Centralizers of semisimple elements in E7(q)_sc -------------------------------------------- |G(q)| = q^63 phi1^7 phi2^7 phi3^3 phi4^2 phi5 phi6^3 phi7 phi8 phi9 phi10 phi\ 12 phi14 phi18 Semisimple class types: i = 1: Pi = [ 1, 2, 3, 4, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [1,1,1] Dynkin type is E_7(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 12: 2 q congruent 2 modulo 12: 1 q congruent 3 modulo 12: 2 q congruent 4 modulo 12: 1 q congruent 5 modulo 12: 2 q congruent 7 modulo 12: 2 q congruent 8 modulo 12: 1 q congruent 9 modulo 12: 2 q congruent 11 modulo 12: 2 Fusion of maximal tori of C^F in those of G^F: [ 1 .. 60 ] elements of other class types in center: [ ] i = 2: Pi = [ 1, 2, 3, 4, 5, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [2,1,1] Dynkin type is D_6(q) + A_1(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 2 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 2 q congruent 7 modulo 12: 2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 2 q congruent 11 modulo 12: 2 Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 33, 3, 34, 2, 31, 32, 4, 41, 10, 35, 5, 40, 11, 34, 2, 4, 35, 9, 42, 13, 43, 5, 34, 12, 39, 33, 5, 35, 3, 42, 12, 6, 45, 16, 48, 18, 46, 15, 36, 45, 18, 57, 28, 48, 15, 58, 27, 8, 49, 19, 38, 41, 13, 53, 23, 43, 11, 10, 43, 13, 40, 24, 54, 14, 56, 26, 44, 50, 21, 51, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 3: Pi = [ 1, 2, 3, 4, 6, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [3,1,1] Dynkin type is A_5(q) + A_2(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 12: 2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 1 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 6, 32, 4, 45, 4, 35, 18, 33, 5, 46, 6, 45, 8, 45, 18, 49, 8, 49, 7, 41, 13, 58, 10, 43, 27, 14, 56, 30, 50, 21, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 1, 4)( 2,126)( 6, 7) [3,1,2] Dynkin type is ^2A_5(q) + ^2A_2(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 12: 0 q congruent 2 modulo 12: 1 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 2 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 1 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 2 Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 36, 2, 34, 15, 34, 5, 48, 3, 35, 16, 36, 15, 38, 15, 48, 19, 38, 19, 37, 11, 43, 28, 40, 13, 57, 44, 26, 60, 20, 51, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 4: Pi = [ 1, 2, 3, 5, 6, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [4,1,1] Dynkin type is A_3(q) + A_3(q) + A_1(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 4 8, 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 12: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 4, 33, 6, 45, 41, 10, 32, 4, 4, 35, 35, 5, 45, 18, 13, 43, 4, 33, 35, 5, 3, 34, 18, 46, 40, 11, 6, 45, 45, 18, 18, 46, 8, 49, 58, 27, 41, 10, 13, 43, 40, 11, 58, 27, 12, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 3,126)( 5, 7) [4,1,2] Dynkin type is ^2A_3(q) + ^2A_3(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 8, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1 Fusion of maximal tori of C^F in those of G^F: [ 2, 31, 34, 2, 3, 34, 15, 36, 40, 11, 34, 2, 5, 34, 35, 5, 48, 15, 13, 43, 3, 34, 35, 5, 4, 33, 16, 48, 41, 10, 15, 36, 48, 15, 16, 48, 19, 38, 57, 28, 40, 11, 13, 43, 41, 10, 57, 28, 9, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 3: F-action on Pi is ( 1, 6)( 3, 5)( 7,126) [4,1,3] Dynkin type is A_3(q^2) + 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 4, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 33, 5, 10, 43, 42, 12, 50, 21, 24, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 4: F-action on Pi is ( 1, 6)( 3, 7)( 5,126) [4,1,4] Dynkin type is A_3(q^2) + 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 4, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 35, 3, 13, 40, 42, 12, 51, 20, 24, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 5: Pi = [ 1, 3, 4, 5, 6, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [5,1,1] Dynkin type is A_7(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 12: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 35, 3, 6, 45, 18, 8, 49, 41, 13, 40, 58, 12, 14, 56, 30, 51, 20, 22, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 1, 6)( 3, 5)( 7,126) [5,1,2] Dynkin type is ^2A_7(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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1 Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 34, 5, 33, 36, 15, 48, 38, 19, 11, 43, 10, 28, 42, 44, 26, 60, 21, 50, 52, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 6: Pi = [ 1, 2, 3, 4, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [6,1,1] Dynkin type is E_6(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-3 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-2 ) q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 ( q-3 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 3, 4, 7, 6, 8, 9, 13, 14, 17, 16, 20, 18, 25, 29, 32, 35, 40, 41, 45, 49, 51, 53, 56, 57 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 2: F-action on Pi is (1,6)(3,5) [6,1,2] Dynkin type is ^2E_6(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 1/2 q q congruent 3 modulo 12: 1/2 phi1 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 phi1 q congruent 8 modulo 12: 1/2 q q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 31, 33, 34, 37, 36, 38, 39, 43, 44, 47, 46, 50, 48, 55, 59, 2, 5, 10, 11, 15, 19, 21, 23, 26, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 7: Pi = [ 1, 2, 3, 4, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [7,1,1] Dynkin type is D_5(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 12: ( q-3 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-2 ) q congruent 5 modulo 12: ( q-3 ) q congruent 7 modulo 12: ( q-3 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: ( q-3 ) q congruent 11 modulo 12: ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 33, 3, 34, 32, 4, 41, 10, 35, 5, 40, 11, 4, 35, 9, 42, 13, 43, 6, 45, 16, 48, 18, 46, 45, 18, 57, 28, 41, 13, 53, 23, 14, 56 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 2: F-action on Pi is (2,5) [7,1,2] Dynkin type is ^2D_5(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 12: phi1 q congruent 2 modulo 12: 1/2 q q congruent 3 modulo 12: phi1 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: phi1 q congruent 7 modulo 12: phi1 q congruent 8 modulo 12: 1/2 q q congruent 9 modulo 12: phi1 q congruent 11 modulo 12: phi1 Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 3, 34, 2, 31, 41, 10, 35, 5, 40, 11, 34, 2, 13, 43, 5, 34, 12, 39, 16, 48, 18, 46, 15, 36, 48, 15, 58, 27, 53, 23, 43, 11, 26, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 8: Pi = [ 1, 2, 3, 4, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [8,1,1] Dynkin type is A_4(q) + A_2(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-9 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-4 ) q congruent 5 modulo 12: 1/2 ( q-5 ) q congruent 7 modulo 12: 1/2 ( q-7 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 ( q-5 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 6, 32, 4, 45, 4, 35, 18, 6, 45, 8, 45, 18, 49, 41, 13, 58, 14, 56, 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ] ] k = 2: F-action on Pi is (1,2)(3,4)(6,7) [8,1,2] Dynkin type is ^2A_4(q) + ^2A_2(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 1/2 ( q-5 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 ( q-7 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 36, 2, 34, 15, 34, 5, 48, 36, 15, 38, 15, 48, 19, 11, 43, 28, 44, 26, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ] ] i = 9: Pi = [ 1, 2, 3, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [9,1,1] Dynkin type is A_3(q) + A_2(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 12: ( q-7 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-4 ) q congruent 5 modulo 12: ( q-5 ) q congruent 7 modulo 12: ( q-5 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: ( q-5 ) q congruent 11 modulo 12: ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 6, 45, 32, 4, 4, 35, 45, 18, 4, 33, 35, 5, 18, 46, 6, 45, 45, 18, 8, 49, 41, 10, 13, 43, 58, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ] ] k = 2: F-action on Pi is (1,3)(5,7) [9,1,2] Dynkin type is ^2A_3(q) + ^2A_2(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 12: phi1 q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: ( q-3 ) q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: ( q-3 ) q congruent 7 modulo 12: ( q-3 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: phi1 q congruent 11 modulo 12: ( q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 31, 34, 2, 15, 36, 34, 2, 5, 34, 48, 15, 3, 34, 35, 5, 16, 48, 15, 36, 48, 15, 19, 38, 40, 11, 13, 43, 57, 28 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ] ] i = 10: Pi = [ 1, 2, 3, 5, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [10,1,1] Dynkin type is A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 ( q-5 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 ( q-5 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 33, 32, 4, 4, 35, 4, 35, 35, 5, 4, 35, 35, 3, 33, 5, 5, 34, 6, 45, 45, 18, 45, 18, 18, 46, 41, 13, 13, 40, 10, 43, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 2 ] ] k = 2: F-action on Pi is (5,7) [10,1,2] Dynkin type is A_3(q) + A_1(q) + A_1(q^2) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 33, 10, 35, 13, 5, 43, 3, 40, 34, 11, 18, 58, 46, 27, 40, 12, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 7, 1, 2, 2 ] ] k = 3: F-action on Pi is ( 3,126)( 5, 7) [10,1,3] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q^2) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 40, 34, 11, 35, 13, 5, 43, 4, 41, 33, 10, 16, 57, 48, 28, 41, 9, 10, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ] ] k = 4: F-action on Pi is ( 3,126) [10,1,4] Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 34, 2, 34, 2, 2, 31, 35, 5, 5, 34, 5, 34, 34, 2, 4, 35, 35, 3, 33, 5, 5, 34, 16, 48, 48, 15, 48, 15, 15, 36, 41, 13, 13, 40, 10, 43, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 2 ] ] i = 11: Pi = [ 1, 2, 4, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [11,1,1] Dynkin type is A_5(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 12: ( q-5 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-4 ) q congruent 5 modulo 12: ( q-3 ) q congruent 7 modulo 12: ( q-5 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: ( q-3 ) q congruent 11 modulo 12: ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 4, 35, 33, 5, 6, 45, 45, 18, 8, 49, 41, 13, 10, 43, 14, 56, 50, 21 ] 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 (2,7)(4,6) [11,1,2] Dynkin type is ^2A_5(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 12: phi1 q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: phi1 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: ( q-3 ) q congruent 7 modulo 12: phi1 q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: phi1 q congruent 11 modulo 12: ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 31, 34, 2, 5, 34, 35, 3, 15, 36, 48, 15, 19, 38, 43, 11, 13, 40, 26, 44, 51, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ] ] i = 12: Pi = [ 1, 2, 4, 6, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [12,1,1] Dynkin type is A_2(q) + A_2(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 12: 1/6 ( q-7 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 1/6 ( q-4 ) q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1/6 ( q-7 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 6, 32, 4, 45, 6, 45, 8, 32, 4, 45, 4, 35, 18, 45, 18, 49, 6, 45, 8, 45, 18, 49, 8, 49, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 6, 1, 1, 2 ] ] k = 2: F-action on Pi is (2,6)(4,7) [12,1,2] Dynkin type is A_2(q) + A_2(q^2) + 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 12: 1/2 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1/2 phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 33, 10, 50, 5, 43, 21, 46, 27, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 2, 2 ] ] k = 3: F-action on Pi is ( 1, 2, 6)( 4, 7,126) [12,1,3] Dynkin type is A_2(q^3) + 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 12: 1/3 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 1/3 phi1 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1/3 phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 8, 51, 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 6, 1, 1, 2 ] ] k = 4: F-action on Pi is ( 1, 4, 6,126, 2, 7) [12,1,4] Dynkin type is ^2A_2(q^3) + 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 12: 0 q congruent 2 modulo 12: 1/3 phi2 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/3 phi2 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 1/3 phi2 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1/3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 38, 21, 55 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 6, 1, 2, 2 ] ] k = 5: F-action on Pi is ( 1, 4)( 2,126)( 6, 7) [12,1,5] Dynkin type is A_2(q^2) + ^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 12: 0 q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 35, 16, 40, 13, 57, 20, 51, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ] ] k = 6: F-action on Pi is ( 1,126)( 2, 4)( 6, 7) [12,1,6] Dynkin type is ^2A_2(q) + ^2A_2(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 12: 0 q congruent 2 modulo 12: 1/6 ( q-2 ) q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 ( q-5 ) q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 1/6 ( q-2 ) q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1/6 ( q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 36, 2, 34, 15, 36, 15, 38, 2, 34, 15, 34, 5, 48, 15, 48, 19, 36, 15, 38, 15, 48, 19, 38, 19, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 6 ], [ 6, 1, 2, 2 ] ] i = 13: Pi = [ 1, 3, 4, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [13,1,1] Dynkin type is A_6(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-5 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-2 ) q congruent 5 modulo 12: 1/2 ( q-5 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 ( q-5 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 35, 6, 45, 18, 8, 41, 13, 58, 14, 56, 51, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 1, 2 ] ] k = 2: F-action on Pi is (1,7)(3,6)(4,5) [13,1,2] Dynkin type is ^2A_6(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 1/2 q q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 1/2 q q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 34, 5, 36, 15, 48, 38, 11, 43, 28, 44, 26, 21, 52 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 2, 2 ] ] i = 14: Pi = [ 1, 3, 4, 5, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [14,1,1] Dynkin type is A_5(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 12: 1/2 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 ( q-5 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 ( q-5 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 4, 35, 35, 3, 6, 45, 45, 18, 8, 49, 41, 13, 13, 40, 14, 56, 51, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 1, 4)( 5,126) [14,1,2] Dynkin type is ^2A_5(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 12: 1/2 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 31, 34, 2, 5, 34, 33, 5, 15, 36, 48, 15, 19, 38, 43, 11, 10, 43, 26, 44, 50, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ] ] i = 15: Pi = [ 1, 3, 5, 6, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [15,1,1] Dynkin type is A_3(q) + A_3(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 12: 1/4 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 ( q-5 ) q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 6, 41, 32, 4, 35, 45, 13, 4, 35, 3, 18, 40, 6, 45, 18, 8, 58, 41, 13, 40, 58, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 16, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 3,126)( 5, 7) [15,1,2] Dynkin type is ^2A_3(q) + ^2A_3(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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 34, 3, 15, 40, 34, 5, 35, 48, 13, 3, 35, 4, 16, 41, 15, 48, 16, 19, 57, 40, 13, 41, 57, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 16, 1, 1, 2 ] ] k = 3: F-action on Pi is () [15,1,3] Dynkin type is A_3(q) + A_3(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 12: 1/4 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 33, 45, 10, 4, 35, 5, 18, 43, 33, 5, 34, 46, 11, 45, 18, 46, 49, 27, 10, 43, 11, 27, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 16, 1, 2, 2 ] ] k = 4: F-action on Pi is ( 3,126)( 5, 7) [15,1,4] Dynkin type is ^2A_3(q) + ^2A_3(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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 34, 36, 11, 2, 34, 5, 15, 43, 34, 5, 33, 48, 10, 36, 15, 48, 38, 28, 11, 43, 10, 28, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 16, 1, 2, 2 ] ] k = 5: F-action on Pi is ( 1, 6)( 3, 5)( 7,126) [15,1,5] Dynkin type is A_3(q^2) + 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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 10, 42, 50, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 3, 4 ], [ 5, 1, 2, 4 ], [ 16, 1, 1, 2 ] ] k = 6: F-action on Pi is ( 1, 6)( 3, 7)( 5,126) [15,1,6] Dynkin type is A_3(q^2) + 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 12: 1/4 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 35, 13, 42, 51, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 4, 4 ], [ 16, 1, 1, 2 ] ] k = 7: F-action on Pi is ( 1, 6)( 3, 5)( 7,126) [15,1,7] Dynkin type is A_3(q^2) + 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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1/4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 5, 43, 12, 21, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 3, 4 ], [ 16, 1, 2, 2 ] ] k = 8: F-action on Pi is ( 1, 6)( 3, 7)( 5,126) [15,1,8] Dynkin type is A_3(q^2) + 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 12: 1/4 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 3, 40, 12, 20, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 4, 4 ], [ 5, 1, 1, 4 ], [ 16, 1, 2, 2 ] ] i = 16: Pi = [ 2, 3, 4, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [16,1,1] Dynkin type is D_6(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 12: ( q-3 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-2 ) q congruent 5 modulo 12: ( q-3 ) q congruent 7 modulo 12: ( q-3 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: ( q-3 ) q congruent 11 modulo 12: ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 4, 3, 2, 32, 41, 35, 40, 34, 4, 9, 13, 5, 12, 33, 35, 42, 6, 16, 18, 15, 45, 57, 48, 58, 8, 19, 41, 53, 43, 10, 13, 24, 14, 26, 50, 51 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 2: F-action on Pi is () [16,1,2] Dynkin type is D_6(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 12: phi1 q congruent 2 modulo 12: 1/2 q q congruent 3 modulo 12: phi1 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: phi1 q congruent 7 modulo 12: phi1 q congruent 8 modulo 12: 1/2 q q congruent 9 modulo 12: phi1 q congruent 11 modulo 12: phi1 Fusion of maximal tori of C^F in those of G^F: [ 32, 33, 34, 31, 4, 10, 5, 11, 2, 35, 42, 43, 34, 39, 5, 3, 12, 45, 48, 46, 36, 18, 28, 15, 27, 49, 38, 13, 23, 11, 43, 40, 54, 56, 44, 21, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 17: Pi = [ 2, 3, 4, 5, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [17,1,1] Dynkin type is D_4(q) + A_1(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 ( q-3 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 4, 33, 35, 5, 3, 34, 34, 2, 32, 4, 4, 35, 41, 10, 13, 43, 35, 5, 5, 34, 4, 35, 33, 5, 4, 35, 35, 3, 9, 42, 42, 12, 6, 45, 45, 18, 16, 48, 48, 15, 41, 13, 10, 43, 41, 13, 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 3, 5)( 7,126) [17,1,2] Dynkin type is ^2D_4(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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 33, 10, 34, 11, 10, 42, 5, 43, 11, 39, 43, 12, 48, 28, 46, 27, 23, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 16, 1, 2, 2 ] ] k = 3: F-action on Pi is () [17,1,3] Dynkin type is D_4(q) + A_1(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 phi1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 33, 35, 5, 3, 34, 34, 2, 2, 31, 4, 35, 35, 5, 13, 43, 40, 11, 5, 34, 34, 2, 35, 3, 5, 34, 33, 5, 5, 34, 42, 12, 12, 39, 45, 18, 18, 46, 48, 15, 15, 36, 13, 40, 43, 11, 10, 43, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 2, 2 ] ] k = 4: F-action on Pi is ( 3, 5)( 7,126) [17,1,4] Dynkin type is ^2D_4(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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 3, 40, 41, 9, 35, 13, 40, 12, 13, 42, 16, 57, 18, 58, 53, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 16, 1, 1, 2 ] ] i = 18: Pi = [ 1, 2, 3, 4, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [18,1,1] Dynkin type is D_5(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/4 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 4, 3, 32, 41, 35, 40, 4, 9, 13, 6, 16, 18, 45, 57, 41, 53, 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 16, 1, 1, 2 ] ] k = 2: F-action on Pi is () [18,1,2] Dynkin type is D_5(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 33, 34, 4, 10, 5, 11, 35, 42, 43, 45, 48, 46, 18, 28, 13, 23, 56 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 16, 1, 2, 2 ] ] k = 3: F-action on Pi is (2,5) [18,1,3] Dynkin type is ^2D_5(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 34, 31, 10, 5, 11, 2, 43, 34, 39, 48, 46, 36, 15, 27, 23, 11, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 16, 1, 2, 2 ] ] k = 4: F-action on Pi is (2,5) [18,1,4] Dynkin type is ^2D_5(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 3, 2, 41, 35, 40, 34, 13, 5, 12, 16, 18, 15, 48, 58, 53, 43, 26 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 16, 1, 1, 2 ] ] i = 19: Pi = [ 1, 2, 3, 4, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [19,1,1] Dynkin type is A_4(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q^2-10*q+29 ) q congruent 2 modulo 12: 1/2 ( q^2-7*q+10 ) q congruent 3 modulo 12: 1/2 ( q^2-10*q+21 ) q congruent 4 modulo 12: 1/2 ( q^2-7*q+12 ) q congruent 5 modulo 12: 1/2 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/2 ( q^2-10*q+25 ) q congruent 8 modulo 12: 1/2 ( q^2-7*q+10 ) q congruent 9 modulo 12: 1/2 ( q^2-10*q+25 ) q congruent 11 modulo 12: 1/2 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 4, 35, 6, 45, 45, 18, 41, 13, 14, 56 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 1, 2 ], [ 14, 1, 1, 2 ] ] k = 2: F-action on Pi is (1,2)(3,4) [19,1,2] Dynkin type is ^2A_4(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 ( q-5 ) q congruent 2 modulo 12: 1/2 phi1 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/2 q ( q-3 ) q congruent 5 modulo 12: 1/2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/2 phi1 ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 ( q-5 ) q congruent 11 modulo 12: 1/2 ( q^2-6*q+13 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 31, 34, 2, 5, 34, 15, 36, 48, 15, 43, 11, 26, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 13, 1, 2, 2 ], [ 14, 1, 2, 2 ] ] i = 20: Pi = [ 1, 2, 3, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [20,1,1] Dynkin type is A_2(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 12: 1/4 ( q^2-14*q+57 ) q congruent 2 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/4 ( q^2-12*q+27 ) q congruent 4 modulo 12: 1/4 ( q^2-10*q+24 ) q congruent 5 modulo 12: 1/4 ( q^2-12*q+35 ) q congruent 7 modulo 12: 1/4 ( q^2-14*q+49 ) q congruent 8 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/4 ( q^2-12*q+35 ) q congruent 11 modulo 12: 1/4 ( q^2-12*q+27 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 6, 45, 32, 4, 4, 35, 45, 18, 6, 45, 45, 18, 8, 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 2 ] ] k = 2: F-action on Pi is (1,3)(5,6) [20,1,2] Dynkin type is ^2A_2(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 12: 1/4 phi1 ( q-7 ) q congruent 2 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/4 q ( q-4 ) q congruent 5 modulo 12: 1/4 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/4 phi1 ( q-7 ) q congruent 11 modulo 12: 1/4 ( q^2-10*q+33 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 31, 34, 2, 15, 36, 34, 2, 5, 34, 48, 15, 15, 36, 48, 15, 19, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 14, 1, 2, 2 ] ] k = 3: F-action on Pi is (1,5)(3,6) [20,1,3] Dynkin type is A_2(q^2) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 3, 13, 40, 51, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 4, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 5, 4 ], [ 14, 1, 1, 2 ] ] k = 4: F-action on Pi is (1,6)(3,5) [20,1,4] Dynkin type is A_2(q^2) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-5 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-4 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-5 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 5, 10, 43, 50, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 3, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 2 ] ] i = 21: Pi = [ 1, 2, 3, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [21,1,1] Dynkin type is A_2(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 12: 1/6 ( q^2-11*q+34 ) q congruent 2 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/6 ( q^2-11*q+24 ) q congruent 4 modulo 12: 1/12 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/6 ( q^2-11*q+30 ) q congruent 7 modulo 12: 1/6 ( q^2-11*q+28 ) q congruent 8 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/6 ( q^2-11*q+30 ) q congruent 11 modulo 12: 1/6 ( q^2-11*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 33, 32, 4, 4, 35, 4, 35, 35, 5, 6, 45, 45, 18, 45, 18, 18, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ] ] k = 2: F-action on Pi is (5,7) [21,1,2] Dynkin type is A_2(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 12: 1/2 phi1 ( q-2 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/2 q ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/2 phi1 ( q-2 ) q congruent 7 modulo 12: 1/2 q ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 ( q-2 ) q congruent 11 modulo 12: 1/2 q ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 33, 10, 35, 13, 5, 43, 18, 58, 46, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ] ] k = 3: F-action on Pi is (1,3)(2,5) [21,1,3] Dynkin type is ^2A_2(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 12: 1/2 phi1 ( q-2 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/2 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/2 phi1 ( q-2 ) q congruent 7 modulo 12: 1/2 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 ( q-2 ) q congruent 11 modulo 12: 1/2 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 40, 11, 35, 5, 13, 43, 16, 48, 57, 28 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ] ] k = 4: F-action on Pi is (1,3)(2,5,7) [21,1,4] Dynkin type is ^2A_2(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 12: 1/3 q phi1 q congruent 2 modulo 12: 1/6 phi2 ( q-2 ) q congruent 3 modulo 12: 1/3 q phi1 q congruent 4 modulo 12: 1/6 q phi1 q congruent 5 modulo 12: 1/3 phi2 ( q-2 ) q congruent 7 modulo 12: 1/3 q phi1 q congruent 8 modulo 12: 1/6 phi2 ( q-2 ) q congruent 9 modulo 12: 1/3 q phi1 q congruent 11 modulo 12: 1/3 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 38, 51, 19, 17, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ] ] k = 5: F-action on Pi is (2,7,5) [21,1,5] Dynkin type is A_2(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 12: 1/3 phi1 ( q+2 ) q congruent 2 modulo 12: 1/6 q phi2 q congruent 3 modulo 12: 1/3 q phi2 q congruent 4 modulo 12: 1/6 phi1 ( q+2 ) q congruent 5 modulo 12: 1/3 q phi2 q congruent 7 modulo 12: 1/3 phi1 ( q+2 ) q congruent 8 modulo 12: 1/6 q phi2 q congruent 9 modulo 12: 1/3 q phi2 q congruent 11 modulo 12: 1/3 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 8, 50, 49, 21, 7, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ] ] k = 6: F-action on Pi is (1,3) [21,1,6] Dynkin type is ^2A_2(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 12: 1/6 phi1 ( q-6 ) q congruent 2 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/6 ( q^2-7*q+12 ) q congruent 4 modulo 12: 1/12 q ( q-4 ) q congruent 5 modulo 12: 1/6 ( q^2-7*q+10 ) q congruent 7 modulo 12: 1/6 ( q^2-7*q+12 ) q congruent 8 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/6 phi1 ( q-6 ) q congruent 11 modulo 12: 1/6 ( q^2-7*q+16 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 34, 2, 34, 2, 2, 31, 35, 5, 5, 34, 5, 34, 34, 2, 16, 48, 48, 15, 48, 15, 15, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ] ] i = 22: Pi = [ 1, 2, 4, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [22,1,1] Dynkin type is A_3(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 12: 1/2 ( q^2-10*q+29 ) q congruent 2 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/2 ( q^2-10*q+21 ) q congruent 4 modulo 12: 1/4 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/2 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/2 ( q^2-10*q+25 ) q congruent 8 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/2 ( q^2-10*q+25 ) q congruent 11 modulo 12: 1/2 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 35, 4, 33, 35, 5, 6, 45, 45, 18, 41, 10, 13, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ] ] k = 2: F-action on Pi is () [22,1,2] Dynkin type is A_3(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 12: 1/2 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/2 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/2 phi1 ( q-3 ) q congruent 7 modulo 12: 1/2 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 ( q-3 ) q congruent 11 modulo 12: 1/2 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 33, 4, 35, 35, 5, 35, 5, 3, 34, 45, 18, 18, 46, 13, 43, 40, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ] ] k = 3: F-action on Pi is (2,5) [22,1,3] Dynkin type is ^2A_3(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 12: 1/2 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/2 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/2 phi1 ( q-3 ) q congruent 7 modulo 12: 1/2 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 ( q-3 ) q congruent 11 modulo 12: 1/2 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 34, 2, 35, 5, 5, 34, 4, 33, 35, 5, 16, 48, 48, 15, 41, 10, 13, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ] ] k = 4: F-action on Pi is (2,5) [22,1,4] Dynkin type is ^2A_3(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 12: 1/2 phi1 ( q-5 ) q congruent 2 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/4 q ( q-4 ) q congruent 5 modulo 12: 1/2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/2 phi1 ( q-5 ) q congruent 11 modulo 12: 1/2 ( q^2-6*q+13 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 2, 2, 31, 5, 34, 34, 2, 35, 5, 3, 34, 48, 15, 15, 36, 13, 43, 40, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ] ] i = 23: Pi = [ 1, 3, 4, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [23,1,1] Dynkin type is A_5(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 ( q^2-8*q+19 ) q congruent 2 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/4 ( q^2-8*q+19 ) q congruent 7 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/4 ( q^2-8*q+19 ) q congruent 11 modulo 12: 1/4 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 35, 6, 45, 8, 41, 13, 14, 51 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 16, 1, 1, 2 ] ] k = 2: F-action on Pi is () [23,1,2] Dynkin type is A_5(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 35, 3, 45, 18, 49, 13, 40, 56, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 16, 1, 2, 2 ] ] k = 3: F-action on Pi is (1,6)(3,5) [23,1,3] Dynkin type is ^2A_5(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 34, 5, 33, 15, 48, 19, 43, 10, 26, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 16, 1, 1, 2 ] ] k = 4: F-action on Pi is (1,6)(3,5) [23,1,4] Dynkin type is ^2A_5(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 ( q^2-4*q+7 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 ( q^2-4*q+7 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 ( q^2-4*q+7 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 34, 5, 36, 15, 38, 11, 43, 44, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 2 ], [ 16, 1, 2, 2 ] ] i = 24: Pi = [ 1, 3, 4, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [24,1,1] Dynkin type is A_3(q) + A_2(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 ( q^2-12*q+43 ) q congruent 2 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/4 ( q^2-10*q+21 ) q congruent 4 modulo 12: 1/4 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/4 ( q^2-12*q+35 ) q congruent 7 modulo 12: 1/4 ( q^2-10*q+29 ) q congruent 8 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/4 ( q^2-12*q+35 ) q congruent 11 modulo 12: 1/4 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 6, 32, 4, 45, 4, 35, 18, 6, 45, 8, 41, 13, 58 ] 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 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ] ] k = 2: F-action on Pi is () [24,1,2] Dynkin type is A_3(q) + A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-5 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-5 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-5 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 45, 4, 35, 18, 33, 5, 46, 45, 18, 49, 10, 43, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ] ] k = 3: F-action on Pi is (1,4)(6,7) [24,1,3] Dynkin type is ^2A_3(q) + ^2A_2(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-5 ) q congruent 2 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/4 q ( q-4 ) q congruent 5 modulo 12: 1/4 ( q^2-6*q+13 ) q congruent 7 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/4 phi1 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q^2-8*q+23 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 36, 2, 34, 15, 34, 5, 48, 36, 15, 38, 11, 43, 28 ] 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 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ] ] k = 4: F-action on Pi is (1,4)(6,7) [24,1,4] Dynkin type is ^2A_3(q) + ^2A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 34, 15, 34, 5, 48, 3, 35, 16, 15, 48, 19, 40, 13, 57 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ] ] i = 25: Pi = [ 1, 3, 5, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [25,1,1] Dynkin type is A_3(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 12: 1/8 ( q^2-12*q+35 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 ( q^2-12*q+35 ) q congruent 7 modulo 12: 1/8 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 ( q^2-12*q+35 ) q congruent 11 modulo 12: 1/8 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 35, 4, 35, 35, 3, 6, 45, 45, 18, 41, 13, 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 18, 1, 1, 4 ] ] k = 2: F-action on Pi is (5,7) [25,1,2] Dynkin type is A_3(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 12: 1/8 phi1 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-3 ) q congruent 7 modulo 12: 1/8 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-3 ) q congruent 11 modulo 12: 1/8 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 35, 13, 3, 40, 18, 58, 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 4 ] ] k = 3: F-action on Pi is ( 3,126)( 5, 7) [25,1,3] Dynkin type is ^2A_3(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 12: 1/8 phi1 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-3 ) q congruent 7 modulo 12: 1/8 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-3 ) q congruent 11 modulo 12: 1/8 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 40, 35, 13, 4, 41, 16, 57, 41, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 1, 4 ] ] k = 4: F-action on Pi is ( 3,126) [25,1,4] Dynkin type is ^2A_3(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 12: 1/8 phi1 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-3 ) q congruent 7 modulo 12: 1/8 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-3 ) q congruent 11 modulo 12: 1/8 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 34, 2, 35, 5, 5, 34, 4, 35, 35, 3, 16, 48, 48, 15, 41, 13, 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 18, 1, 4, 4 ] ] k = 5: F-action on Pi is () [25,1,5] Dynkin type is A_3(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 12: 1/8 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-5 ) q congruent 7 modulo 12: 1/8 phi1 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-5 ) q congruent 11 modulo 12: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 33, 4, 35, 35, 5, 33, 5, 5, 34, 45, 18, 18, 46, 10, 43, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ] ] k = 6: F-action on Pi is (5,7) [25,1,6] Dynkin type is A_3(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 12: 1/8 phi1^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1^2 q congruent 7 modulo 12: 1/8 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1^2 q congruent 11 modulo 12: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 33, 10, 5, 43, 34, 11, 46, 27, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 3, 4 ] ] k = 7: F-action on Pi is ( 3,126)( 5, 7) [25,1,7] Dynkin type is ^2A_3(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 12: 1/8 phi1^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1^2 q congruent 7 modulo 12: 1/8 phi1 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1^2 q congruent 11 modulo 12: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 11, 5, 43, 33, 10, 48, 28, 10, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 2, 4 ] ] k = 8: F-action on Pi is ( 3,126) [25,1,8] Dynkin type is ^2A_3(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 12: 1/8 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-5 ) q congruent 7 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-5 ) q congruent 11 modulo 12: 1/8 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 2, 2, 31, 5, 34, 34, 2, 33, 5, 5, 34, 48, 15, 15, 36, 10, 43, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 18, 1, 3, 4 ] ] i = 26: Pi = [ 2, 3, 4, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [26,1,1] Dynkin type is D_4(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 12: 1/4 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/8 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/8 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/8 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/4 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 35, 3, 34, 32, 4, 41, 13, 35, 5, 4, 33, 4, 35, 9, 42, 6, 45, 16, 48, 41, 10, 41, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ] ] k = 2: F-action on Pi is () [26,1,2] Dynkin type is D_4(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 12: 1/2 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/2 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/2 phi1 ( q-3 ) q congruent 7 modulo 12: 1/2 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 ( q-3 ) q congruent 11 modulo 12: 1/2 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 35, 3, 34, 2, 4, 35, 13, 40, 5, 34, 35, 5, 33, 5, 42, 12, 45, 18, 48, 15, 13, 43, 10, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ] ] k = 3: F-action on Pi is () [26,1,3] Dynkin type is D_4(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 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/8 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/8 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/8 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 5, 34, 2, 31, 35, 5, 43, 11, 34, 2, 3, 34, 5, 34, 12, 39, 18, 46, 15, 36, 40, 11, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 2, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ] ] k = 4: F-action on Pi is (2,5) [26,1,4] Dynkin type is ^2D_4(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 12: 1/2 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/2 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/2 phi1^2 q congruent 7 modulo 12: 1/2 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/2 phi1^2 q congruent 11 modulo 12: 1/2 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 3, 34, 41, 10, 35, 5, 40, 11, 13, 43, 16, 48, 18, 46, 53, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ] ] k = 5: F-action on Pi is (2,5) [26,1,5] Dynkin type is ^2D_4(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 12: 1/2 phi1 phi2 q congruent 2 modulo 12: 1/4 q^2 q congruent 3 modulo 12: 1/2 phi1 phi2 q congruent 4 modulo 12: 1/4 q^2 q congruent 5 modulo 12: 1/2 phi1 phi2 q congruent 7 modulo 12: 1/2 phi1 phi2 q congruent 8 modulo 12: 1/4 q^2 q congruent 9 modulo 12: 1/2 phi1 phi2 q congruent 11 modulo 12: 1/2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 41, 10, 40, 11, 9, 42, 13, 43, 12, 39, 42, 12, 57, 28, 58, 27, 24, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 27: Pi = [ 2, 3, 5, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [27,1,1] Dynkin type is A_1(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 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 ( q^2-10*q+25 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/16 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 ( q^2-10*q+25 ) q congruent 11 modulo 12: 1/16 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 35, 32, 4, 4, 35, 4, 35, 35, 3, 32, 4, 4, 35, 4, 35, 33, 5, 4, 33, 35, 5, 35, 5, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 24 ], [ 26, 1, 1, 8 ] ] k = 2: F-action on Pi is (5,7) [27,1,2] Dynkin type is A_1(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 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 41, 13, 35, 3, 13, 40, 33, 5, 10, 43, 5, 34, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 26, 1, 4, 4 ] ] k = 3: F-action on Pi is ( 3,126)( 5, 7) [27,1,3] Dynkin type is A_1(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 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 ( q-5 ) q congruent 7 modulo 12: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q-5 ) q congruent 11 modulo 12: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 41, 9, 33, 10, 10, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 26, 1, 1, 8 ] ] k = 4: F-action on Pi is ( 3, 5)( 7,126) [27,1,4] Dynkin type is A_1(q) + A_1(q^2) + 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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 33, 10, 10, 42, 5, 43, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 26, 1, 2, 4 ] ] k = 5: F-action on Pi is ( 3, 5,126, 7) [27,1,5] Dynkin type is A_1(q) + A_1(q^4) + 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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 42, 24, 12, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 3, 4 ], [ 4, 1, 4, 4 ], [ 26, 1, 5, 4 ] ] k = 6: F-action on Pi is ( 3, 7)( 5,126) [27,1,6] Dynkin type is A_1(q) + A_1(q^2) + 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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 35, 13, 13, 42, 3, 40, 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 4, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 26, 1, 2, 4 ] ] k = 7: F-action on Pi is (5,7) [27,1,7] Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + A_1(q) + T(phi4) Order of center |Z^F|: phi4 times 1, q congruent 0 modulo 2 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 phi2 q congruent 7 modulo 12: 1/4 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 phi2 q congruent 11 modulo 12: 1/4 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 41, 13, 9, 42, 13, 40, 42, 12, 10, 43, 42, 12, 43, 11, 12, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 26, 1, 5, 4 ] ] k = 8: F-action on Pi is () [27,1,8] Dynkin type is A_1(q) + A_1(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 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35, 4, 33, 35, 5, 4, 35, 33, 5, 35, 5, 5, 34, 4, 35, 35, 3, 35, 5, 5, 34, 35, 5, 5, 34, 3, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 12 ], [ 26, 1, 2, 4 ] ] k = 9: F-action on Pi is ( 3,126)( 5, 7) [27,1,9] Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 phi2 q congruent 7 modulo 12: 1/8 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 phi2 q congruent 11 modulo 12: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 35, 13, 13, 42, 5, 43, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 26, 1, 2, 4 ] ] k = 10: F-action on Pi is ( 3, 5,126, 7) [27,1,10] Dynkin type is A_1(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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 13, 53, 43, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 26, 1, 4, 4 ] ] k = 11: F-action on Pi is ( 3, 5)( 7,126) [27,1,11] Dynkin type is A_1(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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 5, 43, 43, 12, 34, 11, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 2, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 26, 1, 3, 8 ] ] k = 12: F-action on Pi is () [27,1,12] Dynkin type is A_1(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 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 ( q-5 ) q congruent 7 modulo 12: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q-5 ) q congruent 11 modulo 12: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 35, 5, 35, 5, 3, 34, 35, 3, 5, 34, 5, 34, 34, 2, 33, 5, 5, 34, 5, 34, 34, 2, 5, 34, 34, 2, 34, 2, 2, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 24 ], [ 26, 1, 3, 8 ] ] k = 13: F-action on Pi is ( 3,126)( 5, 7) [27,1,13] Dynkin type is A_1(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 4, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1^2 q congruent 7 modulo 12: 1/16 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1^2 q congruent 11 modulo 12: 1/16 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 40, 40, 12, 34, 11, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 26, 1, 3, 8 ] ] k = 14: F-action on Pi is ( 3, 5)( 7,126) [27,1,14] Dynkin type is A_1(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 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 41, 9, 35, 13, 13, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 1, 4, 8 ], [ 26, 1, 1, 8 ] ] i = 28: Pi = [ 2, 4, 5, 6, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [28,1,1] Dynkin type is A_5(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 12: 1/6 ( q^2-8*q+19 ) q congruent 2 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/6 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/12 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/6 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/6 ( q^2-8*q+19 ) q congruent 8 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/6 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/6 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 33, 6, 45, 8, 41, 10, 14, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 6 ], [ 16, 1, 1, 6 ] ] k = 2: F-action on Pi is (2,7)(4,6) [28,1,2] Dynkin type is ^2A_5(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 12: 1/2 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/2 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/2 phi1^2 q congruent 7 modulo 12: 1/2 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/2 phi1^2 q congruent 11 modulo 12: 1/2 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 2, 34, 5, 35, 15, 48, 19, 43, 13, 26, 51 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 16, 1, 1, 2 ] ] k = 3: F-action on Pi is () [28,1,3] Dynkin type is A_5(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 12: 1/2 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/2 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/2 phi1^2 q congruent 7 modulo 12: 1/2 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/2 phi1^2 q congruent 11 modulo 12: 1/2 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 35, 5, 45, 18, 49, 13, 43, 56, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 16, 1, 2, 2 ] ] k = 4: F-action on Pi is (2,7)(4,6) [28,1,4] Dynkin type is ^2A_5(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 12: 1/3 q phi1 q congruent 2 modulo 12: 1/6 phi2 ( q-2 ) q congruent 3 modulo 12: 1/3 q phi1 q congruent 4 modulo 12: 1/6 q phi1 q congruent 5 modulo 12: 1/3 phi2 ( q-2 ) q congruent 7 modulo 12: 1/3 q phi1 q congruent 8 modulo 12: 1/6 phi2 ( q-2 ) q congruent 9 modulo 12: 1/3 q phi1 q congruent 11 modulo 12: 1/3 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 36, 15, 48, 16, 38, 19, 37, 28, 57, 60, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ] ] k = 5: F-action on Pi is () [28,1,5] Dynkin type is A_5(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 12: 1/3 phi1 ( q+2 ) q congruent 2 modulo 12: 1/6 q phi2 q congruent 3 modulo 12: 1/3 q phi2 q congruent 4 modulo 12: 1/6 phi1 ( q+2 ) q congruent 5 modulo 12: 1/3 q phi2 q congruent 7 modulo 12: 1/3 phi1 ( q+2 ) q congruent 8 modulo 12: 1/6 q phi2 q congruent 9 modulo 12: 1/3 q phi2 q congruent 11 modulo 12: 1/3 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 6, 45, 18, 46, 8, 49, 7, 58, 27, 30, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ] ] k = 6: F-action on Pi is (2,7)(4,6) [28,1,6] Dynkin type is ^2A_5(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 12: 1/6 phi1 ( q-3 ) q congruent 2 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/6 phi1 ( q-3 ) q congruent 4 modulo 12: 1/12 q ( q-4 ) q congruent 5 modulo 12: 1/6 ( q^2-4*q+7 ) q congruent 7 modulo 12: 1/6 phi1 ( q-3 ) q congruent 8 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/6 phi1 ( q-3 ) q congruent 11 modulo 12: 1/6 ( q^2-4*q+7 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 34, 3, 36, 15, 38, 11, 40, 44, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 6 ], [ 16, 1, 2, 6 ] ] i = 29: Pi = [ 1, 2, 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [29,1,1] Dynkin type is A_4(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 ( q^3-14*q^2+69*q-128 ) q congruent 2 modulo 12: 1/12 ( q^3-13*q^2+52*q-60 ) q congruent 3 modulo 12: 1/12 ( q^3-14*q^2+69*q-108 ) q congruent 4 modulo 12: 1/12 ( q^3-13*q^2+52*q-64 ) q congruent 5 modulo 12: 1/12 ( q^3-14*q^2+69*q-120 ) q congruent 7 modulo 12: 1/12 ( q^3-14*q^2+69*q-116 ) q congruent 8 modulo 12: 1/12 ( q^3-13*q^2+52*q-60 ) q congruent 9 modulo 12: 1/12 ( q^3-14*q^2+69*q-120 ) q congruent 11 modulo 12: 1/12 ( q^3-14*q^2+69*q-108 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 6, 45, 41, 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 6 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 6 ], [ 13, 1, 1, 6 ], [ 14, 1, 1, 6 ], [ 16, 1, 1, 6 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 6 ], [ 23, 1, 1, 12 ], [ 28, 1, 1, 12 ] ] k = 2: F-action on Pi is () [29,1,2] Dynkin type is A_4(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/4 q ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/4 q ( q^2-5*q+6 ) q congruent 5 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/4 q ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 35, 45, 18, 13, 56 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 18, 1, 2, 4 ], [ 19, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 28, 1, 3, 4 ] ] k = 3: F-action on Pi is () [29,1,3] Dynkin type is A_4(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 phi1 ( q^2-q-4 ) q congruent 2 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi2 ( q-3 ) q congruent 4 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 12: 1/6 q phi2 ( q-3 ) q congruent 7 modulo 12: 1/6 phi1 ( q^2-q-4 ) q congruent 8 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi2 ( q-3 ) q congruent 11 modulo 12: 1/6 q phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 45, 18, 8, 49, 58, 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 28, 1, 5, 6 ] ] k = 4: F-action on Pi is (1,2)(3,4) [29,1,4] Dynkin type is ^2A_4(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 phi1 ( q^2-7*q+18 ) q congruent 2 modulo 12: 1/12 ( q^3-7*q^2+12*q-4 ) q congruent 3 modulo 12: 1/12 ( q^3-8*q^2+25*q-30 ) q congruent 4 modulo 12: 1/12 q ( q^2-7*q+12 ) q congruent 5 modulo 12: 1/12 ( q^3-8*q^2+25*q-26 ) q congruent 7 modulo 12: 1/12 ( q^3-8*q^2+25*q-30 ) q congruent 8 modulo 12: 1/12 ( q^3-7*q^2+12*q-4 ) q congruent 9 modulo 12: 1/12 phi1 ( q^2-7*q+18 ) q congruent 11 modulo 12: 1/12 ( q^3-8*q^2+25*q-38 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 34, 36, 15, 11, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 6 ], [ 13, 1, 2, 6 ], [ 14, 1, 2, 6 ], [ 16, 1, 2, 6 ], [ 18, 1, 3, 12 ], [ 19, 1, 2, 6 ], [ 23, 1, 4, 12 ], [ 28, 1, 6, 12 ] ] k = 5: F-action on Pi is (1,2)(3,4) [29,1,5] Dynkin type is ^2A_4(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 2 modulo 12: 1/4 q phi1 ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/4 q phi1 ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 7 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/4 q phi1 ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 11 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 34, 5, 15, 48, 43, 26 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 13, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 18, 1, 4, 4 ], [ 19, 1, 2, 2 ], [ 23, 1, 3, 4 ], [ 28, 1, 2, 4 ] ] k = 6: F-action on Pi is (1,2)(3,4) [29,1,6] Dynkin type is ^2A_4(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q phi1^2 q congruent 2 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/6 q phi1^2 q congruent 4 modulo 12: 1/6 q^2 phi1 q congruent 5 modulo 12: 1/6 phi2 ( q^2-3*q+4 ) q congruent 7 modulo 12: 1/6 q phi1^2 q congruent 8 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/6 q phi1^2 q congruent 11 modulo 12: 1/6 phi2 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 36, 15, 48, 38, 19, 28, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 28, 1, 4, 6 ] ] i = 30: Pi = [ 1, 2, 3, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [30,1,1] Dynkin type is A_2(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 12: 1/8 ( q^3-20*q^2+135*q-340 ) q congruent 2 modulo 12: 1/8 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 12: 1/8 ( q^3-20*q^2+129*q-234 ) q congruent 4 modulo 12: 1/8 ( q^3-16*q^2+80*q-128 ) q congruent 5 modulo 12: 1/8 ( q^3-20*q^2+131*q-280 ) q congruent 7 modulo 12: 1/8 ( q^3-20*q^2+133*q-294 ) q congruent 8 modulo 12: 1/8 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 12: 1/8 ( q^3-20*q^2+131*q-280 ) q congruent 11 modulo 12: 1/8 ( q^3-20*q^2+129*q-234 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 35, 6, 45, 45, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 10 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 8 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 8 ] ] k = 2: F-action on Pi is () [30,1,2] Dynkin type is A_2(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 12: 1/8 phi1 ( q^2-9*q+20 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-9*q+18 ) q congruent 4 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-9*q+20 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-9*q+18 ) q congruent 8 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-9*q+20 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-9*q+18 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 33, 4, 35, 35, 5, 45, 18, 18, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 21, 1, 1, 12 ], [ 22, 1, 2, 8 ], [ 24, 1, 2, 4 ], [ 25, 1, 5, 8 ] ] k = 3: F-action on Pi is (2,5) [30,1,3] Dynkin type is A_2(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 12: 1/8 phi1 ( q^2-3*q-2 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 q phi1 ( q-3 ) q congruent 4 modulo 12: 1/8 q ( q^2-2*q-4 ) q congruent 5 modulo 12: 1/8 phi1^2 ( q-2 ) q congruent 7 modulo 12: 1/8 phi1 phi2 ( q-4 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1^2 ( q-2 ) q congruent 11 modulo 12: 1/8 q phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 10, 5, 43, 46, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 21, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 6, 8 ] ] k = 4: F-action on Pi is (2,5) [30,1,4] Dynkin type is A_2(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 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 q ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/8 q ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/8 q ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 35, 13, 18, 58 ] 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 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 4 ], [ 21, 1, 2, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ] ] k = 5: F-action on Pi is (1,3) [30,1,5] Dynkin type is ^2A_2(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 12: 1/8 phi1 ( q^2-13*q+48 ) q congruent 2 modulo 12: 1/8 ( q^3-10*q^2+28*q-24 ) q congruent 3 modulo 12: 1/8 ( q^3-14*q^2+63*q-90 ) q congruent 4 modulo 12: 1/8 q ( q^2-10*q+24 ) q congruent 5 modulo 12: 1/8 ( q^3-14*q^2+65*q-100 ) q congruent 7 modulo 12: 1/8 ( q^3-14*q^2+63*q-90 ) q congruent 8 modulo 12: 1/8 ( q^3-10*q^2+28*q-24 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-13*q+48 ) q congruent 11 modulo 12: 1/8 ( q^3-14*q^2+67*q-142 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 2, 2, 31, 5, 34, 34, 2, 48, 15, 15, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 10 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 18, 1, 3, 4 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 21, 1, 6, 12 ], [ 22, 1, 4, 8 ], [ 24, 1, 3, 4 ], [ 25, 1, 8, 8 ] ] k = 6: F-action on Pi is (1,3) [30,1,6] Dynkin type is ^2A_2(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 12: 1/8 phi1 ( q^2-7*q+12 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 ( q^3-8*q^2+21*q-18 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-7*q+12 ) q congruent 7 modulo 12: 1/8 ( q^3-8*q^2+21*q-18 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-7*q+12 ) q congruent 11 modulo 12: 1/8 ( q^3-8*q^2+21*q-18 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 34, 2, 35, 5, 5, 34, 16, 48, 48, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 8 ], [ 24, 1, 4, 4 ], [ 25, 1, 4, 8 ] ] k = 7: F-action on Pi is (1,3)(2,5) [30,1,7] Dynkin type is ^2A_2(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 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/8 ( q^3-4*q^2+8 ) q congruent 3 modulo 12: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 ( q^3-6*q^2+7*q+6 ) q congruent 7 modulo 12: 1/8 ( q^3-6*q^2+13*q-12 ) q congruent 8 modulo 12: 1/8 ( q^3-4*q^2+8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/8 q ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 40, 35, 13, 16, 57 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 1, 5, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 1, 4 ], [ 21, 1, 3, 4 ], [ 24, 1, 4, 4 ], [ 25, 1, 3, 8 ] ] k = 8: F-action on Pi is (1,3)(2,5) [30,1,8] Dynkin type is ^2A_2(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 12: 1/8 phi1^2 ( q-2 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1^2 ( q-2 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1^2 ( q-2 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 11, 5, 43, 48, 28 ] 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 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 21, 1, 3, 4 ], [ 24, 1, 3, 4 ], [ 25, 1, 7, 8 ] ] i = 31: Pi = [ 1, 2, 4, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [31,1,1] Dynkin type is A_3(q) + A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 ( q^3-17*q^2+99*q-211 ) q congruent 2 modulo 12: 1/8 ( q^3-14*q^2+60*q-72 ) q congruent 3 modulo 12: 1/8 ( q^3-17*q^2+95*q-159 ) q congruent 4 modulo 12: 1/8 ( q^3-14*q^2+60*q-80 ) q congruent 5 modulo 12: 1/8 ( q^3-17*q^2+99*q-195 ) q congruent 7 modulo 12: 1/8 ( q^3-17*q^2+95*q-175 ) q congruent 8 modulo 12: 1/8 ( q^3-14*q^2+60*q-72 ) q congruent 9 modulo 12: 1/8 ( q^3-17*q^2+99*q-195 ) q congruent 11 modulo 12: 1/8 ( q^3-17*q^2+95*q-159 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 4, 35, 6, 45, 41, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 23, 1, 1, 8 ], [ 24, 1, 1, 8 ], [ 25, 1, 1, 8 ], [ 26, 1, 1, 8 ] ] k = 2: F-action on Pi is () [31,1,2] Dynkin type is A_3(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 12: 1/8 phi1 ( q^2-8*q+19 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-8*q+19 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-8*q+19 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35, 33, 5, 45, 18, 10, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 15, 1, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 22, 1, 1, 4 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 26, 1, 2, 4 ] ] k = 3: F-action on Pi is () [31,1,3] Dynkin type is A_3(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 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35, 35, 3, 45, 18, 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 8 ], [ 25, 1, 1, 8 ], [ 26, 1, 2, 4 ] ] k = 4: F-action on Pi is () [31,1,4] Dynkin type is A_3(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 12: 1/8 phi1^2 ( q-3 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 35, 5, 5, 34, 18, 46, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 22, 1, 2, 4 ], [ 25, 1, 5, 8 ], [ 26, 1, 3, 8 ] ] k = 5: F-action on Pi is (2,5) [31,1,5] Dynkin type is ^2A_3(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 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 2, 5, 34, 33, 5, 48, 15, 10, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 3, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 3, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 2, 4 ] ] k = 6: F-action on Pi is (2,5) [31,1,6] Dynkin type is ^2A_3(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 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 35, 5, 4, 35, 16, 48, 41, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 18, 1, 4, 4 ], [ 22, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 26, 1, 1, 8 ] ] k = 7: F-action on Pi is (2,5) [31,1,7] Dynkin type is ^2A_3(q) + A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q^2-10*q+29 ) q congruent 2 modulo 12: 1/8 ( q^3-8*q^2+16*q-8 ) q congruent 3 modulo 12: 1/8 ( q^3-11*q^2+43*q-57 ) q congruent 4 modulo 12: 1/8 q ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/8 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 12: 1/8 ( q^3-11*q^2+43*q-57 ) q congruent 8 modulo 12: 1/8 ( q^3-8*q^2+16*q-8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-10*q+29 ) q congruent 11 modulo 12: 1/8 ( q^3-11*q^2+43*q-73 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 31, 34, 2, 5, 34, 15, 36, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 8 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 14, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 3, 4 ], [ 19, 1, 2, 8 ], [ 22, 1, 4, 4 ], [ 23, 1, 4, 8 ], [ 24, 1, 3, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 3, 8 ] ] k = 8: F-action on Pi is (2,5) [31,1,8] Dynkin type is ^2A_3(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 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/8 ( q^3-7*q^2+19*q-21 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/8 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 2, 5, 34, 35, 3, 48, 15, 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 4, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 4, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 4 ] ] i = 32: Pi = [ 1, 2, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [32,1,1] Dynkin type is 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 12: 1/24 ( q^3-19*q^2+115*q-241 ) q congruent 2 modulo 12: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 12: 1/24 ( q^3-19*q^2+115*q-201 ) q congruent 4 modulo 12: 1/48 ( q^3-16*q^2+76*q-112 ) q congruent 5 modulo 12: 1/24 ( q^3-19*q^2+115*q-225 ) q congruent 7 modulo 12: 1/24 ( q^3-19*q^2+115*q-217 ) q congruent 8 modulo 12: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 12: 1/24 ( q^3-19*q^2+115*q-225 ) q congruent 11 modulo 12: 1/24 ( q^3-19*q^2+115*q-201 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 33, 32, 4, 4, 35, 4, 35, 35, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 26, 1, 1, 24 ], [ 27, 1, 1, 96 ] ] k = 2: F-action on Pi is (5,7) [32,1,2] Dynkin type is 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 12: 1/4 phi1 ( q^2-6*q+7 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/4 ( q^3-7*q^2+13*q-3 ) q congruent 4 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/4 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 12: 1/4 ( q^3-7*q^2+13*q-3 ) q congruent 8 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/4 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 12: 1/4 ( q^3-7*q^2+13*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 33, 10, 35, 13, 5, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ] ] k = 3: F-action on Pi is () [32,1,3] Dynkin type is 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 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 35, 5, 35, 5, 3, 34, 35, 5, 5, 34, 5, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 22, 1, 3, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ] ] k = 4: F-action on Pi is (5,7) [32,1,4] Dynkin type is A_1(q) + A_1(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 12: 1/4 phi1^2 phi2 q congruent 2 modulo 12: 1/8 q^3 q congruent 3 modulo 12: 1/4 phi1^2 phi2 q congruent 4 modulo 12: 1/8 q^3 q congruent 5 modulo 12: 1/4 phi1^2 phi2 q congruent 7 modulo 12: 1/4 phi1^2 phi2 q congruent 8 modulo 12: 1/8 q^3 q congruent 9 modulo 12: 1/4 phi1^2 phi2 q congruent 11 modulo 12: 1/4 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 13, 42, 43, 12, 40, 12, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ] ] k = 5: F-action on Pi is (5,7) [32,1,5] Dynkin type is A_1(q) + A_1(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 12: 1/4 phi1 ( q^2-4*q+5 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/4 ( q^3-5*q^2+9*q-9 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/4 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 12: 1/4 ( q^3-5*q^2+9*q-9 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/4 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 12: 1/4 ( q^3-5*q^2+9*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 13, 5, 43, 3, 40, 34, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ] ] k = 6: F-action on Pi is () [32,1,6] Dynkin type is 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 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35, 4, 35, 35, 5, 4, 35, 35, 3, 33, 5, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 22, 1, 2, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ] ] k = 7: F-action on Pi is () [32,1,7] Dynkin type is 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 12: 1/24 phi1 ( q^2-12*q+39 ) q congruent 2 modulo 12: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 3 modulo 12: 1/24 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 12: 1/48 q ( q^2-10*q+24 ) q congruent 5 modulo 12: 1/24 ( q^3-13*q^2+51*q-55 ) q congruent 7 modulo 12: 1/24 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 12: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 9 modulo 12: 1/24 phi1 ( q^2-12*q+39 ) q congruent 11 modulo 12: 1/24 ( q^3-13*q^2+51*q-79 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 5, 5, 34, 5, 34, 34, 2, 3, 34, 34, 2, 34, 2, 2, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 36 ], [ 21, 1, 6, 48 ], [ 22, 1, 4, 24 ], [ 26, 1, 3, 24 ], [ 27, 1, 12, 96 ] ] k = 8: F-action on Pi is (5,7) [32,1,8] Dynkin type is A_1(q) + A_1(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 12: 1/4 phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 9, 10, 42, 13, 42, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ] ] k = 9: F-action on Pi is (2,5,7) [32,1,9] Dynkin type is 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 12: 1/3 phi1 ( q^2-2 ) q congruent 2 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/3 q phi2 ( q-2 ) q congruent 4 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 12: 1/3 q phi2 ( q-2 ) q congruent 7 modulo 12: 1/3 phi1 ( q^2-2 ) q congruent 8 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/3 q phi2 ( q-2 ) q congruent 11 modulo 12: 1/3 q phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 50, 49, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 21, 1, 5, 6 ] ] k = 10: F-action on Pi is (2,5,7) [32,1,10] Dynkin type is 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 12: 1/3 q^2 phi1 q congruent 2 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/3 q^2 phi1 q congruent 4 modulo 12: 1/6 q^2 phi1 q congruent 5 modulo 12: 1/3 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/3 q^2 phi1 q congruent 8 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/3 q^2 phi1 q congruent 11 modulo 12: 1/3 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 51, 19, 20, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 21, 1, 4, 6 ] ] i = 33: Pi = [ 1, 3, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [33,1,1] Dynkin type is A_2(q) + A_2(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/24 ( q^3-17*q^2+109*q-285 ) q congruent 2 modulo 12: 1/24 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 12: 1/24 ( q^3-17*q^2+99*q-171 ) q congruent 4 modulo 12: 1/24 ( q^3-16*q^2+80*q-128 ) q congruent 5 modulo 12: 1/24 ( q^3-17*q^2+105*q-225 ) q congruent 7 modulo 12: 1/24 ( q^3-17*q^2+103*q-231 ) q congruent 8 modulo 12: 1/24 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 12: 1/24 ( q^3-17*q^2+105*q-225 ) q congruent 11 modulo 12: 1/24 ( q^3-17*q^2+99*q-171 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 6, 32, 4, 45, 6, 45, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 12 ], [ 11, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 6 ], [ 20, 1, 1, 12 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 24 ], [ 28, 1, 1, 12 ] ] k = 2: F-action on Pi is () [33,1,2] Dynkin type is A_2(q) + A_2(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 phi1 ( q^2-q-6 ) q congruent 2 modulo 12: 1/12 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi2 ( q-3 ) q congruent 4 modulo 12: 1/12 phi1 ( q^2-4 ) q congruent 5 modulo 12: 1/12 q phi2 ( q-3 ) q congruent 7 modulo 12: 1/12 phi1 ( q^2-q-6 ) q congruent 8 modulo 12: 1/12 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi2 ( q-3 ) q congruent 11 modulo 12: 1/12 q phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 45, 8, 45, 18, 49, 8, 49, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 6, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 28, 1, 5, 6 ] ] k = 3: F-action on Pi is () [33,1,3] Dynkin type is A_2(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 12: 1/8 phi1 ( q^2-6*q+11 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-6*q+11 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-6*q+11 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 45, 4, 35, 18, 45, 18, 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 2 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 20, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 8 ], [ 28, 1, 3, 4 ] ] k = 4: F-action on Pi is (1,3)(5,6) [33,1,4] Dynkin type is ^2A_2(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 12: 1/8 phi1 ( q^2-4*q+7 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 ( q^3-5*q^2+13*q-13 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-4*q+7 ) q congruent 7 modulo 12: 1/8 ( q^3-5*q^2+13*q-13 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-4*q+7 ) q congruent 11 modulo 12: 1/8 ( q^3-5*q^2+13*q-13 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 34, 15, 34, 5, 48, 15, 48, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 20, 1, 2, 4 ], [ 23, 1, 3, 4 ], [ 24, 1, 4, 8 ], [ 28, 1, 2, 4 ] ] k = 5: F-action on Pi is (1,3)(5,6) [33,1,5] Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1^2 q congruent 2 modulo 12: 1/12 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1^2 q congruent 4 modulo 12: 1/12 q^2 phi1 q congruent 5 modulo 12: 1/12 phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q phi1^2 q congruent 8 modulo 12: 1/12 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1^2 q congruent 11 modulo 12: 1/12 phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 36, 15, 38, 15, 48, 19, 38, 19, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 6 ], [ 6, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 28, 1, 4, 6 ] ] k = 6: F-action on Pi is (1,3)(5,6) [33,1,6] Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/24 phi1 ( q^2-10*q+33 ) q congruent 2 modulo 12: 1/24 ( q^3-10*q^2+28*q-24 ) q congruent 3 modulo 12: 1/24 ( q^3-11*q^2+49*q-75 ) q congruent 4 modulo 12: 1/24 q ( q^2-10*q+24 ) q congruent 5 modulo 12: 1/24 ( q^3-11*q^2+47*q-85 ) q congruent 7 modulo 12: 1/24 ( q^3-11*q^2+49*q-75 ) q congruent 8 modulo 12: 1/24 ( q^3-10*q^2+28*q-24 ) q congruent 9 modulo 12: 1/24 phi1 ( q^2-10*q+33 ) q congruent 11 modulo 12: 1/24 ( q^3-11*q^2+53*q-127 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 36, 2, 34, 15, 36, 15, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 6 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 12 ], [ 11, 1, 2, 6 ], [ 12, 1, 6, 12 ], [ 13, 1, 2, 12 ], [ 14, 1, 2, 6 ], [ 15, 1, 4, 24 ], [ 16, 1, 2, 6 ], [ 20, 1, 2, 12 ], [ 23, 1, 4, 12 ], [ 24, 1, 3, 24 ], [ 28, 1, 6, 12 ] ] k = 7: F-action on Pi is (1,5)(3,6) [33,1,7] Dynkin type is A_2(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q^2-4*q+1 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-4*q+1 ) q congruent 7 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-4*q+1 ) q congruent 11 modulo 12: 1/8 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 13, 51 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 4, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 5, 4 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 15, 1, 6, 8 ], [ 16, 1, 1, 2 ], [ 20, 1, 3, 4 ], [ 23, 1, 1, 4 ], [ 28, 1, 2, 4 ] ] k = 8: F-action on Pi is (1,5)(3,6) [33,1,8] Dynkin type is A_2(q^2) + T(phi1 phi6) Order of center |Z^F|: phi1 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1 ( q-3 ) q congruent 2 modulo 12: 1/12 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/12 q phi1 ( q-3 ) q congruent 4 modulo 12: 1/12 q phi1 ( q-2 ) q congruent 5 modulo 12: 1/12 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/12 q phi1 ( q-3 ) q congruent 8 modulo 12: 1/12 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/12 q phi1 ( q-3 ) q congruent 11 modulo 12: 1/12 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 57, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 12, 1, 5, 4 ], [ 28, 1, 4, 6 ] ] k = 9: F-action on Pi is (1,5)(3,6) [33,1,9] Dynkin type is A_2(q^2) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/24 phi1 ( q^2-6*q+3 ) q congruent 2 modulo 12: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 12: 1/24 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/24 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/24 ( q^3-7*q^2+13*q-15 ) q congruent 7 modulo 12: 1/24 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/24 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 12: 1/24 phi1 ( q^2-6*q+3 ) q congruent 11 modulo 12: 1/24 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 40, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 4, 12 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 2 ], [ 11, 1, 2, 6 ], [ 12, 1, 5, 4 ], [ 14, 1, 1, 6 ], [ 15, 1, 8, 24 ], [ 16, 1, 2, 6 ], [ 20, 1, 3, 12 ], [ 23, 1, 2, 12 ], [ 28, 1, 6, 12 ] ] k = 10: F-action on Pi is (1,6)(3,5) [33,1,10] Dynkin type is A_2(q^2) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/24 phi1 ( q^2-8*q+19 ) q congruent 2 modulo 12: 1/24 q ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/24 ( q^3-9*q^2+17*q+3 ) q congruent 4 modulo 12: 1/24 q ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/24 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/24 ( q^3-9*q^2+21*q-1 ) q congruent 8 modulo 12: 1/24 q ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/24 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/24 ( q^3-9*q^2+17*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 10, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 3, 12 ], [ 5, 1, 2, 6 ], [ 6, 1, 2, 2 ], [ 11, 1, 1, 6 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 6 ], [ 15, 1, 5, 24 ], [ 16, 1, 1, 6 ], [ 20, 1, 4, 12 ], [ 23, 1, 3, 12 ], [ 28, 1, 1, 12 ] ] k = 11: F-action on Pi is (1,6)(3,5) [33,1,11] Dynkin type is A_2(q^2) + T(phi2 phi3) Order of center |Z^F|: phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 phi1^2 ( q+2 ) q congruent 2 modulo 12: 1/12 q^2 phi2 q congruent 3 modulo 12: 1/12 q phi1 phi2 q congruent 4 modulo 12: 1/12 q phi1 ( q+2 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 q congruent 7 modulo 12: 1/12 phi1^2 ( q+2 ) q congruent 8 modulo 12: 1/12 q^2 phi2 q congruent 9 modulo 12: 1/12 q phi1 phi2 q congruent 11 modulo 12: 1/12 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 46, 27, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 12, 1, 2, 4 ], [ 28, 1, 5, 6 ] ] k = 12: F-action on Pi is (1,6)(3,5) [33,1,12] Dynkin type is A_2(q^2) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1^3 q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi4 ( q-3 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1^3 q congruent 7 modulo 12: 1/8 phi4 ( q-3 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1^3 q congruent 11 modulo 12: 1/8 phi4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 43, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 3, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 2 ], [ 15, 1, 7, 8 ], [ 16, 1, 2, 2 ], [ 20, 1, 4, 4 ], [ 23, 1, 4, 4 ], [ 28, 1, 3, 4 ] ] i = 34: Pi = [ 2, 3, 4, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [34,1,1] Dynkin type is D_4(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 ( q^3-15*q^2+71*q-105 ) q congruent 2 modulo 12: 1/48 ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/48 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 12: 1/48 ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/48 ( q^3-15*q^2+71*q-105 ) q congruent 7 modulo 12: 1/48 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 12: 1/48 ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/48 ( q^3-15*q^2+71*q-105 ) q congruent 11 modulo 12: 1/48 ( q^3-15*q^2+71*q-105 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 4, 3, 32, 41, 35, 4, 4, 9, 6, 16, 41, 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 18, 1, 1, 24 ], [ 26, 1, 1, 24 ] ] k = 2: F-action on Pi is () [34,1,2] Dynkin type is D_4(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 35, 34, 4, 13, 5, 33, 35, 42, 45, 48, 10, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ] ] k = 3: F-action on Pi is () [34,1,3] Dynkin type is D_4(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 3, 2, 35, 40, 34, 5, 5, 12, 18, 15, 43, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ] ] k = 4: F-action on Pi is () [34,1,4] Dynkin type is D_4(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/48 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/48 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/48 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/48 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/48 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/48 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/48 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/48 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 34, 31, 5, 11, 2, 34, 34, 39, 46, 36, 11, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 12 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 12 ], [ 18, 1, 3, 24 ], [ 26, 1, 3, 24 ] ] k = 5: F-action on Pi is (2,3) [34,1,5] Dynkin type is ^2D_4(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 3, 41, 35, 40, 13, 16, 18, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 26, 1, 4, 4 ] ] k = 6: F-action on Pi is (2,3) [34,1,6] Dynkin type is ^2D_4(q) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 40, 9, 13, 12, 42, 57, 58, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 26, 1, 5, 4 ] ] k = 7: F-action on Pi is (2,5) [34,1,7] Dynkin type is ^2D_4(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1^3 q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1^3 q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1^3 q congruent 7 modulo 12: 1/8 phi1^3 q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1^3 q congruent 11 modulo 12: 1/8 phi1^3 Fusion of maximal tori of C^F in those of G^F: [ 33, 34, 10, 5, 11, 43, 48, 46, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 26, 1, 4, 4 ] ] k = 8: F-action on Pi is (2,5) [34,1,8] Dynkin type is ^2D_4(q) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1^2 phi2 q congruent 2 modulo 12: 1/8 q^3 q congruent 3 modulo 12: 1/8 phi1^2 phi2 q congruent 4 modulo 12: 1/8 q^3 q congruent 5 modulo 12: 1/8 phi1^2 phi2 q congruent 7 modulo 12: 1/8 phi1^2 phi2 q congruent 8 modulo 12: 1/8 q^3 q congruent 9 modulo 12: 1/8 phi1^2 phi2 q congruent 11 modulo 12: 1/8 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 10, 11, 42, 43, 39, 12, 28, 27, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 26, 1, 5, 4 ] ] k = 9: F-action on Pi is (2,3,5) [34,1,9] Dynkin type is ^3D_4(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q phi1 phi2 q congruent 2 modulo 12: 1/6 q phi1 phi2 q congruent 3 modulo 12: 1/6 q phi1 phi2 q congruent 4 modulo 12: 1/6 q phi1 phi2 q congruent 5 modulo 12: 1/6 q phi1 phi2 q congruent 7 modulo 12: 1/6 q phi1 phi2 q congruent 8 modulo 12: 1/6 q phi1 phi2 q congruent 9 modulo 12: 1/6 q phi1 phi2 q congruent 11 modulo 12: 1/6 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 8, 51, 49, 20, 7, 29, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 6, 1, 1, 2 ] ] k = 10: F-action on Pi is (2,3,5) [34,1,10] Dynkin type is ^3D_4(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q phi1 phi2 q congruent 2 modulo 12: 1/6 q phi1 phi2 q congruent 3 modulo 12: 1/6 q phi1 phi2 q congruent 4 modulo 12: 1/6 q phi1 phi2 q congruent 5 modulo 12: 1/6 q phi1 phi2 q congruent 7 modulo 12: 1/6 q phi1 phi2 q congruent 8 modulo 12: 1/6 q phi1 phi2 q congruent 9 modulo 12: 1/6 q phi1 phi2 q congruent 11 modulo 12: 1/6 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 50, 19, 21, 38, 47, 59, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 6, 1, 2, 2 ] ] i = 35: Pi = [ 2, 4, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [35,1,1] Dynkin type is A_3(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 12: 1/24 ( q^3-16*q^2+85*q-166 ) q congruent 2 modulo 12: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 12: 1/24 ( q^3-16*q^2+85*q-138 ) q congruent 4 modulo 12: 1/48 ( q^3-16*q^2+76*q-112 ) q congruent 5 modulo 12: 1/24 ( q^3-16*q^2+85*q-150 ) q congruent 7 modulo 12: 1/24 ( q^3-16*q^2+85*q-154 ) q congruent 8 modulo 12: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 12: 1/24 ( q^3-16*q^2+85*q-150 ) q congruent 11 modulo 12: 1/24 ( q^3-16*q^2+85*q-138 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 4, 33, 6, 45, 41, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 22, 1, 1, 24 ], [ 26, 1, 1, 24 ], [ 28, 1, 1, 48 ] ] k = 2: F-action on Pi is () [35,1,2] Dynkin type is A_3(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 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/4 phi1 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35, 35, 5, 45, 18, 13, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 26, 1, 2, 4 ], [ 28, 1, 3, 8 ] ] k = 3: F-action on Pi is (2,5) [35,1,3] Dynkin type is ^2A_3(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 12: 1/8 phi1^2 ( q-4 ) q congruent 2 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 q ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 phi1^2 ( q-4 ) q congruent 7 modulo 12: 1/8 q ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 phi1^2 ( q-4 ) q congruent 11 modulo 12: 1/8 q ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 35, 5, 4, 33, 16, 48, 41, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 22, 1, 3, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ] ] k = 4: F-action on Pi is (2,5) [35,1,4] Dynkin type is ^2A_3(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 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 7 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) q congruent 11 modulo 12: 1/4 phi1 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 2, 5, 34, 35, 5, 48, 15, 13, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 2, 4 ], [ 28, 1, 2, 8 ] ] k = 5: F-action on Pi is () [35,1,5] Dynkin type is A_3(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 12: 1/8 phi1^2 ( q-2 ) q congruent 2 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 ( q^3-4*q^2+5*q-6 ) q congruent 4 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1^2 ( q-2 ) q congruent 7 modulo 12: 1/8 ( q^3-4*q^2+5*q-6 ) q congruent 8 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1^2 ( q-2 ) q congruent 11 modulo 12: 1/8 ( q^3-4*q^2+5*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 35, 5, 3, 34, 18, 46, 40, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 22, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ] ] k = 6: F-action on Pi is () [35,1,6] Dynkin type is A_3(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 12: 1/4 q phi1 phi2 q congruent 2 modulo 12: 1/8 q^3 q congruent 3 modulo 12: 1/4 q phi1 phi2 q congruent 4 modulo 12: 1/8 q^3 q congruent 5 modulo 12: 1/4 q phi1 phi2 q congruent 7 modulo 12: 1/4 q phi1 phi2 q congruent 8 modulo 12: 1/8 q^3 q congruent 9 modulo 12: 1/4 q phi1 phi2 q congruent 11 modulo 12: 1/4 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 41, 10, 13, 43, 40, 11, 58, 27, 12, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 26, 1, 5, 4 ] ] k = 7: F-action on Pi is (2,5) [35,1,7] Dynkin type is ^2A_3(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 12: 1/4 phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/4 phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/4 phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 40, 11, 13, 43, 41, 10, 57, 28, 9, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 26, 1, 5, 4 ] ] k = 8: F-action on Pi is () [35,1,8] Dynkin type is A_3(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 12: 1/3 phi1 ( q^2-2 ) q congruent 2 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/3 q phi2 ( q-2 ) q congruent 4 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 12: 1/3 q phi2 ( q-2 ) q congruent 7 modulo 12: 1/3 phi1 ( q^2-2 ) q congruent 8 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/3 q phi2 ( q-2 ) q congruent 11 modulo 12: 1/3 q phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 45, 45, 18, 18, 46, 8, 49, 58, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 28, 1, 5, 6 ] ] k = 9: F-action on Pi is (2,5) [35,1,9] Dynkin type is ^2A_3(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 12: 1/3 q^2 phi1 q congruent 2 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/3 q^2 phi1 q congruent 4 modulo 12: 1/6 q^2 phi1 q congruent 5 modulo 12: 1/3 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/3 q^2 phi1 q congruent 8 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/3 q^2 phi1 q congruent 11 modulo 12: 1/3 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 15, 36, 48, 15, 16, 48, 19, 38, 57, 28 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 28, 1, 4, 6 ] ] k = 10: F-action on Pi is (2,5) [35,1,10] Dynkin type is ^2A_3(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 12: 1/24 phi1 ( q^2-9*q+24 ) q congruent 2 modulo 12: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 3 modulo 12: 1/24 ( q^3-10*q^2+33*q-36 ) q congruent 4 modulo 12: 1/48 q ( q^2-10*q+24 ) q congruent 5 modulo 12: 1/24 ( q^3-10*q^2+33*q-40 ) q congruent 7 modulo 12: 1/24 ( q^3-10*q^2+33*q-36 ) q congruent 8 modulo 12: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 9 modulo 12: 1/24 phi1 ( q^2-9*q+24 ) q congruent 11 modulo 12: 1/24 ( q^3-10*q^2+33*q-52 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 31, 34, 2, 3, 34, 15, 36, 40, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 22, 1, 4, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 6, 48 ] ] i = 36: Pi = [ 3, 5, 7, 126 ] j = 1: Omega trivial k = 1: F-action on Pi is () [36,1,1] Dynkin type is 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 12: 1/192 ( q^3-21*q^2+143*q-315 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 ( q^3-21*q^2+131*q-231 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 ( q^3-21*q^2+143*q-315 ) q congruent 7 modulo 12: 1/192 ( q^3-21*q^2+131*q-231 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 ( q^3-21*q^2+143*q-315 ) q congruent 11 modulo 12: 1/192 ( q^3-21*q^2+131*q-231 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 35, 32, 4, 4, 35, 4, 35, 35, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 24 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 10, 1, 1, 48 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 18, 1, 1, 24 ], [ 25, 1, 1, 96 ], [ 26, 1, 1, 24 ], [ 27, 1, 1, 96 ], [ 34, 1, 1, 48 ] ] k = 2: F-action on Pi is (5,7) [36,1,2] Dynkin type is A_1(q) + A_1(q^2) + 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 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 41, 13, 35, 3, 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 34, 1, 5, 8 ] ] k = 3: F-action on Pi is ( 3,126)( 5, 7) [36,1,3] Dynkin type is 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 12: 1/64 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/64 ( q^3-9*q^2+27*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 41, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 10, 1, 3, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 24 ], [ 25, 1, 3, 32 ], [ 26, 1, 1, 24 ], [ 27, 1, 3, 32 ], [ 27, 1, 14, 32 ], [ 34, 1, 1, 48 ] ] k = 4: F-action on Pi is () [36,1,4] Dynkin type is 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 12: 1/64 phi1 ( q^2-10*q+25 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/64 phi1 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1 ( q^2-10*q+25 ) q congruent 11 modulo 12: 1/64 phi1 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35, 4, 35, 33, 5, 4, 33, 35, 5, 35, 5, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 15, 1, 3, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 18, 1, 2, 8 ], [ 25, 1, 5, 32 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ], [ 34, 1, 2, 16 ] ] k = 5: F-action on Pi is (5,7) [36,1,5] Dynkin type is 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 12: 1/16 phi1^2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1^2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1^2 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1^2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1^2 ( q-3 ) q congruent 11 modulo 12: 1/16 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 5, 10, 43, 5, 34, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 34, 1, 7, 8 ] ] k = 6: F-action on Pi is ( 3,126)( 5, 7) [36,1,6] Dynkin type is 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 12: 1/64 phi1^2 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 ( q-5 ) q congruent 7 modulo 12: 1/64 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 ( q-5 ) q congruent 11 modulo 12: 1/64 phi2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 10, 10, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 8 ], [ 4, 1, 3, 16 ], [ 5, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 15, 1, 4, 16 ], [ 15, 1, 5, 32 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 25, 1, 7, 32 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 32 ], [ 27, 1, 4, 32 ], [ 34, 1, 2, 16 ] ] k = 7: F-action on Pi is ( 5, 7,126) [36,1,7] Dynkin type is 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 12: 1/6 q phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 q phi1 phi2 q congruent 7 modulo 12: 1/6 q phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi1 phi2 q congruent 11 modulo 12: 1/6 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 50, 19, 21, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 34, 1, 10, 6 ] ] k = 8: F-action on Pi is ( 3, 5, 7,126) [36,1,8] Dynkin type is 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 12: 1/16 phi1 phi2^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 phi2^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 phi2^2 q congruent 7 modulo 12: 1/16 phi1 phi2^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 phi2^2 q congruent 11 modulo 12: 1/16 phi1 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 43, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 10, 8 ], [ 34, 1, 7, 8 ] ] k = 9: F-action on Pi is ( 5, 7,126) [36,1,9] Dynkin type is 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 12: 1/6 q phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 q phi1 phi2 q congruent 7 modulo 12: 1/6 q phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi1 phi2 q congruent 11 modulo 12: 1/6 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 8, 51, 49, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 34, 1, 9, 6 ] ] k = 10: F-action on Pi is ( 5,126) [36,1,10] Dynkin type is 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 12: 1/16 phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1^2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1^2 phi2 q congruent 7 modulo 12: 1/16 phi1^2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1^2 phi2 q congruent 11 modulo 12: 1/16 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 10, 43, 42, 12, 43, 11, 12, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 34, 1, 8, 8 ] ] k = 11: F-action on Pi is ( 3, 5, 7,126) [36,1,11] Dynkin type is 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 12: 1/16 phi1 phi2^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 phi2^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 phi2^2 q congruent 7 modulo 12: 1/16 phi1 phi2^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 phi2^2 q congruent 11 modulo 12: 1/16 phi1 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 12, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 3, 4 ], [ 4, 1, 4, 4 ], [ 5, 1, 1, 4 ], [ 15, 1, 7, 8 ], [ 15, 1, 8, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 34, 1, 8, 8 ] ] k = 12: F-action on Pi is ( 3, 5,126, 7) [36,1,12] Dynkin type is 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 12: 1/16 phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1^2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1^2 phi2 q congruent 7 modulo 12: 1/16 phi1^2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1^2 phi2 q congruent 11 modulo 12: 1/16 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 42, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 3, 4 ], [ 4, 1, 4, 4 ], [ 5, 1, 2, 4 ], [ 15, 1, 5, 8 ], [ 15, 1, 6, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 34, 1, 6, 8 ] ] k = 13: F-action on Pi is ( 3, 7)( 5,126) [36,1,13] Dynkin type is 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 12: 1/32 phi1 ( q^2-2*q-7 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q^2-2*q-7 ) q congruent 7 modulo 12: 1/32 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q^2-2*q-7 ) q congruent 11 modulo 12: 1/32 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 13, 13, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 4, 8 ], [ 7, 1, 1, 4 ], [ 15, 1, 6, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 18, 1, 2, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 6, 16 ], [ 27, 1, 9, 16 ], [ 27, 1, 14, 16 ], [ 34, 1, 2, 16 ] ] k = 14: F-action on Pi is ( 3, 5)( 7,126) [36,1,14] Dynkin type is 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 12: 1/32 phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi2^2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^2 phi2 q congruent 7 modulo 12: 1/32 phi2^2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^2 phi2 q congruent 11 modulo 12: 1/32 phi2^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 43, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 3, 8 ], [ 7, 1, 2, 4 ], [ 15, 1, 7, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 18, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 4, 16 ], [ 27, 1, 9, 16 ], [ 27, 1, 11, 16 ], [ 34, 1, 3, 16 ] ] k = 15: F-action on Pi is ( 3, 7)( 5,126) [36,1,15] Dynkin type is 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 12: 1/64 phi1 phi2 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1 phi2 ( q-5 ) q congruent 7 modulo 12: 1/64 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1 phi2 ( q-5 ) q congruent 11 modulo 12: 1/64 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 40, 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 4, 1, 4, 16 ], [ 5, 1, 1, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 8, 32 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 18, 1, 4, 8 ], [ 25, 1, 2, 32 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 6, 32 ], [ 27, 1, 13, 32 ], [ 34, 1, 3, 16 ] ] k = 16: F-action on Pi is ( 3,126, 5, 7) [36,1,16] Dynkin type is 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 12: 1/16 phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1^2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1^2 phi2 q congruent 7 modulo 12: 1/16 phi1^2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1^2 phi2 q congruent 11 modulo 12: 1/16 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 13, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 10, 8 ], [ 34, 1, 5, 8 ] ] k = 17: F-action on Pi is (3,5) [36,1,17] Dynkin type is A_1(q^2) + 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 12: 1/16 phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 13, 13, 40, 9, 42, 42, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 4, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 34, 1, 6, 8 ] ] k = 18: F-action on Pi is () [36,1,18] Dynkin type is 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 12: 1/64 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/64 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/64 ( q^3-9*q^2+27*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 35, 3, 35, 5, 5, 34, 35, 5, 5, 34, 3, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 18, 1, 4, 8 ], [ 25, 1, 4, 32 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ], [ 34, 1, 3, 16 ] ] k = 19: F-action on Pi is ( 3, 5)( 7,126) [36,1,19] Dynkin type is 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 12: 1/64 phi1^3 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^3 q congruent 7 modulo 12: 1/64 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^3 q congruent 11 modulo 12: 1/64 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 11, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 12 ], [ 10, 1, 2, 16 ], [ 15, 1, 3, 16 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 12 ], [ 18, 1, 3, 24 ], [ 25, 1, 6, 32 ], [ 26, 1, 3, 24 ], [ 27, 1, 11, 32 ], [ 27, 1, 13, 32 ], [ 34, 1, 4, 48 ] ] k = 20: F-action on Pi is () [36,1,20] Dynkin type is 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 12: 1/192 phi1 ( q^2-14*q+45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 phi1 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/192 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/192 ( q^3-15*q^2+71*q-105 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 5, 5, 34, 5, 34, 34, 2, 5, 34, 34, 2, 34, 2, 2, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 24 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 12 ], [ 10, 1, 4, 48 ], [ 14, 1, 2, 32 ], [ 15, 1, 4, 48 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 36 ], [ 18, 1, 3, 24 ], [ 25, 1, 8, 96 ], [ 26, 1, 3, 24 ], [ 27, 1, 12, 96 ], [ 34, 1, 4, 48 ] ] i = 37: Pi = [ 1, 2, 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [37,1,1] Dynkin type is A_2(q) + A_1(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 ( q^4-26*q^3+258*q^2-1186*q+2297 ) q congruent 2 modulo 12: 1/48 ( q^4-25*q^3+220*q^2-780*q+864 ) q congruent 3 modulo 12: 1/48 ( q^4-26*q^3+258*q^2-1146*q+1737 ) q congruent 4 modulo 12: 1/48 ( q^4-25*q^3+220*q^2-796*q+1008 ) q congruent 5 modulo 12: 1/48 ( q^4-26*q^3+258*q^2-1170*q+2025 ) q congruent 7 modulo 12: 1/48 ( q^4-26*q^3+258*q^2-1162*q+2009 ) q congruent 8 modulo 12: 1/48 ( q^4-25*q^3+220*q^2-780*q+864 ) q congruent 9 modulo 12: 1/48 ( q^4-26*q^3+258*q^2-1170*q+2025 ) q congruent 11 modulo 12: 1/48 ( q^4-26*q^3+258*q^2-1146*q+1737 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 6, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 18 ], [ 4, 1, 1, 28 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 40 ], [ 9, 1, 1, 46 ], [ 10, 1, 1, 36 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 48 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 18, 1, 1, 24 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 64 ], [ 21, 1, 1, 36 ], [ 22, 1, 1, 48 ], [ 23, 1, 1, 48 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 26, 1, 1, 24 ], [ 28, 1, 1, 48 ], [ 29, 1, 1, 48 ], [ 30, 1, 1, 48 ], [ 31, 1, 1, 48 ], [ 33, 1, 1, 96 ], [ 35, 1, 1, 48 ] ] k = 2: F-action on Pi is () [37,1,2] Dynkin type is A_2(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 12: 1/8 phi1 ( q^3-11*q^2+41*q-55 ) q congruent 2 modulo 12: 1/8 q ( q^3-11*q^2+38*q-40 ) q congruent 3 modulo 12: 1/8 phi1 ( q^3-11*q^2+41*q-51 ) q congruent 4 modulo 12: 1/8 q ( q^3-11*q^2+38*q-40 ) q congruent 5 modulo 12: 1/8 phi1 ( q^3-11*q^2+41*q-55 ) q congruent 7 modulo 12: 1/8 phi1 ( q^3-11*q^2+41*q-51 ) q congruent 8 modulo 12: 1/8 q ( q^3-11*q^2+38*q-40 ) q congruent 9 modulo 12: 1/8 phi1 ( q^3-11*q^2+41*q-55 ) q congruent 11 modulo 12: 1/8 phi1 ( q^3-11*q^2+41*q-51 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35, 45, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 10 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 8 ], [ 22, 1, 2, 8 ], [ 23, 1, 2, 8 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 5, 8 ], [ 26, 1, 2, 4 ], [ 28, 1, 3, 8 ], [ 29, 1, 2, 8 ], [ 30, 1, 1, 8 ], [ 30, 1, 2, 8 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 33, 1, 3, 16 ], [ 35, 1, 2, 8 ] ] k = 3: F-action on Pi is () [37,1,3] Dynkin type is A_2(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 12: 1/6 phi1 ( q^3-4*q^2-q+10 ) q congruent 2 modulo 12: 1/6 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/6 q phi2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/6 phi1 ( q^3-3*q^2-2*q+6 ) q congruent 5 modulo 12: 1/6 q phi2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/6 phi1 ( q^3-4*q^2-q+10 ) q congruent 8 modulo 12: 1/6 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/6 q phi2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/6 q phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 45, 45, 18, 8, 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 2 ], [ 20, 1, 1, 4 ], [ 28, 1, 5, 6 ], [ 29, 1, 3, 6 ], [ 33, 1, 2, 12 ], [ 35, 1, 8, 6 ] ] k = 4: F-action on Pi is () [37,1,4] Dynkin type is A_2(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 12: 1/8 phi1 phi2^2 ( q-3 ) q congruent 2 modulo 12: 1/8 q^2 phi2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 phi2^2 ( q-3 ) q congruent 4 modulo 12: 1/8 q^2 phi2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 phi2^2 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 phi2^2 ( q-3 ) q congruent 8 modulo 12: 1/8 q^2 phi2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 phi2^2 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1 phi2^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 10, 13, 43, 58, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 35, 1, 6, 8 ] ] k = 5: F-action on Pi is () [37,1,5] Dynkin type is A_2(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 12: 1/16 phi1^2 ( q^2-4*q+1 ) q congruent 2 modulo 12: 1/16 q ( q^3-5*q^2+4*q+4 ) q congruent 3 modulo 12: 1/16 phi4 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^3-5*q^2+4*q+4 ) q congruent 5 modulo 12: 1/16 phi1^2 ( q^2-4*q+1 ) q congruent 7 modulo 12: 1/16 phi4 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/16 q ( q^3-5*q^2+4*q+4 ) q congruent 9 modulo 12: 1/16 phi1^2 ( q^2-4*q+1 ) q congruent 11 modulo 12: 1/16 phi4 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 35, 5, 18, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 8 ], [ 15, 1, 3, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 8 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 8 ], [ 22, 1, 2, 16 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 16 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 30, 1, 2, 16 ], [ 31, 1, 4, 16 ], [ 35, 1, 5, 16 ] ] k = 6: F-action on Pi is (1,3) [37,1,6] Dynkin type is ^2A_2(q) + A_1(q) + T(phi2^4) Order of center |Z^F|: phi2^4 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 phi1 ( q^3-17*q^2+109*q-285 ) q congruent 2 modulo 12: 1/48 ( q^4-17*q^3+94*q^2-184*q+112 ) q congruent 3 modulo 12: 1/48 ( q^4-18*q^3+126*q^2-418*q+525 ) q congruent 4 modulo 12: 1/48 q ( q^3-17*q^2+94*q-168 ) q congruent 5 modulo 12: 1/48 ( q^4-18*q^3+126*q^2-410*q+525 ) q congruent 7 modulo 12: 1/48 ( q^4-18*q^3+126*q^2-418*q+525 ) q congruent 8 modulo 12: 1/48 ( q^4-17*q^3+94*q^2-184*q+112 ) q congruent 9 modulo 12: 1/48 phi1 ( q^3-17*q^2+109*q-285 ) q congruent 11 modulo 12: 1/48 ( q^4-18*q^3+126*q^2-434*q+765 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 31, 34, 2, 15, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 18 ], [ 4, 1, 2, 28 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 18 ], [ 8, 1, 2, 40 ], [ 9, 1, 2, 46 ], [ 10, 1, 4, 36 ], [ 11, 1, 2, 32 ], [ 12, 1, 6, 48 ], [ 13, 1, 2, 24 ], [ 14, 1, 2, 32 ], [ 15, 1, 4, 48 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 18, 1, 3, 24 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 64 ], [ 21, 1, 6, 36 ], [ 22, 1, 4, 48 ], [ 23, 1, 4, 48 ], [ 24, 1, 3, 72 ], [ 25, 1, 8, 48 ], [ 26, 1, 3, 24 ], [ 28, 1, 6, 48 ], [ 29, 1, 4, 48 ], [ 30, 1, 5, 48 ], [ 31, 1, 7, 48 ], [ 33, 1, 6, 96 ], [ 35, 1, 10, 48 ] ] k = 7: F-action on Pi is (1,3) [37,1,7] Dynkin type is ^2A_2(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 12: 1/8 phi1 ( q^3-7*q^2+21*q-27 ) q congruent 2 modulo 12: 1/8 q ( q^3-7*q^2+16*q-12 ) q congruent 3 modulo 12: 1/8 ( q^4-8*q^3+28*q^2-52*q+39 ) q congruent 4 modulo 12: 1/8 q ( q^3-7*q^2+16*q-12 ) q congruent 5 modulo 12: 1/8 phi1 ( q^3-7*q^2+21*q-27 ) q congruent 7 modulo 12: 1/8 ( q^4-8*q^3+28*q^2-52*q+39 ) q congruent 8 modulo 12: 1/8 q ( q^3-7*q^2+16*q-12 ) q congruent 9 modulo 12: 1/8 phi1 ( q^3-7*q^2+21*q-27 ) q congruent 11 modulo 12: 1/8 ( q^4-8*q^3+28*q^2-52*q+39 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 2, 5, 34, 48, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 10 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 4 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 8 ], [ 22, 1, 4, 8 ], [ 23, 1, 3, 8 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 12 ], [ 25, 1, 4, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 2, 4 ], [ 28, 1, 2, 8 ], [ 29, 1, 5, 8 ], [ 30, 1, 5, 8 ], [ 30, 1, 6, 8 ], [ 31, 1, 5, 8 ], [ 31, 1, 8, 8 ], [ 33, 1, 4, 16 ], [ 35, 1, 4, 8 ] ] k = 8: F-action on Pi is (1,3) [37,1,8] Dynkin type is ^2A_2(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 12: 1/6 q phi1^3 q congruent 2 modulo 12: 1/6 phi1 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/6 q phi1^3 q congruent 4 modulo 12: 1/6 q^2 phi1^2 q congruent 5 modulo 12: 1/6 phi2 ( q^3-4*q^2+7*q-6 ) q congruent 7 modulo 12: 1/6 q phi1^3 q congruent 8 modulo 12: 1/6 phi1 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/6 q phi1^3 q congruent 11 modulo 12: 1/6 phi2 ( q^3-4*q^2+7*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 15, 36, 48, 15, 19, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 14, 1, 2, 2 ], [ 20, 1, 2, 4 ], [ 28, 1, 4, 6 ], [ 29, 1, 6, 6 ], [ 33, 1, 5, 12 ], [ 35, 1, 9, 6 ] ] k = 9: F-action on Pi is (1,3) [37,1,9] Dynkin type is ^2A_2(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 12: 1/16 phi1^2 ( q^2-4*q+5 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/16 ( q^4-6*q^3+14*q^2-14*q-3 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-5*q+6 ) q congruent 5 modulo 12: 1/16 phi1^2 ( q^2-4*q+5 ) q congruent 7 modulo 12: 1/16 ( q^4-6*q^3+14*q^2-14*q-3 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/16 phi1^2 ( q^2-4*q+5 ) q congruent 11 modulo 12: 1/16 ( q^4-6*q^3+14*q^2-14*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 35, 5, 16, 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 12 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 18, 1, 4, 8 ], [ 21, 1, 3, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 16 ], [ 24, 1, 4, 8 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 30, 1, 6, 16 ], [ 31, 1, 6, 16 ], [ 35, 1, 3, 16 ] ] k = 10: F-action on Pi is (1,3) [37,1,10] Dynkin type is ^2A_2(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 12: 1/8 phi1^3 phi2 q congruent 2 modulo 12: 1/8 q^3 phi1 q congruent 3 modulo 12: 1/8 phi1^3 phi2 q congruent 4 modulo 12: 1/8 q^3 phi1 q congruent 5 modulo 12: 1/8 phi1^3 phi2 q congruent 7 modulo 12: 1/8 phi1^3 phi2 q congruent 8 modulo 12: 1/8 q^3 phi1 q congruent 9 modulo 12: 1/8 phi1^3 phi2 q congruent 11 modulo 12: 1/8 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 40, 11, 13, 43, 57, 28 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 26, 1, 5, 4 ], [ 35, 1, 7, 8 ] ] i = 38: Pi = [ 1, 2, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [38,1,1] Dynkin type is 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 12: 1/96 ( q^4-30*q^3+332*q^2-1618*q+3139 ) q congruent 2 modulo 12: 1/96 ( q^4-26*q^3+236*q^2-856*q+960 ) q congruent 3 modulo 12: 1/96 ( q^4-30*q^3+332*q^2-1578*q+2475 ) q congruent 4 modulo 12: 1/96 ( q^4-26*q^3+236*q^2-872*q+1120 ) q congruent 5 modulo 12: 1/96 ( q^4-30*q^3+332*q^2-1602*q+2835 ) q congruent 7 modulo 12: 1/96 ( q^4-30*q^3+332*q^2-1594*q+2779 ) q congruent 8 modulo 12: 1/96 ( q^4-26*q^3+236*q^2-856*q+960 ) q congruent 9 modulo 12: 1/96 ( q^4-30*q^3+332*q^2-1602*q+2835 ) q congruent 11 modulo 12: 1/96 ( q^4-30*q^3+332*q^2-1578*q+2475 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 24 ], [ 4, 1, 1, 48 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 24 ], [ 8, 1, 1, 48 ], [ 9, 1, 1, 72 ], [ 10, 1, 1, 96 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 48 ], [ 18, 1, 1, 24 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 96 ], [ 21, 1, 1, 144 ], [ 22, 1, 1, 72 ], [ 23, 1, 1, 16 ], [ 24, 1, 1, 48 ], [ 25, 1, 1, 96 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 192 ], [ 30, 1, 1, 96 ], [ 31, 1, 1, 48 ], [ 32, 1, 1, 144 ], [ 34, 1, 1, 48 ], [ 36, 1, 1, 192 ] ] k = 2: F-action on Pi is () [38,1,2] Dynkin type is 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 12: 1/32 phi1 ( q^3-15*q^2+75*q-125 ) q congruent 2 modulo 12: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/32 phi1 ( q^3-15*q^2+75*q-117 ) q congruent 4 modulo 12: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/32 phi1 ( q^3-15*q^2+75*q-125 ) q congruent 7 modulo 12: 1/32 phi1 ( q^3-15*q^2+75*q-117 ) q congruent 8 modulo 12: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/32 phi1 ( q^3-15*q^2+75*q-125 ) q congruent 11 modulo 12: 1/32 phi1 ( q^3-15*q^2+75*q-117 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 33, 4, 35, 35, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 15, 1, 3, 16 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 12 ], [ 18, 1, 2, 8 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 16 ], [ 24, 1, 2, 16 ], [ 25, 1, 5, 32 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 48 ], [ 30, 1, 2, 32 ], [ 31, 1, 2, 16 ], [ 32, 1, 1, 48 ], [ 32, 1, 6, 32 ], [ 34, 1, 2, 16 ], [ 36, 1, 4, 64 ] ] k = 3: F-action on Pi is () [38,1,3] Dynkin type is 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 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 5, 5, 34, 5, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 24 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 12 ], [ 10, 1, 4, 48 ], [ 14, 1, 2, 32 ], [ 15, 1, 4, 48 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 36 ], [ 18, 1, 3, 24 ], [ 22, 1, 3, 24 ], [ 23, 1, 3, 16 ], [ 25, 1, 8, 96 ], [ 26, 1, 2, 12 ], [ 26, 1, 3, 24 ], [ 27, 1, 8, 48 ], [ 27, 1, 12, 96 ], [ 31, 1, 5, 48 ], [ 32, 1, 3, 48 ], [ 34, 1, 4, 48 ], [ 36, 1, 20, 192 ] ] k = 4: F-action on Pi is () [38,1,4] Dynkin type is 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 12: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 2 modulo 12: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 12: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 12: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 5 modulo 12: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 7 modulo 12: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 12: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 12: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) q congruent 11 modulo 12: 1/32 phi1 ( q^3-9*q^2+27*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 35, 3, 35, 5, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 16 ], [ 10, 1, 4, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 18, 1, 4, 8 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 8 ], [ 25, 1, 4, 32 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 64 ], [ 27, 1, 12, 32 ], [ 31, 1, 6, 16 ], [ 32, 1, 3, 16 ], [ 32, 1, 6, 32 ], [ 34, 1, 3, 16 ], [ 36, 1, 18, 64 ] ] k = 5: F-action on Pi is () [38,1,5] Dynkin type is 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 12: 1/32 phi1^2 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/32 phi1^2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/32 phi1^2 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/32 phi1^2 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/32 phi1^2 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/32 phi1^2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 35, 5, 35, 5, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 16 ], [ 10, 1, 4, 16 ], [ 15, 1, 3, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 18, 1, 2, 8 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 16 ], [ 25, 1, 5, 32 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 64 ], [ 27, 1, 12, 32 ], [ 31, 1, 4, 16 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 16 ], [ 34, 1, 2, 16 ], [ 36, 1, 4, 64 ] ] k = 6: F-action on Pi is () [38,1,6] Dynkin type is 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 12: 1/32 phi1 ( q^3-11*q^2+43*q-57 ) q congruent 2 modulo 12: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/32 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 4 modulo 12: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/32 phi1 ( q^3-11*q^2+43*q-57 ) q congruent 7 modulo 12: 1/32 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 8 modulo 12: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/32 phi1 ( q^3-11*q^2+43*q-57 ) q congruent 11 modulo 12: 1/32 ( q^4-12*q^3+54*q^2-108*q+81 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 5, 3, 34, 5, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 36 ], [ 18, 1, 4, 8 ], [ 21, 1, 6, 48 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 24 ], [ 24, 1, 4, 16 ], [ 25, 1, 4, 32 ], [ 26, 1, 2, 12 ], [ 26, 1, 3, 24 ], [ 27, 1, 8, 48 ], [ 27, 1, 12, 96 ], [ 30, 1, 6, 32 ], [ 31, 1, 8, 16 ], [ 32, 1, 3, 32 ], [ 32, 1, 7, 48 ], [ 34, 1, 3, 16 ], [ 36, 1, 18, 64 ] ] k = 7: F-action on Pi is () [38,1,7] Dynkin type is 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 12: 1/96 phi1 ( q^3-21*q^2+155*q-423 ) q congruent 2 modulo 12: 1/96 ( q^4-18*q^3+104*q^2-208*q+128 ) q congruent 3 modulo 12: 1/96 ( q^4-22*q^3+176*q^2-602*q+735 ) q congruent 4 modulo 12: 1/96 q ( q^3-18*q^2+104*q-192 ) q congruent 5 modulo 12: 1/96 ( q^4-22*q^3+176*q^2-594*q+695 ) q congruent 7 modulo 12: 1/96 ( q^4-22*q^3+176*q^2-602*q+735 ) q congruent 8 modulo 12: 1/96 ( q^4-18*q^3+104*q^2-208*q+128 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-21*q^2+155*q-423 ) q congruent 11 modulo 12: 1/96 ( q^4-22*q^3+176*q^2-618*q+1007 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 34, 34, 2, 34, 2, 2, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 24 ], [ 4, 1, 2, 48 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 24 ], [ 8, 1, 2, 48 ], [ 9, 1, 2, 72 ], [ 10, 1, 4, 96 ], [ 11, 1, 2, 24 ], [ 12, 1, 6, 96 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 32 ], [ 15, 1, 4, 48 ], [ 16, 1, 2, 8 ], [ 17, 1, 3, 48 ], [ 18, 1, 3, 24 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 96 ], [ 21, 1, 6, 144 ], [ 22, 1, 4, 72 ], [ 23, 1, 4, 16 ], [ 24, 1, 3, 48 ], [ 25, 1, 8, 96 ], [ 26, 1, 3, 48 ], [ 27, 1, 12, 192 ], [ 30, 1, 5, 96 ], [ 31, 1, 7, 48 ], [ 32, 1, 7, 144 ], [ 34, 1, 4, 48 ], [ 36, 1, 20, 192 ] ] k = 8: F-action on Pi is () [38,1,8] Dynkin type is 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 12: 1/96 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 2 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/96 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/96 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 7 modulo 12: 1/96 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 11 modulo 12: 1/96 phi1 ( q^3-15*q^2+71*q-105 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35, 4, 35, 35, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 24 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 10, 1, 1, 48 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 12 ], [ 18, 1, 1, 24 ], [ 22, 1, 2, 24 ], [ 23, 1, 2, 16 ], [ 25, 1, 1, 96 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 48 ], [ 31, 1, 3, 48 ], [ 32, 1, 6, 48 ], [ 34, 1, 1, 48 ], [ 36, 1, 1, 192 ] ] k = 9: F-action on Pi is (2,5) [38,1,9] Dynkin type is 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 12: 1/16 phi1 ( q^3-7*q^2+9*q+13 ) q congruent 2 modulo 12: 1/16 q ( q^3-6*q^2+4*q+8 ) q congruent 3 modulo 12: 1/16 phi1 ( q^3-7*q^2+9*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^3-6*q^2+4*q+16 ) q congruent 5 modulo 12: 1/16 phi1 ( q^3-7*q^2+9*q+5 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^2-8*q+17 ) q congruent 8 modulo 12: 1/16 q ( q^3-6*q^2+4*q+8 ) q congruent 9 modulo 12: 1/16 phi1 ( q^3-7*q^2+9*q+5 ) q congruent 11 modulo 12: 1/16 phi1 ( q^3-7*q^2+9*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 10, 5, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 1, 3, 8 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 2, 16 ], [ 14, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 3, 8 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 4, 16 ], [ 30, 1, 3, 16 ], [ 31, 1, 2, 8 ], [ 31, 1, 5, 8 ], [ 32, 1, 2, 8 ], [ 34, 1, 7, 8 ], [ 36, 1, 5, 16 ] ] k = 10: F-action on Pi is (2,5) [38,1,10] Dynkin type is 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 12: 1/16 phi1 ( q^3-9*q^2+25*q-21 ) q congruent 2 modulo 12: 1/16 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/16 ( q^4-10*q^3+34*q^2-42*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/16 phi1 ( q^3-9*q^2+25*q-21 ) q congruent 7 modulo 12: 1/16 ( q^4-10*q^3+34*q^2-42*q+9 ) q congruent 8 modulo 12: 1/16 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/16 phi1 ( q^3-9*q^2+25*q-21 ) q congruent 11 modulo 12: 1/16 ( q^4-10*q^3+34*q^2-42*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 35, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 19, 1, 1, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 8 ], [ 24, 1, 1, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 14, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 1, 8 ], [ 31, 1, 6, 8 ], [ 32, 1, 2, 8 ], [ 34, 1, 5, 8 ], [ 36, 1, 2, 16 ] ] k = 11: F-action on Pi is (2,5) [38,1,11] Dynkin type is 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 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 13, 42, 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 4, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 6, 16 ], [ 27, 1, 7, 8 ], [ 32, 1, 4, 8 ], [ 34, 1, 6, 8 ], [ 36, 1, 17, 16 ] ] k = 12: F-action on Pi is (2,5) [38,1,12] Dynkin type is 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 12: 1/16 phi1^3 phi2 q congruent 2 modulo 12: 1/16 q^4 q congruent 3 modulo 12: 1/16 phi1^3 phi2 q congruent 4 modulo 12: 1/16 q^4 q congruent 5 modulo 12: 1/16 phi1^3 phi2 q congruent 7 modulo 12: 1/16 phi1^3 phi2 q congruent 8 modulo 12: 1/16 q^4 q congruent 9 modulo 12: 1/16 phi1^3 phi2 q congruent 11 modulo 12: 1/16 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 43, 12, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 2, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 11, 16 ], [ 32, 1, 4, 8 ], [ 34, 1, 8, 8 ], [ 36, 1, 10, 16 ] ] k = 13: F-action on Pi is (2,5) [38,1,13] Dynkin type is 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 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 9, 13, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 1, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 14, 16 ], [ 32, 1, 8, 8 ], [ 34, 1, 6, 8 ], [ 36, 1, 17, 16 ] ] k = 14: F-action on Pi is (2,5) [38,1,14] Dynkin type is 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 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 10, 42, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 4, 16 ], [ 27, 1, 7, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 8, 8 ], [ 36, 1, 10, 16 ] ] k = 15: F-action on Pi is (2,5) [38,1,15] Dynkin type is 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 12: 1/16 phi1 ( q^3-7*q^2+13*q-3 ) q congruent 2 modulo 12: 1/16 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 3 modulo 12: 1/16 ( q^4-8*q^3+20*q^2-20*q+15 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/16 ( q^4-8*q^3+20*q^2-8*q-21 ) q congruent 7 modulo 12: 1/16 ( q^4-8*q^3+20*q^2-20*q+15 ) q congruent 8 modulo 12: 1/16 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 9 modulo 12: 1/16 phi1 ( q^3-7*q^2+13*q-3 ) q congruent 11 modulo 12: 1/16 ( q^4-8*q^3+20*q^2-12*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 13, 3, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 1, 4, 8 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 5, 16 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 20, 1, 3, 16 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 8 ], [ 24, 1, 4, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 6, 16 ], [ 30, 1, 7, 16 ], [ 31, 1, 3, 8 ], [ 31, 1, 8, 8 ], [ 32, 1, 5, 8 ], [ 34, 1, 5, 8 ], [ 36, 1, 2, 16 ] ] k = 16: F-action on Pi is (2,5) [38,1,16] Dynkin type is 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 12: 1/16 phi1^2 ( q^2-4*q+5 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 ( q^3-5*q^2+9*q-9 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1^2 ( q^2-4*q+5 ) q congruent 7 modulo 12: 1/16 phi1 ( q^3-5*q^2+9*q-9 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1^2 ( q^2-4*q+5 ) q congruent 11 modulo 12: 1/16 phi1 ( q^3-5*q^2+9*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 43, 34, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 8 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 14, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 19, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 4, 8 ], [ 24, 1, 3, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 11, 16 ], [ 30, 1, 8, 16 ], [ 31, 1, 4, 8 ], [ 31, 1, 7, 8 ], [ 32, 1, 5, 8 ], [ 34, 1, 7, 8 ], [ 36, 1, 5, 16 ] ] k = 17: F-action on Pi is (1,2,5) [38,1,17] Dynkin type is 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 12: 1/12 q phi1^2 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/12 q phi1^2 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 q phi1^2 phi2 q congruent 7 modulo 12: 1/12 q phi1^2 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/12 q phi1^2 phi2 q congruent 11 modulo 12: 1/12 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 49, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 23, 1, 2, 4 ], [ 34, 1, 9, 6 ], [ 36, 1, 9, 6 ] ] k = 18: F-action on Pi is (1,2,5) [38,1,18] Dynkin type is 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 12: 1/12 q phi1^2 phi2 q congruent 2 modulo 12: 1/12 phi2 ( q^3-q^2-4 ) q congruent 3 modulo 12: 1/12 q phi1^2 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 phi2 ( q^3-2*q^2+q-4 ) q congruent 7 modulo 12: 1/12 q phi1^2 phi2 q congruent 8 modulo 12: 1/12 phi2 ( q^3-q^2-4 ) q congruent 9 modulo 12: 1/12 q phi1^2 phi2 q congruent 11 modulo 12: 1/12 phi2 ( q^3-2*q^2+q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 21, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 12, 1, 4, 12 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 2 ], [ 16, 1, 2, 2 ], [ 23, 1, 4, 4 ], [ 34, 1, 10, 6 ], [ 36, 1, 7, 6 ] ] k = 19: F-action on Pi is (1,2,5) [38,1,19] Dynkin type is 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 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/12 q phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 50, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 23, 1, 3, 4 ], [ 34, 1, 10, 6 ], [ 36, 1, 7, 6 ] ] k = 20: F-action on Pi is (1,2,5) [38,1,20] Dynkin type is 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 12: 1/12 phi1 ( q^3-2*q^2-3*q-4 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 1/12 phi1 ( q^3-q^2-2*q-4 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/12 phi1 ( q^3-2*q^2-3*q-4 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/12 q phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 51 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 12, 1, 3, 12 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 16, 1, 1, 2 ], [ 23, 1, 1, 4 ], [ 34, 1, 9, 6 ], [ 36, 1, 9, 6 ] ] i = 39: Pi = [ 1, 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [39,1,1] Dynkin type is A_3(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 ( q^4-23*q^3+201*q^2-801*q+1294 ) q congruent 2 modulo 12: 1/96 ( q^4-22*q^3+172*q^2-552*q+576 ) q congruent 3 modulo 12: 1/96 ( q^4-23*q^3+201*q^2-789*q+1098 ) q congruent 4 modulo 12: 1/96 ( q^4-22*q^3+172*q^2-552*q+608 ) q congruent 5 modulo 12: 1/96 ( q^4-23*q^3+201*q^2-801*q+1230 ) q congruent 7 modulo 12: 1/96 ( q^4-23*q^3+201*q^2-789*q+1162 ) q congruent 8 modulo 12: 1/96 ( q^4-22*q^3+172*q^2-552*q+576 ) q congruent 9 modulo 12: 1/96 ( q^4-23*q^3+201*q^2-801*q+1230 ) q congruent 11 modulo 12: 1/96 ( q^4-23*q^3+201*q^2-789*q+1098 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 4, 6, 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 30 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 14 ], [ 17, 1, 1, 36 ], [ 18, 1, 1, 60 ], [ 19, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 23, 1, 1, 48 ], [ 24, 1, 1, 16 ], [ 25, 1, 1, 24 ], [ 26, 1, 1, 72 ], [ 28, 1, 1, 48 ], [ 29, 1, 1, 96 ], [ 31, 1, 1, 48 ], [ 34, 1, 1, 144 ], [ 35, 1, 1, 48 ] ] k = 2: F-action on Pi is () [39,1,2] Dynkin type is A_3(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q^3-10*q^2+33*q-36 ) q congruent 2 modulo 12: 1/16 q ( q^3-10*q^2+32*q-32 ) q congruent 3 modulo 12: 1/16 phi1 ( q^3-10*q^2+33*q-36 ) q congruent 4 modulo 12: 1/16 q ( q^3-10*q^2+32*q-32 ) q congruent 5 modulo 12: 1/16 phi1 ( q^3-10*q^2+33*q-36 ) q congruent 7 modulo 12: 1/16 phi1 ( q^3-10*q^2+33*q-36 ) q congruent 8 modulo 12: 1/16 q ( q^3-10*q^2+32*q-32 ) q congruent 9 modulo 12: 1/16 phi1 ( q^3-10*q^2+33*q-36 ) q congruent 11 modulo 12: 1/16 phi1 ( q^3-10*q^2+33*q-36 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 35, 45, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 19, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 1, 1, 8 ], [ 23, 1, 2, 8 ], [ 24, 1, 1, 8 ], [ 25, 1, 1, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 29, 1, 2, 16 ], [ 31, 1, 1, 8 ], [ 31, 1, 3, 8 ], [ 34, 1, 2, 16 ], [ 35, 1, 2, 8 ] ] k = 3: F-action on Pi is () [39,1,3] Dynkin type is A_3(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 phi1 ( q^3-4*q^2-q+8 ) q congruent 2 modulo 12: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/12 phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 12: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/12 phi1 ( q^3-4*q^2-q+8 ) q congruent 8 modulo 12: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/12 q phi2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/12 q phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 45, 18, 8, 58 ] 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 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 24, 1, 1, 4 ], [ 28, 1, 5, 6 ], [ 29, 1, 3, 12 ], [ 35, 1, 8, 6 ] ] k = 4: F-action on Pi is () [39,1,4] Dynkin type is A_3(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1^3 ( q-2 ) q congruent 2 modulo 12: 1/32 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/32 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 4 modulo 12: 1/32 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/32 phi1^3 ( q-2 ) q congruent 7 modulo 12: 1/32 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 8 modulo 12: 1/32 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/32 phi1^3 ( q-2 ) q congruent 11 modulo 12: 1/32 phi1 ( q^3-4*q^2+5*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 5, 34, 46, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 12 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 12 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 24 ], [ 22, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 16 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 8 ], [ 31, 1, 4, 16 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 16 ], [ 35, 1, 5, 16 ] ] k = 5: F-action on Pi is () [39,1,5] Dynkin type is A_3(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 12: 1/16 phi1^2 ( q^2-3*q+4 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1^2 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1^2 ( q^2-3*q+4 ) q congruent 7 modulo 12: 1/16 phi1^2 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1^2 ( q^2-3*q+4 ) q congruent 11 modulo 12: 1/16 phi1^2 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 5, 18, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 15, 1, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 28, 1, 3, 8 ], [ 31, 1, 2, 8 ], [ 31, 1, 4, 8 ], [ 34, 1, 3, 16 ], [ 35, 1, 2, 8 ] ] k = 6: F-action on Pi is () [39,1,6] Dynkin type is A_3(q) + T(phi2^2 phi4) Order of center |Z^F|: phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 q phi1^2 phi2 q congruent 2 modulo 12: 1/16 q^4 q congruent 3 modulo 12: 1/16 q phi1^2 phi2 q congruent 4 modulo 12: 1/16 q^4 q congruent 5 modulo 12: 1/16 q phi1^2 phi2 q congruent 7 modulo 12: 1/16 q phi1^2 phi2 q congruent 8 modulo 12: 1/16 q^4 q congruent 9 modulo 12: 1/16 q phi1^2 phi2 q congruent 11 modulo 12: 1/16 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 10, 43, 11, 27, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 25, 1, 6, 8 ], [ 26, 1, 5, 4 ], [ 34, 1, 8, 8 ], [ 35, 1, 6, 8 ] ] k = 7: F-action on Pi is () [39,1,7] Dynkin type is A_3(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1^2 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/12 q phi1^2 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 q phi1^2 phi2 q congruent 7 modulo 12: 1/12 q phi1^2 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/12 q phi1^2 phi2 q congruent 11 modulo 12: 1/12 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 45, 18, 46, 49, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 24, 1, 2, 4 ], [ 28, 1, 5, 6 ], [ 35, 1, 8, 6 ] ] k = 8: F-action on Pi is () [39,1,8] Dynkin type is A_3(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 ( q^3-12*q^2+53*q-90 ) q congruent 2 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/96 phi1 ( q^3-12*q^2+53*q-78 ) q congruent 4 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/96 phi1 ( q^3-12*q^2+53*q-90 ) q congruent 7 modulo 12: 1/96 phi1 ( q^3-12*q^2+53*q-78 ) q congruent 8 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-12*q^2+53*q-90 ) q congruent 11 modulo 12: 1/96 phi1 ( q^3-12*q^2+53*q-78 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 33, 45, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 15, 1, 3, 8 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 18, 1, 2, 12 ], [ 22, 1, 1, 24 ], [ 24, 1, 2, 16 ], [ 25, 1, 5, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 28, 1, 1, 48 ], [ 31, 1, 2, 48 ], [ 34, 1, 2, 48 ], [ 35, 1, 1, 48 ] ] k = 9: F-action on Pi is () [39,1,9] Dynkin type is A_3(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 q phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 q phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 q phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/16 q phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 q phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/16 q phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 13, 40, 58, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 4 ], [ 25, 1, 2, 8 ], [ 26, 1, 5, 4 ], [ 34, 1, 6, 8 ], [ 35, 1, 6, 8 ] ] k = 10: F-action on Pi is () [39,1,10] Dynkin type is A_3(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 12: 1/32 phi1^2 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 12: 1/32 ( q^4-7*q^3+17*q^2-21*q+18 ) q congruent 4 modulo 12: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 5 modulo 12: 1/32 phi1^2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/32 ( q^4-7*q^3+17*q^2-21*q+18 ) q congruent 8 modulo 12: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 12: 1/32 phi1^2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/32 ( q^4-7*q^3+17*q^2-21*q+18 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 3, 18, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 8 ], [ 22, 1, 2, 8 ], [ 23, 1, 2, 16 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 31, 1, 3, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 16 ], [ 35, 1, 5, 16 ] ] k = 11: F-action on Pi is (1,4) [39,1,11] Dynkin type is ^2A_3(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q^3-6*q^2+15*q-18 ) q congruent 2 modulo 12: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 12: 1/16 phi1 ( q^3-6*q^2+15*q-18 ) q congruent 4 modulo 12: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 5 modulo 12: 1/16 phi1 ( q^3-6*q^2+15*q-18 ) q congruent 7 modulo 12: 1/16 phi1 ( q^3-6*q^2+15*q-18 ) q congruent 8 modulo 12: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 12: 1/16 phi1 ( q^3-6*q^2+15*q-18 ) q congruent 11 modulo 12: 1/16 phi1 ( q^3-6*q^2+15*q-18 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 34, 5, 15, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 8 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 14, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 19, 1, 2, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 3, 8 ], [ 23, 1, 4, 8 ], [ 24, 1, 3, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 28, 1, 2, 8 ], [ 29, 1, 5, 16 ], [ 31, 1, 5, 8 ], [ 31, 1, 7, 8 ], [ 34, 1, 3, 16 ], [ 35, 1, 4, 8 ] ] k = 12: F-action on Pi is (1,4) [39,1,12] Dynkin type is ^2A_3(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1^3 q congruent 2 modulo 12: 1/12 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 12: 1/12 q phi1^3 q congruent 4 modulo 12: 1/12 q^2 phi1^2 q congruent 5 modulo 12: 1/12 phi2 ( q^3-4*q^2+7*q-8 ) q congruent 7 modulo 12: 1/12 q phi1^3 q congruent 8 modulo 12: 1/12 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 9 modulo 12: 1/12 q phi1^3 q congruent 11 modulo 12: 1/12 phi2 ( q^3-4*q^2+7*q-8 ) Fusion of maximal tori of C^F in those of G^F: [ 36, 15, 48, 38, 28 ] 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 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 24, 1, 3, 4 ], [ 28, 1, 4, 6 ], [ 29, 1, 6, 12 ], [ 35, 1, 9, 6 ] ] k = 13: F-action on Pi is (1,4) [39,1,13] Dynkin type is ^2A_3(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 12: 1/32 phi1^3 ( q-4 ) q congruent 2 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/32 q phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/32 phi1^3 ( q-4 ) q congruent 7 modulo 12: 1/32 q phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/32 phi1^3 ( q-4 ) q congruent 11 modulo 12: 1/32 q phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 5, 33, 48, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 4 ], [ 22, 1, 3, 8 ], [ 23, 1, 3, 16 ], [ 25, 1, 7, 16 ], [ 25, 1, 8, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 4, 8 ], [ 31, 1, 5, 16 ], [ 34, 1, 2, 16 ], [ 34, 1, 7, 16 ], [ 35, 1, 3, 16 ] ] k = 14: F-action on Pi is (1,4) [39,1,14] Dynkin type is ^2A_3(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^2 phi2 ( q-2 ) q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1^2 phi2 ( q-2 ) q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1^2 phi2 ( q-2 ) q congruent 7 modulo 12: 1/16 phi1^2 phi2 ( q-2 ) q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1^2 phi2 ( q-2 ) q congruent 11 modulo 12: 1/16 phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 11, 43, 10, 28, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 25, 1, 7, 8 ], [ 26, 1, 5, 4 ], [ 34, 1, 8, 8 ], [ 35, 1, 7, 8 ] ] k = 15: F-action on Pi is (1,4) [39,1,15] Dynkin type is ^2A_3(q) + T(phi2^4) Order of center |Z^F|: phi2^4 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 ( q^3-14*q^2+73*q-156 ) q congruent 2 modulo 12: 1/96 ( q^4-14*q^3+64*q^2-96*q+32 ) q congruent 3 modulo 12: 1/96 ( q^4-15*q^3+87*q^2-241*q+264 ) q congruent 4 modulo 12: 1/96 q ( q^3-14*q^2+64*q-96 ) q congruent 5 modulo 12: 1/96 ( q^4-15*q^3+87*q^2-229*q+220 ) q congruent 7 modulo 12: 1/96 ( q^4-15*q^3+87*q^2-241*q+264 ) q congruent 8 modulo 12: 1/96 ( q^4-14*q^3+64*q^2-96*q+32 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-14*q^2+73*q-156 ) q congruent 11 modulo 12: 1/96 ( q^4-15*q^3+87*q^2-241*q+328 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 34, 36, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 30 ], [ 8, 1, 2, 16 ], [ 9, 1, 2, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 24 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 14 ], [ 17, 1, 3, 36 ], [ 18, 1, 3, 60 ], [ 19, 1, 2, 48 ], [ 22, 1, 4, 24 ], [ 23, 1, 4, 48 ], [ 24, 1, 3, 16 ], [ 25, 1, 8, 24 ], [ 26, 1, 3, 72 ], [ 28, 1, 6, 48 ], [ 29, 1, 4, 96 ], [ 31, 1, 7, 48 ], [ 34, 1, 4, 144 ], [ 35, 1, 10, 48 ] ] k = 16: F-action on Pi is (1,4) [39,1,16] Dynkin type is ^2A_3(q) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/12 q phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 15, 48, 16, 19, 57 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 24, 1, 4, 4 ], [ 28, 1, 4, 6 ], [ 35, 1, 9, 6 ] ] k = 17: F-action on Pi is (1,4) [39,1,17] Dynkin type is ^2A_3(q) + T(phi1^2 phi4) Order of center |Z^F|: phi1^2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 phi2 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 40, 13, 41, 57, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 1, 4 ], [ 25, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 34, 1, 6, 8 ], [ 35, 1, 7, 8 ] ] k = 18: F-action on Pi is (1,4) [39,1,18] Dynkin type is ^2A_3(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1^2 ( q^2-7*q+12 ) q congruent 2 modulo 12: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/32 q ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 12: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/32 phi1^2 ( q^2-7*q+12 ) q congruent 7 modulo 12: 1/32 q ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 12: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/32 phi1^2 ( q^2-7*q+12 ) q congruent 11 modulo 12: 1/32 q ( q^3-9*q^2+27*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 35, 4, 16, 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 4 ], [ 22, 1, 3, 8 ], [ 25, 1, 3, 16 ], [ 25, 1, 4, 8 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 8 ], [ 31, 1, 6, 16 ], [ 34, 1, 1, 48 ], [ 34, 1, 5, 16 ], [ 35, 1, 3, 16 ] ] k = 19: F-action on Pi is (1,4) [39,1,19] Dynkin type is ^2A_3(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 12: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 7 modulo 12: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) q congruent 11 modulo 12: 1/16 phi1 ( q^3-4*q^2+5*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 5, 35, 48, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 4 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 4, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 28, 1, 2, 8 ], [ 31, 1, 6, 8 ], [ 31, 1, 8, 8 ], [ 34, 1, 2, 16 ], [ 35, 1, 4, 8 ] ] k = 20: F-action on Pi is (1,4) [39,1,20] Dynkin type is ^2A_3(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 ( q^3-8*q^2+27*q-36 ) q congruent 2 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/96 ( q^4-9*q^3+35*q^2-75*q+72 ) q congruent 4 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/96 phi1 ( q^3-8*q^2+27*q-36 ) q congruent 7 modulo 12: 1/96 ( q^4-9*q^3+35*q^2-75*q+72 ) q congruent 8 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-8*q^2+27*q-36 ) q congruent 11 modulo 12: 1/96 ( q^4-9*q^3+35*q^2-75*q+72 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 34, 3, 15, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 18, 1, 4, 12 ], [ 22, 1, 4, 24 ], [ 24, 1, 4, 16 ], [ 25, 1, 4, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 6, 48 ], [ 31, 1, 8, 48 ], [ 34, 1, 3, 48 ], [ 35, 1, 10, 48 ] ] i = 40: Pi = [ 2, 5, 7 ] j = 1: Omega trivial k = 1: F-action on Pi is () [40,1,1] Dynkin type is 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 12: 1/576 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 2 modulo 12: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 3 modulo 12: 1/576 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 4 modulo 12: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1280 ) q congruent 5 modulo 12: 1/576 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 7 modulo 12: 1/576 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 8 modulo 12: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 9 modulo 12: 1/576 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 11 modulo 12: 1/576 ( q^4-28*q^3+286*q^2-1260*q+1881 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4, 32, 4, 4, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 48 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 11, 1, 1, 96 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 144 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 288 ], [ 26, 1, 1, 144 ], [ 27, 1, 1, 576 ], [ 28, 1, 1, 192 ], [ 32, 1, 1, 576 ], [ 35, 1, 1, 576 ] ] k = 2: F-action on Pi is () [40,1,2] Dynkin type is 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 12: 1/576 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 2 modulo 12: 1/1152 ( q^4-20*q^3+124*q^2-240*q+128 ) q congruent 3 modulo 12: 1/576 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 4 modulo 12: 1/1152 q ( q^3-20*q^2+124*q-240 ) q congruent 5 modulo 12: 1/576 ( q^4-20*q^3+142*q^2-420*q+425 ) q congruent 7 modulo 12: 1/576 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 8 modulo 12: 1/1152 ( q^4-20*q^3+124*q^2-240*q+128 ) q congruent 9 modulo 12: 1/576 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 11 modulo 12: 1/576 ( q^4-20*q^3+142*q^2-420*q+569 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 34, 2, 34, 2, 2, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 48 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 16, 1, 2, 24 ], [ 17, 1, 3, 144 ], [ 21, 1, 6, 192 ], [ 22, 1, 4, 288 ], [ 26, 1, 3, 144 ], [ 27, 1, 12, 576 ], [ 28, 1, 6, 192 ], [ 32, 1, 7, 576 ], [ 35, 1, 10, 576 ] ] k = 3: F-action on Pi is () [40,1,3] Dynkin type is 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 12: 1/32 phi1^2 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/32 phi1^2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/32 phi1^2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/32 phi1^2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/32 phi1^2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/32 phi1^2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 35, 5, 35, 5, 3, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 16 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 16 ], [ 27, 1, 1, 32 ], [ 27, 1, 2, 32 ], [ 27, 1, 8, 64 ], [ 27, 1, 12, 32 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 32 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ] ] k = 4: F-action on Pi is (2,5,7) [40,1,4] Dynkin type is 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 12: 1/18 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/18 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 12: 1/18 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/18 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/18 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/18 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 50 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 6 ], [ 16, 1, 1, 6 ], [ 21, 1, 5, 6 ], [ 28, 1, 1, 12 ], [ 32, 1, 9, 18 ] ] k = 5: F-action on Pi is (2,5,7) [40,1,5] Dynkin type is 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 12: 1/18 q^2 phi1^2 q congruent 2 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 12: 1/18 q^2 phi1^2 q congruent 4 modulo 12: 1/36 q^2 phi1^2 q congruent 5 modulo 12: 1/18 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 12: 1/18 q^2 phi1^2 q congruent 8 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 9 modulo 12: 1/18 q^2 phi1^2 q congruent 11 modulo 12: 1/18 phi2 ( q^3-3*q^2+4*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 6 ], [ 16, 1, 2, 6 ], [ 21, 1, 4, 6 ], [ 28, 1, 6, 12 ], [ 32, 1, 10, 18 ] ] k = 6: F-action on Pi is () [40,1,6] Dynkin type is 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 12: 1/48 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 12: 1/96 q^2 ( q^2-4 ) q congruent 3 modulo 12: 1/48 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 12: 1/96 q^2 ( q^2-4 ) q congruent 5 modulo 12: 1/48 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 12: 1/48 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 12: 1/96 q^2 ( q^2-4 ) q congruent 9 modulo 12: 1/48 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 12: 1/48 phi1 phi2 ( q^2-9 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 42, 42, 12, 42, 12, 12, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ] ] k = 7: F-action on Pi is () [40,1,7] Dynkin type is 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 12: 1/18 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/18 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 12: 1/18 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/18 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/18 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/18 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 45, 45, 18, 45, 18, 18, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 21, 1, 1, 12 ], [ 28, 1, 5, 6 ], [ 35, 1, 8, 18 ] ] k = 8: F-action on Pi is () [40,1,8] Dynkin type is 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 12: 1/18 q^2 phi1^2 q congruent 2 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 12: 1/18 q^2 phi1^2 q congruent 4 modulo 12: 1/36 q^2 phi1^2 q congruent 5 modulo 12: 1/18 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 12: 1/18 q^2 phi1^2 q congruent 8 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 9 modulo 12: 1/18 q^2 phi1^2 q congruent 11 modulo 12: 1/18 phi2 ( q^3-3*q^2+4*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 48, 48, 15, 48, 15, 15, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 21, 1, 6, 12 ], [ 28, 1, 4, 6 ], [ 35, 1, 9, 18 ] ] k = 9: F-action on Pi is (2,7,5) [40,1,9] Dynkin type is 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 12: 1/36 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 2 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 3 modulo 12: 1/36 q phi2 ( q^2+q-6 ) q congruent 4 modulo 12: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 5 modulo 12: 1/36 q phi2 ( q^2+q-6 ) q congruent 7 modulo 12: 1/36 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 8 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 9 modulo 12: 1/36 q phi2 ( q^2+q-6 ) q congruent 11 modulo 12: 1/36 q phi2 ( q^2+q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 21, 1, 5, 24 ], [ 28, 1, 5, 24 ] ] k = 10: F-action on Pi is (2,7,5) [40,1,10] Dynkin type is 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 12: 1/36 q phi1 ( q^2-q-6 ) q congruent 2 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 12: 1/36 q phi1 ( q^2-q-6 ) q congruent 4 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 5 modulo 12: 1/36 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 7 modulo 12: 1/36 q phi1 ( q^2-q-6 ) q congruent 8 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 9 modulo 12: 1/36 q phi1 ( q^2-q-6 ) q congruent 11 modulo 12: 1/36 phi2 ( q^3-3*q^2-2*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 21, 1, 4, 24 ], [ 28, 1, 4, 24 ] ] k = 11: F-action on Pi is (2,5,7) [40,1,11] Dynkin type is 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 12: 1/6 q^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/6 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/6 q^2 phi1 phi2 q congruent 7 modulo 12: 1/6 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/6 q^2 phi1 phi2 q congruent 11 modulo 12: 1/6 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 29, 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 12: F-action on Pi is (5,7) [40,1,12] Dynkin type is A_1(q) + 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 12: 1/48 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 2 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/48 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 4 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/48 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 7 modulo 12: 1/48 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 8 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/48 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 11 modulo 12: 1/48 ( q^4-12*q^3+44*q^2-48*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 41, 33, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 36 ], [ 10, 1, 4, 12 ], [ 11, 1, 1, 24 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 28, 1, 1, 48 ], [ 32, 1, 2, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ] ] k = 13: F-action on Pi is (2,5) [40,1,13] Dynkin type is 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 12: 1/48 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 2 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/48 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 4 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/48 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 7 modulo 12: 1/48 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 8 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/48 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 11 modulo 12: 1/48 ( q^4-8*q^3+20*q^2-28*q+39 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 40, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 36 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 13, 96 ], [ 28, 1, 6, 48 ], [ 32, 1, 5, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ] ] k = 14: F-action on Pi is (5,7) [40,1,14] Dynkin type is A_1(q) + A_1(q^2) + 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 12: 1/6 q^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/6 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/6 q^2 phi1 phi2 q congruent 7 modulo 12: 1/6 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/6 q^2 phi1 phi2 q congruent 11 modulo 12: 1/6 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 18, 58, 46, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 28, 1, 5, 6 ], [ 35, 1, 8, 6 ] ] k = 15: F-action on Pi is (2,5) [40,1,15] Dynkin type is 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 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/6 q phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 48, 57, 28 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 28, 1, 4, 6 ], [ 35, 1, 9, 6 ] ] k = 16: F-action on Pi is (5,7) [40,1,16] Dynkin type is A_1(q) + 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 12: 1/8 phi1^3 phi2 q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1^3 phi2 q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1^3 phi2 q congruent 7 modulo 12: 1/8 phi1^3 phi2 q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1^3 phi2 q congruent 11 modulo 12: 1/8 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 13, 42, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ] ] k = 17: F-action on Pi is () [40,1,17] Dynkin type is 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 12: 1/48 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/48 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/48 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 12: 1/48 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/48 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 12: 1/48 phi1 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35, 4, 35, 35, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 12 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 48 ], [ 28, 1, 3, 16 ], [ 32, 1, 1, 48 ], [ 32, 1, 6, 48 ], [ 35, 1, 2, 48 ] ] k = 18: F-action on Pi is () [40,1,18] Dynkin type is 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 12: 1/48 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 2 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/48 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 4 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/48 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 7 modulo 12: 1/48 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 8 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/48 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 11 modulo 12: 1/48 phi1 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 5, 5, 34, 5, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 36 ], [ 21, 1, 6, 48 ], [ 22, 1, 3, 24 ], [ 22, 1, 4, 24 ], [ 26, 1, 2, 12 ], [ 26, 1, 3, 24 ], [ 27, 1, 8, 48 ], [ 27, 1, 12, 96 ], [ 28, 1, 2, 16 ], [ 32, 1, 3, 48 ], [ 32, 1, 7, 48 ], [ 35, 1, 4, 48 ] ] k = 19: F-action on Pi is (2,5,7) [40,1,19] Dynkin type is 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 12: 1/6 q^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/6 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/6 q^2 phi1 phi2 q congruent 7 modulo 12: 1/6 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/6 q^2 phi1 phi2 q congruent 11 modulo 12: 1/6 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 49, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 21, 1, 5, 6 ], [ 28, 1, 3, 4 ], [ 32, 1, 9, 6 ] ] k = 20: F-action on Pi is (2,5,7) [40,1,20] Dynkin type is 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 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/6 q phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 51, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 21, 1, 4, 6 ], [ 28, 1, 2, 4 ], [ 32, 1, 10, 6 ] ] k = 21: F-action on Pi is () [40,1,21] Dynkin type is 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 12: 1/8 phi1 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/8 phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/8 phi1 phi2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 10, 13, 43, 13, 43, 40, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ] ] k = 22: F-action on Pi is (5,7) [40,1,22] Dynkin type is A_1(q) + 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 12: 1/8 phi1 phi4 ( q-3 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 phi1 phi4 ( q-3 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 phi4 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 phi4 ( q-3 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 phi4 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1 phi4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 13, 5, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 21, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 9, 16 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ] ] k = 23: F-action on Pi is (2,5) [40,1,23] Dynkin type is 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 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 10, 9, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 8 ], [ 32, 1, 8, 16 ], [ 35, 1, 7, 16 ] ] k = 24: F-action on Pi is (5,7) [40,1,24] Dynkin type is A_1(q) + A_1(q^2) + 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 12: 1/16 phi1^3 phi2 q congruent 2 modulo 12: 1/32 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1^3 phi2 q congruent 4 modulo 12: 1/32 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1^3 phi2 q congruent 7 modulo 12: 1/16 phi1^3 phi2 q congruent 8 modulo 12: 1/32 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1^3 phi2 q congruent 11 modulo 12: 1/16 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 40, 12, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 13, 32 ], [ 32, 1, 4, 16 ], [ 35, 1, 6, 16 ] ] k = 25: F-action on Pi is (5,7) [40,1,25] Dynkin type is A_1(q) + A_1(q^2) + 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 12: 1/4 phi1 phi2 phi4 q congruent 2 modulo 12: 1/8 q^4 q congruent 3 modulo 12: 1/4 phi1 phi2 phi4 q congruent 4 modulo 12: 1/8 q^4 q congruent 5 modulo 12: 1/4 phi1 phi2 phi4 q congruent 7 modulo 12: 1/4 phi1 phi2 phi4 q congruent 8 modulo 12: 1/8 q^4 q congruent 9 modulo 12: 1/4 phi1 phi2 phi4 q congruent 11 modulo 12: 1/4 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 53, 24, 23, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 41: Pi = [ 1, 2 ] j = 1: Omega trivial k = 1: F-action on Pi is () [41,1,1] Dynkin type is 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 12: 1/768 ( q^5-39*q^4+602*q^3-4638*q^2+18053*q-30107 ) q congruent 2 modulo 12: 1/768 ( q^5-38*q^4+548*q^3-3688*q^2+11232*q-11520 ) q congruent 3 modulo 12: 1/768 ( q^5-39*q^4+602*q^3-4638*q^2+17685*q-24651 ) q congruent 4 modulo 12: 1/768 ( q^5-38*q^4+548*q^3-3688*q^2+11360*q-12800 ) q congruent 5 modulo 12: 1/768 ( q^5-39*q^4+602*q^3-4638*q^2+17925*q-27675 ) q congruent 7 modulo 12: 1/768 ( q^5-39*q^4+602*q^3-4638*q^2+17813*q-27083 ) q congruent 8 modulo 12: 1/768 ( q^5-38*q^4+548*q^3-3688*q^2+11232*q-11520 ) q congruent 9 modulo 12: 1/768 ( q^5-39*q^4+602*q^3-4638*q^2+17925*q-27675 ) q congruent 11 modulo 12: 1/768 ( q^5-39*q^4+602*q^3-4638*q^2+17685*q-24651 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 32, 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 64 ], [ 4, 1, 1, 144 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 72 ], [ 8, 1, 1, 192 ], [ 9, 1, 1, 320 ], [ 10, 1, 1, 384 ], [ 11, 1, 1, 128 ], [ 12, 1, 1, 384 ], [ 13, 1, 1, 64 ], [ 14, 1, 1, 128 ], [ 15, 1, 1, 224 ], [ 16, 1, 1, 26 ], [ 17, 1, 1, 172 ], [ 18, 1, 1, 112 ], [ 19, 1, 1, 320 ], [ 20, 1, 1, 640 ], [ 21, 1, 1, 768 ], [ 22, 1, 1, 512 ], [ 23, 1, 1, 192 ], [ 24, 1, 1, 448 ], [ 25, 1, 1, 512 ], [ 26, 1, 1, 240 ], [ 27, 1, 1, 960 ], [ 28, 1, 1, 192 ], [ 29, 1, 1, 384 ], [ 30, 1, 1, 896 ], [ 31, 1, 1, 576 ], [ 32, 1, 1, 1152 ], [ 33, 1, 1, 768 ], [ 34, 1, 1, 288 ], [ 35, 1, 1, 576 ], [ 36, 1, 1, 1152 ], [ 37, 1, 1, 768 ], [ 38, 1, 1, 1152 ], [ 39, 1, 1, 384 ], [ 40, 1, 1, 1152 ] ] k = 2: F-action on Pi is () [41,1,2] Dynkin type is 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 12: 1/64 phi1 ( q^4-18*q^3+120*q^2-358*q+415 ) q congruent 2 modulo 12: 1/64 q ( q^4-18*q^3+116*q^2-312*q+288 ) q congruent 3 modulo 12: 1/64 phi1 ( q^4-18*q^3+120*q^2-358*q+399 ) q congruent 4 modulo 12: 1/64 q ( q^4-18*q^3+116*q^2-312*q+288 ) q congruent 5 modulo 12: 1/64 phi1 ( q^4-18*q^3+120*q^2-358*q+415 ) q congruent 7 modulo 12: 1/64 phi1 ( q^4-18*q^3+120*q^2-358*q+399 ) q congruent 8 modulo 12: 1/64 q ( q^4-18*q^3+116*q^2-312*q+288 ) q congruent 9 modulo 12: 1/64 phi1 ( q^4-18*q^3+120*q^2-358*q+415 ) q congruent 11 modulo 12: 1/64 phi1 ( q^4-18*q^3+120*q^2-358*q+399 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 24 ], [ 4, 1, 1, 48 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 24 ], [ 8, 1, 1, 48 ], [ 9, 1, 1, 72 ], [ 10, 1, 1, 96 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 15, 1, 3, 16 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 48 ], [ 17, 1, 3, 12 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 8 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 96 ], [ 21, 1, 1, 144 ], [ 22, 1, 1, 72 ], [ 22, 1, 2, 40 ], [ 23, 1, 1, 16 ], [ 23, 1, 2, 16 ], [ 24, 1, 1, 48 ], [ 24, 1, 2, 32 ], [ 25, 1, 1, 96 ], [ 25, 1, 5, 32 ], [ 26, 1, 1, 48 ], [ 26, 1, 2, 16 ], [ 27, 1, 1, 192 ], [ 27, 1, 8, 64 ], [ 28, 1, 3, 16 ], [ 29, 1, 2, 32 ], [ 30, 1, 1, 96 ], [ 30, 1, 2, 64 ], [ 31, 1, 1, 48 ], [ 31, 1, 2, 32 ], [ 31, 1, 3, 48 ], [ 32, 1, 1, 144 ], [ 32, 1, 6, 80 ], [ 33, 1, 3, 64 ], [ 34, 1, 1, 48 ], [ 34, 1, 2, 16 ], [ 35, 1, 2, 48 ], [ 36, 1, 1, 192 ], [ 36, 1, 4, 64 ], [ 37, 1, 2, 64 ], [ 38, 1, 1, 96 ], [ 38, 1, 2, 64 ], [ 38, 1, 8, 96 ], [ 39, 1, 2, 32 ], [ 40, 1, 17, 96 ] ] k = 3: F-action on Pi is () [41,1,3] Dynkin type is 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 12: 1/24 phi1 ( q^4-8*q^3+15*q^2+12*q-28 ) q congruent 2 modulo 12: 1/24 q phi2 ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 12: 1/24 q phi2 ( q^3-10*q^2+33*q-36 ) q congruent 4 modulo 12: 1/24 phi1^2 ( q^3-6*q^2+4*q+16 ) q congruent 5 modulo 12: 1/24 q phi2 ( q^3-10*q^2+33*q-36 ) q congruent 7 modulo 12: 1/24 phi1 ( q^4-8*q^3+15*q^2+12*q-28 ) q congruent 8 modulo 12: 1/24 q phi2 ( q^3-9*q^2+26*q-24 ) q congruent 9 modulo 12: 1/24 q phi2 ( q^3-10*q^2+33*q-36 ) q congruent 11 modulo 12: 1/24 q phi2 ( q^3-10*q^2+33*q-36 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 45, 45, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 10 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 8 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 8 ], [ 28, 1, 5, 6 ], [ 29, 1, 3, 12 ], [ 30, 1, 1, 8 ], [ 33, 1, 2, 24 ], [ 35, 1, 8, 18 ], [ 37, 1, 3, 24 ], [ 39, 1, 3, 12 ], [ 40, 1, 7, 36 ] ] k = 4: F-action on Pi is () [41,1,4] Dynkin type is 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 12: 1/16 phi1 phi2 ( q^3-5*q^2+q+15 ) q congruent 2 modulo 12: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^3-5*q^2+q+15 ) q congruent 4 modulo 12: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^3-5*q^2+q+15 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^3-5*q^2+q+15 ) q congruent 8 modulo 12: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^3-5*q^2+q+15 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^3-5*q^2+q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 10, 13, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 32, 1, 2, 8 ], [ 32, 1, 8, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 37, 1, 4, 16 ], [ 40, 1, 21, 16 ] ] k = 5: F-action on Pi is () [41,1,5] Dynkin type is 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 12: 1/64 phi1^2 ( q^3-9*q^2+19*q+5 ) q congruent 2 modulo 12: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 3 modulo 12: 1/64 ( q^5-11*q^4+38*q^3-42*q^2+9*q-27 ) q congruent 4 modulo 12: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 5 modulo 12: 1/64 phi1^2 ( q^3-9*q^2+19*q+5 ) q congruent 7 modulo 12: 1/64 ( q^5-11*q^4+38*q^3-42*q^2+9*q-27 ) q congruent 8 modulo 12: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 9 modulo 12: 1/64 phi1^2 ( q^3-9*q^2+19*q+5 ) q congruent 11 modulo 12: 1/64 ( q^5-11*q^4+38*q^3-42*q^2+9*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 33, 35, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 16 ], [ 11, 1, 1, 8 ], [ 15, 1, 3, 32 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 24 ], [ 18, 1, 2, 16 ], [ 21, 1, 1, 48 ], [ 21, 1, 2, 32 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 32 ], [ 22, 1, 3, 24 ], [ 24, 1, 2, 32 ], [ 25, 1, 5, 64 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 16 ], [ 27, 1, 1, 96 ], [ 27, 1, 2, 32 ], [ 27, 1, 8, 96 ], [ 27, 1, 12, 32 ], [ 30, 1, 2, 64 ], [ 31, 1, 2, 32 ], [ 31, 1, 4, 32 ], [ 32, 1, 1, 48 ], [ 32, 1, 2, 32 ], [ 32, 1, 3, 48 ], [ 32, 1, 6, 64 ], [ 34, 1, 2, 32 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 36, 1, 4, 128 ], [ 37, 1, 5, 64 ], [ 38, 1, 2, 64 ], [ 38, 1, 5, 64 ], [ 40, 1, 3, 64 ] ] k = 6: F-action on Pi is () [41,1,6] Dynkin type is 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 12: 1/64 phi1 ( q^4-12*q^3+58*q^2-148*q+165 ) q congruent 2 modulo 12: 1/64 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 3 modulo 12: 1/64 ( q^5-13*q^4+70*q^3-206*q^2+329*q-213 ) q congruent 4 modulo 12: 1/64 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 5 modulo 12: 1/64 phi1 ( q^4-12*q^3+58*q^2-148*q+165 ) q congruent 7 modulo 12: 1/64 ( q^5-13*q^4+70*q^3-206*q^2+329*q-213 ) q congruent 8 modulo 12: 1/64 q ( q^4-12*q^3+52*q^2-96*q+64 ) q congruent 9 modulo 12: 1/64 phi1 ( q^4-12*q^3+58*q^2-148*q+165 ) q congruent 11 modulo 12: 1/64 ( q^5-13*q^4+70*q^3-206*q^2+329*q-213 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 24 ], [ 4, 1, 2, 48 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 24 ], [ 8, 1, 2, 48 ], [ 9, 1, 2, 72 ], [ 10, 1, 4, 96 ], [ 11, 1, 2, 24 ], [ 12, 1, 6, 96 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 32 ], [ 15, 1, 2, 16 ], [ 15, 1, 4, 48 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 8 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 48 ], [ 18, 1, 3, 24 ], [ 18, 1, 4, 8 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 96 ], [ 21, 1, 6, 144 ], [ 22, 1, 3, 40 ], [ 22, 1, 4, 72 ], [ 23, 1, 3, 16 ], [ 23, 1, 4, 16 ], [ 24, 1, 3, 48 ], [ 24, 1, 4, 32 ], [ 25, 1, 4, 32 ], [ 25, 1, 8, 96 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 48 ], [ 27, 1, 8, 64 ], [ 27, 1, 12, 192 ], [ 28, 1, 2, 16 ], [ 29, 1, 5, 32 ], [ 30, 1, 5, 96 ], [ 30, 1, 6, 64 ], [ 31, 1, 5, 48 ], [ 31, 1, 7, 48 ], [ 31, 1, 8, 32 ], [ 32, 1, 3, 80 ], [ 32, 1, 7, 144 ], [ 33, 1, 4, 64 ], [ 34, 1, 3, 16 ], [ 34, 1, 4, 48 ], [ 35, 1, 4, 48 ], [ 36, 1, 18, 64 ], [ 36, 1, 20, 192 ], [ 37, 1, 7, 64 ], [ 38, 1, 3, 96 ], [ 38, 1, 6, 64 ], [ 38, 1, 7, 96 ], [ 39, 1, 11, 32 ], [ 40, 1, 18, 96 ] ] k = 7: F-action on Pi is () [41,1,7] Dynkin type is 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 12: 1/64 phi1^2 ( q^3-7*q^2+15*q-17 ) q congruent 2 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/64 ( q^5-9*q^4+30*q^3-54*q^2+49*q+15 ) q congruent 4 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/64 phi1^2 ( q^3-7*q^2+15*q-17 ) q congruent 7 modulo 12: 1/64 ( q^5-9*q^4+30*q^3-54*q^2+49*q+15 ) q congruent 8 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/64 phi1^2 ( q^3-7*q^2+15*q-17 ) q congruent 11 modulo 12: 1/64 ( q^5-9*q^4+30*q^3-54*q^2+49*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 3, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 24 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 1, 16 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 15, 1, 2, 32 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 36 ], [ 18, 1, 4, 16 ], [ 21, 1, 3, 32 ], [ 21, 1, 6, 48 ], [ 22, 1, 2, 24 ], [ 22, 1, 3, 32 ], [ 22, 1, 4, 24 ], [ 24, 1, 4, 32 ], [ 25, 1, 4, 64 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 16 ], [ 27, 1, 1, 32 ], [ 27, 1, 2, 32 ], [ 27, 1, 8, 96 ], [ 27, 1, 12, 96 ], [ 30, 1, 6, 64 ], [ 31, 1, 6, 32 ], [ 31, 1, 8, 32 ], [ 32, 1, 3, 64 ], [ 32, 1, 5, 32 ], [ 32, 1, 6, 48 ], [ 32, 1, 7, 48 ], [ 34, 1, 3, 32 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 36, 1, 18, 128 ], [ 37, 1, 9, 64 ], [ 38, 1, 4, 64 ], [ 38, 1, 6, 64 ], [ 40, 1, 3, 64 ] ] k = 8: F-action on Pi is () [41,1,8] Dynkin type is 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 12: 1/24 q phi1^3 ( q-2 ) q congruent 2 modulo 12: 1/24 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 3 modulo 12: 1/24 q phi1^3 ( q-2 ) q congruent 4 modulo 12: 1/24 q^2 phi1^2 ( q-2 ) q congruent 5 modulo 12: 1/24 phi2 ( q^4-6*q^3+15*q^2-22*q+20 ) q congruent 7 modulo 12: 1/24 q phi1^3 ( q-2 ) q congruent 8 modulo 12: 1/24 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 9 modulo 12: 1/24 q phi1^3 ( q-2 ) q congruent 11 modulo 12: 1/24 phi2 ( q^4-6*q^3+15*q^2-22*q+20 ) Fusion of maximal tori of C^F in those of G^F: [ 48, 15, 15, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 10 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 18, 1, 3, 4 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 21, 1, 6, 12 ], [ 22, 1, 4, 8 ], [ 24, 1, 3, 4 ], [ 25, 1, 8, 8 ], [ 28, 1, 4, 6 ], [ 29, 1, 6, 12 ], [ 30, 1, 5, 8 ], [ 33, 1, 5, 24 ], [ 35, 1, 9, 18 ], [ 37, 1, 8, 24 ], [ 39, 1, 12, 12 ], [ 40, 1, 8, 36 ] ] k = 9: F-action on Pi is () [41,1,9] Dynkin type is 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 12: 1/16 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/16 q^4 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/16 q^4 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/16 q^4 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 13, 40, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 37, 1, 10, 16 ], [ 40, 1, 21, 16 ] ] k = 10: F-action on Pi is () [41,1,10] Dynkin type is 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 12: 1/128 phi1^3 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/128 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/128 phi1^3 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/128 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/128 phi1^3 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/128 phi1^3 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/128 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/128 phi1^3 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/128 phi1^3 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 5, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 24 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 12 ], [ 10, 1, 1, 16 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 48 ], [ 14, 1, 2, 32 ], [ 15, 1, 3, 16 ], [ 15, 1, 4, 48 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 36 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 24 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 48 ], [ 23, 1, 3, 32 ], [ 25, 1, 5, 32 ], [ 25, 1, 6, 32 ], [ 25, 1, 7, 32 ], [ 25, 1, 8, 96 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 16 ], [ 27, 1, 1, 32 ], [ 27, 1, 2, 32 ], [ 27, 1, 8, 96 ], [ 27, 1, 12, 96 ], [ 31, 1, 4, 32 ], [ 31, 1, 5, 96 ], [ 32, 1, 3, 96 ], [ 32, 1, 6, 32 ], [ 34, 1, 2, 16 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 32 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 36, 1, 4, 64 ], [ 36, 1, 5, 64 ], [ 36, 1, 20, 192 ], [ 38, 1, 3, 192 ], [ 38, 1, 5, 64 ], [ 39, 1, 4, 64 ], [ 39, 1, 13, 64 ], [ 40, 1, 3, 64 ] ] k = 11: F-action on Pi is () [41,1,11] Dynkin type is 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 12: 1/64 phi1^2 ( q^3-7*q^2+19*q-21 ) q congruent 2 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/64 phi1^2 ( q^3-7*q^2+19*q-21 ) q congruent 4 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/64 phi1^2 ( q^3-7*q^2+19*q-21 ) q congruent 7 modulo 12: 1/64 phi1^2 ( q^3-7*q^2+19*q-21 ) q congruent 8 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/64 phi1^2 ( q^3-7*q^2+19*q-21 ) q congruent 11 modulo 12: 1/64 phi1^2 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 35, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 10, 1, 4, 16 ], [ 11, 1, 1, 8 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 16 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 24 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 8 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 40 ], [ 22, 1, 3, 16 ], [ 24, 1, 2, 16 ], [ 25, 1, 4, 32 ], [ 25, 1, 5, 32 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 8 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 96 ], [ 27, 1, 12, 32 ], [ 28, 1, 3, 16 ], [ 30, 1, 2, 32 ], [ 31, 1, 2, 16 ], [ 31, 1, 4, 16 ], [ 31, 1, 6, 32 ], [ 32, 1, 1, 48 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 80 ], [ 34, 1, 2, 16 ], [ 34, 1, 3, 16 ], [ 35, 1, 2, 48 ], [ 36, 1, 4, 64 ], [ 36, 1, 18, 64 ], [ 38, 1, 2, 32 ], [ 38, 1, 4, 64 ], [ 38, 1, 5, 32 ], [ 39, 1, 5, 32 ], [ 40, 1, 17, 96 ] ] k = 12: F-action on Pi is () [41,1,12] Dynkin type is 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 12: 1/32 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/32 q^4 ( q-2 ) q congruent 3 modulo 12: 1/32 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/32 q^4 ( q-2 ) q congruent 5 modulo 12: 1/32 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/32 q^4 ( q-2 ) q congruent 9 modulo 12: 1/32 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 10, 43, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 34, 1, 7, 8 ], [ 34, 1, 8, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 5, 16 ], [ 36, 1, 10, 16 ], [ 39, 1, 6, 16 ], [ 39, 1, 14, 16 ], [ 40, 1, 21, 16 ] ] k = 13: F-action on Pi is () [41,1,13] Dynkin type is 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 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 7 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 11 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 45, 18, 18, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 21, 1, 1, 12 ], [ 22, 1, 2, 8 ], [ 24, 1, 2, 4 ], [ 25, 1, 5, 8 ], [ 28, 1, 5, 6 ], [ 30, 1, 2, 8 ], [ 35, 1, 8, 18 ], [ 39, 1, 7, 12 ], [ 40, 1, 7, 36 ] ] k = 14: F-action on Pi is () [41,1,14] Dynkin type is 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 12: 1/64 phi1^2 phi2 ( q^2-9 ) q congruent 2 modulo 12: 1/64 q^3 ( q^2-4 ) q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q^2-9 ) q congruent 4 modulo 12: 1/64 q^3 ( q^2-4 ) q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q^2-9 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q^2-9 ) q congruent 8 modulo 12: 1/64 q^3 ( q^2-4 ) q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q^2-9 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q^2-9 ) Fusion of maximal tori of C^F in those of G^F: [ 42, 12, 12, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 32, 1, 4, 32 ], [ 34, 1, 8, 16 ], [ 36, 1, 10, 32 ], [ 40, 1, 6, 96 ] ] k = 15: F-action on Pi is () [41,1,15] Dynkin type is 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 12: 1/768 phi1 ( q^4-20*q^3+158*q^2-580*q+825 ) q congruent 2 modulo 12: 1/768 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 3 modulo 12: 1/768 phi1 ( q^4-20*q^3+158*q^2-580*q+777 ) q congruent 4 modulo 12: 1/768 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 5 modulo 12: 1/768 phi1 ( q^4-20*q^3+158*q^2-580*q+825 ) q congruent 7 modulo 12: 1/768 phi1 ( q^4-20*q^3+158*q^2-580*q+777 ) q congruent 8 modulo 12: 1/768 q ( q^4-20*q^3+140*q^2-400*q+384 ) q congruent 9 modulo 12: 1/768 phi1 ( q^4-20*q^3+158*q^2-580*q+825 ) q congruent 11 modulo 12: 1/768 phi1 ( q^4-20*q^3+158*q^2-580*q+777 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 4, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 48 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 11, 1, 1, 96 ], [ 15, 1, 3, 32 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 144 ], [ 17, 1, 3, 28 ], [ 18, 1, 2, 16 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 288 ], [ 22, 1, 2, 32 ], [ 24, 1, 2, 64 ], [ 25, 1, 5, 128 ], [ 26, 1, 1, 144 ], [ 26, 1, 2, 48 ], [ 27, 1, 1, 576 ], [ 27, 1, 8, 192 ], [ 28, 1, 1, 192 ], [ 30, 1, 2, 128 ], [ 31, 1, 2, 192 ], [ 32, 1, 1, 576 ], [ 32, 1, 6, 192 ], [ 34, 1, 2, 96 ], [ 35, 1, 1, 576 ], [ 36, 1, 4, 384 ], [ 38, 1, 2, 384 ], [ 39, 1, 8, 384 ], [ 40, 1, 1, 1152 ] ] k = 16: F-action on Pi is () [41,1,16] Dynkin type is 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 12: 1/768 phi1 ( q^4-28*q^3+302*q^2-1580*q+3609 ) q congruent 2 modulo 12: 1/768 ( q^5-28*q^4+284*q^3-1232*q^2+2048*q-1024 ) q congruent 3 modulo 12: 1/768 ( q^5-29*q^4+330*q^3-1882*q^2+5429*q-6153 ) q congruent 4 modulo 12: 1/768 q ( q^4-28*q^3+284*q^2-1232*q+1920 ) q congruent 5 modulo 12: 1/768 ( q^5-29*q^4+330*q^3-1882*q^2+5317*q-5785 ) q congruent 7 modulo 12: 1/768 ( q^5-29*q^4+330*q^3-1882*q^2+5429*q-6153 ) q congruent 8 modulo 12: 1/768 ( q^5-28*q^4+284*q^3-1232*q^2+2048*q-1024 ) q congruent 9 modulo 12: 1/768 phi1 ( q^4-28*q^3+302*q^2-1580*q+3609 ) q congruent 11 modulo 12: 1/768 ( q^5-29*q^4+330*q^3-1882*q^2+5557*q-8329 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 2, 2, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 2, 64 ], [ 4, 1, 2, 144 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 72 ], [ 8, 1, 2, 192 ], [ 9, 1, 2, 320 ], [ 10, 1, 4, 384 ], [ 11, 1, 2, 128 ], [ 12, 1, 6, 384 ], [ 13, 1, 2, 64 ], [ 14, 1, 2, 128 ], [ 15, 1, 4, 224 ], [ 16, 1, 2, 26 ], [ 17, 1, 3, 172 ], [ 18, 1, 3, 112 ], [ 19, 1, 2, 320 ], [ 20, 1, 2, 640 ], [ 21, 1, 6, 768 ], [ 22, 1, 4, 512 ], [ 23, 1, 4, 192 ], [ 24, 1, 3, 448 ], [ 25, 1, 8, 512 ], [ 26, 1, 3, 240 ], [ 27, 1, 12, 960 ], [ 28, 1, 6, 192 ], [ 29, 1, 4, 384 ], [ 30, 1, 5, 896 ], [ 31, 1, 7, 576 ], [ 32, 1, 7, 1152 ], [ 33, 1, 6, 768 ], [ 34, 1, 4, 288 ], [ 35, 1, 10, 576 ], [ 36, 1, 20, 1152 ], [ 37, 1, 6, 768 ], [ 38, 1, 7, 1152 ], [ 39, 1, 15, 384 ], [ 40, 1, 2, 1152 ] ] k = 17: F-action on Pi is () [41,1,17] Dynkin type is 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 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 48, 48, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 8 ], [ 24, 1, 4, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 4, 6 ], [ 30, 1, 6, 8 ], [ 35, 1, 9, 18 ], [ 39, 1, 16, 12 ], [ 40, 1, 8, 36 ] ] k = 18: F-action on Pi is () [41,1,18] Dynkin type is 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 12: 1/32 phi1 phi2 ( q^3-5*q^2+5*q+3 ) q congruent 2 modulo 12: 1/32 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/32 phi1 phi2 ( q^3-5*q^2+5*q+3 ) q congruent 4 modulo 12: 1/32 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/32 phi1 phi2 ( q^3-5*q^2+5*q+3 ) q congruent 7 modulo 12: 1/32 phi1 phi2 ( q^3-5*q^2+5*q+3 ) q congruent 8 modulo 12: 1/32 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/32 phi1 phi2 ( q^3-5*q^2+5*q+3 ) q congruent 11 modulo 12: 1/32 phi1 phi2 ( q^3-5*q^2+5*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 13, 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 34, 1, 5, 8 ], [ 34, 1, 6, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 2, 16 ], [ 36, 1, 17, 16 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 16 ], [ 40, 1, 21, 16 ] ] k = 19: F-action on Pi is () [41,1,19] Dynkin type is 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 12: 1/128 phi1^2 ( q^3-9*q^2+27*q-27 ) q congruent 2 modulo 12: 1/128 q ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 3 modulo 12: 1/128 phi1^2 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 12: 1/128 q ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 5 modulo 12: 1/128 phi1^2 ( q^3-9*q^2+27*q-27 ) q congruent 7 modulo 12: 1/128 phi1^2 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 12: 1/128 q ( q^4-10*q^3+36*q^2-56*q+32 ) q congruent 9 modulo 12: 1/128 phi1^2 ( q^3-9*q^2+27*q-27 ) q congruent 11 modulo 12: 1/128 phi1^2 ( q^3-9*q^2+27*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 35, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 8 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 48 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 16 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 24 ], [ 17, 1, 4, 16 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 8 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 16 ], [ 23, 1, 2, 32 ], [ 25, 1, 1, 96 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 32 ], [ 25, 1, 4, 32 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 16 ], [ 27, 1, 1, 96 ], [ 27, 1, 2, 32 ], [ 27, 1, 8, 96 ], [ 27, 1, 12, 32 ], [ 31, 1, 3, 96 ], [ 31, 1, 6, 32 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 96 ], [ 34, 1, 1, 48 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 32 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 36, 1, 1, 192 ], [ 36, 1, 2, 64 ], [ 36, 1, 18, 64 ], [ 38, 1, 4, 64 ], [ 38, 1, 8, 192 ], [ 39, 1, 10, 64 ], [ 39, 1, 18, 64 ], [ 40, 1, 3, 64 ] ] k = 20: F-action on Pi is () [41,1,20] Dynkin type is 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 12: 1/64 phi1^2 ( q^3-5*q^2+11*q-15 ) q congruent 2 modulo 12: 1/64 q^2 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 12: 1/64 phi1^2 ( q^3-5*q^2+11*q-15 ) q congruent 4 modulo 12: 1/64 q^2 ( q^3-6*q^2+12*q-8 ) q congruent 5 modulo 12: 1/64 phi1^2 ( q^3-5*q^2+11*q-15 ) q congruent 7 modulo 12: 1/64 phi1^2 ( q^3-5*q^2+11*q-15 ) q congruent 8 modulo 12: 1/64 q^2 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 12: 1/64 phi1^2 ( q^3-5*q^2+11*q-15 ) q congruent 11 modulo 12: 1/64 phi1^2 ( q^3-5*q^2+11*q-15 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 5, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 24 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 1, 16 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 36 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 8 ], [ 21, 1, 6, 48 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 40 ], [ 22, 1, 4, 24 ], [ 24, 1, 4, 16 ], [ 25, 1, 4, 32 ], [ 25, 1, 5, 32 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 96 ], [ 27, 1, 12, 96 ], [ 28, 1, 2, 16 ], [ 30, 1, 6, 32 ], [ 31, 1, 4, 32 ], [ 31, 1, 6, 16 ], [ 31, 1, 8, 16 ], [ 32, 1, 3, 80 ], [ 32, 1, 6, 32 ], [ 32, 1, 7, 48 ], [ 34, 1, 2, 16 ], [ 34, 1, 3, 16 ], [ 35, 1, 4, 48 ], [ 36, 1, 4, 64 ], [ 36, 1, 18, 64 ], [ 38, 1, 4, 32 ], [ 38, 1, 5, 64 ], [ 38, 1, 6, 32 ], [ 39, 1, 19, 32 ], [ 40, 1, 18, 96 ] ] k = 21: F-action on Pi is () [41,1,21] Dynkin type is 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 12: 1/64 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 2 modulo 12: 1/64 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 12: 1/64 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 4 modulo 12: 1/64 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 12: 1/64 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 7 modulo 12: 1/64 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 8 modulo 12: 1/64 q^2 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 12: 1/64 phi1 phi2 ( q^3-3*q^2-9*q+27 ) q congruent 11 modulo 12: 1/64 phi1 phi2 ( q^3-3*q^2-9*q+27 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 42, 42, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 4, 8 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 32, 1, 8, 32 ], [ 34, 1, 6, 16 ], [ 36, 1, 17, 32 ], [ 40, 1, 6, 96 ] ] k = 22: F-action on Pi is () [41,1,22] Dynkin type is 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 12: 1/768 phi1 ( q^4-14*q^3+84*q^2-258*q+315 ) q congruent 2 modulo 12: 1/768 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 3 modulo 12: 1/768 ( q^5-15*q^4+98*q^3-342*q^2+621*q-459 ) q congruent 4 modulo 12: 1/768 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 5 modulo 12: 1/768 phi1 ( q^4-14*q^3+84*q^2-258*q+315 ) q congruent 7 modulo 12: 1/768 ( q^5-15*q^4+98*q^3-342*q^2+621*q-459 ) q congruent 8 modulo 12: 1/768 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 9 modulo 12: 1/768 phi1 ( q^4-14*q^3+84*q^2-258*q+315 ) q congruent 11 modulo 12: 1/768 ( q^5-15*q^4+98*q^3-342*q^2+621*q-459 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 48 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 15, 1, 2, 32 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 24 ], [ 17, 1, 1, 28 ], [ 17, 1, 3, 144 ], [ 18, 1, 4, 16 ], [ 21, 1, 6, 192 ], [ 22, 1, 3, 32 ], [ 22, 1, 4, 288 ], [ 24, 1, 4, 64 ], [ 25, 1, 4, 128 ], [ 26, 1, 2, 48 ], [ 26, 1, 3, 144 ], [ 27, 1, 8, 192 ], [ 27, 1, 12, 576 ], [ 28, 1, 6, 192 ], [ 30, 1, 6, 128 ], [ 31, 1, 8, 192 ], [ 32, 1, 3, 192 ], [ 32, 1, 7, 576 ], [ 34, 1, 3, 96 ], [ 35, 1, 10, 576 ], [ 36, 1, 18, 384 ], [ 38, 1, 6, 384 ], [ 39, 1, 20, 384 ], [ 40, 1, 2, 1152 ] ] k = 23: F-action on Pi is (1,2) [41,1,23] Dynkin type is 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 12: 1/192 phi1^2 ( q^3-7*q^2+13*q-15 ) q congruent 2 modulo 12: 1/192 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/192 phi1 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 4 modulo 12: 1/192 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/192 phi1^2 ( q^3-7*q^2+13*q-15 ) q congruent 7 modulo 12: 1/192 phi1 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 8 modulo 12: 1/192 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/192 phi1^2 ( q^3-7*q^2+13*q-15 ) q congruent 11 modulo 12: 1/192 phi1 ( q^4-8*q^3+20*q^2-28*q+39 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 12 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 30 ], [ 8, 1, 2, 16 ], [ 9, 1, 2, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 36 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 24 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 14 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 36 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 60 ], [ 19, 1, 2, 48 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 1, 4, 48 ], [ 24, 1, 3, 16 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 72 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 24 ], [ 26, 1, 3, 72 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 11, 96 ], [ 27, 1, 13, 96 ], [ 28, 1, 6, 48 ], [ 29, 1, 4, 96 ], [ 30, 1, 8, 32 ], [ 31, 1, 4, 48 ], [ 31, 1, 7, 48 ], [ 32, 1, 5, 48 ], [ 34, 1, 4, 144 ], [ 34, 1, 7, 24 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ], [ 36, 1, 5, 48 ], [ 36, 1, 19, 192 ], [ 38, 1, 16, 96 ], [ 39, 1, 4, 96 ], [ 39, 1, 15, 96 ], [ 40, 1, 13, 96 ] ] k = 24: F-action on Pi is (1,2) [41,1,24] Dynkin type is 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 12: 1/32 phi1^2 phi2 ( q^2-4*q+1 ) q congruent 2 modulo 12: 1/32 q^2 ( q^3-4*q^2+8 ) q congruent 3 modulo 12: 1/32 phi2 phi4 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/32 q^2 ( q^3-4*q^2+8 ) q congruent 5 modulo 12: 1/32 phi1^2 phi2 ( q^2-4*q+1 ) q congruent 7 modulo 12: 1/32 phi2 phi4 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/32 q^2 ( q^3-4*q^2+8 ) q congruent 9 modulo 12: 1/32 phi1^2 phi2 ( q^2-4*q+1 ) q congruent 11 modulo 12: 1/32 phi2 phi4 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 1, 3, 8 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 16 ], [ 13, 1, 2, 8 ], [ 14, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 1, 7, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 3, 8 ], [ 23, 1, 4, 8 ], [ 24, 1, 2, 8 ], [ 24, 1, 3, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 4, 16 ], [ 27, 1, 9, 16 ], [ 27, 1, 11, 16 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 29, 1, 5, 16 ], [ 30, 1, 3, 16 ], [ 30, 1, 8, 16 ], [ 31, 1, 2, 8 ], [ 31, 1, 4, 8 ], [ 31, 1, 5, 8 ], [ 31, 1, 7, 8 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 33, 1, 12, 32 ], [ 34, 1, 3, 16 ], [ 34, 1, 7, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 36, 1, 5, 16 ], [ 36, 1, 14, 32 ], [ 38, 1, 9, 16 ], [ 38, 1, 16, 16 ], [ 39, 1, 5, 16 ], [ 39, 1, 11, 16 ], [ 40, 1, 22, 16 ] ] k = 25: F-action on Pi is (1,2) [41,1,25] Dynkin type is 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 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 7 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) q congruent 11 modulo 12: 1/24 q phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 48, 28 ] 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 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 21, 1, 3, 4 ], [ 24, 1, 3, 4 ], [ 25, 1, 7, 8 ], [ 28, 1, 4, 6 ], [ 29, 1, 6, 12 ], [ 30, 1, 8, 8 ], [ 35, 1, 9, 6 ], [ 39, 1, 12, 12 ], [ 40, 1, 15, 12 ] ] k = 26: F-action on Pi is (1,2) [41,1,26] Dynkin type is 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 12: 1/64 phi1^4 phi2 q congruent 2 modulo 12: 1/64 q^4 ( q-2 ) q congruent 3 modulo 12: 1/64 phi1^4 phi2 q congruent 4 modulo 12: 1/64 q^4 ( q-2 ) q congruent 5 modulo 12: 1/64 phi1^4 phi2 q congruent 7 modulo 12: 1/64 phi1^4 phi2 q congruent 8 modulo 12: 1/64 q^4 ( q-2 ) q congruent 9 modulo 12: 1/64 phi1^4 phi2 q congruent 11 modulo 12: 1/64 phi1^4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 12 ], [ 10, 1, 2, 16 ], [ 15, 1, 3, 16 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 12 ], [ 18, 1, 3, 24 ], [ 25, 1, 6, 32 ], [ 26, 1, 3, 24 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 11, 32 ], [ 27, 1, 13, 32 ], [ 32, 1, 4, 16 ], [ 34, 1, 4, 48 ], [ 34, 1, 8, 8 ], [ 35, 1, 6, 16 ], [ 36, 1, 10, 16 ], [ 36, 1, 19, 64 ], [ 38, 1, 12, 32 ], [ 39, 1, 6, 32 ], [ 40, 1, 24, 32 ] ] k = 27: F-action on Pi is (1,2) [41,1,27] Dynkin type is 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 12: 1/32 phi1^4 phi2 q congruent 2 modulo 12: 1/32 q^4 ( q-2 ) q congruent 3 modulo 12: 1/32 phi1^4 phi2 q congruent 4 modulo 12: 1/32 q^4 ( q-2 ) q congruent 5 modulo 12: 1/32 phi1^4 phi2 q congruent 7 modulo 12: 1/32 phi1^4 phi2 q congruent 8 modulo 12: 1/32 q^4 ( q-2 ) q congruent 9 modulo 12: 1/32 phi1^4 phi2 q congruent 11 modulo 12: 1/32 phi1^4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 3, 8 ], [ 7, 1, 2, 4 ], [ 15, 1, 7, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 18, 1, 4, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 4, 16 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 1, 11, 16 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 3, 16 ], [ 34, 1, 8, 8 ], [ 36, 1, 10, 16 ], [ 36, 1, 14, 32 ], [ 38, 1, 12, 16 ], [ 38, 1, 14, 16 ], [ 40, 1, 16, 16 ] ] k = 28: F-action on Pi is (1,2) [41,1,28] Dynkin type is 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 12: 1/24 phi1^2 ( q^3+q^2-2*q-4 ) q congruent 2 modulo 12: 1/24 q^2 phi2^2 ( q-2 ) q congruent 3 modulo 12: 1/24 q phi1 phi2^2 ( q-2 ) q congruent 4 modulo 12: 1/24 q phi1 ( q^3+q^2-2*q-4 ) q congruent 5 modulo 12: 1/24 q phi1 phi2^2 ( q-2 ) q congruent 7 modulo 12: 1/24 phi1^2 ( q^3+q^2-2*q-4 ) q congruent 8 modulo 12: 1/24 q^2 phi2^2 ( q-2 ) q congruent 9 modulo 12: 1/24 q phi1 phi2^2 ( q-2 ) q congruent 11 modulo 12: 1/24 q phi1 phi2^2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 46, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 21, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 6, 8 ], [ 28, 1, 5, 6 ], [ 30, 1, 3, 8 ], [ 33, 1, 11, 24 ], [ 35, 1, 8, 6 ], [ 39, 1, 7, 12 ], [ 40, 1, 14, 12 ] ] k = 29: F-action on Pi is (1,2) [41,1,29] Dynkin type is A_1(q^2) + T(phi2 phi8) Order of center |Z^F|: phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^2 phi2 phi4 q congruent 2 modulo 12: 1/16 q^5 q congruent 3 modulo 12: 1/16 phi1^2 phi2 phi4 q congruent 4 modulo 12: 1/16 q^5 q congruent 5 modulo 12: 1/16 phi1^2 phi2 phi4 q congruent 7 modulo 12: 1/16 phi1^2 phi2 phi4 q congruent 8 modulo 12: 1/16 q^5 q congruent 9 modulo 12: 1/16 phi1^2 phi2 phi4 q congruent 11 modulo 12: 1/16 phi1^2 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 23, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 40, 1, 25, 8 ] ] k = 30: F-action on Pi is (1,2) [41,1,30] Dynkin type is 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 12: 1/192 phi1 ( q^4-12*q^3+36*q^2+16*q-137 ) q congruent 2 modulo 12: 1/192 q ( q^4-12*q^3+36*q^2+16*q-96 ) q congruent 3 modulo 12: 1/192 phi2 ( q^4-14*q^3+62*q^2-82*q-15 ) q congruent 4 modulo 12: 1/192 q ( q^4-12*q^3+36*q^2+16*q-128 ) q congruent 5 modulo 12: 1/192 phi1 ( q^4-12*q^3+36*q^2+16*q-105 ) q congruent 7 modulo 12: 1/192 ( q^5-13*q^4+48*q^3-20*q^2-129*q+17 ) q congruent 8 modulo 12: 1/192 q ( q^4-12*q^3+36*q^2+16*q-96 ) q congruent 9 modulo 12: 1/192 phi1 ( q^4-12*q^3+36*q^2+16*q-105 ) q congruent 11 modulo 12: 1/192 phi2 ( q^4-14*q^3+62*q^2-82*q-15 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 12 ], [ 4, 1, 3, 48 ], [ 5, 1, 2, 12 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 36 ], [ 10, 1, 4, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 2, 32 ], [ 14, 1, 2, 24 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 24 ], [ 15, 1, 5, 96 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 12 ], [ 18, 1, 2, 12 ], [ 18, 1, 3, 4 ], [ 20, 1, 4, 96 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 1, 3, 48 ], [ 24, 1, 2, 16 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 72 ], [ 25, 1, 8, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 27, 1, 4, 96 ], [ 28, 1, 1, 48 ], [ 30, 1, 3, 32 ], [ 31, 1, 2, 48 ], [ 31, 1, 5, 48 ], [ 32, 1, 2, 48 ], [ 33, 1, 10, 192 ], [ 34, 1, 2, 48 ], [ 34, 1, 7, 24 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 36, 1, 5, 48 ], [ 36, 1, 6, 192 ], [ 38, 1, 9, 96 ], [ 39, 1, 8, 96 ], [ 39, 1, 13, 96 ], [ 40, 1, 12, 96 ] ] k = 31: F-action on Pi is (1,2) [41,1,31] Dynkin type is 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 12: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/64 q^3 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/64 q^3 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/64 q^3 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 10, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 8 ], [ 4, 1, 3, 16 ], [ 5, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 15, 1, 4, 16 ], [ 15, 1, 5, 32 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 25, 1, 7, 32 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 4, 32 ], [ 27, 1, 7, 8 ], [ 32, 1, 8, 16 ], [ 34, 1, 2, 16 ], [ 34, 1, 8, 8 ], [ 35, 1, 7, 16 ], [ 36, 1, 6, 64 ], [ 36, 1, 10, 16 ], [ 38, 1, 14, 32 ], [ 39, 1, 14, 32 ], [ 40, 1, 23, 32 ] ] k = 32: F-action on Pi is (1,2) [41,1,32] Dynkin type is A_1(q^2) + T(phi1 phi8) Order of center |Z^F|: phi1 phi8 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 2 modulo 12: 1/16 q^4 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 4 modulo 12: 1/16 q^4 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 8 modulo 12: 1/16 q^4 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 phi4 ( q-3 ) q congruent 11 modulo 12: 1/16 phi1 phi2 phi4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 53, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 40, 1, 25, 8 ] ] k = 33: F-action on Pi is (1,2) [41,1,33] Dynkin type is 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 12: 1/24 q phi1 ( q^3-4*q^2-q+12 ) q congruent 2 modulo 12: 1/24 phi2^2 ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 12: 1/24 q phi1 ( q^3-4*q^2-q+12 ) q congruent 4 modulo 12: 1/24 q phi1 ( q^3-3*q^2-2*q+8 ) q congruent 5 modulo 12: 1/24 phi2^2 ( q^3-7*q^2+16*q-12 ) q congruent 7 modulo 12: 1/24 q phi1 ( q^3-4*q^2-q+12 ) q congruent 8 modulo 12: 1/24 phi2^2 ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 12: 1/24 q phi1 ( q^3-4*q^2-q+12 ) q congruent 11 modulo 12: 1/24 phi2^2 ( q^3-7*q^2+16*q-12 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 57 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 1, 5, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 1, 4 ], [ 21, 1, 3, 4 ], [ 24, 1, 4, 4 ], [ 25, 1, 3, 8 ], [ 28, 1, 4, 6 ], [ 30, 1, 7, 8 ], [ 33, 1, 8, 24 ], [ 35, 1, 9, 6 ], [ 39, 1, 16, 12 ], [ 40, 1, 15, 12 ] ] k = 34: F-action on Pi is (1,2) [41,1,34] Dynkin type is 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 12: 1/64 phi1 phi2 ( q^3-9*q^2+27*q-27 ) q congruent 2 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/64 phi1 phi2 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/64 phi1 phi2 ( q^3-9*q^2+27*q-27 ) q congruent 7 modulo 12: 1/64 phi1 phi2 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/64 phi1 phi2 ( q^3-9*q^2+27*q-27 ) q congruent 11 modulo 12: 1/64 phi1 phi2 ( q^3-9*q^2+27*q-27 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 10, 1, 3, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 24 ], [ 25, 1, 3, 32 ], [ 26, 1, 1, 24 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 8 ], [ 27, 1, 14, 32 ], [ 32, 1, 8, 16 ], [ 34, 1, 1, 48 ], [ 34, 1, 6, 8 ], [ 35, 1, 7, 16 ], [ 36, 1, 3, 64 ], [ 36, 1, 17, 16 ], [ 38, 1, 13, 32 ], [ 39, 1, 17, 32 ], [ 40, 1, 23, 32 ] ] k = 35: F-action on Pi is (1,2) [41,1,35] Dynkin type is 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 12: 1/32 phi1^3 phi2 ( q-3 ) q congruent 2 modulo 12: 1/32 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/32 phi1^3 phi2 ( q-3 ) q congruent 4 modulo 12: 1/32 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/32 phi1^3 phi2 ( q-3 ) q congruent 7 modulo 12: 1/32 phi1^3 phi2 ( q-3 ) q congruent 8 modulo 12: 1/32 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/32 phi1^3 phi2 ( q-3 ) q congruent 11 modulo 12: 1/32 phi1^3 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 13, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 4, 8 ], [ 7, 1, 1, 4 ], [ 15, 1, 6, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 18, 1, 2, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 6, 16 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 1, 14, 16 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 2, 16 ], [ 34, 1, 6, 8 ], [ 36, 1, 13, 32 ], [ 36, 1, 17, 16 ], [ 38, 1, 11, 16 ], [ 38, 1, 13, 16 ], [ 40, 1, 16, 16 ] ] k = 36: F-action on Pi is (1,2) [41,1,36] Dynkin type is 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 12: 1/192 phi1 ( q^4-14*q^3+66*q^2-114*q+45 ) q congruent 2 modulo 12: 1/192 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 3 modulo 12: 1/192 ( q^5-15*q^4+80*q^3-180*q^2+135*q+27 ) q congruent 4 modulo 12: 1/192 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 5 modulo 12: 1/192 phi1 ( q^4-14*q^3+66*q^2-114*q+45 ) q congruent 7 modulo 12: 1/192 ( q^5-15*q^4+80*q^3-180*q^2+135*q+27 ) q congruent 8 modulo 12: 1/192 q ( q^4-14*q^3+68*q^2-136*q+96 ) q congruent 9 modulo 12: 1/192 phi1 ( q^4-14*q^3+66*q^2-114*q+45 ) q congruent 11 modulo 12: 1/192 ( q^5-15*q^4+80*q^3-180*q^2+135*q+27 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 12 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 30 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 36 ], [ 10, 1, 4, 12 ], [ 11, 1, 1, 24 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 24 ], [ 16, 1, 1, 14 ], [ 17, 1, 1, 36 ], [ 17, 1, 4, 16 ], [ 18, 1, 1, 60 ], [ 18, 1, 4, 4 ], [ 19, 1, 1, 48 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 48 ], [ 24, 1, 1, 16 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 72 ], [ 25, 1, 4, 24 ], [ 26, 1, 1, 72 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 27, 1, 14, 96 ], [ 28, 1, 1, 48 ], [ 29, 1, 1, 96 ], [ 30, 1, 4, 32 ], [ 31, 1, 1, 48 ], [ 31, 1, 6, 48 ], [ 32, 1, 2, 48 ], [ 34, 1, 1, 144 ], [ 34, 1, 5, 24 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 36, 1, 2, 48 ], [ 36, 1, 3, 192 ], [ 38, 1, 10, 96 ], [ 39, 1, 1, 96 ], [ 39, 1, 18, 96 ], [ 40, 1, 12, 96 ] ] k = 37: F-action on Pi is (1,2) [41,1,37] Dynkin type is 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 12: 1/32 phi1 ( q^4-6*q^3+6*q^2+10*q+5 ) q congruent 2 modulo 12: 1/32 q ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 3 modulo 12: 1/32 phi1 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 4 modulo 12: 1/32 q ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 5 modulo 12: 1/32 phi1 ( q^4-6*q^3+6*q^2+10*q+5 ) q congruent 7 modulo 12: 1/32 phi1 phi2 ( q^3-7*q^2+13*q-3 ) q congruent 8 modulo 12: 1/32 q ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 9 modulo 12: 1/32 phi1 ( q^4-6*q^3+6*q^2+10*q+5 ) q congruent 11 modulo 12: 1/32 phi1 phi2 ( q^3-7*q^2+13*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 1, 4, 8 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 5, 16 ], [ 13, 1, 1, 8 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 1, 6, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 4 ], [ 19, 1, 1, 8 ], [ 20, 1, 3, 16 ], [ 21, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 8 ], [ 23, 1, 2, 8 ], [ 24, 1, 1, 8 ], [ 24, 1, 4, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 6, 16 ], [ 27, 1, 9, 16 ], [ 27, 1, 14, 16 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 29, 1, 2, 16 ], [ 30, 1, 4, 16 ], [ 30, 1, 7, 16 ], [ 31, 1, 1, 8 ], [ 31, 1, 3, 8 ], [ 31, 1, 6, 8 ], [ 31, 1, 8, 8 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 33, 1, 7, 32 ], [ 34, 1, 2, 16 ], [ 34, 1, 5, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 36, 1, 2, 16 ], [ 36, 1, 13, 32 ], [ 38, 1, 10, 16 ], [ 38, 1, 15, 16 ], [ 39, 1, 2, 16 ], [ 39, 1, 19, 16 ], [ 40, 1, 22, 16 ] ] k = 38: F-action on Pi is (1,2) [41,1,38] Dynkin type is 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 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/24 q^2 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 58 ] 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 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 4 ], [ 21, 1, 2, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 28, 1, 5, 6 ], [ 29, 1, 3, 12 ], [ 30, 1, 4, 8 ], [ 35, 1, 8, 6 ], [ 39, 1, 3, 12 ], [ 40, 1, 14, 12 ] ] k = 39: F-action on Pi is (1,2) [41,1,39] Dynkin type is 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 12: 1/64 phi1^3 phi2 ( q-3 ) q congruent 2 modulo 12: 1/64 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/64 phi1^3 phi2 ( q-3 ) q congruent 4 modulo 12: 1/64 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/64 phi1^3 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 phi1^3 phi2 ( q-3 ) q congruent 8 modulo 12: 1/64 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/64 phi1^3 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 phi1^3 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 4, 1, 4, 16 ], [ 5, 1, 1, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 8, 32 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 18, 1, 4, 8 ], [ 25, 1, 2, 32 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 6, 32 ], [ 27, 1, 7, 8 ], [ 27, 1, 13, 32 ], [ 32, 1, 4, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 6, 8 ], [ 35, 1, 6, 16 ], [ 36, 1, 15, 64 ], [ 36, 1, 17, 16 ], [ 38, 1, 11, 32 ], [ 39, 1, 9, 32 ], [ 40, 1, 24, 32 ] ] k = 40: F-action on Pi is (1,2) [41,1,40] Dynkin type is 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 12: 1/192 phi1 ( q^4-10*q^3+26*q^2-6*q+21 ) q congruent 2 modulo 12: 1/192 ( q^5-10*q^4+28*q^3-8*q^2-64*q+64 ) q congruent 3 modulo 12: 1/192 ( q^5-11*q^4+36*q^3-32*q^2+3*q-45 ) q congruent 4 modulo 12: 1/192 q ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 5 modulo 12: 1/192 phi2 ( q^4-12*q^3+48*q^2-80*q+75 ) q congruent 7 modulo 12: 1/192 ( q^5-11*q^4+36*q^3-32*q^2+3*q-45 ) q congruent 8 modulo 12: 1/192 ( q^5-10*q^4+28*q^3-8*q^2-64*q+64 ) q congruent 9 modulo 12: 1/192 phi1 ( q^4-10*q^3+26*q^2-6*q+21 ) q congruent 11 modulo 12: 1/192 phi2 ( q^4-12*q^3+48*q^2-80*q+51 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 4 ], [ 4, 1, 4, 48 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 36 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 5, 32 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 15, 1, 2, 8 ], [ 15, 1, 8, 96 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 1, 4, 16 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 12 ], [ 20, 1, 3, 96 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 1, 2, 48 ], [ 24, 1, 4, 16 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 72 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 6, 96 ], [ 27, 1, 13, 96 ], [ 28, 1, 6, 48 ], [ 30, 1, 7, 32 ], [ 31, 1, 3, 48 ], [ 31, 1, 8, 48 ], [ 32, 1, 5, 48 ], [ 33, 1, 9, 192 ], [ 34, 1, 3, 48 ], [ 34, 1, 5, 24 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ], [ 36, 1, 2, 48 ], [ 36, 1, 15, 192 ], [ 38, 1, 15, 96 ], [ 39, 1, 10, 96 ], [ 39, 1, 20, 96 ], [ 40, 1, 13, 96 ] ] i = 42: Pi = [ 1, 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [42,1,1] Dynkin type is A_2(q) + T(phi1^5) Order of center |Z^F|: phi1^5 Numbers of classes in class type: q congruent 1 modulo 12: 1/1440 ( q^5-35*q^4+485*q^3-3385*q^2+12194*q-19340 ) q congruent 2 modulo 12: 1/1440 ( q^5-35*q^4+470*q^3-2980*q^2+8664*q-8640 ) q congruent 3 modulo 12: 1/1440 ( q^5-35*q^4+485*q^3-3385*q^2+11934*q-15840 ) q congruent 4 modulo 12: 1/1440 ( q^5-35*q^4+470*q^3-2980*q^2+8744*q-9440 ) q congruent 5 modulo 12: 1/1440 ( q^5-35*q^4+485*q^3-3385*q^2+12114*q-17820 ) q congruent 7 modulo 12: 1/1440 ( q^5-35*q^4+485*q^3-3385*q^2+12014*q-17360 ) q congruent 8 modulo 12: 1/1440 ( q^5-35*q^4+470*q^3-2980*q^2+8664*q-8640 ) q congruent 9 modulo 12: 1/1440 ( q^5-35*q^4+485*q^3-3385*q^2+12114*q-17820 ) q congruent 11 modulo 12: 1/1440 ( q^5-35*q^4+485*q^3-3385*q^2+11934*q-15840 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32, 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 42 ], [ 4, 1, 1, 60 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 20 ], [ 7, 1, 1, 90 ], [ 8, 1, 1, 132 ], [ 9, 1, 1, 150 ], [ 10, 1, 1, 180 ], [ 11, 1, 1, 120 ], [ 12, 1, 1, 120 ], [ 13, 1, 1, 60 ], [ 14, 1, 1, 120 ], [ 15, 1, 1, 120 ], [ 16, 1, 1, 30 ], [ 17, 1, 1, 180 ], [ 18, 1, 1, 180 ], [ 19, 1, 1, 360 ], [ 20, 1, 1, 240 ], [ 21, 1, 1, 180 ], [ 22, 1, 1, 360 ], [ 23, 1, 1, 240 ], [ 24, 1, 1, 300 ], [ 25, 1, 1, 360 ], [ 26, 1, 1, 360 ], [ 28, 1, 1, 240 ], [ 29, 1, 1, 720 ], [ 30, 1, 1, 360 ], [ 31, 1, 1, 720 ], [ 33, 1, 1, 480 ], [ 34, 1, 1, 720 ], [ 35, 1, 1, 720 ], [ 37, 1, 1, 720 ], [ 39, 1, 1, 1440 ] ] k = 2: F-action on Pi is () [42,1,2] Dynkin type is A_2(q) + T(phi1 phi5) Order of center |Z^F|: phi1 phi5 Numbers of classes in class type: q congruent 1 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 2 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 3 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 4 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 5 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 7 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 8 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 9 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 11 modulo 12: 1/10 q phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 14, 56, 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ] ] k = 3: F-action on Pi is (1,3) [42,1,3] Dynkin type is ^2A_2(q) + T(phi2 phi10) Order of center |Z^F|: phi2 phi10 Numbers of classes in class type: q congruent 1 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 2 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 3 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 4 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 5 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 7 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 8 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 9 modulo 12: 1/10 q phi1 phi2 phi4 q congruent 11 modulo 12: 1/10 q phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 44, 26, 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 2, 2 ] ] k = 4: F-action on Pi is () [42,1,4] Dynkin type is A_2(q) + T(phi1^3 phi3) Order of center |Z^F|: phi1^3 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 phi1 ( q^4-7*q^3+13*q^2+9*q-28 ) q congruent 2 modulo 12: 1/36 q phi2 ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 12: 1/36 q phi2 ( q^3-9*q^2+29*q-33 ) q congruent 4 modulo 12: 1/36 phi1^2 ( q^3-6*q^2+4*q+16 ) q congruent 5 modulo 12: 1/36 q phi2 ( q^3-9*q^2+29*q-33 ) q congruent 7 modulo 12: 1/36 phi1 ( q^4-7*q^3+13*q^2+9*q-28 ) q congruent 8 modulo 12: 1/36 q phi2 ( q^3-9*q^2+26*q-24 ) q congruent 9 modulo 12: 1/36 q phi2 ( q^3-9*q^2+29*q-33 ) q congruent 11 modulo 12: 1/36 q phi2 ( q^3-9*q^2+29*q-33 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 45, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 12 ], [ 11, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 6 ], [ 20, 1, 1, 12 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 24 ], [ 28, 1, 1, 12 ], [ 28, 1, 5, 6 ], [ 29, 1, 3, 18 ], [ 33, 1, 1, 24 ], [ 33, 1, 2, 12 ], [ 35, 1, 8, 18 ], [ 37, 1, 3, 18 ], [ 39, 1, 3, 36 ] ] k = 5: F-action on Pi is () [42,1,5] Dynkin type is A_2(q) + T(phi1 phi3^2) Order of center |Z^F|: phi1 phi3^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 phi1 ( q^4+2*q^3-2*q^2-9*q-10 ) q congruent 2 modulo 12: 1/36 q^2 phi2 ( q^2-4 ) q congruent 3 modulo 12: 1/36 q phi2^2 ( q^2-q-3 ) q congruent 4 modulo 12: 1/36 phi1 ( q^4+2*q^3-2*q^2-6*q-4 ) q congruent 5 modulo 12: 1/36 q phi2^2 ( q^2-q-3 ) q congruent 7 modulo 12: 1/36 phi1 ( q^4+2*q^3-2*q^2-9*q-10 ) q congruent 8 modulo 12: 1/36 q^2 phi2 ( q^2-4 ) q congruent 9 modulo 12: 1/36 q phi2^2 ( q^2-q-3 ) q congruent 11 modulo 12: 1/36 q phi2^2 ( q^2-q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 49, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 6, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 21, 1, 5, 18 ], [ 28, 1, 5, 12 ], [ 33, 1, 2, 24 ], [ 34, 1, 9, 18 ] ] k = 6: F-action on Pi is (1,3) [42,1,6] Dynkin type is ^2A_2(q) + T(phi2^3 phi6) Order of center |Z^F|: phi2^3 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 q phi1^2 ( q^2-2*q+3 ) q congruent 2 modulo 12: 1/36 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 3 modulo 12: 1/36 q phi1^2 ( q^2-2*q+3 ) q congruent 4 modulo 12: 1/36 q^2 phi1^2 ( q-2 ) q congruent 5 modulo 12: 1/36 phi2 ( q^4-5*q^3+13*q^2-21*q+20 ) q congruent 7 modulo 12: 1/36 q phi1^2 ( q^2-2*q+3 ) q congruent 8 modulo 12: 1/36 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) q congruent 9 modulo 12: 1/36 q phi1^2 ( q^2-2*q+3 ) q congruent 11 modulo 12: 1/36 phi2 ( q^4-5*q^3+13*q^2-21*q+20 ) Fusion of maximal tori of C^F in those of G^F: [ 36, 15, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 6 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 12 ], [ 11, 1, 2, 6 ], [ 12, 1, 6, 12 ], [ 13, 1, 2, 12 ], [ 14, 1, 2, 6 ], [ 15, 1, 4, 24 ], [ 16, 1, 2, 6 ], [ 20, 1, 2, 12 ], [ 23, 1, 4, 12 ], [ 24, 1, 3, 24 ], [ 28, 1, 4, 6 ], [ 28, 1, 6, 12 ], [ 29, 1, 6, 18 ], [ 33, 1, 5, 12 ], [ 33, 1, 6, 24 ], [ 35, 1, 9, 18 ], [ 37, 1, 8, 18 ], [ 39, 1, 12, 36 ] ] k = 7: F-action on Pi is () [42,1,7] Dynkin type is A_2(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 12: 1/12 q phi1^3 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1^3 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q phi1^3 phi2 q congruent 7 modulo 12: 1/12 q phi1^3 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1^3 phi2 q congruent 11 modulo 12: 1/12 q phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 45, 18, 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 2 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 20, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 5, 6 ], [ 29, 1, 3, 6 ], [ 33, 1, 2, 12 ], [ 33, 1, 3, 8 ], [ 35, 1, 8, 6 ], [ 37, 1, 3, 6 ], [ 39, 1, 7, 12 ] ] k = 8: F-action on Pi is (1,3) [42,1,8] Dynkin type is ^2A_2(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 12: 1/12 q phi1^3 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1^3 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q phi1^3 phi2 q congruent 7 modulo 12: 1/12 q phi1^3 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1^3 phi2 q congruent 11 modulo 12: 1/12 q phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 15, 48, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 20, 1, 2, 4 ], [ 23, 1, 3, 4 ], [ 24, 1, 4, 8 ], [ 28, 1, 2, 4 ], [ 28, 1, 4, 6 ], [ 29, 1, 6, 6 ], [ 33, 1, 4, 8 ], [ 33, 1, 5, 12 ], [ 35, 1, 9, 6 ], [ 37, 1, 8, 6 ], [ 39, 1, 16, 12 ] ] k = 9: F-action on Pi is () [42,1,9] Dynkin type is A_2(q) + T(phi2 phi3 phi6) Order of center |Z^F|: phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 phi1 ( q^4+2*q^3+2*q^2+q-2 ) q congruent 2 modulo 12: 1/12 q^4 phi2 q congruent 3 modulo 12: 1/12 q phi1 phi2 phi3 q congruent 4 modulo 12: 1/12 q phi1 ( q^3+2*q^2+2*q+2 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 phi3 q congruent 7 modulo 12: 1/12 phi1 ( q^4+2*q^3+2*q^2+q-2 ) q congruent 8 modulo 12: 1/12 q^4 phi2 q congruent 9 modulo 12: 1/12 q phi1 phi2 phi3 q congruent 11 modulo 12: 1/12 q phi1 phi2 phi3 Fusion of maximal tori of C^F in those of G^F: [ 50, 21, 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 12, 1, 2, 4 ], [ 21, 1, 5, 6 ], [ 34, 1, 10, 6 ] ] k = 10: F-action on Pi is (1,3) [42,1,10] Dynkin type is ^2A_2(q) + T(phi1 phi3 phi6) Order of center |Z^F|: phi1 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1 ( q^3-3 ) q congruent 2 modulo 12: 1/12 phi2 ( q^4-2*q^3+2*q^2-4*q+4 ) q congruent 3 modulo 12: 1/12 q phi1 ( q^3-3 ) q congruent 4 modulo 12: 1/12 q phi1 ( q^3-2 ) q congruent 5 modulo 12: 1/12 phi2 ( q^4-2*q^3+2*q^2-5*q+6 ) q congruent 7 modulo 12: 1/12 q phi1 ( q^3-3 ) q congruent 8 modulo 12: 1/12 phi2 ( q^4-2*q^3+2*q^2-4*q+4 ) q congruent 9 modulo 12: 1/12 q phi1 ( q^3-3 ) q congruent 11 modulo 12: 1/12 phi2 ( q^4-2*q^3+2*q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 51, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 12, 1, 5, 4 ], [ 21, 1, 4, 6 ], [ 34, 1, 9, 6 ] ] k = 11: F-action on Pi is (1,3) [42,1,11] Dynkin type is ^2A_2(q) + T(phi2 phi6^2) Order of center |Z^F|: phi2 phi6^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 q phi1 ( q^3-4*q-9 ) q congruent 2 modulo 12: 1/36 phi2 ( q^4-2*q^3-2*q^2+8 ) q congruent 3 modulo 12: 1/36 q phi1 ( q^3-4*q-9 ) q congruent 4 modulo 12: 1/36 q phi1 ( q^3-4*q-6 ) q congruent 5 modulo 12: 1/36 phi2 ( q^4-2*q^3-2*q^2-3*q+14 ) q congruent 7 modulo 12: 1/36 q phi1 ( q^3-4*q-9 ) q congruent 8 modulo 12: 1/36 phi2 ( q^4-2*q^3-2*q^2+8 ) q congruent 9 modulo 12: 1/36 q phi1 ( q^3-4*q-9 ) q congruent 11 modulo 12: 1/36 phi2 ( q^4-2*q^3-2*q^2-3*q+14 ) Fusion of maximal tori of C^F in those of G^F: [ 38, 19, 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 6 ], [ 6, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 21, 1, 4, 18 ], [ 28, 1, 4, 12 ], [ 33, 1, 5, 24 ], [ 34, 1, 10, 18 ] ] k = 12: F-action on Pi is () [42,1,12] Dynkin type is A_2(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 12: 1/32 q phi1^2 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/32 q ( q^4-7*q^3+14*q^2-4*q-8 ) q congruent 3 modulo 12: 1/32 ( q^5-7*q^4+17*q^3-17*q^2+10*q-12 ) q congruent 4 modulo 12: 1/32 q ( q^4-7*q^3+14*q^2-4*q-8 ) q congruent 5 modulo 12: 1/32 q phi1^2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/32 ( q^5-7*q^4+17*q^3-17*q^2+10*q-12 ) q congruent 8 modulo 12: 1/32 q ( q^4-7*q^3+14*q^2-4*q-8 ) q congruent 9 modulo 12: 1/32 q phi1^2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/32 ( q^5-7*q^4+17*q^3-17*q^2+10*q-12 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 10 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 4 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 8 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 3, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 8 ], [ 22, 1, 2, 16 ], [ 23, 1, 2, 16 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 24 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 5, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 3, 16 ], [ 29, 1, 2, 16 ], [ 30, 1, 1, 8 ], [ 30, 1, 2, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 16 ], [ 33, 1, 3, 32 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 16 ], [ 35, 1, 2, 16 ], [ 35, 1, 5, 16 ], [ 37, 1, 2, 16 ], [ 37, 1, 5, 16 ], [ 39, 1, 5, 32 ], [ 39, 1, 10, 32 ] ] k = 13: F-action on Pi is (1,3) [42,1,13] Dynkin type is ^2A_2(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 12: 1/16 q phi1 phi2 ( q^2-q+2 ) q congruent 2 modulo 12: 1/16 q^4 phi1 q congruent 3 modulo 12: 1/16 q phi1 phi2 ( q^2-q+2 ) q congruent 4 modulo 12: 1/16 q^4 phi1 q congruent 5 modulo 12: 1/16 q phi1 phi2 ( q^2-q+2 ) q congruent 7 modulo 12: 1/16 q phi1 phi2 ( q^2-q+2 ) q congruent 8 modulo 12: 1/16 q^4 phi1 q congruent 9 modulo 12: 1/16 q phi1 phi2 ( q^2-q+2 ) q congruent 11 modulo 12: 1/16 q phi1 phi2 ( q^2-q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 11, 43, 28 ] 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 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 21, 1, 3, 4 ], [ 24, 1, 3, 4 ], [ 25, 1, 7, 8 ], [ 26, 1, 5, 4 ], [ 30, 1, 8, 8 ], [ 34, 1, 8, 8 ], [ 35, 1, 7, 8 ], [ 37, 1, 10, 8 ], [ 39, 1, 14, 16 ] ] k = 14: F-action on Pi is () [42,1,14] Dynkin type is A_2(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 12: 1/16 phi1 phi2 ( q^3-3*q^2+2*q+4 ) q congruent 2 modulo 12: 1/16 q^2 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+2*q+4 ) q congruent 4 modulo 12: 1/16 q^2 phi2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+2*q+4 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+2*q+4 ) q congruent 8 modulo 12: 1/16 q^2 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+2*q+4 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+2*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 13, 58 ] 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 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 4 ], [ 21, 1, 2, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 26, 1, 5, 4 ], [ 30, 1, 4, 8 ], [ 34, 1, 6, 8 ], [ 35, 1, 6, 8 ], [ 37, 1, 4, 8 ], [ 39, 1, 9, 16 ] ] k = 15: F-action on Pi is () [42,1,15] Dynkin type is A_2(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 12: 1/16 phi1 phi2^2 ( q^2-2*q+2 ) q congruent 2 modulo 12: 1/16 q^3 phi2 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2^2 ( q^2-2*q+2 ) q congruent 4 modulo 12: 1/16 q^3 phi2 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2^2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/16 phi1 phi2^2 ( q^2-2*q+2 ) q congruent 8 modulo 12: 1/16 q^3 phi2 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2^2 ( q^2-2*q+2 ) q congruent 11 modulo 12: 1/16 phi1 phi2^2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 10, 43, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 21, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 6, 8 ], [ 26, 1, 5, 4 ], [ 30, 1, 3, 8 ], [ 34, 1, 8, 8 ], [ 35, 1, 6, 8 ], [ 37, 1, 4, 8 ], [ 39, 1, 6, 16 ] ] k = 16: F-action on Pi is (1,3) [42,1,16] Dynkin type is ^2A_2(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 12: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 2 modulo 12: 1/16 q^3 phi1 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 4 modulo 12: 1/16 q^3 phi1 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 8 modulo 12: 1/16 q^3 phi1 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) q congruent 11 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 40, 13, 57 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 1, 5, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 1, 4 ], [ 21, 1, 3, 4 ], [ 24, 1, 4, 4 ], [ 25, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 30, 1, 7, 8 ], [ 34, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 37, 1, 10, 8 ], [ 39, 1, 17, 16 ] ] k = 17: F-action on Pi is () [42,1,17] Dynkin type is A_2(q) + T(phi1^4 phi2) Order of center |Z^F|: phi1^4 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 ( q^4-16*q^3+95*q^2-254*q+270 ) q congruent 2 modulo 12: 1/96 q ( q^4-17*q^3+104*q^2-268*q+240 ) q congruent 3 modulo 12: 1/96 phi1 ( q^4-16*q^3+95*q^2-254*q+258 ) q congruent 4 modulo 12: 1/96 q ( q^4-17*q^3+104*q^2-268*q+240 ) q congruent 5 modulo 12: 1/96 phi1 ( q^4-16*q^3+95*q^2-254*q+270 ) q congruent 7 modulo 12: 1/96 phi1 ( q^4-16*q^3+95*q^2-254*q+258 ) q congruent 8 modulo 12: 1/96 q ( q^4-17*q^3+104*q^2-268*q+240 ) q congruent 9 modulo 12: 1/96 phi1 ( q^4-16*q^3+95*q^2-254*q+270 ) q congruent 11 modulo 12: 1/96 phi1 ( q^4-16*q^3+95*q^2-254*q+258 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 18 ], [ 4, 1, 1, 28 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 40 ], [ 9, 1, 1, 46 ], [ 10, 1, 1, 36 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 48 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 15, 1, 3, 8 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 12 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 64 ], [ 21, 1, 1, 36 ], [ 22, 1, 1, 48 ], [ 22, 1, 2, 24 ], [ 23, 1, 1, 48 ], [ 23, 1, 2, 16 ], [ 24, 1, 1, 72 ], [ 24, 1, 2, 20 ], [ 25, 1, 1, 48 ], [ 25, 1, 5, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 28, 1, 1, 48 ], [ 28, 1, 3, 16 ], [ 29, 1, 1, 48 ], [ 29, 1, 2, 48 ], [ 30, 1, 1, 48 ], [ 30, 1, 2, 24 ], [ 31, 1, 1, 48 ], [ 31, 1, 2, 48 ], [ 31, 1, 3, 48 ], [ 33, 1, 1, 96 ], [ 33, 1, 3, 32 ], [ 34, 1, 2, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 2, 48 ], [ 37, 1, 1, 48 ], [ 37, 1, 2, 48 ], [ 39, 1, 2, 96 ], [ 39, 1, 8, 96 ] ] k = 18: F-action on Pi is () [42,1,18] Dynkin type is A_2(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 12: 1/96 phi1 ( q^4-4*q^3-q^2+10*q+10 ) q congruent 2 modulo 12: 1/96 q^2 ( q^3-5*q^2+12 ) q congruent 3 modulo 12: 1/96 phi1 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 4 modulo 12: 1/96 q ( q^4-5*q^3+12*q+16 ) q congruent 5 modulo 12: 1/96 phi1^3 ( q^2-2*q-6 ) q congruent 7 modulo 12: 1/96 phi1 ( q^4-4*q^3-q^2+10*q+22 ) q congruent 8 modulo 12: 1/96 q^2 ( q^3-5*q^2+12 ) q congruent 9 modulo 12: 1/96 phi1^3 ( q^2-2*q-6 ) q congruent 11 modulo 12: 1/96 phi1 phi2 ( q^3-5*q^2+4*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 5, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 12 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 24 ], [ 12, 1, 2, 16 ], [ 15, 1, 3, 24 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 24 ], [ 17, 1, 3, 12 ], [ 18, 1, 2, 12 ], [ 18, 1, 3, 24 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 24 ], [ 22, 1, 2, 24 ], [ 24, 1, 2, 12 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 48 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 24 ], [ 30, 1, 2, 24 ], [ 30, 1, 3, 48 ], [ 31, 1, 4, 48 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 48 ], [ 35, 1, 5, 48 ], [ 37, 1, 5, 48 ], [ 39, 1, 4, 96 ] ] k = 19: F-action on Pi is (1,3) [42,1,19] Dynkin type is ^2A_2(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 12: 1/32 phi1^2 ( q^3-3*q^2+2*q-4 ) q congruent 2 modulo 12: 1/32 q^3 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/32 q phi1 ( q^3-4*q^2+5*q-6 ) q congruent 4 modulo 12: 1/32 q^3 ( q^2-5*q+6 ) q congruent 5 modulo 12: 1/32 phi1^2 ( q^3-3*q^2+2*q-4 ) q congruent 7 modulo 12: 1/32 q phi1 ( q^3-4*q^2+5*q-6 ) q congruent 8 modulo 12: 1/32 q^3 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/32 phi1^2 ( q^3-3*q^2+2*q-4 ) q congruent 11 modulo 12: 1/32 q phi1 ( q^3-4*q^2+5*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 5, 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 10 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 2, 16 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 21, 1, 3, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 3, 16 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 24 ], [ 25, 1, 4, 16 ], [ 25, 1, 7, 16 ], [ 25, 1, 8, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 2, 16 ], [ 29, 1, 5, 16 ], [ 30, 1, 5, 8 ], [ 30, 1, 6, 16 ], [ 30, 1, 8, 16 ], [ 31, 1, 5, 16 ], [ 31, 1, 6, 16 ], [ 31, 1, 8, 16 ], [ 33, 1, 4, 32 ], [ 34, 1, 2, 16 ], [ 34, 1, 7, 16 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 37, 1, 7, 16 ], [ 37, 1, 9, 16 ], [ 39, 1, 13, 32 ], [ 39, 1, 19, 32 ] ] k = 20: F-action on Pi is (1,3) [42,1,20] Dynkin type is ^2A_2(q) + T(phi1 phi2^4) Order of center |Z^F|: phi1 phi2^4 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 ( q^4-10*q^3+41*q^2-98*q+114 ) q congruent 2 modulo 12: 1/96 q ( q^4-11*q^3+44*q^2-76*q+48 ) q congruent 3 modulo 12: 1/96 ( q^5-11*q^4+51*q^3-139*q^2+224*q-150 ) q congruent 4 modulo 12: 1/96 q ( q^4-11*q^3+44*q^2-76*q+48 ) q congruent 5 modulo 12: 1/96 phi1 ( q^4-10*q^3+41*q^2-98*q+114 ) q congruent 7 modulo 12: 1/96 ( q^5-11*q^4+51*q^3-139*q^2+224*q-150 ) q congruent 8 modulo 12: 1/96 q ( q^4-11*q^3+44*q^2-76*q+48 ) q congruent 9 modulo 12: 1/96 phi1 ( q^4-10*q^3+41*q^2-98*q+114 ) q congruent 11 modulo 12: 1/96 ( q^5-11*q^4+51*q^3-139*q^2+224*q-150 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 34, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 18 ], [ 4, 1, 2, 28 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 18 ], [ 8, 1, 2, 40 ], [ 9, 1, 2, 46 ], [ 10, 1, 4, 36 ], [ 11, 1, 2, 32 ], [ 12, 1, 6, 48 ], [ 13, 1, 2, 24 ], [ 14, 1, 2, 32 ], [ 15, 1, 2, 8 ], [ 15, 1, 4, 48 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 18, 1, 3, 24 ], [ 18, 1, 4, 12 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 64 ], [ 21, 1, 6, 36 ], [ 22, 1, 3, 24 ], [ 22, 1, 4, 48 ], [ 23, 1, 3, 16 ], [ 23, 1, 4, 48 ], [ 24, 1, 3, 72 ], [ 24, 1, 4, 20 ], [ 25, 1, 4, 24 ], [ 25, 1, 8, 48 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 2, 16 ], [ 28, 1, 6, 48 ], [ 29, 1, 4, 48 ], [ 29, 1, 5, 48 ], [ 30, 1, 5, 48 ], [ 30, 1, 6, 24 ], [ 31, 1, 5, 48 ], [ 31, 1, 7, 48 ], [ 31, 1, 8, 48 ], [ 33, 1, 4, 32 ], [ 33, 1, 6, 96 ], [ 34, 1, 3, 48 ], [ 35, 1, 4, 48 ], [ 35, 1, 10, 48 ], [ 37, 1, 6, 48 ], [ 37, 1, 7, 48 ], [ 39, 1, 11, 96 ], [ 39, 1, 20, 96 ] ] k = 21: F-action on Pi is (1,3) [42,1,21] Dynkin type is ^2A_2(q) + T(phi2^5) Order of center |Z^F|: phi2^5 Numbers of classes in class type: q congruent 1 modulo 12: 1/1440 phi1 ( q^4-24*q^3+221*q^2-1014*q+2160 ) q congruent 2 modulo 12: 1/1440 ( q^5-25*q^4+230*q^3-920*q^2+1424*q-640 ) q congruent 3 modulo 12: 1/1440 ( q^5-25*q^4+245*q^3-1235*q^2+3354*q-3780 ) q congruent 4 modulo 12: 1/1440 q ( q^4-25*q^3+230*q^2-920*q+1344 ) q congruent 5 modulo 12: 1/1440 ( q^5-25*q^4+245*q^3-1235*q^2+3254*q-3520 ) q congruent 7 modulo 12: 1/1440 ( q^5-25*q^4+245*q^3-1235*q^2+3354*q-3780 ) q congruent 8 modulo 12: 1/1440 ( q^5-25*q^4+230*q^3-920*q^2+1424*q-640 ) q congruent 9 modulo 12: 1/1440 phi1 ( q^4-24*q^3+221*q^2-1014*q+2160 ) q congruent 11 modulo 12: 1/1440 ( q^5-25*q^4+245*q^3-1235*q^2+3434*q-5140 ) Fusion of maximal tori of C^F in those of G^F: [ 31, 2, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 2, 42 ], [ 4, 1, 2, 60 ], [ 5, 1, 2, 12 ], [ 6, 1, 2, 20 ], [ 7, 1, 2, 90 ], [ 8, 1, 2, 132 ], [ 9, 1, 2, 150 ], [ 10, 1, 4, 180 ], [ 11, 1, 2, 120 ], [ 12, 1, 6, 120 ], [ 13, 1, 2, 60 ], [ 14, 1, 2, 120 ], [ 15, 1, 4, 120 ], [ 16, 1, 2, 30 ], [ 17, 1, 3, 180 ], [ 18, 1, 3, 180 ], [ 19, 1, 2, 360 ], [ 20, 1, 2, 240 ], [ 21, 1, 6, 180 ], [ 22, 1, 4, 360 ], [ 23, 1, 4, 240 ], [ 24, 1, 3, 300 ], [ 25, 1, 8, 360 ], [ 26, 1, 3, 360 ], [ 28, 1, 6, 240 ], [ 29, 1, 4, 720 ], [ 30, 1, 5, 360 ], [ 31, 1, 7, 720 ], [ 33, 1, 6, 480 ], [ 34, 1, 4, 720 ], [ 35, 1, 10, 720 ], [ 37, 1, 6, 720 ], [ 39, 1, 15, 1440 ] ] k = 22: F-action on Pi is (1,3) [42,1,22] Dynkin type is ^2A_2(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 12: 1/96 phi1 ( q^4-6*q^3+9*q^2+6*q-18 ) q congruent 2 modulo 12: 1/96 ( q^5-7*q^4+12*q^3+4*q^2-32 ) q congruent 3 modulo 12: 1/96 ( q^5-7*q^4+15*q^3-3*q^2-36*q+54 ) q congruent 4 modulo 12: 1/96 q phi2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/96 ( q^5-7*q^4+15*q^3-3*q^2-8*q-30 ) q congruent 7 modulo 12: 1/96 ( q^5-7*q^4+15*q^3-3*q^2-36*q+54 ) q congruent 8 modulo 12: 1/96 ( q^5-7*q^4+12*q^3+4*q^2-32 ) q congruent 9 modulo 12: 1/96 phi1 ( q^4-6*q^3+9*q^2+6*q-18 ) q congruent 11 modulo 12: 1/96 phi2 ( q^4-8*q^3+23*q^2-26*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 35, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 3, 24 ], [ 10, 1, 4, 12 ], [ 12, 1, 5, 16 ], [ 15, 1, 2, 24 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 24 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 12 ], [ 21, 1, 3, 24 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 24 ], [ 24, 1, 4, 12 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 24 ], [ 30, 1, 6, 24 ], [ 30, 1, 7, 48 ], [ 31, 1, 6, 48 ], [ 34, 1, 1, 48 ], [ 34, 1, 5, 48 ], [ 35, 1, 3, 48 ], [ 37, 1, 9, 48 ], [ 39, 1, 18, 96 ] ] i = 43: Pi = [ 1 ] j = 1: Omega trivial k = 1: F-action on Pi is () [43,1,1] Dynkin type is A_1(q) + T(phi1^6) Order of center |Z^F|: phi1^6 Numbers of classes in class type: q congruent 1 modulo 12: 1/23040 ( q^6-52*q^5+1095*q^4-12080*q^3+74639*q^2-249068*q+369785 ) q congruent 2 modulo 12: 1/23040 ( q^6-52*q^5+1080*q^4-11360*q^3+62864*q^2-168768*q+161280 ) q congruent 3 modulo 12: 1/23040 ( q^6-52*q^5+1095*q^4-12080*q^3+74639*q^2-244908*q+312345 ) q congruent 4 modulo 12: 1/23040 ( q^6-52*q^5+1080*q^4-11360*q^3+62864*q^2-170048*q+174080 ) q congruent 5 modulo 12: 1/23040 ( q^6-52*q^5+1095*q^4-12080*q^3+74639*q^2-247788*q+345465 ) q congruent 7 modulo 12: 1/23040 ( q^6-52*q^5+1095*q^4-12080*q^3+74639*q^2-246188*q+336665 ) q congruent 8 modulo 12: 1/23040 ( q^6-52*q^5+1080*q^4-11360*q^3+62864*q^2-168768*q+161280 ) q congruent 9 modulo 12: 1/23040 ( q^6-52*q^5+1095*q^4-12080*q^3+74639*q^2-247788*q+345465 ) q congruent 11 modulo 12: 1/23040 ( q^6-52*q^5+1095*q^4-12080*q^3+74639*q^2-244908*q+312345 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 32 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 31 ], [ 3, 1, 1, 192 ], [ 4, 1, 1, 520 ], [ 5, 1, 1, 32 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 252 ], [ 8, 1, 1, 832 ], [ 9, 1, 1, 1600 ], [ 10, 1, 1, 2160 ], [ 11, 1, 1, 512 ], [ 12, 1, 1, 1920 ], [ 13, 1, 1, 192 ], [ 14, 1, 1, 512 ], [ 15, 1, 1, 960 ], [ 16, 1, 1, 60 ], [ 17, 1, 1, 840 ], [ 18, 1, 1, 480 ], [ 19, 1, 1, 2112 ], [ 20, 1, 1, 4480 ], [ 21, 1, 1, 5760 ], [ 22, 1, 1, 3840 ], [ 23, 1, 1, 960 ], [ 24, 1, 1, 2880 ], [ 25, 1, 1, 3840 ], [ 26, 1, 1, 1560 ], [ 27, 1, 1, 7200 ], [ 28, 1, 1, 960 ], [ 29, 1, 1, 3840 ], [ 30, 1, 1, 9600 ], [ 31, 1, 1, 6720 ], [ 32, 1, 1, 11520 ], [ 33, 1, 1, 7680 ], [ 34, 1, 1, 2880 ], [ 35, 1, 1, 6720 ], [ 36, 1, 1, 11520 ], [ 37, 1, 1, 15360 ], [ 38, 1, 1, 17280 ], [ 39, 1, 1, 11520 ], [ 40, 1, 1, 17280 ], [ 41, 1, 1, 23040 ], [ 42, 1, 1, 23040 ] ] k = 2: F-action on Pi is () [43,1,2] Dynkin type is 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 12: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 2 modulo 12: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 3 modulo 12: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 4 modulo 12: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 5 modulo 12: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 7 modulo 12: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 8 modulo 12: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 9 modulo 12: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 11 modulo 12: 1/10 q phi1 phi2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 14, 56 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 19, 1, 1, 2 ], [ 42, 1, 2, 10 ] ] k = 3: F-action on Pi is () [43,1,3] Dynkin type is 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 12: 1/10 q^2 phi1 phi2 phi4 q congruent 2 modulo 12: 1/10 q^2 phi1 phi2 phi4 q congruent 3 modulo 12: 1/10 q^2 phi1 phi2 phi4 q congruent 4 modulo 12: 1/10 q^2 phi1 phi2 phi4 q congruent 5 modulo 12: 1/10 q^2 phi1 phi2 phi4 q congruent 7 modulo 12: 1/10 q^2 phi1 phi2 phi4 q congruent 8 modulo 12: 1/10 q^2 phi1 phi2 phi4 q congruent 9 modulo 12: 1/10 q^2 phi1 phi2 phi4 q congruent 11 modulo 12: 1/10 q^2 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 26, 44 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 13, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 19, 1, 2, 2 ], [ 42, 1, 3, 10 ] ] k = 4: F-action on Pi is () [43,1,4] Dynkin type is 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 12: 1/144 phi1 ( q^5-12*q^4+48*q^3-56*q^2-69*q+112 ) q congruent 2 modulo 12: 1/144 q phi2 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 3 modulo 12: 1/144 q phi2 ( q^4-14*q^3+74*q^2-178*q+165 ) q congruent 4 modulo 12: 1/144 phi1 ( q^5-12*q^4+45*q^3-38*q^2-72*q+64 ) q congruent 5 modulo 12: 1/144 q phi2 ( q^4-14*q^3+74*q^2-178*q+165 ) q congruent 7 modulo 12: 1/144 phi1 ( q^5-12*q^4+48*q^3-56*q^2-69*q+112 ) q congruent 8 modulo 12: 1/144 q phi2 ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 9 modulo 12: 1/144 q phi2 ( q^4-14*q^3+74*q^2-178*q+165 ) q congruent 11 modulo 12: 1/144 q phi2 ( q^4-14*q^3+74*q^2-178*q+165 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 18 ], [ 4, 1, 1, 28 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 40 ], [ 9, 1, 1, 46 ], [ 10, 1, 1, 36 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 48 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 18, 1, 1, 24 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 64 ], [ 21, 1, 1, 36 ], [ 22, 1, 1, 48 ], [ 23, 1, 1, 48 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 26, 1, 1, 24 ], [ 28, 1, 1, 48 ], [ 28, 1, 5, 6 ], [ 29, 1, 1, 48 ], [ 29, 1, 3, 24 ], [ 30, 1, 1, 48 ], [ 31, 1, 1, 48 ], [ 33, 1, 1, 96 ], [ 33, 1, 2, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 8, 42 ], [ 37, 1, 1, 48 ], [ 37, 1, 3, 96 ], [ 39, 1, 3, 72 ], [ 40, 1, 7, 108 ], [ 41, 1, 3, 144 ], [ 42, 1, 4, 144 ] ] k = 5: F-action on Pi is () [43,1,5] Dynkin type is 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 12: 1/36 phi1 ( q^5-3*q^3-11*q^2-3*q+10 ) q congruent 2 modulo 12: 1/36 q phi2 ( q^4-2*q^3-q^2-q+6 ) q congruent 3 modulo 12: 1/36 q phi2 ( q^4-2*q^3-q^2-7*q+15 ) q congruent 4 modulo 12: 1/36 phi1 ( q^5-3*q^3-5*q^2+4 ) q congruent 5 modulo 12: 1/36 q phi2 ( q^4-2*q^3-q^2-7*q+15 ) q congruent 7 modulo 12: 1/36 phi1 ( q^5-3*q^3-11*q^2-3*q+10 ) q congruent 8 modulo 12: 1/36 q phi2 ( q^4-2*q^3-q^2-q+6 ) q congruent 9 modulo 12: 1/36 q phi2 ( q^4-2*q^3-q^2-7*q+15 ) q congruent 11 modulo 12: 1/36 q phi2 ( q^4-2*q^3-q^2-7*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 2 ], [ 20, 1, 1, 4 ], [ 21, 1, 5, 18 ], [ 28, 1, 5, 12 ], [ 29, 1, 3, 12 ], [ 32, 1, 9, 18 ], [ 33, 1, 2, 24 ], [ 34, 1, 9, 18 ], [ 35, 1, 8, 12 ], [ 36, 1, 9, 18 ], [ 37, 1, 3, 12 ], [ 42, 1, 5, 36 ] ] k = 6: F-action on Pi is () [43,1,6] Dynkin type is 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 12: 1/48 q phi1 phi2^2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 3 modulo 12: 1/48 q phi1 phi2^2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 5 modulo 12: 1/48 q phi1 phi2^2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/48 q phi1 phi2^2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 9 modulo 12: 1/48 q phi1 phi2^2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/48 q phi1 phi2^2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 8 ], [ 15, 1, 3, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 8 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 8 ], [ 22, 1, 2, 16 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 16 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 5, 6 ], [ 30, 1, 2, 16 ], [ 31, 1, 4, 16 ], [ 35, 1, 5, 16 ], [ 35, 1, 8, 18 ], [ 37, 1, 5, 16 ], [ 39, 1, 7, 24 ], [ 40, 1, 7, 36 ], [ 40, 1, 14, 24 ], [ 41, 1, 13, 48 ] ] k = 7: F-action on Pi is () [43,1,7] Dynkin type is 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 12: 1/24 q phi1^2 phi2^3 q congruent 2 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 3 modulo 12: 1/24 q phi1^2 phi2^3 q congruent 4 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 5 modulo 12: 1/24 q phi1^2 phi2^3 q congruent 7 modulo 12: 1/24 q phi1^2 phi2^3 q congruent 8 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 9 modulo 12: 1/24 q phi1^2 phi2^3 q congruent 11 modulo 12: 1/24 q phi1^2 phi2^3 Fusion of maximal tori of C^F in those of G^F: [ 58, 27 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 28, 1, 5, 6 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 6 ], [ 37, 1, 4, 8 ], [ 40, 1, 14, 12 ] ] k = 8: F-action on Pi is () [43,1,8] Dynkin type is 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 12: 1/24 q phi1^3 phi2^2 q congruent 2 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 3 modulo 12: 1/24 q phi1^3 phi2^2 q congruent 4 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 5 modulo 12: 1/24 q phi1^3 phi2^2 q congruent 7 modulo 12: 1/24 q phi1^3 phi2^2 q congruent 8 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 9 modulo 12: 1/24 q phi1^3 phi2^2 q congruent 11 modulo 12: 1/24 q phi1^3 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 57, 28 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 26, 1, 5, 4 ], [ 28, 1, 4, 6 ], [ 35, 1, 7, 8 ], [ 35, 1, 9, 6 ], [ 37, 1, 10, 8 ], [ 40, 1, 15, 12 ] ] k = 9: F-action on Pi is () [43,1,9] Dynkin type is 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 12: 1/144 q phi1^2 ( q^3-5*q^2+9*q-9 ) q congruent 2 modulo 12: 1/144 phi2 ( q^5-8*q^4+25*q^3-42*q^2+48*q-32 ) q congruent 3 modulo 12: 1/144 q phi1^2 ( q^3-5*q^2+9*q-9 ) q congruent 4 modulo 12: 1/144 q^2 phi1^2 ( q^2-5*q+6 ) q congruent 5 modulo 12: 1/144 phi2 ( q^5-8*q^4+28*q^3-60*q^2+87*q-80 ) q congruent 7 modulo 12: 1/144 q phi1^2 ( q^3-5*q^2+9*q-9 ) q congruent 8 modulo 12: 1/144 phi2 ( q^5-8*q^4+25*q^3-42*q^2+48*q-32 ) q congruent 9 modulo 12: 1/144 q phi1^2 ( q^3-5*q^2+9*q-9 ) q congruent 11 modulo 12: 1/144 phi2 ( q^5-8*q^4+28*q^3-60*q^2+87*q-80 ) Fusion of maximal tori of C^F in those of G^F: [ 15, 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 18 ], [ 4, 1, 2, 28 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 18 ], [ 8, 1, 2, 40 ], [ 9, 1, 2, 46 ], [ 10, 1, 4, 36 ], [ 11, 1, 2, 32 ], [ 12, 1, 6, 48 ], [ 13, 1, 2, 24 ], [ 14, 1, 2, 32 ], [ 15, 1, 4, 48 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 18, 1, 3, 24 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 64 ], [ 21, 1, 6, 36 ], [ 22, 1, 4, 48 ], [ 23, 1, 4, 48 ], [ 24, 1, 3, 72 ], [ 25, 1, 8, 48 ], [ 26, 1, 3, 24 ], [ 28, 1, 4, 6 ], [ 28, 1, 6, 48 ], [ 29, 1, 4, 48 ], [ 29, 1, 6, 24 ], [ 30, 1, 5, 48 ], [ 31, 1, 7, 48 ], [ 33, 1, 5, 48 ], [ 33, 1, 6, 96 ], [ 35, 1, 9, 42 ], [ 35, 1, 10, 48 ], [ 37, 1, 6, 48 ], [ 37, 1, 8, 96 ], [ 39, 1, 12, 72 ], [ 40, 1, 8, 108 ], [ 41, 1, 8, 144 ], [ 42, 1, 6, 144 ] ] k = 10: F-action on Pi is () [43,1,10] Dynkin type is 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 12: 1/48 q phi1 phi2 ( q^3-3*q^2-3*q+13 ) q congruent 2 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-3*q+13 ) q congruent 4 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 5 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-3*q+13 ) q congruent 7 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-3*q+13 ) q congruent 8 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 9 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-3*q+13 ) q congruent 11 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-3*q+13 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 12 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 18, 1, 4, 8 ], [ 21, 1, 3, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 16 ], [ 24, 1, 4, 8 ], [ 25, 1, 4, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 4, 6 ], [ 30, 1, 6, 16 ], [ 31, 1, 6, 16 ], [ 35, 1, 3, 16 ], [ 35, 1, 9, 18 ], [ 37, 1, 9, 16 ], [ 39, 1, 16, 24 ], [ 40, 1, 8, 36 ], [ 40, 1, 15, 24 ], [ 41, 1, 17, 48 ] ] k = 11: F-action on Pi is () [43,1,11] Dynkin type is 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 12: 1/24 q phi1^3 phi2 ( q-3 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/24 q phi1^3 phi2 ( q-3 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 5 modulo 12: 1/24 q phi1^3 phi2 ( q-3 ) q congruent 7 modulo 12: 1/24 q phi1^3 phi2 ( q-3 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/24 q phi1^3 phi2 ( q-3 ) q congruent 11 modulo 12: 1/24 q phi1^3 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 45, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 10 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 8 ], [ 22, 1, 2, 8 ], [ 23, 1, 2, 8 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 5, 8 ], [ 26, 1, 2, 4 ], [ 28, 1, 3, 8 ], [ 28, 1, 5, 6 ], [ 29, 1, 2, 8 ], [ 29, 1, 3, 12 ], [ 30, 1, 1, 8 ], [ 30, 1, 2, 8 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 33, 1, 2, 24 ], [ 33, 1, 3, 16 ], [ 35, 1, 2, 8 ], [ 35, 1, 8, 18 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 24 ], [ 39, 1, 3, 12 ], [ 39, 1, 7, 12 ], [ 40, 1, 7, 36 ], [ 41, 1, 3, 24 ], [ 41, 1, 13, 24 ], [ 42, 1, 7, 24 ] ] k = 12: F-action on Pi is () [43,1,12] Dynkin type is 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 12: 1/24 q phi1^4 phi2 q congruent 2 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q phi1^4 phi2 q congruent 4 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q phi1^4 phi2 q congruent 7 modulo 12: 1/24 q phi1^4 phi2 q congruent 8 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q phi1^4 phi2 q congruent 11 modulo 12: 1/24 q phi1^4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 48, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 10 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 4 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 8 ], [ 22, 1, 4, 8 ], [ 23, 1, 3, 8 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 12 ], [ 25, 1, 4, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 2, 4 ], [ 28, 1, 2, 8 ], [ 28, 1, 4, 6 ], [ 29, 1, 5, 8 ], [ 29, 1, 6, 12 ], [ 30, 1, 5, 8 ], [ 30, 1, 6, 8 ], [ 31, 1, 5, 8 ], [ 31, 1, 8, 8 ], [ 33, 1, 4, 16 ], [ 33, 1, 5, 24 ], [ 35, 1, 4, 8 ], [ 35, 1, 9, 18 ], [ 37, 1, 7, 8 ], [ 37, 1, 8, 24 ], [ 39, 1, 12, 12 ], [ 39, 1, 16, 12 ], [ 40, 1, 8, 36 ], [ 41, 1, 8, 24 ], [ 41, 1, 17, 24 ], [ 42, 1, 8, 24 ] ] k = 13: F-action on Pi is () [43,1,13] Dynkin type is 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 12: 1/36 q phi1 ( q^4-q^2-9*q-3 ) q congruent 2 modulo 12: 1/36 phi2 ( q^5-2*q^4+q^3-3*q^2+6*q-8 ) q congruent 3 modulo 12: 1/36 q phi1 ( q^4-q^2-9*q-3 ) q congruent 4 modulo 12: 1/36 q^2 phi1 ( q^3-q-3 ) q congruent 5 modulo 12: 1/36 phi2 ( q^5-2*q^4+q^3-9*q^2+15*q-14 ) q congruent 7 modulo 12: 1/36 q phi1 ( q^4-q^2-9*q-3 ) q congruent 8 modulo 12: 1/36 phi2 ( q^5-2*q^4+q^3-3*q^2+6*q-8 ) q congruent 9 modulo 12: 1/36 q phi1 ( q^4-q^2-9*q-3 ) q congruent 11 modulo 12: 1/36 phi2 ( q^5-2*q^4+q^3-9*q^2+15*q-14 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 14, 1, 2, 2 ], [ 20, 1, 2, 4 ], [ 21, 1, 4, 18 ], [ 28, 1, 4, 12 ], [ 29, 1, 6, 12 ], [ 32, 1, 10, 18 ], [ 33, 1, 5, 24 ], [ 34, 1, 10, 18 ], [ 35, 1, 9, 12 ], [ 36, 1, 7, 18 ], [ 37, 1, 8, 12 ], [ 42, 1, 11, 36 ] ] k = 14: F-action on Pi is () [43,1,14] Dynkin type is 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 12: 1/12 phi1 ( q^5-q^3-5*q^2-5*q+2 ) q congruent 2 modulo 12: 1/12 q phi2 ( q^4-2*q^3+q^2-3*q+2 ) q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q^3-q^2-5 ) q congruent 4 modulo 12: 1/12 q phi1 ( q^4-q^2-3*q-4 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q^3-q^2-5 ) q congruent 7 modulo 12: 1/12 phi1 ( q^5-q^3-5*q^2-5*q+2 ) q congruent 8 modulo 12: 1/12 q phi2 ( q^4-2*q^3+q^2-3*q+2 ) q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q^3-q^2-5 ) q congruent 11 modulo 12: 1/12 q phi1 phi2 ( q^3-q^2-5 ) Fusion of maximal tori of C^F in those of G^F: [ 50, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 3, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 2 ], [ 20, 1, 4, 4 ], [ 21, 1, 5, 6 ], [ 32, 1, 9, 6 ], [ 34, 1, 10, 6 ], [ 36, 1, 7, 6 ], [ 42, 1, 9, 12 ] ] k = 15: F-action on Pi is () [43,1,15] Dynkin type is 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 12: 1/12 q phi1 ( q^4+q^2-3*q-1 ) q congruent 2 modulo 12: 1/12 phi2 ( q^5-2*q^4+3*q^3-5*q^2+6*q-4 ) q congruent 3 modulo 12: 1/12 q phi1 ( q^4+q^2-3*q-1 ) q congruent 4 modulo 12: 1/12 q^2 phi1 ( q^3+q-1 ) q congruent 5 modulo 12: 1/12 phi2 ( q^5-2*q^4+3*q^3-7*q^2+9*q-6 ) q congruent 7 modulo 12: 1/12 q phi1 ( q^4+q^2-3*q-1 ) q congruent 8 modulo 12: 1/12 phi2 ( q^5-2*q^4+3*q^3-5*q^2+6*q-4 ) q congruent 9 modulo 12: 1/12 q phi1 ( q^4+q^2-3*q-1 ) q congruent 11 modulo 12: 1/12 phi2 ( q^5-2*q^4+3*q^3-7*q^2+9*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 51, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 4, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 5, 4 ], [ 14, 1, 1, 2 ], [ 20, 1, 3, 4 ], [ 21, 1, 4, 6 ], [ 32, 1, 10, 6 ], [ 34, 1, 9, 6 ], [ 36, 1, 9, 6 ], [ 42, 1, 10, 12 ] ] k = 16: F-action on Pi is () [43,1,16] Dynkin type is 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 12: 1/1536 phi1 ( q^5-11*q^4+36*q^3-44*q^2+67*q+15 ) q congruent 2 modulo 12: 1/1536 q ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 ) q congruent 3 modulo 12: 1/1536 phi2 ( q^5-13*q^4+60*q^3-140*q^2+251*q-303 ) q congruent 4 modulo 12: 1/1536 q ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 ) q congruent 5 modulo 12: 1/1536 phi1 ( q^5-11*q^4+36*q^3-44*q^2+67*q+15 ) q congruent 7 modulo 12: 1/1536 phi2 ( q^5-13*q^4+60*q^3-140*q^2+251*q-303 ) q congruent 8 modulo 12: 1/1536 q ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 ) q congruent 9 modulo 12: 1/1536 phi1 ( q^5-11*q^4+36*q^3-44*q^2+67*q+15 ) q congruent 11 modulo 12: 1/1536 phi2 ( q^5-13*q^4+60*q^3-140*q^2+251*q-303 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 48 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 1, 48 ], [ 10, 1, 2, 96 ], [ 10, 1, 3, 32 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 15, 1, 2, 64 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 24 ], [ 17, 1, 1, 56 ], [ 17, 1, 3, 144 ], [ 18, 1, 4, 32 ], [ 21, 1, 3, 128 ], [ 21, 1, 6, 192 ], [ 22, 1, 2, 96 ], [ 22, 1, 3, 64 ], [ 22, 1, 4, 288 ], [ 24, 1, 4, 128 ], [ 25, 1, 4, 256 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 96 ], [ 26, 1, 3, 144 ], [ 26, 1, 4, 32 ], [ 27, 1, 1, 96 ], [ 27, 1, 2, 192 ], [ 27, 1, 8, 384 ], [ 27, 1, 12, 576 ], [ 27, 1, 13, 384 ], [ 28, 1, 6, 192 ], [ 30, 1, 6, 256 ], [ 31, 1, 6, 64 ], [ 31, 1, 8, 384 ], [ 32, 1, 3, 384 ], [ 32, 1, 5, 384 ], [ 32, 1, 6, 192 ], [ 32, 1, 7, 576 ], [ 34, 1, 3, 192 ], [ 35, 1, 3, 64 ], [ 35, 1, 5, 192 ], [ 35, 1, 10, 576 ], [ 36, 1, 18, 768 ], [ 37, 1, 9, 256 ], [ 38, 1, 4, 384 ], [ 38, 1, 6, 768 ], [ 39, 1, 20, 768 ], [ 40, 1, 2, 1152 ], [ 40, 1, 3, 384 ], [ 40, 1, 13, 768 ], [ 41, 1, 7, 768 ], [ 41, 1, 22, 1536 ] ] k = 17: F-action on Pi is () [43,1,17] Dynkin type is 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 12: 1/128 phi1 phi2 ( q^4-4*q^3+28*q-41 ) q congruent 2 modulo 12: 1/128 q^2 ( q^4-4*q^3+16*q-16 ) q congruent 3 modulo 12: 1/128 phi1 phi2 ( q^4-4*q^3+28*q-41 ) q congruent 4 modulo 12: 1/128 q^2 ( q^4-4*q^3+16*q-16 ) q congruent 5 modulo 12: 1/128 phi1 phi2 ( q^4-4*q^3+28*q-41 ) q congruent 7 modulo 12: 1/128 phi1 phi2 ( q^4-4*q^3+28*q-41 ) q congruent 8 modulo 12: 1/128 q^2 ( q^4-4*q^3+16*q-16 ) q congruent 9 modulo 12: 1/128 phi1 phi2 ( q^4-4*q^3+28*q-41 ) q congruent 11 modulo 12: 1/128 phi1 phi2 ( q^4-4*q^3+28*q-41 ) Fusion of maximal tori of C^F in those of G^F: [ 9, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 1, 4, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 24 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 48 ], [ 27, 1, 14, 32 ], [ 32, 1, 8, 64 ], [ 34, 1, 6, 32 ], [ 35, 1, 7, 32 ], [ 36, 1, 17, 64 ], [ 38, 1, 13, 64 ], [ 40, 1, 6, 96 ], [ 40, 1, 23, 64 ], [ 41, 1, 21, 128 ] ] k = 18: F-action on Pi is () [43,1,18] Dynkin type is 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 12: 1/16 phi1 phi2 phi4 ( q^2-3 ) q congruent 2 modulo 12: 1/16 q^4 ( q^2-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-3 ) q congruent 4 modulo 12: 1/16 q^4 ( q^2-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-3 ) q congruent 7 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-3 ) q congruent 8 modulo 12: 1/16 q^4 ( q^2-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-3 ) q congruent 11 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-3 ) Fusion of maximal tori of C^F in those of G^F: [ 53, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 26, 1, 4, 4 ], [ 27, 1, 10, 8 ], [ 40, 1, 25, 8 ] ] k = 19: F-action on Pi is () [43,1,19] Dynkin type is 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 12: 1/128 phi1^2 phi2 ( q^3+q^2-3*q+5 ) q congruent 2 modulo 12: 1/128 q^4 ( q^2-4 ) q congruent 3 modulo 12: 1/128 phi1^2 phi2 ( q^3+q^2-3*q+5 ) q congruent 4 modulo 12: 1/128 q^4 ( q^2-4 ) q congruent 5 modulo 12: 1/128 phi1^2 phi2 ( q^3+q^2-3*q+5 ) q congruent 7 modulo 12: 1/128 phi1^2 phi2 ( q^3+q^2-3*q+5 ) q congruent 8 modulo 12: 1/128 q^4 ( q^2-4 ) q congruent 9 modulo 12: 1/128 phi1^2 phi2 ( q^3+q^2-3*q+5 ) q congruent 11 modulo 12: 1/128 phi1^2 phi2 ( q^3+q^2-3*q+5 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 1, 11, 32 ], [ 27, 1, 13, 32 ], [ 32, 1, 4, 64 ], [ 34, 1, 8, 32 ], [ 35, 1, 6, 32 ], [ 36, 1, 10, 64 ], [ 38, 1, 12, 64 ], [ 40, 1, 6, 96 ], [ 40, 1, 24, 64 ], [ 41, 1, 14, 128 ] ] k = 20: F-action on Pi is () [43,1,20] Dynkin type is A_1(q) + T(phi4 phi8) Order of center |Z^F|: phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^2 phi2^2 phi4 q congruent 2 modulo 12: 1/16 q^6 q congruent 3 modulo 12: 1/16 phi1^2 phi2^2 phi4 q congruent 4 modulo 12: 1/16 q^6 q congruent 5 modulo 12: 1/16 phi1^2 phi2^2 phi4 q congruent 7 modulo 12: 1/16 phi1^2 phi2^2 phi4 q congruent 8 modulo 12: 1/16 q^6 q congruent 9 modulo 12: 1/16 phi1^2 phi2^2 phi4 q congruent 11 modulo 12: 1/16 phi1^2 phi2^2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 24, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 3, 4 ], [ 4, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 40, 1, 25, 8 ] ] k = 21: F-action on Pi is () [43,1,21] Dynkin type is 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 12: 1/64 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 2 modulo 12: 1/64 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 4 modulo 12: 1/64 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 8 modulo 12: 1/64 q^3 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q^3-q^2-5*q+13 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q^3-q^2-5*q+13 ) Fusion of maximal tori of C^F in those of G^F: [ 42, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 3, 8 ], [ 4, 1, 4, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 24 ], [ 27, 1, 4, 16 ], [ 27, 1, 5, 32 ], [ 27, 1, 6, 16 ], [ 27, 1, 7, 48 ], [ 27, 1, 9, 16 ], [ 32, 1, 4, 32 ], [ 32, 1, 8, 32 ], [ 34, 1, 6, 16 ], [ 34, 1, 8, 16 ], [ 36, 1, 10, 32 ], [ 36, 1, 17, 32 ], [ 38, 1, 11, 32 ], [ 38, 1, 14, 32 ], [ 40, 1, 6, 96 ], [ 40, 1, 16, 32 ], [ 41, 1, 14, 64 ], [ 41, 1, 21, 64 ] ] k = 22: F-action on Pi is () [43,1,22] Dynkin type is 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 12: 1/1536 phi1 ( q^5-15*q^4+68*q^3-52*q^2-205*q+75 ) q congruent 2 modulo 12: 1/1536 q ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 ) q congruent 3 modulo 12: 1/1536 phi2 ( q^5-17*q^4+100*q^3-220*q^2+67*q+213 ) q congruent 4 modulo 12: 1/1536 q ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 ) q congruent 5 modulo 12: 1/1536 phi1 ( q^5-15*q^4+68*q^3-52*q^2-205*q+75 ) q congruent 7 modulo 12: 1/1536 phi2 ( q^5-17*q^4+100*q^3-220*q^2+67*q+213 ) q congruent 8 modulo 12: 1/1536 q ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 ) q congruent 9 modulo 12: 1/1536 phi1 ( q^5-15*q^4+68*q^3-52*q^2-205*q+75 ) q congruent 11 modulo 12: 1/1536 phi2 ( q^5-17*q^4+100*q^3-220*q^2+67*q+213 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 48 ], [ 4, 1, 2, 24 ], [ 7, 1, 1, 24 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 10, 1, 2, 32 ], [ 10, 1, 3, 96 ], [ 10, 1, 4, 48 ], [ 11, 1, 1, 96 ], [ 15, 1, 3, 64 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 144 ], [ 17, 1, 3, 56 ], [ 18, 1, 2, 32 ], [ 21, 1, 1, 192 ], [ 21, 1, 2, 128 ], [ 22, 1, 1, 288 ], [ 22, 1, 2, 64 ], [ 22, 1, 3, 96 ], [ 24, 1, 2, 128 ], [ 25, 1, 5, 256 ], [ 26, 1, 1, 144 ], [ 26, 1, 2, 96 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 32 ], [ 27, 1, 1, 576 ], [ 27, 1, 2, 192 ], [ 27, 1, 3, 384 ], [ 27, 1, 8, 384 ], [ 27, 1, 12, 96 ], [ 28, 1, 1, 192 ], [ 30, 1, 2, 256 ], [ 31, 1, 2, 384 ], [ 31, 1, 4, 64 ], [ 32, 1, 1, 576 ], [ 32, 1, 2, 384 ], [ 32, 1, 3, 192 ], [ 32, 1, 6, 384 ], [ 34, 1, 2, 192 ], [ 35, 1, 1, 576 ], [ 35, 1, 3, 192 ], [ 35, 1, 5, 64 ], [ 36, 1, 4, 768 ], [ 37, 1, 5, 256 ], [ 38, 1, 2, 768 ], [ 38, 1, 5, 384 ], [ 39, 1, 8, 768 ], [ 40, 1, 1, 1152 ], [ 40, 1, 3, 384 ], [ 40, 1, 12, 768 ], [ 41, 1, 5, 768 ], [ 41, 1, 15, 1536 ] ] k = 23: F-action on Pi is () [43,1,23] Dynkin type is 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 12: 1/192 phi1 phi2 ( q^4-8*q^3+14*q^2+32*q-87 ) q congruent 2 modulo 12: 1/192 q^2 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 3 modulo 12: 1/192 phi1 phi2 ( q^4-8*q^3+14*q^2+32*q-87 ) q congruent 4 modulo 12: 1/192 q^2 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 5 modulo 12: 1/192 phi1 phi2 ( q^4-8*q^3+14*q^2+32*q-87 ) q congruent 7 modulo 12: 1/192 phi1 phi2 ( q^4-8*q^3+14*q^2+32*q-87 ) q congruent 8 modulo 12: 1/192 q^2 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 9 modulo 12: 1/192 phi1 phi2 ( q^4-8*q^3+14*q^2+32*q-87 ) q congruent 11 modulo 12: 1/192 phi1 phi2 ( q^4-8*q^3+14*q^2+32*q-87 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 12 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 36 ], [ 10, 1, 4, 12 ], [ 11, 1, 1, 24 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 12 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 27, 1, 7, 24 ], [ 28, 1, 1, 48 ], [ 32, 1, 2, 48 ], [ 32, 1, 8, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 24 ], [ 37, 1, 4, 32 ], [ 40, 1, 12, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 23, 96 ], [ 41, 1, 4, 96 ] ] k = 24: F-action on Pi is () [43,1,24] Dynkin type is 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 12: 1/192 phi1^3 phi2^2 ( q-3 ) q congruent 2 modulo 12: 1/192 q^3 ( q^3-4*q^2+2*q+4 ) q congruent 3 modulo 12: 1/192 phi1^3 phi2^2 ( q-3 ) q congruent 4 modulo 12: 1/192 q^3 ( q^3-4*q^2+2*q+4 ) q congruent 5 modulo 12: 1/192 phi1^3 phi2^2 ( q-3 ) q congruent 7 modulo 12: 1/192 phi1^3 phi2^2 ( q-3 ) q congruent 8 modulo 12: 1/192 q^3 ( q^3-4*q^2+2*q+4 ) q congruent 9 modulo 12: 1/192 phi1^3 phi2^2 ( q-3 ) q congruent 11 modulo 12: 1/192 phi1^3 phi2^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 40, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 36 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 12 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 24 ], [ 27, 1, 7, 24 ], [ 27, 1, 13, 96 ], [ 28, 1, 6, 48 ], [ 32, 1, 4, 48 ], [ 32, 1, 5, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 8 ], [ 35, 1, 10, 48 ], [ 37, 1, 10, 32 ], [ 40, 1, 13, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 24, 96 ], [ 41, 1, 9, 96 ] ] k = 25: F-action on Pi is () [43,1,25] Dynkin type is 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 12: 1/32 phi1^3 phi2 ( q^2-3 ) q congruent 2 modulo 12: 1/32 q^3 ( q^3-2*q^2-2*q+4 ) q congruent 3 modulo 12: 1/32 phi1^3 phi2 ( q^2-3 ) q congruent 4 modulo 12: 1/32 q^3 ( q^3-2*q^2-2*q+4 ) q congruent 5 modulo 12: 1/32 phi1^3 phi2 ( q^2-3 ) q congruent 7 modulo 12: 1/32 phi1^3 phi2 ( q^2-3 ) q congruent 8 modulo 12: 1/32 q^3 ( q^3-2*q^2-2*q+4 ) q congruent 9 modulo 12: 1/32 phi1^3 phi2 ( q^2-3 ) q congruent 11 modulo 12: 1/32 phi1^3 phi2 ( q^2-3 ) Fusion of maximal tori of C^F in those of G^F: [ 13, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 21, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 1, 10, 16 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 32, 1, 2, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 32, 1, 8, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 37, 1, 4, 16 ], [ 37, 1, 10, 16 ], [ 40, 1, 16, 16 ], [ 40, 1, 21, 16 ], [ 40, 1, 22, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ] ] k = 26: F-action on Pi is () [43,1,26] Dynkin type is A_1(q) + T(phi2^6) Order of center |Z^F|: phi2^6 Numbers of classes in class type: q congruent 1 modulo 12: 1/23040 phi1 ( q^5-39*q^4+596*q^3-4644*q^2+19875*q-40365 ) q congruent 2 modulo 12: 1/23040 ( q^6-40*q^5+620*q^4-4640*q^3+16704*q^2-24320*q+10240 ) q congruent 3 modulo 12: 1/23040 ( q^6-40*q^5+635*q^4-5240*q^3+24519*q^2-63120*q+67725 ) q congruent 4 modulo 12: 1/23040 q ( q^5-40*q^4+620*q^3-4640*q^2+16704*q-23040 ) q congruent 5 modulo 12: 1/23040 ( q^6-40*q^5+635*q^4-5240*q^3+24519*q^2-61520*q+62125 ) q congruent 7 modulo 12: 1/23040 ( q^6-40*q^5+635*q^4-5240*q^3+24519*q^2-63120*q+67725 ) q congruent 8 modulo 12: 1/23040 ( q^6-40*q^5+620*q^4-4640*q^3+16704*q^2-24320*q+10240 ) q congruent 9 modulo 12: 1/23040 phi1 ( q^5-39*q^4+596*q^3-4644*q^2+19875*q-40365 ) q congruent 11 modulo 12: 1/23040 ( q^6-40*q^5+635*q^4-5240*q^3+24519*q^2-64400*q+89485 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 31 ], [ 3, 1, 2, 192 ], [ 4, 1, 2, 520 ], [ 5, 1, 2, 32 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 252 ], [ 8, 1, 2, 832 ], [ 9, 1, 2, 1600 ], [ 10, 1, 4, 2160 ], [ 11, 1, 2, 512 ], [ 12, 1, 6, 1920 ], [ 13, 1, 2, 192 ], [ 14, 1, 2, 512 ], [ 15, 1, 4, 960 ], [ 16, 1, 2, 60 ], [ 17, 1, 3, 840 ], [ 18, 1, 3, 480 ], [ 19, 1, 2, 2112 ], [ 20, 1, 2, 4480 ], [ 21, 1, 6, 5760 ], [ 22, 1, 4, 3840 ], [ 23, 1, 4, 960 ], [ 24, 1, 3, 2880 ], [ 25, 1, 8, 3840 ], [ 26, 1, 3, 1560 ], [ 27, 1, 12, 7200 ], [ 28, 1, 6, 960 ], [ 29, 1, 4, 3840 ], [ 30, 1, 5, 9600 ], [ 31, 1, 7, 6720 ], [ 32, 1, 7, 11520 ], [ 33, 1, 6, 7680 ], [ 34, 1, 4, 2880 ], [ 35, 1, 10, 6720 ], [ 36, 1, 20, 11520 ], [ 37, 1, 6, 15360 ], [ 38, 1, 7, 17280 ], [ 39, 1, 15, 11520 ], [ 40, 1, 2, 17280 ], [ 41, 1, 16, 23040 ], [ 42, 1, 21, 23040 ] ] k = 27: F-action on Pi is () [43,1,27] Dynkin type is 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 12: 1/768 phi1 ( q^5-17*q^4+114*q^3-418*q^2+941*q-1005 ) q congruent 2 modulo 12: 1/768 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 ) q congruent 3 modulo 12: 1/768 ( q^6-18*q^5+131*q^4-532*q^3+1359*q^2-2042*q+1293 ) q congruent 4 modulo 12: 1/768 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 ) q congruent 5 modulo 12: 1/768 phi1 ( q^5-17*q^4+114*q^3-418*q^2+941*q-1005 ) q congruent 7 modulo 12: 1/768 ( q^6-18*q^5+131*q^4-532*q^3+1359*q^2-2042*q+1293 ) q congruent 8 modulo 12: 1/768 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 ) q congruent 9 modulo 12: 1/768 phi1 ( q^5-17*q^4+114*q^3-418*q^2+941*q-1005 ) q congruent 11 modulo 12: 1/768 ( q^6-18*q^5+131*q^4-532*q^3+1359*q^2-2042*q+1293 ) Fusion of maximal tori of C^F in those of G^F: [ 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 2, 64 ], [ 4, 1, 2, 144 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 72 ], [ 8, 1, 2, 192 ], [ 9, 1, 2, 320 ], [ 10, 1, 4, 384 ], [ 11, 1, 2, 128 ], [ 12, 1, 6, 384 ], [ 13, 1, 2, 64 ], [ 14, 1, 2, 128 ], [ 15, 1, 2, 32 ], [ 15, 1, 4, 224 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 26 ], [ 17, 1, 1, 28 ], [ 17, 1, 3, 172 ], [ 18, 1, 3, 112 ], [ 18, 1, 4, 16 ], [ 19, 1, 2, 320 ], [ 20, 1, 2, 640 ], [ 21, 1, 6, 768 ], [ 22, 1, 3, 128 ], [ 22, 1, 4, 512 ], [ 23, 1, 3, 32 ], [ 23, 1, 4, 192 ], [ 24, 1, 3, 448 ], [ 24, 1, 4, 96 ], [ 25, 1, 4, 128 ], [ 25, 1, 8, 512 ], [ 26, 1, 2, 52 ], [ 26, 1, 3, 240 ], [ 27, 1, 8, 240 ], [ 27, 1, 12, 960 ], [ 28, 1, 2, 32 ], [ 28, 1, 6, 192 ], [ 29, 1, 4, 384 ], [ 29, 1, 5, 128 ], [ 30, 1, 5, 896 ], [ 30, 1, 6, 320 ], [ 31, 1, 5, 224 ], [ 31, 1, 7, 576 ], [ 31, 1, 8, 224 ], [ 32, 1, 3, 384 ], [ 32, 1, 7, 1152 ], [ 33, 1, 4, 256 ], [ 33, 1, 6, 768 ], [ 34, 1, 3, 96 ], [ 34, 1, 4, 288 ], [ 35, 1, 4, 224 ], [ 35, 1, 10, 576 ], [ 36, 1, 18, 384 ], [ 36, 1, 20, 1152 ], [ 37, 1, 6, 768 ], [ 37, 1, 7, 512 ], [ 38, 1, 3, 576 ], [ 38, 1, 6, 576 ], [ 38, 1, 7, 1152 ], [ 39, 1, 11, 384 ], [ 39, 1, 15, 384 ], [ 39, 1, 20, 384 ], [ 40, 1, 2, 1152 ], [ 40, 1, 18, 576 ], [ 41, 1, 6, 768 ], [ 41, 1, 16, 768 ], [ 41, 1, 22, 768 ], [ 42, 1, 20, 768 ] ] k = 28: F-action on Pi is () [43,1,28] Dynkin type is 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 12: 1/768 phi1 ( q^5-25*q^4+242*q^3-1154*q^2+2781*q-2805 ) q congruent 2 modulo 12: 1/768 q ( q^5-26*q^4+260*q^3-1240*q^2+2784*q-2304 ) q congruent 3 modulo 12: 1/768 phi1 ( q^5-25*q^4+242*q^3-1154*q^2+2781*q-2709 ) q congruent 4 modulo 12: 1/768 q ( q^5-26*q^4+260*q^3-1240*q^2+2784*q-2304 ) q congruent 5 modulo 12: 1/768 phi1 ( q^5-25*q^4+242*q^3-1154*q^2+2781*q-2805 ) q congruent 7 modulo 12: 1/768 phi1 ( q^5-25*q^4+242*q^3-1154*q^2+2781*q-2709 ) q congruent 8 modulo 12: 1/768 q ( q^5-26*q^4+260*q^3-1240*q^2+2784*q-2304 ) q congruent 9 modulo 12: 1/768 phi1 ( q^5-25*q^4+242*q^3-1154*q^2+2781*q-2805 ) q congruent 11 modulo 12: 1/768 phi1 ( q^5-25*q^4+242*q^3-1154*q^2+2781*q-2709 ) Fusion of maximal tori of C^F in those of G^F: [ 32, 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 64 ], [ 4, 1, 1, 144 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 72 ], [ 8, 1, 1, 192 ], [ 9, 1, 1, 320 ], [ 10, 1, 1, 384 ], [ 11, 1, 1, 128 ], [ 12, 1, 1, 384 ], [ 13, 1, 1, 64 ], [ 14, 1, 1, 128 ], [ 15, 1, 1, 224 ], [ 15, 1, 3, 32 ], [ 16, 1, 1, 26 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 172 ], [ 17, 1, 3, 28 ], [ 18, 1, 1, 112 ], [ 18, 1, 2, 16 ], [ 19, 1, 1, 320 ], [ 20, 1, 1, 640 ], [ 21, 1, 1, 768 ], [ 22, 1, 1, 512 ], [ 22, 1, 2, 128 ], [ 23, 1, 1, 192 ], [ 23, 1, 2, 32 ], [ 24, 1, 1, 448 ], [ 24, 1, 2, 96 ], [ 25, 1, 1, 512 ], [ 25, 1, 5, 128 ], [ 26, 1, 1, 240 ], [ 26, 1, 2, 52 ], [ 27, 1, 1, 960 ], [ 27, 1, 8, 240 ], [ 28, 1, 1, 192 ], [ 28, 1, 3, 32 ], [ 29, 1, 1, 384 ], [ 29, 1, 2, 128 ], [ 30, 1, 1, 896 ], [ 30, 1, 2, 320 ], [ 31, 1, 1, 576 ], [ 31, 1, 2, 224 ], [ 31, 1, 3, 224 ], [ 32, 1, 1, 1152 ], [ 32, 1, 6, 384 ], [ 33, 1, 1, 768 ], [ 33, 1, 3, 256 ], [ 34, 1, 1, 288 ], [ 34, 1, 2, 96 ], [ 35, 1, 1, 576 ], [ 35, 1, 2, 224 ], [ 36, 1, 1, 1152 ], [ 36, 1, 4, 384 ], [ 37, 1, 1, 768 ], [ 37, 1, 2, 512 ], [ 38, 1, 1, 1152 ], [ 38, 1, 2, 576 ], [ 38, 1, 8, 576 ], [ 39, 1, 1, 384 ], [ 39, 1, 2, 384 ], [ 39, 1, 8, 384 ], [ 40, 1, 1, 1152 ], [ 40, 1, 17, 576 ], [ 41, 1, 1, 768 ], [ 41, 1, 2, 768 ], [ 41, 1, 15, 768 ], [ 42, 1, 17, 768 ] ] k = 29: F-action on Pi is () [43,1,29] Dynkin type is 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 12: 1/128 phi1 phi2 ( q^4-6*q^3+8*q^2-2*q+15 ) q congruent 2 modulo 12: 1/128 q^2 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 3 modulo 12: 1/128 phi1 phi2 ( q^4-6*q^3+8*q^2-2*q+15 ) q congruent 4 modulo 12: 1/128 q^2 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 5 modulo 12: 1/128 phi1 phi2 ( q^4-6*q^3+8*q^2-2*q+15 ) q congruent 7 modulo 12: 1/128 phi1 phi2 ( q^4-6*q^3+8*q^2-2*q+15 ) q congruent 8 modulo 12: 1/128 q^2 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 9 modulo 12: 1/128 phi1 phi2 ( q^4-6*q^3+8*q^2-2*q+15 ) q congruent 11 modulo 12: 1/128 phi1 phi2 ( q^4-6*q^3+8*q^2-2*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 24 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 12 ], [ 9, 1, 1, 24 ], [ 9, 1, 2, 24 ], [ 10, 1, 1, 48 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 48 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 8 ], [ 15, 1, 2, 32 ], [ 15, 1, 3, 32 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 36 ], [ 18, 1, 2, 16 ], [ 18, 1, 4, 16 ], [ 21, 1, 1, 48 ], [ 21, 1, 2, 32 ], [ 21, 1, 3, 32 ], [ 21, 1, 6, 48 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 56 ], [ 22, 1, 3, 56 ], [ 22, 1, 4, 24 ], [ 24, 1, 2, 32 ], [ 24, 1, 4, 32 ], [ 25, 1, 4, 64 ], [ 25, 1, 5, 64 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 36 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 16 ], [ 27, 1, 1, 96 ], [ 27, 1, 2, 32 ], [ 27, 1, 8, 144 ], [ 27, 1, 9, 32 ], [ 27, 1, 12, 96 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 30, 1, 2, 64 ], [ 30, 1, 6, 64 ], [ 31, 1, 2, 32 ], [ 31, 1, 4, 64 ], [ 31, 1, 6, 64 ], [ 31, 1, 8, 32 ], [ 32, 1, 1, 48 ], [ 32, 1, 2, 32 ], [ 32, 1, 3, 112 ], [ 32, 1, 5, 32 ], [ 32, 1, 6, 112 ], [ 32, 1, 7, 48 ], [ 34, 1, 2, 32 ], [ 34, 1, 3, 32 ], [ 35, 1, 2, 48 ], [ 35, 1, 3, 32 ], [ 35, 1, 4, 48 ], [ 35, 1, 5, 32 ], [ 36, 1, 4, 128 ], [ 36, 1, 18, 128 ], [ 37, 1, 5, 64 ], [ 37, 1, 9, 64 ], [ 38, 1, 2, 64 ], [ 38, 1, 4, 128 ], [ 38, 1, 5, 128 ], [ 38, 1, 6, 64 ], [ 39, 1, 5, 64 ], [ 39, 1, 19, 64 ], [ 40, 1, 3, 64 ], [ 40, 1, 17, 96 ], [ 40, 1, 18, 96 ], [ 40, 1, 22, 64 ], [ 41, 1, 5, 64 ], [ 41, 1, 7, 64 ], [ 41, 1, 11, 128 ], [ 41, 1, 20, 128 ] ] k = 30: F-action on Pi is () [43,1,30] Dynkin type is 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 12: 1/128 phi1^2 ( q^4-6*q^3+10*q^2-10*q+13 ) q congruent 2 modulo 12: 1/128 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/128 phi1 ( q^5-7*q^4+16*q^3-20*q^2+23*q+3 ) q congruent 4 modulo 12: 1/128 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/128 phi1^2 ( q^4-6*q^3+10*q^2-10*q+13 ) q congruent 7 modulo 12: 1/128 phi1 ( q^5-7*q^4+16*q^3-20*q^2+23*q+3 ) q congruent 8 modulo 12: 1/128 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/128 phi1^2 ( q^4-6*q^3+10*q^2-10*q+13 ) q congruent 11 modulo 12: 1/128 phi1 ( q^5-7*q^4+16*q^3-20*q^2+23*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 24 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 48 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 24 ], [ 8, 1, 2, 48 ], [ 9, 1, 2, 72 ], [ 10, 1, 1, 16 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 96 ], [ 11, 1, 2, 24 ], [ 12, 1, 6, 96 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 32 ], [ 15, 1, 2, 32 ], [ 15, 1, 3, 16 ], [ 15, 1, 4, 48 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 8 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 48 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 24 ], [ 18, 1, 4, 16 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 96 ], [ 21, 1, 3, 32 ], [ 21, 1, 6, 144 ], [ 22, 1, 2, 24 ], [ 22, 1, 3, 80 ], [ 22, 1, 4, 72 ], [ 23, 1, 3, 32 ], [ 23, 1, 4, 16 ], [ 24, 1, 3, 48 ], [ 24, 1, 4, 64 ], [ 25, 1, 4, 64 ], [ 25, 1, 5, 32 ], [ 25, 1, 6, 32 ], [ 25, 1, 7, 32 ], [ 25, 1, 8, 96 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 32 ], [ 26, 1, 3, 48 ], [ 26, 1, 4, 16 ], [ 27, 1, 1, 32 ], [ 27, 1, 2, 32 ], [ 27, 1, 8, 128 ], [ 27, 1, 11, 32 ], [ 27, 1, 12, 192 ], [ 28, 1, 2, 32 ], [ 29, 1, 5, 64 ], [ 30, 1, 5, 96 ], [ 30, 1, 6, 128 ], [ 30, 1, 8, 64 ], [ 31, 1, 4, 48 ], [ 31, 1, 5, 96 ], [ 31, 1, 6, 32 ], [ 31, 1, 7, 48 ], [ 31, 1, 8, 64 ], [ 32, 1, 3, 160 ], [ 32, 1, 5, 32 ], [ 32, 1, 6, 48 ], [ 32, 1, 7, 144 ], [ 33, 1, 4, 128 ], [ 34, 1, 2, 16 ], [ 34, 1, 3, 32 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 32 ], [ 35, 1, 3, 32 ], [ 35, 1, 4, 96 ], [ 35, 1, 5, 32 ], [ 36, 1, 4, 64 ], [ 36, 1, 5, 64 ], [ 36, 1, 18, 128 ], [ 36, 1, 20, 192 ], [ 37, 1, 7, 128 ], [ 37, 1, 9, 64 ], [ 38, 1, 3, 192 ], [ 38, 1, 4, 64 ], [ 38, 1, 5, 96 ], [ 38, 1, 6, 128 ], [ 38, 1, 7, 96 ], [ 38, 1, 16, 64 ], [ 39, 1, 4, 64 ], [ 39, 1, 11, 64 ], [ 39, 1, 13, 64 ], [ 39, 1, 19, 64 ], [ 40, 1, 3, 64 ], [ 40, 1, 18, 192 ], [ 41, 1, 6, 128 ], [ 41, 1, 7, 64 ], [ 41, 1, 10, 128 ], [ 41, 1, 20, 128 ], [ 42, 1, 19, 128 ] ] k = 31: F-action on Pi is () [43,1,31] Dynkin type is 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 12: 1/384 phi1 ( q^5-9*q^4+22*q^3+6*q^2-55*q+3 ) q congruent 2 modulo 12: 1/384 ( q^6-10*q^5+28*q^4-8*q^3-32*q^2-64*q+128 ) q congruent 3 modulo 12: 1/384 ( q^6-10*q^5+31*q^4-16*q^3-61*q^2+106*q-147 ) q congruent 4 modulo 12: 1/384 q^2 ( q^4-10*q^3+28*q^2-8*q-32 ) q congruent 5 modulo 12: 1/384 ( q^6-10*q^5+31*q^4-16*q^3-61*q^2-6*q+189 ) q congruent 7 modulo 12: 1/384 ( q^6-10*q^5+31*q^4-16*q^3-61*q^2+106*q-147 ) q congruent 8 modulo 12: 1/384 ( q^6-10*q^5+28*q^4-8*q^3-32*q^2-64*q+128 ) q congruent 9 modulo 12: 1/384 phi1 ( q^5-9*q^4+22*q^3+6*q^2-55*q+3 ) q congruent 11 modulo 12: 1/384 phi2 ( q^5-11*q^4+42*q^3-58*q^2-3*q+45 ) Fusion of maximal tori of C^F in those of G^F: [ 35, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 24 ], [ 4, 1, 4, 16 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 1, 48 ], [ 10, 1, 2, 48 ], [ 10, 1, 3, 48 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 12, 1, 5, 64 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 15, 1, 2, 48 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 36 ], [ 17, 1, 4, 48 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 24 ], [ 20, 1, 3, 64 ], [ 21, 1, 3, 96 ], [ 21, 1, 6, 48 ], [ 22, 1, 2, 72 ], [ 22, 1, 3, 48 ], [ 22, 1, 4, 24 ], [ 23, 1, 2, 48 ], [ 24, 1, 4, 48 ], [ 25, 1, 1, 96 ], [ 25, 1, 2, 96 ], [ 25, 1, 3, 96 ], [ 25, 1, 4, 96 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 36 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 48 ], [ 27, 1, 1, 96 ], [ 27, 1, 2, 96 ], [ 27, 1, 6, 96 ], [ 27, 1, 8, 144 ], [ 27, 1, 12, 96 ], [ 30, 1, 6, 96 ], [ 30, 1, 7, 192 ], [ 31, 1, 3, 144 ], [ 31, 1, 6, 96 ], [ 31, 1, 8, 48 ], [ 32, 1, 3, 96 ], [ 32, 1, 5, 96 ], [ 32, 1, 6, 144 ], [ 32, 1, 7, 48 ], [ 34, 1, 1, 48 ], [ 34, 1, 3, 48 ], [ 34, 1, 5, 96 ], [ 35, 1, 3, 96 ], [ 35, 1, 5, 96 ], [ 36, 1, 1, 192 ], [ 36, 1, 2, 192 ], [ 36, 1, 18, 192 ], [ 37, 1, 9, 192 ], [ 38, 1, 4, 192 ], [ 38, 1, 6, 96 ], [ 38, 1, 8, 288 ], [ 38, 1, 15, 192 ], [ 39, 1, 10, 192 ], [ 39, 1, 18, 192 ], [ 40, 1, 3, 192 ], [ 41, 1, 7, 192 ], [ 41, 1, 19, 384 ], [ 42, 1, 22, 384 ] ] k = 32: F-action on Pi is () [43,1,32] Dynkin type is 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 12: 1/128 phi1^2 ( q^4-10*q^3+30*q^2-22*q-15 ) q congruent 2 modulo 12: 1/128 q ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 ) q congruent 3 modulo 12: 1/128 ( q^6-12*q^5+51*q^4-92*q^3+59*q^2-8*q+33 ) q congruent 4 modulo 12: 1/128 q ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 ) q congruent 5 modulo 12: 1/128 phi1^2 ( q^4-10*q^3+30*q^2-22*q-15 ) q congruent 7 modulo 12: 1/128 ( q^6-12*q^5+51*q^4-92*q^3+59*q^2-8*q+33 ) q congruent 8 modulo 12: 1/128 q ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 ) q congruent 9 modulo 12: 1/128 phi1^2 ( q^4-10*q^3+30*q^2-22*q-15 ) q congruent 11 modulo 12: 1/128 ( q^6-12*q^5+51*q^4-92*q^3+59*q^2-8*q+33 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 24 ], [ 4, 1, 1, 48 ], [ 4, 1, 2, 8 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 24 ], [ 7, 1, 2, 4 ], [ 8, 1, 1, 48 ], [ 9, 1, 1, 72 ], [ 10, 1, 1, 96 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 16 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 32 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 48 ], [ 17, 1, 3, 24 ], [ 17, 1, 4, 16 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 16 ], [ 18, 1, 4, 8 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 96 ], [ 21, 1, 1, 144 ], [ 21, 1, 2, 32 ], [ 22, 1, 1, 72 ], [ 22, 1, 2, 80 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 16 ], [ 23, 1, 2, 32 ], [ 24, 1, 1, 48 ], [ 24, 1, 2, 64 ], [ 25, 1, 1, 96 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 32 ], [ 25, 1, 4, 32 ], [ 25, 1, 5, 64 ], [ 26, 1, 1, 48 ], [ 26, 1, 2, 32 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 16 ], [ 27, 1, 1, 192 ], [ 27, 1, 2, 32 ], [ 27, 1, 8, 128 ], [ 27, 1, 12, 32 ], [ 27, 1, 14, 32 ], [ 28, 1, 3, 32 ], [ 29, 1, 2, 64 ], [ 30, 1, 1, 96 ], [ 30, 1, 2, 128 ], [ 30, 1, 4, 64 ], [ 31, 1, 1, 48 ], [ 31, 1, 2, 64 ], [ 31, 1, 3, 96 ], [ 31, 1, 4, 32 ], [ 31, 1, 6, 48 ], [ 32, 1, 1, 144 ], [ 32, 1, 2, 32 ], [ 32, 1, 3, 48 ], [ 32, 1, 6, 160 ], [ 33, 1, 3, 128 ], [ 34, 1, 1, 48 ], [ 34, 1, 2, 32 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 32 ], [ 35, 1, 2, 96 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 36, 1, 1, 192 ], [ 36, 1, 2, 64 ], [ 36, 1, 4, 128 ], [ 36, 1, 18, 64 ], [ 37, 1, 2, 128 ], [ 37, 1, 5, 64 ], [ 38, 1, 1, 96 ], [ 38, 1, 2, 128 ], [ 38, 1, 4, 96 ], [ 38, 1, 5, 64 ], [ 38, 1, 8, 192 ], [ 38, 1, 10, 64 ], [ 39, 1, 2, 64 ], [ 39, 1, 5, 64 ], [ 39, 1, 10, 64 ], [ 39, 1, 18, 64 ], [ 40, 1, 3, 64 ], [ 40, 1, 17, 192 ], [ 41, 1, 2, 128 ], [ 41, 1, 5, 64 ], [ 41, 1, 11, 128 ], [ 41, 1, 19, 128 ], [ 42, 1, 12, 128 ] ] k = 33: F-action on Pi is () [43,1,33] Dynkin type is 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 12: 1/32 phi1 phi2 ( q^4-4*q^3+2*q^2+6*q-9 ) q congruent 2 modulo 12: 1/32 q^3 ( q^3-4*q^2+8 ) q congruent 3 modulo 12: 1/32 phi1 phi2 ( q^4-4*q^3+2*q^2+6*q-9 ) q congruent 4 modulo 12: 1/32 q^3 ( q^3-4*q^2+8 ) q congruent 5 modulo 12: 1/32 phi1 phi2 ( q^4-4*q^3+2*q^2+6*q-9 ) q congruent 7 modulo 12: 1/32 phi1 phi2 ( q^4-4*q^3+2*q^2+6*q-9 ) q congruent 8 modulo 12: 1/32 q^3 ( q^3-4*q^2+8 ) q congruent 9 modulo 12: 1/32 phi1 phi2 ( q^4-4*q^3+2*q^2+6*q-9 ) q congruent 11 modulo 12: 1/32 phi1 phi2 ( q^4-4*q^3+2*q^2+6*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 10, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 1, 3, 8 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 2, 16 ], [ 14, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 3, 8 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 4, 16 ], [ 27, 1, 7, 8 ], [ 30, 1, 3, 16 ], [ 31, 1, 2, 8 ], [ 31, 1, 5, 8 ], [ 32, 1, 2, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 7, 8 ], [ 34, 1, 8, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 5, 16 ], [ 36, 1, 10, 16 ], [ 37, 1, 4, 16 ], [ 38, 1, 9, 16 ], [ 38, 1, 14, 16 ], [ 39, 1, 6, 16 ], [ 39, 1, 14, 16 ], [ 40, 1, 21, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 12, 32 ], [ 42, 1, 15, 32 ] ] k = 34: F-action on Pi is () [43,1,34] Dynkin type is 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 12: 1/32 phi1^2 phi2 ( q^3-3*q^2+3*q+1 ) q congruent 2 modulo 12: 1/32 q^4 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/32 phi1^2 phi2 ( q^3-3*q^2+3*q+1 ) q congruent 4 modulo 12: 1/32 q^4 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/32 phi1^2 phi2 ( q^3-3*q^2+3*q+1 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 ( q^3-3*q^2+3*q+1 ) q congruent 8 modulo 12: 1/32 q^4 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/32 phi1^2 phi2 ( q^3-3*q^2+3*q+1 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 ( q^3-3*q^2+3*q+1 ) Fusion of maximal tori of C^F in those of G^F: [ 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 1, 4, 8 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 5, 16 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 20, 1, 3, 16 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 8 ], [ 24, 1, 4, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 6, 16 ], [ 27, 1, 7, 8 ], [ 30, 1, 7, 16 ], [ 31, 1, 3, 8 ], [ 31, 1, 8, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 34, 1, 5, 8 ], [ 34, 1, 6, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 2, 16 ], [ 36, 1, 17, 16 ], [ 37, 1, 10, 16 ], [ 38, 1, 11, 16 ], [ 38, 1, 15, 16 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 16 ], [ 40, 1, 21, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 18, 32 ], [ 42, 1, 16, 32 ] ] k = 35: F-action on Pi is () [43,1,35] Dynkin type is 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 12: 1/32 phi1^2 phi2 ( q^3-q^2+q+1 ) q congruent 2 modulo 12: 1/32 q^5 ( q-2 ) q congruent 3 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2+q+1 ) q congruent 4 modulo 12: 1/32 q^5 ( q-2 ) q congruent 5 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2+q+1 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2+q+1 ) q congruent 8 modulo 12: 1/32 q^5 ( q-2 ) q congruent 9 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2+q+1 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2+q+1 ) Fusion of maximal tori of C^F in those of G^F: [ 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 8 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 14, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 19, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 4, 8 ], [ 24, 1, 3, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 1, 11, 16 ], [ 30, 1, 8, 16 ], [ 31, 1, 4, 8 ], [ 31, 1, 7, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 34, 1, 7, 8 ], [ 34, 1, 8, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 5, 16 ], [ 36, 1, 10, 16 ], [ 37, 1, 10, 16 ], [ 38, 1, 12, 16 ], [ 38, 1, 16, 16 ], [ 39, 1, 6, 16 ], [ 39, 1, 14, 16 ], [ 40, 1, 21, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 12, 32 ], [ 42, 1, 13, 32 ] ] k = 36: F-action on Pi is () [43,1,36] Dynkin type is 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 12: 1/32 phi1 phi2 ( q^4-6*q^3+10*q^2+4*q-21 ) q congruent 2 modulo 12: 1/32 q^2 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 3 modulo 12: 1/32 phi1 phi2 ( q^4-6*q^3+10*q^2+4*q-21 ) q congruent 4 modulo 12: 1/32 q^2 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 5 modulo 12: 1/32 phi1 phi2 ( q^4-6*q^3+10*q^2+4*q-21 ) q congruent 7 modulo 12: 1/32 phi1 phi2 ( q^4-6*q^3+10*q^2+4*q-21 ) q congruent 8 modulo 12: 1/32 q^2 ( q^4-6*q^3+8*q^2+8*q-16 ) q congruent 9 modulo 12: 1/32 phi1 phi2 ( q^4-6*q^3+10*q^2+4*q-21 ) q congruent 11 modulo 12: 1/32 phi1 phi2 ( q^4-6*q^3+10*q^2+4*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 41, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 19, 1, 1, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 8 ], [ 24, 1, 1, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 1, 14, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 1, 8 ], [ 31, 1, 6, 8 ], [ 32, 1, 2, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 5, 8 ], [ 34, 1, 6, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 2, 16 ], [ 36, 1, 17, 16 ], [ 37, 1, 4, 16 ], [ 38, 1, 10, 16 ], [ 38, 1, 13, 16 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 16 ], [ 40, 1, 21, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 18, 32 ], [ 42, 1, 14, 32 ] ] k = 37: F-action on Pi is () [43,1,37] Dynkin type is 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 12: 1/384 phi1 ( q^5-9*q^4+14*q^3+46*q^2-71*q-109 ) q congruent 2 modulo 12: 1/384 q ( q^5-10*q^4+20*q^3+40*q^2-64*q-64 ) q congruent 3 modulo 12: 1/384 phi1 phi2 ( q^4-10*q^3+24*q^2+22*q-93 ) q congruent 4 modulo 12: 1/384 q ( q^5-10*q^4+20*q^3+40*q^2-64*q-128 ) q congruent 5 modulo 12: 1/384 phi1 ( q^5-9*q^4+14*q^3+46*q^2-71*q-45 ) q congruent 7 modulo 12: 1/384 phi1 ( q^5-9*q^4+14*q^3+46*q^2-71*q-157 ) q congruent 8 modulo 12: 1/384 q ( q^5-10*q^4+20*q^3+40*q^2-64*q-64 ) q congruent 9 modulo 12: 1/384 phi1 ( q^5-9*q^4+14*q^3+46*q^2-71*q-45 ) q congruent 11 modulo 12: 1/384 phi1 phi2 ( q^4-10*q^3+24*q^2+22*q-93 ) Fusion of maximal tori of C^F in those of G^F: [ 33, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 24 ], [ 4, 1, 3, 16 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 10, 1, 2, 48 ], [ 10, 1, 3, 48 ], [ 10, 1, 4, 48 ], [ 11, 1, 1, 8 ], [ 12, 1, 2, 64 ], [ 14, 1, 2, 32 ], [ 15, 1, 3, 48 ], [ 15, 1, 4, 48 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 36 ], [ 17, 1, 2, 48 ], [ 17, 1, 3, 36 ], [ 18, 1, 2, 24 ], [ 18, 1, 3, 24 ], [ 20, 1, 4, 64 ], [ 21, 1, 1, 48 ], [ 21, 1, 2, 96 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 72 ], [ 23, 1, 3, 48 ], [ 24, 1, 2, 48 ], [ 25, 1, 5, 96 ], [ 25, 1, 6, 96 ], [ 25, 1, 7, 96 ], [ 25, 1, 8, 96 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 36 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 48 ], [ 27, 1, 1, 96 ], [ 27, 1, 2, 96 ], [ 27, 1, 4, 96 ], [ 27, 1, 8, 144 ], [ 27, 1, 12, 96 ], [ 30, 1, 2, 96 ], [ 30, 1, 3, 192 ], [ 31, 1, 2, 48 ], [ 31, 1, 4, 96 ], [ 31, 1, 5, 144 ], [ 32, 1, 1, 48 ], [ 32, 1, 2, 96 ], [ 32, 1, 3, 144 ], [ 32, 1, 6, 96 ], [ 34, 1, 2, 48 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 96 ], [ 35, 1, 3, 96 ], [ 35, 1, 5, 96 ], [ 36, 1, 4, 192 ], [ 36, 1, 5, 192 ], [ 36, 1, 20, 192 ], [ 37, 1, 5, 192 ], [ 38, 1, 2, 96 ], [ 38, 1, 3, 288 ], [ 38, 1, 5, 192 ], [ 38, 1, 9, 192 ], [ 39, 1, 4, 192 ], [ 39, 1, 13, 192 ], [ 40, 1, 3, 192 ], [ 41, 1, 5, 192 ], [ 41, 1, 10, 384 ], [ 42, 1, 18, 384 ] ] i = 44: Pi = [ ] j = 1: Omega trivial k = 1: F-action on Pi is () [44,1,1] Dynkin type is A_0(q) + T(phi1^7) Order of center |Z^F|: phi1^7 Numbers of classes in class type: q congruent 1 modulo 12: 1/2903040 ( q^7-70*q^6+2016*q^5-31115*q^4+280889*q^3-1505700*q^2+4523014\ *q-6172075 ) q congruent 2 modulo 12: 1/2903040 ( q^7-70*q^6+2016*q^5-30800*q^4+267344*q^3-1300320*q^2+3199104\ *q-2903040 ) q congruent 3 modulo 12: 1/2903040 ( q^7-70*q^6+2016*q^5-31115*q^4+280889*q^3-1505700*q^2+4459734\ *q-5332635 ) q congruent 4 modulo 12: 1/2903040 ( q^7-70*q^6+2016*q^5-30800*q^4+267344*q^3-1300320*q^2+3217024\ *q-3082240 ) q congruent 5 modulo 12: 1/2903040 ( q^7-70*q^6+2016*q^5-31115*q^4+280889*q^3-1505700*q^2+4505094\ *q-5831595 ) q congruent 7 modulo 12: 1/2903040 ( q^7-70*q^6+2016*q^5-31115*q^4+280889*q^3-1505700*q^2+4477654\ *q-5673115 ) q congruent 8 modulo 12: 1/2903040 ( q^7-70*q^6+2016*q^5-30800*q^4+267344*q^3-1300320*q^2+3199104\ *q-2903040 ) q congruent 9 modulo 12: 1/2903040 ( q^7-70*q^6+2016*q^5-31115*q^4+280889*q^3-1505700*q^2+4505094\ *q-5831595 ) q congruent 11 modulo 12: 1/2903040 ( q^7-70*q^6+2016*q^5-31115*q^4+280889*q^3-1505700*q^2+4459734\ *q-5332635 ) 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, 63 ], [ 3, 1, 1, 672 ], [ 4, 1, 1, 2520 ], [ 5, 1, 1, 72 ], [ 6, 1, 1, 56 ], [ 7, 1, 1, 756 ], [ 8, 1, 1, 4032 ], [ 9, 1, 1, 10080 ], [ 10, 1, 1, 15120 ], [ 11, 1, 1, 2016 ], [ 12, 1, 1, 13440 ], [ 13, 1, 1, 576 ], [ 14, 1, 1, 2016 ], [ 15, 1, 1, 5040 ], [ 16, 1, 1, 126 ], [ 17, 1, 1, 3780 ], [ 18, 1, 1, 1512 ], [ 19, 1, 1, 12096 ], [ 20, 1, 1, 40320 ], [ 21, 1, 1, 60480 ], [ 22, 1, 1, 30240 ], [ 23, 1, 1, 4032 ], [ 24, 1, 1, 20160 ], [ 25, 1, 1, 30240 ], [ 26, 1, 1, 7560 ], [ 27, 1, 1, 90720 ], [ 28, 1, 1, 4032 ], [ 29, 1, 1, 24192 ], [ 30, 1, 1, 120960 ], [ 31, 1, 1, 60480 ], [ 32, 1, 1, 181440 ], [ 33, 1, 1, 80640 ], [ 34, 1, 1, 15120 ], [ 35, 1, 1, 60480 ], [ 36, 1, 1, 181440 ], [ 37, 1, 1, 241920 ], [ 38, 1, 1, 362880 ], [ 39, 1, 1, 120960 ], [ 40, 1, 1, 362880 ], [ 41, 1, 1, 725760 ], [ 42, 1, 1, 483840 ], [ 43, 1, 1, 1451520 ] ] k = 2: F-action on Pi is () [44,1,2] Dynkin type is A_0(q) + T(phi1 phi2^6) Order of center |Z^F|: phi1 phi2^6 Numbers of classes in class type: q congruent 1 modulo 12: 1/46080 phi1 ( q^6-25*q^5+243*q^4-1232*q^3+3857*q^2-8007*q+8235 ) q congruent 2 modulo 12: 1/46080 q ( q^6-26*q^5+268*q^4-1400*q^3+3904*q^2-5504*q+3072 ) q congruent 3 modulo 12: 1/46080 ( q^7-26*q^6+268*q^5-1475*q^4+5089*q^3-11864*q^2+16962*q-10395 ) q congruent 4 modulo 12: 1/46080 q ( q^6-26*q^5+268*q^4-1400*q^3+3904*q^2-5504*q+3072 ) q congruent 5 modulo 12: 1/46080 phi1 ( q^6-25*q^5+243*q^4-1232*q^3+3857*q^2-8007*q+8235 ) q congruent 7 modulo 12: 1/46080 ( q^7-26*q^6+268*q^5-1475*q^4+5089*q^3-11864*q^2+16962*q-10395 ) q congruent 8 modulo 12: 1/46080 q ( q^6-26*q^5+268*q^4-1400*q^3+3904*q^2-5504*q+3072 ) q congruent 9 modulo 12: 1/46080 phi1 ( q^6-25*q^5+243*q^4-1232*q^3+3857*q^2-8007*q+8235 ) q congruent 11 modulo 12: 1/46080 ( q^7-26*q^6+268*q^5-1475*q^4+5089*q^3-11864*q^2+16962*q-10395 ) 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, 31 ], [ 3, 1, 2, 192 ], [ 4, 1, 2, 520 ], [ 5, 1, 2, 32 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 252 ], [ 8, 1, 2, 832 ], [ 9, 1, 2, 1600 ], [ 10, 1, 4, 2160 ], [ 11, 1, 2, 512 ], [ 12, 1, 6, 1920 ], [ 13, 1, 2, 192 ], [ 14, 1, 2, 512 ], [ 15, 1, 2, 80 ], [ 15, 1, 4, 960 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 60 ], [ 17, 1, 1, 60 ], [ 17, 1, 3, 840 ], [ 18, 1, 3, 480 ], [ 18, 1, 4, 24 ], [ 19, 1, 2, 2112 ], [ 20, 1, 2, 4480 ], [ 21, 1, 6, 5760 ], [ 22, 1, 3, 480 ], [ 22, 1, 4, 3840 ], [ 23, 1, 3, 64 ], [ 23, 1, 4, 960 ], [ 24, 1, 3, 2880 ], [ 24, 1, 4, 320 ], [ 25, 1, 4, 480 ], [ 25, 1, 8, 3840 ], [ 26, 1, 2, 120 ], [ 26, 1, 3, 1560 ], [ 27, 1, 8, 1440 ], [ 27, 1, 12, 7200 ], [ 28, 1, 2, 64 ], [ 28, 1, 6, 960 ], [ 29, 1, 4, 3840 ], [ 29, 1, 5, 384 ], [ 30, 1, 5, 9600 ], [ 30, 1, 6, 1920 ], [ 31, 1, 5, 960 ], [ 31, 1, 7, 6720 ], [ 31, 1, 8, 960 ], [ 32, 1, 3, 2880 ], [ 32, 1, 7, 11520 ], [ 33, 1, 4, 1280 ], [ 33, 1, 6, 7680 ], [ 34, 1, 3, 240 ], [ 34, 1, 4, 2880 ], [ 35, 1, 4, 960 ], [ 35, 1, 10, 6720 ], [ 36, 1, 18, 2880 ], [ 36, 1, 20, 11520 ], [ 37, 1, 6, 15360 ], [ 37, 1, 7, 3840 ], [ 38, 1, 3, 5760 ], [ 38, 1, 6, 5760 ], [ 38, 1, 7, 17280 ], [ 39, 1, 11, 1920 ], [ 39, 1, 15, 11520 ], [ 39, 1, 20, 1920 ], [ 40, 1, 2, 17280 ], [ 40, 1, 18, 5760 ], [ 41, 1, 6, 11520 ], [ 41, 1, 16, 23040 ], [ 41, 1, 22, 11520 ], [ 42, 1, 20, 7680 ], [ 42, 1, 21, 23040 ], [ 43, 1, 26, 23040 ], [ 43, 1, 27, 23040 ] ] k = 3: F-action on Pi is () [44,1,3] Dynkin type is A_0(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 12: 1/9216 phi1 ( q^6-13*q^5+43*q^4+48*q^3-343*q^2+141*q-261 ) q congruent 2 modulo 12: 1/9216 ( q^7-14*q^6+56*q^5-336*q^3+224*q^2+896*q-1024 ) q congruent 3 modulo 12: 1/9216 ( q^7-14*q^6+56*q^5+5*q^4-391*q^3+484*q^2-258*q+981 ) q congruent 4 modulo 12: 1/9216 q ( q^6-14*q^5+56*q^4-336*q^2+224*q+384 ) q congruent 5 modulo 12: 1/9216 ( q^7-14*q^6+56*q^5+5*q^4-391*q^3+484*q^2+110*q-1275 ) q congruent 7 modulo 12: 1/9216 ( q^7-14*q^6+56*q^5+5*q^4-391*q^3+484*q^2-258*q+981 ) q congruent 8 modulo 12: 1/9216 ( q^7-14*q^6+56*q^5-336*q^3+224*q^2+896*q-1024 ) q congruent 9 modulo 12: 1/9216 phi1 ( q^6-13*q^5+43*q^4+48*q^3-343*q^2+141*q-261 ) q congruent 11 modulo 12: 1/9216 phi2 ( q^6-15*q^5+71*q^4-66*q^3-325*q^2+809*q-555 ) 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, 15 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 72 ], [ 4, 1, 2, 48 ], [ 4, 1, 4, 192 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 1, 144 ], [ 10, 1, 2, 288 ], [ 10, 1, 3, 96 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 12, 1, 5, 256 ], [ 14, 1, 1, 96 ], [ 15, 1, 1, 144 ], [ 15, 1, 2, 96 ], [ 15, 1, 8, 384 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 24 ], [ 17, 1, 1, 84 ], [ 17, 1, 3, 144 ], [ 17, 1, 4, 96 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 48 ], [ 20, 1, 3, 768 ], [ 21, 1, 3, 384 ], [ 21, 1, 6, 192 ], [ 22, 1, 2, 288 ], [ 22, 1, 3, 96 ], [ 22, 1, 4, 288 ], [ 23, 1, 2, 192 ], [ 24, 1, 4, 192 ], [ 25, 1, 1, 288 ], [ 25, 1, 2, 576 ], [ 25, 1, 3, 192 ], [ 25, 1, 4, 384 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 144 ], [ 26, 1, 3, 144 ], [ 26, 1, 4, 96 ], [ 27, 1, 1, 288 ], [ 27, 1, 2, 576 ], [ 27, 1, 6, 1152 ], [ 27, 1, 8, 576 ], [ 27, 1, 12, 576 ], [ 27, 1, 13, 1152 ], [ 28, 1, 6, 192 ], [ 30, 1, 6, 384 ], [ 30, 1, 7, 768 ], [ 31, 1, 3, 576 ], [ 31, 1, 6, 192 ], [ 31, 1, 8, 576 ], [ 32, 1, 3, 576 ], [ 32, 1, 5, 1152 ], [ 32, 1, 6, 576 ], [ 32, 1, 7, 576 ], [ 33, 1, 9, 1536 ], [ 34, 1, 1, 48 ], [ 34, 1, 3, 288 ], [ 34, 1, 5, 192 ], [ 35, 1, 3, 192 ], [ 35, 1, 5, 576 ], [ 35, 1, 10, 576 ], [ 36, 1, 1, 576 ], [ 36, 1, 2, 1152 ], [ 36, 1, 15, 2304 ], [ 36, 1, 18, 1152 ], [ 37, 1, 9, 768 ], [ 38, 1, 4, 1152 ], [ 38, 1, 6, 1152 ], [ 38, 1, 8, 1152 ], [ 38, 1, 15, 2304 ], [ 39, 1, 10, 1152 ], [ 39, 1, 18, 384 ], [ 39, 1, 20, 1152 ], [ 40, 1, 2, 1152 ], [ 40, 1, 3, 1152 ], [ 40, 1, 13, 2304 ], [ 41, 1, 7, 2304 ], [ 41, 1, 19, 2304 ], [ 41, 1, 22, 2304 ], [ 41, 1, 40, 4608 ], [ 42, 1, 22, 1536 ], [ 43, 1, 16, 4608 ], [ 43, 1, 31, 4608 ] ] k = 4: F-action on Pi is () [44,1,4] Dynkin type is A_0(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 12: 1/3072 phi1 ( q^6-17*q^5+99*q^4-208*q^3-15*q^2+433*q-165 ) q congruent 2 modulo 12: 1/3072 q ( q^6-18*q^5+116*q^4-296*q^3+96*q^2+704*q-768 ) q congruent 3 modulo 12: 1/3072 phi2 ( q^6-19*q^5+135*q^4-442*q^3+635*q^2-187*q-267 ) q congruent 4 modulo 12: 1/3072 q ( q^6-18*q^5+116*q^4-296*q^3+96*q^2+704*q-768 ) q congruent 5 modulo 12: 1/3072 phi1 ( q^6-17*q^5+99*q^4-208*q^3-15*q^2+433*q-165 ) q congruent 7 modulo 12: 1/3072 phi2 ( q^6-19*q^5+135*q^4-442*q^3+635*q^2-187*q-267 ) q congruent 8 modulo 12: 1/3072 q ( q^6-18*q^5+116*q^4-296*q^3+96*q^2+704*q-768 ) q congruent 9 modulo 12: 1/3072 phi1 ( q^6-17*q^5+99*q^4-208*q^3-15*q^2+433*q-165 ) q congruent 11 modulo 12: 1/3072 phi2 ( q^6-19*q^5+135*q^4-442*q^3+635*q^2-187*q-267 ) 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, 15 ], [ 3, 1, 1, 64 ], [ 4, 1, 1, 144 ], [ 4, 1, 2, 24 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 72 ], [ 7, 1, 2, 4 ], [ 8, 1, 1, 192 ], [ 9, 1, 1, 320 ], [ 10, 1, 1, 384 ], [ 10, 1, 2, 32 ], [ 10, 1, 3, 96 ], [ 10, 1, 4, 48 ], [ 11, 1, 1, 128 ], [ 12, 1, 1, 384 ], [ 13, 1, 1, 64 ], [ 14, 1, 1, 128 ], [ 15, 1, 1, 224 ], [ 15, 1, 2, 48 ], [ 15, 1, 3, 64 ], [ 16, 1, 1, 26 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 172 ], [ 17, 1, 3, 56 ], [ 17, 1, 4, 32 ], [ 18, 1, 1, 112 ], [ 18, 1, 2, 32 ], [ 18, 1, 4, 8 ], [ 19, 1, 1, 320 ], [ 20, 1, 1, 640 ], [ 21, 1, 1, 768 ], [ 21, 1, 2, 128 ], [ 22, 1, 1, 512 ], [ 22, 1, 2, 256 ], [ 22, 1, 3, 96 ], [ 23, 1, 1, 192 ], [ 23, 1, 2, 64 ], [ 24, 1, 1, 448 ], [ 24, 1, 2, 192 ], [ 25, 1, 1, 512 ], [ 25, 1, 2, 64 ], [ 25, 1, 3, 192 ], [ 25, 1, 4, 96 ], [ 25, 1, 5, 256 ], [ 26, 1, 1, 240 ], [ 26, 1, 2, 104 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 32 ], [ 27, 1, 1, 960 ], [ 27, 1, 2, 192 ], [ 27, 1, 3, 384 ], [ 27, 1, 8, 480 ], [ 27, 1, 12, 96 ], [ 27, 1, 14, 384 ], [ 28, 1, 1, 192 ], [ 28, 1, 3, 64 ], [ 29, 1, 1, 384 ], [ 29, 1, 2, 256 ], [ 30, 1, 1, 896 ], [ 30, 1, 2, 640 ], [ 30, 1, 4, 256 ], [ 31, 1, 1, 576 ], [ 31, 1, 2, 448 ], [ 31, 1, 3, 448 ], [ 31, 1, 4, 64 ], [ 31, 1, 6, 192 ], [ 32, 1, 1, 1152 ], [ 32, 1, 2, 384 ], [ 32, 1, 3, 192 ], [ 32, 1, 6, 768 ], [ 33, 1, 1, 768 ], [ 33, 1, 3, 512 ], [ 34, 1, 1, 288 ], [ 34, 1, 2, 192 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 64 ], [ 35, 1, 1, 576 ], [ 35, 1, 2, 448 ], [ 35, 1, 3, 192 ], [ 35, 1, 5, 64 ], [ 36, 1, 1, 1152 ], [ 36, 1, 2, 384 ], [ 36, 1, 3, 768 ], [ 36, 1, 4, 768 ], [ 36, 1, 18, 192 ], [ 37, 1, 1, 768 ], [ 37, 1, 2, 1024 ], [ 37, 1, 5, 256 ], [ 38, 1, 1, 1152 ], [ 38, 1, 2, 1152 ], [ 38, 1, 4, 384 ], [ 38, 1, 5, 384 ], [ 38, 1, 8, 1152 ], [ 38, 1, 10, 768 ], [ 39, 1, 1, 384 ], [ 39, 1, 2, 768 ], [ 39, 1, 5, 128 ], [ 39, 1, 8, 768 ], [ 39, 1, 10, 128 ], [ 39, 1, 18, 384 ], [ 40, 1, 1, 1152 ], [ 40, 1, 3, 384 ], [ 40, 1, 12, 768 ], [ 40, 1, 17, 1152 ], [ 41, 1, 1, 768 ], [ 41, 1, 2, 1536 ], [ 41, 1, 5, 768 ], [ 41, 1, 11, 768 ], [ 41, 1, 15, 1536 ], [ 41, 1, 19, 768 ], [ 41, 1, 36, 1536 ], [ 42, 1, 12, 512 ], [ 42, 1, 17, 1536 ], [ 43, 1, 22, 1536 ], [ 43, 1, 28, 1536 ], [ 43, 1, 32, 1536 ] ] k = 5: F-action on Pi is () [44,1,5] Dynkin type is A_0(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 12: 1/768 phi1^2 phi2 ( q^4-5*q^3-4*q^2+35*q-3 ) q congruent 2 modulo 12: 1/768 q^2 ( q^5-6*q^4+40*q^2-16*q-64 ) q congruent 3 modulo 12: 1/768 phi2 ( q^6-7*q^5+7*q^4+38*q^3-77*q^2+41*q-51 ) q congruent 4 modulo 12: 1/768 q^2 ( q^5-6*q^4+40*q^2-16*q-64 ) q congruent 5 modulo 12: 1/768 phi1^2 phi2 ( q^4-5*q^3-4*q^2+35*q-3 ) q congruent 7 modulo 12: 1/768 phi2 ( q^6-7*q^5+7*q^4+38*q^3-77*q^2+41*q-51 ) q congruent 8 modulo 12: 1/768 q^2 ( q^5-6*q^4+40*q^2-16*q-64 ) q congruent 9 modulo 12: 1/768 phi1^2 phi2 ( q^4-5*q^3-4*q^2+35*q-3 ) q congruent 11 modulo 12: 1/768 phi2 ( q^6-7*q^5+7*q^4+38*q^3-77*q^2+41*q-51 ) 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, 7 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 24 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 48 ], [ 4, 1, 3, 16 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 24 ], [ 8, 1, 2, 48 ], [ 9, 1, 1, 24 ], [ 9, 1, 2, 72 ], [ 10, 1, 1, 48 ], [ 10, 1, 2, 48 ], [ 10, 1, 3, 48 ], [ 10, 1, 4, 96 ], [ 11, 1, 1, 8 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 64 ], [ 12, 1, 6, 96 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 32 ], [ 15, 1, 2, 48 ], [ 15, 1, 3, 48 ], [ 15, 1, 4, 48 ], [ 15, 1, 7, 32 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 8 ], [ 17, 1, 1, 36 ], [ 17, 1, 2, 48 ], [ 17, 1, 3, 48 ], [ 18, 1, 2, 24 ], [ 18, 1, 3, 24 ], [ 18, 1, 4, 24 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 96 ], [ 20, 1, 4, 64 ], [ 21, 1, 1, 48 ], [ 21, 1, 2, 96 ], [ 21, 1, 3, 96 ], [ 21, 1, 6, 144 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 72 ], [ 22, 1, 3, 120 ], [ 22, 1, 4, 72 ], [ 23, 1, 3, 48 ], [ 23, 1, 4, 16 ], [ 24, 1, 2, 48 ], [ 24, 1, 3, 48 ], [ 24, 1, 4, 96 ], [ 25, 1, 4, 96 ], [ 25, 1, 5, 96 ], [ 25, 1, 6, 96 ], [ 25, 1, 7, 96 ], [ 25, 1, 8, 96 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 48 ], [ 26, 1, 3, 48 ], [ 26, 1, 4, 48 ], [ 27, 1, 1, 96 ], [ 27, 1, 2, 96 ], [ 27, 1, 4, 96 ], [ 27, 1, 8, 192 ], [ 27, 1, 9, 96 ], [ 27, 1, 11, 96 ], [ 27, 1, 12, 192 ], [ 28, 1, 2, 48 ], [ 28, 1, 3, 16 ], [ 29, 1, 5, 96 ], [ 30, 1, 2, 96 ], [ 30, 1, 3, 192 ], [ 30, 1, 5, 96 ], [ 30, 1, 6, 192 ], [ 30, 1, 8, 192 ], [ 31, 1, 2, 48 ], [ 31, 1, 4, 144 ], [ 31, 1, 5, 144 ], [ 31, 1, 6, 96 ], [ 31, 1, 7, 48 ], [ 31, 1, 8, 96 ], [ 32, 1, 1, 48 ], [ 32, 1, 2, 96 ], [ 32, 1, 3, 240 ], [ 32, 1, 5, 96 ], [ 32, 1, 6, 144 ], [ 32, 1, 7, 144 ], [ 33, 1, 4, 192 ], [ 33, 1, 12, 128 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 96 ], [ 35, 1, 2, 48 ], [ 35, 1, 3, 96 ], [ 35, 1, 4, 144 ], [ 35, 1, 5, 96 ], [ 36, 1, 4, 192 ], [ 36, 1, 5, 192 ], [ 36, 1, 14, 192 ], [ 36, 1, 18, 192 ], [ 36, 1, 20, 192 ], [ 37, 1, 5, 192 ], [ 37, 1, 7, 192 ], [ 37, 1, 9, 192 ], [ 38, 1, 2, 96 ], [ 38, 1, 3, 288 ], [ 38, 1, 4, 192 ], [ 38, 1, 5, 288 ], [ 38, 1, 6, 192 ], [ 38, 1, 7, 96 ], [ 38, 1, 9, 192 ], [ 38, 1, 16, 192 ], [ 39, 1, 4, 192 ], [ 39, 1, 5, 96 ], [ 39, 1, 11, 96 ], [ 39, 1, 13, 192 ], [ 39, 1, 19, 192 ], [ 40, 1, 3, 192 ], [ 40, 1, 17, 96 ], [ 40, 1, 18, 288 ], [ 40, 1, 22, 192 ], [ 41, 1, 5, 192 ], [ 41, 1, 6, 192 ], [ 41, 1, 7, 192 ], [ 41, 1, 10, 384 ], [ 41, 1, 11, 192 ], [ 41, 1, 20, 384 ], [ 41, 1, 24, 384 ], [ 42, 1, 18, 384 ], [ 42, 1, 19, 384 ], [ 43, 1, 29, 384 ], [ 43, 1, 30, 384 ], [ 43, 1, 37, 384 ] ] k = 6: F-action on Pi is () [44,1,6] Dynkin type is A_0(q) + T(phi1^5 phi3) Order of center |Z^F|: phi1^5 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/4320 phi1 ( q^6-18*q^5+117*q^4-323*q^3+246*q^2+465*q-560 ) q congruent 2 modulo 12: 1/4320 q phi2 ( q^5-20*q^4+155*q^3-580*q^2+1044*q-720 ) q congruent 3 modulo 12: 1/4320 q phi2 ( q^5-20*q^4+155*q^3-595*q^2+1164*q-945 ) q congruent 4 modulo 12: 1/4320 phi1 ( q^6-18*q^5+117*q^4-308*q^3+156*q^2+480*q-320 ) q congruent 5 modulo 12: 1/4320 q phi2 ( q^5-20*q^4+155*q^3-595*q^2+1164*q-945 ) q congruent 7 modulo 12: 1/4320 phi1 ( q^6-18*q^5+117*q^4-323*q^3+246*q^2+465*q-560 ) q congruent 8 modulo 12: 1/4320 q phi2 ( q^5-20*q^4+155*q^3-580*q^2+1044*q-720 ) q congruent 9 modulo 12: 1/4320 q phi2 ( q^5-20*q^4+155*q^3-595*q^2+1164*q-945 ) q congruent 11 modulo 12: 1/4320 q phi2 ( q^5-20*q^4+155*q^3-595*q^2+1164*q-945 ) Fusion of maximal tori of C^F in those of G^F: [ 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 42 ], [ 4, 1, 1, 60 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 20 ], [ 7, 1, 1, 90 ], [ 8, 1, 1, 132 ], [ 9, 1, 1, 150 ], [ 10, 1, 1, 180 ], [ 11, 1, 1, 120 ], [ 12, 1, 1, 120 ], [ 13, 1, 1, 60 ], [ 14, 1, 1, 120 ], [ 15, 1, 1, 120 ], [ 16, 1, 1, 30 ], [ 17, 1, 1, 180 ], [ 18, 1, 1, 180 ], [ 19, 1, 1, 360 ], [ 20, 1, 1, 240 ], [ 21, 1, 1, 180 ], [ 22, 1, 1, 360 ], [ 23, 1, 1, 240 ], [ 24, 1, 1, 300 ], [ 25, 1, 1, 360 ], [ 26, 1, 1, 360 ], [ 28, 1, 1, 240 ], [ 28, 1, 5, 6 ], [ 29, 1, 1, 720 ], [ 29, 1, 3, 36 ], [ 30, 1, 1, 360 ], [ 31, 1, 1, 720 ], [ 33, 1, 1, 480 ], [ 33, 1, 2, 120 ], [ 34, 1, 1, 720 ], [ 35, 1, 1, 720 ], [ 35, 1, 8, 90 ], [ 37, 1, 1, 720 ], [ 37, 1, 3, 360 ], [ 39, 1, 1, 1440 ], [ 39, 1, 3, 180 ], [ 40, 1, 7, 540 ], [ 41, 1, 3, 1080 ], [ 42, 1, 1, 1440 ], [ 42, 1, 4, 720 ], [ 43, 1, 4, 2160 ] ] k = 7: F-action on Pi is () [44,1,7] Dynkin type is A_0(q) + T(phi1 phi3^3) Order of center |Z^F|: phi1 phi3^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/1296 phi1 ( q^6+3*q^5-6*q^4-35*q^3-45*q^2+54*q+136 ) q congruent 2 modulo 12: 1/1296 q phi2 ( q^5+q^4-10*q^3-10*q^2+18*q+36 ) q congruent 3 modulo 12: 1/1296 q phi2 ( q^5+q^4-10*q^3-19*q^2+9*q+90 ) q congruent 4 modulo 12: 1/1296 phi1 ( q^6+3*q^5-6*q^4-26*q^3-18*q^2+36*q+64 ) q congruent 5 modulo 12: 1/1296 q phi2 ( q^5+q^4-10*q^3-19*q^2+9*q+90 ) q congruent 7 modulo 12: 1/1296 phi1 ( q^6+3*q^5-6*q^4-35*q^3-45*q^2+54*q+136 ) q congruent 8 modulo 12: 1/1296 q phi2 ( q^5+q^4-10*q^3-10*q^2+18*q+36 ) q congruent 9 modulo 12: 1/1296 q phi2 ( q^5+q^4-10*q^3-19*q^2+9*q+90 ) q congruent 11 modulo 12: 1/1296 q phi2 ( q^5+q^4-10*q^3-19*q^2+9*q+90 ) Fusion of maximal tori of C^F in those of G^F: [ 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 24 ], [ 6, 1, 1, 2 ], [ 12, 1, 1, 48 ], [ 21, 1, 5, 216 ], [ 28, 1, 5, 72 ], [ 33, 1, 2, 144 ], [ 34, 1, 9, 54 ], [ 40, 1, 9, 648 ], [ 42, 1, 5, 432 ] ] k = 8: F-action on Pi is () [44,1,8] Dynkin type is A_0(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 12: 1/216 phi1 ( q^6-3*q^5-3*q^4-8*q^3+42*q^2+39*q+4 ) q congruent 2 modulo 12: 1/216 q phi2 ( q^5-5*q^4+5*q^3-7*q^2+36*q-36 ) q congruent 3 modulo 12: 1/216 q phi2 ( q^5-5*q^4+5*q^3-10*q^2+60*q-63 ) q congruent 4 modulo 12: 1/216 phi1 ( q^6-3*q^5-3*q^4-5*q^3+24*q^2+24*q+16 ) q congruent 5 modulo 12: 1/216 q phi2 ( q^5-5*q^4+5*q^3-10*q^2+60*q-63 ) q congruent 7 modulo 12: 1/216 phi1 ( q^6-3*q^5-3*q^4-8*q^3+42*q^2+39*q+4 ) q congruent 8 modulo 12: 1/216 q phi2 ( q^5-5*q^4+5*q^3-7*q^2+36*q-36 ) q congruent 9 modulo 12: 1/216 q phi2 ( q^5-5*q^4+5*q^3-10*q^2+60*q-63 ) q congruent 11 modulo 12: 1/216 q phi2 ( q^5-5*q^4+5*q^3-10*q^2+60*q-63 ) 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, 3 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 12 ], [ 11, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 12, 1, 3, 36 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 6 ], [ 20, 1, 1, 12 ], [ 21, 1, 5, 18 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 24 ], [ 28, 1, 1, 12 ], [ 28, 1, 5, 12 ], [ 29, 1, 3, 36 ], [ 32, 1, 9, 54 ], [ 33, 1, 1, 24 ], [ 33, 1, 2, 24 ], [ 34, 1, 9, 18 ], [ 35, 1, 8, 36 ], [ 36, 1, 9, 54 ], [ 37, 1, 3, 36 ], [ 38, 1, 20, 108 ], [ 39, 1, 3, 72 ], [ 40, 1, 4, 108 ], [ 42, 1, 4, 72 ], [ 42, 1, 5, 36 ], [ 43, 1, 5, 108 ] ] k = 9: F-action on Pi is () [44,1,9] Dynkin type is A_0(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 12: 1/768 phi1 phi2 ( q^5-6*q^4+9*q^3+15*q^2-66*q+63 ) q congruent 2 modulo 12: 1/768 q^2 ( q^5-6*q^4+8*q^3+16*q^2-48*q+32 ) q congruent 3 modulo 12: 1/768 phi1 phi2 ( q^5-6*q^4+9*q^3+15*q^2-66*q+63 ) q congruent 4 modulo 12: 1/768 q^2 ( q^5-6*q^4+8*q^3+16*q^2-48*q+32 ) q congruent 5 modulo 12: 1/768 phi1 phi2 ( q^5-6*q^4+9*q^3+15*q^2-66*q+63 ) q congruent 7 modulo 12: 1/768 phi1 phi2 ( q^5-6*q^4+9*q^3+15*q^2-66*q+63 ) q congruent 8 modulo 12: 1/768 q^2 ( q^5-6*q^4+8*q^3+16*q^2-48*q+32 ) q congruent 9 modulo 12: 1/768 phi1 phi2 ( q^5-6*q^4+9*q^3+15*q^2-66*q+63 ) q congruent 11 modulo 12: 1/768 phi1 phi2 ( q^5-6*q^4+9*q^3+15*q^2-66*q+63 ) 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, 3 ], [ 4, 1, 2, 24 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 10, 1, 3, 48 ], [ 15, 1, 2, 48 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 24 ], [ 18, 1, 1, 24 ], [ 25, 1, 3, 96 ], [ 26, 1, 1, 24 ], [ 26, 1, 5, 24 ], [ 27, 1, 3, 96 ], [ 27, 1, 7, 48 ], [ 27, 1, 14, 96 ], [ 32, 1, 8, 96 ], [ 34, 1, 1, 48 ], [ 34, 1, 6, 48 ], [ 35, 1, 7, 96 ], [ 36, 1, 3, 192 ], [ 36, 1, 17, 96 ], [ 38, 1, 13, 192 ], [ 39, 1, 17, 192 ], [ 40, 1, 6, 96 ], [ 40, 1, 23, 192 ], [ 41, 1, 21, 192 ], [ 41, 1, 34, 384 ], [ 43, 1, 17, 384 ] ] k = 10: F-action on Pi is () [44,1,10] Dynkin type is A_0(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 12: 1/384 phi1 phi2 ( q^5-8*q^4+15*q^3+13*q^2-56*q+51 ) q congruent 2 modulo 12: 1/384 q^3 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 3 modulo 12: 1/384 phi1 phi2 ( q^5-8*q^4+15*q^3+13*q^2-56*q+51 ) q congruent 4 modulo 12: 1/384 q^3 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 5 modulo 12: 1/384 phi1 phi2 ( q^5-8*q^4+15*q^3+13*q^2-56*q+51 ) q congruent 7 modulo 12: 1/384 phi1 phi2 ( q^5-8*q^4+15*q^3+13*q^2-56*q+51 ) q congruent 8 modulo 12: 1/384 q^3 ( q^4-8*q^3+14*q^2+20*q-48 ) q congruent 9 modulo 12: 1/384 phi1 phi2 ( q^5-8*q^4+15*q^3+13*q^2-56*q+51 ) q congruent 11 modulo 12: 1/384 phi1 phi2 ( q^5-8*q^4+15*q^3+13*q^2-56*q+51 ) Fusion of maximal tori of C^F in those of G^F: [ 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 12 ], [ 4, 1, 3, 48 ], [ 5, 1, 2, 12 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 36 ], [ 10, 1, 4, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 2, 32 ], [ 14, 1, 2, 24 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 24 ], [ 15, 1, 5, 96 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 12 ], [ 18, 1, 2, 12 ], [ 18, 1, 3, 4 ], [ 20, 1, 4, 96 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 1, 3, 48 ], [ 24, 1, 2, 16 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 72 ], [ 25, 1, 8, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 4, 12 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 27, 1, 4, 96 ], [ 27, 1, 7, 24 ], [ 28, 1, 1, 48 ], [ 30, 1, 3, 32 ], [ 31, 1, 2, 48 ], [ 31, 1, 5, 48 ], [ 32, 1, 2, 48 ], [ 32, 1, 8, 48 ], [ 33, 1, 10, 192 ], [ 34, 1, 2, 48 ], [ 34, 1, 7, 24 ], [ 34, 1, 8, 8 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 24 ], [ 36, 1, 5, 48 ], [ 36, 1, 6, 192 ], [ 36, 1, 10, 48 ], [ 37, 1, 4, 32 ], [ 38, 1, 9, 96 ], [ 38, 1, 14, 96 ], [ 39, 1, 6, 16 ], [ 39, 1, 8, 96 ], [ 39, 1, 13, 96 ], [ 39, 1, 14, 48 ], [ 40, 1, 12, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 23, 96 ], [ 41, 1, 4, 96 ], [ 41, 1, 12, 96 ], [ 41, 1, 30, 192 ], [ 41, 1, 31, 192 ], [ 42, 1, 15, 64 ], [ 43, 1, 23, 192 ], [ 43, 1, 33, 192 ] ] k = 11: F-action on Pi is () [44,1,11] Dynkin type is A_0(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 12: 1/384 phi1^2 phi2^2 phi6 ( q-3 ) q congruent 2 modulo 12: 1/384 q^4 ( q^3-4*q^2+2*q+4 ) q congruent 3 modulo 12: 1/384 phi1^2 phi2^2 phi6 ( q-3 ) q congruent 4 modulo 12: 1/384 q^4 ( q^3-4*q^2+2*q+4 ) q congruent 5 modulo 12: 1/384 phi1^2 phi2^2 phi6 ( q-3 ) q congruent 7 modulo 12: 1/384 phi1^2 phi2^2 phi6 ( q-3 ) q congruent 8 modulo 12: 1/384 q^4 ( q^3-4*q^2+2*q+4 ) q congruent 9 modulo 12: 1/384 phi1^2 phi2^2 phi6 ( q-3 ) q congruent 11 modulo 12: 1/384 phi1^2 phi2^2 phi6 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 12 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 30 ], [ 8, 1, 2, 16 ], [ 9, 1, 2, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 36 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 24 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 14 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 36 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 60 ], [ 19, 1, 2, 48 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 1, 4, 48 ], [ 24, 1, 3, 16 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 72 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 24 ], [ 26, 1, 3, 72 ], [ 26, 1, 4, 12 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 24 ], [ 27, 1, 7, 24 ], [ 27, 1, 11, 96 ], [ 27, 1, 13, 96 ], [ 28, 1, 6, 48 ], [ 29, 1, 4, 96 ], [ 30, 1, 8, 32 ], [ 31, 1, 4, 48 ], [ 31, 1, 7, 48 ], [ 32, 1, 4, 48 ], [ 32, 1, 5, 48 ], [ 34, 1, 4, 144 ], [ 34, 1, 7, 24 ], [ 34, 1, 8, 8 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 8 ], [ 35, 1, 10, 48 ], [ 36, 1, 5, 48 ], [ 36, 1, 10, 48 ], [ 36, 1, 19, 192 ], [ 37, 1, 10, 32 ], [ 38, 1, 12, 96 ], [ 38, 1, 16, 96 ], [ 39, 1, 4, 96 ], [ 39, 1, 6, 48 ], [ 39, 1, 14, 16 ], [ 39, 1, 15, 96 ], [ 40, 1, 13, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 24, 96 ], [ 41, 1, 9, 96 ], [ 41, 1, 12, 96 ], [ 41, 1, 23, 192 ], [ 41, 1, 26, 192 ], [ 42, 1, 13, 64 ], [ 43, 1, 24, 192 ], [ 43, 1, 35, 192 ] ] k = 12: F-action on Pi is () [44,1,12] Dynkin type is A_0(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 12: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 2 modulo 12: 1/256 q^4 ( q^3-2*q^2-4*q+8 ) q congruent 3 modulo 12: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 4 modulo 12: 1/256 q^4 ( q^3-2*q^2-4*q+8 ) q congruent 5 modulo 12: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 7 modulo 12: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 8 modulo 12: 1/256 q^4 ( q^3-2*q^2-4*q+8 ) q congruent 9 modulo 12: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3+11*q^2-22*q-1 ) q congruent 11 modulo 12: 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: [ 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 4, 1, 3, 16 ], [ 4, 1, 4, 16 ], [ 5, 1, 1, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 7, 32 ], [ 15, 1, 8, 32 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 18, 1, 4, 8 ], [ 25, 1, 2, 32 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 24 ], [ 27, 1, 4, 32 ], [ 27, 1, 5, 64 ], [ 27, 1, 6, 32 ], [ 27, 1, 7, 48 ], [ 27, 1, 9, 32 ], [ 27, 1, 11, 32 ], [ 27, 1, 13, 32 ], [ 32, 1, 4, 64 ], [ 32, 1, 8, 32 ], [ 34, 1, 3, 16 ], [ 34, 1, 6, 16 ], [ 34, 1, 8, 32 ], [ 35, 1, 6, 32 ], [ 36, 1, 10, 64 ], [ 36, 1, 11, 128 ], [ 36, 1, 14, 64 ], [ 36, 1, 15, 64 ], [ 36, 1, 17, 32 ], [ 38, 1, 11, 64 ], [ 38, 1, 12, 64 ], [ 38, 1, 14, 64 ], [ 39, 1, 9, 64 ], [ 40, 1, 6, 96 ], [ 40, 1, 16, 64 ], [ 40, 1, 24, 64 ], [ 41, 1, 14, 128 ], [ 41, 1, 21, 64 ], [ 41, 1, 27, 128 ], [ 41, 1, 39, 128 ], [ 43, 1, 19, 128 ], [ 43, 1, 21, 128 ] ] k = 13: F-action on Pi is () [44,1,13] Dynkin type is A_0(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 12: 1/64 phi1^2 phi2 ( q^4-3*q^3+5*q-7 ) q congruent 2 modulo 12: 1/64 q^3 ( q^4-4*q^3+2*q^2+8*q-8 ) q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q^4-3*q^3+5*q-7 ) q congruent 4 modulo 12: 1/64 q^3 ( q^4-4*q^3+2*q^2+8*q-8 ) q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q^4-3*q^3+5*q-7 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q^4-3*q^3+5*q-7 ) q congruent 8 modulo 12: 1/64 q^3 ( q^4-4*q^3+2*q^2+8*q-8 ) q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q^4-3*q^3+5*q-7 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q^4-3*q^3+5*q-7 ) 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, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 1, 4, 8 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 5, 16 ], [ 13, 1, 1, 8 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 1, 6, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 4 ], [ 19, 1, 1, 8 ], [ 20, 1, 3, 16 ], [ 21, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 1, 8 ], [ 23, 1, 2, 8 ], [ 24, 1, 1, 8 ], [ 24, 1, 4, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 6, 16 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 1, 10, 16 ], [ 27, 1, 14, 16 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 29, 1, 2, 16 ], [ 30, 1, 4, 16 ], [ 30, 1, 7, 16 ], [ 31, 1, 1, 8 ], [ 31, 1, 3, 8 ], [ 31, 1, 6, 8 ], [ 31, 1, 8, 8 ], [ 32, 1, 2, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 32, 1, 8, 8 ], [ 33, 1, 7, 32 ], [ 34, 1, 2, 16 ], [ 34, 1, 5, 8 ], [ 34, 1, 6, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 2, 16 ], [ 36, 1, 13, 32 ], [ 36, 1, 16, 32 ], [ 36, 1, 17, 16 ], [ 37, 1, 4, 16 ], [ 37, 1, 10, 16 ], [ 38, 1, 10, 16 ], [ 38, 1, 11, 16 ], [ 38, 1, 13, 16 ], [ 38, 1, 15, 16 ], [ 39, 1, 2, 16 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 16 ], [ 39, 1, 19, 16 ], [ 40, 1, 16, 16 ], [ 40, 1, 21, 16 ], [ 40, 1, 22, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 18, 32 ], [ 41, 1, 35, 32 ], [ 41, 1, 37, 32 ], [ 42, 1, 14, 32 ], [ 42, 1, 16, 32 ], [ 43, 1, 25, 32 ], [ 43, 1, 34, 32 ], [ 43, 1, 36, 32 ] ] k = 14: F-action on Pi is () [44,1,14] Dynkin type is A_0(q) + T(phi1^3 phi5) Order of center |Z^F|: phi1^3 phi5 Numbers of classes in class type: q congruent 1 modulo 12: 1/60 q phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/60 q phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/60 q phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/60 q phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 5 modulo 12: 1/60 q phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/60 q phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/60 q phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/60 q phi1 phi2 phi4 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/60 q phi1 phi2 phi4 ( q^2-5*q+6 ) 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, 3 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 6 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 6 ], [ 13, 1, 1, 6 ], [ 14, 1, 1, 6 ], [ 16, 1, 1, 6 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 6 ], [ 23, 1, 1, 12 ], [ 28, 1, 1, 12 ], [ 29, 1, 1, 12 ], [ 42, 1, 2, 10 ], [ 43, 1, 2, 30 ] ] k = 15: F-action on Pi is () [44,1,15] Dynkin type is A_0(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 12: 1/288 q phi1^2 phi2 phi6 ( q-3 ) q congruent 2 modulo 12: 1/288 q^2 phi1^2 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/288 q phi1^2 phi2 phi6 ( q-3 ) q congruent 4 modulo 12: 1/288 q^2 phi1^2 phi2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/288 q phi1^2 phi2 phi6 ( q-3 ) q congruent 7 modulo 12: 1/288 q phi1^2 phi2 phi6 ( q-3 ) q congruent 8 modulo 12: 1/288 q^2 phi1^2 phi2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/288 q phi1^2 phi2 phi6 ( q-3 ) q congruent 11 modulo 12: 1/288 q phi1^2 phi2 phi6 ( q-3 ) 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, 7 ], [ 3, 1, 2, 18 ], [ 4, 1, 2, 28 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 18 ], [ 8, 1, 2, 40 ], [ 9, 1, 2, 46 ], [ 10, 1, 4, 36 ], [ 11, 1, 2, 32 ], [ 12, 1, 6, 48 ], [ 13, 1, 2, 24 ], [ 14, 1, 2, 32 ], [ 15, 1, 2, 8 ], [ 15, 1, 4, 48 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 18, 1, 3, 24 ], [ 18, 1, 4, 12 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 64 ], [ 21, 1, 6, 36 ], [ 22, 1, 3, 24 ], [ 22, 1, 4, 48 ], [ 23, 1, 3, 16 ], [ 23, 1, 4, 48 ], [ 24, 1, 3, 72 ], [ 24, 1, 4, 20 ], [ 25, 1, 4, 24 ], [ 25, 1, 8, 48 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 2, 16 ], [ 28, 1, 4, 6 ], [ 28, 1, 6, 48 ], [ 29, 1, 4, 48 ], [ 29, 1, 5, 48 ], [ 29, 1, 6, 24 ], [ 30, 1, 5, 48 ], [ 30, 1, 6, 24 ], [ 31, 1, 5, 48 ], [ 31, 1, 7, 48 ], [ 31, 1, 8, 48 ], [ 33, 1, 4, 32 ], [ 33, 1, 5, 48 ], [ 33, 1, 6, 96 ], [ 34, 1, 3, 48 ], [ 35, 1, 4, 48 ], [ 35, 1, 9, 42 ], [ 35, 1, 10, 48 ], [ 37, 1, 6, 48 ], [ 37, 1, 7, 48 ], [ 37, 1, 8, 96 ], [ 39, 1, 11, 96 ], [ 39, 1, 12, 72 ], [ 39, 1, 16, 12 ], [ 39, 1, 20, 96 ], [ 40, 1, 8, 108 ], [ 41, 1, 8, 144 ], [ 41, 1, 17, 72 ], [ 42, 1, 6, 144 ], [ 42, 1, 8, 48 ], [ 42, 1, 20, 96 ], [ 43, 1, 9, 144 ], [ 43, 1, 12, 144 ] ] k = 16: F-action on Pi is () [44,1,16] Dynkin type is A_0(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 12: 1/288 q phi1 ( q^5-4*q^4-5*q^3+33*q^2-4*q-69 ) q congruent 2 modulo 12: 1/288 phi2 ( q^6-6*q^5+5*q^4+28*q^3-52*q^2+32 ) q congruent 3 modulo 12: 1/288 q phi1 ( q^5-4*q^4-5*q^3+33*q^2-4*q-69 ) q congruent 4 modulo 12: 1/288 q phi1 ( q^5-4*q^4-5*q^3+28*q^2+4*q-48 ) q congruent 5 modulo 12: 1/288 phi2 ( q^6-6*q^5+5*q^4+33*q^3-70*q^2+5*q+48 ) q congruent 7 modulo 12: 1/288 q phi1 ( q^5-4*q^4-5*q^3+33*q^2-4*q-69 ) q congruent 8 modulo 12: 1/288 phi2 ( q^6-6*q^5+5*q^4+28*q^3-52*q^2+32 ) q congruent 9 modulo 12: 1/288 q phi1 ( q^5-4*q^4-5*q^3+33*q^2-4*q-69 ) q congruent 11 modulo 12: 1/288 phi2 ( q^6-6*q^5+5*q^4+33*q^3-70*q^2+5*q+48 ) 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, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 3, 24 ], [ 10, 1, 4, 12 ], [ 12, 1, 5, 16 ], [ 15, 1, 2, 24 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 24 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 12 ], [ 21, 1, 3, 24 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 24 ], [ 24, 1, 4, 12 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 24 ], [ 28, 1, 4, 6 ], [ 30, 1, 6, 24 ], [ 30, 1, 7, 48 ], [ 31, 1, 6, 48 ], [ 33, 1, 8, 48 ], [ 34, 1, 1, 48 ], [ 34, 1, 5, 48 ], [ 35, 1, 3, 48 ], [ 35, 1, 9, 18 ], [ 37, 1, 9, 48 ], [ 39, 1, 16, 36 ], [ 39, 1, 18, 96 ], [ 40, 1, 8, 36 ], [ 40, 1, 15, 72 ], [ 41, 1, 17, 72 ], [ 41, 1, 33, 144 ], [ 42, 1, 22, 96 ], [ 43, 1, 10, 144 ] ] k = 17: F-action on Pi is () [44,1,17] Dynkin type is A_0(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 12: 1/144 q phi1 ( q^5-q^4-2*q^3-3*q^2-q+18 ) q congruent 2 modulo 12: 1/144 phi2 ( q^6-3*q^5+2*q^4-2*q^3+2*q^2+12*q-16 ) q congruent 3 modulo 12: 1/144 q phi1 ( q^5-q^4-2*q^3-3*q^2-q+18 ) q congruent 4 modulo 12: 1/144 q phi1 ( q^5-q^4-2*q^3-2*q^2-2*q+12 ) q congruent 5 modulo 12: 1/144 phi2 ( q^6-3*q^5+2*q^4-3*q^3+5*q^2+14*q-24 ) q congruent 7 modulo 12: 1/144 q phi1 ( q^5-q^4-2*q^3-3*q^2-q+18 ) q congruent 8 modulo 12: 1/144 phi2 ( q^6-3*q^5+2*q^4-2*q^3+2*q^2+12*q-16 ) q congruent 9 modulo 12: 1/144 q phi1 ( q^5-q^4-2*q^3-3*q^2-q+18 ) q congruent 11 modulo 12: 1/144 phi2 ( q^6-3*q^5+2*q^4-3*q^3+5*q^2+14*q-24 ) Fusion of maximal tori of C^F in those of G^F: [ 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 1, 2 ], [ 12, 1, 5, 16 ], [ 21, 1, 4, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 8, 48 ], [ 34, 1, 9, 6 ], [ 40, 1, 10, 72 ], [ 42, 1, 10, 48 ] ] k = 18: F-action on Pi is () [44,1,18] Dynkin type is A_0(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 12: 1/96 q phi1 phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 2 modulo 12: 1/96 q^2 phi1 phi2^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/96 q phi1 phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 4 modulo 12: 1/96 q^2 phi1 phi2^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/96 q phi1 phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 7 modulo 12: 1/96 q phi1 phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 8 modulo 12: 1/96 q^2 phi1 phi2^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/96 q phi1 phi2^2 ( q^3-4*q^2+4*q+1 ) q congruent 11 modulo 12: 1/96 q phi1 phi2^2 ( q^3-4*q^2+4*q+1 ) 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, 3 ], [ 3, 1, 1, 10 ], [ 4, 1, 1, 12 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 4 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 8 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 3, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 8 ], [ 22, 1, 2, 16 ], [ 23, 1, 2, 16 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 24 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 5, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 3, 16 ], [ 28, 1, 5, 6 ], [ 29, 1, 2, 16 ], [ 29, 1, 3, 12 ], [ 30, 1, 1, 8 ], [ 30, 1, 2, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 16 ], [ 33, 1, 2, 24 ], [ 33, 1, 3, 32 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 16 ], [ 35, 1, 2, 16 ], [ 35, 1, 5, 16 ], [ 35, 1, 8, 18 ], [ 37, 1, 2, 16 ], [ 37, 1, 3, 24 ], [ 37, 1, 5, 16 ], [ 39, 1, 3, 12 ], [ 39, 1, 5, 32 ], [ 39, 1, 7, 24 ], [ 39, 1, 10, 32 ], [ 40, 1, 7, 36 ], [ 40, 1, 14, 24 ], [ 41, 1, 3, 24 ], [ 41, 1, 13, 48 ], [ 41, 1, 38, 48 ], [ 42, 1, 7, 48 ], [ 42, 1, 12, 32 ], [ 43, 1, 6, 48 ], [ 43, 1, 11, 48 ] ] k = 19: F-action on Pi is () [44,1,19] Dynkin type is A_0(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 12: 1/72 q phi1 phi2 ( q^4-2*q^3-q^2-7*q+21 ) q congruent 2 modulo 12: 1/72 q phi1 phi2 ( q^4-2*q^3-q^2-4*q+12 ) q congruent 3 modulo 12: 1/72 q phi1 phi2 ( q^4-2*q^3-q^2-7*q+21 ) q congruent 4 modulo 12: 1/72 q phi1 phi2 ( q^4-2*q^3-q^2-4*q+12 ) q congruent 5 modulo 12: 1/72 q phi1 phi2 ( q^4-2*q^3-q^2-7*q+21 ) q congruent 7 modulo 12: 1/72 q phi1 phi2 ( q^4-2*q^3-q^2-7*q+21 ) q congruent 8 modulo 12: 1/72 q phi1 phi2 ( q^4-2*q^3-q^2-4*q+12 ) q congruent 9 modulo 12: 1/72 q phi1 phi2 ( q^4-2*q^3-q^2-7*q+21 ) q congruent 11 modulo 12: 1/72 q phi1 phi2 ( q^4-2*q^3-q^2-7*q+21 ) 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, 1 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 20, 1, 2, 4 ], [ 21, 1, 4, 18 ], [ 23, 1, 3, 4 ], [ 24, 1, 4, 8 ], [ 28, 1, 2, 4 ], [ 28, 1, 4, 12 ], [ 29, 1, 6, 12 ], [ 32, 1, 10, 18 ], [ 33, 1, 4, 8 ], [ 33, 1, 5, 24 ], [ 34, 1, 10, 18 ], [ 35, 1, 9, 12 ], [ 36, 1, 7, 18 ], [ 37, 1, 8, 12 ], [ 38, 1, 19, 36 ], [ 39, 1, 16, 24 ], [ 40, 1, 20, 36 ], [ 42, 1, 8, 24 ], [ 42, 1, 11, 36 ], [ 43, 1, 13, 36 ] ] k = 20: F-action on Pi is () [44,1,20] Dynkin type is A_0(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 12: 1/72 q phi1^2 ( q^4+q^2-5*q-3 ) q congruent 2 modulo 12: 1/72 phi2 ( q^6-3*q^5+5*q^4-11*q^3+14*q^2-12*q+8 ) q congruent 3 modulo 12: 1/72 q phi1^2 ( q^4+q^2-5*q-3 ) q congruent 4 modulo 12: 1/72 q^2 phi1 ( q^4-q^3+q^2-5*q-2 ) q congruent 5 modulo 12: 1/72 phi2 ( q^6-3*q^5+5*q^4-12*q^3+20*q^2-19*q+12 ) q congruent 7 modulo 12: 1/72 q phi1^2 ( q^4+q^2-5*q-3 ) q congruent 8 modulo 12: 1/72 phi2 ( q^6-3*q^5+5*q^4-11*q^3+14*q^2-12*q+8 ) q congruent 9 modulo 12: 1/72 q phi1^2 ( q^4+q^2-5*q-3 ) q congruent 11 modulo 12: 1/72 phi2 ( q^6-3*q^5+5*q^4-12*q^3+20*q^2-19*q+12 ) 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, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 4, 12 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 2 ], [ 11, 1, 2, 6 ], [ 12, 1, 5, 4 ], [ 14, 1, 1, 6 ], [ 15, 1, 8, 24 ], [ 16, 1, 2, 6 ], [ 20, 1, 3, 12 ], [ 21, 1, 4, 6 ], [ 23, 1, 2, 12 ], [ 28, 1, 6, 12 ], [ 32, 1, 10, 18 ], [ 33, 1, 9, 24 ], [ 34, 1, 9, 6 ], [ 36, 1, 9, 18 ], [ 38, 1, 17, 36 ], [ 40, 1, 5, 36 ], [ 42, 1, 10, 12 ], [ 43, 1, 15, 36 ] ] k = 21: F-action on Pi is () [44,1,21] Dynkin type is A_0(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 12: 1/24 q phi1^2 phi2 ( q^3+q^2+2*q-1 ) q congruent 2 modulo 12: 1/24 q^2 phi1^2 phi2 ( q^2+q+2 ) q congruent 3 modulo 12: 1/24 q phi1^2 phi2 ( q^3+q^2+2*q-1 ) q congruent 4 modulo 12: 1/24 q^2 phi1^2 phi2 ( q^2+q+2 ) q congruent 5 modulo 12: 1/24 q phi1^2 phi2 ( q^3+q^2+2*q-1 ) q congruent 7 modulo 12: 1/24 q phi1^2 phi2 ( q^3+q^2+2*q-1 ) q congruent 8 modulo 12: 1/24 q^2 phi1^2 phi2 ( q^2+q+2 ) q congruent 9 modulo 12: 1/24 q phi1^2 phi2 ( q^3+q^2+2*q-1 ) q congruent 11 modulo 12: 1/24 q phi1^2 phi2 ( q^3+q^2+2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 3, 4 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 12, 1, 4, 12 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 2 ], [ 15, 1, 7, 8 ], [ 16, 1, 2, 2 ], [ 20, 1, 4, 4 ], [ 21, 1, 5, 6 ], [ 23, 1, 4, 4 ], [ 28, 1, 3, 4 ], [ 32, 1, 9, 6 ], [ 33, 1, 12, 8 ], [ 34, 1, 10, 6 ], [ 36, 1, 7, 6 ], [ 38, 1, 18, 12 ], [ 40, 1, 19, 12 ], [ 42, 1, 9, 12 ], [ 43, 1, 14, 12 ] ] k = 22: F-action on Pi is () [44,1,22] Dynkin type is A_0(q) + T(phi1 phi7) Order of center |Z^F|: phi1 phi7 Numbers of classes in class type: q congruent 1 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 2 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 3 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 4 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 5 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 7 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 8 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 9 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 11 modulo 12: 1/14 q phi1 phi2 phi3 phi6 Fusion of maximal tori of C^F in those of G^F: [ 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 13, 1, 1, 2 ] ] k = 23: F-action on Pi is () [44,1,23] Dynkin type is A_0(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 12: 1/32 phi1^2 phi2 phi4 ( q^2+q-1 ) q congruent 2 modulo 12: 1/32 q^5 ( q^2-2 ) q congruent 3 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2+q-1 ) q congruent 4 modulo 12: 1/32 q^5 ( q^2-2 ) q congruent 5 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2+q-1 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2+q-1 ) q congruent 8 modulo 12: 1/32 q^5 ( q^2-2 ) q congruent 9 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2+q-1 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2+q-1 ) 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, 1 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 10, 8 ], [ 34, 1, 7, 8 ], [ 36, 1, 8, 16 ], [ 40, 1, 25, 8 ], [ 41, 1, 29, 16 ], [ 43, 1, 18, 16 ] ] k = 24: F-action on Pi is () [44,1,24] Dynkin type is A_0(q) + T(phi1 phi4 phi8) Order of center |Z^F|: phi1 phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 2 modulo 12: 1/32 q^6 ( q-2 ) q congruent 3 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 4 modulo 12: 1/32 q^6 ( q-2 ) q congruent 5 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 8 modulo 12: 1/32 q^6 ( q-2 ) q congruent 9 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-1 ) 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, 1 ], [ 4, 1, 3, 4 ], [ 4, 1, 4, 4 ], [ 5, 1, 2, 4 ], [ 15, 1, 5, 8 ], [ 15, 1, 6, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 34, 1, 6, 8 ], [ 36, 1, 12, 16 ], [ 40, 1, 25, 8 ], [ 41, 1, 32, 16 ], [ 43, 1, 20, 16 ] ] k = 25: F-action on Pi is () [44,1,25] Dynkin type is A_0(q) + T(phi1 phi9) Order of center |Z^F|: phi1 phi9 Numbers of classes in class type: q congruent 1 modulo 12: 1/18 phi1^2 phi3 ( q^3+2 ) q congruent 2 modulo 12: 1/18 q^3 phi1 phi2 phi6 q congruent 3 modulo 12: 1/18 q^3 phi1 phi2 phi6 q congruent 4 modulo 12: 1/18 phi1^2 phi3 ( q^3+2 ) q congruent 5 modulo 12: 1/18 q^3 phi1 phi2 phi6 q congruent 7 modulo 12: 1/18 phi1^2 phi3 ( q^3+2 ) q congruent 8 modulo 12: 1/18 q^3 phi1 phi2 phi6 q congruent 9 modulo 12: 1/18 q^3 phi1 phi2 phi6 q congruent 11 modulo 12: 1/18 q^3 phi1 phi2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 6, 1, 1, 2 ], [ 12, 1, 3, 6 ] ] k = 26: F-action on Pi is () [44,1,26] Dynkin type is A_0(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 12: 1/20 q phi1 phi2^2 phi4 ( q-2 ) q congruent 2 modulo 12: 1/20 q phi1 phi2^2 phi4 ( q-2 ) q congruent 3 modulo 12: 1/20 q phi1 phi2^2 phi4 ( q-2 ) q congruent 4 modulo 12: 1/20 q phi1 phi2^2 phi4 ( q-2 ) q congruent 5 modulo 12: 1/20 q phi1 phi2^2 phi4 ( q-2 ) q congruent 7 modulo 12: 1/20 q phi1 phi2^2 phi4 ( q-2 ) q congruent 8 modulo 12: 1/20 q phi1 phi2^2 phi4 ( q-2 ) q congruent 9 modulo 12: 1/20 q phi1 phi2^2 phi4 ( q-2 ) q congruent 11 modulo 12: 1/20 q phi1 phi2^2 phi4 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 26 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 13, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 18, 1, 4, 4 ], [ 19, 1, 2, 2 ], [ 23, 1, 3, 4 ], [ 28, 1, 2, 4 ], [ 29, 1, 5, 4 ], [ 42, 1, 3, 10 ], [ 43, 1, 3, 10 ] ] k = 27: F-action on Pi is () [44,1,27] Dynkin type is A_0(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 12: 1/48 q phi1 phi2^3 phi6 q congruent 2 modulo 12: 1/48 q^4 phi1 phi2^2 q congruent 3 modulo 12: 1/48 q phi1 phi2^3 phi6 q congruent 4 modulo 12: 1/48 q^4 phi1 phi2^2 q congruent 5 modulo 12: 1/48 q phi1 phi2^3 phi6 q congruent 7 modulo 12: 1/48 q phi1 phi2^3 phi6 q congruent 8 modulo 12: 1/48 q^4 phi1 phi2^2 q congruent 9 modulo 12: 1/48 q phi1 phi2^3 phi6 q congruent 11 modulo 12: 1/48 q phi1 phi2^3 phi6 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, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 21, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 6, 8 ], [ 26, 1, 5, 4 ], [ 28, 1, 5, 6 ], [ 30, 1, 3, 8 ], [ 33, 1, 11, 24 ], [ 34, 1, 8, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 6 ], [ 37, 1, 4, 8 ], [ 39, 1, 6, 16 ], [ 39, 1, 7, 12 ], [ 40, 1, 14, 12 ], [ 41, 1, 28, 24 ], [ 42, 1, 15, 16 ], [ 43, 1, 7, 24 ] ] k = 28: F-action on Pi is () [44,1,28] Dynkin type is A_0(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 12: 1/48 q phi1^2 phi2^2 phi6 q congruent 2 modulo 12: 1/48 q^4 phi1^2 phi2 q congruent 3 modulo 12: 1/48 q phi1^2 phi2^2 phi6 q congruent 4 modulo 12: 1/48 q^4 phi1^2 phi2 q congruent 5 modulo 12: 1/48 q phi1^2 phi2^2 phi6 q congruent 7 modulo 12: 1/48 q phi1^2 phi2^2 phi6 q congruent 8 modulo 12: 1/48 q^4 phi1^2 phi2 q congruent 9 modulo 12: 1/48 q phi1^2 phi2^2 phi6 q congruent 11 modulo 12: 1/48 q phi1^2 phi2^2 phi6 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, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 21, 1, 3, 4 ], [ 24, 1, 3, 4 ], [ 25, 1, 7, 8 ], [ 26, 1, 5, 4 ], [ 28, 1, 4, 6 ], [ 29, 1, 6, 12 ], [ 30, 1, 8, 8 ], [ 34, 1, 8, 8 ], [ 35, 1, 7, 8 ], [ 35, 1, 9, 6 ], [ 37, 1, 10, 8 ], [ 39, 1, 12, 12 ], [ 39, 1, 14, 16 ], [ 40, 1, 15, 12 ], [ 41, 1, 25, 24 ], [ 42, 1, 13, 16 ], [ 43, 1, 8, 24 ] ] k = 29: F-action on Pi is () [44,1,29] Dynkin type is A_0(q) + T(phi1 phi3 phi12) Order of center |Z^F|: phi1 phi3 phi12 Numbers of classes in class type: q congruent 1 modulo 12: 1/24 q^2 phi1 phi2 ( q^3-3 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q^3-2 ) q congruent 3 modulo 12: 1/24 q^2 phi1 phi2 ( q^3-3 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q^3-2 ) q congruent 5 modulo 12: 1/24 q^2 phi1 phi2 ( q^3-3 ) q congruent 7 modulo 12: 1/24 q^2 phi1 phi2 ( q^3-3 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q^3-2 ) q congruent 9 modulo 12: 1/24 q^2 phi1 phi2 ( q^3-3 ) q congruent 11 modulo 12: 1/24 q^2 phi1 phi2 ( q^3-3 ) Fusion of maximal tori of C^F in those of G^F: [ 29 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 6, 1, 1, 2 ], [ 34, 1, 9, 6 ], [ 40, 1, 11, 12 ] ] k = 30: F-action on Pi is () [44,1,30] Dynkin type is A_0(q) + T(phi1 phi3 phi5) Order of center |Z^F|: phi1 phi3 phi5 Numbers of classes in class type: q congruent 1 modulo 12: 1/30 q^2 phi1 phi2^2 phi4 q congruent 2 modulo 12: 1/30 q^2 phi1 phi2^2 phi4 q congruent 3 modulo 12: 1/30 q^2 phi1 phi2^2 phi4 q congruent 4 modulo 12: 1/30 q^2 phi1 phi2^2 phi4 q congruent 5 modulo 12: 1/30 q^2 phi1 phi2^2 phi4 q congruent 7 modulo 12: 1/30 q^2 phi1 phi2^2 phi4 q congruent 8 modulo 12: 1/30 q^2 phi1 phi2^2 phi4 q congruent 9 modulo 12: 1/30 q^2 phi1 phi2^2 phi4 q congruent 11 modulo 12: 1/30 q^2 phi1 phi2^2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 30 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 28, 1, 5, 6 ], [ 29, 1, 3, 6 ], [ 42, 1, 2, 10 ] ] k = 31: F-action on Pi is () [44,1,31] Dynkin type is A_0(q) + T(phi2^7) Order of center |Z^F|: phi2^7 Numbers of classes in class type: q congruent 1 modulo 12: 1/2903040 phi1 ( q^6-55*q^5+1205*q^4-13670*q^3+88299*q^2-333675*q+626535\ ) q congruent 2 modulo 12: 1/2903040 ( q^7-56*q^6+1260*q^5-14560*q^4+90944*q^3-290304*q^2+386560*q-\ 143360 ) q congruent 3 modulo 12: 1/2903040 ( q^7-56*q^6+1260*q^5-14875*q^4+101969*q^3-421974*q^2+1005570*\ q-1034775 ) q congruent 4 modulo 12: 1/2903040 q ( q^6-56*q^5+1260*q^4-14560*q^3+90944*q^2-290304*q+368640 ) q congruent 5 modulo 12: 1/2903040 ( q^7-56*q^6+1260*q^5-14875*q^4+101969*q^3-421974*q^2+978130*q\ -931175 ) q congruent 7 modulo 12: 1/2903040 ( q^7-56*q^6+1260*q^5-14875*q^4+101969*q^3-421974*q^2+1005570*\ q-1034775 ) q congruent 8 modulo 12: 1/2903040 ( q^7-56*q^6+1260*q^5-14560*q^4+90944*q^3-290304*q^2+386560*q-\ 143360 ) q congruent 9 modulo 12: 1/2903040 phi1 ( q^6-55*q^5+1205*q^4-13670*q^3+88299*q^2-333675*q+626535\ ) q congruent 11 modulo 12: 1/2903040 ( q^7-56*q^6+1260*q^5-14875*q^4+101969*q^3-421974*q^2+1023490*\ q-1339415 ) 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, 63 ], [ 3, 1, 2, 672 ], [ 4, 1, 2, 2520 ], [ 5, 1, 2, 72 ], [ 6, 1, 2, 56 ], [ 7, 1, 2, 756 ], [ 8, 1, 2, 4032 ], [ 9, 1, 2, 10080 ], [ 10, 1, 4, 15120 ], [ 11, 1, 2, 2016 ], [ 12, 1, 6, 13440 ], [ 13, 1, 2, 576 ], [ 14, 1, 2, 2016 ], [ 15, 1, 4, 5040 ], [ 16, 1, 2, 126 ], [ 17, 1, 3, 3780 ], [ 18, 1, 3, 1512 ], [ 19, 1, 2, 12096 ], [ 20, 1, 2, 40320 ], [ 21, 1, 6, 60480 ], [ 22, 1, 4, 30240 ], [ 23, 1, 4, 4032 ], [ 24, 1, 3, 20160 ], [ 25, 1, 8, 30240 ], [ 26, 1, 3, 7560 ], [ 27, 1, 12, 90720 ], [ 28, 1, 6, 4032 ], [ 29, 1, 4, 24192 ], [ 30, 1, 5, 120960 ], [ 31, 1, 7, 60480 ], [ 32, 1, 7, 181440 ], [ 33, 1, 6, 80640 ], [ 34, 1, 4, 15120 ], [ 35, 1, 10, 60480 ], [ 36, 1, 20, 181440 ], [ 37, 1, 6, 241920 ], [ 38, 1, 7, 362880 ], [ 39, 1, 15, 120960 ], [ 40, 1, 2, 362880 ], [ 41, 1, 16, 725760 ], [ 42, 1, 21, 483840 ], [ 43, 1, 26, 1451520 ] ] k = 32: F-action on Pi is () [44,1,32] Dynkin type is A_0(q) + T(phi1^6 phi2) Order of center |Z^F|: phi1^6 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/46080 phi1 ( q^6-35*q^5+485*q^4-3430*q^3+13299*q^2-27615*q+24975 ) q congruent 2 modulo 12: 1/46080 q ( q^6-36*q^5+520*q^4-3840*q^3+15184*q^2-30144*q+23040 ) q congruent 3 modulo 12: 1/46080 phi1 ( q^6-35*q^5+485*q^4-3430*q^3+13299*q^2-27615*q+24255 ) q congruent 4 modulo 12: 1/46080 q ( q^6-36*q^5+520*q^4-3840*q^3+15184*q^2-30144*q+23040 ) q congruent 5 modulo 12: 1/46080 phi1 ( q^6-35*q^5+485*q^4-3430*q^3+13299*q^2-27615*q+24975 ) q congruent 7 modulo 12: 1/46080 phi1 ( q^6-35*q^5+485*q^4-3430*q^3+13299*q^2-27615*q+24255 ) q congruent 8 modulo 12: 1/46080 q ( q^6-36*q^5+520*q^4-3840*q^3+15184*q^2-30144*q+23040 ) q congruent 9 modulo 12: 1/46080 phi1 ( q^6-35*q^5+485*q^4-3430*q^3+13299*q^2-27615*q+24975 ) q congruent 11 modulo 12: 1/46080 phi1 ( q^6-35*q^5+485*q^4-3430*q^3+13299*q^2-27615*q+24255 ) Fusion of maximal tori of C^F in those of G^F: [ 32 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 31 ], [ 3, 1, 1, 192 ], [ 4, 1, 1, 520 ], [ 5, 1, 1, 32 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 252 ], [ 8, 1, 1, 832 ], [ 9, 1, 1, 1600 ], [ 10, 1, 1, 2160 ], [ 11, 1, 1, 512 ], [ 12, 1, 1, 1920 ], [ 13, 1, 1, 192 ], [ 14, 1, 1, 512 ], [ 15, 1, 1, 960 ], [ 15, 1, 3, 80 ], [ 16, 1, 1, 60 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 840 ], [ 17, 1, 3, 60 ], [ 18, 1, 1, 480 ], [ 18, 1, 2, 24 ], [ 19, 1, 1, 2112 ], [ 20, 1, 1, 4480 ], [ 21, 1, 1, 5760 ], [ 22, 1, 1, 3840 ], [ 22, 1, 2, 480 ], [ 23, 1, 1, 960 ], [ 23, 1, 2, 64 ], [ 24, 1, 1, 2880 ], [ 24, 1, 2, 320 ], [ 25, 1, 1, 3840 ], [ 25, 1, 5, 480 ], [ 26, 1, 1, 1560 ], [ 26, 1, 2, 120 ], [ 27, 1, 1, 7200 ], [ 27, 1, 8, 1440 ], [ 28, 1, 1, 960 ], [ 28, 1, 3, 64 ], [ 29, 1, 1, 3840 ], [ 29, 1, 2, 384 ], [ 30, 1, 1, 9600 ], [ 30, 1, 2, 1920 ], [ 31, 1, 1, 6720 ], [ 31, 1, 2, 960 ], [ 31, 1, 3, 960 ], [ 32, 1, 1, 11520 ], [ 32, 1, 6, 2880 ], [ 33, 1, 1, 7680 ], [ 33, 1, 3, 1280 ], [ 34, 1, 1, 2880 ], [ 34, 1, 2, 240 ], [ 35, 1, 1, 6720 ], [ 35, 1, 2, 960 ], [ 36, 1, 1, 11520 ], [ 36, 1, 4, 2880 ], [ 37, 1, 1, 15360 ], [ 37, 1, 2, 3840 ], [ 38, 1, 1, 17280 ], [ 38, 1, 2, 5760 ], [ 38, 1, 8, 5760 ], [ 39, 1, 1, 11520 ], [ 39, 1, 2, 1920 ], [ 39, 1, 8, 1920 ], [ 40, 1, 1, 17280 ], [ 40, 1, 17, 5760 ], [ 41, 1, 1, 23040 ], [ 41, 1, 2, 11520 ], [ 41, 1, 15, 11520 ], [ 42, 1, 1, 23040 ], [ 42, 1, 17, 7680 ], [ 43, 1, 1, 23040 ], [ 43, 1, 28, 23040 ] ] k = 33: F-action on Pi is () [44,1,33] Dynkin type is A_0(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 12: 1/9216 phi1 ( q^6-15*q^5+53*q^4+122*q^3-757*q^2+45*q+2087 ) q congruent 2 modulo 12: 1/9216 q ( q^6-16*q^5+68*q^4+64*q^3-736*q^2+128*q+1536 ) q congruent 3 modulo 12: 1/9216 phi2 ( q^6-17*q^5+85*q^4-16*q^3-863*q^2+1665*q-279 ) q congruent 4 modulo 12: 1/9216 q ( q^6-16*q^5+68*q^4+64*q^3-736*q^2+128*q+2048 ) q congruent 5 modulo 12: 1/9216 phi1 ( q^6-15*q^5+53*q^4+122*q^3-757*q^2+45*q+1575 ) q congruent 7 modulo 12: 1/9216 ( q^7-16*q^6+68*q^5+69*q^4-879*q^3+802*q^2+1898*q-791 ) q congruent 8 modulo 12: 1/9216 q ( q^6-16*q^5+68*q^4+64*q^3-736*q^2+128*q+1536 ) q congruent 9 modulo 12: 1/9216 phi1 ( q^6-15*q^5+53*q^4+122*q^3-757*q^2+45*q+1575 ) q congruent 11 modulo 12: 1/9216 phi2 ( q^6-17*q^5+85*q^4-16*q^3-863*q^2+1665*q-279 ) 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, 15 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 48 ], [ 4, 1, 2, 72 ], [ 4, 1, 3, 192 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 24 ], [ 7, 1, 2, 12 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 10, 1, 2, 96 ], [ 10, 1, 3, 288 ], [ 10, 1, 4, 144 ], [ 11, 1, 1, 96 ], [ 12, 1, 2, 256 ], [ 14, 1, 2, 96 ], [ 15, 1, 3, 96 ], [ 15, 1, 4, 144 ], [ 15, 1, 5, 384 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 144 ], [ 17, 1, 2, 96 ], [ 17, 1, 3, 84 ], [ 18, 1, 2, 48 ], [ 18, 1, 3, 24 ], [ 20, 1, 4, 768 ], [ 21, 1, 1, 192 ], [ 21, 1, 2, 384 ], [ 22, 1, 1, 288 ], [ 22, 1, 2, 96 ], [ 22, 1, 3, 288 ], [ 23, 1, 3, 192 ], [ 24, 1, 2, 192 ], [ 25, 1, 5, 384 ], [ 25, 1, 6, 192 ], [ 25, 1, 7, 576 ], [ 25, 1, 8, 288 ], [ 26, 1, 1, 144 ], [ 26, 1, 2, 144 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 96 ], [ 27, 1, 1, 576 ], [ 27, 1, 2, 576 ], [ 27, 1, 3, 1152 ], [ 27, 1, 4, 1152 ], [ 27, 1, 8, 576 ], [ 27, 1, 12, 288 ], [ 28, 1, 1, 192 ], [ 30, 1, 2, 384 ], [ 30, 1, 3, 768 ], [ 31, 1, 2, 576 ], [ 31, 1, 4, 192 ], [ 31, 1, 5, 576 ], [ 32, 1, 1, 576 ], [ 32, 1, 2, 1152 ], [ 32, 1, 3, 576 ], [ 32, 1, 6, 576 ], [ 33, 1, 10, 1536 ], [ 34, 1, 2, 288 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 192 ], [ 35, 1, 1, 576 ], [ 35, 1, 3, 576 ], [ 35, 1, 5, 192 ], [ 36, 1, 4, 1152 ], [ 36, 1, 5, 1152 ], [ 36, 1, 6, 2304 ], [ 36, 1, 20, 576 ], [ 37, 1, 5, 768 ], [ 38, 1, 2, 1152 ], [ 38, 1, 3, 1152 ], [ 38, 1, 5, 1152 ], [ 38, 1, 9, 2304 ], [ 39, 1, 4, 384 ], [ 39, 1, 8, 1152 ], [ 39, 1, 13, 1152 ], [ 40, 1, 1, 1152 ], [ 40, 1, 3, 1152 ], [ 40, 1, 12, 2304 ], [ 41, 1, 5, 2304 ], [ 41, 1, 10, 2304 ], [ 41, 1, 15, 2304 ], [ 41, 1, 30, 4608 ], [ 42, 1, 18, 1536 ], [ 43, 1, 22, 4608 ], [ 43, 1, 37, 4608 ] ] k = 34: F-action on Pi is () [44,1,34] Dynkin type is A_0(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 12: 1/3072 phi1^3 ( q^4-9*q^3+18*q^2+7*q+15 ) q congruent 2 modulo 12: 1/3072 q^2 ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 ) q congruent 3 modulo 12: 1/3072 phi1 phi2 ( q^5-12*q^4+49*q^3-87*q^2+106*q-129 ) q congruent 4 modulo 12: 1/3072 q^2 ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 ) q congruent 5 modulo 12: 1/3072 phi1^3 ( q^4-9*q^3+18*q^2+7*q+15 ) q congruent 7 modulo 12: 1/3072 phi1 phi2 ( q^5-12*q^4+49*q^3-87*q^2+106*q-129 ) q congruent 8 modulo 12: 1/3072 q^2 ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 ) q congruent 9 modulo 12: 1/3072 phi1^3 ( q^4-9*q^3+18*q^2+7*q+15 ) q congruent 11 modulo 12: 1/3072 phi1 phi2 ( q^5-12*q^4+49*q^3-87*q^2+106*q-129 ) 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, 15 ], [ 3, 1, 2, 64 ], [ 4, 1, 1, 24 ], [ 4, 1, 2, 144 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 72 ], [ 8, 1, 2, 192 ], [ 9, 1, 2, 320 ], [ 10, 1, 1, 48 ], [ 10, 1, 2, 96 ], [ 10, 1, 3, 32 ], [ 10, 1, 4, 384 ], [ 11, 1, 2, 128 ], [ 12, 1, 6, 384 ], [ 13, 1, 2, 64 ], [ 14, 1, 2, 128 ], [ 15, 1, 2, 64 ], [ 15, 1, 3, 48 ], [ 15, 1, 4, 224 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 26 ], [ 17, 1, 1, 56 ], [ 17, 1, 2, 32 ], [ 17, 1, 3, 172 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 112 ], [ 18, 1, 4, 32 ], [ 19, 1, 2, 320 ], [ 20, 1, 2, 640 ], [ 21, 1, 3, 128 ], [ 21, 1, 6, 768 ], [ 22, 1, 2, 96 ], [ 22, 1, 3, 256 ], [ 22, 1, 4, 512 ], [ 23, 1, 3, 64 ], [ 23, 1, 4, 192 ], [ 24, 1, 3, 448 ], [ 24, 1, 4, 192 ], [ 25, 1, 4, 256 ], [ 25, 1, 5, 96 ], [ 25, 1, 6, 192 ], [ 25, 1, 7, 64 ], [ 25, 1, 8, 512 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 104 ], [ 26, 1, 3, 240 ], [ 26, 1, 4, 32 ], [ 27, 1, 1, 96 ], [ 27, 1, 2, 192 ], [ 27, 1, 8, 480 ], [ 27, 1, 11, 384 ], [ 27, 1, 12, 960 ], [ 27, 1, 13, 384 ], [ 28, 1, 2, 64 ], [ 28, 1, 6, 192 ], [ 29, 1, 4, 384 ], [ 29, 1, 5, 256 ], [ 30, 1, 5, 896 ], [ 30, 1, 6, 640 ], [ 30, 1, 8, 256 ], [ 31, 1, 4, 192 ], [ 31, 1, 5, 448 ], [ 31, 1, 6, 64 ], [ 31, 1, 7, 576 ], [ 31, 1, 8, 448 ], [ 32, 1, 3, 768 ], [ 32, 1, 5, 384 ], [ 32, 1, 6, 192 ], [ 32, 1, 7, 1152 ], [ 33, 1, 4, 512 ], [ 33, 1, 6, 768 ], [ 34, 1, 2, 16 ], [ 34, 1, 3, 192 ], [ 34, 1, 4, 288 ], [ 34, 1, 7, 64 ], [ 35, 1, 3, 64 ], [ 35, 1, 4, 448 ], [ 35, 1, 5, 192 ], [ 35, 1, 10, 576 ], [ 36, 1, 4, 192 ], [ 36, 1, 5, 384 ], [ 36, 1, 18, 768 ], [ 36, 1, 19, 768 ], [ 36, 1, 20, 1152 ], [ 37, 1, 6, 768 ], [ 37, 1, 7, 1024 ], [ 37, 1, 9, 256 ], [ 38, 1, 3, 1152 ], [ 38, 1, 4, 384 ], [ 38, 1, 5, 384 ], [ 38, 1, 6, 1152 ], [ 38, 1, 7, 1152 ], [ 38, 1, 16, 768 ], [ 39, 1, 4, 384 ], [ 39, 1, 11, 768 ], [ 39, 1, 13, 128 ], [ 39, 1, 15, 384 ], [ 39, 1, 19, 128 ], [ 39, 1, 20, 768 ], [ 40, 1, 2, 1152 ], [ 40, 1, 3, 384 ], [ 40, 1, 13, 768 ], [ 40, 1, 18, 1152 ], [ 41, 1, 6, 1536 ], [ 41, 1, 7, 768 ], [ 41, 1, 10, 768 ], [ 41, 1, 16, 768 ], [ 41, 1, 20, 768 ], [ 41, 1, 22, 1536 ], [ 41, 1, 23, 1536 ], [ 42, 1, 19, 512 ], [ 42, 1, 20, 1536 ], [ 43, 1, 16, 1536 ], [ 43, 1, 27, 1536 ], [ 43, 1, 30, 1536 ] ] k = 35: F-action on Pi is () [44,1,35] Dynkin type is A_0(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 12: 1/768 phi1 ( q^6-7*q^5+5*q^4+50*q^3-61*q^2-83*q-33 ) q congruent 2 modulo 12: 1/768 q ( q^6-8*q^5+12*q^4+40*q^3-96*q^2-32*q+128 ) q congruent 3 modulo 12: 1/768 phi1 phi2 ( q^5-8*q^4+13*q^3+37*q^2-98*q+15 ) q congruent 4 modulo 12: 1/768 q ( q^6-8*q^5+12*q^4+40*q^3-96*q^2-32*q+128 ) q congruent 5 modulo 12: 1/768 phi1 ( q^6-7*q^5+5*q^4+50*q^3-61*q^2-83*q-33 ) q congruent 7 modulo 12: 1/768 phi1 phi2 ( q^5-8*q^4+13*q^3+37*q^2-98*q+15 ) q congruent 8 modulo 12: 1/768 q ( q^6-8*q^5+12*q^4+40*q^3-96*q^2-32*q+128 ) q congruent 9 modulo 12: 1/768 phi1 ( q^6-7*q^5+5*q^4+50*q^3-61*q^2-83*q-33 ) q congruent 11 modulo 12: 1/768 phi1 phi2 ( q^5-8*q^4+13*q^3+37*q^2-98*q+15 ) 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, 7 ], [ 3, 1, 1, 24 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 48 ], [ 4, 1, 2, 24 ], [ 4, 1, 4, 16 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 24 ], [ 7, 1, 2, 12 ], [ 8, 1, 1, 48 ], [ 9, 1, 1, 72 ], [ 9, 1, 2, 24 ], [ 10, 1, 1, 96 ], [ 10, 1, 2, 48 ], [ 10, 1, 3, 48 ], [ 10, 1, 4, 48 ], [ 11, 1, 1, 24 ], [ 11, 1, 2, 8 ], [ 12, 1, 1, 96 ], [ 12, 1, 5, 64 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 15, 1, 2, 48 ], [ 15, 1, 3, 48 ], [ 15, 1, 6, 32 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 48 ], [ 17, 1, 3, 36 ], [ 17, 1, 4, 48 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 24 ], [ 18, 1, 4, 24 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 96 ], [ 20, 1, 3, 64 ], [ 21, 1, 1, 144 ], [ 21, 1, 2, 96 ], [ 21, 1, 3, 96 ], [ 21, 1, 6, 48 ], [ 22, 1, 1, 72 ], [ 22, 1, 2, 120 ], [ 22, 1, 3, 72 ], [ 22, 1, 4, 24 ], [ 23, 1, 1, 16 ], [ 23, 1, 2, 48 ], [ 24, 1, 1, 48 ], [ 24, 1, 2, 96 ], [ 24, 1, 4, 48 ], [ 25, 1, 1, 96 ], [ 25, 1, 2, 96 ], [ 25, 1, 3, 96 ], [ 25, 1, 4, 96 ], [ 25, 1, 5, 96 ], [ 26, 1, 1, 48 ], [ 26, 1, 2, 48 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 48 ], [ 27, 1, 1, 192 ], [ 27, 1, 2, 96 ], [ 27, 1, 6, 96 ], [ 27, 1, 8, 192 ], [ 27, 1, 9, 96 ], [ 27, 1, 12, 96 ], [ 27, 1, 14, 96 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 48 ], [ 29, 1, 2, 96 ], [ 30, 1, 1, 96 ], [ 30, 1, 2, 192 ], [ 30, 1, 4, 192 ], [ 30, 1, 6, 96 ], [ 30, 1, 7, 192 ], [ 31, 1, 1, 48 ], [ 31, 1, 2, 96 ], [ 31, 1, 3, 144 ], [ 31, 1, 4, 96 ], [ 31, 1, 6, 144 ], [ 31, 1, 8, 48 ], [ 32, 1, 1, 144 ], [ 32, 1, 2, 96 ], [ 32, 1, 3, 144 ], [ 32, 1, 5, 96 ], [ 32, 1, 6, 240 ], [ 32, 1, 7, 48 ], [ 33, 1, 3, 192 ], [ 33, 1, 7, 128 ], [ 34, 1, 1, 48 ], [ 34, 1, 2, 48 ], [ 34, 1, 3, 48 ], [ 34, 1, 5, 96 ], [ 35, 1, 2, 144 ], [ 35, 1, 3, 96 ], [ 35, 1, 4, 48 ], [ 35, 1, 5, 96 ], [ 36, 1, 1, 192 ], [ 36, 1, 2, 192 ], [ 36, 1, 4, 192 ], [ 36, 1, 13, 192 ], [ 36, 1, 18, 192 ], [ 37, 1, 2, 192 ], [ 37, 1, 5, 192 ], [ 37, 1, 9, 192 ], [ 38, 1, 1, 96 ], [ 38, 1, 2, 192 ], [ 38, 1, 4, 288 ], [ 38, 1, 5, 192 ], [ 38, 1, 6, 96 ], [ 38, 1, 8, 288 ], [ 38, 1, 10, 192 ], [ 38, 1, 15, 192 ], [ 39, 1, 2, 96 ], [ 39, 1, 5, 192 ], [ 39, 1, 10, 192 ], [ 39, 1, 18, 192 ], [ 39, 1, 19, 96 ], [ 40, 1, 3, 192 ], [ 40, 1, 17, 288 ], [ 40, 1, 18, 96 ], [ 40, 1, 22, 192 ], [ 41, 1, 2, 192 ], [ 41, 1, 5, 192 ], [ 41, 1, 7, 192 ], [ 41, 1, 11, 384 ], [ 41, 1, 19, 384 ], [ 41, 1, 20, 192 ], [ 41, 1, 37, 384 ], [ 42, 1, 12, 384 ], [ 42, 1, 22, 384 ], [ 43, 1, 29, 384 ], [ 43, 1, 31, 384 ], [ 43, 1, 32, 384 ] ] k = 36: F-action on Pi is () [44,1,36] Dynkin type is A_0(q) + T(phi2^5 phi6) Order of center |Z^F|: phi2^5 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/4320 q phi1^2 ( q^4-9*q^3+26*q^2-39*q+45 ) q congruent 2 modulo 12: 1/4320 phi2 ( q^6-12*q^5+57*q^4-142*q^3+216*q^2-240*q+160 ) q congruent 3 modulo 12: 1/4320 q phi1^2 ( q^4-9*q^3+26*q^2-39*q+45 ) q congruent 4 modulo 12: 1/4320 q^2 phi1^2 ( q^3-9*q^2+26*q-24 ) q congruent 5 modulo 12: 1/4320 phi2 ( q^6-12*q^5+57*q^4-157*q^3+306*q^2-435*q+400 ) q congruent 7 modulo 12: 1/4320 q phi1^2 ( q^4-9*q^3+26*q^2-39*q+45 ) q congruent 8 modulo 12: 1/4320 phi2 ( q^6-12*q^5+57*q^4-142*q^3+216*q^2-240*q+160 ) q congruent 9 modulo 12: 1/4320 q phi1^2 ( q^4-9*q^3+26*q^2-39*q+45 ) q congruent 11 modulo 12: 1/4320 phi2 ( q^6-12*q^5+57*q^4-157*q^3+306*q^2-435*q+400 ) Fusion of maximal tori of C^F in those of G^F: [ 36 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 2, 42 ], [ 4, 1, 2, 60 ], [ 5, 1, 2, 12 ], [ 6, 1, 2, 20 ], [ 7, 1, 2, 90 ], [ 8, 1, 2, 132 ], [ 9, 1, 2, 150 ], [ 10, 1, 4, 180 ], [ 11, 1, 2, 120 ], [ 12, 1, 6, 120 ], [ 13, 1, 2, 60 ], [ 14, 1, 2, 120 ], [ 15, 1, 4, 120 ], [ 16, 1, 2, 30 ], [ 17, 1, 3, 180 ], [ 18, 1, 3, 180 ], [ 19, 1, 2, 360 ], [ 20, 1, 2, 240 ], [ 21, 1, 6, 180 ], [ 22, 1, 4, 360 ], [ 23, 1, 4, 240 ], [ 24, 1, 3, 300 ], [ 25, 1, 8, 360 ], [ 26, 1, 3, 360 ], [ 28, 1, 4, 6 ], [ 28, 1, 6, 240 ], [ 29, 1, 4, 720 ], [ 29, 1, 6, 36 ], [ 30, 1, 5, 360 ], [ 31, 1, 7, 720 ], [ 33, 1, 5, 120 ], [ 33, 1, 6, 480 ], [ 34, 1, 4, 720 ], [ 35, 1, 9, 90 ], [ 35, 1, 10, 720 ], [ 37, 1, 6, 720 ], [ 37, 1, 8, 360 ], [ 39, 1, 12, 180 ], [ 39, 1, 15, 1440 ], [ 40, 1, 8, 540 ], [ 41, 1, 8, 1080 ], [ 42, 1, 6, 720 ], [ 42, 1, 21, 1440 ], [ 43, 1, 9, 2160 ] ] k = 37: F-action on Pi is () [44,1,37] Dynkin type is A_0(q) + T(phi2 phi6^3) Order of center |Z^F|: phi2 phi6^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/1296 q phi1 ( q^5-q^4-10*q^3-17*q^2+45*q+126 ) q congruent 2 modulo 12: 1/1296 phi2 ( q^6-3*q^5-6*q^4+8*q^3+36*q^2-80 ) q congruent 3 modulo 12: 1/1296 q phi1 ( q^5-q^4-10*q^3-17*q^2+45*q+126 ) q congruent 4 modulo 12: 1/1296 q phi1 ( q^5-q^4-10*q^3-8*q^2+36*q+72 ) q congruent 5 modulo 12: 1/1296 phi2 ( q^6-3*q^5-6*q^4-q^3+63*q^2+18*q-152 ) q congruent 7 modulo 12: 1/1296 q phi1 ( q^5-q^4-10*q^3-17*q^2+45*q+126 ) q congruent 8 modulo 12: 1/1296 phi2 ( q^6-3*q^5-6*q^4+8*q^3+36*q^2-80 ) q congruent 9 modulo 12: 1/1296 q phi1 ( q^5-q^4-10*q^3-17*q^2+45*q+126 ) q congruent 11 modulo 12: 1/1296 phi2 ( q^6-3*q^5-6*q^4-q^3+63*q^2+18*q-152 ) Fusion of maximal tori of C^F in those of G^F: [ 37 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 24 ], [ 6, 1, 2, 2 ], [ 12, 1, 6, 48 ], [ 21, 1, 4, 216 ], [ 28, 1, 4, 72 ], [ 33, 1, 5, 144 ], [ 34, 1, 10, 54 ], [ 40, 1, 10, 648 ], [ 42, 1, 11, 432 ] ] k = 38: F-action on Pi is () [44,1,38] Dynkin type is A_0(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 12: 1/216 q phi1^2 ( q^4-q^2-15*q-9 ) q congruent 2 modulo 12: 1/216 phi2 ( q^6-3*q^5+3*q^4-13*q^3+18*q^2-12*q+40 ) q congruent 3 modulo 12: 1/216 q phi1^2 ( q^4-q^2-15*q-9 ) q congruent 4 modulo 12: 1/216 q^2 phi1 ( q^4-q^3-q^2-11*q-6 ) q congruent 5 modulo 12: 1/216 phi2 ( q^6-3*q^5+3*q^4-16*q^3+36*q^2-33*q+52 ) q congruent 7 modulo 12: 1/216 q phi1^2 ( q^4-q^2-15*q-9 ) q congruent 8 modulo 12: 1/216 phi2 ( q^6-3*q^5+3*q^4-13*q^3+18*q^2-12*q+40 ) q congruent 9 modulo 12: 1/216 q phi1^2 ( q^4-q^2-15*q-9 ) q congruent 11 modulo 12: 1/216 phi2 ( q^6-3*q^5+3*q^4-16*q^3+36*q^2-33*q+52 ) 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, 3 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 6 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 12 ], [ 11, 1, 2, 6 ], [ 12, 1, 4, 36 ], [ 12, 1, 6, 12 ], [ 13, 1, 2, 12 ], [ 14, 1, 2, 6 ], [ 15, 1, 4, 24 ], [ 16, 1, 2, 6 ], [ 20, 1, 2, 12 ], [ 21, 1, 4, 18 ], [ 23, 1, 4, 12 ], [ 24, 1, 3, 24 ], [ 28, 1, 4, 12 ], [ 28, 1, 6, 12 ], [ 29, 1, 6, 36 ], [ 32, 1, 10, 54 ], [ 33, 1, 5, 24 ], [ 33, 1, 6, 24 ], [ 34, 1, 10, 18 ], [ 35, 1, 9, 36 ], [ 36, 1, 7, 54 ], [ 37, 1, 8, 36 ], [ 38, 1, 18, 108 ], [ 39, 1, 12, 72 ], [ 40, 1, 5, 108 ], [ 42, 1, 6, 72 ], [ 42, 1, 11, 36 ], [ 43, 1, 13, 108 ] ] k = 39: F-action on Pi is () [44,1,39] Dynkin type is A_0(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 12: 1/768 phi1^3 phi2 ( q^3+2*q^2+3 ) q congruent 2 modulo 12: 1/768 q^5 ( q^2-4 ) q congruent 3 modulo 12: 1/768 phi1^3 phi2 ( q^3+2*q^2+3 ) q congruent 4 modulo 12: 1/768 q^5 ( q^2-4 ) q congruent 5 modulo 12: 1/768 phi1^3 phi2 ( q^3+2*q^2+3 ) q congruent 7 modulo 12: 1/768 phi1^3 phi2 ( q^3+2*q^2+3 ) q congruent 8 modulo 12: 1/768 q^5 ( q^2-4 ) q congruent 9 modulo 12: 1/768 phi1^3 phi2 ( q^3+2*q^2+3 ) q congruent 11 modulo 12: 1/768 phi1^3 phi2 ( q^3+2*q^2+3 ) Fusion of maximal tori of C^F in those of G^F: [ 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 24 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 12 ], [ 10, 1, 2, 48 ], [ 15, 1, 3, 48 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 24 ], [ 17, 1, 3, 12 ], [ 18, 1, 3, 24 ], [ 25, 1, 6, 96 ], [ 26, 1, 3, 24 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 1, 11, 96 ], [ 27, 1, 13, 96 ], [ 32, 1, 4, 96 ], [ 34, 1, 4, 48 ], [ 34, 1, 8, 48 ], [ 35, 1, 6, 96 ], [ 36, 1, 10, 96 ], [ 36, 1, 19, 192 ], [ 38, 1, 12, 192 ], [ 39, 1, 6, 192 ], [ 40, 1, 6, 96 ], [ 40, 1, 24, 192 ], [ 41, 1, 14, 192 ], [ 41, 1, 26, 384 ], [ 43, 1, 19, 384 ] ] k = 40: F-action on Pi is () [44,1,40] Dynkin type is A_0(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 12: 1/384 phi1^3 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 2 modulo 12: 1/384 q^3 ( q^4-6*q^3+10*q^2-8 ) q congruent 3 modulo 12: 1/384 phi1^3 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 4 modulo 12: 1/384 q^3 ( q^4-6*q^3+10*q^2-8 ) q congruent 5 modulo 12: 1/384 phi1^3 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 7 modulo 12: 1/384 phi1^3 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 8 modulo 12: 1/384 q^3 ( q^4-6*q^3+10*q^2-8 ) q congruent 9 modulo 12: 1/384 phi1^3 phi2 ( q^3-4*q^2+2*q+3 ) q congruent 11 modulo 12: 1/384 phi1^3 phi2 ( q^3-4*q^2+2*q+3 ) 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, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 4 ], [ 4, 1, 4, 48 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 36 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 5, 32 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 15, 1, 2, 8 ], [ 15, 1, 8, 96 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 1, 4, 16 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 12 ], [ 20, 1, 3, 96 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 1, 2, 48 ], [ 24, 1, 4, 16 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 72 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 12 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 24 ], [ 27, 1, 6, 96 ], [ 27, 1, 7, 24 ], [ 27, 1, 13, 96 ], [ 28, 1, 6, 48 ], [ 30, 1, 7, 32 ], [ 31, 1, 3, 48 ], [ 31, 1, 8, 48 ], [ 32, 1, 4, 48 ], [ 32, 1, 5, 48 ], [ 33, 1, 9, 192 ], [ 34, 1, 3, 48 ], [ 34, 1, 5, 24 ], [ 34, 1, 6, 8 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 8 ], [ 35, 1, 10, 48 ], [ 36, 1, 2, 48 ], [ 36, 1, 15, 192 ], [ 36, 1, 17, 48 ], [ 37, 1, 10, 32 ], [ 38, 1, 11, 96 ], [ 38, 1, 15, 96 ], [ 39, 1, 9, 48 ], [ 39, 1, 10, 96 ], [ 39, 1, 17, 16 ], [ 39, 1, 20, 96 ], [ 40, 1, 13, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 24, 96 ], [ 41, 1, 9, 96 ], [ 41, 1, 18, 96 ], [ 41, 1, 39, 192 ], [ 41, 1, 40, 192 ], [ 42, 1, 16, 64 ], [ 43, 1, 24, 192 ], [ 43, 1, 34, 192 ] ] k = 41: F-action on Pi is () [44,1,41] Dynkin type is A_0(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 12: 1/384 phi1 phi2 ( q^5-10*q^4+31*q^3-17*q^2-80*q+123 ) q congruent 2 modulo 12: 1/384 q^2 ( q^5-10*q^4+30*q^3-8*q^2-88*q+96 ) q congruent 3 modulo 12: 1/384 phi1 phi2 ( q^5-10*q^4+31*q^3-17*q^2-80*q+123 ) q congruent 4 modulo 12: 1/384 q^2 ( q^5-10*q^4+30*q^3-8*q^2-88*q+96 ) q congruent 5 modulo 12: 1/384 phi1 phi2 ( q^5-10*q^4+31*q^3-17*q^2-80*q+123 ) q congruent 7 modulo 12: 1/384 phi1 phi2 ( q^5-10*q^4+31*q^3-17*q^2-80*q+123 ) q congruent 8 modulo 12: 1/384 q^2 ( q^5-10*q^4+30*q^3-8*q^2-88*q+96 ) q congruent 9 modulo 12: 1/384 phi1 phi2 ( q^5-10*q^4+31*q^3-17*q^2-80*q+123 ) q congruent 11 modulo 12: 1/384 phi1 phi2 ( q^5-10*q^4+31*q^3-17*q^2-80*q+123 ) 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, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 12 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 30 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 36 ], [ 10, 1, 4, 12 ], [ 11, 1, 1, 24 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 24 ], [ 16, 1, 1, 14 ], [ 17, 1, 1, 36 ], [ 17, 1, 4, 16 ], [ 18, 1, 1, 60 ], [ 18, 1, 4, 4 ], [ 19, 1, 1, 48 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 48 ], [ 24, 1, 1, 16 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 72 ], [ 25, 1, 4, 24 ], [ 26, 1, 1, 72 ], [ 26, 1, 4, 12 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 27, 1, 7, 24 ], [ 27, 1, 14, 96 ], [ 28, 1, 1, 48 ], [ 29, 1, 1, 96 ], [ 30, 1, 4, 32 ], [ 31, 1, 1, 48 ], [ 31, 1, 6, 48 ], [ 32, 1, 2, 48 ], [ 32, 1, 8, 48 ], [ 34, 1, 1, 144 ], [ 34, 1, 5, 24 ], [ 34, 1, 6, 8 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 24 ], [ 36, 1, 2, 48 ], [ 36, 1, 3, 192 ], [ 36, 1, 17, 48 ], [ 37, 1, 4, 32 ], [ 38, 1, 10, 96 ], [ 38, 1, 13, 96 ], [ 39, 1, 1, 96 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 48 ], [ 39, 1, 18, 96 ], [ 40, 1, 12, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 23, 96 ], [ 41, 1, 4, 96 ], [ 41, 1, 18, 96 ], [ 41, 1, 34, 192 ], [ 41, 1, 36, 192 ], [ 42, 1, 14, 64 ], [ 43, 1, 23, 192 ], [ 43, 1, 36, 192 ] ] k = 42: F-action on Pi is () [44,1,42] Dynkin type is A_0(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 12: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 2 modulo 12: 1/256 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 3 modulo 12: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 4 modulo 12: 1/256 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 5 modulo 12: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 7 modulo 12: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 8 modulo 12: 1/256 q^3 ( q^4-4*q^3+16*q-16 ) q congruent 9 modulo 12: 1/256 phi1^2 phi2 ( q^4-3*q^3-2*q^2+15*q-27 ) q congruent 11 modulo 12: 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: [ 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 8 ], [ 4, 1, 3, 16 ], [ 4, 1, 4, 16 ], [ 5, 1, 2, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 15, 1, 4, 16 ], [ 15, 1, 5, 32 ], [ 15, 1, 6, 32 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 16 ], [ 18, 1, 2, 8 ], [ 25, 1, 7, 32 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 5, 24 ], [ 27, 1, 3, 32 ], [ 27, 1, 4, 32 ], [ 27, 1, 5, 64 ], [ 27, 1, 6, 32 ], [ 27, 1, 7, 48 ], [ 27, 1, 9, 32 ], [ 27, 1, 14, 32 ], [ 32, 1, 4, 32 ], [ 32, 1, 8, 64 ], [ 34, 1, 2, 16 ], [ 34, 1, 6, 32 ], [ 34, 1, 8, 16 ], [ 35, 1, 7, 32 ], [ 36, 1, 6, 64 ], [ 36, 1, 10, 32 ], [ 36, 1, 12, 128 ], [ 36, 1, 13, 64 ], [ 36, 1, 17, 64 ], [ 38, 1, 11, 64 ], [ 38, 1, 13, 64 ], [ 38, 1, 14, 64 ], [ 39, 1, 14, 64 ], [ 40, 1, 6, 96 ], [ 40, 1, 16, 64 ], [ 40, 1, 23, 64 ], [ 41, 1, 14, 64 ], [ 41, 1, 21, 128 ], [ 41, 1, 31, 128 ], [ 41, 1, 35, 128 ], [ 43, 1, 17, 128 ], [ 43, 1, 21, 128 ] ] k = 43: F-action on Pi is () [44,1,43] Dynkin type is A_0(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 12: 1/64 phi1 phi2 ( q^5-2*q^4-q^3+3*q^2-8*q-1 ) q congruent 2 modulo 12: 1/64 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 3 modulo 12: 1/64 phi1 phi2 ( q^5-2*q^4-q^3+3*q^2-8*q-1 ) q congruent 4 modulo 12: 1/64 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 5 modulo 12: 1/64 phi1 phi2 ( q^5-2*q^4-q^3+3*q^2-8*q-1 ) q congruent 7 modulo 12: 1/64 phi1 phi2 ( q^5-2*q^4-q^3+3*q^2-8*q-1 ) q congruent 8 modulo 12: 1/64 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 9 modulo 12: 1/64 phi1 phi2 ( q^5-2*q^4-q^3+3*q^2-8*q-1 ) q congruent 11 modulo 12: 1/64 phi1 phi2 ( q^5-2*q^4-q^3+3*q^2-8*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, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 1, 3, 8 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 16 ], [ 13, 1, 2, 8 ], [ 14, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 1, 7, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 3, 8 ], [ 23, 1, 4, 8 ], [ 24, 1, 2, 8 ], [ 24, 1, 3, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 4, 16 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 1, 10, 16 ], [ 27, 1, 11, 16 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 29, 1, 5, 16 ], [ 30, 1, 3, 16 ], [ 30, 1, 8, 16 ], [ 31, 1, 2, 8 ], [ 31, 1, 4, 8 ], [ 31, 1, 5, 8 ], [ 31, 1, 7, 8 ], [ 32, 1, 2, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 32, 1, 8, 8 ], [ 33, 1, 12, 32 ], [ 34, 1, 3, 16 ], [ 34, 1, 7, 8 ], [ 34, 1, 8, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 36, 1, 5, 16 ], [ 36, 1, 8, 32 ], [ 36, 1, 10, 16 ], [ 36, 1, 14, 32 ], [ 37, 1, 4, 16 ], [ 37, 1, 10, 16 ], [ 38, 1, 9, 16 ], [ 38, 1, 12, 16 ], [ 38, 1, 14, 16 ], [ 38, 1, 16, 16 ], [ 39, 1, 5, 16 ], [ 39, 1, 6, 16 ], [ 39, 1, 11, 16 ], [ 39, 1, 14, 16 ], [ 40, 1, 16, 16 ], [ 40, 1, 21, 16 ], [ 40, 1, 22, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 12, 32 ], [ 41, 1, 24, 32 ], [ 41, 1, 27, 32 ], [ 42, 1, 13, 32 ], [ 42, 1, 15, 32 ], [ 43, 1, 25, 32 ], [ 43, 1, 33, 32 ], [ 43, 1, 35, 32 ] ] k = 44: F-action on Pi is () [44,1,44] Dynkin type is A_0(q) + T(phi2^3 phi10) Order of center |Z^F|: phi2^3 phi10 Numbers of classes in class type: q congruent 1 modulo 12: 1/60 q^2 phi1^2 phi2 phi4 q congruent 2 modulo 12: 1/60 q^2 phi1^2 phi2 phi4 q congruent 3 modulo 12: 1/60 q^2 phi1^2 phi2 phi4 q congruent 4 modulo 12: 1/60 q^2 phi1^2 phi2 phi4 q congruent 5 modulo 12: 1/60 q^2 phi1^2 phi2 phi4 q congruent 7 modulo 12: 1/60 q^2 phi1^2 phi2 phi4 q congruent 8 modulo 12: 1/60 q^2 phi1^2 phi2 phi4 q congruent 9 modulo 12: 1/60 q^2 phi1^2 phi2 phi4 q congruent 11 modulo 12: 1/60 q^2 phi1^2 phi2 phi4 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, 3 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 6 ], [ 13, 1, 2, 6 ], [ 14, 1, 2, 6 ], [ 16, 1, 2, 6 ], [ 18, 1, 3, 12 ], [ 19, 1, 2, 6 ], [ 23, 1, 4, 12 ], [ 28, 1, 6, 12 ], [ 29, 1, 4, 12 ], [ 42, 1, 3, 10 ], [ 43, 1, 3, 30 ] ] k = 45: F-action on Pi is () [44,1,45] Dynkin type is A_0(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 12: 1/288 q phi1^2 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 2 modulo 12: 1/288 q^2 phi1 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 12: 1/288 q phi1^2 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 4 modulo 12: 1/288 q^2 phi1 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 5 modulo 12: 1/288 q phi1^2 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 7 modulo 12: 1/288 q phi1^2 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 8 modulo 12: 1/288 q^2 phi1 phi2 ( q^3-9*q^2+26*q-24 ) q congruent 9 modulo 12: 1/288 q phi1^2 phi2 ( q^3-8*q^2+18*q-9 ) q congruent 11 modulo 12: 1/288 q phi1^2 phi2 ( q^3-8*q^2+18*q-9 ) 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, 7 ], [ 3, 1, 1, 18 ], [ 4, 1, 1, 28 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 40 ], [ 9, 1, 1, 46 ], [ 10, 1, 1, 36 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 48 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 32 ], [ 15, 1, 1, 48 ], [ 15, 1, 3, 8 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 12 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 64 ], [ 21, 1, 1, 36 ], [ 22, 1, 1, 48 ], [ 22, 1, 2, 24 ], [ 23, 1, 1, 48 ], [ 23, 1, 2, 16 ], [ 24, 1, 1, 72 ], [ 24, 1, 2, 20 ], [ 25, 1, 1, 48 ], [ 25, 1, 5, 24 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 28, 1, 1, 48 ], [ 28, 1, 3, 16 ], [ 28, 1, 5, 6 ], [ 29, 1, 1, 48 ], [ 29, 1, 2, 48 ], [ 29, 1, 3, 24 ], [ 30, 1, 1, 48 ], [ 30, 1, 2, 24 ], [ 31, 1, 1, 48 ], [ 31, 1, 2, 48 ], [ 31, 1, 3, 48 ], [ 33, 1, 1, 96 ], [ 33, 1, 2, 48 ], [ 33, 1, 3, 32 ], [ 34, 1, 2, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 2, 48 ], [ 35, 1, 8, 42 ], [ 37, 1, 1, 48 ], [ 37, 1, 2, 48 ], [ 37, 1, 3, 96 ], [ 39, 1, 2, 96 ], [ 39, 1, 3, 72 ], [ 39, 1, 7, 12 ], [ 39, 1, 8, 96 ], [ 40, 1, 7, 108 ], [ 41, 1, 3, 144 ], [ 41, 1, 13, 72 ], [ 42, 1, 4, 144 ], [ 42, 1, 7, 48 ], [ 42, 1, 17, 96 ], [ 43, 1, 4, 144 ], [ 43, 1, 11, 144 ] ] k = 46: F-action on Pi is () [44,1,46] Dynkin type is A_0(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 12: 1/288 phi1^2 ( q^5+q^4-6*q^3-7*q^2+7*q+16 ) q congruent 2 modulo 12: 1/288 q^2 phi2^2 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 12: 1/288 q phi1 phi2^2 ( q^3-2*q^2-4*q+9 ) q congruent 4 modulo 12: 1/288 q phi1 ( q^5-7*q^3-6*q^2+8*q+16 ) q congruent 5 modulo 12: 1/288 q phi1 phi2^2 ( q^3-2*q^2-4*q+9 ) q congruent 7 modulo 12: 1/288 phi1^2 ( q^5+q^4-6*q^3-7*q^2+7*q+16 ) q congruent 8 modulo 12: 1/288 q^2 phi2^2 ( q^3-3*q^2-2*q+8 ) q congruent 9 modulo 12: 1/288 q phi1 phi2^2 ( q^3-2*q^2-4*q+9 ) q congruent 11 modulo 12: 1/288 q phi1 phi2^2 ( q^3-2*q^2-4*q+9 ) 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 ], [ 4, 1, 1, 12 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 12 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 24 ], [ 12, 1, 2, 16 ], [ 15, 1, 3, 24 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 24 ], [ 17, 1, 3, 12 ], [ 18, 1, 2, 12 ], [ 18, 1, 3, 24 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 24 ], [ 22, 1, 2, 24 ], [ 24, 1, 2, 12 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 48 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 24 ], [ 28, 1, 5, 6 ], [ 30, 1, 2, 24 ], [ 30, 1, 3, 48 ], [ 31, 1, 4, 48 ], [ 33, 1, 11, 48 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 8, 18 ], [ 37, 1, 5, 48 ], [ 39, 1, 4, 96 ], [ 39, 1, 7, 36 ], [ 40, 1, 7, 36 ], [ 40, 1, 14, 72 ], [ 41, 1, 13, 72 ], [ 41, 1, 28, 144 ], [ 42, 1, 18, 96 ], [ 43, 1, 6, 144 ] ] k = 47: F-action on Pi is () [44,1,47] Dynkin type is A_0(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 12: 1/144 phi1^2 ( q^5+4*q^4+6*q^3+5*q^2-2*q-8 ) q congruent 2 modulo 12: 1/144 q^2 phi2 ( q^4+q^3-2*q^2-4 ) q congruent 3 modulo 12: 1/144 q phi1 phi2 ( q^4+2*q^3-q-6 ) q congruent 4 modulo 12: 1/144 q phi1 ( q^5+3*q^4+2*q^3-4*q-8 ) q congruent 5 modulo 12: 1/144 q phi1 phi2 ( q^4+2*q^3-q-6 ) q congruent 7 modulo 12: 1/144 phi1^2 ( q^5+4*q^4+6*q^3+5*q^2-2*q-8 ) q congruent 8 modulo 12: 1/144 q^2 phi2 ( q^4+q^3-2*q^2-4 ) q congruent 9 modulo 12: 1/144 q phi1 phi2 ( q^4+2*q^3-q-6 ) q congruent 11 modulo 12: 1/144 q phi1 phi2 ( q^4+2*q^3-q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 47 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 2, 2 ], [ 12, 1, 2, 16 ], [ 21, 1, 5, 24 ], [ 28, 1, 5, 24 ], [ 33, 1, 11, 48 ], [ 34, 1, 10, 6 ], [ 40, 1, 9, 72 ], [ 42, 1, 9, 48 ] ] k = 48: F-action on Pi is () [44,1,48] Dynkin type is A_0(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 12: 1/96 q phi1^3 phi2 ( q^2-q-5 ) q congruent 2 modulo 12: 1/96 q^2 phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 12: 1/96 q phi1^3 phi2 ( q^2-q-5 ) q congruent 4 modulo 12: 1/96 q^2 phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 5 modulo 12: 1/96 q phi1^3 phi2 ( q^2-q-5 ) q congruent 7 modulo 12: 1/96 q phi1^3 phi2 ( q^2-q-5 ) q congruent 8 modulo 12: 1/96 q^2 phi1 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 9 modulo 12: 1/96 q phi1^3 phi2 ( q^2-q-5 ) q congruent 11 modulo 12: 1/96 q phi1^3 phi2 ( q^2-q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 10 ], [ 4, 1, 2, 12 ], [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 2, 16 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 21, 1, 3, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 3, 16 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 24 ], [ 25, 1, 4, 16 ], [ 25, 1, 7, 16 ], [ 25, 1, 8, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 2, 16 ], [ 28, 1, 4, 6 ], [ 29, 1, 5, 16 ], [ 29, 1, 6, 12 ], [ 30, 1, 5, 8 ], [ 30, 1, 6, 16 ], [ 30, 1, 8, 16 ], [ 31, 1, 5, 16 ], [ 31, 1, 6, 16 ], [ 31, 1, 8, 16 ], [ 33, 1, 4, 32 ], [ 33, 1, 5, 24 ], [ 34, 1, 2, 16 ], [ 34, 1, 7, 16 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 1, 9, 18 ], [ 37, 1, 7, 16 ], [ 37, 1, 8, 24 ], [ 37, 1, 9, 16 ], [ 39, 1, 12, 12 ], [ 39, 1, 13, 32 ], [ 39, 1, 16, 24 ], [ 39, 1, 19, 32 ], [ 40, 1, 8, 36 ], [ 40, 1, 15, 24 ], [ 41, 1, 8, 24 ], [ 41, 1, 17, 48 ], [ 41, 1, 25, 48 ], [ 42, 1, 8, 48 ], [ 42, 1, 19, 32 ], [ 43, 1, 10, 48 ], [ 43, 1, 12, 48 ] ] k = 49: F-action on Pi is () [44,1,49] Dynkin type is A_0(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 12: 1/72 q phi1 phi2 ( q^4-q^2-9*q+3 ) q congruent 2 modulo 12: 1/72 q^2 phi1 phi2 ( q^3-q-6 ) q congruent 3 modulo 12: 1/72 q phi1 phi2 ( q^4-q^2-9*q+3 ) q congruent 4 modulo 12: 1/72 q^2 phi1 phi2 ( q^3-q-6 ) q congruent 5 modulo 12: 1/72 q phi1 phi2 ( q^4-q^2-9*q+3 ) q congruent 7 modulo 12: 1/72 q phi1 phi2 ( q^4-q^2-9*q+3 ) q congruent 8 modulo 12: 1/72 q^2 phi1 phi2 ( q^3-q-6 ) q congruent 9 modulo 12: 1/72 q phi1 phi2 ( q^4-q^2-9*q+3 ) q congruent 11 modulo 12: 1/72 q phi1 phi2 ( q^4-q^2-9*q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 49 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 2 ], [ 15, 1, 3, 8 ], [ 16, 1, 2, 2 ], [ 20, 1, 1, 4 ], [ 21, 1, 5, 18 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 5, 12 ], [ 29, 1, 3, 12 ], [ 32, 1, 9, 18 ], [ 33, 1, 2, 24 ], [ 33, 1, 3, 8 ], [ 34, 1, 9, 18 ], [ 35, 1, 8, 12 ], [ 36, 1, 9, 18 ], [ 37, 1, 3, 12 ], [ 38, 1, 17, 36 ], [ 39, 1, 7, 24 ], [ 40, 1, 19, 36 ], [ 42, 1, 5, 36 ], [ 42, 1, 7, 24 ], [ 43, 1, 5, 36 ] ] k = 50: F-action on Pi is () [44,1,50] Dynkin type is A_0(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 12: 1/72 phi1 ( q^6-3*q^5-q^4-4*q^3+14*q^2+21*q-4 ) q congruent 2 modulo 12: 1/72 q phi2 ( q^5-5*q^4+7*q^3-9*q^2+20*q-12 ) q congruent 3 modulo 12: 1/72 q phi1 phi2 ( q^4-4*q^3+3*q^2-7*q+21 ) q congruent 4 modulo 12: 1/72 q phi1 ( q^5-3*q^4-q^3-3*q^2+8*q+16 ) q congruent 5 modulo 12: 1/72 q phi1 phi2 ( q^4-4*q^3+3*q^2-7*q+21 ) q congruent 7 modulo 12: 1/72 phi1 ( q^6-3*q^5-q^4-4*q^3+14*q^2+21*q-4 ) q congruent 8 modulo 12: 1/72 q phi2 ( q^5-5*q^4+7*q^3-9*q^2+20*q-12 ) q congruent 9 modulo 12: 1/72 q phi1 phi2 ( q^4-4*q^3+3*q^2-7*q+21 ) q congruent 11 modulo 12: 1/72 q phi1 phi2 ( q^4-4*q^3+3*q^2-7*q+21 ) 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, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 3, 12 ], [ 5, 1, 2, 6 ], [ 6, 1, 2, 2 ], [ 11, 1, 1, 6 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 6 ], [ 15, 1, 5, 24 ], [ 16, 1, 1, 6 ], [ 20, 1, 4, 12 ], [ 21, 1, 5, 6 ], [ 23, 1, 3, 12 ], [ 28, 1, 1, 12 ], [ 32, 1, 9, 18 ], [ 33, 1, 10, 24 ], [ 34, 1, 10, 6 ], [ 36, 1, 7, 18 ], [ 38, 1, 19, 36 ], [ 40, 1, 4, 36 ], [ 42, 1, 9, 12 ], [ 43, 1, 14, 36 ] ] k = 51: F-action on Pi is () [44,1,51] Dynkin type is A_0(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 12: 1/24 q phi1 phi2 ( q^4-2*q^3+q^2-5*q+7 ) q congruent 2 modulo 12: 1/24 q phi1^2 phi2 ( q^3-q^2-4 ) q congruent 3 modulo 12: 1/24 q phi1 phi2 ( q^4-2*q^3+q^2-5*q+7 ) q congruent 4 modulo 12: 1/24 q phi1^2 phi2 ( q^3-q^2-4 ) q congruent 5 modulo 12: 1/24 q phi1 phi2 ( q^4-2*q^3+q^2-5*q+7 ) q congruent 7 modulo 12: 1/24 q phi1 phi2 ( q^4-2*q^3+q^2-5*q+7 ) q congruent 8 modulo 12: 1/24 q phi1^2 phi2 ( q^3-q^2-4 ) q congruent 9 modulo 12: 1/24 q phi1 phi2 ( q^4-2*q^3+q^2-5*q+7 ) q congruent 11 modulo 12: 1/24 q phi1 phi2 ( q^4-2*q^3+q^2-5*q+7 ) 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, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 4, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 3, 12 ], [ 12, 1, 5, 4 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 15, 1, 6, 8 ], [ 16, 1, 1, 2 ], [ 20, 1, 3, 4 ], [ 21, 1, 4, 6 ], [ 23, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 32, 1, 10, 6 ], [ 33, 1, 7, 8 ], [ 34, 1, 9, 6 ], [ 36, 1, 9, 6 ], [ 38, 1, 20, 12 ], [ 40, 1, 20, 12 ], [ 42, 1, 10, 12 ], [ 43, 1, 15, 12 ] ] k = 52: F-action on Pi is () [44,1,52] Dynkin type is A_0(q) + T(phi2 phi14) Order of center |Z^F|: phi2 phi14 Numbers of classes in class type: q congruent 1 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 2 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 3 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 4 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 5 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 7 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 8 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 9 modulo 12: 1/14 q phi1 phi2 phi3 phi6 q congruent 11 modulo 12: 1/14 q phi1 phi2 phi3 phi6 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, 2, 2 ], [ 13, 1, 2, 2 ] ] k = 53: F-action on Pi is () [44,1,53] Dynkin type is A_0(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 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-2*q+5 ) q congruent 2 modulo 12: 1/32 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 3 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-2*q+5 ) q congruent 4 modulo 12: 1/32 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 5 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-2*q+5 ) q congruent 7 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-2*q+5 ) q congruent 8 modulo 12: 1/32 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 9 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-2*q+5 ) q congruent 11 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-2*q+5 ) Fusion of maximal tori of C^F in those of G^F: [ 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 10, 8 ], [ 34, 1, 5, 8 ], [ 36, 1, 16, 16 ], [ 40, 1, 25, 8 ], [ 41, 1, 32, 16 ], [ 43, 1, 18, 16 ] ] k = 54: F-action on Pi is () [44,1,54] Dynkin type is A_0(q) + T(phi2 phi4 phi8) Order of center |Z^F|: phi2 phi4 phi8 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1 phi2^2 phi4 phi6 q congruent 2 modulo 12: 1/32 q^7 q congruent 3 modulo 12: 1/32 phi1 phi2^2 phi4 phi6 q congruent 4 modulo 12: 1/32 q^7 q congruent 5 modulo 12: 1/32 phi1 phi2^2 phi4 phi6 q congruent 7 modulo 12: 1/32 phi1 phi2^2 phi4 phi6 q congruent 8 modulo 12: 1/32 q^7 q congruent 9 modulo 12: 1/32 phi1 phi2^2 phi4 phi6 q congruent 11 modulo 12: 1/32 phi1 phi2^2 phi4 phi6 Fusion of maximal tori of C^F in those of G^F: [ 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 3, 4 ], [ 4, 1, 4, 4 ], [ 5, 1, 1, 4 ], [ 15, 1, 7, 8 ], [ 15, 1, 8, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 34, 1, 8, 8 ], [ 36, 1, 11, 16 ], [ 40, 1, 25, 8 ], [ 41, 1, 29, 16 ], [ 43, 1, 20, 16 ] ] k = 55: F-action on Pi is () [44,1,55] Dynkin type is A_0(q) + T(phi2 phi18) Order of center |Z^F|: phi2 phi18 Numbers of classes in class type: q congruent 1 modulo 12: 1/18 q^3 phi1 phi2 phi3 q congruent 2 modulo 12: 1/18 phi2^2 phi6 ( q^3-2 ) q congruent 3 modulo 12: 1/18 q^3 phi1 phi2 phi3 q congruent 4 modulo 12: 1/18 q^3 phi1 phi2 phi3 q congruent 5 modulo 12: 1/18 phi2^2 phi6 ( q^3-2 ) q congruent 7 modulo 12: 1/18 q^3 phi1 phi2 phi3 q congruent 8 modulo 12: 1/18 phi2^2 phi6 ( q^3-2 ) q congruent 9 modulo 12: 1/18 q^3 phi1 phi2 phi3 q congruent 11 modulo 12: 1/18 phi2^2 phi6 ( q^3-2 ) Fusion of maximal tori of C^F in those of G^F: [ 55 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 6, 1, 2, 2 ], [ 12, 1, 4, 6 ] ] k = 56: F-action on Pi is () [44,1,56] Dynkin type is A_0(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 12: 1/20 q^2 phi1^2 phi2 phi4 q congruent 2 modulo 12: 1/20 q^2 phi1^2 phi2 phi4 q congruent 3 modulo 12: 1/20 q^2 phi1^2 phi2 phi4 q congruent 4 modulo 12: 1/20 q^2 phi1^2 phi2 phi4 q congruent 5 modulo 12: 1/20 q^2 phi1^2 phi2 phi4 q congruent 7 modulo 12: 1/20 q^2 phi1^2 phi2 phi4 q congruent 8 modulo 12: 1/20 q^2 phi1^2 phi2 phi4 q congruent 9 modulo 12: 1/20 q^2 phi1^2 phi2 phi4 q congruent 11 modulo 12: 1/20 q^2 phi1^2 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 56 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 18, 1, 2, 4 ], [ 19, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 29, 1, 2, 4 ], [ 42, 1, 2, 10 ], [ 43, 1, 2, 10 ] ] k = 57: F-action on Pi is () [44,1,57] Dynkin type is A_0(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 12: 1/48 q phi1^3 phi2 ( q^2-q-1 ) q congruent 2 modulo 12: 1/48 q^3 phi1^2 phi2 ( q-2 ) q congruent 3 modulo 12: 1/48 q phi1^3 phi2 ( q^2-q-1 ) q congruent 4 modulo 12: 1/48 q^3 phi1^2 phi2 ( q-2 ) q congruent 5 modulo 12: 1/48 q phi1^3 phi2 ( q^2-q-1 ) q congruent 7 modulo 12: 1/48 q phi1^3 phi2 ( q^2-q-1 ) q congruent 8 modulo 12: 1/48 q^3 phi1^2 phi2 ( q-2 ) q congruent 9 modulo 12: 1/48 q phi1^3 phi2 ( q^2-q-1 ) q congruent 11 modulo 12: 1/48 q phi1^3 phi2 ( q^2-q-1 ) 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, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 1, 5, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 1, 4 ], [ 21, 1, 3, 4 ], [ 24, 1, 4, 4 ], [ 25, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 28, 1, 4, 6 ], [ 30, 1, 7, 8 ], [ 33, 1, 8, 24 ], [ 34, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 1, 9, 6 ], [ 37, 1, 10, 8 ], [ 39, 1, 16, 12 ], [ 39, 1, 17, 16 ], [ 40, 1, 15, 12 ], [ 41, 1, 33, 24 ], [ 42, 1, 16, 16 ], [ 43, 1, 8, 24 ] ] k = 58: F-action on Pi is () [44,1,58] Dynkin type is A_0(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 12: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 2 modulo 12: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 3 modulo 12: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 4 modulo 12: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 5 modulo 12: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 7 modulo 12: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 8 modulo 12: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 9 modulo 12: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) q congruent 11 modulo 12: 1/48 q phi1^2 phi2^2 ( q^2-q-1 ) 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, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 4 ], [ 21, 1, 2, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 26, 1, 5, 4 ], [ 28, 1, 5, 6 ], [ 29, 1, 3, 12 ], [ 30, 1, 4, 8 ], [ 34, 1, 6, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 6 ], [ 37, 1, 4, 8 ], [ 39, 1, 3, 12 ], [ 39, 1, 9, 16 ], [ 40, 1, 14, 12 ], [ 41, 1, 38, 24 ], [ 42, 1, 14, 16 ], [ 43, 1, 7, 24 ] ] k = 59: F-action on Pi is () [44,1,59] Dynkin type is A_0(q) + T(phi2 phi6 phi12) Order of center |Z^F|: phi2 phi6 phi12 Numbers of classes in class type: q congruent 1 modulo 12: 1/24 q^2 phi1^2 phi2 phi3 q congruent 2 modulo 12: 1/24 q^5 phi1 phi2 q congruent 3 modulo 12: 1/24 q^2 phi1^2 phi2 phi3 q congruent 4 modulo 12: 1/24 q^5 phi1 phi2 q congruent 5 modulo 12: 1/24 q^2 phi1^2 phi2 phi3 q congruent 7 modulo 12: 1/24 q^2 phi1^2 phi2 phi3 q congruent 8 modulo 12: 1/24 q^5 phi1 phi2 q congruent 9 modulo 12: 1/24 q^2 phi1^2 phi2 phi3 q congruent 11 modulo 12: 1/24 q^2 phi1^2 phi2 phi3 Fusion of maximal tori of C^F in those of G^F: [ 59 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 6, 1, 2, 2 ], [ 34, 1, 10, 6 ], [ 40, 1, 11, 12 ] ] k = 60: F-action on Pi is () [44,1,60] Dynkin type is A_0(q) + T(phi2 phi6 phi10) Order of center |Z^F|: phi2 phi6 phi10 Numbers of classes in class type: q congruent 1 modulo 12: 1/30 q^2 phi1^2 phi2 phi4 q congruent 2 modulo 12: 1/30 q^2 phi1^2 phi2 phi4 q congruent 3 modulo 12: 1/30 q^2 phi1^2 phi2 phi4 q congruent 4 modulo 12: 1/30 q^2 phi1^2 phi2 phi4 q congruent 5 modulo 12: 1/30 q^2 phi1^2 phi2 phi4 q congruent 7 modulo 12: 1/30 q^2 phi1^2 phi2 phi4 q congruent 8 modulo 12: 1/30 q^2 phi1^2 phi2 phi4 q congruent 9 modulo 12: 1/30 q^2 phi1^2 phi2 phi4 q congruent 11 modulo 12: 1/30 q^2 phi1^2 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 60 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 28, 1, 4, 6 ], [ 29, 1, 6, 6 ], [ 42, 1, 3, 10 ] ]