ( q^7-12*q^6+46*q^5-50*q^4-27*q^3+10*q^2-24*q+96 ) q congruent 2 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 3 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 4 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 5 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 7 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 8 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 9 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 11 modulo 60: 1/1200 phi1 ( q^7-12*q^6+46*q^5-50*q^4-27*q^3+10*q^2-24*q+96 ) q congruent 13 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 16 modulo 60: 1/1200 phi1 ( q^7-12*q^6+46*q^5-50*q^4-27*q^3+10*q^2-24*q+96 ) q congruent 17 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 19 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 21 modulo 60: 1/1200 phi1 ( q^7-12*q^6+46*q^5-50*q^4-27*q^3+10*q^2-24*q+96 ) q congruent 23 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 25 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 27 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 29 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 31 modulo 60: 1/1200 phi1 ( q^7-12*q^6+46*q^5-50*q^4-27*q^3+10*q^2-24*q+96 ) q congruent 32 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 37 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 41 modulo 60: 1/1200 phi1 ( q^7-12*q^6+46*q^5-50*q^4-27*q^3+10*q^2-24*q+96 ) q congruent 43 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 47 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 49 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 53 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 59 modulo 60: 1/1200 q phi2 phi4 ( q^4-14*q^3+71*q^2-154*q+120 ) Fusion of maximal tori of C^F in those of G^F: [ 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 10 ], [ 3, 1, 1, 20 ], [ 4, 1, 1, 10 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 20 ], [ 7, 1, 1, 20 ], [ 8, 1, 1, 10 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 20 ], [ 11, 1, 1, 60 ], [ 12, 1, 1, 40 ], [ 13, 1, 1, 60 ], [ 14, 1, 1, 10 ], [ 15, 1, 1, 20 ], [ 18, 1, 1, 60 ], [ 19, 1, 1, 60 ], [ 21, 1, 1, 40 ], [ 22, 1, 1, 40 ], [ 23, 1, 1, 30 ], [ 24, 1, 1, 60 ], [ 26, 1, 1, 40 ], [ 27, 1, 1, 120 ], [ 28, 1, 1, 120 ], [ 29, 1, 1, 40 ], [ 30, 1, 1, 60 ], [ 34, 1, 1, 120 ], [ 36, 1, 1, 120 ], [ 39, 1, 1, 120 ], [ 42, 1, 1, 120 ], [ 44, 1, 1, 240 ], [ 45, 1, 1, 120 ], [ 50, 1, 1, 240 ], [ 54, 1, 1, 240 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 100 ], [ 63, 1, 2, 50 ], [ 64, 1, 2, 300 ], [ 65, 1, 2, 200 ], [ 66, 1, 4, 600 ] ] k = 24: F-action on Pi is () [67,1,24] Dynkin type is A_0(q) + T(phi2^4 phi10) Order of center |Z^F|: phi2^4 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 2 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/1200 phi2 ( q^7-8*q^6+26*q^5-50*q^4+73*q^3-90*q^2+96*q-96 ) q congruent 5 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/1200 phi2 ( q^7-8*q^6+26*q^5-50*q^4+73*q^3-90*q^2+96*q-96 ) q congruent 11 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 17 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/1200 phi2 ( q^7-8*q^6+26*q^5-50*q^4+73*q^3-90*q^2+96*q-96 ) q congruent 21 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/1200 phi2 ( q^7-8*q^6+26*q^5-50*q^4+73*q^3-90*q^2+96*q-96 ) q congruent 31 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/1200 phi2 ( q^7-8*q^6+26*q^5-50*q^4+73*q^3-90*q^2+96*q-96 ) q congruent 53 modulo 60: 1/1200 q^2 phi1^2 phi4 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/1200 phi2 ( q^7-8*q^6+26*q^5-50*q^4+73*q^3-90*q^2+96*q-96 ) Fusion of maximal tori of C^F in those of G^F: [ 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 10 ], [ 3, 1, 2, 20 ], [ 4, 1, 2, 10 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 20 ], [ 7, 1, 2, 20 ], [ 8, 1, 2, 10 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 20 ], [ 11, 1, 2, 60 ], [ 12, 1, 2, 40 ], [ 13, 1, 4, 60 ], [ 14, 1, 2, 10 ], [ 15, 1, 2, 20 ], [ 18, 1, 2, 60 ], [ 19, 1, 2, 60 ], [ 21, 1, 2, 40 ], [ 22, 1, 4, 40 ], [ 23, 1, 2, 30 ], [ 24, 1, 2, 60 ], [ 26, 1, 4, 40 ], [ 27, 1, 6, 120 ], [ 28, 1, 4, 120 ], [ 29, 1, 4, 40 ], [ 30, 1, 3, 60 ], [ 34, 1, 4, 120 ], [ 36, 1, 4, 120 ], [ 39, 1, 3, 120 ], [ 42, 1, 6, 120 ], [ 44, 1, 10, 240 ], [ 45, 1, 6, 120 ], [ 50, 1, 12, 240 ], [ 54, 1, 8, 10 ], [ 54, 1, 14, 240 ], [ 61, 1, 3, 100 ], [ 63, 1, 3, 50 ], [ 64, 1, 5, 300 ], [ 65, 1, 4, 200 ], [ 66, 1, 9, 600 ] ] k = 25: F-action on Pi is () [67,1,25] Dynkin type is A_0(q) + T(phi5^2) Order of center |Z^F|: phi5^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/600 phi1 ( q^7+3*q^6+6*q^5+10*q^4+3*q^3-5*q^2-14*q-24 ) q congruent 2 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 3 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 4 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 5 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 7 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 8 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 9 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 11 modulo 60: 1/600 phi1 ( q^7+3*q^6+6*q^5+10*q^4+3*q^3-5*q^2-14*q-24 ) q congruent 13 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 16 modulo 60: 1/600 phi1 ( q^7+3*q^6+6*q^5+10*q^4+3*q^3-5*q^2-14*q-24 ) q congruent 17 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 19 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 21 modulo 60: 1/600 phi1 ( q^7+3*q^6+6*q^5+10*q^4+3*q^3-5*q^2-14*q-24 ) q congruent 23 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 25 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 27 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 29 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 31 modulo 60: 1/600 phi1 ( q^7+3*q^6+6*q^5+10*q^4+3*q^3-5*q^2-14*q-24 ) q congruent 32 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 37 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 41 modulo 60: 1/600 phi1 ( q^7+3*q^6+6*q^5+10*q^4+3*q^3-5*q^2-14*q-24 ) q congruent 43 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 47 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 49 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 53 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) q congruent 59 modulo 60: 1/600 q phi2 phi4 ( q^4+q^3+q^2+q-10 ) Fusion of maximal tori of C^F in those of G^F: [ 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 1, 24 ], [ 54, 1, 6, 120 ] ] k = 26: F-action on Pi is () [67,1,26] Dynkin type is A_0(q) + T(phi10^2) Order of center |Z^F|: phi10^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 2 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 3 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 4 modulo 60: 1/600 phi2 ( q^7-3*q^6+6*q^5-10*q^4+3*q^3+5*q^2-14*q+24 ) q congruent 5 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 7 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 8 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 9 modulo 60: 1/600 phi2 ( q^7-3*q^6+6*q^5-10*q^4+3*q^3+5*q^2-14*q+24 ) q congruent 11 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 13 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 16 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 17 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 19 modulo 60: 1/600 phi2 ( q^7-3*q^6+6*q^5-10*q^4+3*q^3+5*q^2-14*q+24 ) q congruent 21 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 23 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 25 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 27 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 29 modulo 60: 1/600 phi2 ( q^7-3*q^6+6*q^5-10*q^4+3*q^3+5*q^2-14*q+24 ) q congruent 31 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 32 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 37 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 41 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 43 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 47 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 49 modulo 60: 1/600 phi2 ( q^7-3*q^6+6*q^5-10*q^4+3*q^3+5*q^2-14*q+24 ) q congruent 53 modulo 60: 1/600 q phi1 phi4 ( q^4-q^3+q^2-q-10 ) q congruent 59 modulo 60: 1/600 phi2 ( q^7-3*q^6+6*q^5-10*q^4+3*q^3+5*q^2-14*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 26 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 2, 24 ], [ 54, 1, 8, 120 ] ] k = 27: F-action on Pi is () [67,1,27] Dynkin type is A_0(q) + T(phi1^2 phi2^4 phi3) Order of center |Z^F|: phi1^2 phi2^4 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/6912 phi1^2 ( q^6-7*q^5+52*q^3+7*q^2-101*q-192 ) q congruent 2 modulo 60: 1/6912 q phi2 ( q^6-10*q^5+25*q^4+20*q^3-84*q^2-48*q+128 ) q congruent 3 modulo 60: 1/6912 q phi1 phi2 ( q^5-9*q^4+16*q^3+36*q^2-81*q-27 ) q congruent 4 modulo 60: 1/6912 q phi1 ( q^6-8*q^5+7*q^4+52*q^3-12*q^2-144*q-256 ) q congruent 5 modulo 60: 1/6912 q phi2^2 ( q^5-11*q^4+36*q^3-16*q^2-101*q+155 ) q congruent 7 modulo 60: 1/6912 phi1^2 ( q^6-7*q^5+52*q^3+7*q^2-101*q-192 ) q congruent 8 modulo 60: 1/6912 q phi2 ( q^6-10*q^5+25*q^4+20*q^3-84*q^2-48*q+128 ) q congruent 9 modulo 60: 1/6912 q phi1 phi2 ( q^5-9*q^4+16*q^3+36*q^2-81*q-27 ) q congruent 11 modulo 60: 1/6912 q phi2^2 ( q^5-11*q^4+36*q^3-16*q^2-101*q+155 ) q congruent 13 modulo 60: 1/6912 phi1^2 ( q^6-7*q^5+52*q^3+7*q^2-101*q-192 ) q congruent 16 modulo 60: 1/6912 q phi1 ( q^6-8*q^5+7*q^4+52*q^3-12*q^2-144*q-256 ) q congruent 17 modulo 60: 1/6912 q phi2^2 ( q^5-11*q^4+36*q^3-16*q^2-101*q+155 ) q congruent 19 modulo 60: 1/6912 phi1^2 ( q^6-7*q^5+52*q^3+7*q^2-101*q-192 ) q congruent 21 modulo 60: 1/6912 q phi1 phi2 ( q^5-9*q^4+16*q^3+36*q^2-81*q-27 ) q congruent 23 modulo 60: 1/6912 q phi2^2 ( q^5-11*q^4+36*q^3-16*q^2-101*q+155 ) q congruent 25 modulo 60: 1/6912 phi1^2 ( q^6-7*q^5+52*q^3+7*q^2-101*q-192 ) q congruent 27 modulo 60: 1/6912 q phi1 phi2 ( q^5-9*q^4+16*q^3+36*q^2-81*q-27 ) q congruent 29 modulo 60: 1/6912 q phi2^2 ( q^5-11*q^4+36*q^3-16*q^2-101*q+155 ) q congruent 31 modulo 60: 1/6912 phi1^2 ( q^6-7*q^5+52*q^3+7*q^2-101*q-192 ) q congruent 32 modulo 60: 1/6912 q phi2 ( q^6-10*q^5+25*q^4+20*q^3-84*q^2-48*q+128 ) q congruent 37 modulo 60: 1/6912 phi1^2 ( q^6-7*q^5+52*q^3+7*q^2-101*q-192 ) q congruent 41 modulo 60: 1/6912 q phi2^2 ( q^5-11*q^4+36*q^3-16*q^2-101*q+155 ) q congruent 43 modulo 60: 1/6912 phi1^2 ( q^6-7*q^5+52*q^3+7*q^2-101*q-192 ) q congruent 47 modulo 60: 1/6912 q phi2^2 ( q^5-11*q^4+36*q^3-16*q^2-101*q+155 ) q congruent 49 modulo 60: 1/6912 phi1^2 ( q^6-7*q^5+52*q^3+7*q^2-101*q-192 ) q congruent 53 modulo 60: 1/6912 q phi2^2 ( q^5-11*q^4+36*q^3-16*q^2-101*q+155 ) q congruent 59 modulo 60: 1/6912 q phi2^2 ( q^5-11*q^4+36*q^3-16*q^2-101*q+155 ) Fusion of maximal tori of C^F in those of G^F: [ 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 42 ], [ 4, 1, 2, 24 ], [ 6, 1, 1, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 1, 6 ], [ 12, 1, 2, 96 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 144 ], [ 13, 1, 4, 144 ], [ 16, 1, 1, 72 ], [ 16, 1, 2, 48 ], [ 16, 1, 4, 192 ], [ 17, 1, 2, 192 ], [ 20, 1, 2, 288 ], [ 22, 1, 2, 48 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 72 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 192 ], [ 27, 1, 5, 6 ], [ 27, 1, 6, 192 ], [ 28, 1, 2, 144 ], [ 28, 1, 4, 288 ], [ 31, 1, 2, 144 ], [ 32, 1, 2, 192 ], [ 33, 1, 1, 144 ], [ 33, 1, 2, 288 ], [ 35, 1, 3, 288 ], [ 35, 1, 4, 576 ], [ 37, 1, 2, 96 ], [ 38, 1, 6, 384 ], [ 38, 1, 9, 192 ], [ 39, 1, 2, 48 ], [ 39, 1, 3, 144 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 192 ], [ 40, 1, 3, 48 ], [ 40, 1, 6, 192 ], [ 41, 1, 4, 288 ], [ 41, 1, 9, 288 ], [ 41, 1, 10, 576 ], [ 42, 1, 3, 72 ], [ 43, 1, 8, 96 ], [ 43, 1, 12, 576 ], [ 44, 1, 3, 18 ], [ 44, 1, 5, 288 ], [ 44, 1, 10, 576 ], [ 46, 1, 9, 576 ], [ 47, 1, 2, 288 ], [ 47, 1, 4, 576 ], [ 48, 1, 3, 576 ], [ 50, 1, 6, 144 ], [ 51, 1, 3, 384 ], [ 51, 1, 5, 288 ], [ 51, 1, 6, 96 ], [ 52, 1, 4, 576 ], [ 52, 1, 10, 576 ], [ 53, 1, 9, 576 ], [ 53, 1, 16, 216 ], [ 53, 1, 17, 144 ], [ 53, 1, 19, 1152 ], [ 55, 1, 5, 576 ], [ 55, 1, 10, 1152 ], [ 55, 1, 18, 576 ], [ 56, 1, 8, 432 ], [ 56, 1, 10, 1152 ], [ 58, 1, 4, 384 ], [ 58, 1, 27, 1152 ], [ 59, 1, 2, 1152 ], [ 59, 1, 4, 36 ], [ 59, 1, 18, 1152 ], [ 59, 1, 19, 144 ], [ 60, 1, 2, 432 ], [ 60, 1, 11, 864 ], [ 61, 1, 17, 1152 ], [ 62, 1, 5, 864 ], [ 62, 1, 11, 1728 ], [ 63, 1, 5, 864 ], [ 63, 1, 13, 288 ], [ 63, 1, 14, 2304 ], [ 64, 1, 8, 1728 ], [ 64, 1, 13, 3456 ], [ 65, 1, 30, 1152 ], [ 65, 1, 32, 2304 ], [ 66, 1, 35, 3456 ] ] k = 28: F-action on Pi is () [67,1,28] Dynkin type is A_0(q) + T(phi1^4 phi2^2 phi6) Order of center |Z^F|: phi1^4 phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1523 ) q congruent 2 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-540*q^3+1008*q^2+128*q-768 ) q congruent 3 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1395 ) q congruent 4 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-516*q^2-48*q+1280 ) q congruent 5 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-573*q^3+1188*q^2+77*q-960 ) q congruent 7 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1523 ) q congruent 8 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-540*q^3+1008*q^2+128*q-768 ) q congruent 9 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1395 ) q congruent 11 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-573*q^3+1188*q^2+77*q-960 ) q congruent 13 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1523 ) q congruent 16 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-516*q^2-48*q+1280 ) q congruent 17 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-573*q^3+1188*q^2+77*q-960 ) q congruent 19 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1523 ) q congruent 21 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1395 ) q congruent 23 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-573*q^3+1188*q^2+77*q-960 ) q congruent 25 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1523 ) q congruent 27 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1395 ) q congruent 29 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-573*q^3+1188*q^2+77*q-960 ) q congruent 31 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1523 ) q congruent 32 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-540*q^3+1008*q^2+128*q-768 ) q congruent 37 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1523 ) q congruent 41 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-573*q^3+1188*q^2+77*q-960 ) q congruent 43 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1523 ) q congruent 47 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-573*q^3+1188*q^2+77*q-960 ) q congruent 49 modulo 60: 1/6912 q phi1 ( q^6-14*q^5+49*q^4+76*q^3-549*q^2+66*q+1523 ) q congruent 53 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-573*q^3+1188*q^2+77*q-960 ) q congruent 59 modulo 60: 1/6912 phi2 ( q^7-16*q^6+79*q^5-52*q^4-573*q^3+1188*q^2+77*q-960 ) Fusion of maximal tori of C^F in those of G^F: [ 28 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 32 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 42 ], [ 6, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 12, 1, 2, 6 ], [ 13, 1, 1, 144 ], [ 13, 1, 3, 144 ], [ 13, 1, 4, 72 ], [ 16, 1, 2, 192 ], [ 16, 1, 3, 72 ], [ 16, 1, 4, 48 ], [ 17, 1, 3, 192 ], [ 20, 1, 3, 288 ], [ 22, 1, 3, 48 ], [ 23, 1, 1, 24 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 25, 1, 2, 192 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 48 ], [ 27, 1, 1, 192 ], [ 27, 1, 4, 6 ], [ 28, 1, 1, 288 ], [ 28, 1, 3, 144 ], [ 31, 1, 3, 144 ], [ 32, 1, 2, 192 ], [ 33, 1, 6, 288 ], [ 33, 1, 8, 144 ], [ 35, 1, 5, 576 ], [ 35, 1, 6, 288 ], [ 37, 1, 2, 96 ], [ 38, 1, 4, 192 ], [ 38, 1, 7, 384 ], [ 39, 1, 1, 144 ], [ 39, 1, 2, 48 ], [ 40, 1, 1, 192 ], [ 40, 1, 2, 48 ], [ 40, 1, 3, 192 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 288 ], [ 41, 1, 3, 576 ], [ 41, 1, 4, 288 ], [ 42, 1, 5, 72 ], [ 43, 1, 3, 576 ], [ 43, 1, 8, 96 ], [ 44, 1, 1, 576 ], [ 44, 1, 7, 18 ], [ 44, 1, 9, 288 ], [ 46, 1, 10, 576 ], [ 47, 1, 7, 288 ], [ 47, 1, 9, 576 ], [ 48, 1, 4, 576 ], [ 50, 1, 7, 144 ], [ 51, 1, 3, 96 ], [ 51, 1, 6, 384 ], [ 51, 1, 10, 288 ], [ 52, 1, 1, 576 ], [ 52, 1, 3, 576 ], [ 53, 1, 5, 1152 ], [ 53, 1, 6, 576 ], [ 53, 1, 15, 144 ], [ 53, 1, 18, 216 ], [ 55, 1, 7, 576 ], [ 55, 1, 14, 576 ], [ 55, 1, 16, 1152 ], [ 56, 1, 12, 432 ], [ 56, 1, 14, 1152 ], [ 58, 1, 4, 384 ], [ 58, 1, 22, 1152 ], [ 59, 1, 1, 1152 ], [ 59, 1, 5, 36 ], [ 59, 1, 17, 1152 ], [ 59, 1, 20, 144 ], [ 60, 1, 8, 432 ], [ 60, 1, 10, 864 ], [ 61, 1, 22, 1152 ], [ 62, 1, 6, 864 ], [ 62, 1, 8, 1728 ], [ 63, 1, 8, 864 ], [ 63, 1, 12, 288 ], [ 63, 1, 20, 2304 ], [ 64, 1, 16, 1728 ], [ 64, 1, 17, 3456 ], [ 65, 1, 31, 1152 ], [ 65, 1, 37, 2304 ], [ 66, 1, 36, 3456 ] ] k = 29: F-action on Pi is () [67,1,29] Dynkin type is A_0(q) + T(phi3^2 phi6^2) Order of center |Z^F|: phi3^2 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 2 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 3 modulo 60: 1/1728 q^2 phi1 phi2 ( q^4-5*q^2-12 ) q congruent 4 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 5 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 7 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 8 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 9 modulo 60: 1/1728 q^2 phi1 phi2 ( q^4-5*q^2-12 ) q congruent 11 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 13 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 16 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 17 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 19 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 21 modulo 60: 1/1728 q^2 phi1 phi2 ( q^4-5*q^2-12 ) q congruent 23 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 25 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 27 modulo 60: 1/1728 q^2 phi1 phi2 ( q^4-5*q^2-12 ) q congruent 29 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 31 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 32 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 37 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 41 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 43 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 47 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 49 modulo 60: 1/1728 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-20*q-32 ) q congruent 53 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) q congruent 59 modulo 60: 1/1728 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-20*q+32 ) Fusion of maximal tori of C^F in those of G^F: [ 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 27, 1, 4, 24 ], [ 27, 1, 5, 24 ], [ 38, 1, 4, 192 ], [ 38, 1, 9, 192 ], [ 40, 1, 4, 24 ], [ 40, 1, 5, 24 ], [ 58, 1, 6, 192 ], [ 58, 1, 24, 576 ], [ 59, 1, 9, 72 ], [ 59, 1, 10, 72 ], [ 65, 1, 11, 576 ], [ 65, 1, 14, 576 ] ] k = 30: F-action on Pi is () [67,1,30] Dynkin type is A_0(q) + T(phi1^4 phi2^2 phi3) Order of center |Z^F|: phi1^4 phi2^2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 2 modulo 60: 1/1152 q^2 phi1 phi2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 3 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 4 modulo 60: 1/1152 q^2 phi1 phi2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 5 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 7 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 8 modulo 60: 1/1152 q^2 phi1 phi2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 9 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 11 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 13 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 16 modulo 60: 1/1152 q^2 phi1 phi2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 17 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 19 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 21 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 23 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 25 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 27 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 29 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 31 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 32 modulo 60: 1/1152 q^2 phi1 phi2 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 37 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 41 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 43 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 47 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 49 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 53 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 59 modulo 60: 1/1152 q phi1 phi2^2 ( q^4-10*q^3+30*q^2-18*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 26 ], [ 4, 1, 1, 46 ], [ 4, 1, 2, 12 ], [ 5, 1, 1, 80 ], [ 6, 1, 1, 96 ], [ 7, 1, 1, 40 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 40 ], [ 12, 1, 1, 70 ], [ 13, 1, 1, 72 ], [ 13, 1, 2, 24 ], [ 13, 1, 3, 48 ], [ 13, 1, 4, 24 ], [ 14, 1, 1, 120 ], [ 15, 1, 1, 152 ], [ 16, 1, 1, 176 ], [ 16, 1, 2, 24 ], [ 17, 1, 1, 240 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 112 ], [ 20, 1, 1, 144 ], [ 20, 1, 2, 112 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 120 ], [ 22, 1, 2, 72 ], [ 23, 1, 1, 18 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 36 ], [ 24, 1, 2, 28 ], [ 25, 1, 1, 60 ], [ 25, 1, 2, 24 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 48 ], [ 26, 1, 3, 32 ], [ 27, 1, 1, 48 ], [ 27, 1, 2, 32 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 72 ], [ 28, 1, 2, 72 ], [ 28, 1, 3, 48 ], [ 29, 1, 1, 144 ], [ 29, 1, 2, 160 ], [ 30, 1, 1, 144 ], [ 30, 1, 2, 96 ], [ 31, 1, 1, 168 ], [ 31, 1, 2, 184 ], [ 32, 1, 1, 224 ], [ 33, 1, 1, 144 ], [ 33, 1, 2, 48 ], [ 33, 1, 4, 96 ], [ 34, 1, 1, 96 ], [ 34, 1, 2, 128 ], [ 35, 1, 1, 144 ], [ 35, 1, 2, 96 ], [ 35, 1, 3, 144 ], [ 36, 1, 1, 48 ], [ 36, 1, 2, 96 ], [ 37, 1, 1, 96 ], [ 37, 1, 2, 48 ], [ 38, 1, 1, 288 ], [ 38, 1, 3, 144 ], [ 38, 1, 5, 192 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 48 ], [ 40, 1, 1, 36 ], [ 40, 1, 3, 40 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 96 ], [ 41, 1, 3, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], [ 42, 1, 1, 96 ], [ 42, 1, 3, 48 ], [ 42, 1, 4, 128 ], [ 43, 1, 1, 96 ], [ 43, 1, 2, 192 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 32 ], [ 44, 1, 1, 48 ], [ 44, 1, 2, 96 ], [ 44, 1, 3, 42 ], [ 44, 1, 5, 48 ], [ 44, 1, 9, 96 ], [ 45, 1, 1, 96 ], [ 45, 1, 2, 192 ], [ 45, 1, 3, 120 ], [ 46, 1, 1, 192 ], [ 46, 1, 2, 256 ], [ 46, 1, 3, 240 ], [ 47, 1, 1, 144 ], [ 47, 1, 2, 144 ], [ 47, 1, 3, 96 ], [ 48, 1, 1, 96 ], [ 48, 1, 2, 192 ], [ 48, 1, 3, 96 ], [ 48, 1, 7, 192 ], [ 50, 1, 2, 192 ], [ 50, 1, 3, 72 ], [ 50, 1, 4, 192 ], [ 50, 1, 5, 64 ], [ 50, 1, 6, 24 ], [ 51, 1, 1, 48 ], [ 51, 1, 2, 288 ], [ 51, 1, 5, 80 ], [ 51, 1, 6, 48 ], [ 52, 1, 2, 96 ], [ 52, 1, 3, 96 ], [ 52, 1, 9, 96 ], [ 53, 1, 1, 96 ], [ 53, 1, 2, 192 ], [ 53, 1, 3, 192 ], [ 53, 1, 9, 96 ], [ 53, 1, 16, 192 ], [ 53, 1, 17, 72 ], [ 54, 1, 2, 192 ], [ 54, 1, 3, 144 ], [ 54, 1, 5, 192 ], [ 54, 1, 7, 96 ], [ 55, 1, 1, 96 ], [ 55, 1, 2, 192 ], [ 55, 1, 3, 336 ], [ 55, 1, 5, 96 ], [ 55, 1, 9, 192 ], [ 56, 1, 2, 192 ], [ 56, 1, 3, 216 ], [ 56, 1, 5, 192 ], [ 56, 1, 6, 192 ], [ 56, 1, 7, 192 ], [ 56, 1, 8, 168 ], [ 58, 1, 2, 384 ], [ 58, 1, 3, 288 ], [ 58, 1, 7, 192 ], [ 58, 1, 9, 128 ], [ 59, 1, 3, 192 ], [ 59, 1, 4, 108 ], [ 59, 1, 17, 192 ], [ 59, 1, 19, 24 ], [ 60, 1, 2, 432 ], [ 60, 1, 5, 288 ], [ 60, 1, 11, 144 ], [ 61, 1, 4, 288 ], [ 61, 1, 7, 384 ], [ 61, 1, 12, 192 ], [ 61, 1, 19, 192 ], [ 62, 1, 2, 432 ], [ 62, 1, 5, 432 ], [ 62, 1, 10, 288 ], [ 63, 1, 4, 144 ], [ 63, 1, 5, 48 ], [ 63, 1, 10, 288 ], [ 63, 1, 13, 144 ], [ 63, 1, 21, 384 ], [ 63, 1, 29, 384 ], [ 64, 1, 6, 288 ], [ 64, 1, 8, 288 ], [ 64, 1, 14, 576 ], [ 64, 1, 19, 576 ], [ 65, 1, 23, 192 ], [ 65, 1, 28, 576 ], [ 65, 1, 39, 384 ], [ 66, 1, 27, 576 ], [ 66, 1, 34, 576 ] ] k = 31: F-action on Pi is () [67,1,31] Dynkin type is A_0(q) + T(phi1^2 phi2^4 phi6) Order of center |Z^F|: phi1^2 phi2^4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 2 modulo 60: 1/1152 q^2 phi1 phi2^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 4 modulo 60: 1/1152 q^2 phi1 phi2^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 7 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 8 modulo 60: 1/1152 q^2 phi1 phi2^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 11 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 13 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 16 modulo 60: 1/1152 q^2 phi1 phi2^2 ( q^3-8*q^2+20*q-16 ) q congruent 17 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 19 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 21 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 23 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 25 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 27 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 29 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 31 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 32 modulo 60: 1/1152 q^2 phi1 phi2^2 ( q^3-8*q^2+20*q-16 ) q congruent 37 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 41 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 43 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 47 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 49 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 53 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) q congruent 59 modulo 60: 1/1152 q phi1^2 phi2^2 ( q^3-7*q^2+13*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 26 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 46 ], [ 5, 1, 2, 80 ], [ 6, 1, 2, 96 ], [ 7, 1, 2, 40 ], [ 8, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 40 ], [ 12, 1, 2, 70 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 48 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 72 ], [ 14, 1, 2, 120 ], [ 15, 1, 2, 152 ], [ 16, 1, 3, 176 ], [ 16, 1, 4, 24 ], [ 17, 1, 4, 240 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 112 ], [ 20, 1, 3, 112 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 48 ], [ 22, 1, 3, 72 ], [ 22, 1, 4, 120 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 18 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 36 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 60 ], [ 25, 1, 4, 24 ], [ 26, 1, 2, 32 ], [ 26, 1, 4, 48 ], [ 27, 1, 3, 32 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 48 ], [ 28, 1, 3, 72 ], [ 28, 1, 4, 72 ], [ 29, 1, 3, 160 ], [ 29, 1, 4, 144 ], [ 30, 1, 3, 144 ], [ 30, 1, 4, 96 ], [ 31, 1, 3, 184 ], [ 31, 1, 4, 168 ], [ 32, 1, 3, 224 ], [ 33, 1, 6, 48 ], [ 33, 1, 8, 144 ], [ 33, 1, 10, 96 ], [ 34, 1, 3, 128 ], [ 34, 1, 4, 96 ], [ 35, 1, 6, 144 ], [ 35, 1, 7, 96 ], [ 35, 1, 8, 144 ], [ 36, 1, 3, 96 ], [ 36, 1, 4, 48 ], [ 37, 1, 2, 48 ], [ 37, 1, 3, 96 ], [ 38, 1, 8, 192 ], [ 38, 1, 11, 144 ], [ 38, 1, 12, 288 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 48 ], [ 40, 1, 2, 40 ], [ 40, 1, 6, 36 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 96 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 96 ], [ 42, 1, 2, 128 ], [ 42, 1, 5, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 3, 32 ], [ 43, 1, 4, 192 ], [ 43, 1, 8, 48 ], [ 43, 1, 13, 96 ], [ 44, 1, 5, 96 ], [ 44, 1, 7, 42 ], [ 44, 1, 8, 96 ], [ 44, 1, 9, 48 ], [ 44, 1, 10, 48 ], [ 45, 1, 4, 120 ], [ 45, 1, 5, 192 ], [ 45, 1, 6, 96 ], [ 46, 1, 4, 240 ], [ 46, 1, 5, 256 ], [ 46, 1, 6, 192 ], [ 47, 1, 7, 144 ], [ 47, 1, 8, 144 ], [ 47, 1, 10, 96 ], [ 48, 1, 4, 96 ], [ 48, 1, 5, 192 ], [ 48, 1, 6, 96 ], [ 48, 1, 10, 192 ], [ 50, 1, 7, 24 ], [ 50, 1, 8, 64 ], [ 50, 1, 9, 192 ], [ 50, 1, 10, 72 ], [ 50, 1, 11, 192 ], [ 51, 1, 3, 48 ], [ 51, 1, 8, 288 ], [ 51, 1, 9, 48 ], [ 51, 1, 10, 80 ], [ 52, 1, 2, 96 ], [ 52, 1, 4, 96 ], [ 52, 1, 9, 96 ], [ 53, 1, 6, 96 ], [ 53, 1, 8, 192 ], [ 53, 1, 12, 192 ], [ 53, 1, 15, 72 ], [ 53, 1, 18, 192 ], [ 53, 1, 20, 96 ], [ 54, 1, 10, 144 ], [ 54, 1, 11, 96 ], [ 54, 1, 12, 192 ], [ 54, 1, 13, 192 ], [ 55, 1, 12, 336 ], [ 55, 1, 13, 192 ], [ 55, 1, 14, 96 ], [ 55, 1, 15, 96 ], [ 55, 1, 20, 192 ], [ 56, 1, 12, 168 ], [ 56, 1, 13, 192 ], [ 56, 1, 15, 192 ], [ 56, 1, 17, 216 ], [ 56, 1, 18, 192 ], [ 56, 1, 19, 192 ], [ 58, 1, 10, 192 ], [ 58, 1, 11, 128 ], [ 58, 1, 12, 384 ], [ 58, 1, 14, 288 ], [ 59, 1, 3, 192 ], [ 59, 1, 5, 108 ], [ 59, 1, 18, 192 ], [ 59, 1, 20, 24 ], [ 60, 1, 8, 432 ], [ 60, 1, 9, 288 ], [ 60, 1, 10, 144 ], [ 61, 1, 6, 288 ], [ 61, 1, 8, 384 ], [ 61, 1, 18, 192 ], [ 61, 1, 20, 192 ], [ 62, 1, 6, 432 ], [ 62, 1, 7, 432 ], [ 62, 1, 9, 288 ], [ 63, 1, 8, 48 ], [ 63, 1, 9, 144 ], [ 63, 1, 11, 288 ], [ 63, 1, 12, 144 ], [ 63, 1, 28, 384 ], [ 63, 1, 34, 384 ], [ 64, 1, 15, 288 ], [ 64, 1, 16, 288 ], [ 64, 1, 18, 576 ], [ 64, 1, 22, 576 ], [ 65, 1, 26, 192 ], [ 65, 1, 29, 576 ], [ 65, 1, 46, 384 ], [ 66, 1, 32, 576 ], [ 66, 1, 37, 576 ] ] k = 32: F-action on Pi is () [67,1,32] Dynkin type is A_0(q) + T(phi12^2) Order of center |Z^F|: phi12^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 2 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 3 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 4 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 5 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 7 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 8 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 9 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 11 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 13 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 16 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 17 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 19 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 21 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 23 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 25 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 27 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 29 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 31 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 32 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 37 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 41 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 43 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 47 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 49 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 53 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) q congruent 59 modulo 60: 1/288 q^2 phi1 phi2 ( q^4-q^2-12 ) Fusion of maximal tori of C^F in those of G^F: [ 32 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 58, 1, 20, 96 ], [ 59, 1, 11, 72 ] ] k = 33: F-action on Pi is () [67,1,33] Dynkin type is A_0(q) + T(phi1^2 phi3 phi6^2) Order of center |Z^F|: phi1^2 phi3 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-106 ) q congruent 2 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+18*q^3-88*q+96 ) q congruent 3 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-90 ) q congruent 4 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+6*q^2+24*q-88 ) q congruent 5 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+21*q^3-9*q^2-94*q+120 ) q congruent 7 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-106 ) q congruent 8 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+18*q^3-88*q+96 ) q congruent 9 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-90 ) q congruent 11 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+21*q^3-9*q^2-94*q+120 ) q congruent 13 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-106 ) q congruent 16 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+6*q^2+24*q-88 ) q congruent 17 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+21*q^3-9*q^2-94*q+120 ) q congruent 19 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-106 ) q congruent 21 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-90 ) q congruent 23 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+21*q^3-9*q^2-94*q+120 ) q congruent 25 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-106 ) q congruent 27 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-90 ) q congruent 29 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+21*q^3-9*q^2-94*q+120 ) q congruent 31 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-106 ) q congruent 32 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+18*q^3-88*q+96 ) q congruent 37 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-106 ) q congruent 41 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+21*q^3-9*q^2-94*q+120 ) q congruent 43 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-106 ) q congruent 47 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+21*q^3-9*q^2-94*q+120 ) q congruent 49 modulo 60: 1/864 q phi1 ( q^6-5*q^5+4*q^4+4*q^3+9*q^2+21*q-106 ) q congruent 53 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+21*q^3-9*q^2-94*q+120 ) q congruent 59 modulo 60: 1/864 phi2 ( q^7-7*q^6+16*q^5-16*q^4+21*q^3-9*q^2-94*q+120 ) Fusion of maximal tori of C^F in those of G^F: [ 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 24 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 3, 48 ], [ 22, 1, 3, 48 ], [ 27, 1, 1, 12 ], [ 27, 1, 4, 24 ], [ 33, 1, 7, 72 ], [ 38, 1, 4, 48 ], [ 38, 1, 7, 96 ], [ 40, 1, 4, 24 ], [ 40, 1, 5, 6 ], [ 42, 1, 5, 72 ], [ 46, 1, 10, 144 ], [ 47, 1, 11, 144 ], [ 50, 1, 7, 144 ], [ 52, 1, 6, 18 ], [ 58, 1, 6, 48 ], [ 58, 1, 22, 288 ], [ 59, 1, 7, 36 ], [ 59, 1, 10, 72 ], [ 60, 1, 15, 216 ], [ 61, 1, 10, 144 ], [ 62, 1, 13, 432 ], [ 65, 1, 11, 144 ], [ 65, 1, 19, 288 ], [ 66, 1, 14, 432 ] ] k = 34: F-action on Pi is () [67,1,34] Dynkin type is A_0(q) + T(phi2^2 phi3^2 phi6) Order of center |Z^F|: phi2^2 phi3^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/864 phi1^2 ( q^6+2*q^5-2*q^3-11*q^2-2*q+24 ) q congruent 2 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-12*q^2+24*q-16 ) q congruent 3 modulo 60: 1/864 q phi1 phi2 ( q^5-2*q^3-9*q+18 ) q congruent 4 modulo 60: 1/864 q phi1 ( q^6+q^5-2*q^4-2*q^3-12*q^2+32 ) q congruent 5 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-9*q^2+27*q-34 ) q congruent 7 modulo 60: 1/864 phi1^2 ( q^6+2*q^5-2*q^3-11*q^2-2*q+24 ) q congruent 8 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-12*q^2+24*q-16 ) q congruent 9 modulo 60: 1/864 q phi1 phi2 ( q^5-2*q^3-9*q+18 ) q congruent 11 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-9*q^2+27*q-34 ) q congruent 13 modulo 60: 1/864 phi1^2 ( q^6+2*q^5-2*q^3-11*q^2-2*q+24 ) q congruent 16 modulo 60: 1/864 q phi1 ( q^6+q^5-2*q^4-2*q^3-12*q^2+32 ) q congruent 17 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-9*q^2+27*q-34 ) q congruent 19 modulo 60: 1/864 phi1^2 ( q^6+2*q^5-2*q^3-11*q^2-2*q+24 ) q congruent 21 modulo 60: 1/864 q phi1 phi2 ( q^5-2*q^3-9*q+18 ) q congruent 23 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-9*q^2+27*q-34 ) q congruent 25 modulo 60: 1/864 phi1^2 ( q^6+2*q^5-2*q^3-11*q^2-2*q+24 ) q congruent 27 modulo 60: 1/864 q phi1 phi2 ( q^5-2*q^3-9*q+18 ) q congruent 29 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-9*q^2+27*q-34 ) q congruent 31 modulo 60: 1/864 phi1^2 ( q^6+2*q^5-2*q^3-11*q^2-2*q+24 ) q congruent 32 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-12*q^2+24*q-16 ) q congruent 37 modulo 60: 1/864 phi1^2 ( q^6+2*q^5-2*q^3-11*q^2-2*q+24 ) q congruent 41 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-9*q^2+27*q-34 ) q congruent 43 modulo 60: 1/864 phi1^2 ( q^6+2*q^5-2*q^3-11*q^2-2*q+24 ) q congruent 47 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-9*q^2+27*q-34 ) q congruent 49 modulo 60: 1/864 phi1^2 ( q^6+2*q^5-2*q^3-11*q^2-2*q+24 ) q congruent 53 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-9*q^2+27*q-34 ) q congruent 59 modulo 60: 1/864 q phi2 ( q^6-q^5-2*q^4+2*q^3-9*q^2+27*q-34 ) Fusion of maximal tori of C^F in those of G^F: [ 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 24 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 48 ], [ 22, 1, 2, 48 ], [ 27, 1, 5, 24 ], [ 27, 1, 6, 12 ], [ 33, 1, 3, 72 ], [ 38, 1, 6, 96 ], [ 38, 1, 9, 48 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 24 ], [ 42, 1, 3, 72 ], [ 46, 1, 9, 144 ], [ 47, 1, 6, 144 ], [ 50, 1, 6, 144 ], [ 52, 1, 7, 18 ], [ 58, 1, 6, 48 ], [ 58, 1, 27, 288 ], [ 59, 1, 8, 36 ], [ 59, 1, 9, 72 ], [ 60, 1, 4, 216 ], [ 61, 1, 11, 144 ], [ 62, 1, 12, 432 ], [ 65, 1, 14, 144 ], [ 65, 1, 22, 288 ], [ 66, 1, 17, 432 ] ] k = 35: F-action on Pi is () [67,1,35] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi3 phi6) Order of center |Z^F|: phi1^2 phi2^2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/432 phi1^2 ( q^6-4*q^5+3*q^4-8*q^3+22*q^2+10*q-12 ) q congruent 2 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+72*q^3-96*q^2+80*q-48 ) q congruent 3 modulo 60: 1/432 q phi1 ( q^6-5*q^5+7*q^4-11*q^3+30*q^2-12*q-18 ) q congruent 4 modulo 60: 1/432 q phi1^2 ( q^5-4*q^4+3*q^3-8*q^2+16*q+16 ) q congruent 5 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+78*q^3-120*q^2+110*q-60 ) q congruent 7 modulo 60: 1/432 phi1^2 ( q^6-4*q^5+3*q^4-8*q^3+22*q^2+10*q-12 ) q congruent 8 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+72*q^3-96*q^2+80*q-48 ) q congruent 9 modulo 60: 1/432 q phi1 ( q^6-5*q^5+7*q^4-11*q^3+30*q^2-12*q-18 ) q congruent 11 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+78*q^3-120*q^2+110*q-60 ) q congruent 13 modulo 60: 1/432 phi1^2 ( q^6-4*q^5+3*q^4-8*q^3+22*q^2+10*q-12 ) q congruent 16 modulo 60: 1/432 q phi1^2 ( q^5-4*q^4+3*q^3-8*q^2+16*q+16 ) q congruent 17 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+78*q^3-120*q^2+110*q-60 ) q congruent 19 modulo 60: 1/432 phi1^2 ( q^6-4*q^5+3*q^4-8*q^3+22*q^2+10*q-12 ) q congruent 21 modulo 60: 1/432 q phi1 ( q^6-5*q^5+7*q^4-11*q^3+30*q^2-12*q-18 ) q congruent 23 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+78*q^3-120*q^2+110*q-60 ) q congruent 25 modulo 60: 1/432 phi1^2 ( q^6-4*q^5+3*q^4-8*q^3+22*q^2+10*q-12 ) q congruent 27 modulo 60: 1/432 q phi1 ( q^6-5*q^5+7*q^4-11*q^3+30*q^2-12*q-18 ) q congruent 29 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+78*q^3-120*q^2+110*q-60 ) q congruent 31 modulo 60: 1/432 phi1^2 ( q^6-4*q^5+3*q^4-8*q^3+22*q^2+10*q-12 ) q congruent 32 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+72*q^3-96*q^2+80*q-48 ) q congruent 37 modulo 60: 1/432 phi1^2 ( q^6-4*q^5+3*q^4-8*q^3+22*q^2+10*q-12 ) q congruent 41 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+78*q^3-120*q^2+110*q-60 ) q congruent 43 modulo 60: 1/432 phi1^2 ( q^6-4*q^5+3*q^4-8*q^3+22*q^2+10*q-12 ) q congruent 47 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+78*q^3-120*q^2+110*q-60 ) q congruent 49 modulo 60: 1/432 phi1^2 ( q^6-4*q^5+3*q^4-8*q^3+22*q^2+10*q-12 ) q congruent 53 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+78*q^3-120*q^2+110*q-60 ) q congruent 59 modulo 60: 1/432 phi2 ( q^7-7*q^6+19*q^5-37*q^4+78*q^3-120*q^2+110*q-60 ) Fusion of maximal tori of C^F in those of G^F: [ 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 6 ], [ 6, 1, 2, 6 ], [ 7, 1, 1, 18 ], [ 7, 1, 2, 18 ], [ 9, 1, 1, 9 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 17, 1, 3, 12 ], [ 19, 1, 1, 18 ], [ 19, 1, 2, 18 ], [ 20, 1, 5, 72 ], [ 20, 1, 8, 72 ], [ 22, 1, 2, 12 ], [ 22, 1, 3, 12 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 18 ], [ 26, 1, 1, 36 ], [ 26, 1, 4, 36 ], [ 27, 1, 1, 12 ], [ 27, 1, 6, 12 ], [ 32, 1, 4, 36 ], [ 33, 1, 3, 18 ], [ 33, 1, 7, 18 ], [ 34, 1, 2, 36 ], [ 34, 1, 3, 36 ], [ 38, 1, 6, 24 ], [ 38, 1, 7, 24 ], [ 39, 1, 4, 36 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 1, 36 ], [ 42, 1, 6, 36 ], [ 43, 1, 5, 144 ], [ 46, 1, 7, 72 ], [ 46, 1, 12, 72 ], [ 47, 1, 6, 36 ], [ 47, 1, 11, 36 ], [ 49, 1, 3, 54 ], [ 49, 1, 6, 54 ], [ 50, 1, 4, 72 ], [ 50, 1, 9, 72 ], [ 52, 1, 6, 18 ], [ 52, 1, 7, 18 ], [ 57, 1, 13, 108 ], [ 57, 1, 14, 108 ], [ 58, 1, 6, 12 ], [ 58, 1, 25, 144 ], [ 59, 1, 7, 36 ], [ 59, 1, 8, 36 ], [ 60, 1, 3, 108 ], [ 60, 1, 14, 108 ], [ 61, 1, 10, 36 ], [ 61, 1, 11, 36 ], [ 62, 1, 18, 216 ], [ 62, 1, 23, 216 ], [ 64, 1, 25, 108 ], [ 65, 1, 19, 72 ], [ 65, 1, 22, 72 ], [ 66, 1, 21, 216 ], [ 66, 1, 24, 216 ] ] k = 36: F-action on Pi is () [67,1,36] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi3 phi6) Order of center |Z^F|: phi1^2 phi2^2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 2 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 3 modulo 60: 1/216 q^2 phi1 phi2 ( q^4-5*q^2+6 ) q congruent 4 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 5 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 7 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 8 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 9 modulo 60: 1/216 q^2 phi1 phi2 ( q^4-5*q^2+6 ) q congruent 11 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 13 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 16 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 17 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 19 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 21 modulo 60: 1/216 q^2 phi1 phi2 ( q^4-5*q^2+6 ) q congruent 23 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 25 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 27 modulo 60: 1/216 q^2 phi1 phi2 ( q^4-5*q^2+6 ) q congruent 29 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 31 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 32 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 37 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 41 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 43 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 47 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 49 modulo 60: 1/216 q phi1^2 ( q^5+2*q^4-3*q^3-8*q^2-2*q+4 ) q congruent 53 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) q congruent 59 modulo 60: 1/216 q phi2^2 ( q^5-2*q^4-3*q^3+8*q^2-2*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 12, 1, 2, 6 ], [ 16, 1, 2, 12 ], [ 16, 1, 4, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 12 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 12 ], [ 27, 1, 4, 6 ], [ 27, 1, 5, 6 ], [ 32, 1, 2, 12 ], [ 37, 1, 2, 24 ], [ 38, 1, 4, 12 ], [ 38, 1, 9, 12 ], [ 39, 1, 2, 12 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 12 ], [ 40, 1, 3, 12 ], [ 40, 1, 6, 12 ], [ 43, 1, 8, 24 ], [ 44, 1, 3, 18 ], [ 44, 1, 7, 18 ], [ 51, 1, 3, 24 ], [ 51, 1, 6, 24 ], [ 53, 1, 15, 36 ], [ 53, 1, 17, 36 ], [ 55, 1, 7, 36 ], [ 55, 1, 18, 36 ], [ 58, 1, 4, 24 ], [ 58, 1, 24, 36 ], [ 59, 1, 4, 36 ], [ 59, 1, 5, 36 ], [ 59, 1, 19, 36 ], [ 59, 1, 20, 36 ], [ 63, 1, 12, 72 ], [ 63, 1, 13, 72 ], [ 64, 1, 26, 108 ], [ 65, 1, 30, 72 ], [ 65, 1, 31, 72 ] ] k = 37: F-action on Pi is () [67,1,37] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi3^2) Order of center |Z^F|: phi1^2 phi2^2 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 2 modulo 60: 1/288 q^3 phi1 phi2 ( q^3-q-6 ) q congruent 3 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 4 modulo 60: 1/288 q^3 phi1 phi2 ( q^3-q-6 ) q congruent 5 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 7 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 8 modulo 60: 1/288 q^3 phi1 phi2 ( q^3-q-6 ) q congruent 9 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 11 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 13 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 16 modulo 60: 1/288 q^3 phi1 phi2 ( q^3-q-6 ) q congruent 17 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 19 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 21 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 23 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 25 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 27 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 29 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 31 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 32 modulo 60: 1/288 q^3 phi1 phi2 ( q^3-q-6 ) q congruent 37 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 41 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 43 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 47 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 49 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 53 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) q congruent 59 modulo 60: 1/288 q^2 phi1^2 phi2 ( q^3+q^2-6 ) Fusion of maximal tori of C^F in those of G^F: [ 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 24 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 16 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 5, 12 ], [ 29, 1, 2, 16 ], [ 31, 1, 2, 16 ], [ 32, 1, 1, 8 ], [ 33, 1, 3, 36 ], [ 34, 1, 2, 8 ], [ 38, 1, 3, 72 ], [ 38, 1, 5, 48 ], [ 39, 1, 3, 8 ], [ 40, 1, 3, 16 ], [ 40, 1, 5, 36 ], [ 42, 1, 3, 24 ], [ 42, 1, 4, 8 ], [ 43, 1, 12, 32 ], [ 44, 1, 3, 12 ], [ 45, 1, 3, 24 ], [ 46, 1, 2, 16 ], [ 46, 1, 3, 48 ], [ 47, 1, 6, 72 ], [ 49, 1, 3, 36 ], [ 50, 1, 5, 16 ], [ 50, 1, 6, 48 ], [ 51, 1, 5, 32 ], [ 52, 1, 6, 36 ], [ 53, 1, 16, 24 ], [ 54, 1, 7, 48 ], [ 55, 1, 3, 24 ], [ 56, 1, 8, 48 ], [ 57, 1, 13, 72 ], [ 58, 1, 7, 96 ], [ 58, 1, 8, 72 ], [ 58, 1, 9, 32 ], [ 59, 1, 14, 72 ], [ 59, 1, 19, 48 ], [ 60, 1, 12, 72 ], [ 61, 1, 5, 72 ], [ 61, 1, 7, 48 ], [ 62, 1, 22, 144 ], [ 63, 1, 5, 96 ], [ 64, 1, 7, 72 ], [ 65, 1, 17, 144 ], [ 65, 1, 23, 96 ], [ 66, 1, 22, 144 ] ] k = 38: F-action on Pi is () [67,1,38] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi6^2) Order of center |Z^F|: phi1^2 phi2^2 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 2 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+20*q-24 ) q congruent 3 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 4 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+20*q-24 ) q congruent 5 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 7 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 8 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+20*q-24 ) q congruent 9 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 11 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 13 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 16 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+20*q-24 ) q congruent 17 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 19 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 21 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 23 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 25 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 27 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 29 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 31 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 32 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+20*q-24 ) q congruent 37 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 41 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 43 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 47 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 49 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 53 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) q congruent 59 modulo 60: 1/288 q phi1 phi2 ( q^5-4*q^4+3*q^3-2*q^2+26*q-36 ) Fusion of maximal tori of C^F in those of G^F: [ 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 20, 1, 3, 16 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 16 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 27, 1, 4, 12 ], [ 29, 1, 3, 16 ], [ 31, 1, 3, 16 ], [ 32, 1, 3, 8 ], [ 33, 1, 7, 36 ], [ 34, 1, 3, 8 ], [ 38, 1, 8, 48 ], [ 38, 1, 11, 72 ], [ 39, 1, 1, 8 ], [ 40, 1, 2, 16 ], [ 40, 1, 4, 36 ], [ 42, 1, 2, 8 ], [ 42, 1, 5, 24 ], [ 43, 1, 3, 32 ], [ 44, 1, 7, 12 ], [ 45, 1, 4, 24 ], [ 46, 1, 4, 48 ], [ 46, 1, 5, 16 ], [ 47, 1, 11, 72 ], [ 49, 1, 6, 36 ], [ 50, 1, 7, 48 ], [ 50, 1, 8, 16 ], [ 51, 1, 10, 32 ], [ 52, 1, 7, 36 ], [ 53, 1, 18, 24 ], [ 54, 1, 11, 48 ], [ 55, 1, 12, 24 ], [ 56, 1, 12, 48 ], [ 57, 1, 14, 72 ], [ 58, 1, 10, 96 ], [ 58, 1, 11, 32 ], [ 58, 1, 13, 72 ], [ 59, 1, 15, 72 ], [ 59, 1, 20, 48 ], [ 60, 1, 13, 72 ], [ 61, 1, 8, 48 ], [ 61, 1, 9, 72 ], [ 62, 1, 19, 144 ], [ 63, 1, 8, 96 ], [ 64, 1, 23, 72 ], [ 65, 1, 16, 144 ], [ 65, 1, 26, 96 ], [ 66, 1, 23, 144 ] ] k = 39: F-action on Pi is () [67,1,39] Dynkin type is A_0(q) + T(phi4^2 phi12) Order of center |Z^F|: phi4^2 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 2 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 3 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 4 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 5 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 7 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 8 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 9 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 11 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 13 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 16 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 17 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 19 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 21 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 23 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 25 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 27 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 29 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 31 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 32 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 37 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 41 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 43 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 47 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 49 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 53 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 59 modulo 60: 1/72 q^4 phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 12 ], [ 5, 1, 4, 12 ], [ 9, 1, 1, 3 ], [ 32, 1, 5, 12 ], [ 37, 1, 5, 24 ], [ 39, 1, 5, 12 ], [ 43, 1, 10, 24 ], [ 58, 1, 20, 12 ], [ 58, 1, 21, 24 ], [ 64, 1, 24, 36 ] ] k = 40: F-action on Pi is () [67,1,40] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi3 phi6) Order of center |Z^F|: phi1^2 phi2^2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 2 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-4 ) q congruent 3 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 4 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-4 ) q congruent 5 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 7 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 8 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-4 ) q congruent 9 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 11 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 13 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 16 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-4 ) q congruent 17 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 19 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 21 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 23 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 25 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 27 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 29 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 31 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 32 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-4 ) q congruent 37 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 41 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 43 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 47 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 49 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 53 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) q congruent 59 modulo 60: 1/48 q phi1^2 phi2 ( q^4-q^3-4*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 5, 12 ], [ 17, 1, 6, 12 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ], [ 20, 1, 6, 8 ], [ 20, 1, 7, 8 ], [ 21, 1, 1, 4 ], [ 21, 1, 2, 4 ], [ 22, 1, 1, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 2, 4 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 32, 1, 4, 4 ], [ 33, 1, 3, 6 ], [ 33, 1, 7, 6 ], [ 34, 1, 1, 4 ], [ 34, 1, 4, 4 ], [ 36, 1, 2, 8 ], [ 36, 1, 3, 8 ], [ 37, 1, 4, 16 ], [ 38, 1, 2, 8 ], [ 38, 1, 10, 8 ], [ 38, 1, 15, 24 ], [ 38, 1, 16, 24 ], [ 39, 1, 4, 4 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 2, 4 ], [ 42, 1, 4, 4 ], [ 43, 1, 7, 16 ], [ 46, 1, 8, 8 ], [ 46, 1, 11, 8 ], [ 47, 1, 5, 12 ], [ 47, 1, 12, 12 ], [ 49, 1, 3, 6 ], [ 49, 1, 6, 6 ], [ 50, 1, 2, 8 ], [ 50, 1, 11, 8 ], [ 52, 1, 6, 6 ], [ 52, 1, 7, 6 ], [ 57, 1, 12, 12 ], [ 57, 1, 15, 12 ], [ 58, 1, 6, 12 ], [ 58, 1, 17, 16 ], [ 59, 1, 14, 12 ], [ 59, 1, 15, 12 ], [ 60, 1, 12, 12 ], [ 60, 1, 13, 12 ], [ 61, 1, 10, 12 ], [ 61, 1, 11, 12 ], [ 62, 1, 17, 24 ], [ 62, 1, 20, 24 ], [ 64, 1, 25, 12 ], [ 65, 1, 20, 24 ], [ 65, 1, 21, 24 ], [ 66, 1, 20, 24 ], [ 66, 1, 25, 24 ] ] k = 41: F-action on Pi is () [67,1,41] Dynkin type is A_0(q) + T(phi1^2 phi7) Order of center |Z^F|: phi1^2 phi7 Numbers of classes in class type: q congruent 1 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 2 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 3 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 4 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 5 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 7 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 8 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 9 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 11 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 13 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 16 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 17 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 19 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 21 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 23 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 25 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 27 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 29 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 31 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 32 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 37 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 41 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 43 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 47 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 49 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 53 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 59 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 18, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 23, 1, 1, 4 ], [ 26, 1, 1, 4 ], [ 36, 1, 1, 4 ], [ 66, 1, 2, 14 ] ] k = 42: F-action on Pi is () [67,1,42] Dynkin type is A_0(q) + T(phi2^2 phi14) Order of center |Z^F|: phi2^2 phi14 Numbers of classes in class type: q congruent 1 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 2 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 3 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 4 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 5 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 7 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 8 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 9 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 11 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 13 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 16 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 17 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 19 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 21 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 23 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 25 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 27 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 29 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 31 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 32 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 37 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 41 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 43 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 47 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 49 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 53 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 59 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 Fusion of maximal tori of C^F in those of G^F: [ 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 18, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 23, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 36, 1, 4, 4 ], [ 66, 1, 3, 14 ] ] k = 43: F-action on Pi is () [67,1,43] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi8) Order of center |Z^F|: phi1^2 phi2^2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 2 modulo 60: 1/64 q^5 ( q^3-2*q^2-2*q+4 ) q congruent 3 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 4 modulo 60: 1/64 q^5 ( q^3-2*q^2-2*q+4 ) q congruent 5 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 7 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 8 modulo 60: 1/64 q^5 ( q^3-2*q^2-2*q+4 ) q congruent 9 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 11 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 13 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 16 modulo 60: 1/64 q^5 ( q^3-2*q^2-2*q+4 ) q congruent 17 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 19 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 21 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 23 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 25 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 27 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 29 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 31 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 32 modulo 60: 1/64 q^5 ( q^3-2*q^2-2*q+4 ) q congruent 37 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 41 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 43 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 47 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 49 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 53 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) q congruent 59 modulo 60: 1/64 phi1^2 phi2 phi4 ( q^3-q^2-3*q+1 ) Fusion of maximal tori of C^F in those of G^F: [ 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 5, 16 ], [ 33, 1, 9, 16 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 8 ], [ 41, 1, 4, 8 ], [ 41, 1, 7, 8 ], [ 43, 1, 11, 16 ], [ 44, 1, 2, 8 ], [ 44, 1, 8, 8 ], [ 49, 1, 12, 16 ], [ 49, 1, 16, 16 ], [ 52, 1, 3, 8 ], [ 52, 1, 4, 8 ], [ 59, 1, 22, 16 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 60, 1, 25, 32 ], [ 62, 1, 27, 16 ], [ 62, 1, 28, 16 ], [ 63, 1, 17, 16 ], [ 63, 1, 18, 16 ], [ 64, 1, 31, 32 ], [ 64, 1, 32, 32 ], [ 65, 1, 34, 32 ], [ 65, 1, 35, 32 ], [ 66, 1, 43, 32 ], [ 66, 1, 44, 32 ] ] k = 44: F-action on Pi is () [67,1,44] Dynkin type is A_0(q) + T(phi1^2 phi4 phi8) Order of center |Z^F|: phi1^2 phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 2 modulo 60: 1/128 q^6 ( q^2-4*q+4 ) q congruent 3 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 4 modulo 60: 1/128 q^6 ( q^2-4*q+4 ) q congruent 5 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 7 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 8 modulo 60: 1/128 q^6 ( q^2-4*q+4 ) q congruent 9 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 11 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 13 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 16 modulo 60: 1/128 q^6 ( q^2-4*q+4 ) q congruent 17 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 19 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 21 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 23 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 25 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 27 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 29 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 31 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 32 modulo 60: 1/128 q^6 ( q^2-4*q+4 ) q congruent 37 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 41 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 43 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 47 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 49 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 53 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) q congruent 59 modulo 60: 1/128 phi1^3 phi2 phi4 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 20, 1, 6, 16 ], [ 20, 1, 8, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 26, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 3, 16 ], [ 41, 1, 8, 8 ], [ 43, 1, 6, 32 ], [ 44, 1, 6, 16 ], [ 49, 1, 17, 32 ], [ 52, 1, 8, 16 ], [ 59, 1, 23, 32 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 60, 1, 35, 64 ], [ 62, 1, 28, 32 ], [ 63, 1, 17, 32 ], [ 64, 1, 30, 64 ], [ 64, 1, 34, 32 ], [ 66, 1, 40, 64 ] ] k = 45: F-action on Pi is () [67,1,45] Dynkin type is A_0(q) + T(phi2^2 phi4 phi8) Order of center |Z^F|: phi2^2 phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 2 modulo 60: 1/128 q^8 q congruent 3 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 4 modulo 60: 1/128 q^8 q congruent 5 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 7 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 8 modulo 60: 1/128 q^8 q congruent 9 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 11 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 13 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 16 modulo 60: 1/128 q^8 q congruent 17 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 19 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 21 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 23 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 25 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 27 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 29 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 31 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 32 modulo 60: 1/128 q^8 q congruent 37 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 41 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 43 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 47 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 49 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 53 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 q congruent 59 modulo 60: 1/128 phi1^2 phi2^2 phi4^2 Fusion of maximal tori of C^F in those of G^F: [ 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 20, 1, 5, 16 ], [ 20, 1, 7, 16 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 8 ], [ 26, 1, 3, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 41, 1, 10, 16 ], [ 43, 1, 14, 32 ], [ 44, 1, 4, 16 ], [ 49, 1, 13, 32 ], [ 52, 1, 5, 16 ], [ 59, 1, 24, 32 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 60, 1, 36, 64 ], [ 62, 1, 27, 32 ], [ 63, 1, 18, 32 ], [ 64, 1, 29, 64 ], [ 64, 1, 34, 32 ], [ 66, 1, 41, 64 ] ] k = 46: F-action on Pi is () [67,1,46] Dynkin type is A_0(q) + T(phi1^2 phi9) Order of center |Z^F|: phi1^2 phi9 Numbers of classes in class type: q congruent 1 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 2 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 5 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 8 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 16 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 17 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 21 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 27 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 32 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 41 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 47 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/108 phi1 phi3 ( q^5-5*q^4+6*q^3+2*q^2-10*q+12 ) q congruent 53 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/108 q^3 phi2 phi6 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 5, 18 ], [ 27, 1, 1, 12 ], [ 38, 1, 13, 36 ], [ 65, 1, 7, 18 ], [ 66, 1, 11, 54 ] ] k = 47: F-action on Pi is () [67,1,47] Dynkin type is A_0(q) + T(phi2^2 phi18) Order of center |Z^F|: phi2^2 phi18 Numbers of classes in class type: q congruent 1 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 2 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 3 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 4 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 5 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 7 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 8 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 9 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 11 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 13 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 16 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 17 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 19 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 21 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 23 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 25 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 27 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 29 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 31 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 32 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 37 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 41 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 43 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 47 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 49 modulo 60: 1/108 q^4 phi1^2 phi3 q congruent 53 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) q congruent 59 modulo 60: 1/108 q phi1 phi2 phi6 ( q^3-2 ) Fusion of maximal tori of C^F in those of G^F: [ 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 6, 18 ], [ 27, 1, 6, 12 ], [ 38, 1, 18, 36 ], [ 65, 1, 15, 18 ], [ 66, 1, 19, 54 ] ] k = 48: F-action on Pi is () [67,1,48] Dynkin type is A_0(q) + T(phi3 phi9) Order of center |Z^F|: phi3 phi9 Numbers of classes in class type: q congruent 1 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 2 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 3 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 4 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 5 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 7 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 8 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 9 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 11 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 13 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 16 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 17 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 19 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 21 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 23 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 25 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 27 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 29 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 31 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 32 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 37 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 41 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 43 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 47 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 49 modulo 60: 1/54 q phi1 phi2 phi3 ( q^3+2 ) q congruent 53 modulo 60: 1/54 q^4 phi2^2 phi6 q congruent 59 modulo 60: 1/54 q^4 phi2^2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 8, 1, 1, 6 ], [ 27, 1, 5, 6 ], [ 38, 1, 14, 18 ], [ 65, 1, 7, 18 ] ] k = 49: F-action on Pi is () [67,1,49] Dynkin type is A_0(q) + T(phi6 phi18) Order of center |Z^F|: phi6 phi18 Numbers of classes in class type: q congruent 1 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 2 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 3 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 4 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 5 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 7 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 8 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 9 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 11 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 13 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 16 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 17 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 19 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 21 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 23 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 25 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 27 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 29 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 31 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 32 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 37 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 41 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 43 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 47 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 49 modulo 60: 1/54 q^4 phi1^2 phi3 q congruent 53 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) q congruent 59 modulo 60: 1/54 q phi1 phi2 phi6 ( q^3-2 ) Fusion of maximal tori of C^F in those of G^F: [ 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 8, 1, 2, 6 ], [ 27, 1, 4, 6 ], [ 38, 1, 17, 18 ], [ 65, 1, 15, 18 ] ] k = 50: F-action on Pi is () [67,1,50] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi5) Order of center |Z^F|: phi1^2 phi2^2 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 17 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/80 q^2 phi1 phi2^2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 8 ], [ 14, 1, 1, 2 ], [ 15, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 4 ], [ 22, 1, 2, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 2, 8 ], [ 29, 1, 2, 8 ], [ 30, 1, 1, 4 ], [ 30, 1, 2, 8 ], [ 34, 1, 2, 8 ], [ 36, 1, 2, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 42, 1, 4, 8 ], [ 44, 1, 5, 16 ], [ 45, 1, 2, 8 ], [ 50, 1, 5, 16 ], [ 54, 1, 5, 16 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 20 ], [ 63, 1, 2, 10 ], [ 64, 1, 2, 20 ], [ 64, 1, 3, 40 ], [ 65, 1, 3, 40 ], [ 66, 1, 7, 40 ] ] k = 51: F-action on Pi is () [67,1,51] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi10) Order of center |Z^F|: phi1^2 phi2^2 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 2 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 4 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 5 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 7 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 8 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 9 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 11 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 13 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 16 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 17 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 19 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 21 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 23 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 25 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 27 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 29 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 31 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 32 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 37 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 41 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 43 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 47 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 49 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 53 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) q congruent 59 modulo 60: 1/80 q phi1 phi2 phi4 ( q^3-3*q^2-2*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 51 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 4 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 4 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 8 ], [ 29, 1, 3, 8 ], [ 30, 1, 3, 4 ], [ 30, 1, 4, 8 ], [ 34, 1, 3, 8 ], [ 36, 1, 3, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 42, 1, 2, 8 ], [ 44, 1, 9, 16 ], [ 45, 1, 5, 8 ], [ 50, 1, 8, 16 ], [ 54, 1, 8, 10 ], [ 54, 1, 13, 16 ], [ 61, 1, 3, 20 ], [ 63, 1, 3, 10 ], [ 64, 1, 4, 40 ], [ 64, 1, 5, 20 ], [ 65, 1, 5, 40 ], [ 66, 1, 8, 40 ] ] k = 52: F-action on Pi is () [67,1,52] Dynkin type is A_0(q) + T(phi20) Order of center |Z^F|: phi20 Numbers of classes in class type: q congruent 1 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 2 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 3 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 4 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 5 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 7 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 8 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 9 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 11 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 13 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 16 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 17 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 19 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 21 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 23 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 25 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 27 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 29 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 31 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 32 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 37 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 41 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 43 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 47 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 49 modulo 60: 1/20 q^2 phi1 phi2 phi8 q congruent 53 modulo 60: 1/20 phi4 ( q^6-2*q^4+3*q^2-4 ) q congruent 59 modulo 60: 1/20 q^2 phi1 phi2 phi8 Fusion of maximal tori of C^F in those of G^F: [ 52 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ] ] k = 53: F-action on Pi is () [67,1,53] Dynkin type is A_0(q) + T(phi1^2 phi3 phi4^2) Order of center |Z^F|: phi1^2 phi3 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 2 modulo 60: 1/576 q^3 phi1^2 phi2 ( q^2-4 ) q congruent 3 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 4 modulo 60: 1/576 q^3 phi1^2 phi2 ( q^2-4 ) q congruent 5 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 7 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 8 modulo 60: 1/576 q^3 phi1^2 phi2 ( q^2-4 ) q congruent 9 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 11 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 13 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 16 modulo 60: 1/576 q^3 phi1^2 phi2 ( q^2-4 ) q congruent 17 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 19 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 21 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 23 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 25 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 27 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 29 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 31 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 32 modulo 60: 1/576 q^3 phi1^2 phi2 ( q^2-4 ) q congruent 37 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 41 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 43 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 47 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 49 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 53 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) q congruent 59 modulo 60: 1/576 q phi1^3 phi2^2 ( q^2-3 ) Fusion of maximal tori of C^F in those of G^F: [ 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 3, 24 ], [ 16, 1, 2, 24 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 33, 1, 4, 48 ], [ 39, 1, 5, 24 ], [ 40, 1, 1, 12 ], [ 41, 1, 5, 48 ], [ 43, 1, 9, 48 ], [ 44, 1, 3, 18 ], [ 44, 1, 6, 48 ], [ 48, 1, 8, 96 ], [ 51, 1, 7, 48 ], [ 53, 1, 10, 96 ], [ 53, 1, 17, 72 ], [ 55, 1, 6, 96 ], [ 59, 1, 4, 36 ], [ 59, 1, 6, 96 ], [ 60, 1, 5, 144 ], [ 63, 1, 7, 144 ], [ 63, 1, 16, 192 ], [ 64, 1, 9, 288 ], [ 65, 1, 33, 192 ] ] k = 54: F-action on Pi is () [67,1,54] Dynkin type is A_0(q) + T(phi2^2 phi4^2 phi6) Order of center |Z^F|: phi2^2 phi4^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 2 modulo 60: 1/576 q^3 phi1 phi2^2 ( q^2-4 ) q congruent 3 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 4 modulo 60: 1/576 q^3 phi1 phi2^2 ( q^2-4 ) q congruent 5 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 7 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 8 modulo 60: 1/576 q^3 phi1 phi2^2 ( q^2-4 ) q congruent 9 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 11 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 13 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 16 modulo 60: 1/576 q^3 phi1 phi2^2 ( q^2-4 ) q congruent 17 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 19 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 21 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 23 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 25 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 27 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 29 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 31 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 32 modulo 60: 1/576 q^3 phi1 phi2^2 ( q^2-4 ) q congruent 37 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 41 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 43 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 47 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 49 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 53 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) q congruent 59 modulo 60: 1/576 q phi1^2 phi2^3 ( q^2-3 ) Fusion of maximal tori of C^F in those of G^F: [ 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 2, 24 ], [ 16, 1, 4, 24 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], [ 33, 1, 10, 48 ], [ 39, 1, 5, 24 ], [ 40, 1, 6, 12 ], [ 41, 1, 5, 48 ], [ 43, 1, 9, 48 ], [ 44, 1, 4, 48 ], [ 44, 1, 7, 18 ], [ 48, 1, 9, 96 ], [ 51, 1, 4, 48 ], [ 53, 1, 14, 96 ], [ 53, 1, 15, 72 ], [ 55, 1, 19, 96 ], [ 59, 1, 5, 36 ], [ 59, 1, 6, 96 ], [ 60, 1, 9, 144 ], [ 63, 1, 6, 144 ], [ 63, 1, 15, 192 ], [ 64, 1, 12, 288 ], [ 65, 1, 36, 192 ] ] k = 55: F-action on Pi is () [67,1,55] Dynkin type is A_0(q) + T(phi3^2 phi12) Order of center |Z^F|: phi3^2 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 2 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 3 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 4 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 5 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 7 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 8 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 9 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 11 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 13 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 16 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 17 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 19 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 21 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 23 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 25 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 27 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 29 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 31 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 32 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 37 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 41 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 43 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 47 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 49 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 53 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) q congruent 59 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 55 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 27, 1, 5, 24 ], [ 40, 1, 5, 24 ], [ 59, 1, 9, 72 ], [ 59, 1, 11, 12 ], [ 65, 1, 12, 96 ] ] k = 56: F-action on Pi is () [67,1,56] Dynkin type is A_0(q) + T(phi6^2 phi12) Order of center |Z^F|: phi6^2 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 2 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 3 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 4 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 5 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 7 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 8 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 9 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 11 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 13 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 16 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 17 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 19 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 21 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 23 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 25 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 27 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 29 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 31 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 32 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 37 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 41 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 43 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 47 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 49 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 53 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) q congruent 59 modulo 60: 1/288 q^3 phi1^2 phi2^2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 56 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 27, 1, 4, 24 ], [ 40, 1, 4, 24 ], [ 59, 1, 10, 72 ], [ 59, 1, 11, 12 ], [ 65, 1, 13, 96 ] ] k = 57: F-action on Pi is () [67,1,57] Dynkin type is A_0(q) + T(phi1^2 phi3 phi12) Order of center |Z^F|: phi1^2 phi3 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 2 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+12 ) q congruent 3 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 4 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+12 ) q congruent 5 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 7 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 8 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+12 ) q congruent 9 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 11 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 13 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 16 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+12 ) q congruent 17 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 19 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 21 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 23 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 25 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 27 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 29 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 31 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 32 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+12 ) q congruent 37 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 41 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 43 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 47 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 49 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 53 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) q congruent 59 modulo 60: 1/144 q^2 phi1 phi2 ( q^4-4*q^3+2*q^2-2*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 57 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 27, 1, 1, 12 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 18 ], [ 59, 1, 7, 36 ], [ 59, 1, 11, 12 ], [ 60, 1, 16, 36 ], [ 62, 1, 14, 72 ], [ 65, 1, 12, 24 ], [ 66, 1, 16, 72 ] ] k = 58: F-action on Pi is () [67,1,58] Dynkin type is A_0(q) + T(phi2^2 phi6 phi12) Order of center |Z^F|: phi2^2 phi6 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 2 modulo 60: 1/144 q^3 phi1 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 3 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 4 modulo 60: 1/144 q^3 phi1 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 5 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 7 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 8 modulo 60: 1/144 q^3 phi1 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 9 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 11 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 13 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 16 modulo 60: 1/144 q^3 phi1 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 17 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 19 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 21 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 23 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 25 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 27 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 29 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 31 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 32 modulo 60: 1/144 q^3 phi1 phi2 ( q^3-2*q^2+2*q-4 ) q congruent 37 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 41 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 43 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 47 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 49 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 53 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) q congruent 59 modulo 60: 1/144 q^2 phi1^2 phi2 ( q^3-q^2+q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 58 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 27, 1, 6, 12 ], [ 40, 1, 4, 6 ], [ 52, 1, 7, 18 ], [ 59, 1, 8, 36 ], [ 59, 1, 11, 12 ], [ 60, 1, 16, 36 ], [ 62, 1, 15, 72 ], [ 65, 1, 13, 24 ], [ 66, 1, 15, 72 ] ] k = 59: F-action on Pi is () [67,1,59] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi3 phi4) Order of center |Z^F|: phi1^2 phi2^2 phi3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 2 modulo 60: 1/96 q^4 phi1 phi2^2 ( q-2 ) q congruent 3 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 4 modulo 60: 1/96 q^4 phi1 phi2^2 ( q-2 ) q congruent 5 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 7 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 8 modulo 60: 1/96 q^4 phi1 phi2^2 ( q-2 ) q congruent 9 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 11 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 13 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 16 modulo 60: 1/96 q^4 phi1 phi2^2 ( q-2 ) q congruent 17 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 19 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 21 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 23 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 25 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 27 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 29 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 31 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 32 modulo 60: 1/96 q^4 phi1 phi2^2 ( q-2 ) q congruent 37 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 41 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 43 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 47 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 49 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 53 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) q congruent 59 modulo 60: 1/96 q phi1 phi2^3 ( q^3-3*q^2+3*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 3, 8 ], [ 27, 1, 5, 6 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 29, 1, 2, 8 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 33, 1, 5, 16 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 36, 1, 2, 8 ], [ 38, 1, 2, 16 ], [ 38, 1, 9, 24 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 42, 1, 3, 12 ], [ 43, 1, 2, 16 ], [ 43, 1, 9, 8 ], [ 44, 1, 3, 6 ], [ 44, 1, 4, 8 ], [ 44, 1, 8, 8 ], [ 45, 1, 3, 12 ], [ 46, 1, 9, 24 ], [ 47, 1, 3, 8 ], [ 47, 1, 4, 8 ], [ 50, 1, 3, 12 ], [ 50, 1, 6, 12 ], [ 51, 1, 2, 8 ], [ 51, 1, 4, 16 ], [ 51, 1, 7, 8 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 4, 16 ], [ 53, 1, 11, 16 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 12 ], [ 54, 1, 4, 16 ], [ 54, 1, 7, 24 ], [ 55, 1, 4, 16 ], [ 55, 1, 8, 16 ], [ 55, 1, 18, 24 ], [ 56, 1, 3, 12 ], [ 56, 1, 4, 16 ], [ 56, 1, 8, 12 ], [ 56, 1, 9, 16 ], [ 58, 1, 5, 16 ], [ 58, 1, 18, 48 ], [ 59, 1, 19, 12 ], [ 59, 1, 21, 16 ], [ 60, 1, 7, 48 ], [ 60, 1, 11, 24 ], [ 61, 1, 13, 16 ], [ 61, 1, 15, 16 ], [ 62, 1, 10, 24 ], [ 62, 1, 11, 24 ], [ 63, 1, 7, 24 ], [ 63, 1, 10, 24 ], [ 63, 1, 27, 32 ], [ 64, 1, 10, 48 ], [ 64, 1, 20, 48 ], [ 65, 1, 24, 48 ], [ 65, 1, 45, 32 ], [ 66, 1, 28, 48 ], [ 66, 1, 31, 48 ] ] k = 60: F-action on Pi is () [67,1,60] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi4 phi6) Order of center |Z^F|: phi1^2 phi2^2 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 2 modulo 60: 1/96 q^4 phi1^2 phi2 ( q-2 ) q congruent 3 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 4 modulo 60: 1/96 q^4 phi1^2 phi2 ( q-2 ) q congruent 5 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 7 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 8 modulo 60: 1/96 q^4 phi1^2 phi2 ( q-2 ) q congruent 9 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 11 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 13 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 16 modulo 60: 1/96 q^4 phi1^2 phi2 ( q-2 ) q congruent 17 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 19 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 21 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 23 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 25 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 27 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 29 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 31 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 32 modulo 60: 1/96 q^4 phi1^2 phi2 ( q-2 ) q congruent 37 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 41 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 43 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 47 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 49 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 53 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 59 modulo 60: 1/96 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 2, 8 ], [ 27, 1, 4, 6 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 29, 1, 3, 8 ], [ 30, 1, 4, 8 ], [ 31, 1, 3, 4 ], [ 31, 1, 4, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 33, 1, 9, 16 ], [ 35, 1, 5, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 3, 8 ], [ 38, 1, 4, 24 ], [ 38, 1, 10, 16 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 42, 1, 5, 12 ], [ 43, 1, 4, 16 ], [ 43, 1, 9, 8 ], [ 44, 1, 2, 8 ], [ 44, 1, 6, 8 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 46, 1, 10, 24 ], [ 47, 1, 9, 8 ], [ 47, 1, 10, 8 ], [ 50, 1, 7, 12 ], [ 50, 1, 10, 12 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 16 ], [ 51, 1, 8, 8 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 53, 1, 7, 16 ], [ 53, 1, 13, 16 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 12 ], [ 54, 1, 9, 16 ], [ 54, 1, 11, 24 ], [ 55, 1, 7, 24 ], [ 55, 1, 11, 16 ], [ 55, 1, 17, 16 ], [ 56, 1, 11, 16 ], [ 56, 1, 12, 12 ], [ 56, 1, 16, 16 ], [ 56, 1, 17, 12 ], [ 58, 1, 5, 16 ], [ 58, 1, 23, 48 ], [ 59, 1, 20, 12 ], [ 59, 1, 21, 16 ], [ 60, 1, 6, 48 ], [ 60, 1, 10, 24 ], [ 61, 1, 14, 16 ], [ 61, 1, 16, 16 ], [ 62, 1, 8, 24 ], [ 62, 1, 9, 24 ], [ 63, 1, 6, 24 ], [ 63, 1, 11, 24 ], [ 63, 1, 26, 32 ], [ 64, 1, 11, 48 ], [ 64, 1, 21, 48 ], [ 65, 1, 25, 48 ], [ 65, 1, 44, 32 ], [ 66, 1, 29, 48 ], [ 66, 1, 30, 48 ] ] k = 61: F-action on Pi is () [67,1,61] Dynkin type is A_0(q) + T(phi24) Order of center |Z^F|: phi24 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 2 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 3 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 4 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 5 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 7 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 8 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 9 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 11 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 13 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 16 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 17 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 19 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 21 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 23 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 25 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 27 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 29 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 31 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 32 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 37 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 41 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 43 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 47 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 49 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 53 modulo 60: 1/24 q^4 phi1 phi2 phi4 q congruent 59 modulo 60: 1/24 q^4 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 61 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 62: F-action on Pi is () [67,1,62] Dynkin type is A_0(q) + T(phi1^2 phi3 phi5) Order of center |Z^F|: phi1^2 phi3 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 17 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/60 q^2 phi1 phi2^2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 62 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 26, 1, 1, 4 ], [ 27, 1, 5, 6 ], [ 29, 1, 1, 4 ], [ 42, 1, 3, 6 ], [ 44, 1, 3, 12 ], [ 45, 1, 3, 6 ], [ 50, 1, 3, 12 ], [ 54, 1, 3, 12 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 10 ], [ 63, 1, 2, 20 ], [ 65, 1, 2, 20 ], [ 66, 1, 5, 30 ] ] k = 63: F-action on Pi is () [67,1,63] Dynkin type is A_0(q) + T(phi2^2 phi6 phi10) Order of center |Z^F|: phi2^2 phi6 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 2 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 3 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 4 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 5 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 7 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 8 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 9 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 11 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 13 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 16 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 17 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 19 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 21 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 23 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 25 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 27 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 29 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 31 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 32 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 37 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 41 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 43 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 47 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 49 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 53 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 q congruent 59 modulo 60: 1/60 q^3 phi1^2 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 63 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 29, 1, 4, 4 ], [ 42, 1, 5, 6 ], [ 44, 1, 7, 12 ], [ 45, 1, 4, 6 ], [ 50, 1, 10, 12 ], [ 54, 1, 8, 10 ], [ 54, 1, 10, 12 ], [ 61, 1, 3, 10 ], [ 63, 1, 3, 20 ], [ 65, 1, 4, 20 ], [ 66, 1, 6, 30 ] ] k = 64: F-action on Pi is () [67,1,64] Dynkin type is A_0(q) + T(phi15) Order of center |Z^F|: phi15 Numbers of classes in class type: q congruent 1 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 2 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 3 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 4 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 5 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 7 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 8 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 9 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 11 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 13 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 16 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 17 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 19 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 21 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 23 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 25 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 27 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 29 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 31 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 32 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 37 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 41 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 43 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 47 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 49 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 53 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) q congruent 59 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3-q^2+1 ) Fusion of maximal tori of C^F in those of G^F: [ 64 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 65: F-action on Pi is () [67,1,65] Dynkin type is A_0(q) + T(phi30) Order of center |Z^F|: phi30 Numbers of classes in class type: q congruent 1 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 2 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 3 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 4 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 5 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 7 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 8 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 9 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 11 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 13 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 16 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 17 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 19 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 21 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 23 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 25 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 27 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 29 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 31 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 32 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 37 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 41 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 43 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 47 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 49 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 53 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) q congruent 59 modulo 60: 1/30 q phi1 phi2 phi4 ( q^3+q^2-1 ) Fusion of maximal tori of C^F in those of G^F: [ 65 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 66: F-action on Pi is () [67,1,66] Dynkin type is A_0(q) + T(phi1^7 phi2) Order of center |Z^F|: phi1^7 phi2 Numbers of classes in class type: q congruent 1 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 55245*q-2330055 ) q congruent 2 modulo 60: 1/5806080 q ( q^7-70*q^6+2016*q^5-30800*q^4+267344*q^3-1300320*q^2+31991\ 04*q-2903040 ) q congruent 3 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3638844\ *q^2-4615380*q+1715175 ) q congruent 4 modulo 60: 1/5806080 q ( q^7-70*q^6+2016*q^5-30800*q^4+267344*q^3-1300320*q^2+32170\ 24*q-3082240 ) q congruent 5 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 37325*q-2168775 ) q congruent 7 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3656764\ *q^2-4794580*q+1876455 ) q congruent 8 modulo 60: 1/5806080 q ( q^7-70*q^6+2016*q^5-30800*q^4+267344*q^3-1300320*q^2+31991\ 04*q-2903040 ) q congruent 9 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 37325*q-2168775 ) q congruent 11 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3638844\ *q^2-4615380*q+1715175 ) q congruent 13 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 55245*q-2330055 ) q congruent 16 modulo 60: 1/5806080 q ( q^7-70*q^6+2016*q^5-30800*q^4+267344*q^3-1300320*q^2+32170\ 24*q-3082240 ) q congruent 17 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 37325*q-2168775 ) q congruent 19 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3656764\ *q^2-4794580*q+1876455 ) q congruent 21 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 37325*q-2168775 ) q congruent 23 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3638844\ *q^2-4615380*q+1715175 ) q congruent 25 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 55245*q-2330055 ) q congruent 27 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3638844\ *q^2-4615380*q+1715175 ) q congruent 29 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 37325*q-2168775 ) q congruent 31 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3656764\ *q^2-4794580*q+1876455 ) q congruent 32 modulo 60: 1/5806080 q ( q^7-70*q^6+2016*q^5-30800*q^4+267344*q^3-1300320*q^2+31991\ 04*q-2903040 ) q congruent 37 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 55245*q-2330055 ) q congruent 41 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 37325*q-2168775 ) q congruent 43 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3656764\ *q^2-4794580*q+1876455 ) q congruent 47 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3638844\ *q^2-4615380*q+1715175 ) q congruent 49 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 55245*q-2330055 ) q congruent 53 modulo 60: 1/5806080 phi1 ( q^7-69*q^6+1947*q^5-28853*q^4+239751*q^3-1101519*q^2+25\ 37325*q-2168775 ) q congruent 59 modulo 60: 1/5806080 ( q^8-70*q^7+2016*q^6-30800*q^5+268604*q^4-1341270*q^3+3638844\ *q^2-4615380*q+1715175 ) Fusion of maximal tori of C^F in those of G^F: [ 66 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 64 ], [ 3, 1, 1, 728 ], [ 4, 1, 1, 3276 ], [ 5, 1, 1, 8064 ], [ 6, 1, 1, 12768 ], [ 7, 1, 1, 2088 ], [ 8, 1, 1, 576 ], [ 9, 1, 1, 63 ], [ 10, 1, 1, 126 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2072 ], [ 12, 1, 1, 11592 ], [ 13, 1, 1, 16632 ], [ 14, 1, 1, 32256 ], [ 15, 1, 1, 56448 ], [ 16, 1, 1, 110880 ], [ 17, 1, 1, 134400 ], [ 18, 1, 1, 12672 ], [ 19, 1, 1, 34272 ], [ 20, 1, 1, 65520 ], [ 20, 1, 2, 5040 ], [ 21, 1, 1, 4032 ], [ 22, 1, 1, 24192 ], [ 22, 1, 2, 1344 ], [ 23, 1, 1, 756 ], [ 24, 1, 1, 3906 ], [ 24, 1, 2, 126 ], [ 25, 1, 1, 22680 ], [ 26, 1, 1, 4032 ], [ 26, 1, 3, 144 ], [ 27, 1, 1, 4032 ], [ 27, 1, 2, 112 ], [ 28, 1, 1, 31752 ], [ 28, 1, 2, 1512 ], [ 29, 1, 1, 104832 ], [ 29, 1, 2, 8064 ], [ 30, 1, 1, 145152 ], [ 31, 1, 1, 201600 ], [ 31, 1, 2, 20160 ], [ 32, 1, 1, 322560 ], [ 33, 1, 1, 423360 ], [ 34, 1, 1, 64512 ], [ 34, 1, 2, 4032 ], [ 35, 1, 1, 272160 ], [ 35, 1, 3, 30240 ], [ 36, 1, 1, 24192 ], [ 36, 1, 2, 1152 ], [ 37, 1, 1, 120960 ], [ 38, 1, 1, 241920 ], [ 38, 1, 5, 26880 ], [ 39, 1, 1, 7560 ], [ 39, 1, 4, 252 ], [ 40, 1, 1, 75600 ], [ 41, 1, 1, 105840 ], [ 41, 1, 6, 7560 ], [ 42, 1, 1, 64512 ], [ 42, 1, 4, 4032 ], [ 43, 1, 1, 120960 ], [ 43, 1, 2, 10080 ], [ 44, 1, 1, 60480 ], [ 44, 1, 2, 3024 ], [ 45, 1, 1, 266112 ], [ 45, 1, 2, 24192 ], [ 46, 1, 1, 564480 ], [ 46, 1, 2, 80640 ], [ 47, 1, 1, 725760 ], [ 47, 1, 2, 120960 ], [ 48, 1, 1, 483840 ], [ 48, 1, 2, 60480 ], [ 49, 1, 1, 907200 ], [ 49, 1, 9, 181440 ], [ 50, 1, 1, 120960 ], [ 50, 1, 2, 8064 ], [ 50, 1, 4, 8064 ], [ 51, 1, 1, 362880 ], [ 51, 1, 2, 40320 ], [ 52, 1, 1, 196560 ], [ 52, 1, 2, 15120 ], [ 53, 1, 1, 483840 ], [ 53, 1, 3, 60480 ], [ 54, 1, 1, 483840 ], [ 54, 1, 2, 48384 ], [ 55, 1, 1, 1209600 ], [ 55, 1, 2, 241920 ], [ 56, 1, 1, 846720 ], [ 56, 1, 2, 120960 ], [ 56, 1, 6, 120960 ], [ 57, 1, 1, 1451520 ], [ 57, 1, 2, 362880 ], [ 58, 1, 1, 967680 ], [ 58, 1, 2, 161280 ], [ 59, 1, 1, 362880 ], [ 59, 1, 12, 30240 ], [ 60, 1, 1, 1451520 ], [ 60, 1, 40, 362880 ], [ 61, 1, 1, 1935360 ], [ 61, 1, 19, 483840 ], [ 62, 1, 1, 2177280 ], [ 62, 1, 30, 725760 ], [ 62, 1, 41, 725760 ], [ 63, 1, 1, 1451520 ], [ 63, 1, 33, 241920 ], [ 64, 1, 1, 2903040 ], [ 64, 1, 51, 1451520 ], [ 65, 1, 1, 2903040 ], [ 65, 1, 47, 967680 ], [ 66, 1, 1, 2903040 ], [ 66, 1, 58, 2903040 ] ] k = 67: F-action on Pi is () [67,1,67] Dynkin type is A_0(q) + T(phi1 phi2^7) Order of center |Z^F|: phi1 phi2^7 Numbers of classes in class type: q congruent 1 modulo 60: 1/5806080 phi1 ( q^7-57*q^6+1315*q^5-15765*q^4+105559*q^3-401283*q^2+862\ 965*q-921375 ) q congruent 2 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+120064*q^4-472192*q^3+967168*q\ ^2-916480*q+286720 ) q congruent 3 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1264248*\ q^2-1875060*q+1374975 ) q congruent 4 modulo 60: 1/5806080 q ( q^7-58*q^6+1372*q^5-17080*q^4+120064*q^3-472192*q^2+949248\ *q-737280 ) q congruent 5 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1282168*\ q^2-1963540*q+1369375 ) q congruent 7 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1264248*\ q^2-1875060*q+1374975 ) q congruent 8 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+120064*q^4-472192*q^3+967168*q\ ^2-916480*q+286720 ) q congruent 9 modulo 60: 1/5806080 phi1 ( q^7-57*q^6+1315*q^5-15765*q^4+105559*q^3-401283*q^2+862\ 965*q-921375 ) q congruent 11 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1282168*\ q^2-2054260*q+1822975 ) q congruent 13 modulo 60: 1/5806080 phi1 ( q^7-57*q^6+1315*q^5-15765*q^4+105559*q^3-401283*q^2+862\ 965*q-921375 ) q congruent 16 modulo 60: 1/5806080 q ( q^7-58*q^6+1372*q^5-17080*q^4+120064*q^3-472192*q^2+949248\ *q-737280 ) q congruent 17 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1282168*\ q^2-1963540*q+1369375 ) q congruent 19 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1264248*\ q^2-1875060*q+1374975 ) q congruent 21 modulo 60: 1/5806080 phi1 ( q^7-57*q^6+1315*q^5-15765*q^4+105559*q^3-401283*q^2+862\ 965*q-921375 ) q congruent 23 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1282168*\ q^2-2054260*q+1822975 ) q congruent 25 modulo 60: 1/5806080 phi1 ( q^7-57*q^6+1315*q^5-15765*q^4+105559*q^3-401283*q^2+862\ 965*q-921375 ) q congruent 27 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1264248*\ q^2-1875060*q+1374975 ) q congruent 29 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1282168*\ q^2-1963540*q+1369375 ) q congruent 31 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1264248*\ q^2-1875060*q+1374975 ) q congruent 32 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+120064*q^4-472192*q^3+967168*q\ ^2-916480*q+286720 ) q congruent 37 modulo 60: 1/5806080 phi1 ( q^7-57*q^6+1315*q^5-15765*q^4+105559*q^3-401283*q^2+862\ 965*q-921375 ) q congruent 41 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1282168*\ q^2-1963540*q+1369375 ) q congruent 43 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1264248*\ q^2-1875060*q+1374975 ) q congruent 47 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1282168*\ q^2-2054260*q+1822975 ) q congruent 49 modulo 60: 1/5806080 phi1 ( q^7-57*q^6+1315*q^5-15765*q^4+105559*q^3-401283*q^2+862\ 965*q-921375 ) q congruent 53 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1282168*\ q^2-1963540*q+1369375 ) q congruent 59 modulo 60: 1/5806080 ( q^8-58*q^7+1372*q^6-17080*q^5+121324*q^4-506842*q^3+1282168*\ q^2-2054260*q+1822975 ) Fusion of maximal tori of C^F in those of G^F: [ 67 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 64 ], [ 3, 1, 2, 728 ], [ 4, 1, 2, 3276 ], [ 5, 1, 2, 8064 ], [ 6, 1, 2, 12768 ], [ 7, 1, 2, 2088 ], [ 8, 1, 2, 576 ], [ 9, 1, 1, 63 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 126 ], [ 11, 1, 2, 2072 ], [ 12, 1, 2, 11592 ], [ 13, 1, 4, 16632 ], [ 14, 1, 2, 32256 ], [ 15, 1, 2, 56448 ], [ 16, 1, 3, 110880 ], [ 17, 1, 4, 134400 ], [ 18, 1, 2, 12672 ], [ 19, 1, 2, 34272 ], [ 20, 1, 3, 5040 ], [ 20, 1, 4, 65520 ], [ 21, 1, 2, 4032 ], [ 22, 1, 3, 1344 ], [ 22, 1, 4, 24192 ], [ 23, 1, 2, 756 ], [ 24, 1, 1, 126 ], [ 24, 1, 2, 3906 ], [ 25, 1, 3, 22680 ], [ 26, 1, 2, 144 ], [ 26, 1, 4, 4032 ], [ 27, 1, 3, 112 ], [ 27, 1, 6, 4032 ], [ 28, 1, 3, 1512 ], [ 28, 1, 4, 31752 ], [ 29, 1, 3, 8064 ], [ 29, 1, 4, 104832 ], [ 30, 1, 3, 145152 ], [ 31, 1, 3, 20160 ], [ 31, 1, 4, 201600 ], [ 32, 1, 3, 322560 ], [ 33, 1, 8, 423360 ], [ 34, 1, 3, 4032 ], [ 34, 1, 4, 64512 ], [ 35, 1, 6, 30240 ], [ 35, 1, 8, 272160 ], [ 36, 1, 3, 1152 ], [ 36, 1, 4, 24192 ], [ 37, 1, 3, 120960 ], [ 38, 1, 8, 26880 ], [ 38, 1, 12, 241920 ], [ 39, 1, 3, 7560 ], [ 39, 1, 4, 252 ], [ 40, 1, 6, 75600 ], [ 41, 1, 6, 7560 ], [ 41, 1, 9, 105840 ], [ 42, 1, 2, 4032 ], [ 42, 1, 6, 64512 ], [ 43, 1, 4, 10080 ], [ 43, 1, 13, 120960 ], [ 44, 1, 8, 3024 ], [ 44, 1, 10, 60480 ], [ 45, 1, 5, 24192 ], [ 45, 1, 6, 266112 ], [ 46, 1, 5, 80640 ], [ 46, 1, 6, 564480 ], [ 47, 1, 7, 120960 ], [ 47, 1, 8, 725760 ], [ 48, 1, 5, 60480 ], [ 48, 1, 6, 483840 ], [ 49, 1, 5, 181440 ], [ 49, 1, 10, 907200 ], [ 50, 1, 9, 8064 ], [ 50, 1, 11, 8064 ], [ 50, 1, 12, 120960 ], [ 51, 1, 8, 40320 ], [ 51, 1, 9, 362880 ], [ 52, 1, 9, 15120 ], [ 52, 1, 10, 196560 ], [ 53, 1, 8, 60480 ], [ 53, 1, 20, 483840 ], [ 54, 1, 12, 48384 ], [ 54, 1, 14, 483840 ], [ 55, 1, 13, 241920 ], [ 55, 1, 15, 1209600 ], [ 56, 1, 15, 120960 ], [ 56, 1, 18, 120960 ], [ 56, 1, 20, 846720 ], [ 57, 1, 6, 362880 ], [ 57, 1, 10, 1451520 ], [ 58, 1, 12, 161280 ], [ 58, 1, 15, 967680 ], [ 59, 1, 2, 362880 ], [ 59, 1, 13, 30240 ], [ 60, 1, 17, 1451520 ], [ 60, 1, 41, 362880 ], [ 61, 1, 20, 483840 ], [ 61, 1, 21, 1935360 ], [ 62, 1, 24, 725760 ], [ 62, 1, 29, 2177280 ], [ 62, 1, 43, 725760 ], [ 63, 1, 19, 1451520 ], [ 63, 1, 36, 241920 ], [ 64, 1, 47, 2903040 ], [ 64, 1, 52, 1451520 ], [ 65, 1, 38, 2903040 ], [ 65, 1, 49, 967680 ], [ 66, 1, 54, 2903040 ], [ 66, 1, 57, 2903040 ] ] k = 68: F-action on Pi is () [67,1,68] Dynkin type is A_0(q) + T(phi1^5 phi2^3) Order of center |Z^F|: phi1^5 phi2^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2693*q+433 ) q congruent 2 modulo 60: 1/18432 q ( q^7-18*q^6+100*q^5-72*q^4-864*q^3+1600*q^2+1280*q-3072 ) q congruent 3 modulo 60: 1/18432 phi2 ( q^7-19*q^6+119*q^5-191*q^4-693*q^3+2307*q^2-867*q-1233 ) q congruent 4 modulo 60: 1/18432 q ( q^7-18*q^6+100*q^5-72*q^4-864*q^3+1600*q^2+1792*q-4096 ) q congruent 5 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2181*q+945 ) q congruent 7 modulo 60: 1/18432 ( q^8-18*q^7+100*q^6-72*q^5-884*q^4+1614*q^3+1952*q^2-3124*q-721\ ) q congruent 8 modulo 60: 1/18432 q ( q^7-18*q^6+100*q^5-72*q^4-864*q^3+1600*q^2+1280*q-3072 ) q congruent 9 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2181*q+945 ) q congruent 11 modulo 60: 1/18432 phi2 ( q^7-19*q^6+119*q^5-191*q^4-693*q^3+2307*q^2-867*q-1233 ) q congruent 13 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2693*q+433 ) q congruent 16 modulo 60: 1/18432 q ( q^7-18*q^6+100*q^5-72*q^4-864*q^3+1600*q^2+1792*q-4096 ) q congruent 17 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2181*q+945 ) q congruent 19 modulo 60: 1/18432 ( q^8-18*q^7+100*q^6-72*q^5-884*q^4+1614*q^3+1952*q^2-3124*q-721\ ) q congruent 21 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2181*q+945 ) q congruent 23 modulo 60: 1/18432 phi2 ( q^7-19*q^6+119*q^5-191*q^4-693*q^3+2307*q^2-867*q-1233 ) q congruent 25 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2693*q+433 ) q congruent 27 modulo 60: 1/18432 phi2 ( q^7-19*q^6+119*q^5-191*q^4-693*q^3+2307*q^2-867*q-1233 ) q congruent 29 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2181*q+945 ) q congruent 31 modulo 60: 1/18432 ( q^8-18*q^7+100*q^6-72*q^5-884*q^4+1614*q^3+1952*q^2-3124*q-721\ ) q congruent 32 modulo 60: 1/18432 q ( q^7-18*q^6+100*q^5-72*q^4-864*q^3+1600*q^2+1280*q-3072 ) q congruent 37 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2693*q+433 ) q congruent 41 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2181*q+945 ) q congruent 43 modulo 60: 1/18432 ( q^8-18*q^7+100*q^6-72*q^5-884*q^4+1614*q^3+1952*q^2-3124*q-721\ ) q congruent 47 modulo 60: 1/18432 phi2 ( q^7-19*q^6+119*q^5-191*q^4-693*q^3+2307*q^2-867*q-1233 ) q congruent 49 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2693*q+433 ) q congruent 53 modulo 60: 1/18432 phi1 ( q^7-17*q^6+83*q^5+11*q^4-873*q^3+741*q^2+2181*q+945 ) q congruent 59 modulo 60: 1/18432 phi2 ( q^7-19*q^6+119*q^5-191*q^4-693*q^3+2307*q^2-867*q-1233 ) Fusion of maximal tori of C^F in those of G^F: [ 68 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 80 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 216 ], [ 4, 1, 2, 84 ], [ 5, 1, 1, 384 ], [ 6, 1, 1, 512 ], [ 6, 1, 2, 96 ], [ 7, 1, 1, 144 ], [ 7, 1, 2, 24 ], [ 8, 1, 1, 64 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 26 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 144 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 432 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 528 ], [ 13, 1, 2, 96 ], [ 13, 1, 3, 288 ], [ 13, 1, 4, 168 ], [ 14, 1, 1, 768 ], [ 15, 1, 1, 1152 ], [ 16, 1, 1, 1920 ], [ 16, 1, 2, 960 ], [ 16, 1, 3, 288 ], [ 16, 1, 4, 192 ], [ 17, 1, 1, 2304 ], [ 17, 1, 2, 256 ], [ 17, 1, 3, 768 ], [ 18, 1, 1, 384 ], [ 19, 1, 1, 768 ], [ 19, 1, 2, 96 ], [ 20, 1, 1, 1248 ], [ 20, 1, 2, 864 ], [ 20, 1, 3, 720 ], [ 20, 1, 4, 144 ], [ 20, 1, 6, 384 ], [ 20, 1, 8, 384 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 640 ], [ 22, 1, 2, 384 ], [ 22, 1, 3, 192 ], [ 23, 1, 1, 72 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 198 ], [ 24, 1, 2, 90 ], [ 25, 1, 1, 624 ], [ 25, 1, 2, 384 ], [ 25, 1, 3, 168 ], [ 25, 1, 4, 192 ], [ 26, 1, 1, 192 ], [ 26, 1, 2, 48 ], [ 26, 1, 3, 96 ], [ 27, 1, 1, 192 ], [ 27, 1, 2, 96 ], [ 27, 1, 3, 16 ], [ 28, 1, 1, 624 ], [ 28, 1, 2, 432 ], [ 28, 1, 3, 312 ], [ 28, 1, 4, 24 ], [ 29, 1, 1, 1152 ], [ 29, 1, 2, 1152 ], [ 30, 1, 1, 1536 ], [ 30, 1, 2, 768 ], [ 31, 1, 1, 1920 ], [ 31, 1, 2, 1920 ], [ 31, 1, 3, 576 ], [ 32, 1, 1, 3072 ], [ 32, 1, 2, 768 ], [ 32, 1, 4, 768 ], [ 33, 1, 1, 4224 ], [ 33, 1, 2, 1920 ], [ 33, 1, 4, 2304 ], [ 33, 1, 6, 1152 ], [ 33, 1, 8, 576 ], [ 34, 1, 1, 768 ], [ 34, 1, 2, 768 ], [ 34, 1, 3, 192 ], [ 35, 1, 1, 2688 ], [ 35, 1, 2, 1344 ], [ 35, 1, 3, 2304 ], [ 35, 1, 4, 192 ], [ 35, 1, 5, 1728 ], [ 35, 1, 6, 1440 ], [ 35, 1, 7, 576 ], [ 35, 1, 8, 288 ], [ 36, 1, 1, 384 ], [ 36, 1, 2, 384 ], [ 37, 1, 1, 1152 ], [ 37, 1, 2, 768 ], [ 38, 1, 1, 2304 ], [ 38, 1, 2, 512 ], [ 38, 1, 5, 2304 ], [ 38, 1, 7, 1536 ], [ 39, 1, 1, 240 ], [ 39, 1, 2, 96 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 156 ], [ 40, 1, 1, 1056 ], [ 40, 1, 2, 192 ], [ 40, 1, 3, 576 ], [ 40, 1, 6, 48 ], [ 41, 1, 1, 1440 ], [ 41, 1, 2, 576 ], [ 41, 1, 3, 1152 ], [ 41, 1, 4, 768 ], [ 41, 1, 6, 1032 ], [ 41, 1, 7, 192 ], [ 41, 1, 9, 336 ], [ 42, 1, 1, 768 ], [ 42, 1, 2, 192 ], [ 42, 1, 4, 768 ], [ 43, 1, 1, 1152 ], [ 43, 1, 2, 1344 ], [ 43, 1, 3, 1152 ], [ 43, 1, 4, 288 ], [ 43, 1, 6, 768 ], [ 43, 1, 8, 768 ], [ 43, 1, 12, 384 ], [ 44, 1, 1, 576 ], [ 44, 1, 2, 672 ], [ 44, 1, 5, 192 ], [ 44, 1, 8, 48 ], [ 44, 1, 9, 576 ], [ 45, 1, 1, 1152 ], [ 45, 1, 2, 1920 ], [ 46, 1, 1, 2304 ], [ 46, 1, 2, 3840 ], [ 46, 1, 7, 1536 ], [ 46, 1, 11, 1536 ], [ 47, 1, 1, 3840 ], [ 47, 1, 2, 4608 ], [ 47, 1, 3, 3072 ], [ 47, 1, 4, 768 ], [ 47, 1, 7, 1152 ], [ 47, 1, 9, 2304 ], [ 48, 1, 1, 2304 ], [ 48, 1, 2, 3072 ], [ 48, 1, 3, 1536 ], [ 48, 1, 4, 2304 ], [ 48, 1, 5, 576 ], [ 48, 1, 7, 2304 ], [ 49, 1, 1, 5760 ], [ 49, 1, 2, 3456 ], [ 49, 1, 5, 2880 ], [ 49, 1, 8, 1152 ], [ 49, 1, 9, 5760 ], [ 49, 1, 10, 576 ], [ 49, 1, 11, 2304 ], [ 49, 1, 18, 2304 ], [ 49, 1, 20, 2304 ], [ 50, 1, 1, 384 ], [ 50, 1, 2, 1152 ], [ 50, 1, 4, 1152 ], [ 50, 1, 5, 384 ], [ 50, 1, 8, 384 ], [ 51, 1, 1, 1152 ], [ 51, 1, 2, 2688 ], [ 51, 1, 3, 384 ], [ 51, 1, 5, 1152 ], [ 51, 1, 6, 1920 ], [ 51, 1, 10, 1152 ], [ 52, 1, 1, 1440 ], [ 52, 1, 2, 1440 ], [ 52, 1, 3, 1344 ], [ 52, 1, 4, 192 ], [ 52, 1, 9, 624 ], [ 52, 1, 10, 48 ], [ 53, 1, 1, 2304 ], [ 53, 1, 2, 2304 ], [ 53, 1, 3, 3072 ], [ 53, 1, 4, 384 ], [ 53, 1, 5, 2304 ], [ 53, 1, 6, 2304 ], [ 53, 1, 7, 1152 ], [ 53, 1, 8, 576 ], [ 53, 1, 9, 1536 ], [ 54, 1, 2, 2304 ], [ 54, 1, 5, 1536 ], [ 55, 1, 1, 2304 ], [ 55, 1, 2, 5376 ], [ 55, 1, 5, 3840 ], [ 55, 1, 8, 1536 ], [ 55, 1, 9, 4608 ], [ 55, 1, 14, 2304 ], [ 55, 1, 16, 4608 ], [ 56, 1, 1, 1152 ], [ 56, 1, 2, 3456 ], [ 56, 1, 5, 2688 ], [ 56, 1, 6, 3456 ], [ 56, 1, 7, 2688 ], [ 56, 1, 10, 384 ], [ 56, 1, 13, 1152 ], [ 56, 1, 14, 3456 ], [ 56, 1, 19, 1152 ], [ 57, 1, 1, 4608 ], [ 57, 1, 2, 6912 ], [ 57, 1, 3, 4608 ], [ 57, 1, 4, 2304 ], [ 57, 1, 5, 4608 ], [ 57, 1, 6, 1152 ], [ 58, 1, 2, 4608 ], [ 58, 1, 4, 1536 ], [ 58, 1, 9, 3072 ], [ 58, 1, 16, 3072 ], [ 59, 1, 1, 1152 ], [ 59, 1, 3, 1152 ], [ 59, 1, 12, 1728 ], [ 59, 1, 13, 96 ], [ 59, 1, 17, 2304 ], [ 59, 1, 22, 384 ], [ 60, 1, 1, 4608 ], [ 60, 1, 27, 4608 ], [ 60, 1, 40, 6912 ], [ 60, 1, 41, 1152 ], [ 60, 1, 42, 4608 ], [ 60, 1, 44, 4608 ], [ 60, 1, 45, 2304 ], [ 61, 1, 12, 6144 ], [ 61, 1, 17, 1536 ], [ 61, 1, 19, 4608 ], [ 61, 1, 22, 4608 ], [ 62, 1, 1, 2304 ], [ 62, 1, 30, 6912 ], [ 62, 1, 31, 2304 ], [ 62, 1, 32, 6912 ], [ 62, 1, 41, 6912 ], [ 62, 1, 42, 2304 ], [ 62, 1, 45, 4608 ], [ 62, 1, 46, 6912 ], [ 62, 1, 47, 4608 ], [ 62, 1, 50, 4608 ], [ 63, 1, 20, 4608 ], [ 63, 1, 21, 4608 ], [ 63, 1, 29, 4608 ], [ 63, 1, 32, 768 ], [ 63, 1, 33, 2304 ], [ 63, 1, 35, 2304 ], [ 64, 1, 37, 9216 ], [ 64, 1, 51, 4608 ], [ 64, 1, 53, 9216 ], [ 64, 1, 60, 4608 ], [ 64, 1, 62, 9216 ], [ 64, 1, 64, 4608 ], [ 65, 1, 37, 9216 ], [ 65, 1, 39, 9216 ], [ 65, 1, 48, 3072 ], [ 66, 1, 47, 9216 ], [ 66, 1, 56, 9216 ], [ 66, 1, 59, 9216 ] ] k = 69: F-action on Pi is () [67,1,69] Dynkin type is A_0(q) + T(phi1^3 phi2^5) Order of center |Z^F|: phi1^3 phi2^5 Numbers of classes in class type: q congruent 1 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q-297 ) q congruent 2 modulo 60: 1/18432 q ( q^7-14*q^6+56*q^5-336*q^3+224*q^2+896*q-1024 ) q congruent 3 modulo 60: 1/18432 ( q^8-14*q^7+56*q^6-356*q^4+354*q^3-140*q^2+1260*q-9 ) q congruent 4 modulo 60: 1/18432 q^2 ( q^6-14*q^5+56*q^4-336*q^2+224*q+384 ) q congruent 5 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q+215 ) q congruent 7 modulo 60: 1/18432 ( q^8-14*q^7+56*q^6-356*q^4+354*q^3-140*q^2+1260*q-9 ) q congruent 8 modulo 60: 1/18432 q ( q^7-14*q^6+56*q^5-336*q^3+224*q^2+896*q-1024 ) q congruent 9 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q-297 ) q congruent 11 modulo 60: 1/18432 phi2 ( q^7-15*q^6+71*q^5-71*q^4-285*q^3+639*q^2-267*q+503 ) q congruent 13 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q-297 ) q congruent 16 modulo 60: 1/18432 q^2 ( q^6-14*q^5+56*q^4-336*q^2+224*q+384 ) q congruent 17 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q+215 ) q congruent 19 modulo 60: 1/18432 ( q^8-14*q^7+56*q^6-356*q^4+354*q^3-140*q^2+1260*q-9 ) q congruent 21 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q-297 ) q congruent 23 modulo 60: 1/18432 phi2 ( q^7-15*q^6+71*q^5-71*q^4-285*q^3+639*q^2-267*q+503 ) q congruent 25 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q-297 ) q congruent 27 modulo 60: 1/18432 ( q^8-14*q^7+56*q^6-356*q^4+354*q^3-140*q^2+1260*q-9 ) q congruent 29 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q+215 ) q congruent 31 modulo 60: 1/18432 ( q^8-14*q^7+56*q^6-356*q^4+354*q^3-140*q^2+1260*q-9 ) q congruent 32 modulo 60: 1/18432 q ( q^7-14*q^6+56*q^5-336*q^3+224*q^2+896*q-1024 ) q congruent 37 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q-297 ) q congruent 41 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q+215 ) q congruent 43 modulo 60: 1/18432 ( q^8-14*q^7+56*q^6-356*q^4+354*q^3-140*q^2+1260*q-9 ) q congruent 47 modulo 60: 1/18432 phi2 ( q^7-15*q^6+71*q^5-71*q^4-285*q^3+639*q^2-267*q+503 ) q congruent 49 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q-297 ) q congruent 53 modulo 60: 1/18432 phi1^2 ( q^6-12*q^5+31*q^4+74*q^3-239*q^2-198*q+215 ) q congruent 59 modulo 60: 1/18432 phi2 ( q^7-15*q^6+71*q^5-71*q^4-285*q^3+639*q^2-267*q+503 ) Fusion of maximal tori of C^F in those of G^F: [ 69 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 80 ], [ 4, 1, 1, 84 ], [ 4, 1, 2, 216 ], [ 5, 1, 2, 384 ], [ 6, 1, 1, 96 ], [ 6, 1, 2, 512 ], [ 7, 1, 1, 24 ], [ 7, 1, 2, 144 ], [ 8, 1, 2, 64 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 26 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 144 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 432 ], [ 13, 1, 1, 168 ], [ 13, 1, 2, 288 ], [ 13, 1, 3, 96 ], [ 13, 1, 4, 528 ], [ 14, 1, 2, 768 ], [ 15, 1, 2, 1152 ], [ 16, 1, 1, 288 ], [ 16, 1, 2, 192 ], [ 16, 1, 3, 1920 ], [ 16, 1, 4, 960 ], [ 17, 1, 2, 768 ], [ 17, 1, 3, 256 ], [ 17, 1, 4, 2304 ], [ 18, 1, 2, 384 ], [ 19, 1, 1, 96 ], [ 19, 1, 2, 768 ], [ 20, 1, 1, 144 ], [ 20, 1, 2, 720 ], [ 20, 1, 3, 864 ], [ 20, 1, 4, 1248 ], [ 20, 1, 5, 384 ], [ 20, 1, 7, 384 ], [ 21, 1, 2, 192 ], [ 22, 1, 2, 192 ], [ 22, 1, 3, 384 ], [ 22, 1, 4, 640 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 72 ], [ 24, 1, 1, 90 ], [ 24, 1, 2, 198 ], [ 25, 1, 1, 168 ], [ 25, 1, 2, 192 ], [ 25, 1, 3, 624 ], [ 25, 1, 4, 384 ], [ 26, 1, 2, 96 ], [ 26, 1, 3, 48 ], [ 26, 1, 4, 192 ], [ 27, 1, 2, 16 ], [ 27, 1, 3, 96 ], [ 27, 1, 6, 192 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 312 ], [ 28, 1, 3, 432 ], [ 28, 1, 4, 624 ], [ 29, 1, 3, 1152 ], [ 29, 1, 4, 1152 ], [ 30, 1, 3, 1536 ], [ 30, 1, 4, 768 ], [ 31, 1, 2, 576 ], [ 31, 1, 3, 1920 ], [ 31, 1, 4, 1920 ], [ 32, 1, 2, 768 ], [ 32, 1, 3, 3072 ], [ 32, 1, 4, 768 ], [ 33, 1, 1, 576 ], [ 33, 1, 2, 1152 ], [ 33, 1, 6, 1920 ], [ 33, 1, 8, 4224 ], [ 33, 1, 10, 2304 ], [ 34, 1, 2, 192 ], [ 34, 1, 3, 768 ], [ 34, 1, 4, 768 ], [ 35, 1, 1, 288 ], [ 35, 1, 2, 576 ], [ 35, 1, 3, 1440 ], [ 35, 1, 4, 1728 ], [ 35, 1, 5, 192 ], [ 35, 1, 6, 2304 ], [ 35, 1, 7, 1344 ], [ 35, 1, 8, 2688 ], [ 36, 1, 3, 384 ], [ 36, 1, 4, 384 ], [ 37, 1, 2, 768 ], [ 37, 1, 3, 1152 ], [ 38, 1, 6, 1536 ], [ 38, 1, 8, 2304 ], [ 38, 1, 10, 512 ], [ 38, 1, 12, 2304 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 96 ], [ 39, 1, 3, 240 ], [ 39, 1, 4, 156 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 576 ], [ 40, 1, 3, 192 ], [ 40, 1, 6, 1056 ], [ 41, 1, 1, 336 ], [ 41, 1, 2, 576 ], [ 41, 1, 4, 768 ], [ 41, 1, 6, 1032 ], [ 41, 1, 7, 192 ], [ 41, 1, 9, 1440 ], [ 41, 1, 10, 1152 ], [ 42, 1, 2, 768 ], [ 42, 1, 4, 192 ], [ 42, 1, 6, 768 ], [ 43, 1, 2, 288 ], [ 43, 1, 3, 384 ], [ 43, 1, 4, 1344 ], [ 43, 1, 8, 768 ], [ 43, 1, 12, 1152 ], [ 43, 1, 13, 1152 ], [ 43, 1, 14, 768 ], [ 44, 1, 2, 48 ], [ 44, 1, 5, 576 ], [ 44, 1, 8, 672 ], [ 44, 1, 9, 192 ], [ 44, 1, 10, 576 ], [ 45, 1, 5, 1920 ], [ 45, 1, 6, 1152 ], [ 46, 1, 5, 3840 ], [ 46, 1, 6, 2304 ], [ 46, 1, 8, 1536 ], [ 46, 1, 12, 1536 ], [ 47, 1, 2, 1152 ], [ 47, 1, 4, 2304 ], [ 47, 1, 7, 4608 ], [ 47, 1, 8, 3840 ], [ 47, 1, 9, 768 ], [ 47, 1, 10, 3072 ], [ 48, 1, 2, 576 ], [ 48, 1, 3, 2304 ], [ 48, 1, 4, 1536 ], [ 48, 1, 5, 3072 ], [ 48, 1, 6, 2304 ], [ 48, 1, 10, 2304 ], [ 49, 1, 1, 576 ], [ 49, 1, 2, 1152 ], [ 49, 1, 5, 5760 ], [ 49, 1, 8, 3456 ], [ 49, 1, 9, 2880 ], [ 49, 1, 10, 5760 ], [ 49, 1, 14, 2304 ], [ 49, 1, 15, 2304 ], [ 49, 1, 19, 2304 ], [ 50, 1, 5, 384 ], [ 50, 1, 8, 384 ], [ 50, 1, 9, 1152 ], [ 50, 1, 11, 1152 ], [ 50, 1, 12, 384 ], [ 51, 1, 3, 1920 ], [ 51, 1, 5, 1152 ], [ 51, 1, 6, 384 ], [ 51, 1, 8, 2688 ], [ 51, 1, 9, 1152 ], [ 51, 1, 10, 1152 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 624 ], [ 52, 1, 3, 192 ], [ 52, 1, 4, 1344 ], [ 52, 1, 9, 1440 ], [ 52, 1, 10, 1440 ], [ 53, 1, 3, 576 ], [ 53, 1, 4, 1152 ], [ 53, 1, 6, 1536 ], [ 53, 1, 7, 384 ], [ 53, 1, 8, 3072 ], [ 53, 1, 9, 2304 ], [ 53, 1, 12, 2304 ], [ 53, 1, 19, 2304 ], [ 53, 1, 20, 2304 ], [ 54, 1, 12, 2304 ], [ 54, 1, 13, 1536 ], [ 55, 1, 5, 2304 ], [ 55, 1, 10, 4608 ], [ 55, 1, 13, 5376 ], [ 55, 1, 14, 3840 ], [ 55, 1, 15, 2304 ], [ 55, 1, 17, 1536 ], [ 55, 1, 20, 4608 ], [ 56, 1, 5, 1152 ], [ 56, 1, 7, 1152 ], [ 56, 1, 10, 3456 ], [ 56, 1, 13, 2688 ], [ 56, 1, 14, 384 ], [ 56, 1, 15, 3456 ], [ 56, 1, 18, 3456 ], [ 56, 1, 19, 2688 ], [ 56, 1, 20, 1152 ], [ 57, 1, 2, 1152 ], [ 57, 1, 4, 2304 ], [ 57, 1, 5, 4608 ], [ 57, 1, 6, 6912 ], [ 57, 1, 9, 4608 ], [ 57, 1, 10, 4608 ], [ 58, 1, 4, 1536 ], [ 58, 1, 11, 3072 ], [ 58, 1, 12, 4608 ], [ 58, 1, 26, 3072 ], [ 59, 1, 2, 1152 ], [ 59, 1, 3, 1152 ], [ 59, 1, 12, 96 ], [ 59, 1, 13, 1728 ], [ 59, 1, 18, 2304 ], [ 59, 1, 22, 384 ], [ 60, 1, 17, 4608 ], [ 60, 1, 27, 4608 ], [ 60, 1, 39, 4608 ], [ 60, 1, 40, 1152 ], [ 60, 1, 41, 6912 ], [ 60, 1, 43, 4608 ], [ 60, 1, 45, 2304 ], [ 61, 1, 17, 4608 ], [ 61, 1, 18, 6144 ], [ 61, 1, 20, 4608 ], [ 61, 1, 22, 1536 ], [ 62, 1, 24, 6912 ], [ 62, 1, 29, 2304 ], [ 62, 1, 31, 6912 ], [ 62, 1, 32, 2304 ], [ 62, 1, 42, 6912 ], [ 62, 1, 43, 6912 ], [ 62, 1, 44, 4608 ], [ 62, 1, 46, 2304 ], [ 62, 1, 48, 4608 ], [ 62, 1, 49, 4608 ], [ 63, 1, 14, 4608 ], [ 63, 1, 28, 4608 ], [ 63, 1, 32, 2304 ], [ 63, 1, 34, 4608 ], [ 63, 1, 35, 768 ], [ 63, 1, 36, 2304 ], [ 64, 1, 27, 9216 ], [ 64, 1, 52, 4608 ], [ 64, 1, 58, 9216 ], [ 64, 1, 60, 4608 ], [ 64, 1, 63, 9216 ], [ 64, 1, 64, 4608 ], [ 65, 1, 32, 9216 ], [ 65, 1, 46, 9216 ], [ 65, 1, 50, 3072 ], [ 66, 1, 38, 9216 ], [ 66, 1, 55, 9216 ], [ 66, 1, 60, 9216 ] ] k = 70: F-action on Pi is () [67,1,70] Dynkin type is A_0(q) + T(phi1^5 phi2 phi4) Order of center |Z^F|: phi1^5 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 2 modulo 60: 1/15360 q^2 ( q^6-24*q^5+210*q^4-760*q^3+584*q^2+2464*q-3840 ) q congruent 3 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 4 modulo 60: 1/15360 q^2 ( q^6-24*q^5+210*q^4-760*q^3+584*q^2+2464*q-3840 ) q congruent 5 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 7 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 8 modulo 60: 1/15360 q^2 ( q^6-24*q^5+210*q^4-760*q^3+584*q^2+2464*q-3840 ) q congruent 9 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 11 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 13 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 16 modulo 60: 1/15360 q^2 ( q^6-24*q^5+210*q^4-760*q^3+584*q^2+2464*q-3840 ) q congruent 17 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 19 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 21 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 23 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 25 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 27 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 29 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 31 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 32 modulo 60: 1/15360 q^2 ( q^6-24*q^5+210*q^4-760*q^3+584*q^2+2464*q-3840 ) q congruent 37 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 41 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 43 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 47 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 49 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 53 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) q congruent 59 modulo 60: 1/15360 phi1 phi2 ( q^6-24*q^5+211*q^4-784*q^3+775*q^2+1960*q-3675 ) Fusion of maximal tori of C^F in those of G^F: [ 70 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 20 ], [ 3, 1, 1, 80 ], [ 4, 1, 1, 102 ], [ 4, 1, 2, 30 ], [ 5, 1, 1, 64 ], [ 6, 1, 1, 160 ], [ 7, 1, 1, 80 ], [ 8, 1, 1, 32 ], [ 9, 1, 1, 11 ], [ 10, 1, 1, 40 ], [ 11, 1, 1, 240 ], [ 12, 1, 1, 400 ], [ 13, 1, 1, 600 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 100 ], [ 13, 1, 4, 40 ], [ 14, 1, 1, 192 ], [ 15, 1, 1, 320 ], [ 16, 1, 1, 160 ], [ 16, 1, 2, 480 ], [ 18, 1, 1, 320 ], [ 19, 1, 1, 480 ], [ 20, 1, 1, 160 ], [ 20, 1, 3, 480 ], [ 21, 1, 1, 160 ], [ 22, 1, 1, 320 ], [ 23, 1, 1, 90 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 280 ], [ 25, 1, 1, 260 ], [ 25, 1, 2, 200 ], [ 25, 1, 3, 20 ], [ 25, 1, 4, 40 ], [ 26, 1, 1, 160 ], [ 27, 1, 1, 480 ], [ 28, 1, 1, 1200 ], [ 28, 1, 3, 80 ], [ 29, 1, 1, 640 ], [ 30, 1, 1, 960 ], [ 30, 1, 2, 64 ], [ 31, 1, 1, 320 ], [ 33, 1, 2, 320 ], [ 33, 1, 4, 1280 ], [ 34, 1, 1, 960 ], [ 35, 1, 1, 480 ], [ 35, 1, 2, 160 ], [ 35, 1, 5, 1440 ], [ 35, 1, 6, 480 ], [ 36, 1, 1, 640 ], [ 37, 1, 1, 320 ], [ 37, 1, 2, 160 ], [ 39, 1, 1, 560 ], [ 39, 1, 2, 20 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 960 ], [ 40, 1, 3, 160 ], [ 41, 1, 1, 1440 ], [ 41, 1, 2, 40 ], [ 41, 1, 3, 640 ], [ 41, 1, 4, 240 ], [ 41, 1, 5, 40 ], [ 41, 1, 8, 80 ], [ 42, 1, 1, 960 ], [ 43, 1, 1, 320 ], [ 43, 1, 3, 960 ], [ 43, 1, 8, 160 ], [ 43, 1, 9, 80 ], [ 44, 1, 1, 2400 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 40 ], [ 44, 1, 9, 160 ], [ 45, 1, 1, 1920 ], [ 47, 1, 3, 640 ], [ 48, 1, 1, 960 ], [ 48, 1, 4, 960 ], [ 48, 1, 7, 320 ], [ 48, 1, 8, 320 ], [ 49, 1, 2, 960 ], [ 49, 1, 7, 960 ], [ 49, 1, 11, 3840 ], [ 50, 1, 1, 1920 ], [ 51, 1, 1, 640 ], [ 51, 1, 6, 640 ], [ 51, 1, 7, 320 ], [ 52, 1, 1, 2880 ], [ 52, 1, 3, 480 ], [ 52, 1, 8, 160 ], [ 53, 1, 1, 960 ], [ 53, 1, 2, 320 ], [ 53, 1, 5, 2880 ], [ 53, 1, 6, 960 ], [ 53, 1, 10, 320 ], [ 53, 1, 11, 160 ], [ 53, 1, 13, 480 ], [ 54, 1, 1, 3840 ], [ 54, 1, 4, 128 ], [ 55, 1, 4, 640 ], [ 55, 1, 6, 1280 ], [ 55, 1, 9, 1280 ], [ 56, 1, 1, 1920 ], [ 56, 1, 4, 320 ], [ 56, 1, 11, 960 ], [ 56, 1, 14, 1920 ], [ 57, 1, 3, 1920 ], [ 57, 1, 11, 1920 ], [ 59, 1, 1, 5760 ], [ 59, 1, 16, 80 ], [ 59, 1, 17, 960 ], [ 59, 1, 23, 320 ], [ 60, 1, 22, 7680 ], [ 60, 1, 28, 960 ], [ 60, 1, 31, 1920 ], [ 60, 1, 44, 1920 ], [ 61, 1, 13, 1280 ], [ 62, 1, 33, 3840 ], [ 62, 1, 37, 1920 ], [ 62, 1, 47, 3840 ], [ 63, 1, 1, 3840 ], [ 63, 1, 20, 3840 ], [ 63, 1, 23, 640 ], [ 63, 1, 24, 1920 ], [ 63, 1, 31, 640 ], [ 64, 1, 38, 7680 ], [ 64, 1, 43, 3840 ], [ 64, 1, 49, 7680 ], [ 64, 1, 54, 3840 ], [ 65, 1, 40, 2560 ], [ 66, 1, 49, 7680 ] ] k = 71: F-action on Pi is () [67,1,71] Dynkin type is A_0(q) + T(phi1 phi2^5 phi4) Order of center |Z^F|: phi1 phi2^5 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 2 modulo 60: 1/15360 q^3 ( q^5-16*q^4+90*q^3-200*q^2+104*q+96 ) q congruent 3 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 4 modulo 60: 1/15360 q^3 ( q^5-16*q^4+90*q^3-200*q^2+104*q+96 ) q congruent 5 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 7 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 8 modulo 60: 1/15360 q^3 ( q^5-16*q^4+90*q^3-200*q^2+104*q+96 ) q congruent 9 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 11 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 13 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 16 modulo 60: 1/15360 q^3 ( q^5-16*q^4+90*q^3-200*q^2+104*q+96 ) q congruent 17 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 19 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 21 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 23 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 25 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 27 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 29 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 31 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 32 modulo 60: 1/15360 q^3 ( q^5-16*q^4+90*q^3-200*q^2+104*q+96 ) q congruent 37 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 41 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 43 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 47 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 49 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 53 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) q congruent 59 modulo 60: 1/15360 phi1^2 phi2 ( q^5-15*q^4+76*q^3-140*q^2+35*q+75 ) Fusion of maximal tori of C^F in those of G^F: [ 71 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 20 ], [ 3, 1, 2, 80 ], [ 4, 1, 1, 30 ], [ 4, 1, 2, 102 ], [ 5, 1, 2, 64 ], [ 6, 1, 2, 160 ], [ 7, 1, 2, 80 ], [ 8, 1, 2, 32 ], [ 9, 1, 1, 11 ], [ 10, 1, 2, 40 ], [ 11, 1, 2, 240 ], [ 12, 1, 2, 400 ], [ 13, 1, 1, 40 ], [ 13, 1, 2, 100 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 600 ], [ 14, 1, 2, 192 ], [ 15, 1, 2, 320 ], [ 16, 1, 3, 160 ], [ 16, 1, 4, 480 ], [ 18, 1, 2, 320 ], [ 19, 1, 2, 480 ], [ 20, 1, 2, 480 ], [ 20, 1, 4, 160 ], [ 21, 1, 2, 160 ], [ 22, 1, 4, 320 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 90 ], [ 24, 1, 2, 280 ], [ 25, 1, 1, 20 ], [ 25, 1, 2, 40 ], [ 25, 1, 3, 260 ], [ 25, 1, 4, 200 ], [ 26, 1, 4, 160 ], [ 27, 1, 6, 480 ], [ 28, 1, 2, 80 ], [ 28, 1, 4, 1200 ], [ 29, 1, 4, 640 ], [ 30, 1, 3, 960 ], [ 30, 1, 4, 64 ], [ 31, 1, 4, 320 ], [ 33, 1, 6, 320 ], [ 33, 1, 10, 1280 ], [ 34, 1, 4, 960 ], [ 35, 1, 3, 480 ], [ 35, 1, 4, 1440 ], [ 35, 1, 7, 160 ], [ 35, 1, 8, 480 ], [ 36, 1, 4, 640 ], [ 37, 1, 2, 160 ], [ 37, 1, 3, 320 ], [ 39, 1, 2, 20 ], [ 39, 1, 3, 560 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 160 ], [ 40, 1, 6, 960 ], [ 41, 1, 2, 40 ], [ 41, 1, 4, 240 ], [ 41, 1, 5, 40 ], [ 41, 1, 8, 80 ], [ 41, 1, 9, 1440 ], [ 41, 1, 10, 640 ], [ 42, 1, 6, 960 ], [ 43, 1, 8, 160 ], [ 43, 1, 9, 80 ], [ 43, 1, 12, 960 ], [ 43, 1, 13, 320 ], [ 44, 1, 4, 40 ], [ 44, 1, 5, 160 ], [ 44, 1, 6, 8 ], [ 44, 1, 10, 2400 ], [ 45, 1, 6, 1920 ], [ 47, 1, 10, 640 ], [ 48, 1, 3, 960 ], [ 48, 1, 6, 960 ], [ 48, 1, 9, 320 ], [ 48, 1, 10, 320 ], [ 49, 1, 4, 960 ], [ 49, 1, 8, 960 ], [ 49, 1, 19, 3840 ], [ 50, 1, 12, 1920 ], [ 51, 1, 3, 640 ], [ 51, 1, 4, 320 ], [ 51, 1, 9, 640 ], [ 52, 1, 4, 480 ], [ 52, 1, 5, 160 ], [ 52, 1, 10, 2880 ], [ 53, 1, 9, 960 ], [ 53, 1, 11, 480 ], [ 53, 1, 12, 320 ], [ 53, 1, 13, 160 ], [ 53, 1, 14, 320 ], [ 53, 1, 19, 2880 ], [ 53, 1, 20, 960 ], [ 54, 1, 9, 128 ], [ 54, 1, 14, 3840 ], [ 55, 1, 11, 640 ], [ 55, 1, 19, 1280 ], [ 55, 1, 20, 1280 ], [ 56, 1, 9, 960 ], [ 56, 1, 10, 1920 ], [ 56, 1, 16, 320 ], [ 56, 1, 20, 1920 ], [ 57, 1, 8, 1920 ], [ 57, 1, 9, 1920 ], [ 59, 1, 2, 5760 ], [ 59, 1, 16, 80 ], [ 59, 1, 18, 960 ], [ 59, 1, 24, 320 ], [ 60, 1, 26, 7680 ], [ 60, 1, 28, 960 ], [ 60, 1, 30, 1920 ], [ 60, 1, 43, 1920 ], [ 61, 1, 16, 1280 ], [ 62, 1, 35, 3840 ], [ 62, 1, 39, 1920 ], [ 62, 1, 48, 3840 ], [ 63, 1, 14, 3840 ], [ 63, 1, 19, 3840 ], [ 63, 1, 22, 1920 ], [ 63, 1, 25, 640 ], [ 63, 1, 30, 640 ], [ 64, 1, 39, 7680 ], [ 64, 1, 42, 3840 ], [ 64, 1, 50, 7680 ], [ 64, 1, 55, 3840 ], [ 65, 1, 42, 2560 ], [ 66, 1, 51, 7680 ] ] k = 72: F-action on Pi is () [67,1,72] Dynkin type is A_0(q) + T(phi1^3 phi2^3 phi4) Order of center |Z^F|: phi1^3 phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 2 modulo 60: 1/4608 q^3 ( q^5-12*q^4+46*q^3-48*q^2-56*q+96 ) q congruent 3 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 4 modulo 60: 1/4608 q^3 ( q^5-12*q^4+46*q^3-48*q^2-56*q+96 ) q congruent 5 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 7 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 8 modulo 60: 1/4608 q^3 ( q^5-12*q^4+46*q^3-48*q^2-56*q+96 ) q congruent 9 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 11 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 13 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 16 modulo 60: 1/4608 q^3 ( q^5-12*q^4+46*q^3-48*q^2-56*q+96 ) q congruent 17 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 19 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 21 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 23 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 25 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 27 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 29 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 31 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 32 modulo 60: 1/4608 q^3 ( q^5-12*q^4+46*q^3-48*q^2-56*q+96 ) q congruent 37 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 41 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 43 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 47 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 49 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 53 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) q congruent 59 modulo 60: 1/4608 phi1^2 phi2 ( q^5-11*q^4+36*q^3-24*q^2-21*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 72 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 26 ], [ 4, 1, 2, 26 ], [ 6, 1, 1, 48 ], [ 6, 1, 2, 48 ], [ 7, 1, 1, 72 ], [ 7, 1, 2, 72 ], [ 9, 1, 1, 19 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 12 ], [ 11, 1, 1, 24 ], [ 11, 1, 2, 24 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 48 ], [ 13, 1, 2, 84 ], [ 13, 1, 3, 84 ], [ 13, 1, 4, 48 ], [ 16, 1, 1, 48 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 48 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 192 ], [ 17, 1, 3, 192 ], [ 19, 1, 1, 144 ], [ 19, 1, 2, 144 ], [ 20, 1, 1, 144 ], [ 20, 1, 2, 48 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 144 ], [ 20, 1, 5, 576 ], [ 20, 1, 8, 576 ], [ 22, 1, 2, 96 ], [ 22, 1, 3, 96 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 84 ], [ 24, 1, 2, 84 ], [ 25, 1, 1, 108 ], [ 25, 1, 2, 72 ], [ 25, 1, 3, 108 ], [ 25, 1, 4, 72 ], [ 26, 1, 1, 144 ], [ 26, 1, 4, 144 ], [ 27, 1, 1, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 72 ], [ 28, 1, 3, 72 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 96 ], [ 31, 1, 3, 96 ], [ 32, 1, 2, 64 ], [ 32, 1, 4, 576 ], [ 33, 1, 2, 96 ], [ 33, 1, 6, 96 ], [ 34, 1, 2, 288 ], [ 34, 1, 3, 288 ], [ 35, 1, 1, 144 ], [ 35, 1, 2, 432 ], [ 35, 1, 3, 144 ], [ 35, 1, 4, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 144 ], [ 35, 1, 7, 432 ], [ 35, 1, 8, 144 ], [ 38, 1, 6, 384 ], [ 38, 1, 7, 384 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 36 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 144 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 48 ], [ 40, 1, 3, 48 ], [ 41, 1, 1, 144 ], [ 41, 1, 2, 360 ], [ 41, 1, 3, 192 ], [ 41, 1, 4, 144 ], [ 41, 1, 5, 72 ], [ 41, 1, 6, 288 ], [ 41, 1, 8, 48 ], [ 41, 1, 9, 144 ], [ 41, 1, 10, 192 ], [ 42, 1, 1, 288 ], [ 42, 1, 6, 288 ], [ 43, 1, 1, 288 ], [ 43, 1, 3, 96 ], [ 43, 1, 5, 1152 ], [ 43, 1, 8, 288 ], [ 43, 1, 9, 80 ], [ 43, 1, 12, 96 ], [ 43, 1, 13, 288 ], [ 44, 1, 1, 48 ], [ 44, 1, 4, 24 ], [ 44, 1, 5, 144 ], [ 44, 1, 6, 24 ], [ 44, 1, 9, 144 ], [ 44, 1, 10, 48 ], [ 46, 1, 7, 1152 ], [ 46, 1, 12, 1152 ], [ 47, 1, 4, 192 ], [ 47, 1, 9, 192 ], [ 48, 1, 2, 288 ], [ 48, 1, 5, 288 ], [ 49, 1, 2, 288 ], [ 49, 1, 4, 288 ], [ 49, 1, 7, 288 ], [ 49, 1, 8, 288 ], [ 49, 1, 14, 1152 ], [ 49, 1, 20, 1152 ], [ 50, 1, 4, 576 ], [ 50, 1, 9, 576 ], [ 51, 1, 4, 32 ], [ 51, 1, 5, 192 ], [ 51, 1, 7, 32 ], [ 51, 1, 10, 192 ], [ 52, 1, 2, 288 ], [ 52, 1, 3, 144 ], [ 52, 1, 4, 144 ], [ 52, 1, 5, 48 ], [ 52, 1, 8, 48 ], [ 52, 1, 9, 288 ], [ 53, 1, 1, 288 ], [ 53, 1, 2, 864 ], [ 53, 1, 5, 96 ], [ 53, 1, 6, 288 ], [ 53, 1, 9, 288 ], [ 53, 1, 10, 288 ], [ 53, 1, 11, 192 ], [ 53, 1, 12, 864 ], [ 53, 1, 13, 192 ], [ 53, 1, 14, 288 ], [ 53, 1, 19, 96 ], [ 53, 1, 20, 288 ], [ 55, 1, 4, 192 ], [ 55, 1, 10, 384 ], [ 55, 1, 11, 192 ], [ 55, 1, 16, 384 ], [ 56, 1, 4, 288 ], [ 56, 1, 5, 576 ], [ 56, 1, 6, 576 ], [ 56, 1, 9, 96 ], [ 56, 1, 11, 96 ], [ 56, 1, 15, 576 ], [ 56, 1, 16, 288 ], [ 56, 1, 19, 576 ], [ 57, 1, 4, 576 ], [ 57, 1, 7, 576 ], [ 58, 1, 5, 128 ], [ 58, 1, 25, 2304 ], [ 59, 1, 3, 576 ], [ 59, 1, 16, 144 ], [ 59, 1, 17, 288 ], [ 59, 1, 18, 288 ], [ 59, 1, 23, 96 ], [ 59, 1, 24, 96 ], [ 60, 1, 28, 576 ], [ 60, 1, 29, 1152 ], [ 60, 1, 30, 576 ], [ 60, 1, 31, 576 ], [ 60, 1, 34, 2304 ], [ 60, 1, 43, 576 ], [ 60, 1, 44, 576 ], [ 61, 1, 14, 384 ], [ 61, 1, 15, 384 ], [ 62, 1, 34, 1152 ], [ 62, 1, 36, 1152 ], [ 62, 1, 37, 576 ], [ 62, 1, 39, 576 ], [ 62, 1, 44, 1152 ], [ 62, 1, 45, 1152 ], [ 63, 1, 21, 1152 ], [ 63, 1, 22, 192 ], [ 63, 1, 23, 576 ], [ 63, 1, 24, 192 ], [ 63, 1, 25, 576 ], [ 63, 1, 28, 1152 ], [ 64, 1, 40, 2304 ], [ 64, 1, 42, 1152 ], [ 64, 1, 43, 1152 ], [ 64, 1, 56, 1152 ], [ 64, 1, 61, 2304 ], [ 65, 1, 41, 768 ], [ 65, 1, 43, 768 ], [ 66, 1, 48, 2304 ], [ 66, 1, 50, 2304 ] ] k = 73: F-action on Pi is () [67,1,73] Dynkin type is A_0(q) + T(phi1^3 phi2 phi4^2) Order of center |Z^F|: phi1^3 phi2 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 2 modulo 60: 1/1536 q^3 ( q^5-6*q^4+8*q^3+16*q^2-48*q+32 ) q congruent 3 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 4 modulo 60: 1/1536 q^3 ( q^5-6*q^4+8*q^3+16*q^2-48*q+32 ) q congruent 5 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 7 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 8 modulo 60: 1/1536 q^3 ( q^5-6*q^4+8*q^3+16*q^2-48*q+32 ) q congruent 9 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 11 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 13 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 16 modulo 60: 1/1536 q^3 ( q^5-6*q^4+8*q^3+16*q^2-48*q+32 ) q congruent 17 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 19 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 21 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 23 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 25 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 27 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 29 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 31 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 32 modulo 60: 1/1536 q^3 ( q^5-6*q^4+8*q^3+16*q^2-48*q+32 ) q congruent 37 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 41 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 43 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 47 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 49 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 53 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) q congruent 59 modulo 60: 1/1536 phi1^2 phi2 ( q^5-5*q^4+4*q^3+14*q^2-45*q+63 ) Fusion of maximal tori of C^F in those of G^F: [ 73 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 24 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 48 ], [ 16, 1, 2, 96 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 48 ], [ 20, 1, 6, 96 ], [ 20, 1, 8, 96 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 48 ], [ 26, 1, 2, 48 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 33, 1, 4, 192 ], [ 35, 1, 5, 96 ], [ 35, 1, 7, 96 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 12 ], [ 39, 1, 5, 24 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 3, 96 ], [ 41, 1, 5, 48 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 48 ], [ 41, 1, 8, 96 ], [ 43, 1, 4, 96 ], [ 43, 1, 6, 192 ], [ 43, 1, 9, 96 ], [ 44, 1, 2, 48 ], [ 44, 1, 6, 96 ], [ 48, 1, 8, 192 ], [ 49, 1, 4, 96 ], [ 49, 1, 7, 288 ], [ 49, 1, 11, 192 ], [ 49, 1, 17, 384 ], [ 49, 1, 18, 192 ], [ 49, 1, 20, 192 ], [ 51, 1, 7, 192 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ], [ 52, 1, 5, 48 ], [ 52, 1, 8, 144 ], [ 53, 1, 7, 192 ], [ 53, 1, 10, 192 ], [ 53, 1, 13, 192 ], [ 55, 1, 6, 384 ], [ 56, 1, 11, 192 ], [ 56, 1, 16, 192 ], [ 57, 1, 7, 192 ], [ 57, 1, 11, 384 ], [ 59, 1, 6, 96 ], [ 59, 1, 12, 96 ], [ 59, 1, 21, 96 ], [ 59, 1, 23, 192 ], [ 60, 1, 18, 384 ], [ 60, 1, 31, 384 ], [ 60, 1, 33, 192 ], [ 60, 1, 35, 768 ], [ 60, 1, 42, 384 ], [ 62, 1, 25, 192 ], [ 62, 1, 26, 576 ], [ 62, 1, 33, 384 ], [ 62, 1, 34, 384 ], [ 62, 1, 40, 384 ], [ 63, 1, 16, 384 ], [ 63, 1, 26, 384 ], [ 64, 1, 28, 768 ], [ 64, 1, 35, 384 ], [ 64, 1, 45, 768 ], [ 65, 1, 33, 768 ], [ 66, 1, 42, 768 ], [ 66, 1, 46, 768 ] ] k = 74: F-action on Pi is () [67,1,74] Dynkin type is A_0(q) + T(phi1 phi2^3 phi4^2) Order of center |Z^F|: phi1 phi2^3 phi4^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 2 modulo 60: 1/1536 q^5 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 4 modulo 60: 1/1536 q^5 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 7 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 8 modulo 60: 1/1536 q^5 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 11 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 13 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 16 modulo 60: 1/1536 q^5 ( q^3-2*q^2-4*q+8 ) q congruent 17 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 19 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 21 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 23 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 25 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 27 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 29 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 31 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 32 modulo 60: 1/1536 q^5 ( q^3-2*q^2-4*q+8 ) q congruent 37 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 41 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 43 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 47 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 49 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 53 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) q congruent 59 modulo 60: 1/1536 phi1^2 phi2 ( q^5-q^4-4*q^3+2*q^2-21*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 74 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 2, 48 ], [ 13, 1, 4, 24 ], [ 16, 1, 4, 96 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 48 ], [ 20, 1, 5, 96 ], [ 20, 1, 7, 96 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 48 ], [ 26, 1, 3, 48 ], [ 27, 1, 3, 16 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 10, 192 ], [ 35, 1, 2, 96 ], [ 35, 1, 4, 96 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 39, 1, 5, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 5, 48 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 48 ], [ 41, 1, 8, 96 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 96 ], [ 43, 1, 2, 96 ], [ 43, 1, 9, 96 ], [ 43, 1, 14, 192 ], [ 44, 1, 4, 96 ], [ 44, 1, 8, 48 ], [ 48, 1, 9, 192 ], [ 49, 1, 4, 288 ], [ 49, 1, 7, 96 ], [ 49, 1, 13, 384 ], [ 49, 1, 14, 192 ], [ 49, 1, 15, 192 ], [ 49, 1, 19, 192 ], [ 51, 1, 4, 192 ], [ 52, 1, 5, 144 ], [ 52, 1, 8, 48 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ], [ 53, 1, 4, 192 ], [ 53, 1, 11, 192 ], [ 53, 1, 14, 192 ], [ 55, 1, 19, 384 ], [ 56, 1, 4, 192 ], [ 56, 1, 9, 192 ], [ 57, 1, 7, 192 ], [ 57, 1, 8, 384 ], [ 59, 1, 6, 96 ], [ 59, 1, 13, 96 ], [ 59, 1, 21, 96 ], [ 59, 1, 24, 192 ], [ 60, 1, 18, 384 ], [ 60, 1, 30, 384 ], [ 60, 1, 33, 192 ], [ 60, 1, 36, 768 ], [ 60, 1, 39, 384 ], [ 62, 1, 25, 576 ], [ 62, 1, 26, 192 ], [ 62, 1, 35, 384 ], [ 62, 1, 36, 384 ], [ 62, 1, 38, 384 ], [ 63, 1, 15, 384 ], [ 63, 1, 27, 384 ], [ 64, 1, 33, 768 ], [ 64, 1, 35, 384 ], [ 64, 1, 44, 768 ], [ 65, 1, 36, 768 ], [ 66, 1, 39, 768 ], [ 66, 1, 45, 768 ] ] k = 75: F-action on Pi is () [67,1,75] Dynkin type is A_0(q) + T(phi1 phi2 phi4^3) Order of center |Z^F|: phi1 phi2 phi4^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 2 modulo 60: 1/768 q^2 ( q^6-14*q^4+56*q^2-64 ) q congruent 3 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 4 modulo 60: 1/768 q^2 ( q^6-14*q^4+56*q^2-64 ) q congruent 5 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 7 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 8 modulo 60: 1/768 q^2 ( q^6-14*q^4+56*q^2-64 ) q congruent 9 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 11 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 13 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 16 modulo 60: 1/768 q^2 ( q^6-14*q^4+56*q^2-64 ) q congruent 17 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 19 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 21 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 23 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 25 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 27 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 29 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 31 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 32 modulo 60: 1/768 q^2 ( q^6-14*q^4+56*q^2-64 ) q congruent 37 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 41 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 43 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 47 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 49 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 53 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) q congruent 59 modulo 60: 1/768 phi1 phi2 ( q^6-13*q^4+55*q^2-75 ) Fusion of maximal tori of C^F in those of G^F: [ 75 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 5, 1, 3, 64 ], [ 5, 1, 4, 64 ], [ 9, 1, 1, 7 ], [ 13, 1, 2, 12 ], [ 13, 1, 3, 12 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 12 ], [ 25, 1, 3, 12 ], [ 32, 1, 5, 256 ], [ 37, 1, 5, 192 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 60 ], [ 41, 1, 2, 24 ], [ 41, 1, 5, 168 ], [ 43, 1, 9, 48 ], [ 43, 1, 10, 192 ], [ 43, 1, 11, 32 ], [ 44, 1, 4, 24 ], [ 44, 1, 6, 24 ], [ 48, 1, 8, 96 ], [ 48, 1, 9, 96 ], [ 53, 1, 10, 96 ], [ 53, 1, 14, 96 ], [ 57, 1, 17, 192 ], [ 57, 1, 18, 384 ], [ 58, 1, 19, 128 ], [ 58, 1, 21, 384 ], [ 59, 1, 6, 288 ], [ 59, 1, 16, 48 ], [ 60, 1, 20, 384 ], [ 60, 1, 29, 192 ], [ 60, 1, 32, 192 ], [ 63, 1, 15, 192 ], [ 63, 1, 16, 192 ], [ 64, 1, 36, 384 ], [ 64, 1, 48, 384 ], [ 64, 1, 59, 384 ] ] k = 76: F-action on Pi is () [67,1,76] Dynkin type is A_0(q) + T(phi1^3 phi2^3 phi4) Order of center |Z^F|: phi1^3 phi2^3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 2 modulo 60: 1/256 q^3 ( q^5-4*q^4-2*q^3+16*q^2-16 ) q congruent 3 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 4 modulo 60: 1/256 q^3 ( q^5-4*q^4-2*q^3+16*q^2-16 ) q congruent 5 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 7 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 8 modulo 60: 1/256 q^3 ( q^5-4*q^4-2*q^3+16*q^2-16 ) q congruent 9 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 11 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 13 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 16 modulo 60: 1/256 q^3 ( q^5-4*q^4-2*q^3+16*q^2-16 ) q congruent 17 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 19 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 21 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 23 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 25 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 27 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 29 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 31 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 32 modulo 60: 1/256 q^3 ( q^5-4*q^4-2*q^3+16*q^2-16 ) q congruent 37 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 41 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 43 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 47 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 49 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 53 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) q congruent 59 modulo 60: 1/256 phi1 phi2^2 ( q^5-5*q^4+4*q^3+8*q^2-13*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 76 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 10 ], [ 4, 1, 2, 10 ], [ 5, 1, 1, 16 ], [ 5, 1, 2, 16 ], [ 6, 1, 1, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 1, 8 ], [ 7, 1, 2, 8 ], [ 8, 1, 1, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 20 ], [ 13, 1, 3, 20 ], [ 13, 1, 4, 16 ], [ 14, 1, 1, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 16 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 32 ], [ 17, 1, 3, 32 ], [ 18, 1, 1, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 1, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 1, 16 ], [ 20, 1, 2, 16 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 16 ], [ 20, 1, 6, 32 ], [ 20, 1, 7, 32 ], [ 21, 1, 1, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 16 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 27, 1, 3, 16 ], [ 28, 1, 1, 8 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 8 ], [ 29, 1, 2, 32 ], [ 29, 1, 3, 32 ], [ 30, 1, 1, 16 ], [ 30, 1, 2, 48 ], [ 30, 1, 3, 16 ], [ 30, 1, 4, 48 ], [ 31, 1, 1, 16 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 16 ], [ 32, 1, 2, 32 ], [ 32, 1, 4, 32 ], [ 33, 1, 2, 32 ], [ 33, 1, 5, 64 ], [ 33, 1, 6, 32 ], [ 33, 1, 9, 64 ], [ 34, 1, 1, 16 ], [ 34, 1, 2, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 4, 16 ], [ 35, 1, 1, 16 ], [ 35, 1, 2, 16 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 1, 5, 16 ], [ 35, 1, 6, 16 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 16 ], [ 36, 1, 2, 32 ], [ 36, 1, 3, 32 ], [ 37, 1, 1, 16 ], [ 37, 1, 2, 16 ], [ 37, 1, 3, 16 ], [ 37, 1, 4, 64 ], [ 38, 1, 2, 64 ], [ 38, 1, 10, 64 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 20 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 16 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 40 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 32 ], [ 41, 1, 7, 32 ], [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 2, 32 ], [ 42, 1, 4, 32 ], [ 43, 1, 2, 32 ], [ 43, 1, 4, 32 ], [ 43, 1, 7, 64 ], [ 43, 1, 9, 16 ], [ 43, 1, 11, 32 ], [ 44, 1, 2, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 5, 32 ], [ 44, 1, 6, 8 ], [ 44, 1, 8, 16 ], [ 44, 1, 9, 32 ], [ 45, 1, 2, 32 ], [ 45, 1, 5, 32 ], [ 46, 1, 8, 64 ], [ 46, 1, 11, 64 ], [ 47, 1, 3, 32 ], [ 47, 1, 4, 32 ], [ 47, 1, 9, 32 ], [ 47, 1, 10, 32 ], [ 48, 1, 1, 16 ], [ 48, 1, 2, 16 ], [ 48, 1, 3, 16 ], [ 48, 1, 4, 16 ], [ 48, 1, 5, 16 ], [ 48, 1, 6, 16 ], [ 48, 1, 7, 48 ], [ 48, 1, 8, 16 ], [ 48, 1, 9, 16 ], [ 48, 1, 10, 48 ], [ 49, 1, 2, 32 ], [ 49, 1, 4, 32 ], [ 49, 1, 7, 32 ], [ 49, 1, 8, 32 ], [ 49, 1, 12, 64 ], [ 49, 1, 15, 64 ], [ 49, 1, 16, 64 ], [ 49, 1, 18, 64 ], [ 50, 1, 2, 32 ], [ 50, 1, 5, 32 ], [ 50, 1, 8, 32 ], [ 50, 1, 11, 32 ], [ 51, 1, 2, 32 ], [ 51, 1, 4, 32 ], [ 51, 1, 7, 32 ], [ 51, 1, 8, 32 ], [ 52, 1, 2, 32 ], [ 52, 1, 3, 16 ], [ 52, 1, 4, 16 ], [ 52, 1, 5, 16 ], [ 52, 1, 8, 16 ], [ 52, 1, 9, 32 ], [ 53, 1, 3, 32 ], [ 53, 1, 4, 32 ], [ 53, 1, 7, 32 ], [ 53, 1, 8, 32 ], [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 54, 1, 4, 32 ], [ 54, 1, 5, 64 ], [ 54, 1, 9, 32 ], [ 54, 1, 13, 64 ], [ 55, 1, 4, 64 ], [ 55, 1, 8, 64 ], [ 55, 1, 11, 64 ], [ 55, 1, 17, 64 ], [ 56, 1, 2, 32 ], [ 56, 1, 4, 32 ], [ 56, 1, 7, 32 ], [ 56, 1, 9, 32 ], [ 56, 1, 11, 32 ], [ 56, 1, 13, 32 ], [ 56, 1, 16, 32 ], [ 56, 1, 18, 32 ], [ 57, 1, 3, 32 ], [ 57, 1, 4, 32 ], [ 57, 1, 7, 32 ], [ 57, 1, 8, 32 ], [ 57, 1, 9, 32 ], [ 57, 1, 11, 32 ], [ 57, 1, 16, 128 ], [ 57, 1, 17, 64 ], [ 58, 1, 5, 64 ], [ 58, 1, 17, 128 ], [ 59, 1, 3, 64 ], [ 59, 1, 16, 16 ], [ 59, 1, 21, 32 ], [ 59, 1, 22, 32 ], [ 60, 1, 25, 128 ], [ 60, 1, 28, 64 ], [ 60, 1, 32, 64 ], [ 60, 1, 33, 64 ], [ 60, 1, 38, 128 ], [ 60, 1, 45, 64 ], [ 61, 1, 13, 64 ], [ 61, 1, 14, 64 ], [ 61, 1, 15, 64 ], [ 61, 1, 16, 64 ], [ 62, 1, 37, 64 ], [ 62, 1, 38, 64 ], [ 62, 1, 39, 64 ], [ 62, 1, 40, 64 ], [ 62, 1, 49, 64 ], [ 62, 1, 50, 64 ], [ 63, 1, 26, 64 ], [ 63, 1, 27, 64 ], [ 63, 1, 29, 64 ], [ 63, 1, 30, 32 ], [ 63, 1, 31, 32 ], [ 63, 1, 34, 64 ], [ 64, 1, 41, 128 ], [ 64, 1, 46, 128 ], [ 64, 1, 54, 64 ], [ 64, 1, 55, 64 ], [ 64, 1, 56, 64 ], [ 64, 1, 57, 128 ], [ 64, 1, 65, 128 ], [ 65, 1, 44, 128 ], [ 65, 1, 45, 128 ], [ 66, 1, 52, 128 ], [ 66, 1, 53, 128 ] ] k = 77: F-action on Pi is () [67,1,77] Dynkin type is A_0(q) + T(phi1^5 phi2 phi3) Order of center |Z^F|: phi1^5 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/8640 phi1 ( q^7-18*q^6+117*q^5-308*q^4+171*q^3+390*q^2-305*q+240 ) q congruent 2 modulo 60: 1/8640 q^2 phi2 ( q^5-20*q^4+155*q^3-580*q^2+1044*q-720 ) q congruent 3 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 4 modulo 60: 1/8640 q phi1 ( q^6-18*q^5+117*q^4-308*q^3+156*q^2+480*q-320 ) q congruent 5 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 7 modulo 60: 1/8640 phi1 ( q^7-18*q^6+117*q^5-308*q^4+171*q^3+390*q^2-305*q+240 ) q congruent 8 modulo 60: 1/8640 q^2 phi2 ( q^5-20*q^4+155*q^3-580*q^2+1044*q-720 ) q congruent 9 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 11 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 13 modulo 60: 1/8640 phi1 ( q^7-18*q^6+117*q^5-308*q^4+171*q^3+390*q^2-305*q+240 ) q congruent 16 modulo 60: 1/8640 q phi1 ( q^6-18*q^5+117*q^4-308*q^3+156*q^2+480*q-320 ) q congruent 17 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 19 modulo 60: 1/8640 phi1 ( q^7-18*q^6+117*q^5-308*q^4+171*q^3+390*q^2-305*q+240 ) q congruent 21 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 23 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 25 modulo 60: 1/8640 phi1 ( q^7-18*q^6+117*q^5-308*q^4+171*q^3+390*q^2-305*q+240 ) q congruent 27 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 29 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 31 modulo 60: 1/8640 phi1 ( q^7-18*q^6+117*q^5-308*q^4+171*q^3+390*q^2-305*q+240 ) q congruent 32 modulo 60: 1/8640 q^2 phi2 ( q^5-20*q^4+155*q^3-580*q^2+1044*q-720 ) q congruent 37 modulo 60: 1/8640 phi1 ( q^7-18*q^6+117*q^5-308*q^4+171*q^3+390*q^2-305*q+240 ) q congruent 41 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 43 modulo 60: 1/8640 phi1 ( q^7-18*q^6+117*q^5-308*q^4+171*q^3+390*q^2-305*q+240 ) q congruent 47 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 49 modulo 60: 1/8640 phi1 ( q^7-18*q^6+117*q^5-308*q^4+171*q^3+390*q^2-305*q+240 ) q congruent 53 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 59 modulo 60: 1/8640 q phi1 phi2 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) Fusion of maximal tori of C^F in those of G^F: [ 77 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 62 ], [ 4, 1, 1, 150 ], [ 5, 1, 1, 264 ], [ 6, 1, 1, 312 ], [ 7, 1, 1, 132 ], [ 8, 1, 1, 60 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 30 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 140 ], [ 12, 1, 1, 330 ], [ 13, 1, 1, 360 ], [ 14, 1, 1, 660 ], [ 15, 1, 1, 732 ], [ 16, 1, 1, 840 ], [ 17, 1, 1, 840 ], [ 18, 1, 1, 420 ], [ 19, 1, 1, 600 ], [ 20, 1, 1, 840 ], [ 20, 1, 2, 120 ], [ 21, 1, 1, 240 ], [ 22, 1, 1, 540 ], [ 22, 1, 2, 84 ], [ 23, 1, 1, 90 ], [ 24, 1, 1, 210 ], [ 24, 1, 2, 30 ], [ 25, 1, 1, 540 ], [ 26, 1, 1, 240 ], [ 26, 1, 3, 24 ], [ 27, 1, 1, 240 ], [ 27, 1, 2, 40 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 540 ], [ 28, 1, 2, 180 ], [ 29, 1, 1, 1200 ], [ 29, 1, 2, 264 ], [ 30, 1, 1, 1080 ], [ 31, 1, 1, 1380 ], [ 31, 1, 2, 300 ], [ 32, 1, 1, 1200 ], [ 33, 1, 1, 720 ], [ 34, 1, 1, 960 ], [ 34, 1, 2, 240 ], [ 35, 1, 1, 1080 ], [ 35, 1, 3, 360 ], [ 36, 1, 1, 720 ], [ 36, 1, 2, 120 ], [ 37, 1, 1, 1440 ], [ 38, 1, 1, 1440 ], [ 38, 1, 3, 360 ], [ 38, 1, 5, 240 ], [ 39, 1, 1, 360 ], [ 39, 1, 4, 60 ], [ 40, 1, 1, 900 ], [ 41, 1, 1, 720 ], [ 41, 1, 6, 360 ], [ 42, 1, 1, 960 ], [ 42, 1, 3, 96 ], [ 42, 1, 4, 240 ], [ 43, 1, 1, 1440 ], [ 43, 1, 2, 240 ], [ 44, 1, 1, 720 ], [ 44, 1, 2, 360 ], [ 44, 1, 3, 90 ], [ 45, 1, 1, 1440 ], [ 45, 1, 2, 720 ], [ 45, 1, 3, 396 ], [ 46, 1, 1, 1920 ], [ 46, 1, 2, 480 ], [ 46, 1, 3, 840 ], [ 47, 1, 1, 1080 ], [ 47, 1, 2, 360 ], [ 48, 1, 1, 1440 ], [ 48, 1, 2, 720 ], [ 50, 1, 1, 1440 ], [ 50, 1, 2, 480 ], [ 50, 1, 3, 180 ], [ 50, 1, 4, 480 ], [ 50, 1, 6, 12 ], [ 51, 1, 1, 2160 ], [ 51, 1, 2, 600 ], [ 52, 1, 1, 720 ], [ 52, 1, 2, 720 ], [ 53, 1, 1, 1440 ], [ 53, 1, 3, 720 ], [ 53, 1, 16, 720 ], [ 54, 1, 1, 1440 ], [ 54, 1, 2, 1440 ], [ 54, 1, 3, 720 ], [ 54, 1, 7, 72 ], [ 55, 1, 1, 1440 ], [ 55, 1, 2, 720 ], [ 55, 1, 3, 1800 ], [ 56, 1, 1, 1440 ], [ 56, 1, 2, 1440 ], [ 56, 1, 3, 1260 ], [ 56, 1, 6, 1440 ], [ 56, 1, 8, 180 ], [ 58, 1, 1, 2880 ], [ 58, 1, 2, 960 ], [ 58, 1, 3, 1440 ], [ 58, 1, 7, 240 ], [ 59, 1, 4, 540 ], [ 59, 1, 12, 1440 ], [ 60, 1, 2, 2160 ], [ 61, 1, 1, 1440 ], [ 61, 1, 4, 2880 ], [ 61, 1, 7, 720 ], [ 61, 1, 19, 1440 ], [ 62, 1, 2, 3240 ], [ 62, 1, 5, 1080 ], [ 63, 1, 4, 2160 ], [ 63, 1, 10, 360 ], [ 63, 1, 33, 2880 ], [ 64, 1, 6, 4320 ], [ 64, 1, 19, 2160 ], [ 65, 1, 9, 4320 ], [ 65, 1, 28, 1440 ], [ 65, 1, 47, 2880 ], [ 66, 1, 13, 4320 ], [ 66, 1, 34, 4320 ] ] k = 78: F-action on Pi is () [67,1,78] Dynkin type is A_0(q) + T(phi1 phi2^5 phi6) Order of center |Z^F|: phi1 phi2^5 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 2 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+500*q^3-672*q^2+640*q-320 ) q congruent 3 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 4 modulo 60: 1/8640 q^2 phi1^2 ( q^4-11*q^3+44*q^2-76*q+48 ) q congruent 5 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+515*q^3-762*q^2+835*q-560 ) q congruent 7 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 8 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+500*q^3-672*q^2+640*q-320 ) q congruent 9 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 11 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+515*q^3-762*q^2+835*q-560 ) q congruent 13 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 16 modulo 60: 1/8640 q^2 phi1^2 ( q^4-11*q^3+44*q^2-76*q+48 ) q congruent 17 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+515*q^3-762*q^2+835*q-560 ) q congruent 19 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 21 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 23 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+515*q^3-762*q^2+835*q-560 ) q congruent 25 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 27 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 29 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+515*q^3-762*q^2+835*q-560 ) q congruent 31 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 32 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+500*q^3-672*q^2+640*q-320 ) q congruent 37 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 41 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+515*q^3-762*q^2+835*q-560 ) q congruent 43 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 47 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+515*q^3-762*q^2+835*q-560 ) q congruent 49 modulo 60: 1/8640 q phi1^2 ( q^5-11*q^4+44*q^3-76*q^2+63*q-45 ) q congruent 53 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+515*q^3-762*q^2+835*q-560 ) q congruent 59 modulo 60: 1/8640 phi2 ( q^7-14*q^6+81*q^5-256*q^4+515*q^3-762*q^2+835*q-560 ) Fusion of maximal tori of C^F in those of G^F: [ 78 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 62 ], [ 4, 1, 2, 150 ], [ 5, 1, 2, 264 ], [ 6, 1, 2, 312 ], [ 7, 1, 2, 132 ], [ 8, 1, 2, 60 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 30 ], [ 11, 1, 2, 140 ], [ 12, 1, 2, 330 ], [ 13, 1, 4, 360 ], [ 14, 1, 2, 660 ], [ 15, 1, 2, 732 ], [ 16, 1, 3, 840 ], [ 17, 1, 4, 840 ], [ 18, 1, 2, 420 ], [ 19, 1, 2, 600 ], [ 20, 1, 3, 120 ], [ 20, 1, 4, 840 ], [ 21, 1, 2, 240 ], [ 22, 1, 3, 84 ], [ 22, 1, 4, 540 ], [ 23, 1, 2, 90 ], [ 24, 1, 1, 30 ], [ 24, 1, 2, 210 ], [ 25, 1, 3, 540 ], [ 26, 1, 2, 24 ], [ 26, 1, 4, 240 ], [ 27, 1, 3, 40 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 240 ], [ 28, 1, 3, 180 ], [ 28, 1, 4, 540 ], [ 29, 1, 3, 264 ], [ 29, 1, 4, 1200 ], [ 30, 1, 3, 1080 ], [ 31, 1, 3, 300 ], [ 31, 1, 4, 1380 ], [ 32, 1, 3, 1200 ], [ 33, 1, 8, 720 ], [ 34, 1, 3, 240 ], [ 34, 1, 4, 960 ], [ 35, 1, 6, 360 ], [ 35, 1, 8, 1080 ], [ 36, 1, 3, 120 ], [ 36, 1, 4, 720 ], [ 37, 1, 3, 1440 ], [ 38, 1, 8, 240 ], [ 38, 1, 11, 360 ], [ 38, 1, 12, 1440 ], [ 39, 1, 3, 360 ], [ 39, 1, 4, 60 ], [ 40, 1, 6, 900 ], [ 41, 1, 6, 360 ], [ 41, 1, 9, 720 ], [ 42, 1, 2, 240 ], [ 42, 1, 5, 96 ], [ 42, 1, 6, 960 ], [ 43, 1, 4, 240 ], [ 43, 1, 13, 1440 ], [ 44, 1, 7, 90 ], [ 44, 1, 8, 360 ], [ 44, 1, 10, 720 ], [ 45, 1, 4, 396 ], [ 45, 1, 5, 720 ], [ 45, 1, 6, 1440 ], [ 46, 1, 4, 840 ], [ 46, 1, 5, 480 ], [ 46, 1, 6, 1920 ], [ 47, 1, 7, 360 ], [ 47, 1, 8, 1080 ], [ 48, 1, 5, 720 ], [ 48, 1, 6, 1440 ], [ 50, 1, 7, 12 ], [ 50, 1, 9, 480 ], [ 50, 1, 10, 180 ], [ 50, 1, 11, 480 ], [ 50, 1, 12, 1440 ], [ 51, 1, 8, 600 ], [ 51, 1, 9, 2160 ], [ 52, 1, 9, 720 ], [ 52, 1, 10, 720 ], [ 53, 1, 8, 720 ], [ 53, 1, 18, 720 ], [ 53, 1, 20, 1440 ], [ 54, 1, 10, 720 ], [ 54, 1, 11, 72 ], [ 54, 1, 12, 1440 ], [ 54, 1, 14, 1440 ], [ 55, 1, 12, 1800 ], [ 55, 1, 13, 720 ], [ 55, 1, 15, 1440 ], [ 56, 1, 12, 180 ], [ 56, 1, 15, 1440 ], [ 56, 1, 17, 1260 ], [ 56, 1, 18, 1440 ], [ 56, 1, 20, 1440 ], [ 58, 1, 10, 240 ], [ 58, 1, 12, 960 ], [ 58, 1, 14, 1440 ], [ 58, 1, 15, 2880 ], [ 59, 1, 5, 540 ], [ 59, 1, 13, 1440 ], [ 60, 1, 8, 2160 ], [ 61, 1, 6, 2880 ], [ 61, 1, 8, 720 ], [ 61, 1, 20, 1440 ], [ 61, 1, 21, 1440 ], [ 62, 1, 6, 1080 ], [ 62, 1, 7, 3240 ], [ 63, 1, 9, 2160 ], [ 63, 1, 11, 360 ], [ 63, 1, 36, 2880 ], [ 64, 1, 15, 4320 ], [ 64, 1, 22, 2160 ], [ 65, 1, 27, 4320 ], [ 65, 1, 29, 1440 ], [ 65, 1, 49, 2880 ], [ 66, 1, 33, 4320 ], [ 66, 1, 37, 4320 ] ] k = 79: F-action on Pi is () [67,1,79] Dynkin type is A_0(q) + T(phi1 phi2 phi3^3) Order of center |Z^F|: phi1 phi2 phi3^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/2592 phi1^2 ( q^6+4*q^5-2*q^4-28*q^3-37*q^2+26*q+72 ) q congruent 2 modulo 60: 1/2592 q^2 phi2 ( q^5+q^4-10*q^3-10*q^2+18*q+36 ) q congruent 3 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 4 modulo 60: 1/2592 q phi1 ( q^6+3*q^5-6*q^4-26*q^3-18*q^2+36*q+64 ) q congruent 5 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 7 modulo 60: 1/2592 phi1^2 ( q^6+4*q^5-2*q^4-28*q^3-37*q^2+26*q+72 ) q congruent 8 modulo 60: 1/2592 q^2 phi2 ( q^5+q^4-10*q^3-10*q^2+18*q+36 ) q congruent 9 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 11 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 13 modulo 60: 1/2592 phi1^2 ( q^6+4*q^5-2*q^4-28*q^3-37*q^2+26*q+72 ) q congruent 16 modulo 60: 1/2592 q phi1 ( q^6+3*q^5-6*q^4-26*q^3-18*q^2+36*q+64 ) q congruent 17 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 19 modulo 60: 1/2592 phi1^2 ( q^6+4*q^5-2*q^4-28*q^3-37*q^2+26*q+72 ) q congruent 21 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 23 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 25 modulo 60: 1/2592 phi1^2 ( q^6+4*q^5-2*q^4-28*q^3-37*q^2+26*q+72 ) q congruent 27 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 29 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 31 modulo 60: 1/2592 phi1^2 ( q^6+4*q^5-2*q^4-28*q^3-37*q^2+26*q+72 ) q congruent 32 modulo 60: 1/2592 q^2 phi2 ( q^5+q^4-10*q^3-10*q^2+18*q+36 ) q congruent 37 modulo 60: 1/2592 phi1^2 ( q^6+4*q^5-2*q^4-28*q^3-37*q^2+26*q+72 ) q congruent 41 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 43 modulo 60: 1/2592 phi1^2 ( q^6+4*q^5-2*q^4-28*q^3-37*q^2+26*q+72 ) q congruent 47 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 49 modulo 60: 1/2592 phi1^2 ( q^6+4*q^5-2*q^4-28*q^3-37*q^2+26*q+72 ) q congruent 53 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) q congruent 59 modulo 60: 1/2592 q phi1 phi2 ( q^5+2*q^4-8*q^3-18*q^2+9*q+54 ) Fusion of maximal tori of C^F in those of G^F: [ 79 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 26 ], [ 6, 1, 1, 24 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 1, 48 ], [ 22, 1, 2, 48 ], [ 27, 1, 2, 4 ], [ 27, 1, 5, 72 ], [ 33, 1, 3, 216 ], [ 38, 1, 3, 432 ], [ 38, 1, 5, 96 ], [ 40, 1, 5, 270 ], [ 42, 1, 3, 72 ], [ 46, 1, 3, 144 ], [ 47, 1, 6, 432 ], [ 50, 1, 6, 144 ], [ 52, 1, 6, 54 ], [ 58, 1, 7, 288 ], [ 58, 1, 8, 864 ], [ 59, 1, 9, 648 ], [ 59, 1, 14, 108 ], [ 60, 1, 4, 648 ], [ 61, 1, 5, 432 ], [ 62, 1, 12, 1296 ], [ 65, 1, 6, 1296 ], [ 65, 1, 17, 864 ], [ 66, 1, 10, 1296 ] ] k = 80: F-action on Pi is () [67,1,80] Dynkin type is A_0(q) + T(phi1 phi2 phi6^3) Order of center |Z^F|: phi1 phi2 phi6^3 Numbers of classes in class type: q congruent 1 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 2 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+20*q^3-72*q^2-80*q+160 ) q congruent 3 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 4 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+52*q^2-144 ) q congruent 5 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+29*q^3-99*q^2-98*q+232 ) q congruent 7 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 8 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+20*q^3-72*q^2-80*q+160 ) q congruent 9 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 11 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+29*q^3-99*q^2-98*q+232 ) q congruent 13 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 16 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+52*q^2-144 ) q congruent 17 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+29*q^3-99*q^2-98*q+232 ) q congruent 19 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 21 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 23 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+29*q^3-99*q^2-98*q+232 ) q congruent 25 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 27 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 29 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+29*q^3-99*q^2-98*q+232 ) q congruent 31 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 32 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+20*q^3-72*q^2-80*q+160 ) q congruent 37 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 41 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+29*q^3-99*q^2-98*q+232 ) q congruent 43 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 47 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+29*q^3-99*q^2-98*q+232 ) q congruent 49 modulo 60: 1/2592 q phi1 ( q^6-3*q^5-8*q^4+12*q^3+61*q^2-9*q-198 ) q congruent 53 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+29*q^3-99*q^2-98*q+232 ) q congruent 59 modulo 60: 1/2592 phi2 ( q^7-5*q^6+20*q^4+29*q^3-99*q^2-98*q+232 ) Fusion of maximal tori of C^F in those of G^F: [ 80 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 26 ], [ 6, 1, 2, 24 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 4, 48 ], [ 22, 1, 3, 48 ], [ 27, 1, 3, 4 ], [ 27, 1, 4, 72 ], [ 33, 1, 7, 216 ], [ 38, 1, 8, 96 ], [ 38, 1, 11, 432 ], [ 40, 1, 4, 270 ], [ 42, 1, 5, 72 ], [ 46, 1, 4, 144 ], [ 47, 1, 11, 432 ], [ 50, 1, 7, 144 ], [ 52, 1, 7, 54 ], [ 58, 1, 10, 288 ], [ 58, 1, 13, 864 ], [ 59, 1, 10, 648 ], [ 59, 1, 15, 108 ], [ 60, 1, 15, 648 ], [ 61, 1, 9, 432 ], [ 62, 1, 13, 1296 ], [ 65, 1, 10, 1296 ], [ 65, 1, 16, 864 ], [ 66, 1, 18, 1296 ] ] k = 81: F-action on Pi is () [67,1,81] Dynkin type is A_0(q) + T(phi1^3 phi2^3 phi3) Order of center |Z^F|: phi1^3 phi2^3 phi3 Numbers of classes in class type: q congruent 1 modulo 60: 1/576 phi1^3 ( q^5-8*q^3-8*q^2+7*q+16 ) q congruent 2 modulo 60: 1/576 q^2 phi2^2 ( q^4-5*q^3+4*q^2+12*q-16 ) q congruent 3 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 4 modulo 60: 1/576 q phi1 ( q^6-2*q^5-7*q^4+8*q^3+20*q^2-32 ) q congruent 5 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 7 modulo 60: 1/576 phi1^3 ( q^5-8*q^3-8*q^2+7*q+16 ) q congruent 8 modulo 60: 1/576 q^2 phi2^2 ( q^4-5*q^3+4*q^2+12*q-16 ) q congruent 9 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 11 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 13 modulo 60: 1/576 phi1^3 ( q^5-8*q^3-8*q^2+7*q+16 ) q congruent 16 modulo 60: 1/576 q phi1 ( q^6-2*q^5-7*q^4+8*q^3+20*q^2-32 ) q congruent 17 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 19 modulo 60: 1/576 phi1^3 ( q^5-8*q^3-8*q^2+7*q+16 ) q congruent 21 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 23 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 25 modulo 60: 1/576 phi1^3 ( q^5-8*q^3-8*q^2+7*q+16 ) q congruent 27 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 29 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 31 modulo 60: 1/576 phi1^3 ( q^5-8*q^3-8*q^2+7*q+16 ) q congruent 32 modulo 60: 1/576 q^2 phi2^2 ( q^4-5*q^3+4*q^2+12*q-16 ) q congruent 37 modulo 60: 1/576 phi1^3 ( q^5-8*q^3-8*q^2+7*q+16 ) q congruent 41 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 43 modulo 60: 1/576 phi1^3 ( q^5-8*q^3-8*q^2+7*q+16 ) q congruent 47 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 49 modulo 60: 1/576 phi1^3 ( q^5-8*q^3-8*q^2+7*q+16 ) q congruent 53 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) q congruent 59 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2-3*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 81 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 18 ], [ 4, 1, 2, 12 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 18 ], [ 12, 1, 2, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 24 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], [ 16, 1, 1, 48 ], [ 16, 1, 2, 24 ], [ 16, 1, 4, 48 ], [ 17, 1, 1, 72 ], [ 17, 1, 2, 16 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 72 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 60 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 18 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 24 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 48 ], [ 26, 1, 3, 24 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 16 ], [ 27, 1, 5, 6 ], [ 28, 1, 1, 12 ], [ 28, 1, 2, 36 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 29, 1, 2, 72 ], [ 30, 1, 1, 24 ], [ 30, 1, 2, 48 ], [ 31, 1, 1, 12 ], [ 31, 1, 2, 84 ], [ 32, 1, 1, 48 ], [ 32, 1, 2, 48 ], [ 33, 1, 1, 48 ], [ 33, 1, 2, 48 ], [ 34, 1, 2, 48 ], [ 35, 1, 1, 24 ], [ 35, 1, 2, 48 ], [ 35, 1, 3, 72 ], [ 35, 1, 4, 48 ], [ 36, 1, 2, 24 ], [ 37, 1, 2, 48 ], [ 38, 1, 2, 32 ], [ 38, 1, 3, 72 ], [ 38, 1, 5, 144 ], [ 38, 1, 9, 48 ], [ 39, 1, 2, 24 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 12 ], [ 40, 1, 2, 48 ], [ 40, 1, 3, 72 ], [ 40, 1, 6, 48 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 48 ], [ 41, 1, 9, 48 ], [ 42, 1, 3, 24 ], [ 42, 1, 4, 48 ], [ 43, 1, 2, 48 ], [ 43, 1, 8, 48 ], [ 43, 1, 12, 96 ], [ 44, 1, 2, 24 ], [ 44, 1, 3, 18 ], [ 44, 1, 5, 48 ], [ 44, 1, 8, 48 ], [ 45, 1, 2, 48 ], [ 45, 1, 3, 36 ], [ 46, 1, 2, 96 ], [ 46, 1, 3, 72 ], [ 46, 1, 9, 48 ], [ 47, 1, 1, 24 ], [ 47, 1, 2, 72 ], [ 47, 1, 3, 48 ], [ 47, 1, 4, 48 ], [ 48, 1, 2, 48 ], [ 48, 1, 3, 96 ], [ 50, 1, 3, 12 ], [ 50, 1, 5, 96 ], [ 50, 1, 6, 36 ], [ 51, 1, 2, 24 ], [ 51, 1, 3, 96 ], [ 51, 1, 5, 144 ], [ 51, 1, 6, 48 ], [ 52, 1, 3, 48 ], [ 52, 1, 4, 48 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ], [ 53, 1, 3, 48 ], [ 53, 1, 4, 96 ], [ 53, 1, 9, 96 ], [ 53, 1, 16, 72 ], [ 53, 1, 17, 72 ], [ 54, 1, 5, 96 ], [ 54, 1, 7, 72 ], [ 55, 1, 2, 48 ], [ 55, 1, 3, 72 ], [ 55, 1, 5, 96 ], [ 55, 1, 8, 96 ], [ 55, 1, 18, 144 ], [ 56, 1, 3, 36 ], [ 56, 1, 5, 96 ], [ 56, 1, 7, 96 ], [ 56, 1, 8, 108 ], [ 56, 1, 10, 96 ], [ 58, 1, 4, 96 ], [ 58, 1, 7, 144 ], [ 58, 1, 9, 192 ], [ 58, 1, 18, 96 ], [ 59, 1, 4, 36 ], [ 59, 1, 13, 96 ], [ 59, 1, 19, 72 ], [ 59, 1, 22, 96 ], [ 60, 1, 2, 144 ], [ 60, 1, 11, 144 ], [ 61, 1, 7, 144 ], [ 61, 1, 12, 96 ], [ 61, 1, 17, 96 ], [ 62, 1, 2, 72 ], [ 62, 1, 5, 216 ], [ 62, 1, 10, 144 ], [ 62, 1, 11, 144 ], [ 63, 1, 5, 144 ], [ 63, 1, 10, 72 ], [ 63, 1, 13, 144 ], [ 63, 1, 32, 192 ], [ 64, 1, 8, 288 ], [ 64, 1, 19, 144 ], [ 64, 1, 20, 288 ], [ 65, 1, 23, 288 ], [ 65, 1, 30, 288 ], [ 65, 1, 48, 192 ], [ 66, 1, 27, 288 ], [ 66, 1, 35, 288 ] ] k = 82: F-action on Pi is () [67,1,82] Dynkin type is A_0(q) + T(phi1^3 phi2^3 phi6) Order of center |Z^F|: phi1^3 phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 2 modulo 60: 1/576 q phi2 ( q^6-6*q^5+5*q^4+28*q^3-52*q^2+32 ) q congruent 3 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 4 modulo 60: 1/576 q^2 phi1 ( q^5-4*q^4-5*q^3+28*q^2+4*q-48 ) q congruent 5 modulo 60: 1/576 phi1^2 phi2 ( q^5-4*q^4-4*q^3+24*q^2-5*q-16 ) q congruent 7 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 8 modulo 60: 1/576 q phi2 ( q^6-6*q^5+5*q^4+28*q^3-52*q^2+32 ) q congruent 9 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 11 modulo 60: 1/576 phi1^2 phi2 ( q^5-4*q^4-4*q^3+24*q^2-5*q-16 ) q congruent 13 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 16 modulo 60: 1/576 q^2 phi1 ( q^5-4*q^4-5*q^3+28*q^2+4*q-48 ) q congruent 17 modulo 60: 1/576 phi1^2 phi2 ( q^5-4*q^4-4*q^3+24*q^2-5*q-16 ) q congruent 19 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 21 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 23 modulo 60: 1/576 phi1^2 phi2 ( q^5-4*q^4-4*q^3+24*q^2-5*q-16 ) q congruent 25 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 27 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 29 modulo 60: 1/576 phi1^2 phi2 ( q^5-4*q^4-4*q^3+24*q^2-5*q-16 ) q congruent 31 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 32 modulo 60: 1/576 q phi2 ( q^6-6*q^5+5*q^4+28*q^3-52*q^2+32 ) q congruent 37 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 41 modulo 60: 1/576 phi1^2 phi2 ( q^5-4*q^4-4*q^3+24*q^2-5*q-16 ) q congruent 43 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 47 modulo 60: 1/576 phi1^2 phi2 ( q^5-4*q^4-4*q^3+24*q^2-5*q-16 ) q congruent 49 modulo 60: 1/576 q phi1^2 ( q^5-3*q^4-8*q^3+20*q^2+19*q-21 ) q congruent 53 modulo 60: 1/576 phi1^2 phi2 ( q^5-4*q^4-4*q^3+24*q^2-5*q-16 ) q congruent 59 modulo 60: 1/576 phi1^2 phi2 ( q^5-4*q^4-4*q^3+24*q^2-5*q-16 ) Fusion of maximal tori of C^F in those of G^F: [ 82 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 14 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 18 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 12 ], [ 12, 1, 1, 24 ], [ 12, 1, 2, 18 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], [ 16, 1, 2, 48 ], [ 16, 1, 3, 48 ], [ 16, 1, 4, 24 ], [ 17, 1, 3, 16 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], [ 20, 1, 3, 72 ], [ 20, 1, 4, 24 ], [ 22, 1, 3, 60 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 48 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 24 ], [ 26, 1, 2, 24 ], [ 27, 1, 2, 16 ], [ 27, 1, 3, 24 ], [ 27, 1, 4, 6 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 28, 1, 3, 36 ], [ 28, 1, 4, 12 ], [ 29, 1, 3, 72 ], [ 30, 1, 3, 24 ], [ 30, 1, 4, 48 ], [ 31, 1, 3, 84 ], [ 31, 1, 4, 12 ], [ 32, 1, 2, 48 ], [ 32, 1, 3, 48 ], [ 33, 1, 6, 48 ], [ 33, 1, 8, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 72 ], [ 35, 1, 7, 48 ], [ 35, 1, 8, 24 ], [ 36, 1, 3, 24 ], [ 37, 1, 2, 48 ], [ 38, 1, 4, 48 ], [ 38, 1, 8, 144 ], [ 38, 1, 10, 32 ], [ 38, 1, 11, 72 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], [ 40, 1, 2, 72 ], [ 40, 1, 3, 48 ], [ 40, 1, 6, 12 ], [ 41, 1, 1, 48 ], [ 41, 1, 4, 48 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 48 ], [ 42, 1, 2, 48 ], [ 42, 1, 5, 24 ], [ 43, 1, 3, 96 ], [ 43, 1, 4, 48 ], [ 43, 1, 8, 48 ], [ 44, 1, 2, 48 ], [ 44, 1, 7, 18 ], [ 44, 1, 8, 24 ], [ 44, 1, 9, 48 ], [ 45, 1, 4, 36 ], [ 45, 1, 5, 48 ], [ 46, 1, 4, 72 ], [ 46, 1, 5, 96 ], [ 46, 1, 10, 48 ], [ 47, 1, 7, 72 ], [ 47, 1, 8, 24 ], [ 47, 1, 9, 48 ], [ 47, 1, 10, 48 ], [ 48, 1, 4, 96 ], [ 48, 1, 5, 48 ], [ 50, 1, 7, 36 ], [ 50, 1, 8, 96 ], [ 50, 1, 10, 12 ], [ 51, 1, 3, 48 ], [ 51, 1, 6, 96 ], [ 51, 1, 8, 24 ], [ 51, 1, 10, 144 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ], [ 52, 1, 3, 48 ], [ 52, 1, 4, 48 ], [ 53, 1, 6, 96 ], [ 53, 1, 7, 96 ], [ 53, 1, 8, 48 ], [ 53, 1, 15, 72 ], [ 53, 1, 18, 72 ], [ 54, 1, 11, 72 ], [ 54, 1, 13, 96 ], [ 55, 1, 7, 144 ], [ 55, 1, 12, 72 ], [ 55, 1, 13, 48 ], [ 55, 1, 14, 96 ], [ 55, 1, 17, 96 ], [ 56, 1, 12, 108 ], [ 56, 1, 13, 96 ], [ 56, 1, 14, 96 ], [ 56, 1, 17, 36 ], [ 56, 1, 19, 96 ], [ 58, 1, 4, 96 ], [ 58, 1, 10, 144 ], [ 58, 1, 11, 192 ], [ 58, 1, 23, 96 ], [ 59, 1, 5, 36 ], [ 59, 1, 12, 96 ], [ 59, 1, 20, 72 ], [ 59, 1, 22, 96 ], [ 60, 1, 8, 144 ], [ 60, 1, 10, 144 ], [ 61, 1, 8, 144 ], [ 61, 1, 18, 96 ], [ 61, 1, 22, 96 ], [ 62, 1, 6, 216 ], [ 62, 1, 7, 72 ], [ 62, 1, 8, 144 ], [ 62, 1, 9, 144 ], [ 63, 1, 8, 144 ], [ 63, 1, 11, 72 ], [ 63, 1, 12, 144 ], [ 63, 1, 35, 192 ], [ 64, 1, 16, 288 ], [ 64, 1, 21, 288 ], [ 64, 1, 22, 144 ], [ 65, 1, 26, 288 ], [ 65, 1, 31, 288 ], [ 65, 1, 50, 192 ], [ 66, 1, 32, 288 ], [ 66, 1, 36, 288 ] ] k = 83: F-action on Pi is () [67,1,83] Dynkin type is A_0(q) + T(phi1^3 phi2 phi3^2) Order of center |Z^F|: phi1^3 phi2 phi3^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/432 phi1 ( q^7-3*q^6-3*q^5-5*q^4+36*q^3+24*q^2+10*q+12 ) q congruent 2 modulo 60: 1/432 q^2 phi2 ( q^5-5*q^4+5*q^3-7*q^2+36*q-36 ) q congruent 3 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 4 modulo 60: 1/432 q phi1 ( q^6-3*q^5-3*q^4-5*q^3+24*q^2+24*q+16 ) q congruent 5 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 7 modulo 60: 1/432 phi1 ( q^7-3*q^6-3*q^5-5*q^4+36*q^3+24*q^2+10*q+12 ) q congruent 8 modulo 60: 1/432 q^2 phi2 ( q^5-5*q^4+5*q^3-7*q^2+36*q-36 ) q congruent 9 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 11 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 13 modulo 60: 1/432 phi1 ( q^7-3*q^6-3*q^5-5*q^4+36*q^3+24*q^2+10*q+12 ) q congruent 16 modulo 60: 1/432 q phi1 ( q^6-3*q^5-3*q^4-5*q^3+24*q^2+24*q+16 ) q congruent 17 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 19 modulo 60: 1/432 phi1 ( q^7-3*q^6-3*q^5-5*q^4+36*q^3+24*q^2+10*q+12 ) q congruent 21 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 23 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 25 modulo 60: 1/432 phi1 ( q^7-3*q^6-3*q^5-5*q^4+36*q^3+24*q^2+10*q+12 ) q congruent 27 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 29 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 31 modulo 60: 1/432 phi1 ( q^7-3*q^6-3*q^5-5*q^4+36*q^3+24*q^2+10*q+12 ) q congruent 32 modulo 60: 1/432 q^2 phi2 ( q^5-5*q^4+5*q^3-7*q^2+36*q-36 ) q congruent 37 modulo 60: 1/432 phi1 ( q^7-3*q^6-3*q^5-5*q^4+36*q^3+24*q^2+10*q+12 ) q congruent 41 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 43 modulo 60: 1/432 phi1 ( q^7-3*q^6-3*q^5-5*q^4+36*q^3+24*q^2+10*q+12 ) q congruent 47 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 49 modulo 60: 1/432 phi1 ( q^7-3*q^6-3*q^5-5*q^4+36*q^3+24*q^2+10*q+12 ) q congruent 53 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) q congruent 59 modulo 60: 1/432 q phi1 phi2 ( q^5-4*q^4+q^3-6*q^2+42*q-18 ) Fusion of maximal tori of C^F in those of G^F: [ 83 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 48 ], [ 17, 1, 5, 36 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 24 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 36 ], [ 22, 1, 2, 12 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 1, 12 ], [ 26, 1, 3, 12 ], [ 27, 1, 1, 12 ], [ 27, 1, 2, 4 ], [ 27, 1, 5, 12 ], [ 29, 1, 1, 24 ], [ 29, 1, 2, 24 ], [ 31, 1, 1, 24 ], [ 31, 1, 2, 24 ], [ 32, 1, 1, 24 ], [ 33, 1, 3, 72 ], [ 34, 1, 1, 12 ], [ 34, 1, 2, 12 ], [ 36, 1, 2, 24 ], [ 38, 1, 1, 72 ], [ 38, 1, 3, 72 ], [ 38, 1, 5, 24 ], [ 38, 1, 15, 72 ], [ 39, 1, 4, 12 ], [ 40, 1, 5, 36 ], [ 42, 1, 1, 12 ], [ 42, 1, 3, 48 ], [ 42, 1, 4, 12 ], [ 43, 1, 2, 48 ], [ 44, 1, 3, 36 ], [ 45, 1, 3, 72 ], [ 46, 1, 1, 24 ], [ 46, 1, 2, 24 ], [ 46, 1, 3, 96 ], [ 47, 1, 5, 108 ], [ 47, 1, 6, 36 ], [ 49, 1, 3, 108 ], [ 50, 1, 2, 24 ], [ 50, 1, 3, 72 ], [ 50, 1, 4, 24 ], [ 50, 1, 6, 24 ], [ 51, 1, 2, 48 ], [ 52, 1, 6, 72 ], [ 53, 1, 16, 72 ], [ 54, 1, 3, 72 ], [ 54, 1, 7, 72 ], [ 55, 1, 3, 72 ], [ 56, 1, 3, 72 ], [ 56, 1, 8, 72 ], [ 57, 1, 12, 108 ], [ 57, 1, 13, 108 ], [ 58, 1, 2, 48 ], [ 58, 1, 3, 144 ], [ 58, 1, 7, 48 ], [ 58, 1, 8, 72 ], [ 59, 1, 7, 108 ], [ 59, 1, 14, 36 ], [ 60, 1, 3, 108 ], [ 60, 1, 12, 108 ], [ 61, 1, 4, 72 ], [ 61, 1, 5, 144 ], [ 61, 1, 7, 72 ], [ 62, 1, 18, 216 ], [ 62, 1, 20, 216 ], [ 63, 1, 10, 144 ], [ 64, 1, 7, 216 ], [ 65, 1, 8, 216 ], [ 65, 1, 17, 72 ], [ 65, 1, 28, 144 ], [ 66, 1, 12, 216 ], [ 66, 1, 22, 216 ] ] k = 84: F-action on Pi is () [67,1,84] Dynkin type is A_0(q) + T(phi1 phi2^3 phi6^2) Order of center |Z^F|: phi1 phi2^3 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 2 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+44*q^3-48*q^2+64*q-80 ) q congruent 3 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 4 modulo 60: 1/432 q^2 phi1 ( q^5-3*q^4+q^3-9*q^2+16*q+12 ) q congruent 5 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+56*q^3-84*q^2+94*q-92 ) q congruent 7 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 8 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+44*q^3-48*q^2+64*q-80 ) q congruent 9 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 11 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+56*q^3-84*q^2+94*q-92 ) q congruent 13 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 16 modulo 60: 1/432 q^2 phi1 ( q^5-3*q^4+q^3-9*q^2+16*q+12 ) q congruent 17 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+56*q^3-84*q^2+94*q-92 ) q congruent 19 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 21 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 23 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+56*q^3-84*q^2+94*q-92 ) q congruent 25 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 27 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 29 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+56*q^3-84*q^2+94*q-92 ) q congruent 31 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 32 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+44*q^3-48*q^2+64*q-80 ) q congruent 37 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 41 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+56*q^3-84*q^2+94*q-92 ) q congruent 43 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 47 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+56*q^3-84*q^2+94*q-92 ) q congruent 49 modulo 60: 1/432 q phi1^2 ( q^5-2*q^4-q^3-10*q^2+18*q+18 ) q congruent 53 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+56*q^3-84*q^2+94*q-92 ) q congruent 59 modulo 60: 1/432 phi2 ( q^7-5*q^6+9*q^5-19*q^4+56*q^3-84*q^2+94*q-92 ) Fusion of maximal tori of C^F in those of G^F: [ 84 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 12 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 24 ], [ 16, 1, 3, 24 ], [ 17, 1, 4, 48 ], [ 17, 1, 6, 36 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 20, 1, 3, 24 ], [ 20, 1, 4, 24 ], [ 21, 1, 2, 12 ], [ 22, 1, 3, 12 ], [ 22, 1, 4, 36 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 2, 12 ], [ 26, 1, 4, 12 ], [ 27, 1, 3, 4 ], [ 27, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 29, 1, 3, 24 ], [ 29, 1, 4, 24 ], [ 31, 1, 3, 24 ], [ 31, 1, 4, 24 ], [ 32, 1, 3, 24 ], [ 33, 1, 7, 72 ], [ 34, 1, 3, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 3, 24 ], [ 38, 1, 8, 24 ], [ 38, 1, 11, 72 ], [ 38, 1, 12, 72 ], [ 38, 1, 16, 72 ], [ 39, 1, 4, 12 ], [ 40, 1, 4, 36 ], [ 42, 1, 2, 12 ], [ 42, 1, 5, 48 ], [ 42, 1, 6, 12 ], [ 43, 1, 4, 48 ], [ 44, 1, 7, 36 ], [ 45, 1, 4, 72 ], [ 46, 1, 4, 96 ], [ 46, 1, 5, 24 ], [ 46, 1, 6, 24 ], [ 47, 1, 11, 36 ], [ 47, 1, 12, 108 ], [ 49, 1, 6, 108 ], [ 50, 1, 7, 24 ], [ 50, 1, 9, 24 ], [ 50, 1, 10, 72 ], [ 50, 1, 11, 24 ], [ 51, 1, 8, 48 ], [ 52, 1, 7, 72 ], [ 53, 1, 18, 72 ], [ 54, 1, 10, 72 ], [ 54, 1, 11, 72 ], [ 55, 1, 12, 72 ], [ 56, 1, 12, 72 ], [ 56, 1, 17, 72 ], [ 57, 1, 14, 108 ], [ 57, 1, 15, 108 ], [ 58, 1, 10, 48 ], [ 58, 1, 12, 48 ], [ 58, 1, 13, 72 ], [ 58, 1, 14, 144 ], [ 59, 1, 8, 108 ], [ 59, 1, 15, 36 ], [ 60, 1, 13, 108 ], [ 60, 1, 14, 108 ], [ 61, 1, 6, 72 ], [ 61, 1, 8, 72 ], [ 61, 1, 9, 144 ], [ 62, 1, 17, 216 ], [ 62, 1, 23, 216 ], [ 63, 1, 11, 144 ], [ 64, 1, 23, 216 ], [ 65, 1, 16, 72 ], [ 65, 1, 18, 216 ], [ 65, 1, 29, 144 ], [ 66, 1, 23, 216 ], [ 66, 1, 26, 216 ] ] k = 85: F-action on Pi is () [67,1,85] Dynkin type is A_0(q) + T(phi1 phi2 phi3^2 phi6) Order of center |Z^F|: phi1 phi2 phi3^2 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 phi1^2 ( q^6+2*q^5-2*q^4-6*q^3-9*q^2-6*q+8 ) q congruent 2 modulo 60: 1/288 q^2 phi2 ( q^5-q^4-4*q^3+4*q^2-4*q+8 ) q congruent 3 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 4 modulo 60: 1/288 q phi1 ( q^6+q^5-4*q^4-4*q^3-4*q^2+16 ) q congruent 5 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 7 modulo 60: 1/288 phi1^2 ( q^6+2*q^5-2*q^4-6*q^3-9*q^2-6*q+8 ) q congruent 8 modulo 60: 1/288 q^2 phi2 ( q^5-q^4-4*q^3+4*q^2-4*q+8 ) q congruent 9 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 11 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 13 modulo 60: 1/288 phi1^2 ( q^6+2*q^5-2*q^4-6*q^3-9*q^2-6*q+8 ) q congruent 16 modulo 60: 1/288 q phi1 ( q^6+q^5-4*q^4-4*q^3-4*q^2+16 ) q congruent 17 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 19 modulo 60: 1/288 phi1^2 ( q^6+2*q^5-2*q^4-6*q^3-9*q^2-6*q+8 ) q congruent 21 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 23 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 25 modulo 60: 1/288 phi1^2 ( q^6+2*q^5-2*q^4-6*q^3-9*q^2-6*q+8 ) q congruent 27 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 29 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 31 modulo 60: 1/288 phi1^2 ( q^6+2*q^5-2*q^4-6*q^3-9*q^2-6*q+8 ) q congruent 32 modulo 60: 1/288 q^2 phi2 ( q^5-q^4-4*q^3+4*q^2-4*q+8 ) q congruent 37 modulo 60: 1/288 phi1^2 ( q^6+2*q^5-2*q^4-6*q^3-9*q^2-6*q+8 ) q congruent 41 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 43 modulo 60: 1/288 phi1^2 ( q^6+2*q^5-2*q^4-6*q^3-9*q^2-6*q+8 ) q congruent 47 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 49 modulo 60: 1/288 phi1^2 ( q^6+2*q^5-2*q^4-6*q^3-9*q^2-6*q+8 ) q congruent 53 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) q congruent 59 modulo 60: 1/288 q phi1^2 phi2 ( q^4+q^3-3*q^2-3*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 85 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 8 ], [ 8, 1, 1, 16 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 16 ], [ 22, 1, 1, 16 ], [ 27, 1, 3, 4 ], [ 27, 1, 5, 24 ], [ 33, 1, 3, 24 ], [ 38, 1, 2, 32 ], [ 38, 1, 9, 48 ], [ 38, 1, 14, 144 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 24 ], [ 42, 1, 3, 24 ], [ 46, 1, 9, 48 ], [ 47, 1, 5, 48 ], [ 50, 1, 3, 48 ], [ 52, 1, 7, 6 ], [ 58, 1, 6, 48 ], [ 58, 1, 18, 96 ], [ 59, 1, 9, 72 ], [ 59, 1, 15, 12 ], [ 60, 1, 4, 72 ], [ 61, 1, 11, 48 ], [ 62, 1, 3, 144 ], [ 65, 1, 14, 144 ], [ 65, 1, 20, 96 ], [ 66, 1, 17, 144 ] ] k = 86: F-action on Pi is () [67,1,86] Dynkin type is A_0(q) + T(phi1 phi2 phi3 phi6^2) Order of center |Z^F|: phi1 phi2 phi3 phi6^2 Numbers of classes in class type: q congruent 1 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 2 modulo 60: 1/288 q phi2 ( q^6-3*q^5+2*q^4-2*q^3+2*q^2+12*q-16 ) q congruent 3 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 4 modulo 60: 1/288 q^2 phi1 ( q^5-q^4-2*q^3-2*q^2-2*q+12 ) q congruent 5 modulo 60: 1/288 phi1^2 phi2 ( q^5-q^4-q^3-3*q^2-2*q+8 ) q congruent 7 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 8 modulo 60: 1/288 q phi2 ( q^6-3*q^5+2*q^4-2*q^3+2*q^2+12*q-16 ) q congruent 9 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 11 modulo 60: 1/288 phi1^2 phi2 ( q^5-q^4-q^3-3*q^2-2*q+8 ) q congruent 13 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 16 modulo 60: 1/288 q^2 phi1 ( q^5-q^4-2*q^3-2*q^2-2*q+12 ) q congruent 17 modulo 60: 1/288 phi1^2 phi2 ( q^5-q^4-q^3-3*q^2-2*q+8 ) q congruent 19 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 21 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 23 modulo 60: 1/288 phi1^2 phi2 ( q^5-q^4-q^3-3*q^2-2*q+8 ) q congruent 25 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 27 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 29 modulo 60: 1/288 phi1^2 phi2 ( q^5-q^4-q^3-3*q^2-2*q+8 ) q congruent 31 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 32 modulo 60: 1/288 q phi2 ( q^6-3*q^5+2*q^4-2*q^3+2*q^2+12*q-16 ) q congruent 37 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 41 modulo 60: 1/288 phi1^2 phi2 ( q^5-q^4-q^3-3*q^2-2*q+8 ) q congruent 43 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 47 modulo 60: 1/288 phi1^2 phi2 ( q^5-q^4-q^3-3*q^2-2*q+8 ) q congruent 49 modulo 60: 1/288 q phi1^2 ( q^5-2*q^3-4*q^2-5*q+6 ) q congruent 53 modulo 60: 1/288 phi1^2 phi2 ( q^5-q^4-q^3-3*q^2-2*q+8 ) q congruent 59 modulo 60: 1/288 phi1^2 phi2 ( q^5-q^4-q^3-3*q^2-2*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 86 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 8, 1, 2, 16 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 3, 16 ], [ 22, 1, 4, 16 ], [ 27, 1, 2, 4 ], [ 27, 1, 4, 24 ], [ 33, 1, 7, 24 ], [ 38, 1, 4, 48 ], [ 38, 1, 10, 32 ], [ 38, 1, 17, 144 ], [ 40, 1, 4, 24 ], [ 40, 1, 5, 6 ], [ 42, 1, 5, 24 ], [ 46, 1, 10, 48 ], [ 47, 1, 12, 48 ], [ 50, 1, 10, 48 ], [ 52, 1, 6, 6 ], [ 58, 1, 6, 48 ], [ 58, 1, 23, 96 ], [ 59, 1, 10, 72 ], [ 59, 1, 14, 12 ], [ 60, 1, 15, 72 ], [ 61, 1, 10, 48 ], [ 62, 1, 16, 144 ], [ 65, 1, 11, 144 ], [ 65, 1, 21, 96 ], [ 66, 1, 14, 144 ] ] k = 87: F-action on Pi is () [67,1,87] Dynkin type is A_0(q) + T(phi1^3 phi2 phi3 phi6) Order of center |Z^F|: phi1^3 phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 phi1 ( q^7-5*q^6+5*q^5-q^4+18*q^3-6*q^2-40*q+4 ) q congruent 2 modulo 60: 1/144 q phi2 ( q^6-7*q^5+17*q^4-23*q^3+38*q^2-52*q+24 ) q congruent 3 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 4 modulo 60: 1/144 q phi1 ( q^6-5*q^5+5*q^4-q^3+14*q^2-32 ) q congruent 5 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 7 modulo 60: 1/144 phi1 ( q^7-5*q^6+5*q^5-q^4+18*q^3-6*q^2-40*q+4 ) q congruent 8 modulo 60: 1/144 q phi2 ( q^6-7*q^5+17*q^4-23*q^3+38*q^2-52*q+24 ) q congruent 9 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 11 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 13 modulo 60: 1/144 phi1 ( q^7-5*q^6+5*q^5-q^4+18*q^3-6*q^2-40*q+4 ) q congruent 16 modulo 60: 1/144 q phi1 ( q^6-5*q^5+5*q^4-q^3+14*q^2-32 ) q congruent 17 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 19 modulo 60: 1/144 phi1 ( q^7-5*q^6+5*q^5-q^4+18*q^3-6*q^2-40*q+4 ) q congruent 21 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 23 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 25 modulo 60: 1/144 phi1 ( q^7-5*q^6+5*q^5-q^4+18*q^3-6*q^2-40*q+4 ) q congruent 27 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 29 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 31 modulo 60: 1/144 phi1 ( q^7-5*q^6+5*q^5-q^4+18*q^3-6*q^2-40*q+4 ) q congruent 32 modulo 60: 1/144 q phi2 ( q^6-7*q^5+17*q^4-23*q^3+38*q^2-52*q+24 ) q congruent 37 modulo 60: 1/144 phi1 ( q^7-5*q^6+5*q^5-q^4+18*q^3-6*q^2-40*q+4 ) q congruent 41 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 43 modulo 60: 1/144 phi1 ( q^7-5*q^6+5*q^5-q^4+18*q^3-6*q^2-40*q+4 ) q congruent 47 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 49 modulo 60: 1/144 phi1 ( q^7-5*q^6+5*q^5-q^4+18*q^3-6*q^2-40*q+4 ) q congruent 53 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) q congruent 59 modulo 60: 1/144 q phi1 phi2 ( q^5-6*q^4+11*q^3-12*q^2+30*q-36 ) Fusion of maximal tori of C^F in those of G^F: [ 87 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 8 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 12 ], [ 17, 1, 5, 36 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 6, 24 ], [ 20, 1, 8, 24 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 12 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 12 ], [ 26, 1, 1, 12 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 12 ], [ 27, 1, 3, 4 ], [ 32, 1, 4, 12 ], [ 33, 1, 3, 6 ], [ 33, 1, 7, 18 ], [ 34, 1, 1, 12 ], [ 34, 1, 3, 12 ], [ 36, 1, 1, 24 ], [ 38, 1, 2, 8 ], [ 38, 1, 7, 24 ], [ 38, 1, 13, 72 ], [ 39, 1, 1, 24 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 1, 12 ], [ 42, 1, 2, 12 ], [ 43, 1, 6, 48 ], [ 46, 1, 7, 24 ], [ 46, 1, 11, 24 ], [ 47, 1, 5, 12 ], [ 47, 1, 11, 36 ], [ 49, 1, 3, 18 ], [ 49, 1, 6, 18 ], [ 50, 1, 1, 24 ], [ 50, 1, 8, 24 ], [ 52, 1, 6, 18 ], [ 52, 1, 7, 6 ], [ 57, 1, 12, 36 ], [ 57, 1, 14, 36 ], [ 58, 1, 6, 12 ], [ 58, 1, 16, 48 ], [ 59, 1, 7, 36 ], [ 59, 1, 15, 12 ], [ 60, 1, 3, 36 ], [ 60, 1, 13, 36 ], [ 61, 1, 10, 36 ], [ 61, 1, 11, 12 ], [ 62, 1, 4, 72 ], [ 62, 1, 19, 72 ], [ 64, 1, 25, 36 ], [ 65, 1, 19, 72 ], [ 65, 1, 20, 24 ], [ 66, 1, 21, 72 ], [ 66, 1, 25, 72 ] ] k = 88: F-action on Pi is () [67,1,88] Dynkin type is A_0(q) + T(phi1 phi2^3 phi3 phi6) Order of center |Z^F|: phi1 phi2^3 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 2 modulo 60: 1/144 q phi2 ( q^6-3*q^5+5*q^4-11*q^3+14*q^2-12*q+8 ) q congruent 3 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 4 modulo 60: 1/144 q^3 phi1 ( q^4-q^3+q^2-5*q-2 ) q congruent 5 modulo 60: 1/144 phi1^2 phi2 ( q^5-q^4+2*q^3-6*q^2+4*q-4 ) q congruent 7 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 8 modulo 60: 1/144 q phi2 ( q^6-3*q^5+5*q^4-11*q^3+14*q^2-12*q+8 ) q congruent 9 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 11 modulo 60: 1/144 phi1^2 phi2 ( q^5-q^4+2*q^3-6*q^2+4*q-4 ) q congruent 13 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 16 modulo 60: 1/144 q^3 phi1 ( q^4-q^3+q^2-5*q-2 ) q congruent 17 modulo 60: 1/144 phi1^2 phi2 ( q^5-q^4+2*q^3-6*q^2+4*q-4 ) q congruent 19 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 21 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 23 modulo 60: 1/144 phi1^2 phi2 ( q^5-q^4+2*q^3-6*q^2+4*q-4 ) q congruent 25 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 27 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 29 modulo 60: 1/144 phi1^2 phi2 ( q^5-q^4+2*q^3-6*q^2+4*q-4 ) q congruent 31 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 32 modulo 60: 1/144 q phi2 ( q^6-3*q^5+5*q^4-11*q^3+14*q^2-12*q+8 ) q congruent 37 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 41 modulo 60: 1/144 phi1^2 phi2 ( q^5-q^4+2*q^3-6*q^2+4*q-4 ) q congruent 43 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 47 modulo 60: 1/144 phi1^2 phi2 ( q^5-q^4+2*q^3-6*q^2+4*q-4 ) q congruent 49 modulo 60: 1/144 q^2 phi1^2 ( q^4+q^2-4*q-2 ) q congruent 53 modulo 60: 1/144 phi1^2 phi2 ( q^5-q^4+2*q^3-6*q^2+4*q-4 ) q congruent 59 modulo 60: 1/144 phi1^2 phi2 ( q^5-q^4+2*q^3-6*q^2+4*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 88 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 6 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 8 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 17, 1, 3, 4 ], [ 17, 1, 6, 36 ], [ 18, 1, 2, 12 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 5, 24 ], [ 20, 1, 7, 24 ], [ 21, 1, 2, 12 ], [ 22, 1, 2, 12 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 12 ], [ 26, 1, 3, 12 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 4 ], [ 27, 1, 6, 12 ], [ 32, 1, 4, 12 ], [ 33, 1, 3, 18 ], [ 33, 1, 7, 6 ], [ 34, 1, 2, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 4, 24 ], [ 38, 1, 6, 24 ], [ 38, 1, 10, 8 ], [ 38, 1, 18, 72 ], [ 39, 1, 3, 24 ], [ 40, 1, 4, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 4, 12 ], [ 42, 1, 6, 12 ], [ 43, 1, 14, 48 ], [ 46, 1, 8, 24 ], [ 46, 1, 12, 24 ], [ 47, 1, 6, 36 ], [ 47, 1, 12, 12 ], [ 49, 1, 3, 18 ], [ 49, 1, 6, 18 ], [ 50, 1, 5, 24 ], [ 50, 1, 12, 24 ], [ 52, 1, 6, 6 ], [ 52, 1, 7, 18 ], [ 57, 1, 13, 36 ], [ 57, 1, 15, 36 ], [ 58, 1, 6, 12 ], [ 58, 1, 26, 48 ], [ 59, 1, 8, 36 ], [ 59, 1, 14, 12 ], [ 60, 1, 12, 36 ], [ 60, 1, 14, 36 ], [ 61, 1, 10, 12 ], [ 61, 1, 11, 36 ], [ 62, 1, 21, 72 ], [ 62, 1, 22, 72 ], [ 64, 1, 25, 36 ], [ 65, 1, 21, 24 ], [ 65, 1, 22, 72 ], [ 66, 1, 20, 72 ], [ 66, 1, 24, 72 ] ] k = 89: F-action on Pi is () [67,1,89] Dynkin type is A_0(q) + T(phi1^3 phi2 phi8) Order of center |Z^F|: phi1^3 phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 2 modulo 60: 1/384 q^4 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 3 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 4 modulo 60: 1/384 q^4 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 5 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 7 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 8 modulo 60: 1/384 q^4 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 9 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 11 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 13 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 16 modulo 60: 1/384 q^4 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 17 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 19 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 21 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 23 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 25 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 27 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 29 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 31 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 32 modulo 60: 1/384 q^4 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 37 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 41 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 43 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 47 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 49 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 53 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) q congruent 59 modulo 60: 1/384 phi1 phi2 phi4 ( q^4-8*q^3+14*q^2+20*q-51 ) Fusion of maximal tori of C^F in those of G^F: [ 89 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 12 ], [ 25, 1, 4, 4 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 24 ], [ 33, 1, 5, 32 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 12 ], [ 40, 1, 3, 16 ], [ 41, 1, 3, 48 ], [ 41, 1, 4, 24 ], [ 44, 1, 1, 48 ], [ 44, 1, 9, 48 ], [ 49, 1, 12, 96 ], [ 52, 1, 3, 48 ], [ 59, 1, 17, 96 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 48 ], [ 60, 1, 23, 192 ], [ 62, 1, 28, 96 ], [ 63, 1, 17, 48 ], [ 63, 1, 18, 16 ], [ 64, 1, 30, 192 ], [ 64, 1, 31, 96 ], [ 65, 1, 34, 64 ], [ 66, 1, 43, 192 ] ] k = 90: F-action on Pi is () [67,1,90] Dynkin type is A_0(q) + T(phi1 phi2^3 phi8) Order of center |Z^F|: phi1 phi2^3 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 2 modulo 60: 1/384 q^5 ( q^3-4*q^2+2*q+4 ) q congruent 3 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 4 modulo 60: 1/384 q^5 ( q^3-4*q^2+2*q+4 ) q congruent 5 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 7 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 8 modulo 60: 1/384 q^5 ( q^3-4*q^2+2*q+4 ) q congruent 9 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 11 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 13 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 16 modulo 60: 1/384 q^5 ( q^3-4*q^2+2*q+4 ) q congruent 17 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 19 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 21 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 23 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 25 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 27 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 29 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 31 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 32 modulo 60: 1/384 q^5 ( q^3-4*q^2+2*q+4 ) q congruent 37 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 41 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 43 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 47 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 49 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 53 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) q congruent 59 modulo 60: 1/384 phi1^3 phi2^2 phi4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 90 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 12 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 12 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 9, 32 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 24 ], [ 40, 1, 2, 16 ], [ 41, 1, 4, 24 ], [ 41, 1, 10, 48 ], [ 44, 1, 5, 48 ], [ 44, 1, 10, 48 ], [ 49, 1, 16, 96 ], [ 52, 1, 4, 48 ], [ 59, 1, 18, 96 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 48 ], [ 60, 1, 24, 192 ], [ 62, 1, 27, 96 ], [ 63, 1, 17, 16 ], [ 63, 1, 18, 48 ], [ 64, 1, 29, 192 ], [ 64, 1, 31, 96 ], [ 65, 1, 35, 64 ], [ 66, 1, 44, 192 ] ] k = 91: F-action on Pi is () [67,1,91] Dynkin type is A_0(q) + T(phi1 phi2 phi4 phi8) Order of center |Z^F|: phi1 phi2 phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 2 modulo 60: 1/64 q^7 ( q-2 ) q congruent 3 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 4 modulo 60: 1/64 q^7 ( q-2 ) q congruent 5 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 7 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 8 modulo 60: 1/64 q^7 ( q-2 ) q congruent 9 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 11 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 13 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 16 modulo 60: 1/64 q^7 ( q-2 ) q congruent 17 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 19 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 21 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 23 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 25 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 27 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 29 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 31 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 32 modulo 60: 1/64 q^7 ( q-2 ) q congruent 37 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 41 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 43 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 47 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 49 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 53 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) q congruent 59 modulo 60: 1/64 phi1 phi2^2 phi4 ( q^3-3*q^2+3*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 91 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 5, 8 ], [ 20, 1, 6, 8 ], [ 20, 1, 7, 8 ], [ 20, 1, 8, 8 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 39, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 43, 1, 5, 16 ], [ 43, 1, 7, 16 ], [ 43, 1, 10, 16 ], [ 49, 1, 13, 16 ], [ 49, 1, 17, 16 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 59, 1, 21, 16 ], [ 59, 1, 25, 8 ], [ 60, 1, 19, 16 ], [ 60, 1, 21, 32 ], [ 60, 1, 37, 32 ], [ 62, 1, 27, 16 ], [ 62, 1, 28, 16 ], [ 64, 1, 32, 32 ], [ 64, 1, 34, 32 ], [ 66, 1, 40, 32 ], [ 66, 1, 41, 32 ] ] k = 92: F-action on Pi is () [67,1,92] Dynkin type is A_0(q) + T(phi1 phi2 phi4 phi8) Order of center |Z^F|: phi1 phi2 phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 2 modulo 60: 1/16 q^4 ( q^4-2 ) q congruent 3 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 4 modulo 60: 1/16 q^4 ( q^4-2 ) q congruent 5 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 7 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 8 modulo 60: 1/16 q^4 ( q^4-2 ) q congruent 9 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 11 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 13 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 16 modulo 60: 1/16 q^4 ( q^4-2 ) q congruent 17 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 19 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 21 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 23 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 25 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 27 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 29 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 31 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 32 modulo 60: 1/16 q^4 ( q^4-2 ) q congruent 37 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 41 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 43 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 47 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 49 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 53 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 q congruent 59 modulo 60: 1/16 phi1^2 phi2^2 phi4^2 Fusion of maximal tori of C^F in those of G^F: [ 92 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 21, 1, 1, 2 ], [ 21, 1, 2, 2 ], [ 37, 1, 4, 4 ], [ 37, 1, 5, 4 ], [ 57, 1, 19, 8 ], [ 57, 1, 20, 8 ] ] k = 93: F-action on Pi is () [67,1,93] Dynkin type is A_0(q) + T(phi1^3 phi2 phi5) Order of center |Z^F|: phi1^3 phi2 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 2 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 3 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 4 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 5 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 7 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 8 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 9 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 11 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 13 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 16 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 17 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 19 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 21 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 23 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 25 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 27 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 29 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 31 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 32 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 37 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 41 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 43 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 47 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 49 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 53 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 59 modulo 60: 1/120 q^2 phi1 phi2 phi4 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 93 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 6 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 12 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 15, 1, 1, 8 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 12 ], [ 22, 1, 2, 4 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 1, 12 ], [ 26, 1, 3, 4 ], [ 27, 1, 1, 12 ], [ 27, 1, 2, 12 ], [ 28, 1, 1, 12 ], [ 28, 1, 2, 12 ], [ 29, 1, 1, 12 ], [ 29, 1, 2, 4 ], [ 30, 1, 1, 12 ], [ 34, 1, 1, 12 ], [ 34, 1, 2, 12 ], [ 36, 1, 1, 12 ], [ 36, 1, 2, 12 ], [ 39, 1, 4, 12 ], [ 42, 1, 1, 12 ], [ 42, 1, 4, 12 ], [ 44, 1, 2, 24 ], [ 45, 1, 1, 12 ], [ 45, 1, 2, 12 ], [ 50, 1, 2, 24 ], [ 50, 1, 4, 24 ], [ 54, 1, 2, 24 ], [ 54, 1, 6, 10 ], [ 61, 1, 2, 40 ], [ 63, 1, 2, 30 ], [ 64, 1, 2, 60 ], [ 65, 1, 2, 60 ], [ 65, 1, 3, 20 ], [ 66, 1, 4, 60 ], [ 66, 1, 7, 60 ] ] k = 94: F-action on Pi is () [67,1,94] Dynkin type is A_0(q) + T(phi1 phi2^3 phi10) Order of center |Z^F|: phi1 phi2^3 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 17 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/120 q^2 phi1^2 phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 94 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 6 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 14, 1, 2, 6 ], [ 15, 1, 2, 8 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 21, 1, 2, 12 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 12 ], [ 27, 1, 3, 12 ], [ 27, 1, 6, 12 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 12 ], [ 29, 1, 3, 4 ], [ 29, 1, 4, 12 ], [ 30, 1, 3, 12 ], [ 34, 1, 3, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 3, 12 ], [ 36, 1, 4, 12 ], [ 39, 1, 4, 12 ], [ 42, 1, 2, 12 ], [ 42, 1, 6, 12 ], [ 44, 1, 8, 24 ], [ 45, 1, 5, 12 ], [ 45, 1, 6, 12 ], [ 50, 1, 9, 24 ], [ 50, 1, 11, 24 ], [ 54, 1, 8, 10 ], [ 54, 1, 12, 24 ], [ 61, 1, 3, 40 ], [ 63, 1, 3, 30 ], [ 64, 1, 5, 60 ], [ 65, 1, 4, 60 ], [ 65, 1, 5, 20 ], [ 66, 1, 8, 60 ], [ 66, 1, 9, 60 ] ] k = 95: F-action on Pi is () [67,1,95] Dynkin type is A_0(q) + T(phi1 phi2^3 phi3 phi4) Order of center |Z^F|: phi1 phi2^3 phi3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 2 modulo 60: 1/576 q^4 phi1^2 phi2 ( q-2 ) q congruent 3 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 4 modulo 60: 1/576 q^4 phi1^2 phi2 ( q-2 ) q congruent 5 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 7 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 8 modulo 60: 1/576 q^4 phi1^2 phi2 ( q-2 ) q congruent 9 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 11 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 13 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 16 modulo 60: 1/576 q^4 phi1^2 phi2 ( q-2 ) q congruent 17 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 19 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 21 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 23 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 25 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 27 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 29 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 31 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 32 modulo 60: 1/576 q^4 phi1^2 phi2 ( q-2 ) q congruent 37 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 41 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 43 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 47 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 49 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 53 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 59 modulo 60: 1/576 q phi1^2 phi2^2 ( q^3-3*q^2+3*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 95 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 12 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 8 ], [ 13, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 16 ], [ 17, 1, 2, 48 ], [ 20, 1, 2, 48 ], [ 22, 1, 2, 24 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 4, 36 ], [ 27, 1, 5, 6 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], [ 31, 1, 2, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 2, 24 ], [ 35, 1, 4, 48 ], [ 38, 1, 6, 96 ], [ 38, 1, 9, 48 ], [ 39, 1, 3, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 3, 12 ], [ 41, 1, 8, 24 ], [ 41, 1, 10, 48 ], [ 42, 1, 3, 36 ], [ 43, 1, 9, 8 ], [ 43, 1, 12, 96 ], [ 44, 1, 3, 6 ], [ 44, 1, 4, 24 ], [ 44, 1, 10, 48 ], [ 46, 1, 9, 144 ], [ 47, 1, 4, 48 ], [ 50, 1, 6, 72 ], [ 51, 1, 4, 32 ], [ 51, 1, 5, 48 ], [ 51, 1, 7, 8 ], [ 52, 1, 5, 48 ], [ 53, 1, 11, 48 ], [ 53, 1, 16, 36 ], [ 53, 1, 17, 12 ], [ 53, 1, 19, 96 ], [ 55, 1, 4, 48 ], [ 55, 1, 10, 96 ], [ 55, 1, 18, 48 ], [ 56, 1, 8, 72 ], [ 56, 1, 9, 96 ], [ 58, 1, 5, 32 ], [ 58, 1, 27, 288 ], [ 59, 1, 19, 36 ], [ 59, 1, 24, 96 ], [ 60, 1, 11, 72 ], [ 61, 1, 15, 96 ], [ 62, 1, 11, 144 ], [ 63, 1, 5, 144 ], [ 63, 1, 7, 24 ], [ 63, 1, 22, 192 ], [ 64, 1, 10, 144 ], [ 64, 1, 13, 288 ], [ 65, 1, 24, 96 ], [ 65, 1, 41, 192 ], [ 66, 1, 31, 288 ] ] k = 96: F-action on Pi is () [67,1,96] Dynkin type is A_0(q) + T(phi1^3 phi2 phi4 phi6) Order of center |Z^F|: phi1^3 phi2 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 2 modulo 60: 1/576 q^3 phi1 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 4 modulo 60: 1/576 q^3 phi1 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 5 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 7 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 8 modulo 60: 1/576 q^3 phi1 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 9 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 11 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 13 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 16 modulo 60: 1/576 q^3 phi1 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 17 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 19 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 21 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 23 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 25 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 27 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 29 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 31 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 32 modulo 60: 1/576 q^3 phi1 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 37 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 41 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 43 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 47 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 49 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 53 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) q congruent 59 modulo 60: 1/576 q phi1^2 phi2 ( q^4-8*q^3+18*q^2-6*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 96 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 2 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 12 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 12 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 48 ], [ 20, 1, 3, 48 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 36 ], [ 27, 1, 1, 48 ], [ 27, 1, 4, 6 ], [ 28, 1, 1, 24 ], [ 31, 1, 3, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 6, 24 ], [ 35, 1, 5, 48 ], [ 38, 1, 4, 48 ], [ 38, 1, 7, 96 ], [ 39, 1, 1, 24 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 12 ], [ 41, 1, 3, 48 ], [ 41, 1, 8, 24 ], [ 42, 1, 5, 36 ], [ 43, 1, 3, 96 ], [ 43, 1, 9, 8 ], [ 44, 1, 1, 48 ], [ 44, 1, 6, 24 ], [ 44, 1, 7, 6 ], [ 46, 1, 10, 144 ], [ 47, 1, 9, 48 ], [ 50, 1, 7, 72 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 32 ], [ 51, 1, 10, 48 ], [ 52, 1, 8, 48 ], [ 53, 1, 5, 96 ], [ 53, 1, 13, 48 ], [ 53, 1, 15, 12 ], [ 53, 1, 18, 36 ], [ 55, 1, 7, 48 ], [ 55, 1, 11, 48 ], [ 55, 1, 16, 96 ], [ 56, 1, 11, 96 ], [ 56, 1, 12, 72 ], [ 58, 1, 5, 32 ], [ 58, 1, 22, 288 ], [ 59, 1, 20, 36 ], [ 59, 1, 23, 96 ], [ 60, 1, 10, 72 ], [ 61, 1, 14, 96 ], [ 62, 1, 8, 144 ], [ 63, 1, 6, 24 ], [ 63, 1, 8, 144 ], [ 63, 1, 24, 192 ], [ 64, 1, 11, 144 ], [ 64, 1, 17, 288 ], [ 65, 1, 25, 96 ], [ 65, 1, 43, 192 ], [ 66, 1, 30, 288 ] ] k = 97: F-action on Pi is () [67,1,97] Dynkin type is A_0(q) + T(phi1^3 phi2 phi3 phi4) Order of center |Z^F|: phi1^3 phi2 phi3 phi4 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 2 modulo 60: 1/192 q^3 phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 4 modulo 60: 1/192 q^3 phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 5 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 7 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 8 modulo 60: 1/192 q^3 phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 9 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 11 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 13 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 16 modulo 60: 1/192 q^3 phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 17 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 19 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 21 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 23 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 25 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 27 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 29 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 31 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 32 modulo 60: 1/192 q^3 phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 37 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 41 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 43 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 47 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 49 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 53 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) q congruent 59 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-3*q^2-q+5 ) Fusion of maximal tori of C^F in those of G^F: [ 97 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 12, 1, 1, 10 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 12 ], [ 18, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 8 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 32 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 4 ], [ 26, 1, 1, 16 ], [ 27, 1, 5, 6 ], [ 28, 1, 3, 8 ], [ 29, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 8 ], [ 33, 1, 2, 8 ], [ 33, 1, 4, 32 ], [ 35, 1, 2, 16 ], [ 36, 1, 1, 16 ], [ 37, 1, 1, 32 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 1, 24 ], [ 40, 1, 3, 4 ], [ 41, 1, 2, 16 ], [ 41, 1, 3, 16 ], [ 41, 1, 5, 16 ], [ 41, 1, 8, 8 ], [ 42, 1, 3, 12 ], [ 43, 1, 1, 32 ], [ 43, 1, 8, 16 ], [ 43, 1, 9, 8 ], [ 44, 1, 3, 30 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 16 ], [ 44, 1, 9, 16 ], [ 45, 1, 3, 24 ], [ 47, 1, 3, 16 ], [ 48, 1, 7, 32 ], [ 48, 1, 8, 32 ], [ 50, 1, 3, 24 ], [ 51, 1, 1, 16 ], [ 51, 1, 6, 16 ], [ 51, 1, 7, 8 ], [ 52, 1, 8, 16 ], [ 53, 1, 2, 32 ], [ 53, 1, 10, 32 ], [ 53, 1, 11, 16 ], [ 53, 1, 16, 12 ], [ 53, 1, 17, 36 ], [ 54, 1, 3, 48 ], [ 54, 1, 4, 32 ], [ 55, 1, 4, 16 ], [ 55, 1, 6, 32 ], [ 55, 1, 9, 32 ], [ 56, 1, 3, 24 ], [ 56, 1, 4, 32 ], [ 59, 1, 4, 72 ], [ 59, 1, 16, 32 ], [ 59, 1, 19, 12 ], [ 59, 1, 23, 32 ], [ 60, 1, 5, 96 ], [ 60, 1, 11, 24 ], [ 61, 1, 13, 32 ], [ 62, 1, 10, 48 ], [ 63, 1, 4, 48 ], [ 63, 1, 7, 24 ], [ 63, 1, 13, 48 ], [ 63, 1, 23, 64 ], [ 63, 1, 31, 64 ], [ 64, 1, 9, 96 ], [ 64, 1, 10, 48 ], [ 64, 1, 14, 96 ], [ 65, 1, 40, 64 ], [ 66, 1, 28, 96 ] ] k = 98: F-action on Pi is () [67,1,98] Dynkin type is A_0(q) + T(phi1 phi2^3 phi4 phi6) Order of center |Z^F|: phi1 phi2^3 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 2 modulo 60: 1/192 q^4 phi1 phi2^2 ( q-2 ) q congruent 3 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 4 modulo 60: 1/192 q^4 phi1 phi2^2 ( q-2 ) q congruent 5 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 7 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 8 modulo 60: 1/192 q^4 phi1 phi2^2 ( q-2 ) q congruent 9 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 11 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 13 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 16 modulo 60: 1/192 q^4 phi1 phi2^2 ( q-2 ) q congruent 17 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 19 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 21 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 23 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 25 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 27 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 29 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 31 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 32 modulo 60: 1/192 q^4 phi1 phi2^2 ( q-2 ) q congruent 37 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 41 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 43 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 47 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 49 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 53 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) q congruent 59 modulo 60: 1/192 q phi1^2 phi2^2 ( q^3-q^2-q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 98 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 10 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 12 ], [ 18, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 32 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 16 ], [ 27, 1, 4, 6 ], [ 28, 1, 2, 8 ], [ 29, 1, 4, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 4, 8 ], [ 33, 1, 6, 8 ], [ 33, 1, 10, 32 ], [ 35, 1, 7, 16 ], [ 36, 1, 4, 16 ], [ 37, 1, 2, 16 ], [ 37, 1, 3, 32 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 40, 1, 2, 4 ], [ 40, 1, 6, 24 ], [ 41, 1, 2, 16 ], [ 41, 1, 5, 16 ], [ 41, 1, 8, 8 ], [ 41, 1, 10, 16 ], [ 42, 1, 5, 12 ], [ 43, 1, 8, 16 ], [ 43, 1, 9, 8 ], [ 43, 1, 13, 32 ], [ 44, 1, 4, 16 ], [ 44, 1, 5, 16 ], [ 44, 1, 6, 8 ], [ 44, 1, 7, 30 ], [ 45, 1, 4, 24 ], [ 47, 1, 10, 16 ], [ 48, 1, 9, 32 ], [ 48, 1, 10, 32 ], [ 50, 1, 10, 24 ], [ 51, 1, 3, 16 ], [ 51, 1, 4, 8 ], [ 51, 1, 9, 16 ], [ 52, 1, 5, 16 ], [ 53, 1, 12, 32 ], [ 53, 1, 13, 16 ], [ 53, 1, 14, 32 ], [ 53, 1, 15, 36 ], [ 53, 1, 18, 12 ], [ 54, 1, 9, 32 ], [ 54, 1, 10, 48 ], [ 55, 1, 11, 16 ], [ 55, 1, 19, 32 ], [ 55, 1, 20, 32 ], [ 56, 1, 16, 32 ], [ 56, 1, 17, 24 ], [ 59, 1, 5, 72 ], [ 59, 1, 16, 32 ], [ 59, 1, 20, 12 ], [ 59, 1, 24, 32 ], [ 60, 1, 9, 96 ], [ 60, 1, 10, 24 ], [ 61, 1, 16, 32 ], [ 62, 1, 9, 48 ], [ 63, 1, 6, 24 ], [ 63, 1, 9, 48 ], [ 63, 1, 12, 48 ], [ 63, 1, 25, 64 ], [ 63, 1, 30, 64 ], [ 64, 1, 11, 48 ], [ 64, 1, 12, 96 ], [ 64, 1, 18, 96 ], [ 65, 1, 42, 64 ], [ 66, 1, 29, 96 ] ] k = 99: F-action on Pi is () [67,1,99] Dynkin type is A_0(q) + T(phi1 phi2 phi3 phi4 phi6) Order of center |Z^F|: phi1 phi2 phi3 phi4 phi6 Numbers of classes in class type: q congruent 1 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 2 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 3 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 4 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 5 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 7 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 8 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 9 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 11 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 13 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 16 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 17 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 19 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 21 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 23 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 25 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 27 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 29 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 31 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 32 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 37 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 41 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 43 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 47 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 49 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 53 modulo 60: 1/72 q^4 phi1^2 phi2^2 q congruent 59 modulo 60: 1/72 q^4 phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 99 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 27, 1, 5, 6 ], [ 32, 1, 2, 4 ], [ 38, 1, 4, 12 ], [ 38, 1, 9, 12 ], [ 39, 1, 5, 4 ], [ 43, 1, 9, 8 ], [ 44, 1, 3, 6 ], [ 44, 1, 7, 6 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 8 ], [ 53, 1, 15, 12 ], [ 53, 1, 17, 12 ], [ 55, 1, 7, 12 ], [ 55, 1, 18, 12 ], [ 58, 1, 5, 8 ], [ 58, 1, 24, 36 ], [ 63, 1, 6, 24 ], [ 63, 1, 7, 24 ], [ 64, 1, 26, 36 ], [ 65, 1, 24, 24 ], [ 65, 1, 25, 24 ] ] k = 100: F-action on Pi is () [67,1,100] Dynkin type is A_0(q) + T(phi1 phi2 phi4 phi12) Order of center |Z^F|: phi1 phi2 phi4 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 2 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 3 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 4 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 5 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 7 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 8 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 9 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 11 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 13 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 16 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 17 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 19 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 21 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 23 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 25 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 27 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 29 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 31 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 32 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 37 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 41 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 43 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 47 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 49 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 53 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) q congruent 59 modulo 60: 1/24 q^2 phi1 phi2 phi4 ( q^2-2 ) Fusion of maximal tori of C^F in those of G^F: [ 100 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 32, 1, 5, 4 ], [ 39, 1, 2, 4 ], [ 43, 1, 11, 8 ], [ 58, 1, 19, 8 ], [ 58, 1, 20, 12 ], [ 64, 1, 24, 12 ] ] k = 101: F-action on Pi is () [67,1,101] Dynkin type is A_0(q) + T(phi1 phi2 phi3 phi12) Order of center |Z^F|: phi1 phi2 phi3 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 2 modulo 60: 1/48 q^3 phi1 phi2 ( q^3-2 ) q congruent 3 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 4 modulo 60: 1/48 q^3 phi1 phi2 ( q^3-2 ) q congruent 5 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 7 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 8 modulo 60: 1/48 q^3 phi1 phi2 ( q^3-2 ) q congruent 9 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 11 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 13 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 16 modulo 60: 1/48 q^3 phi1 phi2 ( q^3-2 ) q congruent 17 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 19 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 21 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 23 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 25 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 27 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 29 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 31 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 32 modulo 60: 1/48 q^3 phi1 phi2 ( q^3-2 ) q congruent 37 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 41 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 43 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 47 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 49 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 53 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) q congruent 59 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3+q^2+q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 101 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 27, 1, 2, 4 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 6 ], [ 59, 1, 11, 12 ], [ 59, 1, 14, 12 ], [ 60, 1, 16, 12 ], [ 62, 1, 15, 24 ], [ 65, 1, 12, 24 ], [ 66, 1, 16, 24 ] ] k = 102: F-action on Pi is () [67,1,102] Dynkin type is A_0(q) + T(phi1 phi2 phi6 phi12) Order of center |Z^F|: phi1 phi2 phi6 phi12 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 2 modulo 60: 1/48 q^5 phi1 phi2 ( q-2 ) q congruent 3 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 4 modulo 60: 1/48 q^5 phi1 phi2 ( q-2 ) q congruent 5 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 7 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 8 modulo 60: 1/48 q^5 phi1 phi2 ( q-2 ) q congruent 9 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 11 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 13 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 16 modulo 60: 1/48 q^5 phi1 phi2 ( q-2 ) q congruent 17 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 19 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 21 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 23 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 25 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 27 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 29 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 31 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 32 modulo 60: 1/48 q^5 phi1 phi2 ( q-2 ) q congruent 37 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 41 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 43 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 47 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 49 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 53 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) q congruent 59 modulo 60: 1/48 q^2 phi1^2 phi2 ( q^3-q^2-q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 102 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 27, 1, 3, 4 ], [ 40, 1, 4, 6 ], [ 52, 1, 7, 6 ], [ 59, 1, 11, 12 ], [ 59, 1, 15, 12 ], [ 60, 1, 16, 12 ], [ 62, 1, 14, 24 ], [ 65, 1, 13, 24 ], [ 66, 1, 15, 24 ] ] k = 103: F-action on Pi is () [67,1,103] Dynkin type is A_0(q) + T(phi1 phi2 phi7) Order of center |Z^F|: phi1 phi2 phi7 Numbers of classes in class type: q congruent 1 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 2 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 3 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 4 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 5 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 7 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 8 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 9 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 11 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 13 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 16 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 17 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 19 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 21 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 23 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 25 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 27 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 29 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 31 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 32 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 37 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 41 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 43 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 47 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 49 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 53 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 q congruent 59 modulo 60: 1/28 q^2 phi1 phi2 phi3 phi6 Fusion of maximal tori of C^F in those of G^F: [ 103 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 18, 1, 1, 2 ], [ 26, 1, 3, 4 ], [ 36, 1, 2, 4 ], [ 66, 1, 2, 14 ] ] k = 104: F-action on Pi is () [67,1,104] Dynkin type is A_0(q) + T(phi1 phi2 phi14) Order of center |Z^F|: phi1 phi2 phi14 Numbers of classes in class type: q congruent 1 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 2 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 3 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 4 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 5 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 7 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 8 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 9 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 11 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 13 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 16 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 17 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 19 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 21 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 23 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 25 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 27 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 29 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 31 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 32 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 37 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 41 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 43 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 47 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 49 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 53 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) q congruent 59 modulo 60: 1/28 q phi1 phi2 phi3 phi6 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 104 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 18, 1, 2, 2 ], [ 26, 1, 2, 4 ], [ 36, 1, 3, 4 ], [ 66, 1, 3, 14 ] ] k = 105: F-action on Pi is () [67,1,105] Dynkin type is A_0(q) + T(phi1 phi2 phi9) Order of center |Z^F|: phi1 phi2 phi9 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 2 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 3 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 4 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 5 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 7 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 8 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 9 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 11 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 13 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 16 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 17 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 19 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 21 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 23 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 25 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 27 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 29 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 31 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 32 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 37 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 41 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 43 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 47 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 49 modulo 60: 1/36 q phi1^2 phi3 ( q^3+2 ) q congruent 53 modulo 60: 1/36 q^4 phi1 phi2 phi6 q congruent 59 modulo 60: 1/36 q^4 phi1 phi2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 105 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 5, 6 ], [ 27, 1, 2, 4 ], [ 38, 1, 15, 12 ], [ 65, 1, 7, 18 ], [ 66, 1, 11, 18 ] ] k = 106: F-action on Pi is () [67,1,106] Dynkin type is A_0(q) + T(phi1 phi2 phi18) Order of center |Z^F|: phi1 phi2 phi18 Numbers of classes in class type: q congruent 1 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 2 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 3 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 4 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 5 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 7 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 8 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 9 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 11 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 13 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 16 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 17 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 19 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 21 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 23 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 25 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 27 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 29 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 31 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 32 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 37 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 41 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 43 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 47 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 49 modulo 60: 1/36 q^3 phi1 phi2 phi3 ( q-2 ) q congruent 53 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) q congruent 59 modulo 60: 1/36 phi2^2 phi6 ( q^4-2*q^3-2*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 106 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 6, 6 ], [ 27, 1, 3, 4 ], [ 38, 1, 16, 12 ], [ 65, 1, 15, 18 ], [ 66, 1, 19, 18 ] ] k = 107: F-action on Pi is () [67,1,107] Dynkin type is A_0(q) + T(phi1 phi2 phi4 phi5) Order of center |Z^F|: phi1 phi2 phi4 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 2 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 3 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 4 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 5 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 7 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 8 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 9 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 11 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 13 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 16 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 17 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 19 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 21 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 23 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 25 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 27 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 29 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 31 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 32 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 37 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 41 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 43 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 47 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 49 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 53 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 q congruent 59 modulo 60: 1/40 q^3 phi1 phi2^2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 107 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], [ 14, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 30, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 44, 1, 4, 8 ], [ 54, 1, 4, 8 ], [ 54, 1, 6, 10 ], [ 63, 1, 2, 10 ], [ 64, 1, 3, 20 ] ] k = 108: F-action on Pi is () [67,1,108] Dynkin type is A_0(q) + T(phi1 phi2 phi4 phi10) Order of center |Z^F|: phi1 phi2 phi4 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 2 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 3 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 4 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 5 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 7 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 8 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 9 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 11 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 13 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 16 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 17 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 19 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 21 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 23 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 25 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 27 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 29 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 31 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 32 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 37 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 41 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 43 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 47 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 49 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 53 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 q congruent 59 modulo 60: 1/40 q^3 phi1^2 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 108 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 30, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 44, 1, 6, 8 ], [ 54, 1, 8, 10 ], [ 54, 1, 9, 8 ], [ 63, 1, 3, 10 ], [ 64, 1, 4, 20 ] ] k = 109: F-action on Pi is () [67,1,109] Dynkin type is A_0(q) + T(phi1 phi2 phi3 phi8) Order of center |Z^F|: phi1 phi2 phi3 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 2 modulo 60: 1/48 q^5 phi1 phi2^2 q congruent 3 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 4 modulo 60: 1/48 q^5 phi1 phi2^2 q congruent 5 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 7 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 8 modulo 60: 1/48 q^5 phi1 phi2^2 q congruent 9 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 11 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 13 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 16 modulo 60: 1/48 q^5 phi1 phi2^2 q congruent 17 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 19 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 21 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 23 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 25 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 27 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 29 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 31 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 32 modulo 60: 1/48 q^5 phi1 phi2^2 q congruent 37 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 41 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 43 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 47 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 49 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 53 modulo 60: 1/48 q phi1^2 phi2^3 phi4 q congruent 59 modulo 60: 1/48 q phi1^2 phi2^3 phi4 Fusion of maximal tori of C^F in those of G^F: [ 109 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 33, 1, 5, 8 ], [ 40, 1, 3, 4 ], [ 44, 1, 3, 6 ], [ 59, 1, 19, 12 ], [ 59, 1, 25, 8 ], [ 60, 1, 7, 24 ], [ 63, 1, 18, 16 ], [ 65, 1, 34, 16 ] ] k = 110: F-action on Pi is () [67,1,110] Dynkin type is A_0(q) + T(phi1 phi2 phi6 phi8) Order of center |Z^F|: phi1 phi2 phi6 phi8 Numbers of classes in class type: q congruent 1 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 2 modulo 60: 1/48 q^5 phi1^2 phi2 q congruent 3 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 4 modulo 60: 1/48 q^5 phi1^2 phi2 q congruent 5 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 7 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 8 modulo 60: 1/48 q^5 phi1^2 phi2 q congruent 9 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 11 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 13 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 16 modulo 60: 1/48 q^5 phi1^2 phi2 q congruent 17 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 19 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 21 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 23 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 25 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 27 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 29 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 31 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 32 modulo 60: 1/48 q^5 phi1^2 phi2 q congruent 37 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 41 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 43 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 47 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 49 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 53 modulo 60: 1/48 q phi1^3 phi2^2 phi4 q congruent 59 modulo 60: 1/48 q phi1^3 phi2^2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 110 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 33, 1, 9, 8 ], [ 40, 1, 2, 4 ], [ 44, 1, 7, 6 ], [ 59, 1, 20, 12 ], [ 59, 1, 25, 8 ], [ 60, 1, 6, 24 ], [ 63, 1, 17, 16 ], [ 65, 1, 35, 16 ] ] k = 111: F-action on Pi is () [67,1,111] Dynkin type is A_0(q) + T(phi1 phi2 phi3 phi5) Order of center |Z^F|: phi1 phi2 phi3 phi5 Numbers of classes in class type: q congruent 1 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 2 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 3 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 4 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 5 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 7 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 8 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 9 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 11 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 13 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 16 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 17 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 19 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 21 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 23 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 25 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 27 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 29 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 31 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 32 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 37 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 41 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 43 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 47 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 49 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 53 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 q congruent 59 modulo 60: 1/60 q^3 phi1 phi2^2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 111 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 15, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 26, 1, 3, 4 ], [ 27, 1, 5, 6 ], [ 29, 1, 2, 4 ], [ 42, 1, 3, 6 ], [ 45, 1, 3, 6 ], [ 50, 1, 6, 12 ], [ 54, 1, 6, 10 ], [ 54, 1, 7, 12 ], [ 61, 1, 2, 10 ], [ 65, 1, 3, 20 ], [ 66, 1, 5, 30 ] ] k = 112: F-action on Pi is () [67,1,112] Dynkin type is A_0(q) + T(phi1 phi2 phi6 phi10) Order of center |Z^F|: phi1 phi2 phi6 phi10 Numbers of classes in class type: q congruent 1 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 2 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 3 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 4 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 5 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 7 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 8 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 9 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 11 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 13 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 16 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 17 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 19 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 21 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 23 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 25 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 27 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 29 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 31 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 32 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 37 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 41 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 43 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 47 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 49 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 53 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) q congruent 59 modulo 60: 1/60 q^2 phi1^2 phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 112 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 15, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 26, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 29, 1, 3, 4 ], [ 42, 1, 5, 6 ], [ 45, 1, 4, 6 ], [ 50, 1, 7, 12 ], [ 54, 1, 8, 10 ], [ 54, 1, 11, 12 ], [ 61, 1, 3, 10 ], [ 65, 1, 5, 20 ], [ 66, 1, 6, 30 ] ]