Centralizers of semisimple elements in E7(q)_ad -------------------------------------------- |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 Numbers of classes in class type: q congruent 1 modulo 12: 1 q congruent 2 modulo 12: 1 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 1 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 1 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 1 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 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 1 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 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 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: 1 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 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 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: 1 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, 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 = 2: Omega of order 2, action on Pi: <( 1, 6)( 3, 5)( 7,126)> k = 1: F-action on Pi is () [4,2,1] Dynkin type is (A_3(q) + A_3(q) + A_1(q)).2 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, 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) [4,2,2] Dynkin type is (^2A_3(q) + ^2A_3(q) + A_1(q)).2 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: [ 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) [4,2,3] Dynkin type is (A_3(q^2) + A_1(q)).2 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: [ 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) [4,2,4] Dynkin type is (A_3(q^2) + A_1(q)).2 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: [ 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 = 2: Omega of order 2, action on Pi: <( 1, 6)( 3, 5)( 7,126)> k = 1: F-action on Pi is () [5,2,1] Dynkin type is A_7(q).2 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: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 1 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) [5,2,2] Dynkin type is ^2A_7(q).2 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: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 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 ], [ 6, 2, 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 ], [ 6, 2, 2, 1 ] ] j = 2: Omega of order 2, action on Pi: <(1,6)(3,5)> k = 1: F-action on Pi is () [6,2,1] Dynkin type is (E_6(q) + T(phi1)).2 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: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 1 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) [6,2,2] Dynkin type is (^2E_6(q) + T(phi2)).2 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: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 1 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 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, 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 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: [ 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-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-4 ) q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 ( q-5 ) 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, 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 ], [ 5, 2, 1, 1 ] ] 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 phi1 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 phi1 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-3 ) 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 ], [ 5, 2, 2, 1 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-7 ) 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-5 ) 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, 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 ], [ 4, 2, 1, 2 ] ] 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 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-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 phi1 q congruent 11 modulo 12: 1/2 ( 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 ], [ 4, 2, 2, 2 ] ] 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 2, q congruent 1 modulo 2 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: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( 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 ], [ 4, 2, 1, 2 ], [ 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 2, q congruent 1 modulo 2 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: 1/4 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 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 ], [ 4, 2, 1, 2 ], [ 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 2, q congruent 1 modulo 2 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: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( 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 ], [ 4, 2, 2, 2 ], [ 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 2, q congruent 1 modulo 2 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: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( 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 ], [ 4, 2, 2, 2 ], [ 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 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-4 ) q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 ( q-5 ) 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, 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 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 phi1 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 phi1 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-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 ], [ 6, 2, 1, 1 ], [ 12, 2, 1, 6 ] ] 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 ], [ 6, 2, 2, 1 ], [ 12, 2, 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 ], [ 6, 2, 1, 1 ] ] 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 ], [ 6, 2, 2, 1 ] ] 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 ], [ 6, 2, 1, 1 ], [ 12, 2, 4, 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 ], [ 6, 2, 2, 1 ], [ 12, 2, 3, 6 ] ] j = 2: Omega of order 2, action on Pi: <(2,6)(4,7)> k = 1: F-action on Pi is () [12,2,1] Dynkin type is (A_2(q) + A_2(q) + A_2(q) + T(phi1)).2 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: 1 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: 1 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, 2 ], [ 6, 2, 1, 1 ] ] k = 2: F-action on Pi is (2,6)(4,7) [12,2,2] Dynkin type is (A_2(q) + A_2(q^2) + T(phi2)).2 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: 1 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: 1 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, 2, 2, 1 ] ] k = 3: F-action on Pi is ( 1,126)( 2, 4)( 6, 7) [12,2,3] Dynkin type is (^2A_2(q) + ^2A_2(q) + ^2A_2(q) + T(phi2)).2 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: 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: 0 q congruent 11 modulo 12: 1 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, 2 ], [ 6, 2, 2, 1 ] ] k = 4: F-action on Pi is ( 1,126)( 2, 7)( 4, 6) [12,2,4] Dynkin type is (^2A_2(q) + A_2(q^2) + T(phi1)).2 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: 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: 0 q congruent 11 modulo 12: 1 Fusion of maximal tori of C^F in those of G^F: [ 3, 40, 20, 35, 13, 51, 16, 57, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 2, 1, 1 ] ] 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-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, 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 ], [ 5, 2, 1, 1 ] ] 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 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, 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 ], [ 5, 2, 2, 1 ] ] 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-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, 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 14, 2, 1, 1 ] ] 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 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: [ 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 14, 2, 2, 1 ] ] i = 15: Pi = [ 1, 3, 5, 6, 7, 126 ] j = 4: Omega of order 2, action on Pi: <( 1, 6)( 3, 5)( 7,126)> k = 1: F-action on Pi is () [15,4,1] Dynkin type is (A_3(q) + A_3(q) + T(phi1)).2 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: 1/4 ( q-5 ) 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 2, 1, 2 ], [ 5, 2, 1, 2 ], [ 16, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 3,126)( 5, 7) [15,4,2] Dynkin type is (^2A_3(q) + ^2A_3(q) + T(phi1)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 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, 2, 2, 2 ], [ 16, 1, 1, 2 ] ] k = 3: F-action on Pi is () [15,4,3] Dynkin type is (A_3(q) + A_3(q) + T(phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 phi2 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, 2, 1, 2 ], [ 16, 1, 2, 2 ] ] k = 4: F-action on Pi is ( 3,126)( 5, 7) [15,4,4] Dynkin type is (^2A_3(q) + ^2A_3(q) + T(phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 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, 2, 2, 2 ], [ 5, 2, 2, 2 ], [ 16, 1, 2, 2 ] ] k = 5: F-action on Pi is ( 1, 6)( 3, 5)( 7,126) [15,4,5] Dynkin type is (A_3(q^2) + T(phi1)).2 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: 1/4 ( q-5 ) 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) 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, 2, 3, 2 ], [ 5, 2, 2, 2 ], [ 16, 1, 1, 2 ] ] k = 6: F-action on Pi is ( 1, 6)( 3, 7)( 5,126) [15,4,6] Dynkin type is (A_3(q^2) + T(phi1)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 2, 4, 2 ], [ 16, 1, 1, 2 ] ] k = 7: F-action on Pi is ( 1, 6)( 3, 5)( 7,126) [15,4,7] Dynkin type is (A_3(q^2) + T(phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 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, 2, 3, 2 ], [ 16, 1, 2, 2 ] ] k = 8: F-action on Pi is ( 1, 6)( 3, 7)( 5,126) [15,4,8] Dynkin type is (A_3(q^2) + T(phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 2, 4, 2 ], [ 5, 2, 1, 2 ], [ 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 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, 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 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: [ 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 2, q congruent 1 modulo 2 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: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( 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 ], [ 17, 2, 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 phi2 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 ], [ 17, 2, 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 2, q congruent 1 modulo 2 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: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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 ], [ 17, 2, 3, 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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 ], [ 17, 2, 4, 2 ] ] j = 2: Omega of order 2, action on Pi: <( 3, 5)( 7,126)> k = 1: F-action on Pi is () [17,2,1] Dynkin type is (D_4(q) + A_1(q) + A_1(q) + T(phi1)).2 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, 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, 1 ] ] k = 2: F-action on Pi is ( 3, 5)( 7,126) [17,2,2] Dynkin type is (^2D_4(q) + A_1(q^2) + T(phi2)).2 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: [ 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 ] ] k = 3: F-action on Pi is () [17,2,3] Dynkin type is (D_4(q) + A_1(q) + A_1(q) + T(phi2)).2 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: [ 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, 1 ] ] k = 4: F-action on Pi is ( 3, 5)( 7,126) [17,2,4] Dynkin type is (^2D_4(q) + A_1(q^2) + T(phi1)).2 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: [ 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 ] ] 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^2-6*q+9 ) q congruent 2 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/4 ( q^2-6*q+9 ) 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 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 16, 1, 1, 2 ], [ 18, 2, 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 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^2 q congruent 7 modulo 12: 1/4 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^2 q congruent 11 modulo 12: 1/4 phi1^2 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 ], [ 18, 2, 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 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^2 q congruent 7 modulo 12: 1/4 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^2 q congruent 11 modulo 12: 1/4 phi1^2 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 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 2, 2 ], [ 18, 2, 3, 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 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^2 q congruent 7 modulo 12: 1/4 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^2 q congruent 11 modulo 12: 1/4 phi1^2 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 ], [ 18, 2, 4, 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^2-8*q+17 ) q congruent 2 modulo 12: 1/2 ( q^2-7*q+10 ) q congruent 3 modulo 12: 1/2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/2 ( q^2-7*q+12 ) q congruent 5 modulo 12: 1/2 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/2 ( q^2-8*q+17 ) q congruent 8 modulo 12: 1/2 ( q^2-7*q+10 ) q congruent 9 modulo 12: 1/2 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/2 ( q^2-8*q+15 ) 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ] ] 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-3 ) q congruent 2 modulo 12: 1/2 phi1 ( q-2 ) q congruent 3 modulo 12: 1/2 phi1 ( q-3 ) q congruent 4 modulo 12: 1/2 q ( q-3 ) q congruent 5 modulo 12: 1/2 ( q^2-4*q+5 ) q congruent 7 modulo 12: 1/2 phi1 ( q-3 ) q congruent 8 modulo 12: 1/2 phi1 ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 ( q-3 ) q congruent 11 modulo 12: 1/2 ( q^2-4*q+5 ) 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 13, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ] ] 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^2-12*q+39 ) 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^2-10*q+24 ) q congruent 5 modulo 12: 1/4 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/4 ( q^2-12*q+35 ) q congruent 8 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/4 ( q^2-10*q+25 ) 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, 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 20, 2, 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-5 ) q congruent 2 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/4 q ( q-4 ) q congruent 5 modulo 12: 1/4 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/4 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/4 phi1 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q^2-8*q+19 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 20, 2, 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 ], [ 4, 2, 4, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 2 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 20, 2, 3, 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 ], [ 4, 2, 3, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 20, 2, 4, 2 ] ] j = 2: Omega of order 2, action on Pi: <(1,6)(3,5)> k = 1: F-action on Pi is () [20,2,1] Dynkin type is (A_2(q) + A_2(q) + A_1(q) + T(phi1^2)).2 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-7 ) 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-5 ) 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, 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, 2 ], [ 4, 2, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 11, 1, 1, 2 ], [ 12, 2, 1, 2 ], [ 14, 2, 1, 1 ] ] k = 2: F-action on Pi is (1,3)(5,6) [20,2,2] Dynkin type is (^2A_2(q) + ^2A_2(q) + A_1(q) + T(phi2^2)).2 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 ( q-3 ) 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-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, 15, 36, 48, 15, 19, 38 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 11, 1, 2, 2 ], [ 12, 2, 3, 2 ], [ 14, 2, 2, 1 ] ] k = 3: F-action on Pi is (1,5)(3,6) [20,2,3] Dynkin type is (A_2(q^2) + A_1(q) + T(phi1 phi2)).2 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 ( q-3 ) 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-5 ) 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, 2, 4, 2 ], [ 5, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 2 ], [ 12, 2, 4, 2 ], [ 14, 2, 1, 1 ] ] k = 4: F-action on Pi is (1,6)(3,5) [20,2,4] Dynkin type is (A_2(q^2) + A_1(q) + T(phi1 phi2)).2 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-7 ) 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-5 ) 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: [ 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, 2, 3, 2 ], [ 5, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 2 ], [ 12, 2, 2, 2 ], [ 14, 2, 2, 1 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 ( q^2-11*q+34 ) q congruent 2 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/12 ( q^2-11*q+24 ) q congruent 4 modulo 12: 1/12 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/12 ( q^2-11*q+30 ) q congruent 7 modulo 12: 1/12 ( q^2-11*q+28 ) q congruent 8 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/12 ( q^2-11*q+30 ) q congruent 11 modulo 12: 1/12 ( 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 ], [ 4, 2, 1, 6 ], [ 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-2 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 q ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 q ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 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 ], [ 4, 2, 1, 2 ], [ 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-2 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 ( 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 ], [ 4, 2, 2, 2 ], [ 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q phi1 q congruent 2 modulo 12: 1/6 phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi1 q congruent 4 modulo 12: 1/6 q phi1 q congruent 5 modulo 12: 1/6 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 q congruent 8 modulo 12: 1/6 phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi1 q congruent 11 modulo 12: 1/6 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 phi1 ( q+2 ) q congruent 2 modulo 12: 1/6 q phi2 q congruent 3 modulo 12: 1/6 q phi2 q congruent 4 modulo 12: 1/6 phi1 ( q+2 ) q congruent 5 modulo 12: 1/6 q phi2 q congruent 7 modulo 12: 1/6 phi1 ( q+2 ) q congruent 8 modulo 12: 1/6 q phi2 q congruent 9 modulo 12: 1/6 q phi2 q congruent 11 modulo 12: 1/6 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 phi1 ( q-6 ) q congruent 2 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/12 ( q^2-7*q+12 ) q congruent 4 modulo 12: 1/12 q ( q-4 ) q congruent 5 modulo 12: 1/12 ( q^2-7*q+10 ) q congruent 7 modulo 12: 1/12 ( q^2-7*q+12 ) q congruent 8 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/12 phi1 ( q-6 ) q congruent 11 modulo 12: 1/12 ( 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 ], [ 4, 2, 2, 6 ], [ 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 ( q^2-10*q+29 ) 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^2-10*q+25 ) q congruent 7 modulo 12: 1/4 ( q^2-10*q+25 ) q congruent 8 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/4 ( q^2-10*q+25 ) 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, 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ] ] 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 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, 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ] ] 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 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: [ 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ] ] 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 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^2-6*q+9 ) q congruent 4 modulo 12: 1/4 q ( q-4 ) q congruent 5 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/4 ( q^2-6*q+9 ) 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^2-6*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 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ] ] 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+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, 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 16, 1, 1, 2 ], [ 23, 2, 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 16, 1, 2, 2 ], [ 23, 2, 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 16, 1, 1, 2 ], [ 23, 2, 3, 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 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: [ 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 16, 1, 2, 2 ], [ 23, 2, 4, 2 ] ] j = 2: Omega of order 2, action on Pi: <(1,6)(3,5)> k = 1: F-action on Pi is () [23,2,1] Dynkin type is (A_5(q) + T(phi1^2)).2 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-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, 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, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 14, 2, 1, 1 ], [ 16, 1, 1, 2 ] ] k = 2: F-action on Pi is () [23,2,2] Dynkin type is (A_5(q) + T(phi1 phi2)).2 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 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, 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, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 14, 2, 1, 1 ], [ 16, 1, 2, 2 ] ] k = 3: F-action on Pi is (1,6)(3,5) [23,2,3] Dynkin type is (^2A_5(q) + T(phi1 phi2)).2 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-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: [ 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, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 14, 2, 2, 1 ], [ 16, 1, 1, 2 ] ] k = 4: F-action on Pi is (1,6)(3,5) [23,2,4] Dynkin type is (^2A_5(q) + T(phi2^2)).2 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 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: [ 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, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 14, 2, 2, 1 ], [ 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^2-9*q+24 ) q congruent 2 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/4 ( q^2-9*q+18 ) q congruent 4 modulo 12: 1/4 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/4 ( q^2-9*q+20 ) q congruent 7 modulo 12: 1/4 ( q^2-9*q+22 ) q congruent 8 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/4 ( q^2-9*q+20 ) q congruent 11 modulo 12: 1/4 ( q^2-9*q+18 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 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-2 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 q ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 q ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 q ( 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 ], [ 4, 2, 1, 2 ], [ 9, 1, 1, 2 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 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-4 ) q congruent 2 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/4 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/4 q ( q-4 ) q congruent 5 modulo 12: 1/4 ( q^2-5*q+8 ) q congruent 7 modulo 12: 1/4 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/4 phi1 ( q-4 ) q congruent 11 modulo 12: 1/4 ( q^2-5*q+10 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 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-2 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 ( q^2-3*q+4 ) 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 ], [ 4, 2, 2, 2 ], [ 9, 1, 2, 2 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 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^2-10*q+25 ) 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^2-10*q+25 ) 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^2-10*q+25 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 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 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: [ 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 25, 2, 2, 4 ], [ 25, 3, 2, 4 ], [ 25, 4, 2, 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-5 ) 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-5 ) 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-5 ) 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 ], [ 4, 2, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 25, 2, 3, 4 ], [ 25, 3, 3, 4 ], [ 25, 4, 3, 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 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: [ 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 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-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, 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 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 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1^2 q congruent 7 modulo 12: 1/8 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1^2 q congruent 11 modulo 12: 1/8 phi2 ( q-3 ) 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 ], [ 4, 2, 1, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ], [ 25, 4, 6, 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 ( 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: [ 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 25, 2, 7, 4 ], [ 25, 3, 7, 4 ], [ 25, 4, 7, 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^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-5 ) q congruent 7 modulo 12: 1/8 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-5 ) q congruent 11 modulo 12: 1/8 ( q^2-6*q+9 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 4 ] ] j = 4: Omega of order 2, action on Pi: <( 3,126)( 5, 7)> k = 1: F-action on Pi is () [25,4,1] Dynkin type is (A_3(q) + A_1(q) + A_1(q) + T(phi1^2)).2 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: 1/4 ( q-5 ) 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 1 ], [ 5, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 15, 2, 1, 4 ], [ 17, 2, 1, 2 ] ] k = 2: F-action on Pi is (5,7) [25,4,2] Dynkin type is (A_3(q) + A_1(q^2) + T(phi1 phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( 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 ], [ 5, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 15, 2, 1, 4 ], [ 17, 2, 4, 2 ] ] k = 3: F-action on Pi is ( 3,126)( 5, 7) [25,4,3] Dynkin type is (^2A_3(q) + A_1(q^2) + T(phi1^2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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 ], [ 7, 1, 1, 2 ], [ 15, 2, 2, 4 ], [ 17, 2, 4, 2 ] ] k = 4: F-action on Pi is ( 3,126) [25,4,4] Dynkin type is (^2A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 phi2 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, 1 ], [ 7, 1, 2, 2 ], [ 15, 2, 2, 4 ], [ 17, 2, 1, 2 ] ] k = 5: F-action on Pi is () [25,4,5] Dynkin type is (A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( 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, 1 ], [ 7, 1, 1, 2 ], [ 15, 2, 3, 4 ], [ 17, 2, 3, 2 ] ] k = 6: F-action on Pi is (5,7) [25,4,6] Dynkin type is (A_3(q) + A_1(q^2) + T(phi2^2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 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 ], [ 7, 1, 2, 2 ], [ 15, 2, 3, 4 ], [ 17, 2, 2, 2 ] ] k = 7: F-action on Pi is ( 3,126)( 5, 7) [25,4,7] Dynkin type is (^2A_3(q) + A_1(q^2) + T(phi1 phi2)).2 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: 1/4 ( q-5 ) 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( 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 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 15, 2, 4, 4 ], [ 17, 2, 2, 2 ] ] k = 8: F-action on Pi is ( 3,126) [25,4,8] Dynkin type is (^2A_3(q) + A_1(q) + A_1(q) + T(phi2^2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 1 ], [ 5, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 15, 2, 4, 4 ], [ 17, 2, 3, 2 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/8 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/8 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/8 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/8 ( 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 ], [ 17, 2, 1, 4 ] ] 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 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, 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q-3 ) q congruent 2 modulo 12: 1/8 q ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 ( q-3 ) q congruent 4 modulo 12: 1/8 q ( q-2 ) 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: 1/8 q ( q-2 ) 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: [ 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 ], [ 17, 2, 3, 4 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^2 q congruent 7 modulo 12: 1/4 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^2 q congruent 11 modulo 12: 1/4 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 phi2 q congruent 2 modulo 12: 1/4 q^2 q congruent 3 modulo 12: 1/4 phi1 phi2 q congruent 4 modulo 12: 1/4 q^2 q congruent 5 modulo 12: 1/4 phi1 phi2 q congruent 7 modulo 12: 1/4 phi1 phi2 q congruent 8 modulo 12: 1/4 q^2 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, 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 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 ( q^2-14*q+45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/32 ( 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 ], [ 4, 2, 1, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ], [ 26, 1, 1, 8 ], [ 27, 2, 1, 16 ], [ 27, 3, 1, 16 ] ] 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 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 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: [ 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 27, 2, 2, 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 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q-5 ) q congruent 7 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q-5 ) q congruent 11 modulo 12: 1/32 ( q^2-10*q+21 ) 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 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 26, 1, 1, 8 ], [ 27, 2, 3, 16 ], [ 27, 3, 2, 16 ] ] 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: 1/16 phi1 ( q-5 ) 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 ( q-5 ) q congruent 7 modulo 12: 1/16 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q-5 ) q congruent 11 modulo 12: 1/16 phi2 ( q-3 ) 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 ], [ 4, 2, 3, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 27, 2, 4, 8 ], [ 27, 3, 3, 8 ], [ 27, 3, 14, 8 ] ] 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: 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: [ 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 ], [ 4, 2, 3, 2 ], [ 4, 2, 4, 2 ], [ 26, 1, 5, 4 ], [ 27, 2, 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: 1/16 phi1^2 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 phi1^2 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 phi1^2 q congruent 11 modulo 12: 1/16 ( q^2-6*q+9 ) 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 ], [ 4, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 26, 1, 2, 4 ], [ 27, 2, 6, 8 ], [ 27, 3, 4, 8 ], [ 27, 3, 13, 8 ] ] 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 2, 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: [ 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 ], [ 27, 2, 7, 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 2, 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: [ 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 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 6 ], [ 26, 1, 2, 4 ], [ 27, 2, 8, 8 ], [ 27, 3, 5, 8 ], [ 27, 3, 9, 8 ] ] 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 2, 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: [ 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ] ] 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: 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: [ 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 ], [ 27, 2, 10, 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: 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: [ 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 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 26, 1, 3, 8 ], [ 27, 2, 11, 8 ], [ 27, 3, 7, 8 ], [ 27, 3, 8, 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 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q-5 ) q congruent 7 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q-5 ) q congruent 11 modulo 12: 1/32 ( q^2-10*q+21 ) 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 ], [ 4, 2, 2, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 24 ], [ 17, 2, 3, 12 ], [ 26, 1, 3, 8 ], [ 27, 2, 12, 16 ], [ 27, 3, 11, 16 ] ] 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 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q-5 ) q congruent 7 modulo 12: 1/32 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q-5 ) q congruent 11 modulo 12: 1/32 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 ], [ 4, 2, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 26, 1, 3, 8 ], [ 27, 2, 13, 16 ], [ 27, 3, 12, 16 ] ] 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: 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, 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 ], [ 17, 2, 1, 4 ], [ 17, 2, 4, 4 ], [ 26, 1, 1, 8 ], [ 27, 2, 14, 8 ], [ 27, 3, 15, 8 ], [ 27, 3, 16, 8 ] ] j = 3: Omega of order 2, action on Pi: <( 3, 7)( 5,126)> k = 1: F-action on Pi is () [27,3,1] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2)).2 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, 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, 3 ], [ 4, 2, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 6 ] ] k = 2: F-action on Pi is ( 3,126)( 5, 7) [27,3,2] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1^2)).2 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: [ 4, 41, 41, 9, 33, 10, 10, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ] ] k = 3: F-action on Pi is ( 3, 5)( 7,126) [27,3,3] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2 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: [ 33, 10, 10, 42, 5, 43, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ] ] k = 4: F-action on Pi is ( 3, 7)( 5,126) [27,3,4] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2 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: [ 35, 13, 13, 42, 3, 40, 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ] ] k = 5: F-action on Pi is () [27,3,5] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2)).2 Order of center |Z^F|: phi1 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: [ 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, 3 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ] ] k = 6: F-action on Pi is ( 3,126)( 5, 7) [27,3,6] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2 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, 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 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ] ] k = 7: F-action on Pi is ( 3, 5)( 7,126) [27,3,7] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi2^2)).2 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, 43, 12, 34, 11, 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 ], [ 17, 2, 3, 2 ] ] k = 8: F-action on Pi is ( 3, 7)( 5,126) [27,3,8] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi2^2)).2 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: [ 5, 43, 43, 12, 34, 11, 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 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ] ] k = 9: F-action on Pi is () [27,3,9] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2)).2 Order of center |Z^F|: 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, 4, 33, 4, 35, 35, 5, 4, 35, 35, 5, 33, 5, 5, 34, 4, 35, 35, 5, 35, 3, 5, 34, 35, 5, 3, 34, 5, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ] ] k = 10: F-action on Pi is ( 3,126)( 5, 7) [27,3,10] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2 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: [ 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, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ] ] k = 11: F-action on Pi is () [27,3,11] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2)).2 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: [ 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, 3 ], [ 4, 2, 2, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 6 ] ] k = 12: F-action on Pi is ( 3,126)( 5, 7) [27,3,12] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi2^2)).2 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, 40, 12, 34, 11, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ] ] k = 13: F-action on Pi is ( 3, 5)( 7,126) [27,3,13] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2 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: [ 35, 13, 13, 42, 3, 40, 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ] ] k = 14: F-action on Pi is ( 3, 7)( 5,126) [27,3,14] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2 Order of center |Z^F|: phi1 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: [ 33, 10, 10, 42, 5, 43, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 3, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ] ] k = 15: F-action on Pi is ( 3, 5)( 7,126) [27,3,15] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1^2)).2 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: [ 4, 41, 41, 9, 35, 13, 13, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ] ] k = 16: F-action on Pi is ( 3, 7)( 5,126) [27,3,16] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1^2)).2 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: [ 4, 41, 41, 9, 35, 13, 13, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 4 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 ( q^2-8*q+19 ) q congruent 2 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/12 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/12 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/12 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/12 ( q^2-8*q+19 ) q congruent 8 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/12 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/12 ( 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 ], [ 28, 2, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^2 q congruent 7 modulo 12: 1/4 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^2 q congruent 11 modulo 12: 1/4 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 ], [ 28, 2, 2, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^2 q congruent 7 modulo 12: 1/4 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^2 q congruent 11 modulo 12: 1/4 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 ], [ 28, 2, 4, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q phi1 q congruent 2 modulo 12: 1/6 phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi1 q congruent 4 modulo 12: 1/6 q phi1 q congruent 5 modulo 12: 1/6 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 q congruent 8 modulo 12: 1/6 phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi1 q congruent 11 modulo 12: 1/6 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 ], [ 28, 2, 5, 3 ] ] k = 5: F-action on Pi is () [28,1,5] Dynkin type is A_5(q) + T(phi3) Order of center |Z^F|: phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 phi1 ( q+2 ) q congruent 2 modulo 12: 1/6 q phi2 q congruent 3 modulo 12: 1/6 q phi2 q congruent 4 modulo 12: 1/6 phi1 ( q+2 ) q congruent 5 modulo 12: 1/6 q phi2 q congruent 7 modulo 12: 1/6 phi1 ( q+2 ) q congruent 8 modulo 12: 1/6 q phi2 q congruent 9 modulo 12: 1/6 q phi2 q congruent 11 modulo 12: 1/6 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 ], [ 28, 2, 3, 3 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 phi1 ( q-3 ) q congruent 2 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/12 phi1 ( q-3 ) q congruent 4 modulo 12: 1/12 q ( q-4 ) q congruent 5 modulo 12: 1/12 ( q^2-4*q+7 ) q congruent 7 modulo 12: 1/12 phi1 ( q-3 ) q congruent 8 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/12 phi1 ( q-3 ) q congruent 11 modulo 12: 1/12 ( 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 ], [ 28, 2, 6, 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^3-13*q^2+55*q-79 ) q congruent 2 modulo 12: 1/12 ( q^3-13*q^2+52*q-60 ) q congruent 3 modulo 12: 1/12 ( q^3-13*q^2+55*q-75 ) q congruent 4 modulo 12: 1/12 ( q^3-13*q^2+52*q-64 ) q congruent 5 modulo 12: 1/12 ( q^3-13*q^2+55*q-75 ) q congruent 7 modulo 12: 1/12 ( q^3-13*q^2+55*q-79 ) q congruent 8 modulo 12: 1/12 ( q^3-13*q^2+52*q-60 ) q congruent 9 modulo 12: 1/12 ( q^3-13*q^2+55*q-75 ) q congruent 11 modulo 12: 1/12 ( q^3-13*q^2+55*q-75 ) 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 6 ], [ 6, 2, 1, 3 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 6 ], [ 13, 1, 1, 6 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 3 ], [ 16, 1, 1, 6 ], [ 18, 1, 1, 12 ], [ 18, 2, 1, 6 ], [ 19, 1, 1, 6 ], [ 23, 1, 1, 12 ], [ 23, 2, 1, 6 ], [ 28, 1, 1, 12 ], [ 28, 2, 1, 6 ], [ 29, 2, 1, 6 ] ] 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 phi1^2 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/4 phi1^2 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q^2-5*q+6 ) q congruent 5 modulo 12: 1/4 phi1^2 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1^2 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/4 phi1^2 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1^2 ( q-3 ) 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 16, 1, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 19, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 23, 2, 2, 2 ], [ 28, 1, 3, 4 ], [ 28, 2, 4, 2 ], [ 29, 2, 2, 2 ] ] 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^2-2 ) q congruent 2 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 12: 1/6 q phi2 ( q-2 ) 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 ], [ 5, 2, 1, 1 ], [ 8, 1, 1, 2 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 29, 2, 3, 3 ] ] 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^2-6*q+9 ) q congruent 2 modulo 12: 1/12 ( q^3-7*q^2+12*q-4 ) q congruent 3 modulo 12: 1/12 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/12 q ( q^2-7*q+12 ) q congruent 5 modulo 12: 1/12 ( q^3-7*q^2+15*q-13 ) q congruent 7 modulo 12: 1/12 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/12 ( q^3-7*q^2+12*q-4 ) q congruent 9 modulo 12: 1/12 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/12 ( q^3-7*q^2+15*q-13 ) 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 6 ], [ 6, 2, 2, 3 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 6 ], [ 13, 1, 2, 6 ], [ 14, 1, 2, 6 ], [ 14, 2, 2, 3 ], [ 16, 1, 2, 6 ], [ 18, 1, 3, 12 ], [ 18, 2, 3, 6 ], [ 19, 1, 2, 6 ], [ 23, 1, 4, 12 ], [ 23, 2, 4, 6 ], [ 28, 1, 6, 12 ], [ 28, 2, 6, 6 ], [ 29, 2, 4, 6 ] ] 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 phi1^3 q congruent 2 modulo 12: 1/4 q phi1 ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^3 q congruent 4 modulo 12: 1/4 q phi1 ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^3 q congruent 7 modulo 12: 1/4 phi1^3 q congruent 8 modulo 12: 1/4 q phi1 ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^3 q congruent 11 modulo 12: 1/4 phi1^3 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 13, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 16, 1, 1, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 19, 1, 2, 2 ], [ 23, 1, 3, 4 ], [ 23, 2, 3, 2 ], [ 28, 1, 2, 4 ], [ 28, 2, 2, 2 ], [ 29, 2, 5, 2 ] ] 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^2 phi1 q congruent 2 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/6 q^2 phi1 q congruent 4 modulo 12: 1/6 q^2 phi1 q congruent 5 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/6 q^2 phi1 q congruent 8 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/6 q^2 phi1 q congruent 11 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) 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 ], [ 5, 2, 2, 1 ], [ 8, 1, 2, 2 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 29, 2, 6, 3 ] ] 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^3-17*q^2+95*q-183 ) q congruent 2 modulo 12: 1/8 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 12: 1/8 ( q^3-17*q^2+91*q-147 ) q congruent 4 modulo 12: 1/8 ( q^3-16*q^2+80*q-128 ) q congruent 5 modulo 12: 1/8 ( q^3-17*q^2+91*q-155 ) q congruent 7 modulo 12: 1/8 ( q^3-17*q^2+95*q-175 ) q congruent 8 modulo 12: 1/8 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 12: 1/8 ( q^3-17*q^2+91*q-155 ) q congruent 11 modulo 12: 1/8 ( q^3-17*q^2+91*q-147 ) 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 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 12, 2, 1, 12 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 20, 2, 1, 8 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 8 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 8 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 1, 4 ], [ 30, 2, 1, 4 ] ] 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^2-6*q+7 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 12: 1/8 ( q^3-7*q^2+13*q-3 ) 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 ], [ 4, 2, 1, 6 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 21, 1, 1, 12 ], [ 22, 1, 2, 8 ], [ 24, 1, 2, 4 ], [ 25, 1, 5, 8 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 4 ], [ 30, 2, 2, 4 ] ] 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^2-2*q-7 ) 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 ( q^2-2*q-4 ) q congruent 5 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-2*q-7 ) 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: [ 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 ], [ 4, 2, 1, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 21, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 6, 8 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ], [ 25, 4, 6, 4 ], [ 30, 2, 3, 4 ] ] 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^2-4*q+1 ) 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+5*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 ( q^3-5*q^2+5*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 ( q^3-5*q^2+5*q+3 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 21, 1, 2, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 2, 2, 4 ], [ 25, 3, 2, 4 ], [ 25, 4, 2, 4 ], [ 30, 2, 4, 4 ] ] 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^2-10*q+25 ) q congruent 2 modulo 12: 1/8 ( q^3-10*q^2+28*q-24 ) q congruent 3 modulo 12: 1/8 ( q^3-11*q^2+35*q-33 ) q congruent 4 modulo 12: 1/8 q ( q^2-10*q+24 ) 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+35*q-33 ) q congruent 8 modulo 12: 1/8 ( q^3-10*q^2+28*q-24 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-10*q+25 ) q congruent 11 modulo 12: 1/8 ( q^3-11*q^2+39*q-53 ) 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 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 12, 2, 3, 12 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 20, 2, 2, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 4, 8 ], [ 24, 1, 3, 4 ], [ 25, 1, 8, 8 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 4 ], [ 30, 2, 5, 4 ] ] 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^2-4*q+5 ) 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+9*q-9 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 12: 1/8 ( q^3-5*q^2+9*q-9 ) 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 ], [ 4, 2, 2, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 8 ], [ 24, 1, 4, 4 ], [ 25, 1, 4, 8 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 4, 4 ], [ 30, 2, 6, 4 ] ] 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 phi1^2 ( q-3 ) q congruent 2 modulo 12: 1/8 ( q^3-4*q^2+8 ) 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 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 8 modulo 12: 1/8 ( q^3-4*q^2+8 ) q congruent 9 modulo 12: 1/8 phi1^2 ( q-3 ) q congruent 11 modulo 12: 1/8 phi2 ( 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 ], [ 4, 2, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 1, 5, 8 ], [ 12, 2, 4, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 21, 1, 3, 4 ], [ 24, 1, 4, 4 ], [ 25, 1, 3, 8 ], [ 25, 2, 3, 4 ], [ 25, 3, 3, 4 ], [ 25, 4, 3, 4 ], [ 30, 2, 7, 4 ] ] 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 ( q^2-2*q-1 ) 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 ( q^2-2*q-1 ) 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 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/8 phi4 ( q-3 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 21, 1, 3, 4 ], [ 24, 1, 3, 4 ], [ 25, 1, 7, 8 ], [ 25, 2, 7, 4 ], [ 25, 3, 7, 4 ], [ 25, 4, 7, 4 ], [ 30, 2, 8, 4 ] ] j = 2: Omega of order 2, action on Pi: <(2,5)> k = 1: F-action on Pi is () [30,2,1] Dynkin type is (A_2(q) + A_1(q) + A_1(q) + T(phi1^3)).2 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: 1/4 ( q-9 ) 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-7 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 9, 1, 1, 2 ], [ 12, 2, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 2, 1, 2 ], [ 25, 2, 1, 4 ] ] k = 2: F-action on Pi is () [30,2,2] Dynkin type is (A_2(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 9, 1, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 25, 2, 5, 4 ] ] k = 3: F-action on Pi is (2,5) [30,2,3] Dynkin type is (A_2(q) + A_1(q^2) + T(phi1 phi2^2)).2 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: 1/4 ( q-9 ) 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-7 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( 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 ], [ 4, 2, 1, 2 ], [ 6, 2, 2, 2 ], [ 9, 1, 1, 2 ], [ 12, 2, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 25, 2, 6, 4 ] ] k = 4: F-action on Pi is (2,5) [30,2,4] Dynkin type is (A_2(q) + A_1(q^2) + T(phi1^2 phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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 ], [ 4, 2, 1, 2 ], [ 9, 1, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 4, 2 ], [ 25, 2, 2, 4 ] ] k = 5: F-action on Pi is (1,3) [30,2,5] Dynkin type is (^2A_2(q) + A_1(q) + A_1(q) + T(phi2^3)).2 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: 1/4 phi1 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-7 ) 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, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 9, 1, 2, 2 ], [ 12, 2, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 3, 2 ], [ 25, 2, 8, 4 ] ] k = 6: F-action on Pi is (1,3) [30,2,6] Dynkin type is (^2A_2(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 phi2 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, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 9, 1, 2, 2 ], [ 17, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 25, 2, 4, 4 ] ] k = 7: F-action on Pi is (1,3)(2,5) [30,2,7] Dynkin type is (^2A_2(q) + A_1(q^2) + T(phi1^2 phi2)).2 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: 1/4 phi1 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-7 ) 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 ], [ 4, 2, 2, 2 ], [ 6, 2, 1, 2 ], [ 9, 1, 2, 2 ], [ 12, 2, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ], [ 25, 2, 3, 4 ] ] k = 8: F-action on Pi is (1,3)(2,5) [30,2,8] Dynkin type is (^2A_2(q) + A_1(q^2) + T(phi1 phi2^2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 phi2 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 ], [ 4, 2, 2, 2 ], [ 9, 1, 2, 2 ], [ 17, 2, 2, 2 ], [ 18, 2, 2, 2 ], [ 25, 2, 7, 4 ] ] 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^3-15*q^2+73*q-123 ) q congruent 2 modulo 12: 1/8 ( q^3-14*q^2+60*q-72 ) q congruent 3 modulo 12: 1/8 ( q^3-15*q^2+73*q-111 ) q congruent 4 modulo 12: 1/8 ( q^3-14*q^2+60*q-80 ) q congruent 5 modulo 12: 1/8 ( q^3-15*q^2+73*q-115 ) q congruent 7 modulo 12: 1/8 ( q^3-15*q^2+73*q-119 ) q congruent 8 modulo 12: 1/8 ( q^3-14*q^2+60*q-72 ) q congruent 9 modulo 12: 1/8 ( q^3-15*q^2+73*q-115 ) q congruent 11 modulo 12: 1/8 ( q^3-15*q^2+73*q-111 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 19, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 23, 1, 1, 8 ], [ 23, 2, 1, 4 ], [ 24, 1, 1, 8 ], [ 25, 1, 1, 8 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 1, 4 ], [ 26, 1, 1, 8 ], [ 31, 2, 1, 4 ] ] 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^2-6*q+7 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 12: 1/8 ( q^3-7*q^2+13*q-3 ) 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 22, 1, 1, 4 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 4 ], [ 26, 1, 2, 4 ], [ 31, 2, 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^2-6*q+9 ) 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+9 ) 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+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: [ 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 8 ], [ 23, 2, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 1, 4 ], [ 26, 1, 2, 4 ], [ 31, 2, 3, 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 phi1^3 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: [ 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 22, 1, 2, 4 ], [ 25, 1, 5, 8 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 4 ], [ 26, 1, 3, 8 ], [ 31, 2, 4, 4 ] ] 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 phi1^2 ( 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: [ 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 22, 1, 3, 4 ], [ 23, 1, 3, 8 ], [ 23, 2, 3, 4 ], [ 25, 1, 8, 8 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 2, 4 ], [ 31, 2, 5, 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 phi1^2 ( 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: [ 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 22, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 1, 8 ], [ 31, 2, 6, 4 ] ] 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^2-8*q+17 ) q congruent 2 modulo 12: 1/8 ( q^3-8*q^2+16*q-8 ) q congruent 3 modulo 12: 1/8 ( q^3-9*q^2+25*q-21 ) q congruent 4 modulo 12: 1/8 q ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/8 ( q^3-9*q^2+25*q-25 ) q congruent 7 modulo 12: 1/8 ( q^3-9*q^2+25*q-21 ) q congruent 8 modulo 12: 1/8 ( q^3-8*q^2+16*q-8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-8*q+17 ) q congruent 11 modulo 12: 1/8 ( q^3-9*q^2+25*q-29 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 14, 2, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 19, 1, 2, 8 ], [ 22, 1, 4, 4 ], [ 23, 1, 4, 8 ], [ 23, 2, 4, 4 ], [ 24, 1, 3, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 3, 8 ], [ 31, 2, 7, 4 ] ] 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^2-4*q+5 ) 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+9*q-9 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 12: 1/8 ( q^3-5*q^2+9*q-9 ) 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 22, 1, 4, 4 ], [ 24, 1, 4, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 2, 4 ], [ 31, 2, 8, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 ( 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: 1/48 ( 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: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 7 modulo 12: 1/48 ( 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: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 11 modulo 12: 1/48 ( 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 ], [ 4, 2, 1, 12 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 17, 2, 1, 18 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 26, 1, 1, 24 ], [ 27, 1, 1, 96 ], [ 27, 2, 1, 48 ], [ 27, 3, 1, 48 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q^2-6*q+7 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 12: 1/8 ( 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ] ] 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 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, 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 ], [ 4, 2, 2, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 22, 1, 3, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ], [ 27, 2, 8, 16 ], [ 27, 2, 12, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 11, 16 ] ] 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 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: [ 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 ], [ 17, 2, 3, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q^2-4*q+5 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 12: 1/8 ( 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 3, 2 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ] ] 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 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, 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 ], [ 4, 2, 1, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 6 ], [ 22, 1, 2, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 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: 1/48 ( 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: 1/48 ( q^3-13*q^2+51*q-55 ) q congruent 7 modulo 12: 1/48 ( 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: 1/48 phi1 ( q^2-12*q+39 ) q congruent 11 modulo 12: 1/48 ( 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 ], [ 4, 2, 2, 12 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 36 ], [ 17, 2, 3, 18 ], [ 21, 1, 6, 48 ], [ 22, 1, 4, 24 ], [ 26, 1, 3, 24 ], [ 27, 1, 12, 96 ], [ 27, 2, 12, 48 ], [ 27, 3, 11, 48 ] ] 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 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, 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 ], [ 17, 2, 1, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 2 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 12: 1/6 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q^2 phi1 q congruent 2 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/6 q^2 phi1 q congruent 4 modulo 12: 1/6 q^2 phi1 q congruent 5 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/6 q^2 phi1 q congruent 8 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/6 q^2 phi1 q congruent 11 modulo 12: 1/6 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+97*q-201 ) 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+93*q-153 ) 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+93*q-165 ) q congruent 7 modulo 12: 1/24 ( q^3-17*q^2+97*q-189 ) 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+93*q-165 ) q congruent 11 modulo 12: 1/24 ( q^3-17*q^2+93*q-153 ) 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 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 6 ], [ 5, 2, 1, 3 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 12 ], [ 11, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 3 ], [ 15, 1, 1, 24 ], [ 15, 2, 1, 12 ], [ 15, 3, 1, 12 ], [ 15, 4, 1, 12 ], [ 16, 1, 1, 6 ], [ 20, 1, 1, 12 ], [ 20, 2, 1, 6 ], [ 23, 1, 1, 12 ], [ 23, 2, 1, 6 ], [ 24, 1, 1, 24 ], [ 28, 1, 1, 12 ], [ 28, 2, 1, 6 ], [ 33, 2, 1, 12 ], [ 33, 3, 1, 12 ], [ 33, 4, 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 ], [ 6, 2, 1, 1 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 33, 2, 2, 6 ], [ 33, 3, 2, 6 ], [ 33, 4, 2, 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+7 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 12: 1/8 ( q^3-7*q^2+13*q-3 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 20, 1, 1, 4 ], [ 20, 2, 1, 2 ], [ 23, 1, 2, 4 ], [ 23, 2, 2, 2 ], [ 24, 1, 2, 8 ], [ 28, 1, 3, 4 ], [ 28, 2, 4, 2 ], [ 33, 2, 3, 4 ], [ 33, 3, 3, 4 ], [ 33, 4, 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+5 ) 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+9*q-9 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 12: 1/8 ( 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: 1/8 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 12: 1/8 ( q^3-5*q^2+9*q-9 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 23, 1, 3, 4 ], [ 23, 2, 3, 2 ], [ 24, 1, 4, 8 ], [ 28, 1, 2, 4 ], [ 28, 2, 2, 2 ], [ 33, 2, 4, 4 ], [ 33, 3, 4, 4 ], [ 33, 4, 4, 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 ], [ 6, 2, 2, 1 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 33, 2, 5, 6 ], [ 33, 3, 5, 6 ], [ 33, 4, 5, 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+27 ) 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+37*q-39 ) 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+41*q-55 ) q congruent 7 modulo 12: 1/24 ( q^3-11*q^2+37*q-39 ) 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+27 ) q congruent 11 modulo 12: 1/24 ( q^3-11*q^2+41*q-67 ) 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 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 6 ], [ 5, 2, 2, 3 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 12 ], [ 11, 1, 2, 6 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 13, 1, 2, 12 ], [ 14, 1, 2, 6 ], [ 14, 2, 2, 3 ], [ 15, 1, 4, 24 ], [ 15, 2, 4, 12 ], [ 15, 3, 4, 12 ], [ 15, 4, 4, 12 ], [ 16, 1, 2, 6 ], [ 20, 1, 2, 12 ], [ 20, 2, 2, 6 ], [ 23, 1, 4, 12 ], [ 23, 2, 4, 6 ], [ 24, 1, 3, 24 ], [ 28, 1, 6, 12 ], [ 28, 2, 6, 6 ], [ 33, 2, 6, 12 ], [ 33, 3, 6, 12 ], [ 33, 4, 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 phi1^2 ( 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: [ 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 ], [ 4, 2, 4, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 2 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 15, 1, 6, 8 ], [ 15, 2, 6, 4 ], [ 15, 3, 6, 4 ], [ 15, 4, 6, 4 ], [ 16, 1, 1, 2 ], [ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ], [ 23, 1, 1, 4 ], [ 23, 2, 1, 2 ], [ 28, 1, 2, 4 ], [ 28, 2, 2, 2 ], [ 33, 2, 7, 4 ], [ 33, 3, 7, 4 ], [ 33, 4, 7, 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 ], [ 6, 2, 1, 1 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 33, 2, 8, 6 ], [ 33, 3, 8, 6 ], [ 33, 4, 8, 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+9 ) 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+19*q-21 ) 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+9 ) 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 ], [ 4, 2, 4, 6 ], [ 5, 1, 1, 6 ], [ 5, 2, 1, 3 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 6 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 3 ], [ 15, 1, 8, 24 ], [ 15, 2, 8, 12 ], [ 15, 3, 8, 12 ], [ 15, 4, 8, 12 ], [ 16, 1, 2, 6 ], [ 20, 1, 3, 12 ], [ 20, 2, 3, 6 ], [ 23, 1, 2, 12 ], [ 23, 2, 2, 6 ], [ 28, 1, 6, 12 ], [ 28, 2, 6, 6 ], [ 33, 2, 9, 12 ], [ 33, 3, 9, 12 ], [ 33, 4, 9, 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 phi1 ( q^2-8*q+15 ) 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 phi1 ( q^2-8*q+19 ) 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 phi1 ( q^2-8*q+15 ) 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 ], [ 4, 2, 3, 6 ], [ 5, 1, 2, 6 ], [ 5, 2, 2, 3 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 6 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 14, 1, 2, 6 ], [ 14, 2, 2, 3 ], [ 15, 1, 5, 24 ], [ 15, 2, 5, 12 ], [ 15, 3, 5, 12 ], [ 15, 4, 5, 12 ], [ 16, 1, 1, 6 ], [ 20, 1, 4, 12 ], [ 20, 2, 4, 6 ], [ 23, 1, 3, 12 ], [ 23, 2, 3, 6 ], [ 28, 1, 1, 12 ], [ 28, 2, 1, 6 ], [ 33, 2, 10, 12 ], [ 33, 3, 10, 12 ], [ 33, 4, 10, 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 ], [ 6, 2, 2, 1 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 33, 2, 11, 6 ], [ 33, 3, 11, 6 ], [ 33, 4, 11, 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 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: [ 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 ], [ 4, 2, 3, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 15, 1, 7, 8 ], [ 15, 2, 7, 4 ], [ 15, 3, 7, 4 ], [ 15, 4, 7, 4 ], [ 16, 1, 2, 2 ], [ 20, 1, 4, 4 ], [ 20, 2, 4, 2 ], [ 23, 1, 4, 4 ], [ 23, 2, 4, 2 ], [ 28, 1, 3, 4 ], [ 28, 2, 4, 2 ], [ 33, 2, 12, 4 ], [ 33, 3, 12, 4 ], [ 33, 4, 12, 4 ] ] j = 4: Omega of order 2, action on Pi: <(1,6)(3,5)> k = 1: F-action on Pi is () [33,4,1] Dynkin type is (A_2(q) + A_2(q) + T(phi1^3)).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: 1/12 ( q^2-11*q+34 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 ( q^2-11*q+24 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 ( q^2-11*q+30 ) q congruent 7 modulo 12: 1/12 ( q^2-11*q+28 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 ( q^2-11*q+30 ) q congruent 11 modulo 12: 1/12 ( q^2-11*q+24 ) 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, 2 ], [ 4, 2, 1, 6 ], [ 5, 2, 1, 3 ], [ 6, 2, 1, 1 ], [ 11, 1, 1, 6 ], [ 12, 2, 1, 2 ], [ 14, 2, 1, 3 ], [ 15, 4, 1, 12 ], [ 16, 1, 1, 6 ], [ 20, 2, 1, 6 ], [ 23, 2, 1, 6 ], [ 28, 1, 1, 12 ], [ 28, 2, 1, 6 ] ] k = 2: F-action on Pi is () [33,4,2] Dynkin type is (A_2(q) + A_2(q) + T(phi1 phi3)).2 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: 1/6 phi1 ( q+2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 q phi2 q congruent 7 modulo 12: 1/6 phi1 ( q+2 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi2 q congruent 11 modulo 12: 1/6 q phi2 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, 2 ], [ 6, 2, 1, 1 ], [ 12, 2, 1, 2 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ] ] k = 3: F-action on Pi is () [33,4,3] Dynkin type is (A_2(q) + A_2(q) + T(phi1^2 phi2)).2 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: 1/4 phi1 ( q-2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 q ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 q ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 q ( q-3 ) 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, 2 ], [ 4, 2, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 11, 1, 1, 2 ], [ 12, 2, 1, 2 ], [ 14, 2, 1, 1 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 20, 2, 1, 2 ], [ 23, 2, 2, 2 ], [ 28, 1, 3, 4 ], [ 28, 2, 4, 2 ] ] k = 4: F-action on Pi is (1,3)(5,6) [33,4,4] Dynkin type is (^2A_2(q) + ^2A_2(q) + T(phi1 phi2^2)).2 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: 1/4 phi1 ( q-2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 ( q^2-3*q+4 ) 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, 2 ], [ 4, 2, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 11, 1, 2, 2 ], [ 12, 2, 3, 2 ], [ 14, 2, 2, 1 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 20, 2, 2, 2 ], [ 23, 2, 3, 2 ], [ 28, 1, 2, 4 ], [ 28, 2, 2, 2 ] ] k = 5: F-action on Pi is (1,3)(5,6) [33,4,5] Dynkin type is (^2A_2(q) + ^2A_2(q) + T(phi2 phi6)).2 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: 1/6 q phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi1 q congruent 11 modulo 12: 1/6 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, 2 ], [ 6, 2, 2, 1 ], [ 12, 2, 3, 2 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ] ] k = 6: F-action on Pi is (1,3)(5,6) [33,4,6] Dynkin type is (^2A_2(q) + ^2A_2(q) + T(phi2^3)).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: 1/12 phi1 ( q-6 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 ( q^2-7*q+12 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 ( q^2-7*q+10 ) q congruent 7 modulo 12: 1/12 ( q^2-7*q+12 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 phi1 ( q-6 ) q congruent 11 modulo 12: 1/12 ( q^2-7*q+16 ) 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, 2 ], [ 4, 2, 2, 6 ], [ 5, 2, 2, 3 ], [ 6, 2, 2, 1 ], [ 11, 1, 2, 6 ], [ 12, 2, 3, 2 ], [ 14, 2, 2, 3 ], [ 15, 4, 4, 12 ], [ 16, 1, 2, 6 ], [ 20, 2, 2, 6 ], [ 23, 2, 4, 6 ], [ 28, 1, 6, 12 ], [ 28, 2, 6, 6 ] ] k = 7: F-action on Pi is (1,5)(3,6) [33,4,7] Dynkin type is (A_2(q^2) + T(phi1^2 phi2)).2 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: 1/4 phi1 ( q-2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 ( q^2-3*q+4 ) 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, 2, 4, 2 ], [ 5, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 2 ], [ 12, 2, 4, 2 ], [ 14, 2, 1, 1 ], [ 15, 4, 6, 4 ], [ 16, 1, 1, 2 ], [ 20, 2, 3, 2 ], [ 23, 2, 1, 2 ], [ 28, 1, 2, 4 ], [ 28, 2, 2, 2 ] ] k = 8: F-action on Pi is (1,5)(3,6) [33,4,8] Dynkin type is (A_2(q^2) + T(phi1 phi6)).2 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: 1/6 q phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi1 q congruent 11 modulo 12: 1/6 phi2 ( q-2 ) 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, 2, 1, 1 ], [ 12, 2, 4, 2 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ] ] k = 9: F-action on Pi is (1,5)(3,6) [33,4,9] Dynkin type is (A_2(q^2) + T(phi1 phi2^2)).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: 1/12 phi1 ( q-6 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 ( q^2-7*q+12 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 ( q^2-7*q+10 ) q congruent 7 modulo 12: 1/12 ( q^2-7*q+12 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 phi1 ( q-6 ) q congruent 11 modulo 12: 1/12 ( q^2-7*q+16 ) 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, 2, 4, 6 ], [ 5, 2, 1, 3 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 6 ], [ 12, 2, 4, 2 ], [ 14, 2, 1, 3 ], [ 15, 4, 8, 12 ], [ 16, 1, 2, 6 ], [ 20, 2, 3, 6 ], [ 23, 2, 2, 6 ], [ 28, 1, 6, 12 ], [ 28, 2, 6, 6 ] ] k = 10: F-action on Pi is (1,6)(3,5) [33,4,10] Dynkin type is (A_2(q^2) + T(phi1^2 phi2)).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: 1/12 ( q^2-11*q+34 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 ( q^2-11*q+24 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 ( q^2-11*q+30 ) q congruent 7 modulo 12: 1/12 ( q^2-11*q+28 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 ( q^2-11*q+30 ) q congruent 11 modulo 12: 1/12 ( q^2-11*q+24 ) 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, 2, 3, 6 ], [ 5, 2, 2, 3 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 6 ], [ 12, 2, 2, 2 ], [ 14, 2, 2, 3 ], [ 15, 4, 5, 12 ], [ 16, 1, 1, 6 ], [ 20, 2, 4, 6 ], [ 23, 2, 3, 6 ], [ 28, 1, 1, 12 ], [ 28, 2, 1, 6 ] ] k = 11: F-action on Pi is (1,6)(3,5) [33,4,11] Dynkin type is (A_2(q^2) + T(phi2 phi3)).2 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: 1/6 phi1 ( q+2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 q phi2 q congruent 7 modulo 12: 1/6 phi1 ( q+2 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi2 q congruent 11 modulo 12: 1/6 q 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, 2, 2, 1 ], [ 12, 2, 2, 2 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ] ] k = 12: F-action on Pi is (1,6)(3,5) [33,4,12] Dynkin type is (A_2(q^2) + T(phi1 phi2^2)).2 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: 1/4 phi1 ( q-2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 q ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 q ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 q ( 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, 2, 3, 2 ], [ 5, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 2 ], [ 12, 2, 2, 2 ], [ 14, 2, 2, 1 ], [ 15, 4, 7, 4 ], [ 16, 1, 2, 2 ], [ 20, 2, 4, 2 ], [ 23, 2, 4, 2 ], [ 28, 1, 3, 4 ], [ 28, 2, 4, 2 ] ] 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 phi1 ( q^2-11*q+30 ) q congruent 2 modulo 12: 1/48 ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/48 ( q^3-12*q^2+41*q-42 ) q congruent 4 modulo 12: 1/48 ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/48 phi1 ( q^2-11*q+30 ) q congruent 7 modulo 12: 1/48 ( q^3-12*q^2+41*q-42 ) q congruent 8 modulo 12: 1/48 ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/48 phi1 ( q^2-11*q+30 ) q congruent 11 modulo 12: 1/48 ( q^3-12*q^2+41*q-42 ) 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 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 2, 1, 6 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 26, 1, 1, 24 ], [ 34, 2, 1, 24 ], [ 34, 3, 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 phi1^2 ( q-4 ) q congruent 2 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/16 q ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/16 phi1^2 ( q-4 ) q congruent 7 modulo 12: 1/16 q ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/16 phi1^2 ( q-4 ) q congruent 11 modulo 12: 1/16 q ( q^2-6*q+9 ) 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 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 34, 2, 2, 8 ], [ 34, 3, 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 phi1^2 ( q-2 ) q congruent 2 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 ( 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: 1/16 phi1^2 ( q-2 ) q congruent 7 modulo 12: 1/16 ( 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: 1/16 phi1^2 ( q-2 ) q congruent 11 modulo 12: 1/16 ( q^3-4*q^2+5*q-6 ) 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 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 q phi1 ( q-5 ) q congruent 2 modulo 12: 1/48 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/48 phi2 ( q^2-7*q+12 ) q congruent 4 modulo 12: 1/48 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/48 q phi1 ( q-5 ) q congruent 7 modulo 12: 1/48 phi2 ( q^2-7*q+12 ) q congruent 8 modulo 12: 1/48 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/48 q phi1 ( q-5 ) q congruent 11 modulo 12: 1/48 phi2 ( q^2-7*q+12 ) 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 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 12 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 12 ], [ 17, 2, 3, 6 ], [ 18, 1, 3, 24 ], [ 18, 2, 3, 12 ], [ 26, 1, 3, 24 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 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 ( q^2-3*q-2 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-3*q-2 ) q congruent 7 modulo 12: 1/8 phi2 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-3*q-2 ) q congruent 11 modulo 12: 1/8 phi2 ( q^2-5*q+6 ) 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 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 26, 1, 4, 4 ], [ 34, 2, 4, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 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-2 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/8 phi1 phi2 ( q-2 ) 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 ], [ 17, 2, 4, 2 ], [ 26, 1, 5, 4 ], [ 34, 2, 8, 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 ( q^2-q-4 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 q phi2 ( q-3 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-q-4 ) q congruent 7 modulo 12: 1/8 q phi2 ( q-3 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-q-4 ) q congruent 11 modulo 12: 1/8 q phi2 ( q-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 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 26, 1, 4, 4 ], [ 34, 2, 3, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 8, 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 q phi1 phi2 q congruent 2 modulo 12: 1/8 q^3 q congruent 3 modulo 12: 1/8 q phi1 phi2 q congruent 4 modulo 12: 1/8 q^3 q congruent 5 modulo 12: 1/8 q phi1 phi2 q congruent 7 modulo 12: 1/8 q phi1 phi2 q congruent 8 modulo 12: 1/8 q^3 q congruent 9 modulo 12: 1/8 q phi1 phi2 q congruent 11 modulo 12: 1/8 q phi1 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 ], [ 17, 2, 2, 2 ], [ 26, 1, 5, 4 ], [ 34, 2, 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 ], [ 6, 2, 1, 1 ], [ 34, 2, 7, 3 ] ] 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 ], [ 6, 2, 2, 1 ], [ 34, 2, 6, 3 ] ] j = 3: Omega of order 2, action on Pi: <(2,5)> k = 1: F-action on Pi is () [34,3,1] Dynkin type is (D_4(q) + T(phi1^3)).2 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: 1/4 ( q-5 ) 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 1 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 17, 2, 1, 2 ], [ 18, 2, 1, 2 ] ] k = 2: F-action on Pi is () [34,3,2] Dynkin type is (D_4(q) + T(phi1^2 phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 1 ], [ 7, 1, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ] ] k = 3: F-action on Pi is (2,5) [34,3,3] Dynkin type is (^2D_4(q) + T(phi1 phi2^2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 phi2 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 ], [ 7, 1, 2, 2 ], [ 17, 2, 2, 2 ], [ 18, 2, 2, 2 ] ] k = 4: F-action on Pi is (2,5) [34,3,4] Dynkin type is (^2D_4(q) + T(phi1^2 phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( 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, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ] ] k = 5: F-action on Pi is () [34,3,5] Dynkin type is (D_4(q) + T(phi2^3)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) 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, 1 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 3, 2 ] ] k = 6: F-action on Pi is () [34,3,6] Dynkin type is (D_4(q) + T(phi1 phi2^2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 4, 5, 2, 35, 43, 34, 3, 5, 12, 18, 15, 40, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 17, 2, 1, 2 ], [ 18, 2, 4, 2 ] ] k = 7: F-action on Pi is (2,5) [34,3,7] Dynkin type is (^2D_4(q) + T(phi1^2 phi2)).2 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: 1/4 phi1 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: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( 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 ], [ 7, 1, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 4, 2 ] ] k = 8: F-action on Pi is (2,5) [34,3,8] Dynkin type is (^2D_4(q) + T(phi1 phi2^2)).2 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: 1/4 ( q-5 ) 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: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q-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, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 17, 2, 2, 2 ], [ 18, 2, 3, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 ( 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: 1/48 ( 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: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 7 modulo 12: 1/48 ( 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: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 11 modulo 12: 1/48 ( 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ], [ 22, 1, 1, 24 ], [ 26, 1, 1, 24 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 35, 2, 1, 24 ] ] 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 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^2-6*q+8 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/8 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 ], [ 4, 2, 1, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 26, 1, 2, 4 ], [ 28, 1, 3, 8 ], [ 28, 2, 4, 4 ], [ 35, 2, 2, 4 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^2 ( q-4 ) q congruent 2 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/16 q ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/16 phi1^2 ( q-4 ) q congruent 7 modulo 12: 1/16 q ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/16 phi1^2 ( q-4 ) q congruent 11 modulo 12: 1/16 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 22, 1, 3, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 35, 2, 3, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) 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, 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 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 2, 4 ], [ 28, 1, 2, 8 ], [ 28, 2, 2, 4 ], [ 35, 2, 4, 4 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^2 ( q-2 ) q congruent 2 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 ( 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: 1/16 phi1^2 ( q-2 ) q congruent 7 modulo 12: 1/16 ( 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: 1/16 phi1^2 ( q-2 ) q congruent 11 modulo 12: 1/16 ( 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 22, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 35, 2, 5, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 q phi1 phi2 q congruent 2 modulo 12: 1/8 q^3 q congruent 3 modulo 12: 1/8 q phi1 phi2 q congruent 4 modulo 12: 1/8 q^3 q congruent 5 modulo 12: 1/8 q phi1 phi2 q congruent 7 modulo 12: 1/8 q phi1 phi2 q congruent 8 modulo 12: 1/8 q^3 q congruent 9 modulo 12: 1/8 q phi1 phi2 q congruent 11 modulo 12: 1/8 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 35, 2, 6, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/8 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 26, 1, 5, 4 ], [ 35, 2, 7, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 2 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 12: 1/6 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 ], [ 4, 2, 1, 2 ], [ 9, 1, 1, 2 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 35, 2, 8, 3 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q^2 phi1 q congruent 2 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/6 q^2 phi1 q congruent 4 modulo 12: 1/6 q^2 phi1 q congruent 5 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/6 q^2 phi1 q congruent 8 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/6 q^2 phi1 q congruent 11 modulo 12: 1/6 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 ], [ 4, 2, 2, 2 ], [ 9, 1, 2, 2 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 35, 2, 9, 3 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 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: 1/48 ( 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: 1/48 ( q^3-10*q^2+33*q-40 ) q congruent 7 modulo 12: 1/48 ( 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: 1/48 phi1 ( q^2-9*q+24 ) q congruent 11 modulo 12: 1/48 ( 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 3, 12 ], [ 22, 1, 4, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 35, 2, 10, 24 ] ] 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 ], [ 4, 2, 1, 12 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 10, 1, 1, 48 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 2, 1, 24 ], [ 15, 3, 1, 24 ], [ 15, 4, 1, 24 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 17, 2, 1, 18 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 25, 1, 1, 96 ], [ 25, 2, 1, 48 ], [ 25, 3, 1, 48 ], [ 25, 4, 1, 48 ], [ 26, 1, 1, 24 ], [ 27, 1, 1, 96 ], [ 27, 2, 1, 48 ], [ 27, 3, 1, 48 ], [ 34, 1, 1, 48 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 24 ], [ 36, 2, 1, 96 ], [ 36, 3, 1, 96 ], [ 36, 4, 1, 96 ], [ 36, 5, 1, 96 ], [ 36, 6, 1, 96 ] ] 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 34, 1, 5, 8 ], [ 34, 2, 4, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 36, 2, 2, 8 ], [ 36, 3, 2, 8 ], [ 36, 4, 2, 8 ], [ 36, 5, 2, 8 ], [ 36, 6, 2, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 10, 8 ], [ 36, 6, 11, 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^2-12*q+35 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1 ( q^2-12*q+35 ) q congruent 7 modulo 12: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1 ( q^2-12*q+35 ) q congruent 11 modulo 12: 1/64 ( q^3-13*q^2+51*q-63 ) 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 ], [ 4, 2, 2, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 10, 1, 3, 16 ], [ 15, 1, 2, 16 ], [ 15, 2, 2, 8 ], [ 15, 3, 2, 8 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 6 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 25, 1, 3, 32 ], [ 25, 2, 3, 16 ], [ 25, 3, 3, 16 ], [ 25, 4, 3, 16 ], [ 26, 1, 1, 24 ], [ 27, 1, 3, 32 ], [ 27, 1, 14, 32 ], [ 27, 2, 3, 16 ], [ 27, 2, 14, 16 ], [ 27, 3, 2, 16 ], [ 27, 3, 15, 16 ], [ 27, 3, 16, 16 ], [ 34, 1, 1, 48 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 24 ], [ 36, 2, 3, 32 ], [ 36, 2, 27, 32 ], [ 36, 3, 3, 32 ], [ 36, 3, 27, 32 ], [ 36, 4, 3, 32 ], [ 36, 4, 27, 32 ], [ 36, 5, 3, 32 ], [ 36, 6, 3, 32 ] ] 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 ], [ 4, 2, 1, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 15, 1, 3, 16 ], [ 15, 2, 3, 8 ], [ 15, 3, 3, 8 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 6 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 25, 1, 5, 32 ], [ 25, 2, 5, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 34, 1, 2, 16 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 36, 2, 4, 32 ], [ 36, 2, 14, 32 ], [ 36, 3, 4, 32 ], [ 36, 3, 14, 32 ], [ 36, 4, 4, 32 ], [ 36, 4, 14, 32 ], [ 36, 5, 4, 32 ], [ 36, 6, 5, 32 ] ] 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 14, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 34, 1, 7, 8 ], [ 34, 2, 3, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 8, 4 ], [ 36, 2, 5, 8 ], [ 36, 3, 5, 8 ], [ 36, 4, 5, 8 ], [ 36, 5, 5, 8 ], [ 36, 6, 6, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 14, 8 ], [ 36, 6, 15, 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 ( 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: [ 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 ], [ 4, 2, 2, 4 ], [ 4, 2, 3, 8 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 15, 1, 4, 16 ], [ 15, 1, 5, 32 ], [ 15, 2, 4, 8 ], [ 15, 2, 5, 16 ], [ 15, 3, 4, 8 ], [ 15, 3, 5, 16 ], [ 15, 4, 4, 8 ], [ 15, 4, 5, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 25, 1, 7, 32 ], [ 25, 2, 7, 16 ], [ 25, 3, 7, 16 ], [ 25, 4, 7, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 32 ], [ 27, 1, 4, 32 ], [ 27, 2, 3, 16 ], [ 27, 2, 4, 16 ], [ 27, 3, 2, 16 ], [ 27, 3, 3, 16 ], [ 27, 3, 14, 16 ], [ 34, 1, 2, 16 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 36, 2, 6, 32 ], [ 36, 2, 7, 32 ], [ 36, 3, 6, 32 ], [ 36, 3, 7, 32 ], [ 36, 4, 6, 32 ], [ 36, 4, 7, 32 ], [ 36, 5, 6, 32 ], [ 36, 6, 7, 32 ] ] 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 34, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 36, 5, 7, 3 ] ] 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 phi1^2 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: [ 43, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 26, 1, 4, 4 ], [ 27, 1, 10, 8 ], [ 27, 2, 10, 4 ], [ 34, 1, 7, 8 ], [ 34, 2, 3, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 8, 4 ], [ 36, 2, 21, 8 ], [ 36, 3, 21, 8 ], [ 36, 4, 21, 8 ], [ 36, 5, 8, 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 34, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 36, 5, 9, 3 ] ] 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 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 36, 2, 16, 8 ], [ 36, 3, 16, 8 ], [ 36, 4, 16, 8 ], [ 36, 5, 10, 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 phi1^2 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: [ 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 ], [ 4, 2, 3, 2 ], [ 4, 2, 4, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 15, 1, 7, 8 ], [ 15, 1, 8, 8 ], [ 15, 2, 7, 4 ], [ 15, 2, 8, 4 ], [ 15, 3, 7, 4 ], [ 15, 3, 8, 4 ], [ 15, 4, 7, 4 ], [ 15, 4, 8, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 27, 2, 5, 4 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 36, 2, 11, 8 ], [ 36, 3, 11, 8 ], [ 36, 4, 11, 8 ], [ 36, 5, 11, 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 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: [ 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 ], [ 4, 2, 3, 2 ], [ 4, 2, 4, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 15, 1, 5, 8 ], [ 15, 1, 6, 8 ], [ 15, 2, 5, 4 ], [ 15, 2, 6, 4 ], [ 15, 3, 5, 4 ], [ 15, 3, 6, 4 ], [ 15, 4, 5, 4 ], [ 15, 4, 6, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 27, 2, 5, 4 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 36, 2, 8, 8 ], [ 36, 3, 8, 8 ], [ 36, 4, 8, 8 ], [ 36, 5, 12, 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 phi1^2 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^2 ( q-5 ) q congruent 7 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^2 ( q-5 ) q congruent 11 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) 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 ], [ 4, 2, 4, 4 ], [ 7, 1, 1, 4 ], [ 15, 1, 6, 16 ], [ 15, 2, 6, 8 ], [ 15, 3, 6, 8 ], [ 15, 4, 6, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 6, 16 ], [ 27, 1, 9, 16 ], [ 27, 1, 14, 16 ], [ 27, 2, 6, 8 ], [ 27, 2, 9, 8 ], [ 27, 2, 14, 8 ], [ 27, 3, 4, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 13, 8 ], [ 27, 3, 15, 8 ], [ 27, 3, 16, 8 ], [ 34, 1, 2, 16 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 36, 2, 9, 16 ], [ 36, 2, 15, 16 ], [ 36, 2, 28, 16 ], [ 36, 3, 9, 16 ], [ 36, 3, 15, 16 ], [ 36, 3, 28, 16 ], [ 36, 4, 9, 16 ], [ 36, 4, 15, 16 ], [ 36, 4, 28, 16 ], [ 36, 5, 13, 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 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^2 ( q-3 ) q congruent 7 modulo 12: 1/32 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^2 ( q-3 ) q congruent 11 modulo 12: 1/32 phi2 ( q^2-6*q+9 ) 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 ], [ 4, 2, 3, 4 ], [ 7, 1, 2, 4 ], [ 15, 1, 7, 16 ], [ 15, 2, 7, 8 ], [ 15, 3, 7, 8 ], [ 15, 4, 7, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 4, 16 ], [ 27, 1, 9, 16 ], [ 27, 1, 11, 16 ], [ 27, 2, 4, 8 ], [ 27, 2, 9, 8 ], [ 27, 2, 11, 8 ], [ 27, 3, 3, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 7, 8 ], [ 27, 3, 8, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 14, 8 ], [ 34, 1, 3, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 36, 2, 10, 16 ], [ 36, 2, 18, 16 ], [ 36, 2, 20, 16 ], [ 36, 3, 10, 16 ], [ 36, 3, 18, 16 ], [ 36, 3, 20, 16 ], [ 36, 4, 10, 16 ], [ 36, 4, 18, 16 ], [ 36, 4, 20, 16 ], [ 36, 5, 14, 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 ( 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: [ 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 4, 8 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 8, 32 ], [ 15, 2, 1, 8 ], [ 15, 2, 8, 16 ], [ 15, 3, 1, 8 ], [ 15, 3, 8, 16 ], [ 15, 4, 1, 8 ], [ 15, 4, 8, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 25, 1, 2, 32 ], [ 25, 2, 2, 16 ], [ 25, 3, 2, 16 ], [ 25, 4, 2, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 6, 32 ], [ 27, 1, 13, 32 ], [ 27, 2, 6, 16 ], [ 27, 2, 13, 16 ], [ 27, 3, 4, 16 ], [ 27, 3, 12, 16 ], [ 27, 3, 13, 16 ], [ 34, 1, 3, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 36, 2, 12, 32 ], [ 36, 2, 24, 32 ], [ 36, 3, 12, 32 ], [ 36, 3, 24, 32 ], [ 36, 4, 12, 32 ], [ 36, 4, 24, 32 ], [ 36, 5, 15, 32 ], [ 36, 6, 12, 32 ] ] 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 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: [ 13, 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 26, 1, 4, 4 ], [ 27, 1, 10, 8 ], [ 27, 2, 10, 4 ], [ 34, 1, 5, 8 ], [ 34, 2, 4, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 36, 2, 19, 8 ], [ 36, 3, 19, 8 ], [ 36, 4, 19, 8 ], [ 36, 5, 16, 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 36, 2, 13, 8 ], [ 36, 3, 13, 8 ], [ 36, 4, 13, 8 ], [ 36, 5, 17, 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 ], [ 4, 2, 2, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 15, 1, 2, 16 ], [ 15, 2, 2, 8 ], [ 15, 3, 2, 8 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 25, 1, 4, 32 ], [ 25, 2, 4, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 4, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ], [ 27, 2, 8, 16 ], [ 27, 2, 12, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 11, 16 ], [ 34, 1, 3, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 36, 2, 17, 32 ], [ 36, 2, 23, 32 ], [ 36, 3, 17, 32 ], [ 36, 3, 23, 32 ], [ 36, 4, 17, 32 ], [ 36, 4, 23, 32 ], [ 36, 5, 18, 32 ], [ 36, 6, 9, 32 ] ] 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 phi1^2 ( 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: [ 34, 11, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 12 ], [ 10, 1, 2, 16 ], [ 15, 1, 3, 16 ], [ 15, 2, 3, 8 ], [ 15, 3, 3, 8 ], [ 15, 4, 3, 8 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 12 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 6 ], [ 18, 1, 3, 24 ], [ 18, 2, 3, 12 ], [ 25, 1, 6, 32 ], [ 25, 2, 6, 16 ], [ 25, 3, 6, 16 ], [ 25, 4, 6, 16 ], [ 26, 1, 3, 24 ], [ 27, 1, 11, 32 ], [ 27, 1, 13, 32 ], [ 27, 2, 11, 16 ], [ 27, 2, 13, 16 ], [ 27, 3, 7, 16 ], [ 27, 3, 8, 16 ], [ 27, 3, 12, 16 ], [ 34, 1, 4, 48 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 24 ], [ 36, 2, 22, 32 ], [ 36, 2, 26, 32 ], [ 36, 3, 22, 32 ], [ 36, 3, 26, 32 ], [ 36, 4, 22, 32 ], [ 36, 4, 26, 32 ], [ 36, 5, 19, 32 ], [ 36, 6, 16, 32 ] ] 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 ], [ 4, 2, 2, 12 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 12 ], [ 10, 1, 4, 48 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 4, 48 ], [ 15, 2, 4, 24 ], [ 15, 3, 4, 24 ], [ 15, 4, 4, 24 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 36 ], [ 17, 2, 3, 18 ], [ 18, 1, 3, 24 ], [ 18, 2, 3, 12 ], [ 25, 1, 8, 96 ], [ 25, 2, 8, 48 ], [ 25, 3, 8, 48 ], [ 25, 4, 8, 48 ], [ 26, 1, 3, 24 ], [ 27, 1, 12, 96 ], [ 27, 2, 12, 48 ], [ 27, 3, 11, 48 ], [ 34, 1, 4, 48 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 24 ], [ 36, 2, 25, 96 ], [ 36, 3, 25, 96 ], [ 36, 4, 25, 96 ], [ 36, 5, 20, 96 ], [ 36, 6, 13, 96 ] ] j = 3: Omega of order 2, action on Pi: <( 3,126)( 5, 7)> k = 1: F-action on Pi is () [36,3,1] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^3)).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: 1/32 ( q^2-14*q+45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/32 ( 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 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 1, 8 ], [ 5, 2, 1, 4 ], [ 7, 1, 1, 4 ], [ 15, 2, 1, 8 ], [ 15, 4, 1, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 8 ], [ 25, 4, 1, 16 ], [ 26, 1, 1, 8 ], [ 27, 3, 1, 16 ] ] k = 2: F-action on Pi is (5,7) [36,3,2] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q) + T(phi1^2 phi2)).2 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 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: [ 4, 35, 41, 13, 35, 3, 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 4, 4 ] ] k = 3: F-action on Pi is ( 3,126)( 5, 7) [36,3,3] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^3)).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: 1/32 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q-5 ) q congruent 7 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q-5 ) q congruent 11 modulo 12: 1/32 ( q^2-10*q+21 ) 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 ], [ 7, 1, 1, 4 ], [ 15, 2, 2, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 4, 4 ], [ 25, 4, 3, 16 ], [ 26, 1, 1, 8 ], [ 27, 3, 16, 16 ] ] k = 4: F-action on Pi is () [36,3,4] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)).2 Order of center |Z^F|: phi1^2 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-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q-5 ) q congruent 7 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q-5 ) q congruent 11 modulo 12: 1/32 ( 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, 3 ], [ 7, 1, 1, 4 ], [ 15, 2, 3, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 4 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 8 ], [ 27, 3, 5, 16 ] ] k = 5: F-action on Pi is (5,7) [36,3,5] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2^2)).2 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 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: [ 33, 5, 10, 43, 5, 34, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 4, 4 ] ] k = 6: F-action on Pi is ( 3,126)( 5, 7) [36,3,6] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2 phi2)).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: 1/32 ( q^2-14*q+45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/32 ( q^2-10*q+21 ) 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, 2, 3, 8 ], [ 5, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 15, 2, 4, 8 ], [ 15, 4, 5, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 25, 4, 7, 16 ], [ 26, 1, 1, 8 ], [ 27, 3, 14, 16 ] ] k = 7: F-action on Pi is ( 3, 5)( 7,126) [36,3,7] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2 phi2)).2 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: 1/16 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: [ 33, 10, 10, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 2, 4 ], [ 4, 2, 3, 4 ], [ 5, 2, 2, 4 ], [ 15, 2, 5, 8 ], [ 15, 4, 4, 8 ], [ 15, 4, 5, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 27, 3, 2, 8 ], [ 27, 3, 3, 8 ] ] k = 8: F-action on Pi is ( 3, 5,126, 7) [36,3,8] Dynkin type is (A_1(q^4) + T(phi1 phi4)).2 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: 1/8 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: [ 42, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 2, 2, 2 ], [ 15, 2, 5, 4 ], [ 15, 2, 6, 4 ], [ 26, 1, 5, 4 ] ] k = 9: F-action on Pi is ( 3, 7)( 5,126) [36,3,9] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2 phi2)).2 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: 1/16 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: [ 35, 13, 13, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 15, 2, 6, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 27, 3, 10, 8 ], [ 27, 3, 15, 8 ] ] k = 10: F-action on Pi is ( 3, 5)( 7,126) [36,3,10] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2^2)).2 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: 1/16 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: [ 5, 43, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 15, 2, 7, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 27, 3, 6, 8 ], [ 27, 3, 7, 8 ] ] k = 11: F-action on Pi is ( 3, 5,126, 7) [36,3,11] Dynkin type is (A_1(q^4) + T(phi2 phi4)).2 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: 1/8 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: [ 12, 54 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 2, 1, 2 ], [ 15, 2, 7, 4 ], [ 15, 2, 8, 4 ], [ 26, 1, 5, 4 ] ] k = 12: F-action on Pi is ( 3, 7)( 5,126) [36,3,12] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2^2)).2 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: 1/16 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: [ 3, 40, 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 1, 4 ], [ 4, 2, 4, 4 ], [ 5, 2, 1, 4 ], [ 15, 2, 8, 8 ], [ 15, 4, 1, 8 ], [ 15, 4, 8, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 27, 3, 12, 8 ], [ 27, 3, 13, 8 ] ] k = 13: F-action on Pi is (5,7) [36,3,13] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi4)).2 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: 1/8 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: [ 41, 13, 9, 42, 13, 40, 42, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 26, 1, 5, 4 ] ] k = 14: F-action on Pi is () [36,3,14] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)).2 Order of center |Z^F|: phi1 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-5 ) 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 ( q-5 ) q congruent 7 modulo 12: 1/16 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q-5 ) q congruent 11 modulo 12: 1/16 phi2 ( 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 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 1, 4 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 27, 3, 1, 8 ], [ 27, 3, 9, 8 ] ] k = 15: F-action on Pi is ( 3,126)( 5, 7) [36,3,15] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2 phi2)).2 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: 1/16 phi1^2 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 phi1^2 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 phi1^2 q congruent 11 modulo 12: 1/16 ( q^2-6*q+9 ) 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, 2, 4, 4 ], [ 15, 4, 6, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 26, 1, 2, 4 ], [ 27, 3, 4, 8 ], [ 27, 3, 16, 8 ] ] k = 16: F-action on Pi is (5,7) [36,3,16] Dynkin type is (A_1(q) + A_1(q^2) + A_1(q) + T(phi2 phi4)).2 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: 1/8 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: [ 10, 43, 42, 12, 43, 11, 12, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 26, 1, 5, 4 ] ] k = 17: F-action on Pi is () [36,3,17] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)).2 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: 1/16 phi1^2 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 phi1^2 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 phi1^2 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, 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, 3 ], [ 4, 2, 2, 4 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 6 ], [ 26, 1, 2, 4 ], [ 27, 3, 5, 8 ], [ 27, 3, 11, 8 ] ] k = 18: F-action on Pi is ( 3,126)( 5, 7) [36,3,18] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2^2)).2 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: 1/16 phi1 ( q-5 ) 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 ( q-5 ) q congruent 7 modulo 12: 1/16 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q-5 ) q congruent 11 modulo 12: 1/16 phi2 ( 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, 2, 3, 4 ], [ 15, 4, 7, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 27, 3, 8, 8 ], [ 27, 3, 14, 8 ] ] k = 19: F-action on Pi is ( 3, 5,126, 7) [36,3,19] Dynkin type is (A_1(q^4) + T(phi1^2 phi2)).2 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 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: [ 13, 53 ] 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 = 20: F-action on Pi is ( 3, 5)( 7,126) [36,3,20] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2^2)).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: 1/16 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: [ 5, 43, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 3, 4 ], [ 7, 1, 2, 4 ], [ 15, 4, 7, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 26, 1, 3, 8 ], [ 27, 3, 3, 8 ], [ 27, 3, 10, 8 ] ] k = 21: F-action on Pi is ( 3, 5,126, 7) [36,3,21] Dynkin type is (A_1(q^4) + T(phi1 phi2^2)).2 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 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: [ 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 = 22: F-action on Pi is ( 3, 5)( 7,126) [36,3,22] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi2^3)).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: 1/16 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: [ 34, 11, 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 1, 4 ], [ 7, 1, 2, 4 ], [ 15, 4, 3, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 26, 1, 3, 8 ], [ 27, 3, 7, 8 ], [ 27, 3, 12, 8 ] ] k = 23: F-action on Pi is () [36,3,23] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)).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: 1/32 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q-5 ) q congruent 7 modulo 12: 1/32 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q-5 ) q congruent 11 modulo 12: 1/32 phi2 ( q-3 ) 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 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 2, 4 ], [ 15, 2, 2, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 4 ], [ 25, 4, 4, 16 ], [ 26, 1, 3, 8 ], [ 27, 3, 9, 16 ] ] k = 24: F-action on Pi is ( 3,126)( 5, 7) [36,3,24] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2^2)).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: 1/32 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q-5 ) q congruent 7 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q-5 ) q congruent 11 modulo 12: 1/32 ( q^2-10*q+21 ) 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, 2, 4, 8 ], [ 5, 2, 1, 4 ], [ 7, 1, 2, 4 ], [ 15, 2, 1, 8 ], [ 15, 4, 8, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 25, 4, 2, 16 ], [ 26, 1, 3, 8 ], [ 27, 3, 4, 16 ] ] k = 25: F-action on Pi is () [36,3,25] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^3)).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: 1/32 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q-5 ) q congruent 7 modulo 12: 1/32 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q-5 ) q congruent 11 modulo 12: 1/32 ( q^2-10*q+21 ) 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, 3 ], [ 4, 2, 2, 8 ], [ 5, 2, 2, 4 ], [ 7, 1, 2, 4 ], [ 15, 2, 4, 8 ], [ 15, 4, 4, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 8 ], [ 25, 4, 8, 16 ], [ 26, 1, 3, 8 ], [ 27, 3, 11, 16 ] ] k = 26: F-action on Pi is ( 3,126)( 5, 7) [36,3,26] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi2^3)).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: 1/32 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q-5 ) q congruent 7 modulo 12: 1/32 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q-5 ) q congruent 11 modulo 12: 1/32 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 ], [ 7, 1, 2, 4 ], [ 15, 2, 3, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 25, 4, 6, 16 ], [ 26, 1, 3, 8 ], [ 27, 3, 8, 16 ] ] k = 27: F-action on Pi is ( 3, 5)( 7,126) [36,3,27] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^3)).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: 1/16 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 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 26, 1, 1, 8 ], [ 27, 3, 2, 8 ], [ 27, 3, 15, 8 ] ] k = 28: F-action on Pi is ( 3, 5)( 7,126) [36,3,28] Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2 phi2)).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: 1/16 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: [ 35, 13, 13, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 4, 4 ], [ 7, 1, 1, 4 ], [ 15, 4, 6, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 26, 1, 1, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 13, 8 ] ] 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^4-25*q^3+226*q^2-889*q+1359 ) 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^4-25*q^3+226*q^2-873*q+1179 ) 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^4-25*q^3+226*q^2-873*q+1215 ) q congruent 7 modulo 12: 1/48 ( q^4-25*q^3+226*q^2-889*q+1323 ) 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^4-25*q^3+226*q^2-873*q+1215 ) q congruent 11 modulo 12: 1/48 ( q^4-25*q^3+226*q^2-873*q+1179 ) 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 ], [ 4, 2, 1, 14 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 40 ], [ 9, 1, 1, 46 ], [ 10, 1, 1, 36 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 48 ], [ 12, 2, 1, 24 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 2, 1, 24 ], [ 15, 3, 1, 24 ], [ 15, 4, 1, 24 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 64 ], [ 20, 2, 1, 32 ], [ 21, 1, 1, 36 ], [ 22, 1, 1, 48 ], [ 23, 1, 1, 48 ], [ 23, 2, 1, 24 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 25, 2, 1, 24 ], [ 25, 3, 1, 24 ], [ 25, 4, 1, 24 ], [ 26, 1, 1, 24 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 29, 1, 1, 48 ], [ 29, 2, 1, 24 ], [ 30, 1, 1, 48 ], [ 30, 2, 1, 24 ], [ 31, 1, 1, 48 ], [ 31, 2, 1, 24 ], [ 33, 1, 1, 96 ], [ 33, 2, 1, 48 ], [ 33, 3, 1, 48 ], [ 33, 4, 1, 48 ], [ 35, 1, 1, 48 ], [ 35, 2, 1, 24 ], [ 37, 2, 1, 24 ] ] 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^3-10*q^2+30*q-25 ) q congruent 2 modulo 12: 1/8 q ( q^3-11*q^2+38*q-40 ) q congruent 3 modulo 12: 1/8 ( q^4-11*q^3+40*q^2-55*q+21 ) 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^3-10*q^2+30*q-25 ) q congruent 7 modulo 12: 1/8 ( q^4-11*q^3+40*q^2-55*q+21 ) 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^3-10*q^2+30*q-25 ) q congruent 11 modulo 12: 1/8 ( q^4-11*q^3+40*q^2-55*q+21 ) 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 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 12, 2, 1, 12 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 3, 8 ], [ 15, 2, 1, 4 ], [ 15, 2, 3, 4 ], [ 15, 3, 1, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 1, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 2, 2 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 20, 2, 1, 8 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 8 ], [ 22, 1, 2, 8 ], [ 23, 1, 2, 8 ], [ 23, 2, 2, 4 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 5, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 5, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 5, 4 ], [ 26, 1, 2, 4 ], [ 28, 1, 3, 8 ], [ 28, 2, 4, 4 ], [ 29, 1, 2, 8 ], [ 29, 2, 2, 4 ], [ 30, 1, 1, 8 ], [ 30, 1, 2, 8 ], [ 30, 2, 1, 4 ], [ 30, 2, 2, 4 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 3, 4 ], [ 33, 1, 3, 16 ], [ 33, 2, 3, 8 ], [ 33, 3, 3, 8 ], [ 33, 4, 3, 8 ], [ 35, 1, 2, 8 ], [ 35, 2, 2, 4 ], [ 37, 2, 2, 4 ] ] 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^3-3*q^2-2*q+6 ) q congruent 2 modulo 12: 1/6 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/6 q phi2 ( q^2-5*q+6 ) 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^2-5*q+6 ) q congruent 7 modulo 12: 1/6 phi1 ( q^3-3*q^2-2*q+6 ) q congruent 8 modulo 12: 1/6 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/6 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/6 q phi2 ( q^2-5*q+6 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 20, 1, 1, 4 ], [ 20, 2, 1, 2 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 29, 1, 3, 6 ], [ 29, 2, 3, 3 ], [ 33, 1, 2, 12 ], [ 33, 2, 2, 6 ], [ 33, 3, 2, 6 ], [ 33, 4, 2, 6 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 37, 2, 3, 3 ] ] 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 ( q^2-q-1 ) q congruent 2 modulo 12: 1/8 q^2 phi2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 4 modulo 12: 1/8 q^2 phi2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 7 modulo 12: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 8 modulo 12: 1/8 q^2 phi2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 phi2 ( q^2-q-1 ) q congruent 11 modulo 12: 1/8 phi1 phi2 ( q^2-q-1 ) 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 35, 1, 6, 8 ], [ 35, 2, 6, 4 ], [ 37, 2, 4, 4 ] ] 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^2-3*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 ( q^4-5*q^3+6*q^2-q+3 ) 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^2-3*q-1 ) q congruent 7 modulo 12: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) 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^2-3*q-1 ) q congruent 11 modulo 12: 1/16 ( q^4-5*q^3+6*q^2-q+3 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 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 ], [ 4, 2, 1, 6 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 8 ], [ 15, 1, 3, 16 ], [ 15, 2, 3, 8 ], [ 15, 3, 3, 8 ], [ 15, 4, 3, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 8 ], [ 22, 1, 2, 16 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 16 ], [ 25, 2, 5, 8 ], [ 25, 3, 5, 8 ], [ 25, 4, 5, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 30, 1, 2, 16 ], [ 30, 2, 2, 8 ], [ 31, 1, 4, 16 ], [ 31, 2, 4, 8 ], [ 35, 1, 5, 16 ], [ 35, 2, 5, 8 ], [ 37, 2, 5, 8 ] ] 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^3-16*q^2+84*q-153 ) 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^4-17*q^3+100*q^2-237*q+189 ) q congruent 4 modulo 12: 1/48 q ( q^3-17*q^2+94*q-168 ) q congruent 5 modulo 12: 1/48 ( q^4-17*q^3+100*q^2-253*q+265 ) q congruent 7 modulo 12: 1/48 ( q^4-17*q^3+100*q^2-237*q+189 ) 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^3-16*q^2+84*q-153 ) q congruent 11 modulo 12: 1/48 ( q^4-17*q^3+100*q^2-253*q+301 ) 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 ], [ 4, 2, 2, 14 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 18 ], [ 8, 1, 2, 40 ], [ 9, 1, 2, 46 ], [ 10, 1, 4, 36 ], [ 11, 1, 2, 32 ], [ 12, 1, 6, 48 ], [ 12, 2, 3, 24 ], [ 13, 1, 2, 24 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 4, 48 ], [ 15, 2, 4, 24 ], [ 15, 3, 4, 24 ], [ 15, 4, 4, 24 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 3, 12 ], [ 18, 1, 3, 24 ], [ 18, 2, 3, 12 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 64 ], [ 20, 2, 2, 32 ], [ 21, 1, 6, 36 ], [ 22, 1, 4, 48 ], [ 23, 1, 4, 48 ], [ 23, 2, 4, 24 ], [ 24, 1, 3, 72 ], [ 25, 1, 8, 48 ], [ 25, 2, 8, 24 ], [ 25, 3, 8, 24 ], [ 25, 4, 8, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 29, 1, 4, 48 ], [ 29, 2, 4, 24 ], [ 30, 1, 5, 48 ], [ 30, 2, 5, 24 ], [ 31, 1, 7, 48 ], [ 31, 2, 7, 24 ], [ 33, 1, 6, 96 ], [ 33, 2, 6, 48 ], [ 33, 3, 6, 48 ], [ 33, 4, 6, 48 ], [ 35, 1, 10, 48 ], [ 35, 2, 10, 24 ], [ 37, 2, 6, 24 ] ] 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^3-6*q^2+12*q-11 ) q congruent 2 modulo 12: 1/8 q ( q^3-7*q^2+16*q-12 ) q congruent 3 modulo 12: 1/8 ( q^4-7*q^3+18*q^2-23*q+15 ) 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^3-6*q^2+12*q-11 ) q congruent 7 modulo 12: 1/8 ( q^4-7*q^3+18*q^2-23*q+15 ) 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^3-6*q^2+12*q-11 ) q congruent 11 modulo 12: 1/8 ( q^4-7*q^3+18*q^2-23*q+15 ) 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 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 12, 2, 3, 12 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 15, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 15, 3, 2, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 2, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 3, 2 ], [ 18, 2, 4, 2 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 20, 2, 2, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 8 ], [ 22, 1, 4, 8 ], [ 23, 1, 3, 8 ], [ 23, 2, 3, 4 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 12 ], [ 25, 1, 4, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 4, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 4, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 4, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 2, 4 ], [ 28, 1, 2, 8 ], [ 28, 2, 2, 4 ], [ 29, 1, 5, 8 ], [ 29, 2, 5, 4 ], [ 30, 1, 5, 8 ], [ 30, 1, 6, 8 ], [ 30, 2, 5, 4 ], [ 30, 2, 6, 4 ], [ 31, 1, 5, 8 ], [ 31, 1, 8, 8 ], [ 31, 2, 5, 4 ], [ 31, 2, 8, 4 ], [ 33, 1, 4, 16 ], [ 33, 2, 4, 8 ], [ 33, 3, 4, 8 ], [ 33, 4, 4, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 4, 4 ], [ 37, 2, 7, 4 ] ] 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^2 phi1^2 q congruent 2 modulo 12: 1/6 phi1 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/6 q^2 phi1^2 q congruent 4 modulo 12: 1/6 q^2 phi1^2 q congruent 5 modulo 12: 1/6 phi1 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/6 q^2 phi1^2 q congruent 8 modulo 12: 1/6 phi1 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/6 q^2 phi1^2 q congruent 11 modulo 12: 1/6 phi1 phi2 ( q^2-2*q+2 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 29, 1, 6, 6 ], [ 29, 2, 6, 3 ], [ 33, 1, 5, 12 ], [ 33, 2, 5, 6 ], [ 33, 3, 5, 6 ], [ 33, 4, 5, 6 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 37, 2, 8, 3 ] ] 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^2-3*q+1 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/16 ( q^4-5*q^3+8*q^2-5*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^2-3*q+1 ) q congruent 7 modulo 12: 1/16 ( q^4-5*q^3+8*q^2-5*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^2-3*q+1 ) q congruent 11 modulo 12: 1/16 ( q^4-5*q^3+8*q^2-5*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 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 ], [ 4, 2, 2, 6 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 12 ], [ 15, 1, 2, 16 ], [ 15, 2, 2, 8 ], [ 15, 3, 2, 8 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 21, 1, 3, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 16 ], [ 24, 1, 4, 8 ], [ 25, 1, 4, 16 ], [ 25, 2, 4, 8 ], [ 25, 3, 4, 8 ], [ 25, 4, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 30, 1, 6, 16 ], [ 30, 2, 6, 8 ], [ 31, 1, 6, 16 ], [ 31, 2, 6, 8 ], [ 35, 1, 3, 16 ], [ 35, 2, 3, 8 ], [ 37, 2, 9, 8 ] ] 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 phi2 phi6 q congruent 2 modulo 12: 1/8 q^3 phi1 q congruent 3 modulo 12: 1/8 phi1 phi2 phi6 q congruent 4 modulo 12: 1/8 q^3 phi1 q congruent 5 modulo 12: 1/8 phi1 phi2 phi6 q congruent 7 modulo 12: 1/8 phi1 phi2 phi6 q congruent 8 modulo 12: 1/8 q^3 phi1 q congruent 9 modulo 12: 1/8 phi1 phi2 phi6 q congruent 11 modulo 12: 1/8 phi1 phi2 phi6 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 26, 1, 5, 4 ], [ 35, 1, 7, 8 ], [ 35, 2, 7, 4 ], [ 37, 2, 10, 4 ] ] 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^4-27*q^3+257*q^2-1021*q+1462 ) 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^4-27*q^3+257*q^2-1017*q+1386 ) 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^4-27*q^3+257*q^2-1005*q+1350 ) q congruent 7 modulo 12: 1/96 ( q^4-27*q^3+257*q^2-1033*q+1498 ) 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^4-27*q^3+257*q^2-1005*q+1350 ) q congruent 11 modulo 12: 1/96 ( q^4-27*q^3+257*q^2-1017*q+1386 ) 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 ], [ 4, 2, 1, 24 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 24 ], [ 8, 1, 1, 48 ], [ 9, 1, 1, 72 ], [ 10, 1, 1, 96 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 96 ], [ 12, 2, 1, 48 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 2, 1, 24 ], [ 15, 3, 1, 24 ], [ 15, 4, 1, 24 ], [ 16, 1, 1, 8 ], [ 17, 1, 1, 48 ], [ 17, 2, 1, 24 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 96 ], [ 20, 2, 1, 48 ], [ 21, 1, 1, 144 ], [ 22, 1, 1, 72 ], [ 23, 1, 1, 16 ], [ 23, 2, 1, 8 ], [ 24, 1, 1, 48 ], [ 25, 1, 1, 96 ], [ 25, 2, 1, 48 ], [ 25, 3, 1, 48 ], [ 25, 4, 1, 48 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 192 ], [ 27, 2, 1, 96 ], [ 27, 3, 1, 96 ], [ 30, 1, 1, 96 ], [ 30, 2, 1, 48 ], [ 31, 1, 1, 48 ], [ 31, 2, 1, 24 ], [ 32, 1, 1, 144 ], [ 34, 1, 1, 48 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 24 ], [ 36, 1, 1, 192 ], [ 36, 2, 1, 96 ], [ 36, 3, 1, 96 ], [ 36, 4, 1, 96 ], [ 36, 5, 1, 96 ], [ 36, 6, 1, 96 ], [ 38, 2, 1, 48 ], [ 38, 3, 1, 48 ] ] 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^3-12*q^2+43*q-40 ) q congruent 2 modulo 12: 1/32 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) 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^3-12*q^2+43*q-40 ) q congruent 7 modulo 12: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) 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^3-12*q^2+43*q-40 ) q congruent 11 modulo 12: 1/32 ( q^4-13*q^3+55*q^2-79*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 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 ], [ 4, 2, 1, 12 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 15, 1, 3, 16 ], [ 15, 2, 3, 8 ], [ 15, 3, 3, 8 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 6 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 16 ], [ 24, 1, 2, 16 ], [ 25, 1, 5, 32 ], [ 25, 2, 5, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 48 ], [ 27, 2, 1, 48 ], [ 27, 2, 8, 24 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 24 ], [ 30, 1, 2, 32 ], [ 30, 2, 2, 16 ], [ 31, 1, 2, 16 ], [ 31, 2, 2, 8 ], [ 32, 1, 1, 48 ], [ 32, 1, 6, 32 ], [ 34, 1, 2, 16 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 36, 1, 4, 64 ], [ 36, 2, 4, 32 ], [ 36, 2, 14, 32 ], [ 36, 3, 4, 32 ], [ 36, 3, 14, 32 ], [ 36, 4, 4, 32 ], [ 36, 4, 14, 32 ], [ 36, 5, 4, 32 ], [ 36, 6, 5, 32 ], [ 38, 2, 2, 16 ], [ 38, 3, 2, 16 ] ] 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 q phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/96 phi2 ( q^3-10*q^2+33*q-36 ) q congruent 4 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/96 q phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/96 phi2 ( q^3-10*q^2+33*q-36 ) q congruent 8 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/96 q phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/96 phi2 ( q^3-10*q^2+33*q-36 ) 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 ], [ 4, 2, 2, 12 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 12 ], [ 10, 1, 4, 48 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 4, 48 ], [ 15, 2, 4, 24 ], [ 15, 3, 4, 24 ], [ 15, 4, 4, 24 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 18 ], [ 18, 1, 3, 24 ], [ 18, 2, 3, 12 ], [ 22, 1, 3, 24 ], [ 23, 1, 3, 16 ], [ 23, 2, 3, 8 ], [ 25, 1, 8, 96 ], [ 25, 2, 8, 48 ], [ 25, 3, 8, 48 ], [ 25, 4, 8, 48 ], [ 26, 1, 2, 12 ], [ 26, 1, 3, 24 ], [ 27, 1, 8, 48 ], [ 27, 1, 12, 96 ], [ 27, 2, 8, 24 ], [ 27, 2, 12, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 24 ], [ 27, 3, 11, 48 ], [ 31, 1, 5, 48 ], [ 31, 2, 5, 24 ], [ 32, 1, 3, 48 ], [ 34, 1, 4, 48 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 24 ], [ 36, 1, 20, 192 ], [ 36, 2, 25, 96 ], [ 36, 3, 25, 96 ], [ 36, 4, 25, 96 ], [ 36, 5, 20, 96 ], [ 36, 6, 13, 96 ], [ 38, 2, 3, 48 ], [ 38, 3, 3, 48 ] ] 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 phi1^2 ( 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, 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 16 ], [ 10, 1, 4, 16 ], [ 15, 1, 2, 16 ], [ 15, 2, 2, 8 ], [ 15, 3, 2, 8 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 12 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 8 ], [ 25, 1, 4, 32 ], [ 25, 2, 4, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 4, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 64 ], [ 27, 1, 12, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 32 ], [ 27, 3, 11, 16 ], [ 31, 1, 6, 16 ], [ 31, 2, 6, 8 ], [ 32, 1, 3, 16 ], [ 32, 1, 6, 32 ], [ 34, 1, 3, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 36, 1, 18, 64 ], [ 36, 2, 17, 32 ], [ 36, 2, 23, 32 ], [ 36, 3, 17, 32 ], [ 36, 3, 23, 32 ], [ 36, 4, 17, 32 ], [ 36, 4, 23, 32 ], [ 36, 5, 18, 32 ], [ 36, 6, 9, 32 ], [ 38, 2, 4, 16 ], [ 38, 3, 4, 16 ] ] 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 phi1^3 ( 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: [ 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 16 ], [ 10, 1, 4, 16 ], [ 15, 1, 3, 16 ], [ 15, 2, 3, 8 ], [ 15, 3, 3, 8 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 12 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 16 ], [ 25, 1, 5, 32 ], [ 25, 2, 5, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 64 ], [ 27, 1, 12, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 32 ], [ 27, 3, 11, 16 ], [ 31, 1, 4, 16 ], [ 31, 2, 4, 8 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 16 ], [ 34, 1, 2, 16 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 36, 1, 4, 64 ], [ 36, 2, 4, 32 ], [ 36, 2, 14, 32 ], [ 36, 3, 4, 32 ], [ 36, 3, 14, 32 ], [ 36, 4, 4, 32 ], [ 36, 4, 14, 32 ], [ 36, 5, 4, 32 ], [ 36, 6, 5, 32 ], [ 38, 2, 5, 16 ], [ 38, 3, 8, 16 ] ] 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^3-8*q^2+21*q-22 ) q congruent 2 modulo 12: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) 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^3-8*q^2+21*q-22 ) q congruent 7 modulo 12: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) 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^3-8*q^2+21*q-22 ) q congruent 11 modulo 12: 1/32 ( q^4-9*q^3+29*q^2-47*q+42 ) Fusion of maximal tori of C^F in those of G^F: [ 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 ], [ 4, 2, 2, 12 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 15, 1, 2, 16 ], [ 15, 2, 2, 8 ], [ 15, 3, 2, 8 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 18 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 21, 1, 6, 48 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 24 ], [ 24, 1, 4, 16 ], [ 25, 1, 4, 32 ], [ 25, 2, 4, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 4, 16 ], [ 26, 1, 2, 12 ], [ 26, 1, 3, 24 ], [ 27, 1, 8, 48 ], [ 27, 1, 12, 96 ], [ 27, 2, 8, 24 ], [ 27, 2, 12, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 24 ], [ 27, 3, 11, 48 ], [ 30, 1, 6, 32 ], [ 30, 2, 6, 16 ], [ 31, 1, 8, 16 ], [ 31, 2, 8, 8 ], [ 32, 1, 3, 32 ], [ 32, 1, 7, 48 ], [ 34, 1, 3, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 36, 1, 18, 64 ], [ 36, 2, 17, 32 ], [ 36, 2, 23, 32 ], [ 36, 3, 17, 32 ], [ 36, 3, 23, 32 ], [ 36, 4, 17, 32 ], [ 36, 4, 23, 32 ], [ 36, 5, 18, 32 ], [ 36, 6, 9, 32 ], [ 38, 2, 6, 16 ], [ 38, 3, 6, 16 ] ] 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^3-18*q^2+101*q-180 ) 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 phi1 ( q^3-18*q^2+101*q-168 ) q congruent 4 modulo 12: 1/96 q ( q^3-18*q^2+104*q-192 ) q congruent 5 modulo 12: 1/96 ( q^4-19*q^3+119*q^2-297*q+260 ) q congruent 7 modulo 12: 1/96 phi1 ( q^3-18*q^2+101*q-168 ) 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^3-18*q^2+101*q-180 ) q congruent 11 modulo 12: 1/96 ( q^4-19*q^3+119*q^2-285*q+248 ) 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 ], [ 4, 2, 2, 24 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 24 ], [ 8, 1, 2, 48 ], [ 9, 1, 2, 72 ], [ 10, 1, 4, 96 ], [ 11, 1, 2, 24 ], [ 12, 1, 6, 96 ], [ 12, 2, 3, 48 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 4, 48 ], [ 15, 2, 4, 24 ], [ 15, 3, 4, 24 ], [ 15, 4, 4, 24 ], [ 16, 1, 2, 8 ], [ 17, 1, 3, 48 ], [ 17, 2, 3, 24 ], [ 18, 1, 3, 24 ], [ 18, 2, 3, 12 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 96 ], [ 20, 2, 2, 48 ], [ 21, 1, 6, 144 ], [ 22, 1, 4, 72 ], [ 23, 1, 4, 16 ], [ 23, 2, 4, 8 ], [ 24, 1, 3, 48 ], [ 25, 1, 8, 96 ], [ 25, 2, 8, 48 ], [ 25, 3, 8, 48 ], [ 25, 4, 8, 48 ], [ 26, 1, 3, 48 ], [ 27, 1, 12, 192 ], [ 27, 2, 12, 96 ], [ 27, 3, 11, 96 ], [ 30, 1, 5, 96 ], [ 30, 2, 5, 48 ], [ 31, 1, 7, 48 ], [ 31, 2, 7, 24 ], [ 32, 1, 7, 144 ], [ 34, 1, 4, 48 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 24 ], [ 36, 1, 20, 192 ], [ 36, 2, 25, 96 ], [ 36, 3, 25, 96 ], [ 36, 4, 25, 96 ], [ 36, 5, 20, 96 ], [ 36, 6, 13, 96 ], [ 38, 2, 7, 48 ], [ 38, 3, 5, 48 ] ] 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 phi1^2 ( q^2-11*q+30 ) 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+41*q-42 ) q congruent 4 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/96 phi1^2 ( q^2-11*q+30 ) q congruent 7 modulo 12: 1/96 phi1 ( q^3-12*q^2+41*q-42 ) q congruent 8 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/96 phi1^2 ( q^2-11*q+30 ) q congruent 11 modulo 12: 1/96 phi1 ( q^3-12*q^2+41*q-42 ) 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 ], [ 4, 2, 1, 12 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 10, 1, 1, 48 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 2, 1, 24 ], [ 15, 3, 1, 24 ], [ 15, 4, 1, 24 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 6 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 22, 1, 2, 24 ], [ 23, 1, 2, 16 ], [ 23, 2, 2, 8 ], [ 25, 1, 1, 96 ], [ 25, 2, 1, 48 ], [ 25, 3, 1, 48 ], [ 25, 4, 1, 48 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 48 ], [ 27, 2, 1, 48 ], [ 27, 2, 8, 24 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 24 ], [ 31, 1, 3, 48 ], [ 31, 2, 3, 24 ], [ 32, 1, 6, 48 ], [ 34, 1, 1, 48 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 24 ], [ 36, 1, 1, 192 ], [ 36, 2, 1, 96 ], [ 36, 3, 1, 96 ], [ 36, 4, 1, 96 ], [ 36, 5, 1, 96 ], [ 36, 6, 1, 96 ], [ 38, 2, 8, 48 ], [ 38, 3, 7, 48 ] ] 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^3-6*q^2-q+38 ) q congruent 2 modulo 12: 1/16 q ( q^3-6*q^2+4*q+8 ) q congruent 3 modulo 12: 1/16 ( q^4-7*q^3+5*q^2+27*q-18 ) 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^3-6*q^2-q+30 ) q congruent 7 modulo 12: 1/16 ( q^4-7*q^3+5*q^2+35*q-26 ) 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^3-6*q^2-q+30 ) q congruent 11 modulo 12: 1/16 ( q^4-7*q^3+5*q^2+27*q-18 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 3, 4 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 12, 2, 2, 8 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 20, 1, 4, 16 ], [ 20, 2, 4, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 3, 8 ], [ 23, 2, 3, 4 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 4, 16 ], [ 27, 2, 2, 4 ], [ 27, 2, 4, 8 ], [ 27, 3, 3, 8 ], [ 27, 3, 14, 8 ], [ 30, 1, 3, 16 ], [ 30, 2, 3, 8 ], [ 31, 1, 2, 8 ], [ 31, 1, 5, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 5, 4 ], [ 32, 1, 2, 8 ], [ 34, 1, 7, 8 ], [ 34, 2, 3, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 8, 4 ], [ 36, 1, 5, 16 ], [ 36, 2, 5, 8 ], [ 36, 3, 5, 8 ], [ 36, 4, 5, 8 ], [ 36, 5, 5, 8 ], [ 36, 6, 6, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 14, 8 ], [ 36, 6, 15, 8 ], [ 38, 2, 9, 8 ], [ 38, 3, 9, 8 ], [ 38, 3, 12, 8 ] ] 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^3-8*q^2+15*q+4 ) q congruent 2 modulo 12: 1/16 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/16 ( q^4-9*q^3+23*q^2-7*q-24 ) 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^3-8*q^2+15*q+4 ) q congruent 7 modulo 12: 1/16 ( q^4-9*q^3+23*q^2-7*q-24 ) 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^3-8*q^2+15*q+4 ) q congruent 11 modulo 12: 1/16 ( q^4-9*q^3+23*q^2-7*q-24 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 19, 1, 1, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 8 ], [ 23, 2, 1, 4 ], [ 24, 1, 1, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 14, 16 ], [ 27, 2, 2, 4 ], [ 27, 2, 14, 8 ], [ 27, 3, 15, 8 ], [ 27, 3, 16, 8 ], [ 30, 1, 4, 16 ], [ 30, 2, 4, 8 ], [ 31, 1, 1, 8 ], [ 31, 1, 6, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 6, 4 ], [ 32, 1, 2, 8 ], [ 34, 1, 5, 8 ], [ 34, 2, 4, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 36, 1, 2, 16 ], [ 36, 2, 2, 8 ], [ 36, 3, 2, 8 ], [ 36, 4, 2, 8 ], [ 36, 5, 2, 8 ], [ 36, 6, 2, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 10, 8 ], [ 36, 6, 11, 8 ], [ 38, 2, 10, 8 ], [ 38, 3, 10, 8 ], [ 38, 3, 11, 8 ] ] 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-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: [ 13, 42, 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 4, 8 ], [ 4, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 6, 16 ], [ 27, 1, 7, 8 ], [ 27, 2, 6, 8 ], [ 27, 2, 7, 4 ], [ 27, 3, 4, 8 ], [ 27, 3, 13, 8 ], [ 32, 1, 4, 8 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 36, 1, 17, 16 ], [ 36, 2, 13, 8 ], [ 36, 3, 13, 8 ], [ 36, 4, 13, 8 ], [ 36, 5, 17, 8 ], [ 38, 2, 11, 8 ] ] 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 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: [ 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 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 11, 16 ], [ 27, 2, 7, 4 ], [ 27, 2, 11, 8 ], [ 27, 3, 7, 8 ], [ 27, 3, 8, 8 ], [ 32, 1, 4, 8 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 36, 1, 10, 16 ], [ 36, 2, 16, 8 ], [ 36, 3, 16, 8 ], [ 36, 4, 16, 8 ], [ 36, 5, 10, 8 ], [ 38, 2, 12, 8 ] ] 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^2-5*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: [ 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 ], [ 17, 2, 1, 4 ], [ 17, 2, 4, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 14, 16 ], [ 27, 2, 7, 4 ], [ 27, 2, 14, 8 ], [ 27, 3, 15, 8 ], [ 27, 3, 16, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 36, 1, 17, 16 ], [ 36, 2, 13, 8 ], [ 36, 3, 13, 8 ], [ 36, 4, 13, 8 ], [ 36, 5, 17, 8 ], [ 38, 2, 13, 8 ] ] 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 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: [ 10, 42, 43, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 3, 8 ], [ 4, 2, 3, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 4, 16 ], [ 27, 1, 7, 8 ], [ 27, 2, 4, 8 ], [ 27, 2, 7, 4 ], [ 27, 3, 3, 8 ], [ 27, 3, 14, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 36, 1, 10, 16 ], [ 36, 2, 16, 8 ], [ 36, 3, 16, 8 ], [ 36, 4, 16, 8 ], [ 36, 5, 10, 8 ], [ 38, 2, 14, 8 ] ] 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^3-6*q^2+5*q+8 ) 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 phi1 phi2 ( q^2-7*q+12 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/16 ( q^4-7*q^3+11*q^2+11*q-32 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^2-7*q+12 ) 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^3-6*q^2+5*q+8 ) q congruent 11 modulo 12: 1/16 ( q^4-7*q^3+11*q^2+15*q-36 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 4 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 12, 2, 4, 8 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 20, 1, 3, 16 ], [ 20, 2, 3, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 8 ], [ 23, 2, 2, 4 ], [ 24, 1, 4, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 6, 16 ], [ 27, 2, 2, 4 ], [ 27, 2, 6, 8 ], [ 27, 3, 4, 8 ], [ 27, 3, 13, 8 ], [ 30, 1, 7, 16 ], [ 30, 2, 7, 8 ], [ 31, 1, 3, 8 ], [ 31, 1, 8, 8 ], [ 31, 2, 3, 4 ], [ 31, 2, 8, 4 ], [ 32, 1, 5, 8 ], [ 34, 1, 5, 8 ], [ 34, 2, 4, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 36, 1, 2, 16 ], [ 36, 2, 2, 8 ], [ 36, 3, 2, 8 ], [ 36, 4, 2, 8 ], [ 36, 5, 2, 8 ], [ 36, 6, 2, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 10, 8 ], [ 36, 6, 11, 8 ], [ 38, 2, 15, 8 ], [ 38, 3, 13, 8 ], [ 38, 3, 16, 8 ] ] 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 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 ( q^4-5*q^3+5*q^2+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 ( q^4-5*q^3+5*q^2+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 ( q^4-5*q^3+5*q^2+q+6 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 14, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 19, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 4, 8 ], [ 23, 2, 4, 4 ], [ 24, 1, 3, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 11, 16 ], [ 27, 2, 2, 4 ], [ 27, 2, 11, 8 ], [ 27, 3, 7, 8 ], [ 27, 3, 8, 8 ], [ 30, 1, 8, 16 ], [ 30, 2, 8, 8 ], [ 31, 1, 4, 8 ], [ 31, 1, 7, 8 ], [ 31, 2, 4, 4 ], [ 31, 2, 7, 4 ], [ 32, 1, 5, 8 ], [ 34, 1, 7, 8 ], [ 34, 2, 3, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 8, 4 ], [ 36, 1, 5, 16 ], [ 36, 2, 5, 8 ], [ 36, 3, 5, 8 ], [ 36, 4, 5, 8 ], [ 36, 5, 5, 8 ], [ 36, 6, 6, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 14, 8 ], [ 36, 6, 15, 8 ], [ 38, 2, 16, 8 ], [ 38, 3, 14, 8 ], [ 38, 3, 15, 8 ] ] 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 16, 1, 2, 2 ], [ 23, 1, 2, 4 ], [ 23, 2, 2, 2 ], [ 34, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 36, 1, 9, 6 ], [ 36, 5, 9, 3 ], [ 38, 2, 17, 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 12, 1, 4, 12 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 16, 1, 2, 2 ], [ 23, 1, 4, 4 ], [ 23, 2, 4, 2 ], [ 34, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 36, 1, 7, 6 ], [ 36, 5, 7, 3 ], [ 38, 2, 18, 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 16, 1, 1, 2 ], [ 23, 1, 3, 4 ], [ 23, 2, 3, 2 ], [ 34, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 36, 1, 7, 6 ], [ 36, 5, 7, 3 ], [ 38, 2, 19, 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 12, 1, 3, 12 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 16, 1, 1, 2 ], [ 23, 1, 1, 4 ], [ 23, 2, 1, 2 ], [ 34, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 36, 1, 9, 6 ], [ 36, 5, 9, 3 ], [ 38, 2, 20, 6 ] ] j = 3: Omega of order 2, action on Pi: <(2,5)> k = 1: F-action on Pi is () [38,3,1] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^4)).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^2-14*q+53 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 ( q^2-12*q+27 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/8 ( q^2-12*q+35 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/8 ( q^2-12*q+27 ) 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, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 6 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 12, 2, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 6 ], [ 18, 2, 1, 2 ], [ 20, 2, 1, 8 ], [ 22, 1, 1, 4 ], [ 23, 2, 1, 4 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 1, 4 ], [ 27, 3, 1, 8 ], [ 30, 2, 1, 8 ], [ 31, 2, 1, 4 ], [ 34, 3, 1, 4 ], [ 36, 6, 1, 8 ] ] k = 2: F-action on Pi is () [38,3,2] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^3 phi2)).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-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: [ 32, 4, 4, 33, 4, 35, 35, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 15, 2, 3, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 18, 2, 2, 2 ], [ 22, 1, 1, 4 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 4 ], [ 27, 3, 5, 8 ], [ 30, 2, 2, 8 ], [ 31, 2, 2, 4 ], [ 34, 3, 2, 4 ], [ 36, 6, 5, 8 ] ] k = 3: F-action on Pi is () [38,3,3] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^3)).2 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: [ 33, 5, 5, 34, 5, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 14, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 18, 2, 3, 2 ], [ 22, 1, 3, 4 ], [ 23, 2, 3, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 4 ], [ 27, 3, 5, 8 ], [ 31, 2, 5, 4 ], [ 34, 3, 5, 4 ], [ 36, 6, 13, 8 ] ] k = 4: F-action on Pi is () [38,3,4] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2 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, 35, 35, 3, 35, 5, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 6 ], [ 18, 2, 4, 2 ], [ 22, 1, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 4, 4 ], [ 27, 3, 1, 8 ], [ 31, 2, 6, 4 ], [ 34, 3, 6, 4 ], [ 36, 6, 9, 8 ] ] k = 5: F-action on Pi is () [38,3,5] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi2^4)).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-7 ) 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^2-8*q+15 ) 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 phi1 ( q-7 ) q congruent 11 modulo 12: 1/8 ( q^2-10*q+29 ) 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, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 6 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 12, 2, 3, 8 ], [ 14, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 6 ], [ 18, 2, 3, 2 ], [ 20, 2, 2, 8 ], [ 22, 1, 4, 4 ], [ 23, 2, 4, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 4 ], [ 27, 3, 11, 8 ], [ 30, 2, 5, 8 ], [ 31, 2, 7, 4 ], [ 34, 3, 5, 4 ], [ 36, 6, 13, 8 ] ] k = 6: F-action on Pi is () [38,3,6] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^3)).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-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: [ 35, 5, 5, 34, 3, 34, 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 4, 2 ], [ 22, 1, 4, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 4, 4 ], [ 27, 3, 9, 8 ], [ 30, 2, 6, 8 ], [ 31, 2, 8, 4 ], [ 34, 3, 6, 4 ], [ 36, 6, 9, 8 ] ] k = 7: F-action on Pi is () [38,3,7] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^3 phi2)).2 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, 35, 4, 35, 35, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 1, 2 ], [ 22, 1, 2, 4 ], [ 23, 2, 2, 4 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 1, 4 ], [ 27, 3, 9, 8 ], [ 31, 2, 3, 4 ], [ 34, 3, 1, 4 ], [ 36, 6, 1, 8 ] ] k = 8: F-action on Pi is () [38,3,8] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2 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: [ 4, 35, 35, 5, 33, 5, 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 15, 2, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 6 ], [ 18, 2, 2, 2 ], [ 22, 1, 2, 4 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 4 ], [ 27, 3, 11, 8 ], [ 31, 2, 4, 4 ], [ 34, 3, 2, 4 ], [ 36, 6, 5, 8 ] ] k = 9: F-action on Pi is (2,5) [38,3,9] Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^2 phi2^2)).2 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: [ 33, 10, 5, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 4, 2, 3, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 15, 2, 3, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 18, 2, 2, 2 ], [ 22, 1, 3, 4 ], [ 25, 2, 7, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 6, 4 ], [ 27, 3, 14, 8 ], [ 31, 2, 2, 4 ], [ 34, 3, 3, 4 ], [ 36, 6, 15, 8 ] ] k = 10: F-action on Pi is (2,5) [38,3,10] Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^3 phi2)).2 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: [ 4, 41, 35, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 4, 4 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 22, 1, 3, 4 ], [ 23, 2, 1, 4 ], [ 25, 2, 3, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 2, 4 ], [ 27, 3, 16, 8 ], [ 31, 2, 1, 4 ], [ 34, 3, 4, 4 ], [ 36, 6, 11, 8 ] ] k = 11: F-action on Pi is (2,5) [38,3,11] Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^3 phi2)).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-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: [ 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, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 4 ], [ 18, 2, 4, 2 ], [ 22, 1, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 3, 4 ], [ 27, 3, 16, 8 ], [ 30, 2, 4, 8 ], [ 31, 2, 6, 4 ], [ 34, 3, 7, 4 ], [ 36, 6, 4, 8 ] ] k = 12: F-action on Pi is (2,5) [38,3,12] Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^2 phi2^2)).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^2-14*q+53 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 ( q^2-12*q+27 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/8 ( q^2-12*q+35 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/8 ( q^2-12*q+27 ) 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, 2, 1, 2 ], [ 4, 2, 3, 4 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 12, 2, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 18, 2, 3, 2 ], [ 20, 2, 4, 8 ], [ 22, 1, 1, 4 ], [ 23, 2, 3, 4 ], [ 25, 2, 6, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 7, 4 ], [ 27, 3, 14, 8 ], [ 30, 2, 3, 8 ], [ 31, 2, 5, 4 ], [ 34, 3, 8, 4 ], [ 36, 6, 8, 8 ] ] k = 13: F-action on Pi is (2,5) [38,3,13] Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^2 phi2^2)).2 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: [ 35, 13, 3, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 4, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 2, 4, 2 ], [ 22, 1, 2, 4 ], [ 25, 2, 2, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 3, 4 ], [ 27, 3, 4, 8 ], [ 31, 2, 8, 4 ], [ 34, 3, 7, 4 ], [ 36, 6, 4, 8 ] ] k = 14: F-action on Pi is (2,5) [38,3,14] Dynkin type is (A_1(q) + A_1(q^2) + T(phi1 phi2^3)).2 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: [ 5, 43, 34, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 14, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 3, 2 ], [ 22, 1, 2, 4 ], [ 23, 2, 4, 4 ], [ 25, 2, 6, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 7, 4 ], [ 27, 3, 8, 8 ], [ 31, 2, 7, 4 ], [ 34, 3, 8, 4 ], [ 36, 6, 8, 8 ] ] k = 15: F-action on Pi is (2,5) [38,3,15] Dynkin type is (A_1(q) + A_1(q^2) + T(phi1 phi2^3)).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-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: [ 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, 2, 4 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 15, 2, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 22, 1, 4, 4 ], [ 25, 2, 7, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 6, 4 ], [ 27, 3, 8, 8 ], [ 30, 2, 8, 8 ], [ 31, 2, 4, 4 ], [ 34, 3, 3, 4 ], [ 36, 6, 15, 8 ] ] k = 16: F-action on Pi is (2,5) [38,3,16] Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^2 phi2^2)).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-7 ) 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^2-8*q+15 ) 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 phi1 ( q-7 ) q congruent 11 modulo 12: 1/8 ( q^2-10*q+29 ) 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, 2, 4 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 4 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 12, 2, 4, 8 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 20, 2, 3, 8 ], [ 22, 1, 4, 4 ], [ 23, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 2, 4 ], [ 27, 3, 4, 8 ], [ 30, 2, 7, 8 ], [ 31, 2, 3, 4 ], [ 34, 3, 4, 4 ], [ 36, 6, 11, 8 ] ] 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^4-22*q^3+172*q^2-570*q+707 ) 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^4-22*q^3+172*q^2-570*q+675 ) 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^4-22*q^3+172*q^2-570*q+675 ) q congruent 7 modulo 12: 1/96 ( q^4-22*q^3+172*q^2-570*q+707 ) 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^4-22*q^3+172*q^2-570*q+675 ) q congruent 11 modulo 12: 1/96 ( q^4-22*q^3+172*q^2-570*q+675 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 12 ], [ 6, 2, 1, 6 ], [ 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 ], [ 14, 2, 1, 12 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 14 ], [ 17, 1, 1, 36 ], [ 17, 2, 1, 18 ], [ 18, 1, 1, 60 ], [ 18, 2, 1, 30 ], [ 19, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 23, 1, 1, 48 ], [ 23, 2, 1, 24 ], [ 24, 1, 1, 16 ], [ 25, 1, 1, 24 ], [ 25, 2, 1, 12 ], [ 25, 3, 1, 12 ], [ 25, 4, 1, 12 ], [ 26, 1, 1, 72 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 29, 1, 1, 96 ], [ 29, 2, 1, 48 ], [ 31, 1, 1, 48 ], [ 31, 2, 1, 24 ], [ 34, 1, 1, 144 ], [ 34, 2, 1, 72 ], [ 34, 3, 1, 72 ], [ 35, 1, 1, 48 ], [ 35, 2, 1, 24 ], [ 39, 2, 1, 48 ], [ 39, 3, 1, 48 ], [ 39, 4, 1, 48 ], [ 39, 5, 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 phi1^2 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/16 q ( q^3-10*q^2+32*q-32 ) q congruent 3 modulo 12: 1/16 phi1^2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/16 q ( q^3-10*q^2+32*q-32 ) q congruent 5 modulo 12: 1/16 phi1^2 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/16 phi1^2 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/16 q ( q^3-10*q^2+32*q-32 ) q congruent 9 modulo 12: 1/16 phi1^2 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/16 phi1^2 ( q^2-8*q+15 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 18, 2, 1, 2 ], [ 18, 2, 2, 4 ], [ 19, 1, 1, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 1, 1, 8 ], [ 23, 1, 2, 8 ], [ 23, 2, 1, 4 ], [ 23, 2, 2, 4 ], [ 24, 1, 1, 8 ], [ 25, 1, 1, 8 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 1, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 4, 4 ], [ 29, 1, 2, 16 ], [ 29, 2, 2, 8 ], [ 31, 1, 1, 8 ], [ 31, 1, 3, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 3, 4 ], [ 34, 1, 2, 16 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 35, 1, 2, 8 ], [ 35, 2, 2, 4 ], [ 39, 2, 2, 8 ], [ 39, 3, 2, 8 ], [ 39, 4, 2, 8 ], [ 39, 5, 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 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 12: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/12 phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 12: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/12 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 12: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/12 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/12 q phi2 ( q^2-5*q+6 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 24, 1, 1, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 29, 1, 3, 12 ], [ 29, 2, 3, 6 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 39, 2, 3, 6 ], [ 39, 3, 3, 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 phi1^2 ( q^2-2*q-5 ) q congruent 2 modulo 12: 1/32 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/32 phi2 ( q^3-5*q^2+5*q+3 ) q congruent 4 modulo 12: 1/32 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/32 phi1^2 ( q^2-2*q-5 ) q congruent 7 modulo 12: 1/32 phi2 ( q^3-5*q^2+5*q+3 ) q congruent 8 modulo 12: 1/32 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/32 phi1^2 ( q^2-2*q-5 ) q congruent 11 modulo 12: 1/32 phi2 ( q^3-5*q^2+5*q+3 ) 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 ], [ 4, 2, 1, 2 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 12 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 12 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 6 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 24 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 12 ], [ 22, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 16 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 8 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 8 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 8 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 8 ], [ 31, 1, 4, 16 ], [ 31, 2, 4, 8 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 16 ], [ 34, 2, 3, 8 ], [ 34, 2, 10, 24 ], [ 34, 3, 3, 8 ], [ 34, 3, 5, 24 ], [ 34, 3, 8, 8 ], [ 35, 1, 5, 16 ], [ 35, 2, 5, 8 ], [ 39, 2, 4, 16 ], [ 39, 3, 4, 16 ], [ 39, 4, 3, 16 ], [ 39, 4, 5, 16 ], [ 39, 5, 3, 16 ], [ 39, 5, 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 phi4 ( q-3 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 11 modulo 12: 1/16 phi1 phi4 ( q-3 ) 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 2, 2 ], [ 18, 2, 4, 4 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 4 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 4, 4 ], [ 31, 1, 2, 8 ], [ 31, 1, 4, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 4, 4 ], [ 34, 1, 3, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 35, 1, 2, 8 ], [ 35, 2, 2, 4 ], [ 39, 2, 5, 8 ], [ 39, 3, 5, 8 ], [ 39, 4, 6, 8 ], [ 39, 5, 6, 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 phi1^2 phi2^2 q congruent 2 modulo 12: 1/16 q^4 q congruent 3 modulo 12: 1/16 phi1^2 phi2^2 q congruent 4 modulo 12: 1/16 q^4 q congruent 5 modulo 12: 1/16 phi1^2 phi2^2 q congruent 7 modulo 12: 1/16 phi1^2 phi2^2 q congruent 8 modulo 12: 1/16 q^4 q congruent 9 modulo 12: 1/16 phi1^2 phi2^2 q congruent 11 modulo 12: 1/16 phi1^2 phi2^2 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 ], [ 4, 2, 1, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 25, 1, 6, 8 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ], [ 25, 4, 6, 4 ], [ 26, 1, 5, 4 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 35, 1, 6, 8 ], [ 35, 2, 6, 4 ], [ 39, 2, 6, 8 ], [ 39, 3, 6, 8 ], [ 39, 4, 4, 8 ], [ 39, 5, 4, 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^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 q^2 phi1 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 ], [ 4, 2, 1, 2 ], [ 9, 1, 1, 2 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 24, 1, 2, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 39, 2, 7, 6 ], [ 39, 3, 7, 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^3-11*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: 1/96 ( 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: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 7 modulo 12: 1/96 ( 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: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 11 modulo 12: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 6 ], [ 18, 1, 2, 12 ], [ 18, 2, 2, 6 ], [ 22, 1, 1, 24 ], [ 24, 1, 2, 16 ], [ 25, 1, 5, 24 ], [ 25, 2, 5, 12 ], [ 25, 3, 5, 12 ], [ 25, 4, 5, 12 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 31, 1, 2, 48 ], [ 31, 2, 2, 24 ], [ 34, 1, 2, 48 ], [ 34, 2, 2, 24 ], [ 34, 3, 2, 24 ], [ 35, 1, 1, 48 ], [ 35, 2, 1, 24 ], [ 39, 2, 8, 48 ], [ 39, 3, 8, 48 ], [ 39, 4, 7, 48 ], [ 39, 5, 7, 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 phi1 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 25, 1, 2, 8 ], [ 25, 2, 2, 4 ], [ 25, 3, 2, 4 ], [ 25, 4, 2, 4 ], [ 26, 1, 5, 4 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 35, 1, 6, 8 ], [ 35, 2, 6, 4 ], [ 39, 2, 9, 8 ], [ 39, 3, 9, 8 ], [ 39, 4, 10, 8 ], [ 39, 5, 10, 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 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 5 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/32 q ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 4 ], [ 22, 1, 2, 8 ], [ 23, 1, 2, 16 ], [ 23, 2, 2, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 8 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 8 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 31, 1, 3, 16 ], [ 31, 2, 3, 8 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 16 ], [ 34, 2, 4, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 4, 8 ], [ 34, 3, 6, 8 ], [ 34, 3, 7, 8 ], [ 35, 1, 5, 16 ], [ 35, 2, 5, 8 ], [ 39, 2, 10, 16 ], [ 39, 3, 10, 16 ], [ 39, 4, 8, 16 ], [ 39, 4, 9, 16 ], [ 39, 5, 8, 16 ], [ 39, 5, 9, 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 phi1^3 ( q-3 ) q congruent 2 modulo 12: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 3 modulo 12: 1/16 phi1^3 ( q-3 ) q congruent 4 modulo 12: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 5 modulo 12: 1/16 phi1^3 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1^3 ( q-3 ) q congruent 8 modulo 12: 1/16 q ( q^3-6*q^2+12*q-8 ) q congruent 9 modulo 12: 1/16 phi1^3 ( q-3 ) q congruent 11 modulo 12: 1/16 phi1^3 ( q-3 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 14, 2, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 3, 2 ], [ 18, 2, 4, 4 ], [ 19, 1, 2, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 3, 8 ], [ 23, 1, 4, 8 ], [ 23, 2, 3, 4 ], [ 23, 2, 4, 4 ], [ 24, 1, 3, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 28, 1, 2, 8 ], [ 28, 2, 2, 4 ], [ 29, 1, 5, 16 ], [ 29, 2, 5, 8 ], [ 31, 1, 5, 8 ], [ 31, 1, 7, 8 ], [ 31, 2, 5, 4 ], [ 31, 2, 7, 4 ], [ 34, 1, 3, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 4, 4 ], [ 39, 2, 11, 8 ], [ 39, 3, 11, 8 ], [ 39, 4, 11, 8 ], [ 39, 5, 11, 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^2 phi1^2 q congruent 2 modulo 12: 1/12 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 12: 1/12 q^2 phi1^2 q congruent 4 modulo 12: 1/12 q^2 phi1^2 q congruent 5 modulo 12: 1/12 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 12: 1/12 q^2 phi1^2 q congruent 8 modulo 12: 1/12 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 9 modulo 12: 1/12 q^2 phi1^2 q congruent 11 modulo 12: 1/12 phi2 ( q^3-3*q^2+4*q-4 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 24, 1, 3, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 29, 1, 6, 12 ], [ 29, 2, 6, 6 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 39, 2, 12, 6 ], [ 39, 3, 12, 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 ( q^3-5*q^2-q+21 ) q congruent 2 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/32 phi1 ( q^3-5*q^2-q+21 ) q congruent 4 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/32 phi1 ( q^3-5*q^2-q+21 ) q congruent 7 modulo 12: 1/32 phi1 ( q^3-5*q^2-q+21 ) q congruent 8 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/32 phi1 ( q^3-5*q^2-q+21 ) q congruent 11 modulo 12: 1/32 phi1 ( q^3-5*q^2-q+21 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 4 ], [ 18, 2, 3, 2 ], [ 22, 1, 3, 8 ], [ 23, 1, 3, 16 ], [ 23, 2, 3, 8 ], [ 25, 1, 7, 16 ], [ 25, 1, 8, 8 ], [ 25, 2, 7, 8 ], [ 25, 2, 8, 4 ], [ 25, 3, 7, 8 ], [ 25, 3, 8, 4 ], [ 25, 4, 7, 8 ], [ 25, 4, 8, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 4, 8 ], [ 31, 1, 5, 16 ], [ 31, 2, 5, 8 ], [ 34, 1, 2, 16 ], [ 34, 1, 7, 16 ], [ 34, 2, 2, 8 ], [ 34, 2, 3, 8 ], [ 34, 3, 2, 8 ], [ 34, 3, 3, 8 ], [ 34, 3, 8, 8 ], [ 35, 1, 3, 16 ], [ 35, 2, 3, 8 ], [ 39, 2, 13, 16 ], [ 39, 3, 13, 16 ], [ 39, 4, 12, 16 ], [ 39, 4, 13, 16 ], [ 39, 5, 12, 16 ], [ 39, 5, 13, 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 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 25, 1, 7, 8 ], [ 25, 2, 7, 4 ], [ 25, 3, 7, 4 ], [ 25, 4, 7, 4 ], [ 26, 1, 5, 4 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 35, 1, 7, 8 ], [ 35, 2, 7, 4 ], [ 39, 2, 14, 8 ], [ 39, 3, 14, 8 ], [ 39, 4, 14, 8 ], [ 39, 5, 14, 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^3-13*q^2+51*q-63 ) 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 phi1 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 12: 1/96 q ( q^3-14*q^2+64*q-96 ) q congruent 5 modulo 12: 1/96 ( q^4-14*q^3+64*q^2-114*q+95 ) q congruent 7 modulo 12: 1/96 phi1 ( q^3-13*q^2+51*q-63 ) 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^3-13*q^2+51*q-63 ) q congruent 11 modulo 12: 1/96 ( q^4-14*q^3+64*q^2-114*q+95 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 12 ], [ 6, 2, 2, 6 ], [ 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 ], [ 14, 2, 2, 12 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 14 ], [ 17, 1, 3, 36 ], [ 17, 2, 3, 18 ], [ 18, 1, 3, 60 ], [ 18, 2, 3, 30 ], [ 19, 1, 2, 48 ], [ 22, 1, 4, 24 ], [ 23, 1, 4, 48 ], [ 23, 2, 4, 24 ], [ 24, 1, 3, 16 ], [ 25, 1, 8, 24 ], [ 25, 2, 8, 12 ], [ 25, 3, 8, 12 ], [ 25, 4, 8, 12 ], [ 26, 1, 3, 72 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 29, 1, 4, 96 ], [ 29, 2, 4, 48 ], [ 31, 1, 7, 48 ], [ 31, 2, 7, 24 ], [ 34, 1, 4, 144 ], [ 34, 2, 10, 72 ], [ 34, 3, 5, 72 ], [ 35, 1, 10, 48 ], [ 35, 2, 10, 24 ], [ 39, 2, 15, 48 ], [ 39, 3, 15, 48 ], [ 39, 4, 15, 48 ], [ 39, 5, 15, 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-2 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/12 q phi1 phi2 ( q-2 ) 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 ], [ 4, 2, 2, 2 ], [ 9, 1, 2, 2 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 24, 1, 4, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 39, 2, 16, 6 ], [ 39, 3, 16, 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 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) 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^2 ( q^2-4*q+4 ) 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: [ 40, 13, 41, 57, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 25, 1, 3, 8 ], [ 25, 2, 3, 4 ], [ 25, 3, 3, 4 ], [ 25, 4, 3, 4 ], [ 26, 1, 5, 4 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 35, 1, 7, 8 ], [ 35, 2, 7, 4 ], [ 39, 2, 17, 8 ], [ 39, 3, 17, 8 ], [ 39, 4, 16, 8 ], [ 39, 5, 16, 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 ( q^3-7*q^2+9*q+13 ) q congruent 2 modulo 12: 1/32 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/32 phi2 ( q^3-9*q^2+25*q-21 ) 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^3-7*q^2+9*q+13 ) q congruent 7 modulo 12: 1/32 phi2 ( q^3-9*q^2+25*q-21 ) 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^3-7*q^2+9*q+13 ) q congruent 11 modulo 12: 1/32 phi2 ( q^3-9*q^2+25*q-21 ) 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 ], [ 4, 2, 2, 2 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 6 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 12 ], [ 18, 2, 4, 2 ], [ 22, 1, 3, 8 ], [ 25, 1, 3, 16 ], [ 25, 1, 4, 8 ], [ 25, 2, 3, 8 ], [ 25, 2, 4, 4 ], [ 25, 3, 3, 8 ], [ 25, 3, 4, 4 ], [ 25, 4, 3, 8 ], [ 25, 4, 4, 4 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 8 ], [ 31, 1, 6, 16 ], [ 31, 2, 6, 8 ], [ 34, 1, 1, 48 ], [ 34, 1, 5, 16 ], [ 34, 2, 1, 24 ], [ 34, 2, 4, 8 ], [ 34, 3, 1, 24 ], [ 34, 3, 4, 8 ], [ 34, 3, 7, 8 ], [ 35, 1, 3, 16 ], [ 35, 2, 3, 8 ], [ 39, 2, 18, 16 ], [ 39, 3, 18, 16 ], [ 39, 4, 17, 16 ], [ 39, 4, 18, 16 ], [ 39, 5, 17, 16 ], [ 39, 5, 18, 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 phi4 ( q-3 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 11 modulo 12: 1/16 phi1 phi4 ( q-3 ) 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 4 ], [ 18, 2, 2, 4 ], [ 18, 2, 4, 2 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 4, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 28, 1, 2, 8 ], [ 28, 2, 2, 4 ], [ 31, 1, 6, 8 ], [ 31, 1, 8, 8 ], [ 31, 2, 6, 4 ], [ 31, 2, 8, 4 ], [ 34, 1, 2, 16 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 4, 4 ], [ 39, 2, 19, 8 ], [ 39, 3, 19, 8 ], [ 39, 4, 19, 8 ], [ 39, 5, 19, 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^3-7*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: 1/96 ( 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: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 7 modulo 12: 1/96 ( 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: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 11 modulo 12: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) Fusion of maximal tori of C^F in those of G^F: [ 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 18, 1, 4, 12 ], [ 18, 2, 4, 6 ], [ 22, 1, 4, 24 ], [ 24, 1, 4, 16 ], [ 25, 1, 4, 24 ], [ 25, 2, 4, 12 ], [ 25, 3, 4, 12 ], [ 25, 4, 4, 12 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 31, 1, 8, 48 ], [ 31, 2, 8, 24 ], [ 34, 1, 3, 48 ], [ 34, 2, 9, 24 ], [ 34, 3, 6, 24 ], [ 35, 1, 10, 48 ], [ 35, 2, 10, 24 ], [ 39, 2, 20, 48 ], [ 39, 3, 20, 48 ], [ 39, 4, 20, 48 ], [ 39, 5, 20, 48 ] ] j = 4: Omega of order 2, action on Pi: <(1,4)> k = 1: F-action on Pi is () [39,4,1] Dynkin type is (A_3(q) + T(phi1^4)).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: 1/16 ( 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, 4, 6, 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 4 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 8 ], [ 18, 2, 1, 2 ], [ 23, 2, 1, 8 ], [ 25, 3, 1, 4 ], [ 25, 4, 1, 8 ], [ 26, 1, 1, 8 ], [ 31, 2, 1, 8 ], [ 34, 3, 1, 8 ] ] k = 2: F-action on Pi is () [39,4,2] Dynkin type is (A_3(q) + T(phi1^3 phi2)).2 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 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, 35, 45, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 1, 2 ], [ 23, 2, 1, 4 ], [ 23, 2, 2, 4 ], [ 25, 3, 1, 4 ], [ 26, 1, 2, 4 ], [ 31, 2, 1, 4 ], [ 31, 2, 3, 4 ] ] k = 3: F-action on Pi is () [39,4,3] Dynkin type is (A_3(q) + T(phi1 phi2^3)).2 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 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: [ 33, 5, 34, 46, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 15, 2, 3, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 3, 2 ], [ 25, 3, 6, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 26, 1, 4, 4 ], [ 34, 3, 5, 4 ], [ 34, 3, 8, 4 ] ] k = 4: F-action on Pi is () [39,4,4] Dynkin type is (A_3(q) + T(phi2^2 phi4)).2 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: 1/8 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: [ 10, 43, 11, 27, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 2, 2, 2 ], [ 15, 2, 3, 4 ], [ 18, 2, 3, 2 ], [ 25, 3, 6, 4 ], [ 26, 1, 5, 4 ] ] k = 5: F-action on Pi is () [39,4,5] Dynkin type is (A_3(q) + T(phi1 phi2^3)).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: 1/16 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: [ 33, 5, 34, 46, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 2, 4 ], [ 15, 2, 3, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 2, 2, 2 ], [ 25, 3, 5, 4 ], [ 25, 4, 6, 8 ], [ 26, 1, 3, 8 ], [ 31, 2, 4, 8 ], [ 34, 3, 3, 8 ] ] k = 6: F-action on Pi is () [39,4,6] Dynkin type is (A_3(q) + T(phi1^2 phi2^2)).2 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 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: [ 4, 35, 5, 18, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 15, 2, 3, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 25, 3, 5, 4 ], [ 26, 1, 2, 4 ], [ 31, 2, 2, 4 ], [ 31, 2, 4, 4 ] ] k = 7: F-action on Pi is () [39,4,7] Dynkin type is (A_3(q) + T(phi1^3 phi2)).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: 1/16 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: [ 32, 4, 33, 45, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 1, 4 ], [ 15, 2, 3, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 4 ], [ 18, 2, 2, 2 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 8 ], [ 26, 1, 1, 8 ], [ 31, 2, 2, 8 ], [ 34, 3, 2, 8 ] ] k = 8: F-action on Pi is () [39,4,8] Dynkin type is (A_3(q) + T(phi1^2 phi2^2)).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: 1/16 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, 3, 18, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 2, 4 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 23, 2, 2, 8 ], [ 25, 3, 1, 4 ], [ 25, 4, 2, 8 ], [ 26, 1, 3, 8 ], [ 31, 2, 3, 8 ], [ 34, 3, 4, 8 ] ] k = 9: F-action on Pi is () [39,4,9] Dynkin type is (A_3(q) + T(phi1^2 phi2^2)).2 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 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: [ 4, 35, 3, 18, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 15, 2, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 4, 2 ], [ 25, 3, 2, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 26, 1, 4, 4 ], [ 34, 3, 6, 4 ], [ 34, 3, 7, 4 ] ] k = 10: F-action on Pi is () [39,4,10] Dynkin type is (A_3(q) + T(phi1 phi2 phi4)).2 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: 1/8 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: [ 41, 13, 40, 58, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 2, 1, 2 ], [ 15, 2, 1, 4 ], [ 18, 2, 4, 2 ], [ 25, 3, 2, 4 ], [ 26, 1, 5, 4 ] ] k = 11: F-action on Pi is (1,4) [39,4,11] Dynkin type is (^2A_3(q) + T(phi1 phi2^3)).2 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 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: [ 2, 34, 5, 15, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 14, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 3, 2 ], [ 23, 2, 3, 4 ], [ 23, 2, 4, 4 ], [ 25, 3, 8, 4 ], [ 26, 1, 2, 4 ], [ 31, 2, 5, 4 ], [ 31, 2, 7, 4 ] ] k = 12: F-action on Pi is (1,4) [39,4,12] Dynkin type is (^2A_3(q) + T(phi1^2 phi2^2)).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: 1/16 ( 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: [ 34, 5, 33, 48, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 4 ], [ 14, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 18, 2, 3, 2 ], [ 23, 2, 3, 8 ], [ 25, 3, 8, 4 ], [ 25, 4, 7, 8 ], [ 26, 1, 1, 8 ], [ 31, 2, 5, 8 ], [ 34, 3, 8, 8 ] ] k = 13: F-action on Pi is (1,4) [39,4,13] Dynkin type is (^2A_3(q) + T(phi1^2 phi2^2)).2 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 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: [ 34, 5, 33, 48, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 15, 2, 4, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 25, 3, 7, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 4, 4 ], [ 34, 3, 2, 4 ], [ 34, 3, 3, 4 ] ] k = 14: F-action on Pi is (1,4) [39,4,14] Dynkin type is (^2A_3(q) + T(phi1 phi2 phi4)).2 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: 1/8 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: [ 11, 43, 10, 28, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 2, 2, 2 ], [ 15, 2, 4, 4 ], [ 18, 2, 2, 2 ], [ 25, 3, 7, 4 ], [ 26, 1, 5, 4 ] ] k = 15: F-action on Pi is (1,4) [39,4,15] Dynkin type is (^2A_3(q) + T(phi2^4)).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: 1/16 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: [ 31, 2, 34, 36, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 4 ], [ 14, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 8 ], [ 18, 2, 3, 2 ], [ 23, 2, 4, 8 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 8 ], [ 26, 1, 3, 8 ], [ 31, 2, 7, 8 ], [ 34, 3, 5, 8 ] ] k = 16: F-action on Pi is (1,4) [39,4,16] Dynkin type is (^2A_3(q) + T(phi1^2 phi4)).2 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: 1/8 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: [ 40, 13, 41, 57, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 2, 1, 2 ], [ 15, 2, 2, 4 ], [ 18, 2, 1, 2 ], [ 25, 3, 3, 4 ], [ 26, 1, 5, 4 ] ] k = 17: F-action on Pi is (1,4) [39,4,17] Dynkin type is (^2A_3(q) + T(phi1^3 phi2)).2 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 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: [ 3, 35, 4, 16, 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 15, 2, 2, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ], [ 25, 3, 3, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 4, 4 ], [ 34, 3, 1, 4 ], [ 34, 3, 4, 4 ] ] k = 18: F-action on Pi is (1,4) [39,4,18] Dynkin type is (^2A_3(q) + T(phi1^3 phi2)).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: 1/16 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: [ 3, 35, 4, 16, 41 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 4, 4 ], [ 18, 2, 4, 2 ], [ 25, 3, 4, 4 ], [ 25, 4, 3, 8 ], [ 26, 1, 1, 8 ], [ 31, 2, 6, 8 ], [ 34, 3, 7, 8 ] ] k = 19: F-action on Pi is (1,4) [39,4,19] Dynkin type is (^2A_3(q) + T(phi1^2 phi2^2)).2 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 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: [ 34, 5, 35, 48, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 15, 2, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 4, 2 ], [ 25, 3, 4, 4 ], [ 26, 1, 2, 4 ], [ 31, 2, 6, 4 ], [ 31, 2, 8, 4 ] ] k = 20: F-action on Pi is (1,4) [39,4,20] Dynkin type is (^2A_3(q) + T(phi1 phi2^3)).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: 1/16 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: [ 2, 34, 3, 15, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 7, 1, 2, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 4 ], [ 18, 2, 4, 2 ], [ 25, 3, 4, 4 ], [ 25, 4, 4, 8 ], [ 26, 1, 3, 8 ], [ 31, 2, 8, 8 ], [ 34, 3, 6, 8 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/1152 ( 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: 1/1152 ( 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: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 7 modulo 12: 1/1152 ( 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: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 11 modulo 12: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 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 ], [ 4, 2, 1, 24 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 11, 1, 1, 96 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 144 ], [ 17, 2, 1, 72 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 288 ], [ 26, 1, 1, 144 ], [ 27, 1, 1, 576 ], [ 27, 2, 1, 288 ], [ 27, 3, 1, 288 ], [ 28, 1, 1, 192 ], [ 28, 2, 1, 96 ], [ 32, 1, 1, 576 ], [ 35, 1, 1, 576 ], [ 35, 2, 1, 288 ], [ 40, 2, 1, 576 ], [ 40, 3, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/1152 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: 1/1152 ( 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: 1/1152 ( q^4-20*q^3+142*q^2-420*q+425 ) q congruent 7 modulo 12: 1/1152 ( 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: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 11 modulo 12: 1/1152 ( q^4-20*q^3+142*q^2-420*q+569 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 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 ], [ 4, 2, 2, 24 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 16, 1, 2, 24 ], [ 17, 1, 3, 144 ], [ 17, 2, 3, 72 ], [ 21, 1, 6, 192 ], [ 22, 1, 4, 288 ], [ 26, 1, 3, 144 ], [ 27, 1, 12, 576 ], [ 27, 2, 12, 288 ], [ 27, 3, 11, 288 ], [ 28, 1, 6, 192 ], [ 28, 2, 6, 96 ], [ 32, 1, 7, 576 ], [ 35, 1, 10, 576 ], [ 35, 2, 10, 288 ], [ 40, 2, 13, 576 ], [ 40, 3, 19, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/64 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: 1/64 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: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/64 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: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/64 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 4 ], [ 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 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 12 ], [ 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 32 ], [ 27, 3, 11, 16 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 32 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 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: 1/36 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: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/36 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: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/36 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 ], [ 28, 2, 1, 6 ], [ 32, 1, 9, 18 ], [ 40, 2, 3, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 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: 1/36 q^2 phi1^2 q congruent 4 modulo 12: 1/36 q^2 phi1^2 q congruent 5 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 12: 1/36 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: 1/36 q^2 phi1^2 q congruent 11 modulo 12: 1/36 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 ], [ 28, 2, 6, 6 ], [ 32, 1, 10, 18 ], [ 40, 2, 8, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 12: 1/96 q^2 ( q^2-4 ) q congruent 3 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 12: 1/96 q^2 ( q^2-4 ) q congruent 5 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 12: 1/96 q^2 ( q^2-4 ) q congruent 9 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 12: 1/96 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 ], [ 27, 2, 7, 24 ], [ 40, 2, 14, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 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: 1/36 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: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/36 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: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/36 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 ], [ 4, 2, 1, 6 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 21, 1, 1, 12 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 35, 1, 8, 18 ], [ 35, 2, 8, 9 ], [ 40, 2, 2, 18 ], [ 40, 3, 10, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 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: 1/36 q^2 phi1^2 q congruent 4 modulo 12: 1/36 q^2 phi1^2 q congruent 5 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 12: 1/36 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: 1/36 q^2 phi1^2 q congruent 11 modulo 12: 1/36 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 ], [ 4, 2, 2, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 21, 1, 6, 12 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 35, 1, 9, 18 ], [ 35, 2, 9, 9 ], [ 40, 2, 5, 18 ], [ 40, 3, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/72 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: 1/72 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: 1/72 q phi2 ( q^2+q-6 ) q congruent 7 modulo 12: 1/72 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: 1/72 q phi2 ( q^2+q-6 ) q congruent 11 modulo 12: 1/72 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 ], [ 28, 2, 3, 12 ], [ 40, 2, 4, 36 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/72 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: 1/72 q phi1 ( q^2-q-6 ) q congruent 4 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 5 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 7 modulo 12: 1/72 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: 1/72 q phi1 ( q^2-q-6 ) q congruent 11 modulo 12: 1/72 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 ], [ 28, 2, 5, 12 ], [ 40, 2, 11, 36 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 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 ], [ 40, 2, 12, 6 ] ] 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 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: 1/96 ( 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: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 7 modulo 12: 1/96 ( 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: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 11 modulo 12: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 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 ], [ 17, 2, 1, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 3, 2, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 32, 1, 2, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 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: 1/96 ( 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: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 7 modulo 12: 1/96 ( 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: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 11 modulo 12: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 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 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 3, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 13, 48 ], [ 27, 3, 12, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 32, 1, 5, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 10, 24 ], [ 40, 2, 24, 48 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/12 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^3 phi2 q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1^3 phi2 q congruent 4 modulo 12: 1/16 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: 1/16 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: [ 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ], [ 40, 2, 19, 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 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^3-12*q^2+44*q-48 ) 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^3-12*q^2+44*q-48 ) 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^3-12*q^2+44*q-48 ) 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: [ 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 ], [ 4, 2, 1, 12 ], [ 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 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 6 ], [ 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 ], [ 27, 2, 1, 48 ], [ 27, 2, 8, 24 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 24 ], [ 28, 1, 3, 16 ], [ 28, 2, 4, 8 ], [ 32, 1, 1, 48 ], [ 32, 1, 6, 48 ], [ 35, 1, 2, 48 ], [ 35, 2, 2, 24 ], [ 40, 2, 22, 48 ], [ 40, 3, 4, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 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: 1/96 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: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 7 modulo 12: 1/96 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: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 11 modulo 12: 1/96 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 ], [ 4, 2, 2, 12 ], [ 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 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 18 ], [ 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 ], [ 27, 2, 8, 24 ], [ 27, 2, 12, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 24 ], [ 27, 3, 11, 48 ], [ 28, 1, 2, 16 ], [ 28, 2, 2, 8 ], [ 32, 1, 3, 48 ], [ 32, 1, 7, 48 ], [ 35, 1, 4, 48 ], [ 35, 2, 4, 24 ], [ 40, 2, 23, 48 ], [ 40, 3, 3, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 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 ], [ 28, 2, 4, 2 ], [ 32, 1, 9, 6 ], [ 40, 2, 10, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/12 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 ], [ 28, 2, 2, 2 ], [ 32, 1, 10, 6 ], [ 40, 2, 9, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/16 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 11 modulo 12: 1/16 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 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: 1/32 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: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/32 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: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/32 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 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 8 ], [ 27, 2, 3, 16 ], [ 27, 2, 7, 4 ], [ 27, 3, 2, 16 ], [ 32, 1, 8, 16 ], [ 35, 1, 7, 16 ], [ 35, 2, 7, 8 ], [ 40, 2, 17, 16 ], [ 40, 3, 16, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1^3 phi2 q congruent 2 modulo 12: 1/32 q^3 ( q-2 ) q congruent 3 modulo 12: 1/32 phi1^3 phi2 q congruent 4 modulo 12: 1/32 q^3 ( q-2 ) q congruent 5 modulo 12: 1/32 phi1^3 phi2 q congruent 7 modulo 12: 1/32 phi1^3 phi2 q congruent 8 modulo 12: 1/32 q^3 ( q-2 ) q congruent 9 modulo 12: 1/32 phi1^3 phi2 q congruent 11 modulo 12: 1/32 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 ], [ 4, 2, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 13, 32 ], [ 27, 2, 7, 4 ], [ 27, 2, 13, 16 ], [ 27, 3, 12, 16 ], [ 32, 1, 4, 16 ], [ 35, 1, 6, 16 ], [ 35, 2, 6, 8 ], [ 40, 2, 18, 16 ], [ 40, 3, 14, 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 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 phi4 q congruent 2 modulo 12: 1/8 q^4 q congruent 3 modulo 12: 1/8 phi1 phi2 phi4 q congruent 4 modulo 12: 1/8 q^4 q congruent 5 modulo 12: 1/8 phi1 phi2 phi4 q congruent 7 modulo 12: 1/8 phi1 phi2 phi4 q congruent 8 modulo 12: 1/8 q^4 q congruent 9 modulo 12: 1/8 phi1 phi2 phi4 q congruent 11 modulo 12: 1/8 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 ], [ 40, 2, 15, 4 ] ] 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^5-38*q^4+550*q^3-3776*q^2+12353*q-16002 ) 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^5-38*q^4+550*q^3-3776*q^2+12273*q-14850 ) 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^5-38*q^4+550*q^3-3776*q^2+12225*q-14850 ) q congruent 7 modulo 12: 1/768 ( q^5-38*q^4+550*q^3-3776*q^2+12401*q-16002 ) 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^5-38*q^4+550*q^3-3776*q^2+12225*q-14850 ) q congruent 11 modulo 12: 1/768 ( q^5-38*q^4+550*q^3-3776*q^2+12273*q-14850 ) 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 ], [ 4, 2, 1, 72 ], [ 5, 1, 1, 16 ], [ 5, 2, 1, 8 ], [ 6, 1, 1, 16 ], [ 6, 2, 1, 8 ], [ 7, 1, 1, 72 ], [ 8, 1, 1, 192 ], [ 9, 1, 1, 320 ], [ 10, 1, 1, 384 ], [ 11, 1, 1, 128 ], [ 12, 1, 1, 384 ], [ 12, 2, 1, 192 ], [ 13, 1, 1, 64 ], [ 14, 1, 1, 128 ], [ 14, 2, 1, 64 ], [ 15, 1, 1, 224 ], [ 15, 2, 1, 112 ], [ 15, 3, 1, 112 ], [ 15, 4, 1, 112 ], [ 16, 1, 1, 26 ], [ 17, 1, 1, 172 ], [ 17, 2, 1, 86 ], [ 18, 1, 1, 112 ], [ 18, 2, 1, 56 ], [ 19, 1, 1, 320 ], [ 20, 1, 1, 640 ], [ 20, 2, 1, 320 ], [ 21, 1, 1, 768 ], [ 22, 1, 1, 512 ], [ 23, 1, 1, 192 ], [ 23, 2, 1, 96 ], [ 24, 1, 1, 448 ], [ 25, 1, 1, 512 ], [ 25, 2, 1, 256 ], [ 25, 3, 1, 256 ], [ 25, 4, 1, 256 ], [ 26, 1, 1, 240 ], [ 27, 1, 1, 960 ], [ 27, 2, 1, 480 ], [ 27, 3, 1, 480 ], [ 28, 1, 1, 192 ], [ 28, 2, 1, 96 ], [ 29, 1, 1, 384 ], [ 29, 2, 1, 192 ], [ 30, 1, 1, 896 ], [ 30, 2, 1, 448 ], [ 31, 1, 1, 576 ], [ 31, 2, 1, 288 ], [ 32, 1, 1, 1152 ], [ 33, 1, 1, 768 ], [ 33, 2, 1, 384 ], [ 33, 3, 1, 384 ], [ 33, 4, 1, 384 ], [ 34, 1, 1, 288 ], [ 34, 2, 1, 144 ], [ 34, 3, 1, 144 ], [ 35, 1, 1, 576 ], [ 35, 2, 1, 288 ], [ 36, 1, 1, 1152 ], [ 36, 2, 1, 576 ], [ 36, 3, 1, 576 ], [ 36, 4, 1, 576 ], [ 36, 5, 1, 576 ], [ 36, 6, 1, 576 ], [ 37, 1, 1, 768 ], [ 37, 2, 1, 384 ], [ 38, 1, 1, 1152 ], [ 38, 2, 1, 576 ], [ 38, 3, 1, 576 ], [ 39, 1, 1, 384 ], [ 39, 2, 1, 192 ], [ 39, 3, 1, 192 ], [ 39, 4, 1, 192 ], [ 39, 5, 1, 192 ], [ 40, 1, 1, 1152 ], [ 40, 2, 1, 576 ], [ 40, 3, 1, 576 ], [ 41, 2, 1, 384 ], [ 41, 3, 1, 384 ], [ 41, 4, 1, 384 ], [ 41, 5, 1, 384 ], [ 41, 6, 1, 384 ], [ 41, 7, 1, 384 ] ] 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^4-17*q^3+99*q^2-227*q+160 ) 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^4-17*q^3+99*q^2-227*q+168 ) 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^4-17*q^3+99*q^2-227*q+160 ) q congruent 7 modulo 12: 1/64 phi1 ( q^4-17*q^3+99*q^2-227*q+168 ) 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^4-17*q^3+99*q^2-227*q+160 ) q congruent 11 modulo 12: 1/64 phi1 ( q^4-17*q^3+99*q^2-227*q+168 ) 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 ], [ 4, 2, 1, 24 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 24 ], [ 8, 1, 1, 48 ], [ 9, 1, 1, 72 ], [ 10, 1, 1, 96 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 96 ], [ 12, 2, 1, 48 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 1, 3, 16 ], [ 15, 2, 1, 24 ], [ 15, 2, 3, 8 ], [ 15, 3, 1, 24 ], [ 15, 3, 3, 8 ], [ 15, 4, 1, 24 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 48 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 24 ], [ 17, 2, 3, 6 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 8 ], [ 18, 2, 1, 12 ], [ 18, 2, 2, 4 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 96 ], [ 20, 2, 1, 48 ], [ 21, 1, 1, 144 ], [ 22, 1, 1, 72 ], [ 22, 1, 2, 40 ], [ 23, 1, 1, 16 ], [ 23, 1, 2, 16 ], [ 23, 2, 1, 8 ], [ 23, 2, 2, 8 ], [ 24, 1, 1, 48 ], [ 24, 1, 2, 32 ], [ 25, 1, 1, 96 ], [ 25, 1, 5, 32 ], [ 25, 2, 1, 48 ], [ 25, 2, 5, 16 ], [ 25, 3, 1, 48 ], [ 25, 3, 5, 16 ], [ 25, 4, 1, 48 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 48 ], [ 26, 1, 2, 16 ], [ 27, 1, 1, 192 ], [ 27, 1, 8, 64 ], [ 27, 2, 1, 96 ], [ 27, 2, 8, 32 ], [ 27, 3, 1, 96 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 32 ], [ 28, 1, 3, 16 ], [ 28, 2, 4, 8 ], [ 29, 1, 2, 32 ], [ 29, 2, 2, 16 ], [ 30, 1, 1, 96 ], [ 30, 1, 2, 64 ], [ 30, 2, 1, 48 ], [ 30, 2, 2, 32 ], [ 31, 1, 1, 48 ], [ 31, 1, 2, 32 ], [ 31, 1, 3, 48 ], [ 31, 2, 1, 24 ], [ 31, 2, 2, 16 ], [ 31, 2, 3, 24 ], [ 32, 1, 1, 144 ], [ 32, 1, 6, 80 ], [ 33, 1, 3, 64 ], [ 33, 2, 3, 32 ], [ 33, 3, 3, 32 ], [ 33, 4, 3, 32 ], [ 34, 1, 1, 48 ], [ 34, 1, 2, 16 ], [ 34, 2, 1, 24 ], [ 34, 2, 2, 8 ], [ 34, 3, 1, 24 ], [ 34, 3, 2, 8 ], [ 35, 1, 2, 48 ], [ 35, 2, 2, 24 ], [ 36, 1, 1, 192 ], [ 36, 1, 4, 64 ], [ 36, 2, 1, 96 ], [ 36, 2, 4, 32 ], [ 36, 2, 14, 32 ], [ 36, 3, 1, 96 ], [ 36, 3, 4, 32 ], [ 36, 3, 14, 32 ], [ 36, 4, 1, 96 ], [ 36, 4, 4, 32 ], [ 36, 4, 14, 32 ], [ 36, 5, 1, 96 ], [ 36, 5, 4, 32 ], [ 36, 6, 1, 96 ], [ 36, 6, 5, 32 ], [ 37, 1, 2, 64 ], [ 37, 2, 2, 32 ], [ 38, 1, 1, 96 ], [ 38, 1, 2, 64 ], [ 38, 1, 8, 96 ], [ 38, 2, 1, 48 ], [ 38, 2, 2, 32 ], [ 38, 2, 8, 48 ], [ 38, 3, 1, 48 ], [ 38, 3, 2, 32 ], [ 38, 3, 7, 48 ], [ 39, 1, 2, 32 ], [ 39, 2, 2, 16 ], [ 39, 3, 2, 16 ], [ 39, 4, 2, 16 ], [ 39, 5, 2, 16 ], [ 40, 1, 17, 96 ], [ 40, 2, 22, 48 ], [ 40, 3, 4, 48 ], [ 41, 2, 2, 32 ], [ 41, 3, 2, 32 ], [ 41, 4, 2, 32 ], [ 41, 4, 4, 32 ], [ 41, 5, 2, 32 ], [ 41, 6, 2, 32 ], [ 41, 7, 2, 32 ] ] 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^4-7*q^3+9*q^2+13*q-12 ) 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^3-9*q^2+25*q-21 ) 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^3-9*q^2+25*q-21 ) q congruent 7 modulo 12: 1/24 phi1 ( q^4-7*q^3+9*q^2+13*q-12 ) 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^3-9*q^2+25*q-21 ) q congruent 11 modulo 12: 1/24 q phi2 ( q^3-9*q^2+25*q-21 ) 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 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 12, 2, 1, 12 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 20, 2, 1, 8 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 8 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 8 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 1, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 29, 1, 3, 12 ], [ 29, 2, 3, 6 ], [ 30, 1, 1, 8 ], [ 30, 2, 1, 4 ], [ 33, 1, 2, 24 ], [ 33, 2, 2, 12 ], [ 33, 3, 2, 12 ], [ 33, 4, 2, 12 ], [ 35, 1, 8, 18 ], [ 35, 2, 8, 9 ], [ 37, 1, 3, 24 ], [ 37, 2, 3, 12 ], [ 39, 1, 3, 12 ], [ 39, 2, 3, 6 ], [ 39, 3, 3, 6 ], [ 40, 1, 7, 36 ], [ 40, 2, 2, 18 ], [ 40, 3, 10, 18 ], [ 41, 2, 3, 12 ], [ 41, 3, 3, 12 ], [ 41, 5, 3, 12 ], [ 41, 6, 3, 12 ], [ 41, 7, 3, 12 ] ] 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 phi2^2 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 3 modulo 12: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 5 modulo 12: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/16 q^2 ( q^3-4*q^2+8 ) q congruent 9 modulo 12: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/16 phi1 phi2^2 ( q^2-5*q+6 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 8, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 37, 1, 4, 16 ], [ 37, 2, 4, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 2, 4, 8 ], [ 41, 3, 4, 8 ] ] 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^3-8*q^2+13*q+10 ) 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^5-10*q^4+30*q^3-24*q^2-7*q-6 ) 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^3-8*q^2+13*q+10 ) q congruent 7 modulo 12: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) 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^3-8*q^2+13*q+10 ) q congruent 11 modulo 12: 1/64 ( q^5-10*q^4+30*q^3-24*q^2-7*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 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 ], [ 4, 2, 1, 12 ], [ 4, 2, 2, 4 ], [ 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 ], [ 15, 2, 3, 16 ], [ 15, 3, 3, 16 ], [ 15, 4, 3, 16 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 12 ], [ 18, 1, 2, 16 ], [ 18, 2, 2, 8 ], [ 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 ], [ 25, 2, 5, 32 ], [ 25, 3, 5, 32 ], [ 25, 4, 5, 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 ], [ 27, 2, 1, 48 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 48 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 48 ], [ 27, 3, 9, 48 ], [ 27, 3, 11, 16 ], [ 30, 1, 2, 64 ], [ 30, 2, 2, 32 ], [ 31, 1, 2, 32 ], [ 31, 1, 4, 32 ], [ 31, 2, 2, 16 ], [ 31, 2, 4, 16 ], [ 32, 1, 1, 48 ], [ 32, 1, 2, 32 ], [ 32, 1, 3, 48 ], [ 32, 1, 6, 64 ], [ 34, 1, 2, 32 ], [ 34, 2, 2, 16 ], [ 34, 3, 2, 16 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 1, 4, 128 ], [ 36, 2, 4, 64 ], [ 36, 2, 14, 64 ], [ 36, 3, 4, 64 ], [ 36, 3, 14, 64 ], [ 36, 4, 4, 64 ], [ 36, 4, 14, 64 ], [ 36, 5, 4, 64 ], [ 36, 6, 5, 64 ], [ 37, 1, 5, 64 ], [ 37, 2, 5, 32 ], [ 38, 1, 2, 64 ], [ 38, 1, 5, 64 ], [ 38, 2, 2, 32 ], [ 38, 2, 5, 32 ], [ 38, 3, 2, 32 ], [ 38, 3, 8, 32 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 2, 5, 32 ], [ 41, 3, 5, 32 ], [ 41, 4, 3, 32 ] ] 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^4-11*q^3+41*q^2-65*q+50 ) 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 phi1 ( q^4-11*q^3+41*q^2-65*q+42 ) 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^4-11*q^3+41*q^2-65*q+50 ) q congruent 7 modulo 12: 1/64 phi1 ( q^4-11*q^3+41*q^2-65*q+42 ) 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^4-11*q^3+41*q^2-65*q+50 ) q congruent 11 modulo 12: 1/64 phi1 ( q^4-11*q^3+41*q^2-65*q+42 ) 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 ], [ 4, 2, 2, 24 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 24 ], [ 8, 1, 2, 48 ], [ 9, 1, 2, 72 ], [ 10, 1, 4, 96 ], [ 11, 1, 2, 24 ], [ 12, 1, 6, 96 ], [ 12, 2, 3, 48 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 2, 16 ], [ 15, 1, 4, 48 ], [ 15, 2, 2, 8 ], [ 15, 2, 4, 24 ], [ 15, 3, 2, 8 ], [ 15, 3, 4, 24 ], [ 15, 4, 2, 8 ], [ 15, 4, 4, 24 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 8 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 48 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 24 ], [ 18, 1, 3, 24 ], [ 18, 1, 4, 8 ], [ 18, 2, 3, 12 ], [ 18, 2, 4, 4 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 96 ], [ 20, 2, 2, 48 ], [ 21, 1, 6, 144 ], [ 22, 1, 3, 40 ], [ 22, 1, 4, 72 ], [ 23, 1, 3, 16 ], [ 23, 1, 4, 16 ], [ 23, 2, 3, 8 ], [ 23, 2, 4, 8 ], [ 24, 1, 3, 48 ], [ 24, 1, 4, 32 ], [ 25, 1, 4, 32 ], [ 25, 1, 8, 96 ], [ 25, 2, 4, 16 ], [ 25, 2, 8, 48 ], [ 25, 3, 4, 16 ], [ 25, 3, 8, 48 ], [ 25, 4, 4, 16 ], [ 25, 4, 8, 48 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 48 ], [ 27, 1, 8, 64 ], [ 27, 1, 12, 192 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 96 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 32 ], [ 27, 3, 11, 96 ], [ 28, 1, 2, 16 ], [ 28, 2, 2, 8 ], [ 29, 1, 5, 32 ], [ 29, 2, 5, 16 ], [ 30, 1, 5, 96 ], [ 30, 1, 6, 64 ], [ 30, 2, 5, 48 ], [ 30, 2, 6, 32 ], [ 31, 1, 5, 48 ], [ 31, 1, 7, 48 ], [ 31, 1, 8, 32 ], [ 31, 2, 5, 24 ], [ 31, 2, 7, 24 ], [ 31, 2, 8, 16 ], [ 32, 1, 3, 80 ], [ 32, 1, 7, 144 ], [ 33, 1, 4, 64 ], [ 33, 2, 4, 32 ], [ 33, 3, 4, 32 ], [ 33, 4, 4, 32 ], [ 34, 1, 3, 16 ], [ 34, 1, 4, 48 ], [ 34, 2, 9, 8 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 24 ], [ 34, 3, 6, 8 ], [ 35, 1, 4, 48 ], [ 35, 2, 4, 24 ], [ 36, 1, 18, 64 ], [ 36, 1, 20, 192 ], [ 36, 2, 17, 32 ], [ 36, 2, 23, 32 ], [ 36, 2, 25, 96 ], [ 36, 3, 17, 32 ], [ 36, 3, 23, 32 ], [ 36, 3, 25, 96 ], [ 36, 4, 17, 32 ], [ 36, 4, 23, 32 ], [ 36, 4, 25, 96 ], [ 36, 5, 18, 32 ], [ 36, 5, 20, 96 ], [ 36, 6, 9, 32 ], [ 36, 6, 13, 96 ], [ 37, 1, 7, 64 ], [ 37, 2, 7, 32 ], [ 38, 1, 3, 96 ], [ 38, 1, 6, 64 ], [ 38, 1, 7, 96 ], [ 38, 2, 3, 48 ], [ 38, 2, 6, 32 ], [ 38, 2, 7, 48 ], [ 38, 3, 3, 48 ], [ 38, 3, 5, 48 ], [ 38, 3, 6, 32 ], [ 39, 1, 11, 32 ], [ 39, 2, 11, 16 ], [ 39, 3, 11, 16 ], [ 39, 4, 11, 16 ], [ 39, 5, 11, 16 ], [ 40, 1, 18, 96 ], [ 40, 2, 23, 48 ], [ 40, 3, 3, 48 ], [ 41, 2, 6, 32 ], [ 41, 3, 6, 32 ], [ 41, 4, 10, 32 ], [ 41, 4, 13, 32 ], [ 41, 5, 8, 32 ], [ 41, 6, 8, 32 ], [ 41, 7, 8, 32 ] ] 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 phi1^4 ( q-4 ) 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^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 4 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/64 phi1^4 ( q-4 ) q congruent 7 modulo 12: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) q congruent 8 modulo 12: 1/64 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/64 phi1^4 ( q-4 ) q congruent 11 modulo 12: 1/64 ( q^5-8*q^4+22*q^3-28*q^2+17*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 12 ], [ 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 ], [ 15, 2, 2, 16 ], [ 15, 3, 2, 16 ], [ 15, 4, 2, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 18 ], [ 18, 1, 4, 16 ], [ 18, 2, 4, 8 ], [ 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 ], [ 25, 2, 4, 32 ], [ 25, 3, 4, 32 ], [ 25, 4, 4, 32 ], [ 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 48 ], [ 27, 2, 12, 48 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 48 ], [ 27, 3, 9, 48 ], [ 27, 3, 11, 48 ], [ 30, 1, 6, 64 ], [ 30, 2, 6, 32 ], [ 31, 1, 6, 32 ], [ 31, 1, 8, 32 ], [ 31, 2, 6, 16 ], [ 31, 2, 8, 16 ], [ 32, 1, 3, 64 ], [ 32, 1, 5, 32 ], [ 32, 1, 6, 48 ], [ 32, 1, 7, 48 ], [ 34, 1, 3, 32 ], [ 34, 2, 9, 16 ], [ 34, 3, 6, 16 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 1, 18, 128 ], [ 36, 2, 17, 64 ], [ 36, 2, 23, 64 ], [ 36, 3, 17, 64 ], [ 36, 3, 23, 64 ], [ 36, 4, 17, 64 ], [ 36, 4, 23, 64 ], [ 36, 5, 18, 64 ], [ 36, 6, 9, 64 ], [ 37, 1, 9, 64 ], [ 37, 2, 9, 32 ], [ 38, 1, 4, 64 ], [ 38, 1, 6, 64 ], [ 38, 2, 4, 32 ], [ 38, 2, 6, 32 ], [ 38, 3, 4, 32 ], [ 38, 3, 6, 32 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 2, 7, 32 ], [ 41, 3, 7, 32 ], [ 41, 4, 12, 32 ] ] 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 phi1^2 ( q^2-2*q-1 ) 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 phi1^2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/24 q^2 phi1^2 ( q-2 ) q congruent 5 modulo 12: 1/24 phi1 phi2 ( q^3-4*q^2+5*q-4 ) q congruent 7 modulo 12: 1/24 q phi1^2 ( q^2-2*q-1 ) 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 phi1^2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/24 phi1 phi2 ( q^3-4*q^2+5*q-4 ) 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 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 12, 2, 3, 12 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 20, 2, 2, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 4, 8 ], [ 24, 1, 3, 4 ], [ 25, 1, 8, 8 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 29, 1, 6, 12 ], [ 29, 2, 6, 6 ], [ 30, 1, 5, 8 ], [ 30, 2, 5, 4 ], [ 33, 1, 5, 24 ], [ 33, 2, 5, 12 ], [ 33, 3, 5, 12 ], [ 33, 4, 5, 12 ], [ 35, 1, 9, 18 ], [ 35, 2, 9, 9 ], [ 37, 1, 8, 24 ], [ 37, 2, 8, 12 ], [ 39, 1, 12, 12 ], [ 39, 2, 12, 6 ], [ 39, 3, 12, 6 ], [ 40, 1, 8, 36 ], [ 40, 2, 5, 18 ], [ 40, 3, 9, 18 ], [ 41, 2, 8, 12 ], [ 41, 3, 8, 12 ], [ 41, 5, 9, 12 ], [ 41, 6, 9, 12 ], [ 41, 7, 9, 12 ] ] 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 q phi1^3 phi2 q congruent 2 modulo 12: 1/16 q^4 ( q-2 ) q congruent 3 modulo 12: 1/16 q phi1^3 phi2 q congruent 4 modulo 12: 1/16 q^4 ( q-2 ) q congruent 5 modulo 12: 1/16 q phi1^3 phi2 q congruent 7 modulo 12: 1/16 q phi1^3 phi2 q congruent 8 modulo 12: 1/16 q^4 ( q-2 ) q congruent 9 modulo 12: 1/16 q phi1^3 phi2 q congruent 11 modulo 12: 1/16 q phi1^3 phi2 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 3, 2 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 37, 1, 10, 16 ], [ 37, 2, 10, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 2, 9, 8 ], [ 41, 3, 9, 8 ] ] 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 phi1^2 ( q^3-6*q^2+q+28 ) q congruent 2 modulo 12: 1/128 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/128 ( q^5-8*q^4+14*q^3+20*q^2-71*q+60 ) q congruent 4 modulo 12: 1/128 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/128 phi1^2 ( q^3-6*q^2+q+28 ) q congruent 7 modulo 12: 1/128 ( q^5-8*q^4+14*q^3+20*q^2-71*q+60 ) q congruent 8 modulo 12: 1/128 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/128 phi1^2 ( q^3-6*q^2+q+28 ) q congruent 11 modulo 12: 1/128 ( q^5-8*q^4+14*q^3+20*q^2-71*q+60 ) 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 12 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 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 ], [ 14, 2, 2, 16 ], [ 15, 1, 3, 16 ], [ 15, 1, 4, 48 ], [ 15, 2, 3, 8 ], [ 15, 2, 4, 24 ], [ 15, 3, 3, 8 ], [ 15, 3, 4, 24 ], [ 15, 4, 3, 8 ], [ 15, 4, 4, 24 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 12 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 18 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 24 ], [ 18, 2, 2, 4 ], [ 18, 2, 3, 12 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 48 ], [ 23, 1, 3, 32 ], [ 23, 2, 3, 16 ], [ 25, 1, 5, 32 ], [ 25, 1, 6, 32 ], [ 25, 1, 7, 32 ], [ 25, 1, 8, 96 ], [ 25, 2, 5, 16 ], [ 25, 2, 6, 16 ], [ 25, 2, 7, 16 ], [ 25, 2, 8, 48 ], [ 25, 3, 5, 16 ], [ 25, 3, 6, 16 ], [ 25, 3, 7, 16 ], [ 25, 3, 8, 48 ], [ 25, 4, 5, 16 ], [ 25, 4, 6, 16 ], [ 25, 4, 7, 16 ], [ 25, 4, 8, 48 ], [ 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 48 ], [ 27, 2, 12, 48 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 48 ], [ 27, 3, 9, 48 ], [ 27, 3, 11, 48 ], [ 31, 1, 4, 32 ], [ 31, 1, 5, 96 ], [ 31, 2, 4, 16 ], [ 31, 2, 5, 48 ], [ 32, 1, 3, 96 ], [ 32, 1, 6, 32 ], [ 34, 1, 2, 16 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 32 ], [ 34, 2, 2, 8 ], [ 34, 2, 3, 16 ], [ 34, 2, 10, 24 ], [ 34, 3, 2, 8 ], [ 34, 3, 3, 16 ], [ 34, 3, 5, 24 ], [ 34, 3, 8, 16 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 1, 4, 64 ], [ 36, 1, 5, 64 ], [ 36, 1, 20, 192 ], [ 36, 2, 4, 32 ], [ 36, 2, 5, 32 ], [ 36, 2, 14, 32 ], [ 36, 2, 25, 96 ], [ 36, 3, 4, 32 ], [ 36, 3, 5, 32 ], [ 36, 3, 14, 32 ], [ 36, 3, 25, 96 ], [ 36, 4, 4, 32 ], [ 36, 4, 5, 32 ], [ 36, 4, 14, 32 ], [ 36, 4, 25, 96 ], [ 36, 5, 4, 32 ], [ 36, 5, 5, 32 ], [ 36, 5, 20, 96 ], [ 36, 6, 5, 32 ], [ 36, 6, 6, 32 ], [ 36, 6, 8, 32 ], [ 36, 6, 13, 96 ], [ 36, 6, 14, 32 ], [ 36, 6, 15, 32 ], [ 38, 1, 3, 192 ], [ 38, 1, 5, 64 ], [ 38, 2, 3, 96 ], [ 38, 2, 5, 32 ], [ 38, 3, 3, 96 ], [ 38, 3, 8, 32 ], [ 39, 1, 4, 64 ], [ 39, 1, 13, 64 ], [ 39, 2, 4, 32 ], [ 39, 2, 13, 32 ], [ 39, 3, 4, 32 ], [ 39, 3, 13, 32 ], [ 39, 4, 3, 32 ], [ 39, 4, 5, 32 ], [ 39, 4, 12, 32 ], [ 39, 4, 13, 32 ], [ 39, 5, 3, 32 ], [ 39, 5, 5, 32 ], [ 39, 5, 12, 32 ], [ 39, 5, 13, 32 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 2, 10, 64 ], [ 41, 3, 10, 64 ], [ 41, 4, 5, 64 ], [ 41, 4, 9, 64 ], [ 41, 4, 14, 64 ], [ 41, 5, 4, 64 ], [ 41, 5, 10, 64 ], [ 41, 6, 4, 64 ], [ 41, 6, 10, 64 ], [ 41, 7, 4, 64 ], [ 41, 7, 10, 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 ( q^4-7*q^3+13*q^2-5*q+14 ) 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 ( q^4-7*q^3+13*q^2-5*q+6 ) 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 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 7 modulo 12: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) 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 ( q^4-7*q^3+13*q^2-5*q+14 ) q congruent 11 modulo 12: 1/64 phi1 ( q^4-7*q^3+13*q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 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 ], [ 4, 2, 1, 12 ], [ 4, 2, 2, 4 ], [ 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 ], [ 15, 2, 2, 8 ], [ 15, 2, 3, 8 ], [ 15, 3, 2, 8 ], [ 15, 3, 3, 8 ], [ 15, 4, 2, 8 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 12 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 8 ], [ 18, 2, 2, 4 ], [ 18, 2, 4, 4 ], [ 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 ], [ 25, 2, 4, 16 ], [ 25, 2, 5, 16 ], [ 25, 3, 4, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 4, 16 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 8 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 96 ], [ 27, 1, 12, 32 ], [ 27, 2, 1, 48 ], [ 27, 2, 8, 48 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 48 ], [ 27, 3, 9, 48 ], [ 27, 3, 11, 16 ], [ 28, 1, 3, 16 ], [ 28, 2, 4, 8 ], [ 30, 1, 2, 32 ], [ 30, 2, 2, 16 ], [ 31, 1, 2, 16 ], [ 31, 1, 4, 16 ], [ 31, 1, 6, 32 ], [ 31, 2, 2, 8 ], [ 31, 2, 4, 8 ], [ 31, 2, 6, 16 ], [ 32, 1, 1, 48 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 80 ], [ 34, 1, 2, 16 ], [ 34, 1, 3, 16 ], [ 34, 2, 2, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 2, 8 ], [ 34, 3, 6, 8 ], [ 35, 1, 2, 48 ], [ 35, 2, 2, 24 ], [ 36, 1, 4, 64 ], [ 36, 1, 18, 64 ], [ 36, 2, 4, 32 ], [ 36, 2, 14, 32 ], [ 36, 2, 17, 32 ], [ 36, 2, 23, 32 ], [ 36, 3, 4, 32 ], [ 36, 3, 14, 32 ], [ 36, 3, 17, 32 ], [ 36, 3, 23, 32 ], [ 36, 4, 4, 32 ], [ 36, 4, 14, 32 ], [ 36, 4, 17, 32 ], [ 36, 4, 23, 32 ], [ 36, 5, 4, 32 ], [ 36, 5, 18, 32 ], [ 36, 6, 5, 32 ], [ 36, 6, 9, 32 ], [ 38, 1, 2, 32 ], [ 38, 1, 4, 64 ], [ 38, 1, 5, 32 ], [ 38, 2, 2, 16 ], [ 38, 2, 4, 32 ], [ 38, 2, 5, 16 ], [ 38, 3, 2, 16 ], [ 38, 3, 4, 32 ], [ 38, 3, 8, 16 ], [ 39, 1, 5, 32 ], [ 39, 2, 5, 16 ], [ 39, 3, 5, 16 ], [ 39, 4, 6, 16 ], [ 39, 5, 6, 16 ], [ 40, 1, 17, 96 ], [ 40, 2, 22, 48 ], [ 40, 3, 4, 48 ], [ 41, 2, 11, 32 ], [ 41, 3, 11, 32 ], [ 41, 4, 11, 32 ], [ 41, 4, 15, 32 ], [ 41, 5, 5, 32 ], [ 41, 6, 5, 32 ], [ 41, 7, 5, 32 ] ] 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-q-4 ) q congruent 2 modulo 12: 1/32 q^4 ( q-2 ) q congruent 3 modulo 12: 1/32 phi1^2 phi2 ( q^2-q-4 ) q congruent 4 modulo 12: 1/32 q^4 ( q-2 ) q congruent 5 modulo 12: 1/32 phi1^2 phi2 ( q^2-q-4 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 ( q^2-q-4 ) q congruent 8 modulo 12: 1/32 q^4 ( q-2 ) q congruent 9 modulo 12: 1/32 phi1^2 phi2 ( q^2-q-4 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 ( q^2-q-4 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 14, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 34, 1, 7, 8 ], [ 34, 1, 8, 8 ], [ 34, 2, 3, 4 ], [ 34, 2, 5, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 8, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 1, 5, 16 ], [ 36, 1, 10, 16 ], [ 36, 2, 5, 8 ], [ 36, 2, 16, 8 ], [ 36, 3, 5, 8 ], [ 36, 3, 16, 8 ], [ 36, 4, 5, 8 ], [ 36, 4, 16, 8 ], [ 36, 5, 5, 8 ], [ 36, 5, 10, 8 ], [ 36, 6, 6, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 14, 8 ], [ 36, 6, 15, 8 ], [ 39, 1, 6, 16 ], [ 39, 1, 14, 16 ], [ 39, 2, 6, 8 ], [ 39, 2, 14, 8 ], [ 39, 3, 6, 8 ], [ 39, 3, 14, 8 ], [ 39, 4, 4, 8 ], [ 39, 4, 14, 8 ], [ 39, 5, 4, 8 ], [ 39, 5, 14, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 2, 12, 16 ], [ 41, 3, 12, 16 ], [ 41, 4, 6, 16 ], [ 41, 4, 8, 16 ], [ 41, 5, 6, 16 ], [ 41, 5, 11, 16 ], [ 41, 6, 6, 16 ], [ 41, 6, 11, 16 ], [ 41, 7, 6, 16 ], [ 41, 7, 11, 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 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) 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 ], [ 4, 2, 1, 6 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 21, 1, 1, 12 ], [ 22, 1, 2, 8 ], [ 24, 1, 2, 4 ], [ 25, 1, 5, 8 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 1, 2, 8 ], [ 30, 2, 2, 4 ], [ 35, 1, 8, 18 ], [ 35, 2, 8, 9 ], [ 39, 1, 7, 12 ], [ 39, 2, 7, 6 ], [ 39, 3, 7, 6 ], [ 40, 1, 7, 36 ], [ 40, 2, 2, 18 ], [ 40, 3, 10, 18 ], [ 41, 2, 13, 12 ], [ 41, 3, 13, 12 ], [ 41, 5, 7, 12 ], [ 41, 6, 7, 12 ], [ 41, 7, 7, 12 ] ] 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+q-4 ) q congruent 2 modulo 12: 1/64 q^3 ( q^2-4 ) q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 4 modulo 12: 1/64 q^3 ( q^2-4 ) q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 8 modulo 12: 1/64 q^3 ( q^2-4 ) q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q^2+q-4 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q^2+q-4 ) 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 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 2, 7, 24 ], [ 32, 1, 4, 32 ], [ 34, 1, 8, 16 ], [ 34, 2, 5, 8 ], [ 36, 1, 10, 32 ], [ 36, 2, 16, 16 ], [ 36, 3, 16, 16 ], [ 36, 4, 16, 16 ], [ 36, 5, 10, 16 ], [ 40, 1, 6, 96 ], [ 40, 2, 14, 48 ], [ 41, 2, 14, 32 ], [ 41, 3, 14, 32 ], [ 41, 4, 7, 32 ] ] 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^4-19*q^3+123*q^2-289*q+120 ) 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 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) 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^4-19*q^3+123*q^2-289*q+120 ) q congruent 7 modulo 12: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) 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^4-19*q^3+123*q^2-289*q+120 ) q congruent 11 modulo 12: 1/768 ( q^5-20*q^4+142*q^3-412*q^2+361*q+168 ) Fusion of maximal tori of C^F in those of G^F: [ 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 ], [ 4, 2, 1, 24 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 11, 1, 1, 96 ], [ 15, 1, 3, 32 ], [ 15, 2, 3, 16 ], [ 15, 3, 3, 16 ], [ 15, 4, 3, 16 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 144 ], [ 17, 1, 3, 28 ], [ 17, 2, 1, 72 ], [ 17, 2, 3, 14 ], [ 18, 1, 2, 16 ], [ 18, 2, 2, 8 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 288 ], [ 22, 1, 2, 32 ], [ 24, 1, 2, 64 ], [ 25, 1, 5, 128 ], [ 25, 2, 5, 64 ], [ 25, 3, 5, 64 ], [ 25, 4, 5, 64 ], [ 26, 1, 1, 144 ], [ 26, 1, 2, 48 ], [ 27, 1, 1, 576 ], [ 27, 1, 8, 192 ], [ 27, 2, 1, 288 ], [ 27, 2, 8, 96 ], [ 27, 3, 1, 288 ], [ 27, 3, 5, 96 ], [ 27, 3, 9, 96 ], [ 28, 1, 1, 192 ], [ 28, 2, 1, 96 ], [ 30, 1, 2, 128 ], [ 30, 2, 2, 64 ], [ 31, 1, 2, 192 ], [ 31, 2, 2, 96 ], [ 32, 1, 1, 576 ], [ 32, 1, 6, 192 ], [ 34, 1, 2, 96 ], [ 34, 2, 2, 48 ], [ 34, 3, 2, 48 ], [ 35, 1, 1, 576 ], [ 35, 2, 1, 288 ], [ 36, 1, 4, 384 ], [ 36, 2, 4, 192 ], [ 36, 2, 14, 192 ], [ 36, 3, 4, 192 ], [ 36, 3, 14, 192 ], [ 36, 4, 4, 192 ], [ 36, 4, 14, 192 ], [ 36, 5, 4, 192 ], [ 36, 6, 5, 192 ], [ 38, 1, 2, 384 ], [ 38, 2, 2, 192 ], [ 38, 3, 2, 192 ], [ 39, 1, 8, 384 ], [ 39, 2, 8, 192 ], [ 39, 3, 8, 192 ], [ 39, 4, 7, 192 ], [ 39, 5, 7, 192 ], [ 40, 1, 1, 1152 ], [ 40, 2, 1, 576 ], [ 40, 3, 1, 576 ], [ 41, 2, 15, 384 ], [ 41, 3, 15, 384 ], [ 41, 4, 16, 384 ], [ 41, 5, 12, 384 ], [ 41, 6, 12, 384 ], [ 41, 7, 12, 384 ] ] 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^4-27*q^3+259*q^2-1049*q+1584 ) 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^5-28*q^4+286*q^3-1308*q^2+2585*q-1680 ) 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^5-28*q^4+286*q^3-1308*q^2+2761*q-2480 ) q congruent 7 modulo 12: 1/768 ( q^5-28*q^4+286*q^3-1308*q^2+2585*q-1680 ) 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^4-27*q^3+259*q^2-1049*q+1584 ) q congruent 11 modulo 12: 1/768 ( q^5-28*q^4+286*q^3-1308*q^2+2713*q-2576 ) 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 ], [ 4, 2, 2, 72 ], [ 5, 1, 2, 16 ], [ 5, 2, 2, 8 ], [ 6, 1, 2, 16 ], [ 6, 2, 2, 8 ], [ 7, 1, 2, 72 ], [ 8, 1, 2, 192 ], [ 9, 1, 2, 320 ], [ 10, 1, 4, 384 ], [ 11, 1, 2, 128 ], [ 12, 1, 6, 384 ], [ 12, 2, 3, 192 ], [ 13, 1, 2, 64 ], [ 14, 1, 2, 128 ], [ 14, 2, 2, 64 ], [ 15, 1, 4, 224 ], [ 15, 2, 4, 112 ], [ 15, 3, 4, 112 ], [ 15, 4, 4, 112 ], [ 16, 1, 2, 26 ], [ 17, 1, 3, 172 ], [ 17, 2, 3, 86 ], [ 18, 1, 3, 112 ], [ 18, 2, 3, 56 ], [ 19, 1, 2, 320 ], [ 20, 1, 2, 640 ], [ 20, 2, 2, 320 ], [ 21, 1, 6, 768 ], [ 22, 1, 4, 512 ], [ 23, 1, 4, 192 ], [ 23, 2, 4, 96 ], [ 24, 1, 3, 448 ], [ 25, 1, 8, 512 ], [ 25, 2, 8, 256 ], [ 25, 3, 8, 256 ], [ 25, 4, 8, 256 ], [ 26, 1, 3, 240 ], [ 27, 1, 12, 960 ], [ 27, 2, 12, 480 ], [ 27, 3, 11, 480 ], [ 28, 1, 6, 192 ], [ 28, 2, 6, 96 ], [ 29, 1, 4, 384 ], [ 29, 2, 4, 192 ], [ 30, 1, 5, 896 ], [ 30, 2, 5, 448 ], [ 31, 1, 7, 576 ], [ 31, 2, 7, 288 ], [ 32, 1, 7, 1152 ], [ 33, 1, 6, 768 ], [ 33, 2, 6, 384 ], [ 33, 3, 6, 384 ], [ 33, 4, 6, 384 ], [ 34, 1, 4, 288 ], [ 34, 2, 10, 144 ], [ 34, 3, 5, 144 ], [ 35, 1, 10, 576 ], [ 35, 2, 10, 288 ], [ 36, 1, 20, 1152 ], [ 36, 2, 25, 576 ], [ 36, 3, 25, 576 ], [ 36, 4, 25, 576 ], [ 36, 5, 20, 576 ], [ 36, 6, 13, 576 ], [ 37, 1, 6, 768 ], [ 37, 2, 6, 384 ], [ 38, 1, 7, 1152 ], [ 38, 2, 7, 576 ], [ 38, 3, 5, 576 ], [ 39, 1, 15, 384 ], [ 39, 2, 15, 192 ], [ 39, 3, 15, 192 ], [ 39, 4, 15, 192 ], [ 39, 5, 15, 192 ], [ 40, 1, 2, 1152 ], [ 40, 2, 13, 576 ], [ 40, 3, 19, 576 ], [ 41, 2, 16, 384 ], [ 41, 3, 16, 384 ], [ 41, 4, 17, 384 ], [ 41, 5, 13, 384 ], [ 41, 6, 13, 384 ], [ 41, 7, 13, 384 ] ] 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 phi1 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) 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 ], [ 4, 2, 2, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 8 ], [ 24, 1, 4, 4 ], [ 25, 1, 4, 8 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 4, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 1, 6, 8 ], [ 30, 2, 6, 4 ], [ 35, 1, 9, 18 ], [ 35, 2, 9, 9 ], [ 39, 1, 16, 12 ], [ 39, 2, 16, 6 ], [ 39, 3, 16, 6 ], [ 40, 1, 8, 36 ], [ 40, 2, 5, 18 ], [ 40, 3, 9, 18 ], [ 41, 2, 17, 12 ], [ 41, 3, 17, 12 ], [ 41, 5, 17, 12 ], [ 41, 6, 17, 12 ], [ 41, 7, 17, 12 ] ] 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 phi2^2 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/32 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/32 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/32 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/32 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/32 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/32 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/32 phi1 phi2^2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/32 phi1 phi2^2 ( q^2-5*q+6 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 34, 1, 5, 8 ], [ 34, 1, 6, 8 ], [ 34, 2, 4, 4 ], [ 34, 2, 8, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 1, 2, 16 ], [ 36, 1, 17, 16 ], [ 36, 2, 2, 8 ], [ 36, 2, 13, 8 ], [ 36, 3, 2, 8 ], [ 36, 3, 13, 8 ], [ 36, 4, 2, 8 ], [ 36, 4, 13, 8 ], [ 36, 5, 2, 8 ], [ 36, 5, 17, 8 ], [ 36, 6, 2, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 10, 8 ], [ 36, 6, 11, 8 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 16 ], [ 39, 2, 9, 8 ], [ 39, 2, 17, 8 ], [ 39, 3, 9, 8 ], [ 39, 3, 17, 8 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 8 ], [ 39, 5, 10, 8 ], [ 39, 5, 16, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 2, 18, 16 ], [ 41, 3, 18, 16 ], [ 41, 4, 18, 16 ], [ 41, 4, 21, 16 ], [ 41, 5, 16, 16 ], [ 41, 5, 18, 16 ], [ 41, 6, 16, 16 ], [ 41, 6, 18, 16 ], [ 41, 7, 16, 16 ], [ 41, 7, 18, 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 ( q^4-9*q^3+21*q^2+5*q-50 ) 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 phi2 ( q^4-11*q^3+41*q^2-57*q+18 ) 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 ( q^4-9*q^3+21*q^2+5*q-50 ) q congruent 7 modulo 12: 1/128 phi2 ( q^4-11*q^3+41*q^2-57*q+18 ) 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 ( q^4-9*q^3+21*q^2+5*q-50 ) q congruent 11 modulo 12: 1/128 phi2 ( q^4-11*q^3+41*q^2-57*q+18 ) 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 ], [ 4, 2, 1, 12 ], [ 4, 2, 2, 4 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 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 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 1, 2, 16 ], [ 15, 2, 1, 24 ], [ 15, 2, 2, 8 ], [ 15, 3, 1, 24 ], [ 15, 3, 2, 8 ], [ 15, 4, 1, 24 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 24 ], [ 17, 1, 4, 16 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 12 ], [ 17, 2, 4, 8 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 8 ], [ 18, 2, 1, 12 ], [ 18, 2, 4, 4 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 16 ], [ 23, 1, 2, 32 ], [ 23, 2, 2, 16 ], [ 25, 1, 1, 96 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 32 ], [ 25, 1, 4, 32 ], [ 25, 2, 1, 48 ], [ 25, 2, 2, 16 ], [ 25, 2, 3, 16 ], [ 25, 2, 4, 16 ], [ 25, 3, 1, 48 ], [ 25, 3, 2, 16 ], [ 25, 3, 3, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 1, 48 ], [ 25, 4, 2, 16 ], [ 25, 4, 3, 16 ], [ 25, 4, 4, 16 ], [ 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 ], [ 27, 2, 1, 48 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 48 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 48 ], [ 27, 3, 9, 48 ], [ 27, 3, 11, 16 ], [ 31, 1, 3, 96 ], [ 31, 1, 6, 32 ], [ 31, 2, 3, 48 ], [ 31, 2, 6, 16 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 96 ], [ 34, 1, 1, 48 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 32 ], [ 34, 2, 1, 24 ], [ 34, 2, 4, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 1, 24 ], [ 34, 3, 4, 16 ], [ 34, 3, 6, 8 ], [ 34, 3, 7, 16 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 1, 1, 192 ], [ 36, 1, 2, 64 ], [ 36, 1, 18, 64 ], [ 36, 2, 1, 96 ], [ 36, 2, 2, 32 ], [ 36, 2, 17, 32 ], [ 36, 2, 23, 32 ], [ 36, 3, 1, 96 ], [ 36, 3, 2, 32 ], [ 36, 3, 17, 32 ], [ 36, 3, 23, 32 ], [ 36, 4, 1, 96 ], [ 36, 4, 2, 32 ], [ 36, 4, 17, 32 ], [ 36, 4, 23, 32 ], [ 36, 5, 1, 96 ], [ 36, 5, 2, 32 ], [ 36, 5, 18, 32 ], [ 36, 6, 1, 96 ], [ 36, 6, 2, 32 ], [ 36, 6, 4, 32 ], [ 36, 6, 9, 32 ], [ 36, 6, 10, 32 ], [ 36, 6, 11, 32 ], [ 38, 1, 4, 64 ], [ 38, 1, 8, 192 ], [ 38, 2, 4, 32 ], [ 38, 2, 8, 96 ], [ 38, 3, 4, 32 ], [ 38, 3, 7, 96 ], [ 39, 1, 10, 64 ], [ 39, 1, 18, 64 ], [ 39, 2, 10, 32 ], [ 39, 2, 18, 32 ], [ 39, 3, 10, 32 ], [ 39, 3, 18, 32 ], [ 39, 4, 8, 32 ], [ 39, 4, 9, 32 ], [ 39, 4, 17, 32 ], [ 39, 4, 18, 32 ], [ 39, 5, 8, 32 ], [ 39, 5, 9, 32 ], [ 39, 5, 17, 32 ], [ 39, 5, 18, 32 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 2, 19, 64 ], [ 41, 3, 19, 64 ], [ 41, 4, 19, 64 ], [ 41, 4, 22, 64 ], [ 41, 4, 24, 64 ], [ 41, 5, 14, 64 ], [ 41, 5, 19, 64 ], [ 41, 6, 14, 64 ], [ 41, 6, 19, 64 ], [ 41, 7, 14, 64 ], [ 41, 7, 19, 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^3-4*q^2+3*q-4 ) 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 ( q^4-5*q^3+7*q^2-7*q+12 ) 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^3-4*q^2+3*q-4 ) q congruent 7 modulo 12: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) 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^3-4*q^2+3*q-4 ) q congruent 11 modulo 12: 1/64 phi1 ( q^4-5*q^3+7*q^2-7*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 12 ], [ 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 ], [ 15, 2, 2, 8 ], [ 15, 2, 3, 8 ], [ 15, 3, 2, 8 ], [ 15, 3, 3, 8 ], [ 15, 4, 2, 8 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 18 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 8 ], [ 18, 2, 2, 4 ], [ 18, 2, 4, 4 ], [ 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 ], [ 25, 2, 4, 16 ], [ 25, 2, 5, 16 ], [ 25, 3, 4, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 4, 16 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 96 ], [ 27, 1, 12, 96 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 48 ], [ 27, 2, 12, 48 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 48 ], [ 27, 3, 9, 48 ], [ 27, 3, 11, 48 ], [ 28, 1, 2, 16 ], [ 28, 2, 2, 8 ], [ 30, 1, 6, 32 ], [ 30, 2, 6, 16 ], [ 31, 1, 4, 32 ], [ 31, 1, 6, 16 ], [ 31, 1, 8, 16 ], [ 31, 2, 4, 16 ], [ 31, 2, 6, 8 ], [ 31, 2, 8, 8 ], [ 32, 1, 3, 80 ], [ 32, 1, 6, 32 ], [ 32, 1, 7, 48 ], [ 34, 1, 2, 16 ], [ 34, 1, 3, 16 ], [ 34, 2, 2, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 2, 8 ], [ 34, 3, 6, 8 ], [ 35, 1, 4, 48 ], [ 35, 2, 4, 24 ], [ 36, 1, 4, 64 ], [ 36, 1, 18, 64 ], [ 36, 2, 4, 32 ], [ 36, 2, 14, 32 ], [ 36, 2, 17, 32 ], [ 36, 2, 23, 32 ], [ 36, 3, 4, 32 ], [ 36, 3, 14, 32 ], [ 36, 3, 17, 32 ], [ 36, 3, 23, 32 ], [ 36, 4, 4, 32 ], [ 36, 4, 14, 32 ], [ 36, 4, 17, 32 ], [ 36, 4, 23, 32 ], [ 36, 5, 4, 32 ], [ 36, 5, 18, 32 ], [ 36, 6, 5, 32 ], [ 36, 6, 9, 32 ], [ 38, 1, 4, 32 ], [ 38, 1, 5, 64 ], [ 38, 1, 6, 32 ], [ 38, 2, 4, 16 ], [ 38, 2, 5, 32 ], [ 38, 2, 6, 16 ], [ 38, 3, 4, 16 ], [ 38, 3, 6, 16 ], [ 38, 3, 8, 32 ], [ 39, 1, 19, 32 ], [ 39, 2, 19, 16 ], [ 39, 3, 19, 16 ], [ 39, 4, 19, 16 ], [ 39, 5, 19, 16 ], [ 40, 1, 18, 96 ], [ 40, 2, 23, 48 ], [ 40, 3, 3, 48 ], [ 41, 2, 20, 32 ], [ 41, 3, 20, 32 ], [ 41, 4, 23, 32 ], [ 41, 4, 25, 32 ], [ 41, 5, 15, 32 ], [ 41, 6, 15, 32 ], [ 41, 7, 15, 32 ] ] 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^3-2*q^2-5*q+14 ) 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^3-2*q^2-5*q+14 ) 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^3-2*q^2-5*q+14 ) q congruent 7 modulo 12: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) 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^3-2*q^2-5*q+14 ) q congruent 11 modulo 12: 1/64 phi1 phi2 ( q^3-2*q^2-5*q+14 ) 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 4 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 2, 7, 24 ], [ 32, 1, 8, 32 ], [ 34, 1, 6, 16 ], [ 34, 2, 8, 8 ], [ 36, 1, 17, 32 ], [ 36, 2, 13, 16 ], [ 36, 3, 13, 16 ], [ 36, 4, 13, 16 ], [ 36, 5, 17, 16 ], [ 40, 1, 6, 96 ], [ 40, 2, 14, 48 ], [ 41, 2, 21, 32 ], [ 41, 3, 21, 32 ], [ 41, 4, 20, 32 ] ] 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^4-13*q^3+57*q^2-103*q+90 ) 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^5-14*q^4+70*q^3-160*q^2+241*q-282 ) 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^4-13*q^3+57*q^2-103*q+90 ) q congruent 7 modulo 12: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) 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^4-13*q^3+57*q^2-103*q+90 ) q congruent 11 modulo 12: 1/768 ( q^5-14*q^4+70*q^3-160*q^2+241*q-282 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 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 ], [ 4, 2, 2, 24 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 15, 1, 2, 32 ], [ 15, 2, 2, 16 ], [ 15, 3, 2, 16 ], [ 15, 4, 2, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 24 ], [ 17, 1, 1, 28 ], [ 17, 1, 3, 144 ], [ 17, 2, 1, 14 ], [ 17, 2, 3, 72 ], [ 18, 1, 4, 16 ], [ 18, 2, 4, 8 ], [ 21, 1, 6, 192 ], [ 22, 1, 3, 32 ], [ 22, 1, 4, 288 ], [ 24, 1, 4, 64 ], [ 25, 1, 4, 128 ], [ 25, 2, 4, 64 ], [ 25, 3, 4, 64 ], [ 25, 4, 4, 64 ], [ 26, 1, 2, 48 ], [ 26, 1, 3, 144 ], [ 27, 1, 8, 192 ], [ 27, 1, 12, 576 ], [ 27, 2, 8, 96 ], [ 27, 2, 12, 288 ], [ 27, 3, 5, 96 ], [ 27, 3, 9, 96 ], [ 27, 3, 11, 288 ], [ 28, 1, 6, 192 ], [ 28, 2, 6, 96 ], [ 30, 1, 6, 128 ], [ 30, 2, 6, 64 ], [ 31, 1, 8, 192 ], [ 31, 2, 8, 96 ], [ 32, 1, 3, 192 ], [ 32, 1, 7, 576 ], [ 34, 1, 3, 96 ], [ 34, 2, 9, 48 ], [ 34, 3, 6, 48 ], [ 35, 1, 10, 576 ], [ 35, 2, 10, 288 ], [ 36, 1, 18, 384 ], [ 36, 2, 17, 192 ], [ 36, 2, 23, 192 ], [ 36, 3, 17, 192 ], [ 36, 3, 23, 192 ], [ 36, 4, 17, 192 ], [ 36, 4, 23, 192 ], [ 36, 5, 18, 192 ], [ 36, 6, 9, 192 ], [ 38, 1, 6, 384 ], [ 38, 2, 6, 192 ], [ 38, 3, 6, 192 ], [ 39, 1, 20, 384 ], [ 39, 2, 20, 192 ], [ 39, 3, 20, 192 ], [ 39, 4, 20, 192 ], [ 39, 5, 20, 192 ], [ 40, 1, 2, 1152 ], [ 40, 2, 13, 576 ], [ 40, 3, 19, 576 ], [ 41, 2, 22, 384 ], [ 41, 3, 22, 384 ], [ 41, 4, 26, 384 ], [ 41, 5, 20, 384 ], [ 41, 6, 20, 384 ], [ 41, 7, 20, 384 ] ] 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 ( q^4-7*q^3+9*q^2+23*q-42 ) q congruent 2 modulo 12: 1/192 q^2 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/192 phi2 ( q^4-9*q^3+25*q^2-11*q-30 ) 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 ( q^4-7*q^3+9*q^2+23*q-42 ) q congruent 7 modulo 12: 1/192 phi2 ( q^4-9*q^3+25*q^2-11*q-30 ) 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 ( q^4-7*q^3+9*q^2+23*q-42 ) q congruent 11 modulo 12: 1/192 phi2 ( q^4-9*q^3+25*q^2-11*q-30 ) 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 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 12 ], [ 6, 2, 2, 6 ], [ 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 ], [ 14, 2, 2, 12 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 8 ], [ 15, 2, 3, 12 ], [ 15, 2, 4, 4 ], [ 15, 3, 3, 12 ], [ 15, 3, 4, 4 ], [ 15, 4, 3, 12 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 14 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 36 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 18 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 60 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 30 ], [ 19, 1, 2, 48 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 1, 4, 48 ], [ 23, 2, 4, 24 ], [ 24, 1, 3, 16 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 72 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 24 ], [ 25, 2, 5, 12 ], [ 25, 2, 6, 36 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 12 ], [ 25, 3, 5, 12 ], [ 25, 3, 6, 36 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 12 ], [ 25, 4, 5, 12 ], [ 25, 4, 6, 36 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 12 ], [ 26, 1, 3, 72 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 11, 96 ], [ 27, 1, 13, 96 ], [ 27, 2, 2, 12 ], [ 27, 2, 11, 48 ], [ 27, 2, 13, 48 ], [ 27, 3, 7, 48 ], [ 27, 3, 8, 48 ], [ 27, 3, 12, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 29, 1, 4, 96 ], [ 29, 2, 4, 48 ], [ 30, 1, 8, 32 ], [ 30, 2, 8, 16 ], [ 31, 1, 4, 48 ], [ 31, 1, 7, 48 ], [ 31, 2, 4, 24 ], [ 31, 2, 7, 24 ], [ 32, 1, 5, 48 ], [ 34, 1, 4, 144 ], [ 34, 1, 7, 24 ], [ 34, 2, 3, 12 ], [ 34, 2, 10, 72 ], [ 34, 3, 3, 12 ], [ 34, 3, 5, 72 ], [ 34, 3, 8, 12 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 10, 24 ], [ 36, 1, 5, 48 ], [ 36, 1, 19, 192 ], [ 36, 2, 5, 24 ], [ 36, 2, 22, 96 ], [ 36, 2, 26, 96 ], [ 36, 3, 5, 24 ], [ 36, 3, 22, 96 ], [ 36, 3, 26, 96 ], [ 36, 4, 5, 24 ], [ 36, 4, 22, 96 ], [ 36, 4, 26, 96 ], [ 36, 5, 5, 24 ], [ 36, 5, 19, 96 ], [ 36, 6, 6, 24 ], [ 36, 6, 8, 24 ], [ 36, 6, 14, 24 ], [ 36, 6, 15, 24 ], [ 36, 6, 16, 96 ], [ 38, 1, 16, 96 ], [ 38, 2, 16, 48 ], [ 38, 3, 14, 48 ], [ 38, 3, 15, 48 ], [ 39, 1, 4, 96 ], [ 39, 1, 15, 96 ], [ 39, 2, 4, 48 ], [ 39, 2, 15, 48 ], [ 39, 3, 4, 48 ], [ 39, 3, 15, 48 ], [ 39, 4, 3, 48 ], [ 39, 4, 5, 48 ], [ 39, 4, 15, 48 ], [ 39, 5, 3, 48 ], [ 39, 5, 5, 48 ], [ 39, 5, 15, 48 ], [ 40, 1, 13, 96 ], [ 40, 2, 24, 48 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 48 ], [ 41, 2, 23, 96 ], [ 41, 3, 23, 96 ], [ 41, 4, 27, 96 ], [ 41, 4, 31, 96 ], [ 41, 5, 21, 96 ], [ 41, 5, 25, 96 ], [ 41, 6, 21, 96 ], [ 41, 6, 25, 96 ], [ 41, 7, 21, 96 ], [ 41, 7, 25, 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 phi1^3 ( q^2-q-8 ) q congruent 2 modulo 12: 1/32 q^2 ( q^3-4*q^2+8 ) q congruent 3 modulo 12: 1/32 q phi1 ( q^3-3*q^2-5*q+15 ) q congruent 4 modulo 12: 1/32 q^2 ( q^3-4*q^2+8 ) q congruent 5 modulo 12: 1/32 phi1^3 ( q^2-q-8 ) q congruent 7 modulo 12: 1/32 q phi1 ( q^3-3*q^2-5*q+15 ) q congruent 8 modulo 12: 1/32 q^2 ( q^3-4*q^2+8 ) q congruent 9 modulo 12: 1/32 phi1^3 ( q^2-q-8 ) q congruent 11 modulo 12: 1/32 q phi1 ( q^3-3*q^2-5*q+15 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 3, 4 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 12, 2, 2, 8 ], [ 13, 1, 2, 8 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 1, 7, 16 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 15, 2, 7, 8 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 4 ], [ 15, 3, 7, 8 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 4 ], [ 15, 4, 7, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 18, 2, 4, 4 ], [ 19, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 20, 2, 4, 8 ], [ 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 ], [ 23, 2, 3, 4 ], [ 23, 2, 4, 4 ], [ 24, 1, 2, 8 ], [ 24, 1, 3, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 4, 8 ], [ 27, 2, 9, 8 ], [ 27, 2, 11, 8 ], [ 27, 3, 3, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 7, 8 ], [ 27, 3, 8, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 14, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 29, 1, 5, 16 ], [ 29, 2, 5, 8 ], [ 30, 1, 3, 16 ], [ 30, 1, 8, 16 ], [ 30, 2, 3, 8 ], [ 30, 2, 8, 8 ], [ 31, 1, 2, 8 ], [ 31, 1, 4, 8 ], [ 31, 1, 5, 8 ], [ 31, 1, 7, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 4, 4 ], [ 31, 2, 5, 4 ], [ 31, 2, 7, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 33, 1, 12, 32 ], [ 33, 2, 12, 16 ], [ 33, 3, 12, 16 ], [ 33, 4, 12, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 7, 8 ], [ 34, 2, 3, 4 ], [ 34, 2, 9, 8 ], [ 34, 3, 3, 4 ], [ 34, 3, 6, 8 ], [ 34, 3, 8, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 36, 1, 5, 16 ], [ 36, 1, 14, 32 ], [ 36, 2, 5, 8 ], [ 36, 2, 10, 16 ], [ 36, 2, 18, 16 ], [ 36, 2, 20, 16 ], [ 36, 3, 5, 8 ], [ 36, 3, 10, 16 ], [ 36, 3, 18, 16 ], [ 36, 3, 20, 16 ], [ 36, 4, 5, 8 ], [ 36, 4, 10, 16 ], [ 36, 4, 18, 16 ], [ 36, 4, 20, 16 ], [ 36, 5, 5, 8 ], [ 36, 5, 14, 16 ], [ 36, 6, 6, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 14, 8 ], [ 36, 6, 15, 8 ], [ 38, 1, 9, 16 ], [ 38, 1, 16, 16 ], [ 38, 2, 9, 8 ], [ 38, 2, 16, 8 ], [ 38, 3, 9, 8 ], [ 38, 3, 12, 8 ], [ 38, 3, 14, 8 ], [ 38, 3, 15, 8 ], [ 39, 1, 5, 16 ], [ 39, 1, 11, 16 ], [ 39, 2, 5, 8 ], [ 39, 2, 11, 8 ], [ 39, 3, 5, 8 ], [ 39, 3, 11, 8 ], [ 39, 4, 6, 8 ], [ 39, 4, 11, 8 ], [ 39, 5, 6, 8 ], [ 39, 5, 11, 8 ], [ 40, 1, 22, 16 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 8 ], [ 41, 2, 24, 16 ], [ 41, 3, 24, 16 ], [ 41, 4, 28, 16 ], [ 41, 4, 34, 16 ], [ 41, 5, 22, 16 ], [ 41, 5, 26, 16 ], [ 41, 6, 22, 16 ], [ 41, 6, 26, 16 ], [ 41, 7, 22, 16 ], [ 41, 7, 26, 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 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 21, 1, 3, 4 ], [ 24, 1, 3, 4 ], [ 25, 1, 7, 8 ], [ 25, 2, 7, 4 ], [ 25, 3, 7, 4 ], [ 25, 4, 7, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 29, 1, 6, 12 ], [ 29, 2, 6, 6 ], [ 30, 1, 8, 8 ], [ 30, 2, 8, 4 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 39, 1, 12, 12 ], [ 39, 2, 12, 6 ], [ 39, 3, 12, 6 ], [ 40, 1, 15, 12 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 6 ], [ 41, 2, 25, 12 ], [ 41, 3, 25, 12 ], [ 41, 5, 27, 12 ], [ 41, 6, 27, 12 ], [ 41, 7, 27, 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 phi1^2 phi2^2 ( q-2 ) q congruent 2 modulo 12: 1/64 q^4 ( q-2 ) q congruent 3 modulo 12: 1/64 phi1^2 phi2^2 ( q-2 ) q congruent 4 modulo 12: 1/64 q^4 ( q-2 ) q congruent 5 modulo 12: 1/64 phi1^2 phi2^2 ( q-2 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2^2 ( q-2 ) q congruent 8 modulo 12: 1/64 q^4 ( q-2 ) q congruent 9 modulo 12: 1/64 phi1^2 phi2^2 ( q-2 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2^2 ( q-2 ) 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 ], [ 4, 2, 1, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 12 ], [ 10, 1, 2, 16 ], [ 15, 1, 3, 16 ], [ 15, 2, 3, 8 ], [ 15, 3, 3, 8 ], [ 15, 4, 3, 8 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 12 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 6 ], [ 18, 1, 3, 24 ], [ 18, 2, 3, 12 ], [ 25, 1, 6, 32 ], [ 25, 2, 6, 16 ], [ 25, 3, 6, 16 ], [ 25, 4, 6, 16 ], [ 26, 1, 3, 24 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 11, 32 ], [ 27, 1, 13, 32 ], [ 27, 2, 7, 4 ], [ 27, 2, 11, 16 ], [ 27, 2, 13, 16 ], [ 27, 3, 7, 16 ], [ 27, 3, 8, 16 ], [ 27, 3, 12, 16 ], [ 32, 1, 4, 16 ], [ 34, 1, 4, 48 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 24 ], [ 35, 1, 6, 16 ], [ 35, 2, 6, 8 ], [ 36, 1, 10, 16 ], [ 36, 1, 19, 64 ], [ 36, 2, 16, 8 ], [ 36, 2, 22, 32 ], [ 36, 2, 26, 32 ], [ 36, 3, 16, 8 ], [ 36, 3, 22, 32 ], [ 36, 3, 26, 32 ], [ 36, 4, 16, 8 ], [ 36, 4, 22, 32 ], [ 36, 4, 26, 32 ], [ 36, 5, 10, 8 ], [ 36, 5, 19, 32 ], [ 36, 6, 16, 32 ], [ 38, 1, 12, 32 ], [ 38, 2, 12, 16 ], [ 39, 1, 6, 32 ], [ 39, 2, 6, 16 ], [ 39, 3, 6, 16 ], [ 39, 4, 4, 16 ], [ 39, 5, 4, 16 ], [ 40, 1, 24, 32 ], [ 40, 2, 18, 16 ], [ 40, 3, 14, 16 ], [ 41, 2, 26, 32 ], [ 41, 3, 26, 32 ], [ 41, 4, 30, 32 ], [ 41, 4, 32, 32 ], [ 41, 5, 23, 32 ], [ 41, 6, 23, 32 ], [ 41, 7, 23, 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 q phi1^3 phi2 q congruent 2 modulo 12: 1/32 q^4 ( q-2 ) q congruent 3 modulo 12: 1/32 q phi1^3 phi2 q congruent 4 modulo 12: 1/32 q^4 ( q-2 ) q congruent 5 modulo 12: 1/32 q phi1^3 phi2 q congruent 7 modulo 12: 1/32 q phi1^3 phi2 q congruent 8 modulo 12: 1/32 q^4 ( q-2 ) q congruent 9 modulo 12: 1/32 q phi1^3 phi2 q congruent 11 modulo 12: 1/32 q phi1^3 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 ], [ 4, 2, 3, 4 ], [ 7, 1, 2, 4 ], [ 15, 1, 7, 16 ], [ 15, 2, 7, 8 ], [ 15, 3, 7, 8 ], [ 15, 4, 7, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 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 ], [ 27, 2, 4, 8 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 2, 11, 8 ], [ 27, 3, 3, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 7, 8 ], [ 27, 3, 8, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 14, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 3, 16 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 36, 1, 10, 16 ], [ 36, 1, 14, 32 ], [ 36, 2, 10, 16 ], [ 36, 2, 16, 8 ], [ 36, 2, 18, 16 ], [ 36, 2, 20, 16 ], [ 36, 3, 10, 16 ], [ 36, 3, 16, 8 ], [ 36, 3, 18, 16 ], [ 36, 3, 20, 16 ], [ 36, 4, 10, 16 ], [ 36, 4, 16, 8 ], [ 36, 4, 18, 16 ], [ 36, 4, 20, 16 ], [ 36, 5, 10, 8 ], [ 36, 5, 14, 16 ], [ 38, 1, 12, 16 ], [ 38, 1, 14, 16 ], [ 38, 2, 12, 8 ], [ 38, 2, 14, 8 ], [ 40, 1, 16, 16 ], [ 40, 2, 19, 8 ], [ 41, 2, 27, 16 ], [ 41, 3, 27, 16 ], [ 41, 4, 29, 16 ], [ 41, 4, 33, 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+2*q^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 ( q^2-3 ) 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 ( q^2-3 ) q congruent 7 modulo 12: 1/24 phi1^2 ( q^3+2*q^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 ( q^2-3 ) q congruent 11 modulo 12: 1/24 q phi1 phi2 ( q^2-3 ) 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 ], [ 4, 2, 1, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 21, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 6, 8 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ], [ 25, 4, 6, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 1, 3, 8 ], [ 30, 2, 3, 4 ], [ 33, 1, 11, 24 ], [ 33, 2, 11, 12 ], [ 33, 3, 11, 12 ], [ 33, 4, 11, 12 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 39, 1, 7, 12 ], [ 39, 2, 7, 6 ], [ 39, 3, 7, 6 ], [ 40, 1, 14, 12 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 6 ], [ 41, 2, 28, 12 ], [ 41, 3, 28, 12 ], [ 41, 5, 24, 12 ], [ 41, 6, 24, 12 ], [ 41, 7, 24, 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 q phi1 phi2 phi4 q congruent 2 modulo 12: 1/16 q^5 q congruent 3 modulo 12: 1/16 q phi1 phi2 phi4 q congruent 4 modulo 12: 1/16 q^5 q congruent 5 modulo 12: 1/16 q phi1 phi2 phi4 q congruent 7 modulo 12: 1/16 q phi1 phi2 phi4 q congruent 8 modulo 12: 1/16 q^5 q congruent 9 modulo 12: 1/16 q phi1 phi2 phi4 q congruent 11 modulo 12: 1/16 q phi1 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 ], [ 17, 2, 2, 2 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ], [ 41, 2, 29, 8 ], [ 41, 3, 29, 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^4-11*q^3+21*q^2+99*q-302 ) 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 ( q^5-12*q^4+32*q^3+78*q^2-345*q+198 ) 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^4-11*q^3+21*q^2+99*q-270 ) q congruent 7 modulo 12: 1/192 ( q^5-12*q^4+32*q^3+78*q^2-377*q+230 ) 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^4-11*q^3+21*q^2+99*q-270 ) q congruent 11 modulo 12: 1/192 ( q^5-12*q^4+32*q^3+78*q^2-345*q+198 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 4, 2, 3, 24 ], [ 5, 1, 2, 12 ], [ 5, 2, 2, 6 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 12, 2, 2, 16 ], [ 14, 1, 2, 24 ], [ 14, 2, 2, 12 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 24 ], [ 15, 1, 5, 96 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 12 ], [ 15, 2, 5, 48 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 12 ], [ 15, 3, 5, 48 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 12 ], [ 15, 4, 5, 48 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 6 ], [ 18, 1, 2, 12 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 6 ], [ 18, 2, 3, 2 ], [ 20, 1, 4, 96 ], [ 20, 2, 4, 48 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 1, 3, 48 ], [ 23, 2, 3, 24 ], [ 24, 1, 2, 16 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 72 ], [ 25, 1, 8, 24 ], [ 25, 2, 5, 12 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 36 ], [ 25, 2, 8, 12 ], [ 25, 3, 5, 12 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 36 ], [ 25, 3, 8, 12 ], [ 25, 4, 5, 12 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 36 ], [ 25, 4, 8, 12 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 27, 1, 4, 96 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 2, 4, 48 ], [ 27, 3, 2, 48 ], [ 27, 3, 3, 48 ], [ 27, 3, 14, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 30, 1, 3, 32 ], [ 30, 2, 3, 16 ], [ 31, 1, 2, 48 ], [ 31, 1, 5, 48 ], [ 31, 2, 2, 24 ], [ 31, 2, 5, 24 ], [ 32, 1, 2, 48 ], [ 33, 1, 10, 192 ], [ 33, 2, 10, 96 ], [ 33, 3, 10, 96 ], [ 33, 4, 10, 96 ], [ 34, 1, 2, 48 ], [ 34, 1, 7, 24 ], [ 34, 2, 2, 24 ], [ 34, 2, 3, 12 ], [ 34, 3, 2, 24 ], [ 34, 3, 3, 12 ], [ 34, 3, 8, 12 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 36, 1, 5, 48 ], [ 36, 1, 6, 192 ], [ 36, 2, 5, 24 ], [ 36, 2, 6, 96 ], [ 36, 2, 7, 96 ], [ 36, 3, 5, 24 ], [ 36, 3, 6, 96 ], [ 36, 3, 7, 96 ], [ 36, 4, 5, 24 ], [ 36, 4, 6, 96 ], [ 36, 4, 7, 96 ], [ 36, 5, 5, 24 ], [ 36, 5, 6, 96 ], [ 36, 6, 6, 24 ], [ 36, 6, 7, 96 ], [ 36, 6, 8, 24 ], [ 36, 6, 14, 24 ], [ 36, 6, 15, 24 ], [ 38, 1, 9, 96 ], [ 38, 2, 9, 48 ], [ 38, 3, 9, 48 ], [ 38, 3, 12, 48 ], [ 39, 1, 8, 96 ], [ 39, 1, 13, 96 ], [ 39, 2, 8, 48 ], [ 39, 2, 13, 48 ], [ 39, 3, 8, 48 ], [ 39, 3, 13, 48 ], [ 39, 4, 7, 48 ], [ 39, 4, 12, 48 ], [ 39, 4, 13, 48 ], [ 39, 5, 7, 48 ], [ 39, 5, 12, 48 ], [ 39, 5, 13, 48 ], [ 40, 1, 12, 96 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 48 ], [ 41, 2, 30, 96 ], [ 41, 3, 30, 96 ], [ 41, 4, 35, 96 ], [ 41, 4, 37, 96 ], [ 41, 5, 28, 96 ], [ 41, 5, 30, 96 ], [ 41, 6, 28, 96 ], [ 41, 6, 30, 96 ], [ 41, 7, 28, 96 ], [ 41, 7, 30, 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 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 2 modulo 12: 1/64 q^3 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 4 modulo 12: 1/64 q^3 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 7 modulo 12: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 8 modulo 12: 1/64 q^3 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) q congruent 11 modulo 12: 1/64 phi1 phi2 ( q^3-6*q^2+7*q+6 ) 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 ], [ 4, 2, 2, 4 ], [ 4, 2, 3, 8 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 15, 1, 4, 16 ], [ 15, 1, 5, 32 ], [ 15, 2, 4, 8 ], [ 15, 2, 5, 16 ], [ 15, 3, 4, 8 ], [ 15, 3, 5, 16 ], [ 15, 4, 4, 8 ], [ 15, 4, 5, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 25, 1, 7, 32 ], [ 25, 2, 7, 16 ], [ 25, 3, 7, 16 ], [ 25, 4, 7, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 4, 32 ], [ 27, 1, 7, 8 ], [ 27, 2, 3, 16 ], [ 27, 2, 4, 16 ], [ 27, 2, 7, 4 ], [ 27, 3, 2, 16 ], [ 27, 3, 3, 16 ], [ 27, 3, 14, 16 ], [ 32, 1, 8, 16 ], [ 34, 1, 2, 16 ], [ 34, 1, 8, 8 ], [ 34, 2, 2, 8 ], [ 34, 2, 5, 4 ], [ 34, 3, 2, 8 ], [ 35, 1, 7, 16 ], [ 35, 2, 7, 8 ], [ 36, 1, 6, 64 ], [ 36, 1, 10, 16 ], [ 36, 2, 6, 32 ], [ 36, 2, 7, 32 ], [ 36, 2, 16, 8 ], [ 36, 3, 6, 32 ], [ 36, 3, 7, 32 ], [ 36, 3, 16, 8 ], [ 36, 4, 6, 32 ], [ 36, 4, 7, 32 ], [ 36, 4, 16, 8 ], [ 36, 5, 6, 32 ], [ 36, 5, 10, 8 ], [ 36, 6, 7, 32 ], [ 38, 1, 14, 32 ], [ 38, 2, 14, 16 ], [ 39, 1, 14, 32 ], [ 39, 2, 14, 16 ], [ 39, 3, 14, 16 ], [ 39, 4, 14, 16 ], [ 39, 5, 14, 16 ], [ 40, 1, 23, 32 ], [ 40, 2, 17, 16 ], [ 40, 3, 16, 16 ], [ 41, 2, 31, 32 ], [ 41, 3, 31, 32 ], [ 41, 4, 36, 32 ], [ 41, 4, 38, 32 ], [ 41, 5, 29, 32 ], [ 41, 6, 29, 32 ], [ 41, 7, 29, 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-2 ) q congruent 2 modulo 12: 1/16 q^4 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 4 modulo 12: 1/16 q^4 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 7 modulo 12: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 8 modulo 12: 1/16 q^4 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 phi4 ( q-2 ) q congruent 11 modulo 12: 1/16 phi1 phi2 phi4 ( q-2 ) 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 ], [ 17, 2, 4, 2 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ], [ 41, 2, 32, 8 ], [ 41, 3, 32, 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^3-3*q^2-3*q+9 ) 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^3-3*q^2-3*q+9 ) 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 ( q^4-5*q^3+5*q^2+7*q-12 ) q congruent 7 modulo 12: 1/24 q phi1 ( q^3-3*q^2-3*q+9 ) 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^3-3*q^2-3*q+9 ) q congruent 11 modulo 12: 1/24 phi2 ( q^4-5*q^3+5*q^2+7*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 ], [ 4, 2, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 1, 5, 8 ], [ 12, 2, 4, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 21, 1, 3, 4 ], [ 24, 1, 4, 4 ], [ 25, 1, 3, 8 ], [ 25, 2, 3, 4 ], [ 25, 3, 3, 4 ], [ 25, 4, 3, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 1, 7, 8 ], [ 30, 2, 7, 4 ], [ 33, 1, 8, 24 ], [ 33, 2, 8, 12 ], [ 33, 3, 8, 12 ], [ 33, 4, 8, 12 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 39, 1, 16, 12 ], [ 39, 2, 16, 6 ], [ 39, 3, 16, 6 ], [ 40, 1, 15, 12 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 6 ], [ 41, 2, 33, 12 ], [ 41, 3, 33, 12 ], [ 41, 5, 31, 12 ], [ 41, 6, 31, 12 ], [ 41, 7, 31, 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 phi1^2 phi2 ( q^2-7*q+12 ) 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 phi2 ( q^2-7*q+12 ) 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 phi2 ( q^2-7*q+12 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q^2-7*q+12 ) 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 phi2 ( q^2-7*q+12 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q^2-7*q+12 ) 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 ], [ 4, 2, 2, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 10, 1, 3, 16 ], [ 15, 1, 2, 16 ], [ 15, 2, 2, 8 ], [ 15, 3, 2, 8 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 6 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 25, 1, 3, 32 ], [ 25, 2, 3, 16 ], [ 25, 3, 3, 16 ], [ 25, 4, 3, 16 ], [ 26, 1, 1, 24 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 8 ], [ 27, 1, 14, 32 ], [ 27, 2, 3, 16 ], [ 27, 2, 7, 4 ], [ 27, 2, 14, 16 ], [ 27, 3, 2, 16 ], [ 27, 3, 15, 16 ], [ 27, 3, 16, 16 ], [ 32, 1, 8, 16 ], [ 34, 1, 1, 48 ], [ 34, 1, 6, 8 ], [ 34, 2, 1, 24 ], [ 34, 2, 8, 4 ], [ 34, 3, 1, 24 ], [ 35, 1, 7, 16 ], [ 35, 2, 7, 8 ], [ 36, 1, 3, 64 ], [ 36, 1, 17, 16 ], [ 36, 2, 3, 32 ], [ 36, 2, 13, 8 ], [ 36, 2, 27, 32 ], [ 36, 3, 3, 32 ], [ 36, 3, 13, 8 ], [ 36, 3, 27, 32 ], [ 36, 4, 3, 32 ], [ 36, 4, 13, 8 ], [ 36, 4, 27, 32 ], [ 36, 5, 3, 32 ], [ 36, 5, 17, 8 ], [ 36, 6, 3, 32 ], [ 38, 1, 13, 32 ], [ 38, 2, 13, 16 ], [ 39, 1, 17, 32 ], [ 39, 2, 17, 16 ], [ 39, 3, 17, 16 ], [ 39, 4, 16, 16 ], [ 39, 5, 16, 16 ], [ 40, 1, 23, 32 ], [ 40, 2, 17, 16 ], [ 40, 3, 16, 16 ], [ 41, 2, 34, 32 ], [ 41, 3, 34, 32 ], [ 41, 4, 40, 32 ], [ 41, 4, 43, 32 ], [ 41, 5, 32, 32 ], [ 41, 6, 32, 32 ], [ 41, 7, 32, 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-2 ) 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-2 ) 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-2 ) q congruent 7 modulo 12: 1/32 phi1^3 phi2 ( q-2 ) 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-2 ) q congruent 11 modulo 12: 1/32 phi1^3 phi2 ( q-2 ) 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 ], [ 4, 2, 4, 4 ], [ 7, 1, 1, 4 ], [ 15, 1, 6, 16 ], [ 15, 2, 6, 8 ], [ 15, 3, 6, 8 ], [ 15, 4, 6, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 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 ], [ 27, 2, 6, 8 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 2, 14, 8 ], [ 27, 3, 4, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 13, 8 ], [ 27, 3, 15, 8 ], [ 27, 3, 16, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 2, 16 ], [ 34, 1, 6, 8 ], [ 34, 2, 2, 8 ], [ 34, 2, 8, 4 ], [ 34, 3, 2, 8 ], [ 36, 1, 13, 32 ], [ 36, 1, 17, 16 ], [ 36, 2, 9, 16 ], [ 36, 2, 13, 8 ], [ 36, 2, 15, 16 ], [ 36, 2, 28, 16 ], [ 36, 3, 9, 16 ], [ 36, 3, 13, 8 ], [ 36, 3, 15, 16 ], [ 36, 3, 28, 16 ], [ 36, 4, 9, 16 ], [ 36, 4, 13, 8 ], [ 36, 4, 15, 16 ], [ 36, 4, 28, 16 ], [ 36, 5, 13, 16 ], [ 36, 5, 17, 8 ], [ 38, 1, 11, 16 ], [ 38, 1, 13, 16 ], [ 38, 2, 11, 8 ], [ 38, 2, 13, 8 ], [ 40, 1, 16, 16 ], [ 40, 2, 19, 8 ], [ 41, 2, 35, 16 ], [ 41, 3, 35, 16 ], [ 41, 4, 39, 16 ], [ 41, 4, 45, 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^4-13*q^3+51*q^2-31*q-120 ) 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^5-14*q^4+64*q^3-82*q^2-113*q+240 ) 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^4-13*q^3+51*q^2-31*q-120 ) q congruent 7 modulo 12: 1/192 ( q^5-14*q^4+64*q^3-82*q^2-113*q+240 ) 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^4-13*q^3+51*q^2-31*q-120 ) q congruent 11 modulo 12: 1/192 ( q^5-14*q^4+64*q^3-82*q^2-113*q+240 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 12 ], [ 6, 2, 1, 6 ], [ 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 ], [ 14, 2, 1, 12 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 24 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 12 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 12 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 12 ], [ 16, 1, 1, 14 ], [ 17, 1, 1, 36 ], [ 17, 1, 4, 16 ], [ 17, 2, 1, 18 ], [ 17, 2, 4, 8 ], [ 18, 1, 1, 60 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 30 ], [ 18, 2, 4, 2 ], [ 19, 1, 1, 48 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 48 ], [ 23, 2, 1, 24 ], [ 24, 1, 1, 16 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 72 ], [ 25, 1, 4, 24 ], [ 25, 2, 1, 12 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 36 ], [ 25, 2, 4, 12 ], [ 25, 3, 1, 12 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 36 ], [ 25, 3, 4, 12 ], [ 25, 4, 1, 12 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 36 ], [ 25, 4, 4, 12 ], [ 26, 1, 1, 72 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 27, 1, 14, 96 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 2, 14, 48 ], [ 27, 3, 2, 48 ], [ 27, 3, 15, 48 ], [ 27, 3, 16, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 29, 1, 1, 96 ], [ 29, 2, 1, 48 ], [ 30, 1, 4, 32 ], [ 30, 2, 4, 16 ], [ 31, 1, 1, 48 ], [ 31, 1, 6, 48 ], [ 31, 2, 1, 24 ], [ 31, 2, 6, 24 ], [ 32, 1, 2, 48 ], [ 34, 1, 1, 144 ], [ 34, 1, 5, 24 ], [ 34, 2, 1, 72 ], [ 34, 2, 4, 12 ], [ 34, 3, 1, 72 ], [ 34, 3, 4, 12 ], [ 34, 3, 7, 12 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 36, 1, 2, 48 ], [ 36, 1, 3, 192 ], [ 36, 2, 2, 24 ], [ 36, 2, 3, 96 ], [ 36, 2, 27, 96 ], [ 36, 3, 2, 24 ], [ 36, 3, 3, 96 ], [ 36, 3, 27, 96 ], [ 36, 4, 2, 24 ], [ 36, 4, 3, 96 ], [ 36, 4, 27, 96 ], [ 36, 5, 2, 24 ], [ 36, 5, 3, 96 ], [ 36, 6, 2, 24 ], [ 36, 6, 3, 96 ], [ 36, 6, 4, 24 ], [ 36, 6, 10, 24 ], [ 36, 6, 11, 24 ], [ 38, 1, 10, 96 ], [ 38, 2, 10, 48 ], [ 38, 3, 10, 48 ], [ 38, 3, 11, 48 ], [ 39, 1, 1, 96 ], [ 39, 1, 18, 96 ], [ 39, 2, 1, 48 ], [ 39, 2, 18, 48 ], [ 39, 3, 1, 48 ], [ 39, 3, 18, 48 ], [ 39, 4, 1, 48 ], [ 39, 4, 17, 48 ], [ 39, 4, 18, 48 ], [ 39, 5, 1, 48 ], [ 39, 5, 17, 48 ], [ 39, 5, 18, 48 ], [ 40, 1, 12, 96 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 48 ], [ 41, 2, 36, 96 ], [ 41, 3, 36, 96 ], [ 41, 4, 41, 96 ], [ 41, 4, 44, 96 ], [ 41, 5, 33, 96 ], [ 41, 5, 35, 96 ], [ 41, 6, 33, 96 ], [ 41, 6, 35, 96 ], [ 41, 7, 33, 96 ], [ 41, 7, 35, 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^4-5*q^3+q^2+21*q-10 ) 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 phi1^2 ( q^3-4*q^2-3*q+18 ) 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^4-5*q^3+q^2+21*q-10 ) q congruent 7 modulo 12: 1/32 phi1^2 ( q^3-4*q^2-3*q+18 ) 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^4-5*q^3+q^2+21*q-10 ) q congruent 11 modulo 12: 1/32 phi1^2 ( q^3-4*q^2-3*q+18 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 4 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 12, 2, 4, 8 ], [ 13, 1, 1, 8 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 1, 6, 16 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 2, 6, 8 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 4 ], [ 15, 3, 6, 8 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 4 ], [ 15, 4, 6, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 2, 4 ], [ 18, 2, 4, 2 ], [ 19, 1, 1, 8 ], [ 20, 1, 3, 16 ], [ 20, 2, 3, 8 ], [ 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 ], [ 23, 2, 1, 4 ], [ 23, 2, 2, 4 ], [ 24, 1, 1, 8 ], [ 24, 1, 4, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 6, 8 ], [ 27, 2, 9, 8 ], [ 27, 2, 14, 8 ], [ 27, 3, 4, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 13, 8 ], [ 27, 3, 15, 8 ], [ 27, 3, 16, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 29, 1, 2, 16 ], [ 29, 2, 2, 8 ], [ 30, 1, 4, 16 ], [ 30, 1, 7, 16 ], [ 30, 2, 4, 8 ], [ 30, 2, 7, 8 ], [ 31, 1, 1, 8 ], [ 31, 1, 3, 8 ], [ 31, 1, 6, 8 ], [ 31, 1, 8, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 3, 4 ], [ 31, 2, 6, 4 ], [ 31, 2, 8, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 33, 1, 7, 32 ], [ 33, 2, 7, 16 ], [ 33, 3, 7, 16 ], [ 33, 4, 7, 16 ], [ 34, 1, 2, 16 ], [ 34, 1, 5, 8 ], [ 34, 2, 2, 8 ], [ 34, 2, 4, 4 ], [ 34, 3, 2, 8 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 36, 1, 2, 16 ], [ 36, 1, 13, 32 ], [ 36, 2, 2, 8 ], [ 36, 2, 9, 16 ], [ 36, 2, 15, 16 ], [ 36, 2, 28, 16 ], [ 36, 3, 2, 8 ], [ 36, 3, 9, 16 ], [ 36, 3, 15, 16 ], [ 36, 3, 28, 16 ], [ 36, 4, 2, 8 ], [ 36, 4, 9, 16 ], [ 36, 4, 15, 16 ], [ 36, 4, 28, 16 ], [ 36, 5, 2, 8 ], [ 36, 5, 13, 16 ], [ 36, 6, 2, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 10, 8 ], [ 36, 6, 11, 8 ], [ 38, 1, 10, 16 ], [ 38, 1, 15, 16 ], [ 38, 2, 10, 8 ], [ 38, 2, 15, 8 ], [ 38, 3, 10, 8 ], [ 38, 3, 11, 8 ], [ 38, 3, 13, 8 ], [ 38, 3, 16, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 19, 16 ], [ 39, 2, 2, 8 ], [ 39, 2, 19, 8 ], [ 39, 3, 2, 8 ], [ 39, 3, 19, 8 ], [ 39, 4, 2, 8 ], [ 39, 4, 19, 8 ], [ 39, 5, 2, 8 ], [ 39, 5, 19, 8 ], [ 40, 1, 22, 16 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 8 ], [ 41, 2, 37, 16 ], [ 41, 3, 37, 16 ], [ 41, 4, 42, 16 ], [ 41, 4, 46, 16 ], [ 41, 5, 34, 16 ], [ 41, 5, 36, 16 ], [ 41, 6, 34, 16 ], [ 41, 6, 36, 16 ], [ 41, 7, 34, 16 ], [ 41, 7, 36, 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 phi1 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/24 q phi1 phi2 ( q^2-2*q-1 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 21, 1, 2, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 2, 2, 4 ], [ 25, 3, 2, 4 ], [ 25, 4, 2, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 29, 1, 3, 12 ], [ 29, 2, 3, 6 ], [ 30, 1, 4, 8 ], [ 30, 2, 4, 4 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 39, 1, 3, 12 ], [ 39, 2, 3, 6 ], [ 39, 3, 3, 6 ], [ 40, 1, 14, 12 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 6 ], [ 41, 2, 38, 12 ], [ 41, 3, 38, 12 ], [ 41, 5, 37, 12 ], [ 41, 6, 37, 12 ], [ 41, 7, 37, 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 q phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 1/64 q^3 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 1/64 q^3 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 1/64 q^3 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/64 q phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 q phi1^2 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 4, 8 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 8, 32 ], [ 15, 2, 1, 8 ], [ 15, 2, 8, 16 ], [ 15, 3, 1, 8 ], [ 15, 3, 8, 16 ], [ 15, 4, 1, 8 ], [ 15, 4, 8, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 25, 1, 2, 32 ], [ 25, 2, 2, 16 ], [ 25, 3, 2, 16 ], [ 25, 4, 2, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 6, 32 ], [ 27, 1, 7, 8 ], [ 27, 1, 13, 32 ], [ 27, 2, 6, 16 ], [ 27, 2, 7, 4 ], [ 27, 2, 13, 16 ], [ 27, 3, 4, 16 ], [ 27, 3, 12, 16 ], [ 27, 3, 13, 16 ], [ 32, 1, 4, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 35, 1, 6, 16 ], [ 35, 2, 6, 8 ], [ 36, 1, 15, 64 ], [ 36, 1, 17, 16 ], [ 36, 2, 12, 32 ], [ 36, 2, 13, 8 ], [ 36, 2, 24, 32 ], [ 36, 3, 12, 32 ], [ 36, 3, 13, 8 ], [ 36, 3, 24, 32 ], [ 36, 4, 12, 32 ], [ 36, 4, 13, 8 ], [ 36, 4, 24, 32 ], [ 36, 5, 15, 32 ], [ 36, 5, 17, 8 ], [ 36, 6, 12, 32 ], [ 38, 1, 11, 32 ], [ 38, 2, 11, 16 ], [ 39, 1, 9, 32 ], [ 39, 2, 9, 16 ], [ 39, 3, 9, 16 ], [ 39, 4, 10, 16 ], [ 39, 5, 10, 16 ], [ 40, 1, 24, 32 ], [ 40, 2, 18, 16 ], [ 40, 3, 14, 16 ], [ 41, 2, 39, 32 ], [ 41, 3, 39, 32 ], [ 41, 4, 48, 32 ], [ 41, 4, 49, 32 ], [ 41, 5, 38, 32 ], [ 41, 6, 38, 32 ], [ 41, 7, 38, 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^4-9*q^3+15*q^2+45*q-84 ) 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 phi1 ( q^4-9*q^3+15*q^2+45*q-108 ) 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 ( q^5-10*q^4+24*q^3+30*q^2-161*q+180 ) q congruent 7 modulo 12: 1/192 phi1 ( q^4-9*q^3+15*q^2+45*q-108 ) 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^4-9*q^3+15*q^2+45*q-84 ) q congruent 11 modulo 12: 1/192 ( q^5-10*q^4+24*q^3+30*q^2-185*q+204 ) 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 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 24 ], [ 5, 1, 1, 12 ], [ 5, 2, 1, 6 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 12, 2, 4, 16 ], [ 14, 1, 1, 24 ], [ 14, 2, 1, 12 ], [ 15, 1, 1, 24 ], [ 15, 1, 2, 8 ], [ 15, 1, 8, 96 ], [ 15, 2, 1, 12 ], [ 15, 2, 2, 4 ], [ 15, 2, 8, 48 ], [ 15, 3, 1, 12 ], [ 15, 3, 2, 4 ], [ 15, 3, 8, 48 ], [ 15, 4, 1, 12 ], [ 15, 4, 2, 4 ], [ 15, 4, 8, 48 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 1, 4, 16 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 17, 2, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 12 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 6 ], [ 20, 1, 3, 96 ], [ 20, 2, 3, 48 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 1, 2, 48 ], [ 23, 2, 2, 24 ], [ 24, 1, 4, 16 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 72 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 24 ], [ 25, 2, 1, 12 ], [ 25, 2, 2, 36 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 12 ], [ 25, 3, 1, 12 ], [ 25, 3, 2, 36 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 12 ], [ 25, 4, 1, 12 ], [ 25, 4, 2, 36 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 12 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 6, 96 ], [ 27, 1, 13, 96 ], [ 27, 2, 2, 12 ], [ 27, 2, 6, 48 ], [ 27, 2, 13, 48 ], [ 27, 3, 4, 48 ], [ 27, 3, 12, 48 ], [ 27, 3, 13, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 30, 1, 7, 32 ], [ 30, 2, 7, 16 ], [ 31, 1, 3, 48 ], [ 31, 1, 8, 48 ], [ 31, 2, 3, 24 ], [ 31, 2, 8, 24 ], [ 32, 1, 5, 48 ], [ 33, 1, 9, 192 ], [ 33, 2, 9, 96 ], [ 33, 3, 9, 96 ], [ 33, 4, 9, 96 ], [ 34, 1, 3, 48 ], [ 34, 1, 5, 24 ], [ 34, 2, 4, 12 ], [ 34, 2, 9, 24 ], [ 34, 3, 4, 12 ], [ 34, 3, 6, 24 ], [ 34, 3, 7, 12 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 10, 24 ], [ 36, 1, 2, 48 ], [ 36, 1, 15, 192 ], [ 36, 2, 2, 24 ], [ 36, 2, 12, 96 ], [ 36, 2, 24, 96 ], [ 36, 3, 2, 24 ], [ 36, 3, 12, 96 ], [ 36, 3, 24, 96 ], [ 36, 4, 2, 24 ], [ 36, 4, 12, 96 ], [ 36, 4, 24, 96 ], [ 36, 5, 2, 24 ], [ 36, 5, 15, 96 ], [ 36, 6, 2, 24 ], [ 36, 6, 4, 24 ], [ 36, 6, 10, 24 ], [ 36, 6, 11, 24 ], [ 36, 6, 12, 96 ], [ 38, 1, 15, 96 ], [ 38, 2, 15, 48 ], [ 38, 3, 13, 48 ], [ 38, 3, 16, 48 ], [ 39, 1, 10, 96 ], [ 39, 1, 20, 96 ], [ 39, 2, 10, 48 ], [ 39, 2, 20, 48 ], [ 39, 3, 10, 48 ], [ 39, 3, 20, 48 ], [ 39, 4, 8, 48 ], [ 39, 4, 9, 48 ], [ 39, 4, 20, 48 ], [ 39, 5, 8, 48 ], [ 39, 5, 9, 48 ], [ 39, 5, 20, 48 ], [ 40, 1, 13, 96 ], [ 40, 2, 24, 48 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 48 ], [ 41, 2, 40, 96 ], [ 41, 3, 40, 96 ], [ 41, 4, 47, 96 ], [ 41, 4, 50, 96 ], [ 41, 5, 39, 96 ], [ 41, 5, 40, 96 ], [ 41, 6, 39, 96 ], [ 41, 6, 40, 96 ], [ 41, 7, 39, 96 ], [ 41, 7, 40, 96 ] ] j = 5: Omega of order 2, action on Pi: <(1,2)> k = 1: F-action on Pi is () [41,5,1] Dynkin type is (A_1(q) + A_1(q) + T(phi1^5)).2 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: 1/96 ( q^3-23*q^2+171*q-437 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/96 ( q^3-23*q^2+159*q-297 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 7 modulo 12: 1/96 ( q^3-23*q^2+159*q-329 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 11 modulo 12: 1/96 ( q^3-23*q^2+159*q-297 ) 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, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 26 ], [ 5, 2, 1, 6 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 2, 1, 16 ], [ 14, 2, 1, 12 ], [ 15, 2, 1, 12 ], [ 15, 4, 1, 48 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 20 ], [ 18, 2, 1, 2 ], [ 20, 2, 1, 48 ], [ 22, 1, 1, 24 ], [ 23, 2, 1, 24 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 12 ], [ 25, 4, 1, 36 ], [ 26, 1, 1, 24 ], [ 27, 3, 1, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 30, 2, 1, 16 ], [ 31, 2, 1, 24 ], [ 33, 4, 1, 96 ], [ 34, 3, 1, 12 ], [ 35, 1, 1, 48 ], [ 35, 2, 1, 24 ], [ 36, 3, 1, 96 ], [ 36, 6, 1, 24 ], [ 38, 3, 1, 48 ], [ 39, 4, 1, 48 ] ] k = 2: F-action on Pi is () [41,5,2] Dynkin type is (A_1(q) + A_1(q) + T(phi1^4 phi2)).2 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^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/16 ( q^3-9*q^2+19*q-3 ) 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, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 6 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 12, 2, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 2 ], [ 18, 2, 1, 2 ], [ 20, 2, 1, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 2, 1, 4 ], [ 23, 2, 2, 4 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 1, 4 ], [ 26, 1, 2, 4 ], [ 27, 3, 1, 8 ], [ 27, 3, 9, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 4, 4 ], [ 30, 2, 1, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 3, 4 ], [ 33, 4, 3, 16 ], [ 34, 3, 1, 4 ], [ 35, 1, 2, 8 ], [ 35, 2, 2, 4 ], [ 36, 3, 14, 16 ], [ 36, 6, 1, 8 ], [ 38, 3, 1, 8 ], [ 38, 3, 7, 8 ], [ 39, 4, 2, 8 ] ] k = 3: F-action on Pi is () [41,5,3] Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi3)).2 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: 1/12 phi1 ( q^2-q-4 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q phi2 ( q-3 ) q congruent 7 modulo 12: 1/12 phi1 ( q^2-q-4 ) q congruent 8 modulo 12: 0 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, 45, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 9, 1, 1, 2 ], [ 12, 2, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 2, 1, 2 ], [ 25, 2, 1, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 1, 4 ], [ 33, 4, 2, 12 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ] ] k = 4: F-action on Pi is () [41,5,4] Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^3)).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 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^2 ( q-5 ) q congruent 7 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^2 ( q-5 ) q congruent 11 modulo 12: 1/32 phi1 ( 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, 3 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 8 ], [ 5, 2, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 8 ], [ 15, 4, 4, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 8 ], [ 18, 2, 2, 2 ], [ 22, 1, 2, 8 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 7, 8 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 8 ], [ 25, 4, 7, 8 ], [ 25, 4, 8, 16 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 27, 3, 11, 16 ], [ 31, 2, 4, 8 ], [ 34, 3, 2, 4 ], [ 34, 3, 3, 8 ], [ 35, 1, 5, 16 ], [ 35, 2, 5, 8 ], [ 36, 3, 5, 16 ], [ 36, 3, 25, 32 ], [ 36, 6, 5, 8 ], [ 36, 6, 14, 16 ], [ 38, 3, 8, 16 ], [ 39, 4, 5, 16 ], [ 39, 4, 13, 16 ] ] k = 5: F-action on Pi is () [41,5,5] Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2^2)).2 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^2-4*q-1 ) 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 ( q^2-4*q-1 ) 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 ( q^2-4*q-1 ) q congruent 11 modulo 12: 1/16 phi1^2 ( q-3 ) 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, 3 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 15, 2, 3, 4 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 6 ], [ 18, 2, 2, 2 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 5, 4 ], [ 26, 1, 2, 4 ], [ 27, 3, 5, 8 ], [ 27, 3, 11, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 4, 4 ], [ 30, 2, 2, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 4, 4 ], [ 34, 3, 2, 4 ], [ 35, 1, 2, 8 ], [ 35, 2, 2, 4 ], [ 36, 3, 17, 16 ], [ 36, 6, 5, 8 ], [ 38, 3, 2, 8 ], [ 38, 3, 8, 8 ], [ 39, 4, 6, 8 ] ] k = 6: F-action on Pi is () [41,5,6] Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^2 phi4)).2 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, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 2, 4, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 25, 2, 5, 4 ], [ 25, 3, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 5, 4 ], [ 34, 3, 3, 4 ], [ 35, 1, 6, 8 ], [ 35, 2, 6, 4 ], [ 36, 3, 16, 8 ], [ 36, 6, 14, 8 ], [ 39, 4, 14, 8 ] ] k = 7: F-action on Pi is () [41,5,7] Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2 phi3)).2 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: 1/12 q phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q phi1 phi2 q congruent 7 modulo 12: 1/12 q phi1 phi2 q congruent 8 modulo 12: 0 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: [ 45, 18, 18, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 9, 1, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 25, 2, 5, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 2, 4 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ] ] k = 8: F-action on Pi is () [41,5,8] Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^4)).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 ( q^2-6*q+9 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^3-7*q^2+19*q-21 ) 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 ( q^3-7*q^2+19*q-21 ) 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 ( q^3-7*q^2+19*q-21 ) 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, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 6 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 12, 2, 3, 8 ], [ 14, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 6 ], [ 18, 2, 3, 2 ], [ 20, 2, 2, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 2, 3, 4 ], [ 23, 2, 4, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 2, 4 ], [ 27, 3, 5, 8 ], [ 27, 3, 11, 8 ], [ 28, 1, 2, 8 ], [ 28, 2, 2, 4 ], [ 30, 2, 5, 8 ], [ 31, 2, 5, 4 ], [ 31, 2, 7, 4 ], [ 33, 4, 4, 16 ], [ 34, 3, 5, 4 ], [ 35, 1, 4, 8 ], [ 35, 2, 4, 4 ], [ 36, 3, 17, 16 ], [ 36, 6, 13, 8 ], [ 38, 3, 3, 8 ], [ 38, 3, 5, 8 ], [ 39, 4, 11, 8 ] ] k = 9: F-action on Pi is () [41,5,9] Dynkin type is (A_1(q) + A_1(q) + T(phi2^3 phi6)).2 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: 1/12 q phi1^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi1^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 phi2 ( q^2-3*q+4 ) q congruent 7 modulo 12: 1/12 q phi1^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 q phi1^2 q congruent 11 modulo 12: 1/12 phi2 ( q^2-3*q+4 ) 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, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 9, 1, 2, 2 ], [ 12, 2, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 3, 2 ], [ 25, 2, 8, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 5, 4 ], [ 33, 4, 5, 12 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ] ] k = 10: F-action on Pi is () [41,5,10] Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^3)).2 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^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/32 ( q^3-9*q^2+27*q-27 ) 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, 3 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 8 ], [ 15, 2, 4, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 2, 3, 2 ], [ 22, 1, 3, 8 ], [ 23, 2, 3, 8 ], [ 25, 2, 8, 4 ], [ 25, 3, 6, 8 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 16 ], [ 25, 4, 6, 8 ], [ 25, 4, 7, 8 ], [ 25, 4, 8, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 27, 3, 5, 16 ], [ 31, 2, 5, 8 ], [ 34, 3, 5, 4 ], [ 34, 3, 8, 8 ], [ 35, 1, 3, 16 ], [ 35, 2, 3, 8 ], [ 36, 3, 4, 32 ], [ 36, 3, 5, 16 ], [ 36, 6, 6, 16 ], [ 36, 6, 13, 8 ], [ 38, 3, 3, 16 ], [ 39, 4, 3, 16 ], [ 39, 4, 12, 16 ] ] k = 11: F-action on Pi is () [41,5,11] Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^2 phi4)).2 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: [ 10, 43, 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 2, 3, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 3, 2 ], [ 25, 2, 8, 4 ], [ 25, 3, 6, 4 ], [ 25, 4, 5, 4 ], [ 26, 1, 5, 4 ], [ 34, 3, 8, 4 ], [ 35, 1, 7, 8 ], [ 35, 2, 7, 4 ], [ 36, 3, 16, 8 ], [ 36, 6, 6, 8 ], [ 39, 4, 4, 8 ] ] k = 12: F-action on Pi is () [41,5,12] Dynkin type is (A_1(q) + A_1(q) + T(phi1^4 phi2)).2 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: 1/96 phi1 ( q^2-14*q+45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/96 phi1 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/96 phi1 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/96 ( q^3-15*q^2+71*q-105 ) 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, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 15, 2, 3, 12 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 8 ], [ 18, 2, 2, 2 ], [ 22, 1, 1, 24 ], [ 25, 2, 5, 4 ], [ 25, 3, 5, 12 ], [ 25, 4, 5, 36 ], [ 26, 1, 1, 24 ], [ 27, 3, 5, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 30, 2, 2, 16 ], [ 31, 2, 2, 24 ], [ 34, 3, 2, 12 ], [ 35, 1, 1, 48 ], [ 35, 2, 1, 24 ], [ 36, 3, 4, 96 ], [ 36, 6, 5, 24 ], [ 38, 3, 2, 48 ], [ 39, 4, 7, 48 ] ] k = 13: F-action on Pi is () [41,5,13] Dynkin type is (A_1(q) + A_1(q) + T(phi2^5)).2 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: 1/96 phi1 ( q^2-16*q+63 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/96 ( q^3-17*q^2+79*q-95 ) q congruent 7 modulo 12: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/96 phi1 ( q^2-16*q+63 ) q congruent 11 modulo 12: 1/96 ( q^3-17*q^2+91*q-179 ) 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, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 26 ], [ 5, 2, 2, 6 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 12, 2, 3, 16 ], [ 14, 2, 2, 12 ], [ 15, 2, 4, 12 ], [ 15, 4, 4, 48 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 3, 20 ], [ 18, 2, 3, 2 ], [ 20, 2, 2, 48 ], [ 22, 1, 4, 24 ], [ 23, 2, 4, 24 ], [ 25, 2, 8, 4 ], [ 25, 3, 8, 12 ], [ 25, 4, 8, 36 ], [ 26, 1, 3, 24 ], [ 27, 3, 11, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 30, 2, 5, 16 ], [ 31, 2, 7, 24 ], [ 33, 4, 6, 96 ], [ 34, 3, 5, 12 ], [ 35, 1, 10, 48 ], [ 35, 2, 10, 24 ], [ 36, 3, 25, 96 ], [ 36, 6, 13, 24 ], [ 38, 3, 5, 48 ], [ 39, 4, 15, 48 ] ] k = 14: F-action on Pi is () [41,5,14] Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2^2)).2 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^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/32 ( q^3-9*q^2+19*q-3 ) 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, 3 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 8 ], [ 4, 2, 2, 2 ], [ 5, 2, 1, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 15, 2, 1, 8 ], [ 15, 2, 2, 4 ], [ 15, 4, 1, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 8 ], [ 17, 2, 4, 4 ], [ 18, 2, 4, 2 ], [ 22, 1, 3, 8 ], [ 25, 2, 4, 4 ], [ 25, 3, 2, 8 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 16 ], [ 25, 4, 2, 8 ], [ 25, 4, 3, 8 ], [ 25, 4, 4, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 27, 3, 1, 16 ], [ 31, 2, 6, 8 ], [ 34, 3, 6, 4 ], [ 34, 3, 7, 8 ], [ 35, 1, 3, 16 ], [ 35, 2, 3, 8 ], [ 36, 3, 1, 32 ], [ 36, 3, 2, 16 ], [ 36, 6, 2, 16 ], [ 36, 6, 9, 8 ], [ 38, 3, 4, 16 ], [ 39, 4, 9, 16 ], [ 39, 4, 18, 16 ] ] k = 15: F-action on Pi is () [41,5,15] Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^3)).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 phi1^3 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 phi1^3 q congruent 7 modulo 12: 1/16 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1^3 q congruent 11 modulo 12: 1/16 phi1 phi2 ( q-3 ) 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, 3 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 15, 2, 2, 4 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 2 ], [ 18, 2, 4, 2 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 2, 4 ], [ 27, 3, 1, 8 ], [ 27, 3, 9, 8 ], [ 28, 1, 2, 8 ], [ 28, 2, 2, 4 ], [ 30, 2, 6, 8 ], [ 31, 2, 6, 4 ], [ 31, 2, 8, 4 ], [ 34, 3, 6, 4 ], [ 35, 1, 4, 8 ], [ 35, 2, 4, 4 ], [ 36, 3, 14, 16 ], [ 36, 6, 9, 8 ], [ 38, 3, 4, 8 ], [ 38, 3, 6, 8 ], [ 39, 4, 19, 8 ] ] k = 16: F-action on Pi is () [41,5,16] Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2 phi4)).2 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 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 2, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 4, 2 ], [ 25, 2, 4, 4 ], [ 25, 3, 2, 4 ], [ 25, 4, 1, 4 ], [ 26, 1, 5, 4 ], [ 34, 3, 7, 4 ], [ 35, 1, 7, 8 ], [ 35, 2, 7, 4 ], [ 36, 3, 13, 8 ], [ 36, 6, 2, 8 ], [ 39, 4, 10, 8 ] ] k = 17: F-action on Pi is () [41,5,17] Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^2 phi6)).2 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: 1/12 q phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q phi1 phi2 q congruent 7 modulo 12: 1/12 q phi1 phi2 q congruent 8 modulo 12: 0 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: [ 16, 48, 48, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 9, 1, 2, 2 ], [ 17, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 25, 2, 4, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 6, 4 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ] ] k = 18: F-action on Pi is () [41,5,18] Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2 phi4)).2 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: [ 41, 13, 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 2, 2, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ], [ 25, 2, 1, 4 ], [ 25, 3, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 5, 4 ], [ 34, 3, 4, 4 ], [ 35, 1, 6, 8 ], [ 35, 2, 6, 4 ], [ 36, 3, 13, 8 ], [ 36, 6, 10, 8 ], [ 39, 4, 16, 8 ] ] k = 19: F-action on Pi is () [41,5,19] Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2^2)).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 ( q^2-6*q+13 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q^2-6*q+13 ) q congruent 7 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q^2-6*q+13 ) q congruent 11 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) 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, 3 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 22, 1, 2, 8 ], [ 23, 2, 2, 8 ], [ 25, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 3, 8 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 8 ], [ 25, 4, 3, 8 ], [ 25, 4, 4, 16 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 27, 3, 9, 16 ], [ 31, 2, 3, 8 ], [ 34, 3, 1, 4 ], [ 34, 3, 4, 8 ], [ 35, 1, 5, 16 ], [ 35, 2, 5, 8 ], [ 36, 3, 2, 16 ], [ 36, 3, 23, 32 ], [ 36, 6, 1, 8 ], [ 36, 6, 10, 16 ], [ 38, 3, 7, 16 ], [ 39, 4, 8, 16 ], [ 39, 4, 17, 16 ] ] k = 20: F-action on Pi is () [41,5,20] Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^4)).2 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: 1/96 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/96 phi2 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/96 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/96 phi2 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/96 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/96 phi2 ( q^2-10*q+21 ) 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, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 15, 2, 2, 12 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 8 ], [ 17, 2, 3, 12 ], [ 18, 2, 4, 2 ], [ 22, 1, 4, 24 ], [ 25, 2, 4, 4 ], [ 25, 3, 4, 12 ], [ 25, 4, 4, 36 ], [ 26, 1, 3, 24 ], [ 27, 3, 9, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 30, 2, 6, 16 ], [ 31, 2, 8, 24 ], [ 34, 3, 6, 12 ], [ 35, 1, 10, 48 ], [ 35, 2, 10, 24 ], [ 36, 3, 23, 96 ], [ 36, 6, 9, 24 ], [ 38, 3, 6, 48 ], [ 39, 4, 20, 48 ] ] k = 21: F-action on Pi is (1,2) [41,5,21] Dynkin type is (A_1(q^2) + T(phi1 phi2^4)).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 ( q^2-6*q+13 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q^2-6*q+13 ) q congruent 7 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q^2-6*q+13 ) q congruent 11 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) 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, 3 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 8 ], [ 15, 2, 4, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 8 ], [ 18, 2, 3, 2 ], [ 22, 1, 2, 8 ], [ 23, 2, 4, 8 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 8 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 8 ], [ 25, 4, 6, 16 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 27, 3, 8, 16 ], [ 31, 2, 7, 8 ], [ 34, 3, 5, 8 ], [ 34, 3, 8, 4 ], [ 35, 1, 5, 16 ], [ 35, 2, 5, 8 ], [ 36, 3, 5, 16 ], [ 36, 3, 26, 32 ], [ 36, 6, 8, 8 ], [ 36, 6, 16, 16 ], [ 38, 3, 14, 16 ], [ 39, 4, 3, 16 ], [ 39, 4, 15, 16 ] ] k = 22: F-action on Pi is (1,2) [41,5,22] Dynkin type is (A_1(q^2) + T(phi1^2 phi2^3)).2 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^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/16 ( q^3-9*q^2+19*q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/16 ( q^3-9*q^2+19*q-3 ) 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 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 3, 4 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 12, 2, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 15, 4, 7, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 3, 2 ], [ 20, 2, 4, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 23, 2, 3, 4 ], [ 23, 2, 4, 4 ], [ 25, 2, 6, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 7, 4 ], [ 26, 1, 2, 4 ], [ 27, 3, 8, 8 ], [ 27, 3, 14, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 4, 4 ], [ 30, 2, 3, 8 ], [ 31, 2, 5, 4 ], [ 31, 2, 7, 4 ], [ 33, 4, 12, 16 ], [ 34, 3, 8, 4 ], [ 35, 1, 2, 8 ], [ 35, 2, 2, 4 ], [ 36, 3, 18, 16 ], [ 36, 6, 8, 8 ], [ 38, 3, 12, 8 ], [ 38, 3, 14, 8 ], [ 39, 4, 11, 8 ] ] k = 23: F-action on Pi is (1,2) [41,5,23] Dynkin type is (A_1(q^2) + T(phi2^3 phi4)).2 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: [ 11, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 2, 3, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 3, 2 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ], [ 25, 4, 6, 4 ], [ 26, 1, 5, 4 ], [ 34, 3, 5, 4 ], [ 35, 1, 6, 8 ], [ 35, 2, 6, 4 ], [ 36, 3, 16, 8 ], [ 36, 6, 16, 8 ], [ 39, 4, 4, 8 ] ] k = 24: F-action on Pi is (1,2) [41,5,24] Dynkin type is (A_1(q^2) + T(phi1 phi2^2 phi3)).2 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: 1/12 phi1 ( q^2-q-4 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q phi2 ( q-3 ) q congruent 7 modulo 12: 1/12 phi1 ( q^2-q-4 ) q congruent 8 modulo 12: 0 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: [ 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 ], [ 4, 2, 1, 2 ], [ 6, 2, 2, 2 ], [ 9, 1, 1, 2 ], [ 12, 2, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 25, 2, 6, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 3, 4 ], [ 33, 4, 11, 12 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ] ] k = 25: F-action on Pi is (1,2) [41,5,25] Dynkin type is (A_1(q^2) + T(phi1 phi2^4)).2 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: 1/96 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/96 phi2 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/96 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/96 phi2 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/96 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/96 phi2 ( q^2-10*q+21 ) 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, 2, 4 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 15, 2, 3, 12 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 12 ], [ 18, 2, 2, 2 ], [ 22, 1, 4, 24 ], [ 25, 2, 7, 4 ], [ 25, 3, 5, 12 ], [ 25, 4, 6, 36 ], [ 26, 1, 3, 24 ], [ 27, 3, 8, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 30, 2, 8, 16 ], [ 31, 2, 4, 24 ], [ 34, 3, 3, 12 ], [ 35, 1, 10, 48 ], [ 35, 2, 10, 24 ], [ 36, 3, 26, 96 ], [ 36, 6, 15, 24 ], [ 38, 3, 15, 48 ], [ 39, 4, 5, 48 ] ] k = 26: F-action on Pi is (1,2) [41,5,26] Dynkin type is (A_1(q^2) + T(phi1^2 phi2^3)).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 phi1^3 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 phi1^3 q congruent 7 modulo 12: 1/16 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1^3 q congruent 11 modulo 12: 1/16 phi1 phi2 ( q-3 ) 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, 2, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 4, 2, 3, 4 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 15, 2, 3, 4 ], [ 15, 4, 7, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 25, 2, 7, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 6, 4 ], [ 26, 1, 2, 4 ], [ 27, 3, 8, 8 ], [ 27, 3, 14, 8 ], [ 28, 1, 2, 8 ], [ 28, 2, 2, 4 ], [ 30, 2, 8, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 4, 4 ], [ 34, 3, 3, 4 ], [ 35, 1, 4, 8 ], [ 35, 2, 4, 4 ], [ 36, 3, 18, 16 ], [ 36, 6, 15, 8 ], [ 38, 3, 9, 8 ], [ 38, 3, 15, 8 ], [ 39, 4, 6, 8 ] ] k = 27: F-action on Pi is (1,2) [41,5,27] Dynkin type is (A_1(q^2) + T(phi1 phi2^2 phi6)).2 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: 1/12 q phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q phi1 phi2 q congruent 7 modulo 12: 1/12 q phi1 phi2 q congruent 8 modulo 12: 0 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: [ 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 ], [ 4, 2, 2, 2 ], [ 9, 1, 2, 2 ], [ 17, 2, 2, 2 ], [ 18, 2, 2, 2 ], [ 25, 2, 7, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 8, 4 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ] ] k = 28: F-action on Pi is (1,2) [41,5,28] Dynkin type is (A_1(q^2) + T(phi1^3 phi2^2)).2 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^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/32 ( q^3-9*q^2+19*q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/32 ( q^3-9*q^2+19*q-3 ) 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, 3 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 4, 2, 3, 8 ], [ 5, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 8 ], [ 15, 4, 5, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 2, 2, 2 ], [ 22, 1, 3, 8 ], [ 25, 2, 7, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 7, 8 ], [ 25, 4, 5, 8 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 16 ], [ 25, 4, 8, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 27, 3, 14, 16 ], [ 31, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 34, 3, 3, 4 ], [ 35, 1, 3, 16 ], [ 35, 2, 3, 8 ], [ 36, 3, 5, 16 ], [ 36, 3, 6, 32 ], [ 36, 6, 7, 16 ], [ 36, 6, 15, 8 ], [ 38, 3, 9, 16 ], [ 39, 4, 7, 16 ], [ 39, 4, 13, 16 ] ] k = 29: F-action on Pi is (1,2) [41,5,29] Dynkin type is (A_1(q^2) + T(phi1^2 phi2 phi4)).2 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: [ 10, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 2, 4, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 25, 2, 7, 4 ], [ 25, 3, 7, 4 ], [ 25, 4, 7, 4 ], [ 26, 1, 5, 4 ], [ 34, 3, 2, 4 ], [ 35, 1, 7, 8 ], [ 35, 2, 7, 4 ], [ 36, 3, 16, 8 ], [ 36, 6, 7, 8 ], [ 39, 4, 14, 8 ] ] k = 30: F-action on Pi is (1,2) [41,5,30] Dynkin type is (A_1(q^2) + T(phi1^3 phi2^2)).2 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: 1/96 ( q^3-23*q^2+171*q-437 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/96 ( q^3-23*q^2+159*q-297 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 7 modulo 12: 1/96 ( q^3-23*q^2+159*q-329 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/96 ( q^3-23*q^2+171*q-405 ) q congruent 11 modulo 12: 1/96 ( q^3-23*q^2+159*q-297 ) 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, 2, 1, 2 ], [ 4, 2, 3, 24 ], [ 5, 2, 2, 6 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 2, 2, 16 ], [ 14, 2, 2, 12 ], [ 15, 2, 4, 12 ], [ 15, 4, 5, 48 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 2, 8 ], [ 18, 2, 3, 2 ], [ 20, 2, 4, 48 ], [ 22, 1, 1, 24 ], [ 23, 2, 3, 24 ], [ 25, 2, 6, 4 ], [ 25, 3, 8, 12 ], [ 25, 4, 7, 36 ], [ 26, 1, 1, 24 ], [ 27, 3, 14, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 30, 2, 3, 16 ], [ 31, 2, 5, 24 ], [ 33, 4, 10, 96 ], [ 34, 3, 8, 12 ], [ 35, 1, 1, 48 ], [ 35, 2, 1, 24 ], [ 36, 3, 6, 96 ], [ 36, 6, 8, 24 ], [ 38, 3, 12, 48 ], [ 39, 4, 12, 48 ] ] k = 31: F-action on Pi is (1,2) [41,5,31] Dynkin type is (A_1(q^2) + T(phi1^2 phi2 phi6)).2 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: 1/12 q phi1^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi1^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 phi2 ( q^2-3*q+4 ) q congruent 7 modulo 12: 1/12 q phi1^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 q phi1^2 q congruent 11 modulo 12: 1/12 phi2 ( q^2-3*q+4 ) 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 ], [ 4, 2, 2, 2 ], [ 6, 2, 1, 2 ], [ 9, 1, 2, 2 ], [ 12, 2, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ], [ 25, 2, 3, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 7, 4 ], [ 33, 4, 8, 12 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ] ] k = 32: F-action on Pi is (1,2) [41,5,32] Dynkin type is (A_1(q^2) + T(phi1^3 phi4)).2 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, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 3, 4 ], [ 15, 2, 2, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ], [ 25, 2, 3, 4 ], [ 25, 3, 3, 4 ], [ 25, 4, 3, 4 ], [ 26, 1, 5, 4 ], [ 34, 3, 1, 4 ], [ 35, 1, 7, 8 ], [ 35, 2, 7, 4 ], [ 36, 3, 13, 8 ], [ 36, 6, 3, 8 ], [ 39, 4, 16, 8 ] ] k = 33: F-action on Pi is (1,2) [41,5,33] Dynkin type is (A_1(q^2) + T(phi1^4 phi2)).2 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^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/32 ( q^3-9*q^2+27*q-27 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/32 ( q^3-9*q^2+27*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, 3 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 2 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 4 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 8 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 22, 1, 3, 8 ], [ 23, 2, 1, 8 ], [ 25, 2, 3, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 3, 8 ], [ 25, 4, 1, 8 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 16 ], [ 25, 4, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 27, 3, 16, 16 ], [ 31, 2, 1, 8 ], [ 34, 3, 1, 8 ], [ 34, 3, 4, 4 ], [ 35, 1, 3, 16 ], [ 35, 2, 3, 8 ], [ 36, 3, 2, 16 ], [ 36, 3, 3, 32 ], [ 36, 6, 3, 16 ], [ 36, 6, 11, 8 ], [ 38, 3, 10, 16 ], [ 39, 4, 1, 16 ], [ 39, 4, 17, 16 ] ] k = 34: F-action on Pi is (1,2) [41,5,34] Dynkin type is (A_1(q^2) + T(phi1^3 phi2^2)).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 ( q^2-6*q+9 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^3-7*q^2+19*q-21 ) 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 ( q^3-7*q^2+19*q-21 ) 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 ( q^3-7*q^2+19*q-21 ) 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, 2, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 4 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 4, 4 ], [ 11, 1, 2, 4 ], [ 12, 2, 4, 8 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 4, 6, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 20, 2, 3, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 23, 2, 1, 4 ], [ 23, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 3, 1, 4 ], [ 25, 4, 2, 4 ], [ 26, 1, 2, 4 ], [ 27, 3, 4, 8 ], [ 27, 3, 16, 8 ], [ 28, 1, 2, 8 ], [ 28, 2, 2, 4 ], [ 30, 2, 7, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 3, 4 ], [ 33, 4, 7, 16 ], [ 34, 3, 4, 4 ], [ 35, 1, 4, 8 ], [ 35, 2, 4, 4 ], [ 36, 3, 15, 16 ], [ 36, 6, 11, 8 ], [ 38, 3, 10, 8 ], [ 38, 3, 16, 8 ], [ 39, 4, 2, 8 ] ] k = 35: F-action on Pi is (1,2) [41,5,35] Dynkin type is (A_1(q^2) + T(phi1^4 phi2)).2 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: 1/96 phi1 ( q^2-14*q+45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/96 phi1 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/96 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/96 phi1 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/96 ( q^3-15*q^2+71*q-105 ) 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, 2, 1, 2 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 15, 2, 2, 12 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 4, 8 ], [ 18, 2, 4, 2 ], [ 22, 1, 1, 24 ], [ 25, 2, 2, 4 ], [ 25, 3, 4, 12 ], [ 25, 4, 3, 36 ], [ 26, 1, 1, 24 ], [ 27, 3, 16, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 30, 2, 4, 16 ], [ 31, 2, 6, 24 ], [ 34, 3, 7, 12 ], [ 35, 1, 1, 48 ], [ 35, 2, 1, 24 ], [ 36, 3, 3, 96 ], [ 36, 6, 4, 24 ], [ 38, 3, 11, 48 ], [ 39, 4, 18, 48 ] ] k = 36: F-action on Pi is (1,2) [41,5,36] Dynkin type is (A_1(q^2) + T(phi1^3 phi2^2)).2 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^2-4*q-1 ) 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 ( q^2-4*q-1 ) 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 ( q^2-4*q-1 ) q congruent 11 modulo 12: 1/16 phi1^2 ( 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 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 4, 4 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 4, 6, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 2, 4, 2 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], [ 25, 2, 2, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 3, 4 ], [ 26, 1, 2, 4 ], [ 27, 3, 4, 8 ], [ 27, 3, 16, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 4, 4 ], [ 30, 2, 4, 8 ], [ 31, 2, 6, 4 ], [ 31, 2, 8, 4 ], [ 34, 3, 7, 4 ], [ 35, 1, 2, 8 ], [ 35, 2, 2, 4 ], [ 36, 3, 15, 16 ], [ 36, 6, 4, 8 ], [ 38, 3, 11, 8 ], [ 38, 3, 13, 8 ], [ 39, 4, 19, 8 ] ] k = 37: F-action on Pi is (1,2) [41,5,37] Dynkin type is (A_1(q^2) + T(phi1^2 phi2 phi3)).2 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: 1/12 q phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q phi1 phi2 q congruent 7 modulo 12: 1/12 q phi1 phi2 q congruent 8 modulo 12: 0 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: [ 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 ], [ 4, 2, 1, 2 ], [ 9, 1, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 4, 2 ], [ 25, 2, 2, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 4, 4 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ] ] k = 38: F-action on Pi is (1,2) [41,5,38] Dynkin type is (A_1(q^2) + T(phi1 phi2^2 phi4)).2 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: [ 40, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 15, 2, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 4, 2 ], [ 25, 2, 2, 4 ], [ 25, 3, 2, 4 ], [ 25, 4, 2, 4 ], [ 26, 1, 5, 4 ], [ 34, 3, 6, 4 ], [ 35, 1, 6, 8 ], [ 35, 2, 6, 4 ], [ 36, 3, 13, 8 ], [ 36, 6, 12, 8 ], [ 39, 4, 10, 8 ] ] k = 39: F-action on Pi is (1,2) [41,5,39] Dynkin type is (A_1(q^2) + T(phi1^2 phi2^3)).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 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^2 ( q-5 ) q congruent 7 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^2 ( q-5 ) q congruent 11 modulo 12: 1/32 phi1 ( q^2-6*q+9 ) 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, 3 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 4, 8 ], [ 5, 2, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 8 ], [ 15, 2, 1, 8 ], [ 15, 2, 2, 4 ], [ 15, 4, 8, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 2, 4, 2 ], [ 22, 1, 2, 8 ], [ 25, 2, 2, 4 ], [ 25, 3, 2, 8 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 8 ], [ 25, 4, 2, 16 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 27, 3, 4, 16 ], [ 31, 2, 8, 8 ], [ 34, 3, 6, 8 ], [ 34, 3, 7, 4 ], [ 35, 1, 5, 16 ], [ 35, 2, 5, 8 ], [ 36, 3, 2, 16 ], [ 36, 3, 24, 32 ], [ 36, 6, 4, 8 ], [ 36, 6, 12, 16 ], [ 38, 3, 13, 16 ], [ 39, 4, 9, 16 ], [ 39, 4, 20, 16 ] ] k = 40: F-action on Pi is (1,2) [41,5,40] Dynkin type is (A_1(q^2) + T(phi1^2 phi2^3)).2 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: 1/96 phi1 ( q^2-16*q+63 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/96 ( q^3-17*q^2+79*q-95 ) q congruent 7 modulo 12: 1/96 ( q^3-17*q^2+91*q-147 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/96 phi1 ( q^2-16*q+63 ) q congruent 11 modulo 12: 1/96 ( q^3-17*q^2+91*q-179 ) 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, 2, 4 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 24 ], [ 5, 2, 1, 6 ], [ 6, 2, 1, 2 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 8 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 24 ], [ 12, 2, 4, 16 ], [ 14, 2, 1, 12 ], [ 15, 2, 1, 12 ], [ 15, 4, 8, 48 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 3, 12 ], [ 17, 2, 4, 8 ], [ 18, 2, 1, 2 ], [ 20, 2, 3, 48 ], [ 22, 1, 4, 24 ], [ 23, 2, 2, 24 ], [ 25, 2, 3, 4 ], [ 25, 3, 1, 12 ], [ 25, 4, 2, 36 ], [ 26, 1, 3, 24 ], [ 27, 3, 4, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 30, 2, 7, 16 ], [ 31, 2, 3, 24 ], [ 33, 4, 9, 96 ], [ 34, 3, 4, 12 ], [ 35, 1, 10, 48 ], [ 35, 2, 10, 24 ], [ 36, 3, 24, 96 ], [ 36, 6, 11, 24 ], [ 38, 3, 16, 48 ], [ 39, 4, 8, 48 ] ] 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+470*q^3-3040*q^2+9629*q-12785 ) 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+470*q^3-3040*q^2+9549*q-11385 ) 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+470*q^3-3040*q^2+9549*q-11745 ) q congruent 7 modulo 12: 1/1440 ( q^5-35*q^4+470*q^3-3040*q^2+9629*q-12425 ) 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+470*q^3-3040*q^2+9549*q-11745 ) q congruent 11 modulo 12: 1/1440 ( q^5-35*q^4+470*q^3-3040*q^2+9549*q-11385 ) 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 ], [ 4, 2, 1, 30 ], [ 5, 1, 1, 12 ], [ 5, 2, 1, 6 ], [ 6, 1, 1, 20 ], [ 6, 2, 1, 10 ], [ 7, 1, 1, 90 ], [ 8, 1, 1, 132 ], [ 9, 1, 1, 150 ], [ 10, 1, 1, 180 ], [ 11, 1, 1, 120 ], [ 12, 1, 1, 120 ], [ 12, 2, 1, 60 ], [ 13, 1, 1, 60 ], [ 14, 1, 1, 120 ], [ 14, 2, 1, 60 ], [ 15, 1, 1, 120 ], [ 15, 2, 1, 60 ], [ 15, 3, 1, 60 ], [ 15, 4, 1, 60 ], [ 16, 1, 1, 30 ], [ 17, 1, 1, 180 ], [ 17, 2, 1, 90 ], [ 18, 1, 1, 180 ], [ 18, 2, 1, 90 ], [ 19, 1, 1, 360 ], [ 20, 1, 1, 240 ], [ 20, 2, 1, 120 ], [ 21, 1, 1, 180 ], [ 22, 1, 1, 360 ], [ 23, 1, 1, 240 ], [ 23, 2, 1, 120 ], [ 24, 1, 1, 300 ], [ 25, 1, 1, 360 ], [ 25, 2, 1, 180 ], [ 25, 3, 1, 180 ], [ 25, 4, 1, 180 ], [ 26, 1, 1, 360 ], [ 28, 1, 1, 240 ], [ 28, 2, 1, 120 ], [ 29, 1, 1, 720 ], [ 29, 2, 1, 360 ], [ 30, 1, 1, 360 ], [ 30, 2, 1, 180 ], [ 31, 1, 1, 720 ], [ 31, 2, 1, 360 ], [ 33, 1, 1, 480 ], [ 33, 2, 1, 240 ], [ 33, 3, 1, 240 ], [ 33, 4, 1, 240 ], [ 34, 1, 1, 720 ], [ 34, 2, 1, 360 ], [ 34, 3, 1, 360 ], [ 35, 1, 1, 720 ], [ 35, 2, 1, 360 ], [ 37, 1, 1, 720 ], [ 37, 2, 1, 360 ], [ 39, 1, 1, 1440 ], [ 39, 2, 1, 720 ], [ 39, 3, 1, 720 ], [ 39, 4, 1, 720 ], [ 39, 5, 1, 720 ], [ 42, 2, 1, 720 ], [ 42, 3, 1, 720 ], [ 42, 4, 1, 720 ] ] 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 ], [ 5, 2, 1, 1 ], [ 8, 1, 1, 2 ], [ 42, 4, 2, 5 ] ] 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 ], [ 5, 2, 2, 1 ], [ 8, 1, 2, 2 ], [ 42, 4, 3, 5 ] ] 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 phi1^2 ( q^3-6*q^2+4*q+16 ) 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+26*q-24 ) 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+26*q-24 ) q congruent 7 modulo 12: 1/36 phi1^2 ( q^3-6*q^2+4*q+16 ) 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+26*q-24 ) q congruent 11 modulo 12: 1/36 q phi2 ( q^3-9*q^2+26*q-24 ) 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 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 6 ], [ 5, 2, 1, 3 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 12 ], [ 11, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 3 ], [ 15, 1, 1, 24 ], [ 15, 2, 1, 12 ], [ 15, 3, 1, 12 ], [ 15, 4, 1, 12 ], [ 16, 1, 1, 6 ], [ 20, 1, 1, 12 ], [ 20, 2, 1, 6 ], [ 23, 1, 1, 12 ], [ 23, 2, 1, 6 ], [ 24, 1, 1, 24 ], [ 28, 1, 1, 12 ], [ 28, 1, 5, 6 ], [ 28, 2, 1, 6 ], [ 28, 2, 3, 3 ], [ 29, 1, 3, 18 ], [ 29, 2, 3, 9 ], [ 33, 1, 1, 24 ], [ 33, 1, 2, 12 ], [ 33, 2, 1, 12 ], [ 33, 2, 2, 6 ], [ 33, 3, 1, 12 ], [ 33, 3, 2, 6 ], [ 33, 4, 1, 12 ], [ 33, 4, 2, 6 ], [ 35, 1, 8, 18 ], [ 35, 2, 8, 9 ], [ 37, 1, 3, 18 ], [ 37, 2, 3, 9 ], [ 39, 1, 3, 36 ], [ 39, 2, 3, 18 ], [ 39, 3, 3, 18 ], [ 42, 3, 3, 18 ], [ 42, 4, 4, 18 ] ] 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 ], [ 6, 2, 1, 1 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 21, 1, 5, 18 ], [ 28, 1, 5, 12 ], [ 28, 2, 3, 6 ], [ 33, 1, 2, 24 ], [ 33, 2, 2, 12 ], [ 33, 3, 2, 12 ], [ 33, 4, 2, 12 ], [ 34, 1, 9, 18 ], [ 34, 2, 7, 9 ], [ 42, 2, 9, 18 ], [ 42, 4, 5, 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^2 phi1^2 ( q-2 ) 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^2 phi1^2 ( q-2 ) 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+10*q^2-12*q+8 ) q congruent 7 modulo 12: 1/36 q^2 phi1^2 ( q-2 ) 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^2 phi1^2 ( q-2 ) q congruent 11 modulo 12: 1/36 phi2 ( q^4-5*q^3+10*q^2-12*q+8 ) 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 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 6 ], [ 5, 2, 2, 3 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 12 ], [ 11, 1, 2, 6 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 13, 1, 2, 12 ], [ 14, 1, 2, 6 ], [ 14, 2, 2, 3 ], [ 15, 1, 4, 24 ], [ 15, 2, 4, 12 ], [ 15, 3, 4, 12 ], [ 15, 4, 4, 12 ], [ 16, 1, 2, 6 ], [ 20, 1, 2, 12 ], [ 20, 2, 2, 6 ], [ 23, 1, 4, 12 ], [ 23, 2, 4, 6 ], [ 24, 1, 3, 24 ], [ 28, 1, 4, 6 ], [ 28, 1, 6, 12 ], [ 28, 2, 5, 3 ], [ 28, 2, 6, 6 ], [ 29, 1, 6, 18 ], [ 29, 2, 6, 9 ], [ 33, 1, 5, 12 ], [ 33, 1, 6, 24 ], [ 33, 2, 5, 6 ], [ 33, 2, 6, 12 ], [ 33, 3, 5, 6 ], [ 33, 3, 6, 12 ], [ 33, 4, 5, 6 ], [ 33, 4, 6, 12 ], [ 35, 1, 9, 18 ], [ 35, 2, 9, 9 ], [ 37, 1, 8, 18 ], [ 37, 2, 8, 9 ], [ 39, 1, 12, 36 ], [ 39, 2, 12, 18 ], [ 39, 3, 12, 18 ], [ 42, 3, 18, 18 ], [ 42, 4, 8, 18 ] ] 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^2 phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 20, 1, 1, 4 ], [ 20, 2, 1, 2 ], [ 23, 1, 2, 4 ], [ 23, 2, 2, 2 ], [ 24, 1, 2, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 28, 2, 4, 2 ], [ 29, 1, 3, 6 ], [ 29, 2, 3, 3 ], [ 33, 1, 2, 12 ], [ 33, 1, 3, 8 ], [ 33, 2, 2, 6 ], [ 33, 2, 3, 4 ], [ 33, 3, 2, 6 ], [ 33, 3, 3, 4 ], [ 33, 4, 2, 6 ], [ 33, 4, 3, 4 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 37, 1, 3, 6 ], [ 37, 2, 3, 3 ], [ 39, 1, 7, 12 ], [ 39, 2, 7, 6 ], [ 39, 3, 7, 6 ], [ 42, 3, 8, 6 ], [ 42, 4, 6, 6 ] ] 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^2 phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/12 q^2 phi1 phi2 ( q-2 ) 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 23, 1, 3, 4 ], [ 23, 2, 3, 2 ], [ 24, 1, 4, 8 ], [ 28, 1, 2, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 2, 2 ], [ 28, 2, 5, 3 ], [ 29, 1, 6, 6 ], [ 29, 2, 6, 3 ], [ 33, 1, 4, 8 ], [ 33, 1, 5, 12 ], [ 33, 2, 4, 4 ], [ 33, 2, 5, 6 ], [ 33, 3, 4, 4 ], [ 33, 3, 5, 6 ], [ 33, 4, 4, 4 ], [ 33, 4, 5, 6 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 37, 1, 8, 6 ], [ 37, 2, 8, 3 ], [ 39, 1, 16, 12 ], [ 39, 2, 16, 6 ], [ 39, 3, 16, 6 ], [ 42, 3, 13, 6 ], [ 42, 4, 7, 6 ] ] 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 ], [ 6, 2, 2, 1 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 21, 1, 5, 6 ], [ 34, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 42, 2, 8, 6 ], [ 42, 4, 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 ], [ 6, 2, 1, 1 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 21, 1, 4, 6 ], [ 34, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 42, 2, 17, 6 ], [ 42, 4, 11, 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 ], [ 6, 2, 2, 1 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 21, 1, 4, 18 ], [ 28, 1, 4, 12 ], [ 28, 2, 5, 6 ], [ 33, 1, 5, 24 ], [ 33, 2, 5, 12 ], [ 33, 3, 5, 12 ], [ 33, 4, 5, 12 ], [ 34, 1, 10, 18 ], [ 34, 2, 6, 9 ], [ 42, 2, 16, 18 ], [ 42, 4, 9, 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 phi1 ( q^4-6*q^3+8*q^2+13 ) 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+14*q^3-8*q^2+13*q-21 ) 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 phi1 ( q^4-6*q^3+8*q^2+13 ) q congruent 7 modulo 12: 1/32 ( q^5-7*q^4+14*q^3-8*q^2+13*q-21 ) 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 phi1 ( q^4-6*q^3+8*q^2+13 ) q congruent 11 modulo 12: 1/32 ( q^5-7*q^4+14*q^3-8*q^2+13*q-21 ) 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 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 12, 2, 1, 12 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 3, 16 ], [ 15, 2, 1, 4 ], [ 15, 2, 3, 8 ], [ 15, 3, 1, 4 ], [ 15, 3, 3, 8 ], [ 15, 4, 1, 4 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 8 ], [ 18, 2, 1, 2 ], [ 18, 2, 2, 4 ], [ 18, 2, 4, 4 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 20, 2, 1, 8 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 8 ], [ 22, 1, 2, 16 ], [ 23, 1, 2, 16 ], [ 23, 2, 2, 8 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 24 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 5, 16 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 8 ], [ 25, 2, 5, 8 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 8 ], [ 25, 3, 5, 8 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 8 ], [ 25, 4, 5, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 3, 16 ], [ 28, 2, 4, 8 ], [ 29, 1, 2, 16 ], [ 29, 2, 2, 8 ], [ 30, 1, 1, 8 ], [ 30, 1, 2, 16 ], [ 30, 1, 4, 16 ], [ 30, 2, 1, 4 ], [ 30, 2, 2, 8 ], [ 30, 2, 4, 8 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 16 ], [ 31, 2, 2, 8 ], [ 31, 2, 3, 8 ], [ 31, 2, 4, 8 ], [ 33, 1, 3, 32 ], [ 33, 2, 3, 16 ], [ 33, 3, 3, 16 ], [ 33, 4, 3, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 16 ], [ 34, 2, 4, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 4, 8 ], [ 34, 3, 6, 8 ], [ 34, 3, 7, 8 ], [ 35, 1, 2, 16 ], [ 35, 1, 5, 16 ], [ 35, 2, 2, 8 ], [ 35, 2, 5, 8 ], [ 37, 1, 2, 16 ], [ 37, 1, 5, 16 ], [ 37, 2, 2, 8 ], [ 37, 2, 5, 8 ], [ 39, 1, 5, 32 ], [ 39, 1, 10, 32 ], [ 39, 2, 5, 16 ], [ 39, 2, 10, 16 ], [ 39, 3, 5, 16 ], [ 39, 3, 10, 16 ], [ 39, 4, 6, 16 ], [ 39, 4, 8, 16 ], [ 39, 4, 9, 16 ], [ 39, 5, 6, 16 ], [ 39, 5, 8, 16 ], [ 39, 5, 9, 16 ], [ 42, 2, 4, 16 ], [ 42, 2, 5, 16 ], [ 42, 3, 5, 16 ], [ 42, 3, 7, 16 ], [ 42, 4, 12, 16 ] ] k = 13: F-action on Pi is (1,3) [42,1,13] 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 phi2 ( q^3-3*q^2+3*q-3 ) q congruent 2 modulo 12: 1/16 q^3 phi1 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+3*q-3 ) q congruent 4 modulo 12: 1/16 q^3 phi1 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+3*q-3 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+3*q-3 ) q congruent 8 modulo 12: 1/16 q^3 phi1 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+3*q-3 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^3-3*q^2+3*q-3 ) 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 ], [ 4, 2, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 1, 5, 8 ], [ 12, 2, 4, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 21, 1, 3, 4 ], [ 24, 1, 4, 4 ], [ 25, 1, 3, 8 ], [ 25, 2, 3, 4 ], [ 25, 3, 3, 4 ], [ 25, 4, 3, 4 ], [ 26, 1, 5, 4 ], [ 30, 1, 7, 8 ], [ 30, 2, 7, 4 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 35, 1, 7, 8 ], [ 35, 2, 7, 4 ], [ 37, 1, 10, 8 ], [ 37, 2, 10, 4 ], [ 39, 1, 17, 16 ], [ 39, 2, 17, 8 ], [ 39, 3, 17, 8 ], [ 39, 4, 16, 8 ], [ 39, 5, 16, 8 ], [ 42, 2, 14, 8 ], [ 42, 3, 15, 8 ], [ 42, 4, 16, 8 ] ] k = 14: F-action on Pi is (1,3) [42,1,14] 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 phi1^2 phi2 phi4 q congruent 2 modulo 12: 1/16 q^4 phi1 q congruent 3 modulo 12: 1/16 phi1^2 phi2 phi4 q congruent 4 modulo 12: 1/16 q^4 phi1 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^4 phi1 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: [ 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 21, 1, 3, 4 ], [ 24, 1, 3, 4 ], [ 25, 1, 7, 8 ], [ 25, 2, 7, 4 ], [ 25, 3, 7, 4 ], [ 25, 4, 7, 4 ], [ 26, 1, 5, 4 ], [ 30, 1, 8, 8 ], [ 30, 2, 8, 4 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 35, 1, 7, 8 ], [ 35, 2, 7, 4 ], [ 37, 1, 10, 8 ], [ 37, 2, 10, 4 ], [ 39, 1, 14, 16 ], [ 39, 2, 14, 8 ], [ 39, 3, 14, 8 ], [ 39, 4, 14, 8 ], [ 39, 5, 14, 8 ], [ 42, 2, 18, 8 ], [ 42, 3, 20, 8 ], [ 42, 4, 15, 8 ] ] 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 ( q^3-q^2-q-1 ) q congruent 2 modulo 12: 1/16 q^3 phi2 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^3-q^2-q-1 ) q congruent 4 modulo 12: 1/16 q^3 phi2 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^3-q^2-q-1 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^3-q^2-q-1 ) q congruent 8 modulo 12: 1/16 q^3 phi2 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^3-q^2-q-1 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^3-q^2-q-1 ) 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 ], [ 4, 2, 1, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 21, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 6, 8 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ], [ 25, 4, 6, 4 ], [ 26, 1, 5, 4 ], [ 30, 1, 3, 8 ], [ 30, 2, 3, 4 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 35, 1, 6, 8 ], [ 35, 2, 6, 4 ], [ 37, 1, 4, 8 ], [ 37, 2, 4, 4 ], [ 39, 1, 6, 16 ], [ 39, 2, 6, 8 ], [ 39, 3, 6, 8 ], [ 39, 4, 4, 8 ], [ 39, 5, 4, 8 ], [ 42, 2, 7, 8 ], [ 42, 3, 9, 8 ], [ 42, 4, 14, 8 ] ] k = 16: F-action on Pi is () [42,1,16] 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 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/16 q^2 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1^2 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/16 q^2 phi2 ( q^2-4*q+4 ) 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^2 phi2 ( q^2-4*q+4 ) 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: [ 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 21, 1, 2, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 2, 2, 4 ], [ 25, 3, 2, 4 ], [ 25, 4, 2, 4 ], [ 26, 1, 5, 4 ], [ 30, 1, 4, 8 ], [ 30, 2, 4, 4 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 35, 1, 6, 8 ], [ 35, 2, 6, 4 ], [ 37, 1, 4, 8 ], [ 37, 2, 4, 4 ], [ 39, 1, 9, 16 ], [ 39, 2, 9, 8 ], [ 39, 3, 9, 8 ], [ 39, 4, 10, 8 ], [ 39, 5, 10, 8 ], [ 42, 2, 3, 8 ], [ 42, 3, 4, 8 ], [ 42, 4, 13, 8 ] ] k = 17: F-action on Pi is (1,3) [42,1,17] 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 ( q^4-4*q^3+2*q^2-2*q+11 ) q congruent 2 modulo 12: 1/32 q^3 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/32 ( q^5-5*q^4+6*q^3-4*q^2+13*q-3 ) q congruent 4 modulo 12: 1/32 q^3 ( q^2-5*q+6 ) q congruent 5 modulo 12: 1/32 phi1 ( q^4-4*q^3+2*q^2-2*q+11 ) q congruent 7 modulo 12: 1/32 ( q^5-5*q^4+6*q^3-4*q^2+13*q-3 ) q congruent 8 modulo 12: 1/32 q^3 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/32 phi1 ( q^4-4*q^3+2*q^2-2*q+11 ) q congruent 11 modulo 12: 1/32 ( q^5-5*q^4+6*q^3-4*q^2+13*q-3 ) 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 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 12, 2, 3, 12 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 2, 16 ], [ 15, 1, 4, 8 ], [ 15, 2, 2, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 2, 8 ], [ 15, 3, 4, 4 ], [ 15, 4, 2, 8 ], [ 15, 4, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 2, 4 ], [ 18, 2, 3, 2 ], [ 18, 2, 4, 4 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 20, 2, 2, 8 ], [ 21, 1, 3, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 3, 16 ], [ 23, 2, 3, 8 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 24 ], [ 25, 1, 4, 16 ], [ 25, 1, 7, 16 ], [ 25, 1, 8, 8 ], [ 25, 2, 4, 8 ], [ 25, 2, 7, 8 ], [ 25, 2, 8, 4 ], [ 25, 3, 4, 8 ], [ 25, 3, 7, 8 ], [ 25, 3, 8, 4 ], [ 25, 4, 4, 8 ], [ 25, 4, 7, 8 ], [ 25, 4, 8, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 2, 16 ], [ 28, 2, 2, 8 ], [ 29, 1, 5, 16 ], [ 29, 2, 5, 8 ], [ 30, 1, 5, 8 ], [ 30, 1, 6, 16 ], [ 30, 1, 8, 16 ], [ 30, 2, 5, 4 ], [ 30, 2, 6, 8 ], [ 30, 2, 8, 8 ], [ 31, 1, 5, 16 ], [ 31, 1, 6, 16 ], [ 31, 1, 8, 16 ], [ 31, 2, 5, 8 ], [ 31, 2, 6, 8 ], [ 31, 2, 8, 8 ], [ 33, 1, 4, 32 ], [ 33, 2, 4, 16 ], [ 33, 3, 4, 16 ], [ 33, 4, 4, 16 ], [ 34, 1, 2, 16 ], [ 34, 1, 7, 16 ], [ 34, 2, 2, 8 ], [ 34, 2, 3, 8 ], [ 34, 3, 2, 8 ], [ 34, 3, 3, 8 ], [ 34, 3, 8, 8 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 2, 3, 8 ], [ 35, 2, 4, 8 ], [ 37, 1, 7, 16 ], [ 37, 1, 9, 16 ], [ 37, 2, 7, 8 ], [ 37, 2, 9, 8 ], [ 39, 1, 13, 32 ], [ 39, 1, 19, 32 ], [ 39, 2, 13, 16 ], [ 39, 2, 19, 16 ], [ 39, 3, 13, 16 ], [ 39, 3, 19, 16 ], [ 39, 4, 12, 16 ], [ 39, 4, 13, 16 ], [ 39, 4, 19, 16 ], [ 39, 5, 12, 16 ], [ 39, 5, 13, 16 ], [ 39, 5, 19, 16 ], [ 42, 2, 12, 16 ], [ 42, 2, 19, 16 ], [ 42, 3, 12, 16 ], [ 42, 3, 19, 16 ], [ 42, 4, 17, 16 ] ] k = 18: F-action on Pi is () [42,1,18] 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+88*q^2-192*q+135 ) 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+88*q^2-192*q+135 ) 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+88*q^2-192*q+135 ) q congruent 7 modulo 12: 1/96 phi1 ( q^4-16*q^3+88*q^2-192*q+135 ) 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+88*q^2-192*q+135 ) q congruent 11 modulo 12: 1/96 phi1 ( q^4-16*q^3+88*q^2-192*q+135 ) 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 ], [ 4, 2, 1, 14 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 40 ], [ 9, 1, 1, 46 ], [ 10, 1, 1, 36 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 48 ], [ 12, 2, 1, 24 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 1, 3, 8 ], [ 15, 2, 1, 24 ], [ 15, 2, 3, 4 ], [ 15, 3, 1, 24 ], [ 15, 3, 3, 4 ], [ 15, 4, 1, 24 ], [ 15, 4, 3, 4 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 6 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 12 ], [ 18, 2, 1, 12 ], [ 18, 2, 2, 6 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 64 ], [ 20, 2, 1, 32 ], [ 21, 1, 1, 36 ], [ 22, 1, 1, 48 ], [ 22, 1, 2, 24 ], [ 23, 1, 1, 48 ], [ 23, 1, 2, 16 ], [ 23, 2, 1, 24 ], [ 23, 2, 2, 8 ], [ 24, 1, 1, 72 ], [ 24, 1, 2, 20 ], [ 25, 1, 1, 48 ], [ 25, 1, 5, 24 ], [ 25, 2, 1, 24 ], [ 25, 2, 5, 12 ], [ 25, 3, 1, 24 ], [ 25, 3, 5, 12 ], [ 25, 4, 1, 24 ], [ 25, 4, 5, 12 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 28, 1, 1, 48 ], [ 28, 1, 3, 16 ], [ 28, 2, 1, 24 ], [ 28, 2, 4, 8 ], [ 29, 1, 1, 48 ], [ 29, 1, 2, 48 ], [ 29, 2, 1, 24 ], [ 29, 2, 2, 24 ], [ 30, 1, 1, 48 ], [ 30, 1, 2, 24 ], [ 30, 2, 1, 24 ], [ 30, 2, 2, 12 ], [ 31, 1, 1, 48 ], [ 31, 1, 2, 48 ], [ 31, 1, 3, 48 ], [ 31, 2, 1, 24 ], [ 31, 2, 2, 24 ], [ 31, 2, 3, 24 ], [ 33, 1, 1, 96 ], [ 33, 1, 3, 32 ], [ 33, 2, 1, 48 ], [ 33, 2, 3, 16 ], [ 33, 3, 1, 48 ], [ 33, 3, 3, 16 ], [ 33, 4, 1, 48 ], [ 33, 4, 3, 16 ], [ 34, 1, 2, 48 ], [ 34, 2, 2, 24 ], [ 34, 3, 2, 24 ], [ 35, 1, 1, 48 ], [ 35, 1, 2, 48 ], [ 35, 2, 1, 24 ], [ 35, 2, 2, 24 ], [ 37, 1, 1, 48 ], [ 37, 1, 2, 48 ], [ 37, 2, 1, 24 ], [ 37, 2, 2, 24 ], [ 39, 1, 2, 96 ], [ 39, 1, 8, 96 ], [ 39, 2, 2, 48 ], [ 39, 2, 8, 48 ], [ 39, 3, 2, 48 ], [ 39, 3, 8, 48 ], [ 39, 4, 2, 48 ], [ 39, 4, 7, 48 ], [ 39, 5, 2, 48 ], [ 39, 5, 7, 48 ], [ 42, 2, 2, 48 ], [ 42, 3, 2, 48 ], [ 42, 3, 6, 48 ], [ 42, 4, 20, 48 ] ] k = 19: F-action on Pi is () [42,1,19] 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^3-4*q^2+4*q+67 ) q congruent 2 modulo 12: 1/96 q^2 ( q^3-5*q^2+12 ) q congruent 3 modulo 12: 1/96 phi1 ( q^4-4*q^3-4*q^2+4*q+51 ) q congruent 4 modulo 12: 1/96 q ( q^4-5*q^3+12*q+16 ) q congruent 5 modulo 12: 1/96 phi1 ( q^4-4*q^3-4*q^2+4*q+51 ) q congruent 7 modulo 12: 1/96 phi1 ( q^4-4*q^3-4*q^2+4*q+67 ) q congruent 8 modulo 12: 1/96 q^2 ( q^3-5*q^2+12 ) q congruent 9 modulo 12: 1/96 phi1 ( q^4-4*q^3-4*q^2+4*q+51 ) q congruent 11 modulo 12: 1/96 phi1 ( q^4-4*q^3-4*q^2+4*q+51 ) 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 ], [ 4, 2, 1, 6 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 12 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 24 ], [ 12, 1, 2, 16 ], [ 12, 2, 2, 8 ], [ 15, 1, 3, 24 ], [ 15, 2, 3, 12 ], [ 15, 3, 3, 12 ], [ 15, 4, 3, 12 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 2, 12 ], [ 17, 2, 3, 6 ], [ 18, 1, 2, 12 ], [ 18, 1, 3, 24 ], [ 18, 2, 2, 6 ], [ 18, 2, 3, 12 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 24 ], [ 22, 1, 2, 24 ], [ 24, 1, 2, 12 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 48 ], [ 25, 2, 5, 12 ], [ 25, 2, 6, 24 ], [ 25, 3, 5, 12 ], [ 25, 3, 6, 24 ], [ 25, 4, 5, 12 ], [ 25, 4, 6, 24 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 24 ], [ 30, 1, 2, 24 ], [ 30, 1, 3, 48 ], [ 30, 2, 2, 12 ], [ 30, 2, 3, 24 ], [ 31, 1, 4, 48 ], [ 31, 2, 4, 24 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 48 ], [ 34, 2, 3, 24 ], [ 34, 2, 10, 24 ], [ 34, 3, 3, 24 ], [ 34, 3, 5, 24 ], [ 34, 3, 8, 24 ], [ 35, 1, 5, 48 ], [ 35, 2, 5, 24 ], [ 37, 1, 5, 48 ], [ 37, 2, 5, 24 ], [ 39, 1, 4, 96 ], [ 39, 2, 4, 48 ], [ 39, 3, 4, 48 ], [ 39, 4, 3, 48 ], [ 39, 4, 5, 48 ], [ 39, 5, 3, 48 ], [ 39, 5, 5, 48 ], [ 42, 2, 6, 48 ], [ 42, 2, 10, 48 ], [ 42, 3, 10, 48 ], [ 42, 4, 19, 48 ] ] k = 20: F-action on Pi is (1,3) [42,1,20] 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+6*q^2+6*q+9 ) 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 phi1 ( q^4-6*q^3+6*q^2+6*q+9 ) 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+12*q^3+19*q-57 ) q congruent 7 modulo 12: 1/96 phi1 ( q^4-6*q^3+6*q^2+6*q+9 ) 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+6*q^2+6*q+9 ) q congruent 11 modulo 12: 1/96 ( q^5-7*q^4+12*q^3+19*q-57 ) 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 ], [ 4, 2, 2, 6 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 3, 24 ], [ 10, 1, 4, 12 ], [ 12, 1, 5, 16 ], [ 12, 2, 4, 8 ], [ 15, 1, 2, 24 ], [ 15, 2, 2, 12 ], [ 15, 3, 2, 12 ], [ 15, 4, 2, 12 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 4, 12 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 12 ], [ 18, 2, 1, 12 ], [ 18, 2, 4, 6 ], [ 21, 1, 3, 24 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 24 ], [ 24, 1, 4, 12 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 24 ], [ 25, 2, 3, 24 ], [ 25, 2, 4, 12 ], [ 25, 3, 3, 24 ], [ 25, 3, 4, 12 ], [ 25, 4, 3, 24 ], [ 25, 4, 4, 12 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 24 ], [ 30, 1, 6, 24 ], [ 30, 1, 7, 48 ], [ 30, 2, 6, 12 ], [ 30, 2, 7, 24 ], [ 31, 1, 6, 48 ], [ 31, 2, 6, 24 ], [ 34, 1, 1, 48 ], [ 34, 1, 5, 48 ], [ 34, 2, 1, 24 ], [ 34, 2, 4, 24 ], [ 34, 3, 1, 24 ], [ 34, 3, 4, 24 ], [ 34, 3, 7, 24 ], [ 35, 1, 3, 48 ], [ 35, 2, 3, 24 ], [ 37, 1, 9, 48 ], [ 37, 2, 9, 24 ], [ 39, 1, 18, 96 ], [ 39, 2, 18, 48 ], [ 39, 3, 18, 48 ], [ 39, 4, 17, 48 ], [ 39, 4, 18, 48 ], [ 39, 5, 17, 48 ], [ 39, 5, 18, 48 ], [ 42, 2, 13, 48 ], [ 42, 2, 15, 48 ], [ 42, 3, 14, 48 ], [ 42, 4, 18, 48 ] ] k = 21: F-action on Pi is (1,3) [42,1,21] 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+34*q^2-54*q+45 ) 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 phi1 ( q^4-10*q^3+34*q^2-54*q+45 ) 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+34*q^2-54*q+45 ) q congruent 7 modulo 12: 1/96 phi1 ( q^4-10*q^3+34*q^2-54*q+45 ) 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+34*q^2-54*q+45 ) q congruent 11 modulo 12: 1/96 phi1 ( q^4-10*q^3+34*q^2-54*q+45 ) 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 ], [ 4, 2, 2, 14 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 18 ], [ 8, 1, 2, 40 ], [ 9, 1, 2, 46 ], [ 10, 1, 4, 36 ], [ 11, 1, 2, 32 ], [ 12, 1, 6, 48 ], [ 12, 2, 3, 24 ], [ 13, 1, 2, 24 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 2, 8 ], [ 15, 1, 4, 48 ], [ 15, 2, 2, 4 ], [ 15, 2, 4, 24 ], [ 15, 3, 2, 4 ], [ 15, 3, 4, 24 ], [ 15, 4, 2, 4 ], [ 15, 4, 4, 24 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 18, 1, 3, 24 ], [ 18, 1, 4, 12 ], [ 18, 2, 3, 12 ], [ 18, 2, 4, 6 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 64 ], [ 20, 2, 2, 32 ], [ 21, 1, 6, 36 ], [ 22, 1, 3, 24 ], [ 22, 1, 4, 48 ], [ 23, 1, 3, 16 ], [ 23, 1, 4, 48 ], [ 23, 2, 3, 8 ], [ 23, 2, 4, 24 ], [ 24, 1, 3, 72 ], [ 24, 1, 4, 20 ], [ 25, 1, 4, 24 ], [ 25, 1, 8, 48 ], [ 25, 2, 4, 12 ], [ 25, 2, 8, 24 ], [ 25, 3, 4, 12 ], [ 25, 3, 8, 24 ], [ 25, 4, 4, 12 ], [ 25, 4, 8, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 2, 16 ], [ 28, 1, 6, 48 ], [ 28, 2, 2, 8 ], [ 28, 2, 6, 24 ], [ 29, 1, 4, 48 ], [ 29, 1, 5, 48 ], [ 29, 2, 4, 24 ], [ 29, 2, 5, 24 ], [ 30, 1, 5, 48 ], [ 30, 1, 6, 24 ], [ 30, 2, 5, 24 ], [ 30, 2, 6, 12 ], [ 31, 1, 5, 48 ], [ 31, 1, 7, 48 ], [ 31, 1, 8, 48 ], [ 31, 2, 5, 24 ], [ 31, 2, 7, 24 ], [ 31, 2, 8, 24 ], [ 33, 1, 4, 32 ], [ 33, 1, 6, 96 ], [ 33, 2, 4, 16 ], [ 33, 2, 6, 48 ], [ 33, 3, 4, 16 ], [ 33, 3, 6, 48 ], [ 33, 4, 4, 16 ], [ 33, 4, 6, 48 ], [ 34, 1, 3, 48 ], [ 34, 2, 9, 24 ], [ 34, 3, 6, 24 ], [ 35, 1, 4, 48 ], [ 35, 1, 10, 48 ], [ 35, 2, 4, 24 ], [ 35, 2, 10, 24 ], [ 37, 1, 6, 48 ], [ 37, 1, 7, 48 ], [ 37, 2, 6, 24 ], [ 37, 2, 7, 24 ], [ 39, 1, 11, 96 ], [ 39, 1, 20, 96 ], [ 39, 2, 11, 48 ], [ 39, 2, 20, 48 ], [ 39, 3, 11, 48 ], [ 39, 3, 20, 48 ], [ 39, 4, 11, 48 ], [ 39, 4, 20, 48 ], [ 39, 5, 11, 48 ], [ 39, 5, 20, 48 ], [ 42, 2, 11, 48 ], [ 42, 3, 11, 48 ], [ 42, 3, 17, 48 ], [ 42, 4, 21, 48 ] ] k = 22: F-action on Pi is (1,3) [42,1,22] 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+206*q^2-774*q+1215 ) 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+230*q^3-980*q^2+1989*q-1575 ) 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+230*q^3-980*q^2+2069*q-2095 ) q congruent 7 modulo 12: 1/1440 ( q^5-25*q^4+230*q^3-980*q^2+1989*q-1575 ) 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+206*q^2-774*q+1215 ) q congruent 11 modulo 12: 1/1440 ( q^5-25*q^4+230*q^3-980*q^2+2069*q-2455 ) 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 ], [ 4, 2, 2, 30 ], [ 5, 1, 2, 12 ], [ 5, 2, 2, 6 ], [ 6, 1, 2, 20 ], [ 6, 2, 2, 10 ], [ 7, 1, 2, 90 ], [ 8, 1, 2, 132 ], [ 9, 1, 2, 150 ], [ 10, 1, 4, 180 ], [ 11, 1, 2, 120 ], [ 12, 1, 6, 120 ], [ 12, 2, 3, 60 ], [ 13, 1, 2, 60 ], [ 14, 1, 2, 120 ], [ 14, 2, 2, 60 ], [ 15, 1, 4, 120 ], [ 15, 2, 4, 60 ], [ 15, 3, 4, 60 ], [ 15, 4, 4, 60 ], [ 16, 1, 2, 30 ], [ 17, 1, 3, 180 ], [ 17, 2, 3, 90 ], [ 18, 1, 3, 180 ], [ 18, 2, 3, 90 ], [ 19, 1, 2, 360 ], [ 20, 1, 2, 240 ], [ 20, 2, 2, 120 ], [ 21, 1, 6, 180 ], [ 22, 1, 4, 360 ], [ 23, 1, 4, 240 ], [ 23, 2, 4, 120 ], [ 24, 1, 3, 300 ], [ 25, 1, 8, 360 ], [ 25, 2, 8, 180 ], [ 25, 3, 8, 180 ], [ 25, 4, 8, 180 ], [ 26, 1, 3, 360 ], [ 28, 1, 6, 240 ], [ 28, 2, 6, 120 ], [ 29, 1, 4, 720 ], [ 29, 2, 4, 360 ], [ 30, 1, 5, 360 ], [ 30, 2, 5, 180 ], [ 31, 1, 7, 720 ], [ 31, 2, 7, 360 ], [ 33, 1, 6, 480 ], [ 33, 2, 6, 240 ], [ 33, 3, 6, 240 ], [ 33, 4, 6, 240 ], [ 34, 1, 4, 720 ], [ 34, 2, 10, 360 ], [ 34, 3, 5, 360 ], [ 35, 1, 10, 720 ], [ 35, 2, 10, 360 ], [ 37, 1, 6, 720 ], [ 37, 2, 6, 360 ], [ 39, 1, 15, 1440 ], [ 39, 2, 15, 720 ], [ 39, 3, 15, 720 ], [ 39, 4, 15, 720 ], [ 39, 5, 15, 720 ], [ 42, 2, 20, 720 ], [ 42, 3, 16, 720 ], [ 42, 4, 22, 720 ] ] j = 2: Omega of order 2, action on Pi: <()> k = 1: F-action on Pi is () [42,2,1] Dynkin type is (A_2(q) + T(phi1^5)).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: 1/48 ( q^2-14*q+61 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/48 ( q^2-14*q+33 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/48 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/48 ( q^2-14*q+49 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/48 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/48 ( q^2-14*q+33 ) 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, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 4, 2, 1, 6 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 12, 2, 1, 8 ], [ 17, 2, 1, 12 ], [ 18, 2, 1, 12 ], [ 21, 1, 1, 12 ], [ 25, 2, 1, 24 ], [ 30, 2, 1, 24 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 24 ], [ 39, 5, 1, 48 ] ] k = 2: F-action on Pi is () [42,2,2] Dynkin type is (A_2(q) + T(phi1^4 phi2)).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: 1/16 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: [ 32, 4, 45 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 4, 2, 1, 6 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 17, 2, 3, 4 ], [ 18, 2, 2, 4 ], [ 21, 1, 1, 12 ], [ 25, 2, 5, 8 ], [ 30, 2, 2, 8 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 39, 5, 2, 16 ], [ 39, 5, 7, 16 ] ] k = 3: F-action on Pi is () [42,2,3] Dynkin type is (A_2(q) + T(phi1^2 phi2 phi4)).2 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 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: [ 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 34, 2, 8, 4 ], [ 39, 5, 10, 8 ] ] k = 4: F-action on Pi is () [42,2,4] Dynkin type is (A_2(q) + T(phi1^3 phi2^2)).2 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 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: [ 4, 35, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 2, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 21, 1, 2, 4 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 30, 2, 1, 4 ], [ 30, 2, 4, 4 ], [ 34, 2, 4, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 6, 4 ], [ 39, 5, 9, 8 ] ] k = 5: F-action on Pi is () [42,2,5] Dynkin type is (A_2(q) + T(phi1^3 phi2^2)).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: 1/16 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, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 4, 2, 1, 6 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 17, 2, 4, 4 ], [ 18, 2, 4, 4 ], [ 21, 1, 1, 12 ], [ 25, 2, 2, 8 ], [ 30, 2, 4, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 7, 8 ], [ 39, 5, 6, 16 ], [ 39, 5, 8, 16 ] ] k = 6: F-action on Pi is () [42,2,6] Dynkin type is (A_2(q) + T(phi1^2 phi2^3)).2 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 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: [ 33, 5, 46 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 2, 2, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 21, 1, 2, 4 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 30, 2, 2, 4 ], [ 30, 2, 3, 4 ], [ 34, 2, 3, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 5, 4 ], [ 39, 5, 3, 8 ] ] k = 7: F-action on Pi is () [42,2,7] Dynkin type is (A_2(q) + T(phi1 phi2^2 phi4)).2 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 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: [ 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 34, 2, 5, 4 ], [ 39, 5, 4, 8 ] ] k = 8: F-action on Pi is () [42,2,8] Dynkin type is (A_2(q) + T(phi2 phi3 phi6)).2 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: 1/6 phi1 ( q+2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 q phi2 q congruent 7 modulo 12: 1/6 phi1 ( q+2 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi2 q congruent 11 modulo 12: 1/6 q phi2 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, 2, 2, 1 ], [ 12, 2, 2, 2 ], [ 21, 1, 5, 6 ], [ 34, 2, 6, 3 ] ] k = 9: F-action on Pi is () [42,2,9] Dynkin type is (A_2(q) + T(phi1 phi3^2)).2 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: 1/6 phi1 ( q+2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 q phi2 q congruent 7 modulo 12: 1/6 phi1 ( q+2 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi2 q congruent 11 modulo 12: 1/6 q phi2 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, 2 ], [ 6, 2, 1, 1 ], [ 12, 2, 1, 2 ], [ 21, 1, 5, 6 ], [ 34, 2, 7, 3 ] ] k = 10: F-action on Pi is () [42,2,10] Dynkin type is (A_2(q) + T(phi1^2 phi2^3)).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: 1/48 ( q^2-14*q+61 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/48 ( q^2-14*q+33 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/48 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/48 ( q^2-14*q+49 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/48 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/48 ( q^2-14*q+33 ) 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 ], [ 4, 2, 1, 6 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 12, 2, 2, 8 ], [ 17, 2, 2, 12 ], [ 18, 2, 3, 12 ], [ 21, 1, 1, 12 ], [ 25, 2, 6, 24 ], [ 30, 2, 3, 24 ], [ 34, 2, 10, 24 ], [ 34, 3, 8, 24 ], [ 39, 5, 5, 48 ] ] k = 11: F-action on Pi is (1,3) [42,2,11] Dynkin type is (^2A_2(q) + T(phi1 phi2^4)).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: 1/16 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: [ 2, 34, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 4, 2, 2, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 17, 2, 1, 4 ], [ 18, 2, 4, 4 ], [ 21, 1, 6, 12 ], [ 25, 2, 4, 8 ], [ 30, 2, 6, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 39, 5, 11, 16 ], [ 39, 5, 20, 16 ] ] k = 12: F-action on Pi is (1,3) [42,2,12] Dynkin type is (^2A_2(q) + T(phi1^2 phi2^3)).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: 1/16 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: [ 34, 5, 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 4, 2, 2, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 17, 2, 2, 4 ], [ 18, 2, 2, 4 ], [ 21, 1, 6, 12 ], [ 25, 2, 7, 8 ], [ 30, 2, 8, 8 ], [ 34, 2, 2, 8 ], [ 34, 3, 3, 8 ], [ 39, 5, 12, 16 ], [ 39, 5, 19, 16 ] ] k = 13: F-action on Pi is (1,3) [42,2,13] Dynkin type is (^2A_2(q) + T(phi1^3 phi2^2)).2 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 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: [ 3, 35, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 2, 4, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 21, 1, 3, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 30, 2, 6, 4 ], [ 30, 2, 7, 4 ], [ 34, 2, 4, 4 ], [ 34, 3, 1, 4 ], [ 34, 3, 7, 4 ], [ 39, 5, 17, 8 ] ] k = 14: F-action on Pi is (1,3) [42,2,14] Dynkin type is (^2A_2(q) + T(phi1^2 phi2 phi4)).2 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 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: [ 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 34, 2, 8, 4 ], [ 39, 5, 16, 8 ] ] k = 15: F-action on Pi is (1,3) [42,2,15] Dynkin type is (^2A_2(q) + T(phi1^3 phi2^2)).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: 1/48 phi1 ( q-9 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/48 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/48 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/48 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/48 phi1 ( q-9 ) q congruent 11 modulo 12: 1/48 ( q^2-10*q+37 ) 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 ], [ 4, 2, 2, 6 ], [ 6, 2, 1, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 12, 2, 4, 8 ], [ 17, 2, 4, 12 ], [ 18, 2, 1, 12 ], [ 21, 1, 6, 12 ], [ 25, 2, 3, 24 ], [ 30, 2, 7, 24 ], [ 34, 2, 1, 24 ], [ 34, 3, 4, 24 ], [ 39, 5, 18, 48 ] ] k = 16: F-action on Pi is (1,3) [42,2,16] Dynkin type is (^2A_2(q) + T(phi2 phi6^2)).2 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: 1/6 q phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi1 q congruent 11 modulo 12: 1/6 phi2 ( q-2 ) 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, 2 ], [ 6, 2, 2, 1 ], [ 12, 2, 3, 2 ], [ 21, 1, 4, 6 ], [ 34, 2, 6, 3 ] ] k = 17: F-action on Pi is (1,3) [42,2,17] Dynkin type is (^2A_2(q) + T(phi1 phi3 phi6)).2 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: 1/6 q phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi1 q congruent 11 modulo 12: 1/6 phi2 ( q-2 ) 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, 2, 1, 1 ], [ 12, 2, 4, 2 ], [ 21, 1, 4, 6 ], [ 34, 2, 7, 3 ] ] k = 18: F-action on Pi is (1,3) [42,2,18] Dynkin type is (^2A_2(q) + T(phi1 phi2^2 phi4)).2 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 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: [ 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 34, 2, 5, 4 ], [ 39, 5, 14, 8 ] ] k = 19: F-action on Pi is (1,3) [42,2,19] Dynkin type is (^2A_2(q) + T(phi1^2 phi2^3)).2 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 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: [ 34, 5, 48 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 2, 3, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 21, 1, 3, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 30, 2, 5, 4 ], [ 30, 2, 8, 4 ], [ 34, 2, 3, 4 ], [ 34, 3, 2, 4 ], [ 34, 3, 8, 4 ], [ 39, 5, 13, 8 ] ] k = 20: F-action on Pi is (1,3) [42,2,20] Dynkin type is (^2A_2(q) + T(phi2^5)).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: 1/48 phi1 ( q-9 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/48 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/48 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/48 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/48 phi1 ( q-9 ) q congruent 11 modulo 12: 1/48 ( q^2-10*q+37 ) 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, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 4, 2, 2, 6 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 12, 2, 3, 8 ], [ 17, 2, 3, 12 ], [ 18, 2, 3, 12 ], [ 21, 1, 6, 12 ], [ 25, 2, 8, 24 ], [ 30, 2, 5, 24 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 24 ], [ 39, 5, 15, 48 ] ] 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+1080*q^4-11480*q^3+66209*q^2-199388*q+258830 ) 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+1080*q^4-11480*q^3+66209*q^2-197388*q+230670 ) 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+1080*q^4-11480*q^3+66209*q^2-198108*q+242190 ) q congruent 7 modulo 12: 1/23040 ( q^6-52*q^5+1080*q^4-11480*q^3+66209*q^2-198668*q+247310 ) 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+1080*q^4-11480*q^3+66209*q^2-198108*q+242190 ) q congruent 11 modulo 12: 1/23040 ( q^6-52*q^5+1080*q^4-11480*q^3+66209*q^2-197388*q+230670 ) 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 ], [ 4, 2, 1, 260 ], [ 5, 1, 1, 32 ], [ 5, 2, 1, 16 ], [ 6, 1, 1, 32 ], [ 6, 2, 1, 16 ], [ 7, 1, 1, 252 ], [ 8, 1, 1, 832 ], [ 9, 1, 1, 1600 ], [ 10, 1, 1, 2160 ], [ 11, 1, 1, 512 ], [ 12, 1, 1, 1920 ], [ 12, 2, 1, 960 ], [ 13, 1, 1, 192 ], [ 14, 1, 1, 512 ], [ 14, 2, 1, 256 ], [ 15, 1, 1, 960 ], [ 15, 2, 1, 480 ], [ 15, 3, 1, 480 ], [ 15, 4, 1, 480 ], [ 16, 1, 1, 60 ], [ 17, 1, 1, 840 ], [ 17, 2, 1, 420 ], [ 18, 1, 1, 480 ], [ 18, 2, 1, 240 ], [ 19, 1, 1, 2112 ], [ 20, 1, 1, 4480 ], [ 20, 2, 1, 2240 ], [ 21, 1, 1, 5760 ], [ 22, 1, 1, 3840 ], [ 23, 1, 1, 960 ], [ 23, 2, 1, 480 ], [ 24, 1, 1, 2880 ], [ 25, 1, 1, 3840 ], [ 25, 2, 1, 1920 ], [ 25, 3, 1, 1920 ], [ 25, 4, 1, 1920 ], [ 26, 1, 1, 1560 ], [ 27, 1, 1, 7200 ], [ 27, 2, 1, 3600 ], [ 27, 3, 1, 3600 ], [ 28, 1, 1, 960 ], [ 28, 2, 1, 480 ], [ 29, 1, 1, 3840 ], [ 29, 2, 1, 1920 ], [ 30, 1, 1, 9600 ], [ 30, 2, 1, 4800 ], [ 31, 1, 1, 6720 ], [ 31, 2, 1, 3360 ], [ 32, 1, 1, 11520 ], [ 33, 1, 1, 7680 ], [ 33, 2, 1, 3840 ], [ 33, 3, 1, 3840 ], [ 33, 4, 1, 3840 ], [ 34, 1, 1, 2880 ], [ 34, 2, 1, 1440 ], [ 34, 3, 1, 1440 ], [ 35, 1, 1, 6720 ], [ 35, 2, 1, 3360 ], [ 36, 1, 1, 11520 ], [ 36, 2, 1, 5760 ], [ 36, 3, 1, 5760 ], [ 36, 4, 1, 5760 ], [ 36, 5, 1, 5760 ], [ 36, 6, 1, 5760 ], [ 37, 1, 1, 15360 ], [ 37, 2, 1, 7680 ], [ 38, 1, 1, 17280 ], [ 38, 2, 1, 8640 ], [ 38, 3, 1, 8640 ], [ 39, 1, 1, 11520 ], [ 39, 2, 1, 5760 ], [ 39, 3, 1, 5760 ], [ 39, 4, 1, 5760 ], [ 39, 5, 1, 5760 ], [ 40, 1, 1, 17280 ], [ 40, 2, 1, 8640 ], [ 40, 3, 1, 8640 ], [ 41, 1, 1, 23040 ], [ 41, 2, 1, 11520 ], [ 41, 3, 1, 11520 ], [ 41, 4, 1, 11520 ], [ 41, 5, 1, 11520 ], [ 41, 6, 1, 11520 ], [ 41, 7, 1, 11520 ], [ 42, 1, 1, 23040 ], [ 42, 2, 1, 11520 ], [ 42, 3, 1, 11520 ], [ 42, 4, 1, 11520 ], [ 43, 2, 1, 11520 ], [ 43, 3, 1, 11520 ], [ 43, 4, 1, 11520 ], [ 43, 5, 1, 11520 ] ] 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 19, 1, 1, 2 ], [ 42, 1, 2, 10 ], [ 42, 4, 2, 5 ], [ 43, 3, 2, 5 ] ] 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 13, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 19, 1, 2, 2 ], [ 42, 1, 3, 10 ], [ 42, 4, 3, 5 ], [ 43, 3, 3, 5 ] ] 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+45*q^3-38*q^2-72*q+64 ) 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+71*q^2-154*q+120 ) 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+71*q^2-154*q+120 ) q congruent 7 modulo 12: 1/144 phi1 ( q^5-12*q^4+45*q^3-38*q^2-72*q+64 ) 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+71*q^2-154*q+120 ) q congruent 11 modulo 12: 1/144 q phi2 ( q^4-14*q^3+71*q^2-154*q+120 ) 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 ], [ 4, 2, 1, 14 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 40 ], [ 9, 1, 1, 46 ], [ 10, 1, 1, 36 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 48 ], [ 12, 2, 1, 24 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 2, 1, 24 ], [ 15, 3, 1, 24 ], [ 15, 4, 1, 24 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 64 ], [ 20, 2, 1, 32 ], [ 21, 1, 1, 36 ], [ 22, 1, 1, 48 ], [ 23, 1, 1, 48 ], [ 23, 2, 1, 24 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], [ 25, 2, 1, 24 ], [ 25, 3, 1, 24 ], [ 25, 4, 1, 24 ], [ 26, 1, 1, 24 ], [ 28, 1, 1, 48 ], [ 28, 1, 5, 6 ], [ 28, 2, 1, 24 ], [ 28, 2, 3, 3 ], [ 29, 1, 1, 48 ], [ 29, 1, 3, 24 ], [ 29, 2, 1, 24 ], [ 29, 2, 3, 12 ], [ 30, 1, 1, 48 ], [ 30, 2, 1, 24 ], [ 31, 1, 1, 48 ], [ 31, 2, 1, 24 ], [ 33, 1, 1, 96 ], [ 33, 1, 2, 48 ], [ 33, 2, 1, 48 ], [ 33, 2, 2, 24 ], [ 33, 3, 1, 48 ], [ 33, 3, 2, 24 ], [ 33, 4, 1, 48 ], [ 33, 4, 2, 24 ], [ 35, 1, 1, 48 ], [ 35, 1, 8, 42 ], [ 35, 2, 1, 24 ], [ 35, 2, 8, 21 ], [ 37, 1, 1, 48 ], [ 37, 1, 3, 96 ], [ 37, 2, 1, 24 ], [ 37, 2, 3, 48 ], [ 39, 1, 3, 72 ], [ 39, 2, 3, 36 ], [ 39, 3, 3, 36 ], [ 40, 1, 7, 108 ], [ 40, 2, 2, 54 ], [ 40, 3, 10, 54 ], [ 41, 1, 3, 144 ], [ 41, 2, 3, 72 ], [ 41, 3, 3, 72 ], [ 41, 5, 3, 72 ], [ 41, 6, 3, 72 ], [ 41, 7, 3, 72 ], [ 42, 1, 4, 144 ], [ 42, 3, 3, 72 ], [ 42, 4, 4, 72 ], [ 43, 2, 2, 72 ], [ 43, 3, 4, 72 ], [ 43, 4, 3, 72 ] ] 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 20, 1, 1, 4 ], [ 20, 2, 1, 2 ], [ 21, 1, 5, 18 ], [ 28, 1, 5, 12 ], [ 28, 2, 3, 6 ], [ 29, 1, 3, 12 ], [ 29, 2, 3, 6 ], [ 32, 1, 9, 18 ], [ 33, 1, 2, 24 ], [ 33, 2, 2, 12 ], [ 33, 3, 2, 12 ], [ 33, 4, 2, 12 ], [ 34, 1, 9, 18 ], [ 34, 2, 7, 9 ], [ 35, 1, 8, 12 ], [ 35, 2, 8, 6 ], [ 36, 1, 9, 18 ], [ 36, 5, 9, 9 ], [ 37, 1, 3, 12 ], [ 37, 2, 3, 6 ], [ 42, 1, 5, 36 ], [ 42, 2, 9, 18 ], [ 42, 4, 5, 18 ], [ 43, 3, 5, 18 ], [ 43, 5, 26, 18 ] ] 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^2 phi1 phi2^2 ( q-2 ) q congruent 2 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 3 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 4 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 5 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 7 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 8 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 9 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) q congruent 11 modulo 12: 1/48 q^2 phi1 phi2^2 ( q-2 ) 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 ], [ 4, 2, 1, 6 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 8 ], [ 15, 1, 3, 16 ], [ 15, 2, 3, 8 ], [ 15, 3, 3, 8 ], [ 15, 4, 3, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 8 ], [ 22, 1, 2, 16 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 16 ], [ 25, 2, 5, 8 ], [ 25, 3, 5, 8 ], [ 25, 4, 5, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 1, 2, 16 ], [ 30, 2, 2, 8 ], [ 31, 1, 4, 16 ], [ 31, 2, 4, 8 ], [ 35, 1, 5, 16 ], [ 35, 1, 8, 18 ], [ 35, 2, 5, 8 ], [ 35, 2, 8, 9 ], [ 37, 1, 5, 16 ], [ 37, 2, 5, 8 ], [ 39, 1, 7, 24 ], [ 39, 2, 7, 12 ], [ 39, 3, 7, 12 ], [ 40, 1, 7, 36 ], [ 40, 1, 14, 24 ], [ 40, 2, 2, 18 ], [ 40, 2, 7, 12 ], [ 40, 3, 10, 18 ], [ 40, 3, 13, 12 ], [ 41, 1, 13, 48 ], [ 41, 2, 13, 24 ], [ 41, 3, 13, 24 ], [ 41, 5, 7, 24 ], [ 41, 6, 7, 24 ], [ 41, 7, 7, 24 ], [ 43, 2, 3, 24 ], [ 43, 2, 10, 24 ], [ 43, 3, 6, 24 ], [ 43, 4, 39, 24 ] ] k = 7: F-action on Pi is () [43,1,7] 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^3 phi1^2 phi2 q congruent 2 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 3 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 4 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 5 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 7 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 8 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 9 modulo 12: 1/24 q^3 phi1^2 phi2 q congruent 11 modulo 12: 1/24 q^3 phi1^2 phi2 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 26, 1, 5, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 35, 1, 7, 8 ], [ 35, 1, 9, 6 ], [ 35, 2, 7, 4 ], [ 35, 2, 9, 3 ], [ 37, 1, 10, 8 ], [ 37, 2, 10, 4 ], [ 40, 1, 15, 12 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 6 ], [ 43, 2, 4, 12 ], [ 43, 3, 8, 12 ] ] k = 8: F-action on Pi is () [43,1,8] 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^3 phi1 phi2^2 q congruent 2 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 3 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 4 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 5 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 7 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 8 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 9 modulo 12: 1/24 q^3 phi1 phi2^2 q congruent 11 modulo 12: 1/24 q^3 phi1 phi2^2 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 6 ], [ 35, 2, 6, 4 ], [ 35, 2, 8, 3 ], [ 37, 1, 4, 8 ], [ 37, 2, 4, 4 ], [ 40, 1, 14, 12 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 6 ], [ 43, 2, 5, 12 ], [ 43, 3, 7, 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^2 phi1^2 ( q^2-5*q+6 ) 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^2 phi1^2 ( q^2-5*q+6 ) 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+25*q^3-42*q^2+48*q-32 ) q congruent 7 modulo 12: 1/144 q^2 phi1^2 ( q^2-5*q+6 ) 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^2 phi1^2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/144 phi2 ( q^5-8*q^4+25*q^3-42*q^2+48*q-32 ) 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 ], [ 4, 2, 2, 14 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 18 ], [ 8, 1, 2, 40 ], [ 9, 1, 2, 46 ], [ 10, 1, 4, 36 ], [ 11, 1, 2, 32 ], [ 12, 1, 6, 48 ], [ 12, 2, 3, 24 ], [ 13, 1, 2, 24 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 4, 48 ], [ 15, 2, 4, 24 ], [ 15, 3, 4, 24 ], [ 15, 4, 4, 24 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 3, 12 ], [ 18, 1, 3, 24 ], [ 18, 2, 3, 12 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 64 ], [ 20, 2, 2, 32 ], [ 21, 1, 6, 36 ], [ 22, 1, 4, 48 ], [ 23, 1, 4, 48 ], [ 23, 2, 4, 24 ], [ 24, 1, 3, 72 ], [ 25, 1, 8, 48 ], [ 25, 2, 8, 24 ], [ 25, 3, 8, 24 ], [ 25, 4, 8, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 4, 6 ], [ 28, 1, 6, 48 ], [ 28, 2, 5, 3 ], [ 28, 2, 6, 24 ], [ 29, 1, 4, 48 ], [ 29, 1, 6, 24 ], [ 29, 2, 4, 24 ], [ 29, 2, 6, 12 ], [ 30, 1, 5, 48 ], [ 30, 2, 5, 24 ], [ 31, 1, 7, 48 ], [ 31, 2, 7, 24 ], [ 33, 1, 5, 48 ], [ 33, 1, 6, 96 ], [ 33, 2, 5, 24 ], [ 33, 2, 6, 48 ], [ 33, 3, 5, 24 ], [ 33, 3, 6, 48 ], [ 33, 4, 5, 24 ], [ 33, 4, 6, 48 ], [ 35, 1, 9, 42 ], [ 35, 1, 10, 48 ], [ 35, 2, 9, 21 ], [ 35, 2, 10, 24 ], [ 37, 1, 6, 48 ], [ 37, 1, 8, 96 ], [ 37, 2, 6, 24 ], [ 37, 2, 8, 48 ], [ 39, 1, 12, 72 ], [ 39, 2, 12, 36 ], [ 39, 3, 12, 36 ], [ 40, 1, 8, 108 ], [ 40, 2, 5, 54 ], [ 40, 3, 9, 54 ], [ 41, 1, 8, 144 ], [ 41, 2, 8, 72 ], [ 41, 3, 8, 72 ], [ 41, 5, 9, 72 ], [ 41, 6, 9, 72 ], [ 41, 7, 9, 72 ], [ 42, 1, 6, 144 ], [ 42, 3, 18, 72 ], [ 42, 4, 8, 72 ], [ 43, 2, 7, 72 ], [ 43, 3, 9, 72 ], [ 43, 4, 34, 72 ] ] 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^2-2*q+8 ) 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^2-2*q+8 ) 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^2-2*q+8 ) q congruent 7 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-2*q+8 ) 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^2-2*q+8 ) q congruent 11 modulo 12: 1/48 q phi1 phi2 ( q^3-3*q^2-2*q+8 ) 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 ], [ 4, 2, 2, 6 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 3, 8 ], [ 10, 1, 4, 12 ], [ 15, 1, 2, 16 ], [ 15, 2, 2, 8 ], [ 15, 3, 2, 8 ], [ 15, 4, 2, 8 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 21, 1, 3, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 16 ], [ 24, 1, 4, 8 ], [ 25, 1, 4, 16 ], [ 25, 2, 4, 8 ], [ 25, 3, 4, 8 ], [ 25, 4, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 1, 6, 16 ], [ 30, 2, 6, 8 ], [ 31, 1, 6, 16 ], [ 31, 2, 6, 8 ], [ 35, 1, 3, 16 ], [ 35, 1, 9, 18 ], [ 35, 2, 3, 8 ], [ 35, 2, 9, 9 ], [ 37, 1, 9, 16 ], [ 37, 2, 9, 8 ], [ 39, 1, 16, 24 ], [ 39, 2, 16, 12 ], [ 39, 3, 16, 12 ], [ 40, 1, 8, 36 ], [ 40, 1, 15, 24 ], [ 40, 2, 5, 18 ], [ 40, 2, 6, 12 ], [ 40, 3, 9, 18 ], [ 40, 3, 12, 12 ], [ 41, 1, 17, 48 ], [ 41, 2, 17, 24 ], [ 41, 3, 17, 24 ], [ 41, 5, 17, 24 ], [ 41, 6, 17, 24 ], [ 41, 7, 17, 24 ], [ 43, 2, 6, 24 ], [ 43, 2, 9, 24 ], [ 43, 3, 10, 24 ], [ 43, 4, 21, 24 ] ] 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^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 5 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/24 q^2 phi1 phi2 ( q^2-5*q+6 ) 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 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 14 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 12, 2, 1, 12 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 3, 8 ], [ 15, 2, 1, 4 ], [ 15, 2, 3, 4 ], [ 15, 3, 1, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 1, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 2, 2 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 20, 2, 1, 8 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 8 ], [ 22, 1, 2, 8 ], [ 23, 1, 2, 8 ], [ 23, 2, 2, 4 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 5, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 5, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 5, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 5, 4 ], [ 26, 1, 2, 4 ], [ 28, 1, 3, 8 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 28, 2, 4, 4 ], [ 29, 1, 2, 8 ], [ 29, 1, 3, 12 ], [ 29, 2, 2, 4 ], [ 29, 2, 3, 6 ], [ 30, 1, 1, 8 ], [ 30, 1, 2, 8 ], [ 30, 2, 1, 4 ], [ 30, 2, 2, 4 ], [ 31, 1, 2, 8 ], [ 31, 1, 3, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 3, 4 ], [ 33, 1, 2, 24 ], [ 33, 1, 3, 16 ], [ 33, 2, 2, 12 ], [ 33, 2, 3, 8 ], [ 33, 3, 2, 12 ], [ 33, 3, 3, 8 ], [ 33, 4, 2, 12 ], [ 33, 4, 3, 8 ], [ 35, 1, 2, 8 ], [ 35, 1, 8, 18 ], [ 35, 2, 2, 4 ], [ 35, 2, 8, 9 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 24 ], [ 37, 2, 2, 4 ], [ 37, 2, 3, 12 ], [ 39, 1, 3, 12 ], [ 39, 1, 7, 12 ], [ 39, 2, 3, 6 ], [ 39, 2, 7, 6 ], [ 39, 3, 3, 6 ], [ 39, 3, 7, 6 ], [ 40, 1, 7, 36 ], [ 40, 2, 2, 18 ], [ 40, 3, 10, 18 ], [ 41, 1, 3, 24 ], [ 41, 1, 13, 24 ], [ 41, 2, 3, 12 ], [ 41, 2, 13, 12 ], [ 41, 3, 3, 12 ], [ 41, 3, 13, 12 ], [ 41, 5, 3, 12 ], [ 41, 5, 7, 12 ], [ 41, 6, 3, 12 ], [ 41, 6, 7, 12 ], [ 41, 7, 3, 12 ], [ 41, 7, 7, 12 ], [ 42, 1, 7, 24 ], [ 42, 3, 8, 12 ], [ 42, 4, 6, 12 ], [ 43, 2, 8, 12 ], [ 43, 3, 12, 12 ], [ 43, 4, 13, 12 ], [ 43, 4, 29, 12 ] ] 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^2 phi1^2 phi2 ( q-2 ) q congruent 2 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 3 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 4 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 5 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 7 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 8 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 9 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) q congruent 11 modulo 12: 1/24 q^2 phi1^2 phi2 ( q-2 ) 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 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 14 ], [ 10, 1, 4, 12 ], [ 11, 1, 2, 8 ], [ 12, 1, 6, 24 ], [ 12, 2, 3, 12 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 2, 8 ], [ 15, 1, 4, 8 ], [ 15, 2, 2, 4 ], [ 15, 2, 4, 4 ], [ 15, 3, 2, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 2, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 3, 2 ], [ 18, 2, 4, 2 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 20, 2, 2, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 8 ], [ 22, 1, 4, 8 ], [ 23, 1, 3, 8 ], [ 23, 2, 3, 4 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 12 ], [ 25, 1, 4, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 4, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 4, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 4, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 2, 4 ], [ 28, 1, 2, 8 ], [ 28, 1, 4, 6 ], [ 28, 2, 2, 4 ], [ 28, 2, 5, 3 ], [ 29, 1, 5, 8 ], [ 29, 1, 6, 12 ], [ 29, 2, 5, 4 ], [ 29, 2, 6, 6 ], [ 30, 1, 5, 8 ], [ 30, 1, 6, 8 ], [ 30, 2, 5, 4 ], [ 30, 2, 6, 4 ], [ 31, 1, 5, 8 ], [ 31, 1, 8, 8 ], [ 31, 2, 5, 4 ], [ 31, 2, 8, 4 ], [ 33, 1, 4, 16 ], [ 33, 1, 5, 24 ], [ 33, 2, 4, 8 ], [ 33, 2, 5, 12 ], [ 33, 3, 4, 8 ], [ 33, 3, 5, 12 ], [ 33, 4, 4, 8 ], [ 33, 4, 5, 12 ], [ 35, 1, 4, 8 ], [ 35, 1, 9, 18 ], [ 35, 2, 4, 4 ], [ 35, 2, 9, 9 ], [ 37, 1, 7, 8 ], [ 37, 1, 8, 24 ], [ 37, 2, 7, 4 ], [ 37, 2, 8, 12 ], [ 39, 1, 12, 12 ], [ 39, 1, 16, 12 ], [ 39, 2, 12, 6 ], [ 39, 2, 16, 6 ], [ 39, 3, 12, 6 ], [ 39, 3, 16, 6 ], [ 40, 1, 8, 36 ], [ 40, 2, 5, 18 ], [ 40, 3, 9, 18 ], [ 41, 1, 8, 24 ], [ 41, 1, 17, 24 ], [ 41, 2, 8, 12 ], [ 41, 2, 17, 12 ], [ 41, 3, 8, 12 ], [ 41, 3, 17, 12 ], [ 41, 5, 9, 12 ], [ 41, 5, 17, 12 ], [ 41, 6, 9, 12 ], [ 41, 6, 17, 12 ], [ 41, 7, 9, 12 ], [ 41, 7, 17, 12 ], [ 42, 1, 8, 24 ], [ 42, 3, 13, 12 ], [ 42, 4, 7, 12 ], [ 43, 2, 11, 12 ], [ 43, 3, 11, 12 ], [ 43, 4, 8, 12 ], [ 43, 4, 47, 12 ] ] 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 21, 1, 4, 18 ], [ 28, 1, 4, 12 ], [ 28, 2, 5, 6 ], [ 29, 1, 6, 12 ], [ 29, 2, 6, 6 ], [ 32, 1, 10, 18 ], [ 33, 1, 5, 24 ], [ 33, 2, 5, 12 ], [ 33, 3, 5, 12 ], [ 33, 4, 5, 12 ], [ 34, 1, 10, 18 ], [ 34, 2, 6, 9 ], [ 35, 1, 9, 12 ], [ 35, 2, 9, 6 ], [ 36, 1, 7, 18 ], [ 36, 5, 7, 9 ], [ 37, 1, 8, 12 ], [ 37, 2, 8, 6 ], [ 42, 1, 11, 36 ], [ 42, 2, 16, 18 ], [ 42, 4, 9, 18 ], [ 43, 3, 13, 18 ], [ 43, 5, 33, 18 ] ] 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 ], [ 4, 2, 3, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 20, 1, 4, 4 ], [ 20, 2, 4, 2 ], [ 21, 1, 5, 6 ], [ 32, 1, 9, 6 ], [ 34, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 36, 1, 7, 6 ], [ 36, 5, 7, 3 ], [ 42, 1, 9, 12 ], [ 42, 2, 8, 6 ], [ 42, 4, 10, 6 ], [ 43, 3, 14, 6 ], [ 43, 5, 25, 6 ] ] 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 ], [ 4, 2, 4, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 2 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ], [ 21, 1, 4, 6 ], [ 32, 1, 10, 6 ], [ 34, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 36, 1, 9, 6 ], [ 36, 5, 9, 3 ], [ 42, 1, 10, 12 ], [ 42, 2, 17, 6 ], [ 42, 4, 11, 6 ], [ 43, 3, 15, 6 ], [ 43, 5, 34, 6 ] ] 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+37*q^3-51*q^2+62*q+90 ) 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+61*q^3-149*q^2+262*q-282 ) 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+37*q^3-51*q^2+62*q+90 ) q congruent 7 modulo 12: 1/1536 phi2 ( q^5-13*q^4+61*q^3-149*q^2+262*q-282 ) 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+37*q^3-51*q^2+62*q+90 ) q congruent 11 modulo 12: 1/1536 phi2 ( q^5-13*q^4+61*q^3-149*q^2+262*q-282 ) 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 ], [ 4, 2, 1, 12 ], [ 4, 2, 2, 24 ], [ 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 ], [ 15, 2, 2, 32 ], [ 15, 3, 2, 32 ], [ 15, 4, 2, 32 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 24 ], [ 17, 1, 1, 56 ], [ 17, 1, 3, 144 ], [ 17, 2, 1, 28 ], [ 17, 2, 3, 72 ], [ 18, 1, 4, 32 ], [ 18, 2, 4, 16 ], [ 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 ], [ 25, 2, 4, 128 ], [ 25, 3, 4, 128 ], [ 25, 4, 4, 128 ], [ 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 ], [ 27, 2, 1, 48 ], [ 27, 2, 2, 96 ], [ 27, 2, 8, 192 ], [ 27, 2, 12, 288 ], [ 27, 2, 13, 192 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 192 ], [ 27, 3, 9, 192 ], [ 27, 3, 11, 288 ], [ 27, 3, 12, 192 ], [ 28, 1, 6, 192 ], [ 28, 2, 6, 96 ], [ 30, 1, 6, 256 ], [ 30, 2, 6, 128 ], [ 31, 1, 6, 64 ], [ 31, 1, 8, 384 ], [ 31, 2, 6, 32 ], [ 31, 2, 8, 192 ], [ 32, 1, 3, 384 ], [ 32, 1, 5, 384 ], [ 32, 1, 6, 192 ], [ 32, 1, 7, 576 ], [ 34, 1, 3, 192 ], [ 34, 2, 9, 96 ], [ 34, 3, 6, 96 ], [ 35, 1, 3, 64 ], [ 35, 1, 5, 192 ], [ 35, 1, 10, 576 ], [ 35, 2, 3, 32 ], [ 35, 2, 5, 96 ], [ 35, 2, 10, 288 ], [ 36, 1, 18, 768 ], [ 36, 2, 17, 384 ], [ 36, 2, 23, 384 ], [ 36, 3, 17, 384 ], [ 36, 3, 23, 384 ], [ 36, 4, 17, 384 ], [ 36, 4, 23, 384 ], [ 36, 5, 18, 384 ], [ 36, 6, 9, 384 ], [ 37, 1, 9, 256 ], [ 37, 2, 9, 128 ], [ 38, 1, 4, 384 ], [ 38, 1, 6, 768 ], [ 38, 2, 4, 192 ], [ 38, 2, 6, 384 ], [ 38, 3, 4, 192 ], [ 38, 3, 6, 384 ], [ 39, 1, 20, 768 ], [ 39, 2, 20, 384 ], [ 39, 3, 20, 384 ], [ 39, 4, 20, 384 ], [ 39, 5, 20, 384 ], [ 40, 1, 2, 1152 ], [ 40, 1, 3, 384 ], [ 40, 1, 13, 768 ], [ 40, 2, 13, 576 ], [ 40, 2, 16, 192 ], [ 40, 2, 24, 384 ], [ 40, 3, 2, 192 ], [ 40, 3, 17, 192 ], [ 40, 3, 18, 384 ], [ 40, 3, 19, 576 ], [ 40, 3, 20, 384 ], [ 41, 1, 7, 768 ], [ 41, 1, 22, 1536 ], [ 41, 2, 7, 384 ], [ 41, 2, 22, 768 ], [ 41, 3, 7, 384 ], [ 41, 3, 22, 768 ], [ 41, 4, 12, 384 ], [ 41, 4, 26, 768 ], [ 41, 5, 20, 768 ], [ 41, 6, 20, 768 ], [ 41, 7, 20, 768 ], [ 43, 2, 12, 768 ], [ 43, 2, 23, 768 ], [ 43, 2, 52, 768 ], [ 43, 3, 16, 768 ], [ 43, 4, 26, 768 ], [ 43, 4, 33, 768 ], [ 43, 5, 24, 768 ] ] k = 17: F-action on Pi is () [43,1,17] 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 phi2 ( q^4-3*q^2-6 ) q congruent 2 modulo 12: 1/128 q^4 ( q^2-4 ) q congruent 3 modulo 12: 1/128 phi1 phi2 ( q^4-3*q^2-6 ) q congruent 4 modulo 12: 1/128 q^4 ( q^2-4 ) q congruent 5 modulo 12: 1/128 phi1 phi2 ( q^4-3*q^2-6 ) q congruent 7 modulo 12: 1/128 phi1 phi2 ( q^4-3*q^2-6 ) q congruent 8 modulo 12: 1/128 q^4 ( q^2-4 ) q congruent 9 modulo 12: 1/128 phi1 phi2 ( q^4-3*q^2-6 ) q congruent 11 modulo 12: 1/128 phi1 phi2 ( q^4-3*q^2-6 ) 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 ], [ 4, 2, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 8 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 4 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 1, 11, 32 ], [ 27, 1, 13, 32 ], [ 27, 2, 7, 24 ], [ 27, 2, 11, 16 ], [ 27, 2, 13, 16 ], [ 27, 3, 7, 16 ], [ 27, 3, 8, 16 ], [ 27, 3, 12, 16 ], [ 32, 1, 4, 64 ], [ 34, 1, 8, 32 ], [ 34, 2, 5, 16 ], [ 35, 1, 6, 32 ], [ 35, 2, 6, 16 ], [ 36, 1, 10, 64 ], [ 36, 2, 16, 32 ], [ 36, 3, 16, 32 ], [ 36, 4, 16, 32 ], [ 36, 5, 10, 32 ], [ 38, 1, 12, 64 ], [ 38, 2, 12, 32 ], [ 40, 1, 6, 96 ], [ 40, 1, 24, 64 ], [ 40, 2, 14, 48 ], [ 40, 2, 18, 32 ], [ 40, 3, 14, 32 ], [ 41, 1, 14, 128 ], [ 41, 2, 14, 64 ], [ 41, 3, 14, 64 ], [ 41, 4, 7, 64 ], [ 43, 2, 15, 64 ], [ 43, 2, 24, 64 ], [ 43, 3, 17, 64 ], [ 43, 4, 40, 64 ], [ 43, 5, 29, 64 ] ] k = 18: F-action on Pi is () [43,1,18] 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 q^2 phi1 phi2 phi4 q congruent 2 modulo 12: 1/16 q^6 q congruent 3 modulo 12: 1/16 q^2 phi1 phi2 phi4 q congruent 4 modulo 12: 1/16 q^6 q congruent 5 modulo 12: 1/16 q^2 phi1 phi2 phi4 q congruent 7 modulo 12: 1/16 q^2 phi1 phi2 phi4 q congruent 8 modulo 12: 1/16 q^6 q congruent 9 modulo 12: 1/16 q^2 phi1 phi2 phi4 q congruent 11 modulo 12: 1/16 q^2 phi1 phi2 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 ], [ 4, 2, 3, 2 ], [ 4, 2, 4, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 27, 2, 5, 4 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ], [ 43, 2, 16, 8 ], [ 43, 3, 18, 8 ] ] k = 19: F-action on Pi is () [43,1,19] 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+q^2+12*q-18 ) 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+q^2+12*q-18 ) 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+q^2+12*q-18 ) q congruent 7 modulo 12: 1/128 phi1 phi2 ( q^4-4*q^3+q^2+12*q-18 ) 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+q^2+12*q-18 ) q congruent 11 modulo 12: 1/128 phi1 phi2 ( q^4-4*q^3+q^2+12*q-18 ) 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 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 1, 4, 16 ], [ 17, 2, 1, 4 ], [ 17, 2, 4, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 24 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 48 ], [ 27, 1, 14, 32 ], [ 27, 2, 3, 16 ], [ 27, 2, 7, 24 ], [ 27, 2, 14, 16 ], [ 27, 3, 2, 16 ], [ 27, 3, 15, 16 ], [ 27, 3, 16, 16 ], [ 32, 1, 8, 64 ], [ 34, 1, 6, 32 ], [ 34, 2, 8, 16 ], [ 35, 1, 7, 32 ], [ 35, 2, 7, 16 ], [ 36, 1, 17, 64 ], [ 36, 2, 13, 32 ], [ 36, 3, 13, 32 ], [ 36, 4, 13, 32 ], [ 36, 5, 17, 32 ], [ 38, 1, 13, 64 ], [ 38, 2, 13, 32 ], [ 40, 1, 6, 96 ], [ 40, 1, 23, 64 ], [ 40, 2, 14, 48 ], [ 40, 2, 17, 32 ], [ 40, 3, 16, 32 ], [ 41, 1, 21, 128 ], [ 41, 2, 21, 64 ], [ 41, 3, 21, 64 ], [ 41, 4, 20, 64 ], [ 43, 2, 13, 64 ], [ 43, 2, 25, 64 ], [ 43, 3, 19, 64 ], [ 43, 4, 25, 64 ], [ 43, 5, 21, 64 ] ] k = 20: F-action on Pi is () [43,1,20] 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^2-2 ) q congruent 2 modulo 12: 1/16 q^4 ( q^2-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-2 ) q congruent 4 modulo 12: 1/16 q^4 ( q^2-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-2 ) q congruent 7 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-2 ) q congruent 8 modulo 12: 1/16 q^4 ( q^2-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-2 ) q congruent 11 modulo 12: 1/16 phi1 phi2 phi4 ( q^2-2 ) 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 ], [ 27, 2, 10, 4 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ], [ 43, 2, 14, 8 ], [ 43, 3, 20, 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 phi2 ( q^4-2*q^3-3*q^2+6*q-10 ) 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 phi2 ( q^4-2*q^3-3*q^2+6*q-10 ) 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 phi2 ( q^4-2*q^3-3*q^2+6*q-10 ) q congruent 7 modulo 12: 1/64 phi1 phi2 ( q^4-2*q^3-3*q^2+6*q-10 ) 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 phi2 ( q^4-2*q^3-3*q^2+6*q-10 ) q congruent 11 modulo 12: 1/64 phi1 phi2 ( q^4-2*q^3-3*q^2+6*q-10 ) 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 ], [ 4, 2, 3, 4 ], [ 4, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 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 ], [ 27, 2, 4, 8 ], [ 27, 2, 5, 16 ], [ 27, 2, 6, 8 ], [ 27, 2, 7, 24 ], [ 27, 2, 9, 8 ], [ 27, 3, 3, 8 ], [ 27, 3, 4, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 13, 8 ], [ 27, 3, 14, 8 ], [ 32, 1, 4, 32 ], [ 32, 1, 8, 32 ], [ 34, 1, 6, 16 ], [ 34, 1, 8, 16 ], [ 34, 2, 5, 8 ], [ 34, 2, 8, 8 ], [ 36, 1, 10, 32 ], [ 36, 1, 17, 32 ], [ 36, 2, 13, 16 ], [ 36, 2, 16, 16 ], [ 36, 3, 13, 16 ], [ 36, 3, 16, 16 ], [ 36, 4, 13, 16 ], [ 36, 4, 16, 16 ], [ 36, 5, 10, 16 ], [ 36, 5, 17, 16 ], [ 38, 1, 11, 32 ], [ 38, 1, 14, 32 ], [ 38, 2, 11, 16 ], [ 38, 2, 14, 16 ], [ 40, 1, 6, 96 ], [ 40, 1, 16, 32 ], [ 40, 2, 14, 48 ], [ 40, 2, 19, 16 ], [ 41, 1, 14, 64 ], [ 41, 1, 21, 64 ], [ 41, 2, 14, 32 ], [ 41, 2, 21, 32 ], [ 41, 3, 14, 32 ], [ 41, 3, 21, 32 ], [ 41, 4, 7, 32 ], [ 41, 4, 20, 32 ], [ 43, 2, 17, 32 ], [ 43, 2, 26, 32 ], [ 43, 3, 21, 32 ], [ 43, 4, 14, 32 ], [ 43, 4, 51, 32 ], [ 43, 5, 7, 32 ], [ 43, 5, 31, 32 ] ] 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+69*q^3-83*q^2-66*q+30 ) 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+101*q^3-253*q^2+270*q-126 ) 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+69*q^3-83*q^2-66*q+30 ) q congruent 7 modulo 12: 1/1536 phi2 ( q^5-17*q^4+101*q^3-253*q^2+270*q-126 ) 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+69*q^3-83*q^2-66*q+30 ) q congruent 11 modulo 12: 1/1536 phi2 ( q^5-17*q^4+101*q^3-253*q^2+270*q-126 ) 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 ], [ 4, 2, 1, 24 ], [ 4, 2, 2, 12 ], [ 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 ], [ 15, 2, 3, 32 ], [ 15, 3, 3, 32 ], [ 15, 4, 3, 32 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 144 ], [ 17, 1, 3, 56 ], [ 17, 2, 1, 72 ], [ 17, 2, 3, 28 ], [ 18, 1, 2, 32 ], [ 18, 2, 2, 16 ], [ 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 ], [ 25, 2, 5, 128 ], [ 25, 3, 5, 128 ], [ 25, 4, 5, 128 ], [ 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 ], [ 27, 2, 1, 288 ], [ 27, 2, 2, 96 ], [ 27, 2, 3, 192 ], [ 27, 2, 8, 192 ], [ 27, 2, 12, 48 ], [ 27, 3, 1, 288 ], [ 27, 3, 2, 192 ], [ 27, 3, 5, 192 ], [ 27, 3, 9, 192 ], [ 27, 3, 11, 48 ], [ 28, 1, 1, 192 ], [ 28, 2, 1, 96 ], [ 30, 1, 2, 256 ], [ 30, 2, 2, 128 ], [ 31, 1, 2, 384 ], [ 31, 1, 4, 64 ], [ 31, 2, 2, 192 ], [ 31, 2, 4, 32 ], [ 32, 1, 1, 576 ], [ 32, 1, 2, 384 ], [ 32, 1, 3, 192 ], [ 32, 1, 6, 384 ], [ 34, 1, 2, 192 ], [ 34, 2, 2, 96 ], [ 34, 3, 2, 96 ], [ 35, 1, 1, 576 ], [ 35, 1, 3, 192 ], [ 35, 1, 5, 64 ], [ 35, 2, 1, 288 ], [ 35, 2, 3, 96 ], [ 35, 2, 5, 32 ], [ 36, 1, 4, 768 ], [ 36, 2, 4, 384 ], [ 36, 2, 14, 384 ], [ 36, 3, 4, 384 ], [ 36, 3, 14, 384 ], [ 36, 4, 4, 384 ], [ 36, 4, 14, 384 ], [ 36, 5, 4, 384 ], [ 36, 6, 5, 384 ], [ 37, 1, 5, 256 ], [ 37, 2, 5, 128 ], [ 38, 1, 2, 768 ], [ 38, 1, 5, 384 ], [ 38, 2, 2, 384 ], [ 38, 2, 5, 192 ], [ 38, 3, 2, 384 ], [ 38, 3, 8, 192 ], [ 39, 1, 8, 768 ], [ 39, 2, 8, 384 ], [ 39, 3, 8, 384 ], [ 39, 4, 7, 384 ], [ 39, 5, 7, 384 ], [ 40, 1, 1, 1152 ], [ 40, 1, 3, 384 ], [ 40, 1, 12, 768 ], [ 40, 2, 1, 576 ], [ 40, 2, 16, 192 ], [ 40, 2, 21, 384 ], [ 40, 3, 1, 576 ], [ 40, 3, 2, 192 ], [ 40, 3, 5, 384 ], [ 40, 3, 6, 384 ], [ 40, 3, 17, 192 ], [ 41, 1, 5, 768 ], [ 41, 1, 15, 1536 ], [ 41, 2, 5, 384 ], [ 41, 2, 15, 768 ], [ 41, 3, 5, 384 ], [ 41, 3, 15, 768 ], [ 41, 4, 3, 384 ], [ 41, 4, 16, 768 ], [ 41, 5, 12, 768 ], [ 41, 6, 12, 768 ], [ 41, 7, 12, 768 ], [ 43, 2, 18, 768 ], [ 43, 2, 27, 768 ], [ 43, 2, 50, 768 ], [ 43, 3, 22, 768 ], [ 43, 4, 19, 768 ], [ 43, 4, 43, 768 ], [ 43, 5, 23, 768 ] ] k = 23: F-action on Pi is () [43,1,23] 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 q^2 phi1^2 phi2 ( 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 q^2 phi1^2 phi2 ( 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 q^2 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/192 q^2 phi1^2 phi2 ( 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 q^2 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/192 q^2 phi1^2 phi2 ( 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 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 3, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 7, 12 ], [ 27, 2, 13, 48 ], [ 27, 3, 12, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 32, 1, 4, 48 ], [ 32, 1, 5, 48 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 8 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 6, 12 ], [ 35, 2, 7, 4 ], [ 35, 2, 10, 24 ], [ 37, 1, 10, 32 ], [ 37, 2, 10, 16 ], [ 40, 1, 13, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 24, 96 ], [ 40, 2, 18, 48 ], [ 40, 2, 20, 24 ], [ 40, 2, 24, 48 ], [ 40, 3, 11, 24 ], [ 40, 3, 14, 48 ], [ 40, 3, 15, 24 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 48 ], [ 41, 1, 9, 96 ], [ 41, 2, 9, 48 ], [ 41, 3, 9, 48 ], [ 43, 2, 19, 96 ], [ 43, 2, 29, 96 ], [ 43, 2, 30, 96 ], [ 43, 3, 23, 96 ], [ 43, 4, 35, 96 ] ] k = 24: F-action on Pi is () [43,1,24] 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+15*q^2+12*q-36 ) 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+15*q^2+12*q-36 ) 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+15*q^2+12*q-36 ) q congruent 7 modulo 12: 1/192 phi1 phi2 ( q^4-8*q^3+15*q^2+12*q-36 ) 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+15*q^2+12*q-36 ) q congruent 11 modulo 12: 1/192 phi1 phi2 ( q^4-8*q^3+15*q^2+12*q-36 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 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 ], [ 17, 2, 1, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 2, 7, 12 ], [ 27, 3, 2, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 32, 1, 2, 48 ], [ 32, 1, 8, 48 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 24 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 12 ], [ 37, 1, 4, 32 ], [ 37, 2, 4, 16 ], [ 40, 1, 12, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 23, 96 ], [ 40, 2, 17, 48 ], [ 40, 2, 20, 24 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 48 ], [ 40, 3, 11, 24 ], [ 40, 3, 15, 24 ], [ 40, 3, 16, 48 ], [ 41, 1, 4, 96 ], [ 41, 2, 4, 48 ], [ 41, 3, 4, 48 ], [ 43, 2, 20, 96 ], [ 43, 2, 28, 96 ], [ 43, 2, 31, 96 ], [ 43, 3, 24, 96 ], [ 43, 4, 20, 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 phi2 ( q^4-2*q^3-q^2+2*q-4 ) 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 phi2 ( q^4-2*q^3-q^2+2*q-4 ) 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 phi2 ( q^4-2*q^3-q^2+2*q-4 ) q congruent 7 modulo 12: 1/32 phi1 phi2 ( q^4-2*q^3-q^2+2*q-4 ) 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 phi2 ( q^4-2*q^3-q^2+2*q-4 ) q congruent 11 modulo 12: 1/32 phi1 phi2 ( q^4-2*q^3-q^2+2*q-4 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 2, 10, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 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 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 37, 1, 4, 16 ], [ 37, 1, 10, 16 ], [ 37, 2, 4, 8 ], [ 37, 2, 10, 8 ], [ 40, 1, 16, 16 ], [ 40, 1, 21, 16 ], [ 40, 1, 22, 16 ], [ 40, 2, 19, 8 ], [ 40, 2, 20, 8 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 41, 2, 4, 8 ], [ 41, 2, 9, 8 ], [ 41, 3, 4, 8 ], [ 41, 3, 9, 8 ], [ 43, 2, 21, 16 ], [ 43, 2, 32, 16 ], [ 43, 2, 33, 16 ], [ 43, 3, 25, 16 ], [ 43, 4, 9, 16 ], [ 43, 4, 46, 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+581*q^3-4179*q^2+15150*q-24570 ) 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+620*q^4-4760*q^3+19329*q^2-40440*q+34650 ) 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+620*q^4-4760*q^3+19329*q^2-41000*q+38650 ) q congruent 7 modulo 12: 1/23040 ( q^6-40*q^5+620*q^4-4760*q^3+19329*q^2-40440*q+34650 ) 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+581*q^3-4179*q^2+15150*q-24570 ) q congruent 11 modulo 12: 1/23040 ( q^6-40*q^5+620*q^4-4760*q^3+19329*q^2-41720*q+48730 ) 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 ], [ 4, 2, 2, 260 ], [ 5, 1, 2, 32 ], [ 5, 2, 2, 16 ], [ 6, 1, 2, 32 ], [ 6, 2, 2, 16 ], [ 7, 1, 2, 252 ], [ 8, 1, 2, 832 ], [ 9, 1, 2, 1600 ], [ 10, 1, 4, 2160 ], [ 11, 1, 2, 512 ], [ 12, 1, 6, 1920 ], [ 12, 2, 3, 960 ], [ 13, 1, 2, 192 ], [ 14, 1, 2, 512 ], [ 14, 2, 2, 256 ], [ 15, 1, 4, 960 ], [ 15, 2, 4, 480 ], [ 15, 3, 4, 480 ], [ 15, 4, 4, 480 ], [ 16, 1, 2, 60 ], [ 17, 1, 3, 840 ], [ 17, 2, 3, 420 ], [ 18, 1, 3, 480 ], [ 18, 2, 3, 240 ], [ 19, 1, 2, 2112 ], [ 20, 1, 2, 4480 ], [ 20, 2, 2, 2240 ], [ 21, 1, 6, 5760 ], [ 22, 1, 4, 3840 ], [ 23, 1, 4, 960 ], [ 23, 2, 4, 480 ], [ 24, 1, 3, 2880 ], [ 25, 1, 8, 3840 ], [ 25, 2, 8, 1920 ], [ 25, 3, 8, 1920 ], [ 25, 4, 8, 1920 ], [ 26, 1, 3, 1560 ], [ 27, 1, 12, 7200 ], [ 27, 2, 12, 3600 ], [ 27, 3, 11, 3600 ], [ 28, 1, 6, 960 ], [ 28, 2, 6, 480 ], [ 29, 1, 4, 3840 ], [ 29, 2, 4, 1920 ], [ 30, 1, 5, 9600 ], [ 30, 2, 5, 4800 ], [ 31, 1, 7, 6720 ], [ 31, 2, 7, 3360 ], [ 32, 1, 7, 11520 ], [ 33, 1, 6, 7680 ], [ 33, 2, 6, 3840 ], [ 33, 3, 6, 3840 ], [ 33, 4, 6, 3840 ], [ 34, 1, 4, 2880 ], [ 34, 2, 10, 1440 ], [ 34, 3, 5, 1440 ], [ 35, 1, 10, 6720 ], [ 35, 2, 10, 3360 ], [ 36, 1, 20, 11520 ], [ 36, 2, 25, 5760 ], [ 36, 3, 25, 5760 ], [ 36, 4, 25, 5760 ], [ 36, 5, 20, 5760 ], [ 36, 6, 13, 5760 ], [ 37, 1, 6, 15360 ], [ 37, 2, 6, 7680 ], [ 38, 1, 7, 17280 ], [ 38, 2, 7, 8640 ], [ 38, 3, 5, 8640 ], [ 39, 1, 15, 11520 ], [ 39, 2, 15, 5760 ], [ 39, 3, 15, 5760 ], [ 39, 4, 15, 5760 ], [ 39, 5, 15, 5760 ], [ 40, 1, 2, 17280 ], [ 40, 2, 13, 8640 ], [ 40, 3, 19, 8640 ], [ 41, 1, 16, 23040 ], [ 41, 2, 16, 11520 ], [ 41, 3, 16, 11520 ], [ 41, 4, 17, 11520 ], [ 41, 5, 13, 11520 ], [ 41, 6, 13, 11520 ], [ 41, 7, 13, 11520 ], [ 42, 1, 22, 23040 ], [ 42, 2, 20, 11520 ], [ 42, 3, 16, 11520 ], [ 42, 4, 22, 11520 ], [ 43, 2, 22, 11520 ], [ 43, 3, 26, 11520 ], [ 43, 4, 44, 11520 ], [ 43, 5, 40, 11520 ] ] 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+107*q^3-325*q^2+552*q-510 ) 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+124*q^4-432*q^3+877*q^2-1062*q+558 ) 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+107*q^3-325*q^2+552*q-510 ) q congruent 7 modulo 12: 1/768 ( q^6-18*q^5+124*q^4-432*q^3+877*q^2-1062*q+558 ) 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+107*q^3-325*q^2+552*q-510 ) q congruent 11 modulo 12: 1/768 ( q^6-18*q^5+124*q^4-432*q^3+877*q^2-1062*q+558 ) 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 ], [ 4, 2, 2, 72 ], [ 5, 1, 2, 16 ], [ 5, 2, 2, 8 ], [ 6, 1, 2, 16 ], [ 6, 2, 2, 8 ], [ 7, 1, 2, 72 ], [ 8, 1, 2, 192 ], [ 9, 1, 2, 320 ], [ 10, 1, 4, 384 ], [ 11, 1, 2, 128 ], [ 12, 1, 6, 384 ], [ 12, 2, 3, 192 ], [ 13, 1, 2, 64 ], [ 14, 1, 2, 128 ], [ 14, 2, 2, 64 ], [ 15, 1, 2, 32 ], [ 15, 1, 4, 224 ], [ 15, 2, 2, 16 ], [ 15, 2, 4, 112 ], [ 15, 3, 2, 16 ], [ 15, 3, 4, 112 ], [ 15, 4, 2, 16 ], [ 15, 4, 4, 112 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 26 ], [ 17, 1, 1, 28 ], [ 17, 1, 3, 172 ], [ 17, 2, 1, 14 ], [ 17, 2, 3, 86 ], [ 18, 1, 3, 112 ], [ 18, 1, 4, 16 ], [ 18, 2, 3, 56 ], [ 18, 2, 4, 8 ], [ 19, 1, 2, 320 ], [ 20, 1, 2, 640 ], [ 20, 2, 2, 320 ], [ 21, 1, 6, 768 ], [ 22, 1, 3, 128 ], [ 22, 1, 4, 512 ], [ 23, 1, 3, 32 ], [ 23, 1, 4, 192 ], [ 23, 2, 3, 16 ], [ 23, 2, 4, 96 ], [ 24, 1, 3, 448 ], [ 24, 1, 4, 96 ], [ 25, 1, 4, 128 ], [ 25, 1, 8, 512 ], [ 25, 2, 4, 64 ], [ 25, 2, 8, 256 ], [ 25, 3, 4, 64 ], [ 25, 3, 8, 256 ], [ 25, 4, 4, 64 ], [ 25, 4, 8, 256 ], [ 26, 1, 2, 52 ], [ 26, 1, 3, 240 ], [ 27, 1, 8, 240 ], [ 27, 1, 12, 960 ], [ 27, 2, 8, 120 ], [ 27, 2, 12, 480 ], [ 27, 3, 5, 120 ], [ 27, 3, 9, 120 ], [ 27, 3, 11, 480 ], [ 28, 1, 2, 32 ], [ 28, 1, 6, 192 ], [ 28, 2, 2, 16 ], [ 28, 2, 6, 96 ], [ 29, 1, 4, 384 ], [ 29, 1, 5, 128 ], [ 29, 2, 4, 192 ], [ 29, 2, 5, 64 ], [ 30, 1, 5, 896 ], [ 30, 1, 6, 320 ], [ 30, 2, 5, 448 ], [ 30, 2, 6, 160 ], [ 31, 1, 5, 224 ], [ 31, 1, 7, 576 ], [ 31, 1, 8, 224 ], [ 31, 2, 5, 112 ], [ 31, 2, 7, 288 ], [ 31, 2, 8, 112 ], [ 32, 1, 3, 384 ], [ 32, 1, 7, 1152 ], [ 33, 1, 4, 256 ], [ 33, 1, 6, 768 ], [ 33, 2, 4, 128 ], [ 33, 2, 6, 384 ], [ 33, 3, 4, 128 ], [ 33, 3, 6, 384 ], [ 33, 4, 4, 128 ], [ 33, 4, 6, 384 ], [ 34, 1, 3, 96 ], [ 34, 1, 4, 288 ], [ 34, 2, 9, 48 ], [ 34, 2, 10, 144 ], [ 34, 3, 5, 144 ], [ 34, 3, 6, 48 ], [ 35, 1, 4, 224 ], [ 35, 1, 10, 576 ], [ 35, 2, 4, 112 ], [ 35, 2, 10, 288 ], [ 36, 1, 18, 384 ], [ 36, 1, 20, 1152 ], [ 36, 2, 17, 192 ], [ 36, 2, 23, 192 ], [ 36, 2, 25, 576 ], [ 36, 3, 17, 192 ], [ 36, 3, 23, 192 ], [ 36, 3, 25, 576 ], [ 36, 4, 17, 192 ], [ 36, 4, 23, 192 ], [ 36, 4, 25, 576 ], [ 36, 5, 18, 192 ], [ 36, 5, 20, 576 ], [ 36, 6, 9, 192 ], [ 36, 6, 13, 576 ], [ 37, 1, 6, 768 ], [ 37, 1, 7, 512 ], [ 37, 2, 6, 384 ], [ 37, 2, 7, 256 ], [ 38, 1, 3, 576 ], [ 38, 1, 6, 576 ], [ 38, 1, 7, 1152 ], [ 38, 2, 3, 288 ], [ 38, 2, 6, 288 ], [ 38, 2, 7, 576 ], [ 38, 3, 3, 288 ], [ 38, 3, 5, 576 ], [ 38, 3, 6, 288 ], [ 39, 1, 11, 384 ], [ 39, 1, 15, 384 ], [ 39, 1, 20, 384 ], [ 39, 2, 11, 192 ], [ 39, 2, 15, 192 ], [ 39, 2, 20, 192 ], [ 39, 3, 11, 192 ], [ 39, 3, 15, 192 ], [ 39, 3, 20, 192 ], [ 39, 4, 11, 192 ], [ 39, 4, 15, 192 ], [ 39, 4, 20, 192 ], [ 39, 5, 11, 192 ], [ 39, 5, 15, 192 ], [ 39, 5, 20, 192 ], [ 40, 1, 2, 1152 ], [ 40, 1, 18, 576 ], [ 40, 2, 13, 576 ], [ 40, 2, 23, 288 ], [ 40, 3, 3, 288 ], [ 40, 3, 19, 576 ], [ 41, 1, 6, 768 ], [ 41, 1, 16, 768 ], [ 41, 1, 22, 768 ], [ 41, 2, 6, 384 ], [ 41, 2, 16, 384 ], [ 41, 2, 22, 384 ], [ 41, 3, 6, 384 ], [ 41, 3, 16, 384 ], [ 41, 3, 22, 384 ], [ 41, 4, 10, 384 ], [ 41, 4, 13, 384 ], [ 41, 4, 17, 384 ], [ 41, 4, 26, 384 ], [ 41, 5, 8, 384 ], [ 41, 5, 13, 384 ], [ 41, 5, 20, 384 ], [ 41, 6, 8, 384 ], [ 41, 6, 13, 384 ], [ 41, 6, 20, 384 ], [ 41, 7, 8, 384 ], [ 41, 7, 13, 384 ], [ 41, 7, 20, 384 ], [ 42, 1, 21, 768 ], [ 42, 2, 11, 384 ], [ 42, 3, 11, 384 ], [ 42, 3, 17, 384 ], [ 42, 4, 21, 384 ], [ 43, 2, 34, 384 ], [ 43, 2, 45, 384 ], [ 43, 3, 28, 384 ], [ 43, 4, 18, 384 ], [ 43, 4, 32, 384 ], [ 43, 4, 52, 384 ], [ 43, 5, 17, 384 ], [ 43, 5, 38, 384 ] ] 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+235*q^3-1029*q^2+2088*q-1590 ) 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 ( q^6-26*q^5+260*q^4-1264*q^3+3117*q^2-3678*q+1638 ) 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+235*q^3-1029*q^2+2088*q-1590 ) q congruent 7 modulo 12: 1/768 ( q^6-26*q^5+260*q^4-1264*q^3+3117*q^2-3678*q+1638 ) 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+235*q^3-1029*q^2+2088*q-1590 ) q congruent 11 modulo 12: 1/768 ( q^6-26*q^5+260*q^4-1264*q^3+3117*q^2-3678*q+1638 ) 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 ], [ 4, 2, 1, 72 ], [ 5, 1, 1, 16 ], [ 5, 2, 1, 8 ], [ 6, 1, 1, 16 ], [ 6, 2, 1, 8 ], [ 7, 1, 1, 72 ], [ 8, 1, 1, 192 ], [ 9, 1, 1, 320 ], [ 10, 1, 1, 384 ], [ 11, 1, 1, 128 ], [ 12, 1, 1, 384 ], [ 12, 2, 1, 192 ], [ 13, 1, 1, 64 ], [ 14, 1, 1, 128 ], [ 14, 2, 1, 64 ], [ 15, 1, 1, 224 ], [ 15, 1, 3, 32 ], [ 15, 2, 1, 112 ], [ 15, 2, 3, 16 ], [ 15, 3, 1, 112 ], [ 15, 3, 3, 16 ], [ 15, 4, 1, 112 ], [ 15, 4, 3, 16 ], [ 16, 1, 1, 26 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 172 ], [ 17, 1, 3, 28 ], [ 17, 2, 1, 86 ], [ 17, 2, 3, 14 ], [ 18, 1, 1, 112 ], [ 18, 1, 2, 16 ], [ 18, 2, 1, 56 ], [ 18, 2, 2, 8 ], [ 19, 1, 1, 320 ], [ 20, 1, 1, 640 ], [ 20, 2, 1, 320 ], [ 21, 1, 1, 768 ], [ 22, 1, 1, 512 ], [ 22, 1, 2, 128 ], [ 23, 1, 1, 192 ], [ 23, 1, 2, 32 ], [ 23, 2, 1, 96 ], [ 23, 2, 2, 16 ], [ 24, 1, 1, 448 ], [ 24, 1, 2, 96 ], [ 25, 1, 1, 512 ], [ 25, 1, 5, 128 ], [ 25, 2, 1, 256 ], [ 25, 2, 5, 64 ], [ 25, 3, 1, 256 ], [ 25, 3, 5, 64 ], [ 25, 4, 1, 256 ], [ 25, 4, 5, 64 ], [ 26, 1, 1, 240 ], [ 26, 1, 2, 52 ], [ 27, 1, 1, 960 ], [ 27, 1, 8, 240 ], [ 27, 2, 1, 480 ], [ 27, 2, 8, 120 ], [ 27, 3, 1, 480 ], [ 27, 3, 5, 120 ], [ 27, 3, 9, 120 ], [ 28, 1, 1, 192 ], [ 28, 1, 3, 32 ], [ 28, 2, 1, 96 ], [ 28, 2, 4, 16 ], [ 29, 1, 1, 384 ], [ 29, 1, 2, 128 ], [ 29, 2, 1, 192 ], [ 29, 2, 2, 64 ], [ 30, 1, 1, 896 ], [ 30, 1, 2, 320 ], [ 30, 2, 1, 448 ], [ 30, 2, 2, 160 ], [ 31, 1, 1, 576 ], [ 31, 1, 2, 224 ], [ 31, 1, 3, 224 ], [ 31, 2, 1, 288 ], [ 31, 2, 2, 112 ], [ 31, 2, 3, 112 ], [ 32, 1, 1, 1152 ], [ 32, 1, 6, 384 ], [ 33, 1, 1, 768 ], [ 33, 1, 3, 256 ], [ 33, 2, 1, 384 ], [ 33, 2, 3, 128 ], [ 33, 3, 1, 384 ], [ 33, 3, 3, 128 ], [ 33, 4, 1, 384 ], [ 33, 4, 3, 128 ], [ 34, 1, 1, 288 ], [ 34, 1, 2, 96 ], [ 34, 2, 1, 144 ], [ 34, 2, 2, 48 ], [ 34, 3, 1, 144 ], [ 34, 3, 2, 48 ], [ 35, 1, 1, 576 ], [ 35, 1, 2, 224 ], [ 35, 2, 1, 288 ], [ 35, 2, 2, 112 ], [ 36, 1, 1, 1152 ], [ 36, 1, 4, 384 ], [ 36, 2, 1, 576 ], [ 36, 2, 4, 192 ], [ 36, 2, 14, 192 ], [ 36, 3, 1, 576 ], [ 36, 3, 4, 192 ], [ 36, 3, 14, 192 ], [ 36, 4, 1, 576 ], [ 36, 4, 4, 192 ], [ 36, 4, 14, 192 ], [ 36, 5, 1, 576 ], [ 36, 5, 4, 192 ], [ 36, 6, 1, 576 ], [ 36, 6, 5, 192 ], [ 37, 1, 1, 768 ], [ 37, 1, 2, 512 ], [ 37, 2, 1, 384 ], [ 37, 2, 2, 256 ], [ 38, 1, 1, 1152 ], [ 38, 1, 2, 576 ], [ 38, 1, 8, 576 ], [ 38, 2, 1, 576 ], [ 38, 2, 2, 288 ], [ 38, 2, 8, 288 ], [ 38, 3, 1, 576 ], [ 38, 3, 2, 288 ], [ 38, 3, 7, 288 ], [ 39, 1, 1, 384 ], [ 39, 1, 2, 384 ], [ 39, 1, 8, 384 ], [ 39, 2, 1, 192 ], [ 39, 2, 2, 192 ], [ 39, 2, 8, 192 ], [ 39, 3, 1, 192 ], [ 39, 3, 2, 192 ], [ 39, 3, 8, 192 ], [ 39, 4, 1, 192 ], [ 39, 4, 2, 192 ], [ 39, 4, 7, 192 ], [ 39, 5, 1, 192 ], [ 39, 5, 2, 192 ], [ 39, 5, 7, 192 ], [ 40, 1, 1, 1152 ], [ 40, 1, 17, 576 ], [ 40, 2, 1, 576 ], [ 40, 2, 22, 288 ], [ 40, 3, 1, 576 ], [ 40, 3, 4, 288 ], [ 41, 1, 1, 768 ], [ 41, 1, 2, 768 ], [ 41, 1, 15, 768 ], [ 41, 2, 1, 384 ], [ 41, 2, 2, 384 ], [ 41, 2, 15, 384 ], [ 41, 3, 1, 384 ], [ 41, 3, 2, 384 ], [ 41, 3, 15, 384 ], [ 41, 4, 1, 384 ], [ 41, 4, 2, 384 ], [ 41, 4, 4, 384 ], [ 41, 4, 16, 384 ], [ 41, 5, 1, 384 ], [ 41, 5, 2, 384 ], [ 41, 5, 12, 384 ], [ 41, 6, 1, 384 ], [ 41, 6, 2, 384 ], [ 41, 6, 12, 384 ], [ 41, 7, 1, 384 ], [ 41, 7, 2, 384 ], [ 41, 7, 12, 384 ], [ 42, 1, 18, 768 ], [ 42, 2, 2, 384 ], [ 42, 3, 2, 384 ], [ 42, 3, 6, 384 ], [ 42, 4, 20, 384 ], [ 43, 2, 35, 384 ], [ 43, 2, 43, 384 ], [ 43, 3, 27, 384 ], [ 43, 4, 2, 384 ], [ 43, 4, 17, 384 ], [ 43, 4, 27, 384 ], [ 43, 5, 2, 384 ], [ 43, 5, 16, 384 ] ] 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 ( q^5-5*q^4+3*q^3+3*q^2+8*q+22 ) 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 phi2 ( q^5-7*q^4+15*q^3-15*q^2+20*q-6 ) 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 ( q^5-5*q^4+3*q^3+3*q^2+8*q+22 ) q congruent 7 modulo 12: 1/128 phi2 ( q^5-7*q^4+15*q^3-15*q^2+20*q-6 ) 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 ( q^5-5*q^4+3*q^3+3*q^2+8*q+22 ) q congruent 11 modulo 12: 1/128 phi2 ( q^5-7*q^4+15*q^3-15*q^2+20*q-6 ) 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 ], [ 4, 2, 1, 12 ], [ 4, 2, 2, 12 ], [ 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 ], [ 15, 2, 2, 16 ], [ 15, 2, 3, 16 ], [ 15, 3, 2, 16 ], [ 15, 3, 3, 16 ], [ 15, 4, 2, 16 ], [ 15, 4, 3, 16 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 18 ], [ 18, 1, 2, 16 ], [ 18, 1, 4, 16 ], [ 18, 2, 2, 8 ], [ 18, 2, 4, 8 ], [ 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 ], [ 25, 2, 4, 32 ], [ 25, 2, 5, 32 ], [ 25, 3, 4, 32 ], [ 25, 3, 5, 32 ], [ 25, 4, 4, 32 ], [ 25, 4, 5, 32 ], [ 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 ], [ 27, 2, 1, 48 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 72 ], [ 27, 2, 9, 16 ], [ 27, 2, 12, 48 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 72 ], [ 27, 3, 6, 16 ], [ 27, 3, 9, 72 ], [ 27, 3, 10, 16 ], [ 27, 3, 11, 48 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 28, 2, 2, 8 ], [ 28, 2, 4, 8 ], [ 30, 1, 2, 64 ], [ 30, 1, 6, 64 ], [ 30, 2, 2, 32 ], [ 30, 2, 6, 32 ], [ 31, 1, 2, 32 ], [ 31, 1, 4, 64 ], [ 31, 1, 6, 64 ], [ 31, 1, 8, 32 ], [ 31, 2, 2, 16 ], [ 31, 2, 4, 32 ], [ 31, 2, 6, 32 ], [ 31, 2, 8, 16 ], [ 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 ], [ 34, 2, 2, 16 ], [ 34, 2, 9, 16 ], [ 34, 3, 2, 16 ], [ 34, 3, 6, 16 ], [ 35, 1, 2, 48 ], [ 35, 1, 3, 32 ], [ 35, 1, 4, 48 ], [ 35, 1, 5, 32 ], [ 35, 2, 2, 24 ], [ 35, 2, 3, 16 ], [ 35, 2, 4, 24 ], [ 35, 2, 5, 16 ], [ 36, 1, 4, 128 ], [ 36, 1, 18, 128 ], [ 36, 2, 4, 64 ], [ 36, 2, 14, 64 ], [ 36, 2, 17, 64 ], [ 36, 2, 23, 64 ], [ 36, 3, 4, 64 ], [ 36, 3, 14, 64 ], [ 36, 3, 17, 64 ], [ 36, 3, 23, 64 ], [ 36, 4, 4, 64 ], [ 36, 4, 14, 64 ], [ 36, 4, 17, 64 ], [ 36, 4, 23, 64 ], [ 36, 5, 4, 64 ], [ 36, 5, 18, 64 ], [ 36, 6, 5, 64 ], [ 36, 6, 9, 64 ], [ 37, 1, 5, 64 ], [ 37, 1, 9, 64 ], [ 37, 2, 5, 32 ], [ 37, 2, 9, 32 ], [ 38, 1, 2, 64 ], [ 38, 1, 4, 128 ], [ 38, 1, 5, 128 ], [ 38, 1, 6, 64 ], [ 38, 2, 2, 32 ], [ 38, 2, 4, 64 ], [ 38, 2, 5, 64 ], [ 38, 2, 6, 32 ], [ 38, 3, 2, 32 ], [ 38, 3, 4, 64 ], [ 38, 3, 6, 32 ], [ 38, 3, 8, 64 ], [ 39, 1, 5, 64 ], [ 39, 1, 19, 64 ], [ 39, 2, 5, 32 ], [ 39, 2, 19, 32 ], [ 39, 3, 5, 32 ], [ 39, 3, 19, 32 ], [ 39, 4, 6, 32 ], [ 39, 4, 19, 32 ], [ 39, 5, 6, 32 ], [ 39, 5, 19, 32 ], [ 40, 1, 3, 64 ], [ 40, 1, 17, 96 ], [ 40, 1, 18, 96 ], [ 40, 1, 22, 64 ], [ 40, 2, 16, 32 ], [ 40, 2, 22, 48 ], [ 40, 2, 23, 48 ], [ 40, 2, 25, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 3, 48 ], [ 40, 3, 4, 48 ], [ 40, 3, 7, 32 ], [ 40, 3, 8, 32 ], [ 40, 3, 17, 32 ], [ 41, 1, 5, 64 ], [ 41, 1, 7, 64 ], [ 41, 1, 11, 128 ], [ 41, 1, 20, 128 ], [ 41, 2, 5, 32 ], [ 41, 2, 7, 32 ], [ 41, 2, 11, 64 ], [ 41, 2, 20, 64 ], [ 41, 3, 5, 32 ], [ 41, 3, 7, 32 ], [ 41, 3, 11, 64 ], [ 41, 3, 20, 64 ], [ 41, 4, 3, 32 ], [ 41, 4, 11, 64 ], [ 41, 4, 12, 32 ], [ 41, 4, 15, 64 ], [ 41, 4, 23, 64 ], [ 41, 4, 25, 64 ], [ 41, 5, 5, 64 ], [ 41, 5, 15, 64 ], [ 41, 6, 5, 64 ], [ 41, 6, 15, 64 ], [ 41, 7, 5, 64 ], [ 41, 7, 15, 64 ], [ 43, 2, 44, 64 ], [ 43, 2, 47, 64 ], [ 43, 2, 48, 64 ], [ 43, 2, 53, 64 ], [ 43, 3, 36, 64 ], [ 43, 4, 7, 64 ], [ 43, 4, 24, 64 ], [ 43, 4, 37, 64 ], [ 43, 4, 45, 64 ], [ 43, 5, 11, 64 ], [ 43, 5, 22, 64 ] ] 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 ( q^5-7*q^4+13*q^3-11*q^2+46*q-74 ) q congruent 2 modulo 12: 1/128 q^3 ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/128 ( q^6-8*q^5+20*q^4-24*q^3+57*q^2-104*q+42 ) 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 ( q^5-7*q^4+13*q^3-11*q^2+46*q-74 ) q congruent 7 modulo 12: 1/128 ( q^6-8*q^5+20*q^4-24*q^3+57*q^2-104*q+42 ) 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 ( q^5-7*q^4+13*q^3-11*q^2+46*q-74 ) q congruent 11 modulo 12: 1/128 ( q^6-8*q^5+20*q^4-24*q^3+57*q^2-104*q+42 ) 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 24 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 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 ], [ 12, 2, 3, 48 ], [ 13, 1, 2, 16 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 2, 32 ], [ 15, 1, 3, 16 ], [ 15, 1, 4, 48 ], [ 15, 2, 2, 16 ], [ 15, 2, 3, 8 ], [ 15, 2, 4, 24 ], [ 15, 3, 2, 16 ], [ 15, 3, 3, 8 ], [ 15, 3, 4, 24 ], [ 15, 4, 2, 16 ], [ 15, 4, 3, 8 ], [ 15, 4, 4, 24 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 8 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 48 ], [ 17, 2, 1, 12 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 24 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 24 ], [ 18, 1, 4, 16 ], [ 18, 2, 2, 4 ], [ 18, 2, 3, 12 ], [ 18, 2, 4, 8 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 96 ], [ 20, 2, 2, 48 ], [ 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 ], [ 23, 2, 3, 16 ], [ 23, 2, 4, 8 ], [ 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 ], [ 25, 2, 4, 32 ], [ 25, 2, 5, 16 ], [ 25, 2, 6, 16 ], [ 25, 2, 7, 16 ], [ 25, 2, 8, 48 ], [ 25, 3, 4, 32 ], [ 25, 3, 5, 16 ], [ 25, 3, 6, 16 ], [ 25, 3, 7, 16 ], [ 25, 3, 8, 48 ], [ 25, 4, 4, 32 ], [ 25, 4, 5, 16 ], [ 25, 4, 6, 16 ], [ 25, 4, 7, 16 ], [ 25, 4, 8, 48 ], [ 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 64 ], [ 27, 2, 11, 16 ], [ 27, 2, 12, 96 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 64 ], [ 27, 3, 7, 16 ], [ 27, 3, 8, 16 ], [ 27, 3, 9, 64 ], [ 27, 3, 11, 96 ], [ 28, 1, 2, 32 ], [ 28, 2, 2, 16 ], [ 29, 1, 5, 64 ], [ 29, 2, 5, 32 ], [ 30, 1, 5, 96 ], [ 30, 1, 6, 128 ], [ 30, 1, 8, 64 ], [ 30, 2, 5, 48 ], [ 30, 2, 6, 64 ], [ 30, 2, 8, 32 ], [ 31, 1, 4, 48 ], [ 31, 1, 5, 96 ], [ 31, 1, 6, 32 ], [ 31, 1, 7, 48 ], [ 31, 1, 8, 64 ], [ 31, 2, 4, 24 ], [ 31, 2, 5, 48 ], [ 31, 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], [ 39, 5, 19, 32 ], [ 40, 1, 3, 64 ], [ 40, 1, 18, 192 ], [ 40, 2, 16, 32 ], [ 40, 2, 23, 96 ], [ 40, 3, 2, 32 ], [ 40, 3, 3, 96 ], [ 40, 3, 17, 32 ], [ 41, 1, 6, 128 ], [ 41, 1, 7, 64 ], [ 41, 1, 10, 128 ], [ 41, 1, 20, 128 ], [ 41, 2, 6, 64 ], [ 41, 2, 7, 32 ], [ 41, 2, 10, 64 ], [ 41, 2, 20, 64 ], [ 41, 3, 6, 64 ], [ 41, 3, 7, 32 ], [ 41, 3, 10, 64 ], [ 41, 3, 20, 64 ], [ 41, 4, 5, 64 ], [ 41, 4, 9, 64 ], [ 41, 4, 10, 64 ], [ 41, 4, 12, 32 ], [ 41, 4, 13, 64 ], [ 41, 4, 14, 64 ], [ 41, 4, 23, 64 ], [ 41, 4, 25, 64 ], [ 41, 5, 4, 64 ], [ 41, 5, 8, 64 ], [ 41, 5, 10, 64 ], [ 41, 5, 15, 64 ], [ 41, 6, 4, 64 ], [ 41, 6, 8, 64 ], [ 41, 6, 10, 64 ], [ 41, 6, 15, 64 ], [ 41, 7, 4, 64 ], [ 41, 7, 8, 64 ], [ 41, 7, 10, 64 ], [ 41, 7, 15, 64 ], [ 42, 1, 17, 128 ], [ 42, 2, 12, 64 ], [ 42, 2, 19, 64 ], [ 42, 3, 12, 64 ], [ 42, 3, 19, 64 ], [ 42, 4, 17, 64 ], [ 43, 2, 37, 64 ], [ 43, 2, 51, 64 ], [ 43, 3, 35, 64 ], [ 43, 4, 6, 64 ], [ 43, 4, 36, 64 ], [ 43, 4, 42, 64 ], [ 43, 4, 50, 64 ], [ 43, 5, 9, 64 ], [ 43, 5, 18, 64 ], [ 43, 5, 36, 64 ], [ 43, 5, 39, 64 ] ] 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+19*q^3+3*q^2+56*q-198 ) 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+28*q^4-16*q^3+53*q^2-254*q+150 ) 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+28*q^4-16*q^3+53*q^2-318*q+390 ) q congruent 7 modulo 12: 1/384 ( q^6-10*q^5+28*q^4-16*q^3+53*q^2-254*q+150 ) 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+19*q^3+3*q^2+56*q-198 ) q congruent 11 modulo 12: 1/384 ( q^6-10*q^5+28*q^4-16*q^3+53*q^2-318*q+342 ) 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 ], [ 4, 2, 1, 12 ], [ 4, 2, 2, 12 ], [ 4, 2, 4, 8 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 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 ], [ 12, 2, 4, 32 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 1, 2, 48 ], [ 15, 2, 1, 24 ], [ 15, 2, 2, 24 ], [ 15, 3, 1, 24 ], [ 15, 3, 2, 24 ], [ 15, 4, 1, 24 ], [ 15, 4, 2, 24 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 36 ], [ 17, 1, 4, 48 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 18 ], [ 17, 2, 4, 24 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 24 ], [ 18, 2, 1, 12 ], [ 18, 2, 4, 12 ], [ 20, 1, 3, 64 ], [ 20, 2, 3, 32 ], [ 21, 1, 3, 96 ], [ 21, 1, 6, 48 ], [ 22, 1, 2, 72 ], [ 22, 1, 3, 48 ], [ 22, 1, 4, 24 ], [ 23, 1, 2, 48 ], [ 23, 2, 2, 24 ], [ 24, 1, 4, 48 ], [ 25, 1, 1, 96 ], [ 25, 1, 2, 96 ], [ 25, 1, 3, 96 ], [ 25, 1, 4, 96 ], [ 25, 2, 1, 48 ], [ 25, 2, 2, 48 ], [ 25, 2, 3, 48 ], [ 25, 2, 4, 48 ], [ 25, 3, 1, 48 ], [ 25, 3, 2, 48 ], [ 25, 3, 3, 48 ], [ 25, 3, 4, 48 ], [ 25, 4, 1, 48 ], [ 25, 4, 2, 48 ], [ 25, 4, 3, 48 ], [ 25, 4, 4, 48 ], [ 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 ], [ 27, 2, 1, 48 ], [ 27, 2, 2, 48 ], [ 27, 2, 6, 48 ], [ 27, 2, 8, 72 ], [ 27, 2, 12, 48 ], [ 27, 3, 1, 48 ], [ 27, 3, 4, 48 ], [ 27, 3, 5, 72 ], [ 27, 3, 9, 72 ], [ 27, 3, 11, 48 ], [ 27, 3, 13, 48 ], [ 30, 1, 6, 96 ], [ 30, 1, 7, 192 ], [ 30, 2, 6, 48 ], [ 30, 2, 7, 96 ], [ 31, 1, 3, 144 ], [ 31, 1, 6, 96 ], [ 31, 1, 8, 48 ], [ 31, 2, 3, 72 ], [ 31, 2, 6, 48 ], [ 31, 2, 8, 24 ], [ 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 ], [ 34, 2, 1, 24 ], [ 34, 2, 4, 48 ], [ 34, 2, 9, 24 ], [ 34, 3, 1, 24 ], [ 34, 3, 4, 48 ], [ 34, 3, 6, 24 ], [ 34, 3, 7, 48 ], [ 35, 1, 3, 96 ], [ 35, 1, 5, 96 ], [ 35, 2, 3, 48 ], [ 35, 2, 5, 48 ], [ 36, 1, 1, 192 ], [ 36, 1, 2, 192 ], [ 36, 1, 18, 192 ], [ 36, 2, 1, 96 ], [ 36, 2, 2, 96 ], [ 36, 2, 17, 96 ], [ 36, 2, 23, 96 ], [ 36, 3, 1, 96 ], [ 36, 3, 2, 96 ], [ 36, 3, 17, 96 ], [ 36, 3, 23, 96 ], [ 36, 4, 1, 96 ], [ 36, 4, 2, 96 ], [ 36, 4, 17, 96 ], [ 36, 4, 23, 96 ], [ 36, 5, 1, 96 ], [ 36, 5, 2, 96 ], [ 36, 5, 18, 96 ], [ 36, 6, 1, 96 ], [ 36, 6, 2, 96 ], [ 36, 6, 4, 96 ], [ 36, 6, 9, 96 ], [ 36, 6, 10, 96 ], [ 36, 6, 11, 96 ], [ 37, 1, 9, 192 ], [ 37, 2, 9, 96 ], [ 38, 1, 4, 192 ], [ 38, 1, 6, 96 ], [ 38, 1, 8, 288 ], [ 38, 1, 15, 192 ], [ 38, 2, 4, 96 ], [ 38, 2, 6, 48 ], [ 38, 2, 8, 144 ], [ 38, 2, 15, 96 ], [ 38, 3, 4, 96 ], [ 38, 3, 6, 48 ], [ 38, 3, 7, 144 ], [ 38, 3, 13, 96 ], [ 38, 3, 16, 96 ], [ 39, 1, 10, 192 ], [ 39, 1, 18, 192 ], [ 39, 2, 10, 96 ], [ 39, 2, 18, 96 ], [ 39, 3, 10, 96 ], [ 39, 3, 18, 96 ], [ 39, 4, 8, 96 ], [ 39, 4, 9, 96 ], [ 39, 4, 17, 96 ], [ 39, 4, 18, 96 ], [ 39, 5, 8, 96 ], [ 39, 5, 9, 96 ], [ 39, 5, 17, 96 ], [ 39, 5, 18, 96 ], [ 40, 1, 3, 192 ], [ 40, 2, 16, 96 ], [ 40, 3, 2, 96 ], [ 40, 3, 17, 96 ], [ 41, 1, 7, 192 ], [ 41, 1, 19, 384 ], [ 41, 2, 7, 96 ], [ 41, 2, 19, 192 ], [ 41, 3, 7, 96 ], [ 41, 3, 19, 192 ], [ 41, 4, 12, 96 ], [ 41, 4, 19, 192 ], [ 41, 4, 22, 192 ], [ 41, 4, 24, 192 ], [ 41, 5, 14, 192 ], [ 41, 5, 19, 192 ], [ 41, 6, 14, 192 ], [ 41, 6, 19, 192 ], [ 41, 7, 14, 192 ], [ 41, 7, 19, 192 ], [ 42, 1, 20, 384 ], [ 42, 2, 13, 192 ], [ 42, 2, 15, 192 ], [ 42, 3, 14, 192 ], [ 42, 4, 18, 192 ], [ 43, 2, 46, 192 ], [ 43, 3, 34, 192 ], [ 43, 4, 16, 192 ], [ 43, 4, 49, 192 ], [ 43, 5, 12, 192 ], [ 43, 5, 14, 192 ], [ 43, 5, 19, 192 ] ] 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 ( q^5-11*q^4+37*q^3-35*q^2+22*q-110 ) 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+48*q^4-72*q^3+57*q^2-148*q+174 ) 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 ( q^5-11*q^4+37*q^3-35*q^2+22*q-110 ) q congruent 7 modulo 12: 1/128 ( q^6-12*q^5+48*q^4-72*q^3+57*q^2-148*q+174 ) 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 ( q^5-11*q^4+37*q^3-35*q^2+22*q-110 ) q congruent 11 modulo 12: 1/128 ( q^6-12*q^5+48*q^4-72*q^3+57*q^2-148*q+174 ) 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 ], [ 4, 2, 1, 24 ], [ 4, 2, 2, 4 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 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 ], [ 12, 2, 1, 48 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 32 ], [ 15, 2, 1, 24 ], [ 15, 2, 2, 8 ], [ 15, 2, 3, 16 ], [ 15, 3, 1, 24 ], [ 15, 3, 2, 8 ], [ 15, 3, 3, 16 ], [ 15, 4, 1, 24 ], [ 15, 4, 2, 8 ], [ 15, 4, 3, 16 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 48 ], [ 17, 1, 3, 24 ], [ 17, 1, 4, 16 ], [ 17, 2, 1, 24 ], [ 17, 2, 3, 12 ], [ 17, 2, 4, 8 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 16 ], [ 18, 1, 4, 8 ], [ 18, 2, 1, 12 ], [ 18, 2, 2, 8 ], [ 18, 2, 4, 4 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 96 ], [ 20, 2, 1, 48 ], [ 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 ], [ 23, 2, 1, 8 ], [ 23, 2, 2, 16 ], [ 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 ], [ 25, 2, 1, 48 ], [ 25, 2, 2, 16 ], [ 25, 2, 3, 16 ], [ 25, 2, 4, 16 ], [ 25, 2, 5, 32 ], [ 25, 3, 1, 48 ], [ 25, 3, 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5, 64 ], [ 41, 1, 11, 128 ], [ 41, 1, 19, 128 ], [ 41, 2, 2, 64 ], [ 41, 2, 5, 32 ], [ 41, 2, 11, 64 ], [ 41, 2, 19, 64 ], [ 41, 3, 2, 64 ], [ 41, 3, 5, 32 ], [ 41, 3, 11, 64 ], [ 41, 3, 19, 64 ], [ 41, 4, 2, 64 ], [ 41, 4, 3, 32 ], [ 41, 4, 4, 64 ], [ 41, 4, 11, 64 ], [ 41, 4, 15, 64 ], [ 41, 4, 19, 64 ], [ 41, 4, 22, 64 ], [ 41, 4, 24, 64 ], [ 41, 5, 2, 64 ], [ 41, 5, 5, 64 ], [ 41, 5, 14, 64 ], [ 41, 5, 19, 64 ], [ 41, 6, 2, 64 ], [ 41, 6, 5, 64 ], [ 41, 6, 14, 64 ], [ 41, 6, 19, 64 ], [ 41, 7, 2, 64 ], [ 41, 7, 5, 64 ], [ 41, 7, 14, 64 ], [ 41, 7, 19, 64 ], [ 42, 1, 12, 128 ], [ 42, 2, 4, 64 ], [ 42, 2, 5, 64 ], [ 42, 3, 5, 64 ], [ 42, 3, 7, 64 ], [ 42, 4, 12, 64 ], [ 43, 2, 38, 64 ], [ 43, 2, 49, 64 ], [ 43, 3, 29, 64 ], [ 43, 4, 5, 64 ], [ 43, 4, 11, 64 ], [ 43, 4, 23, 64 ], [ 43, 4, 28, 64 ], [ 43, 5, 4, 64 ], [ 43, 5, 5, 64 ], [ 43, 5, 10, 64 ], [ 43, 5, 13, 64 ] ] k = 33: F-action on Pi is () [43,1,33] 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 phi1^2 phi2 ( q^3-5*q^2+4*q+6 ) 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 phi1^2 phi2 ( q^3-5*q^2+4*q+6 ) 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 phi1^2 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 ( q^3-5*q^2+4*q+6 ) 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 phi1^2 phi2 ( q^3-5*q^2+4*q+6 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 ( q^3-5*q^2+4*q+6 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 19, 1, 1, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 8 ], [ 23, 2, 1, 4 ], [ 24, 1, 1, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 1, 14, 16 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 27, 2, 14, 8 ], [ 27, 3, 15, 8 ], [ 27, 3, 16, 8 ], [ 30, 1, 4, 16 ], [ 30, 2, 4, 8 ], [ 31, 1, 1, 8 ], [ 31, 1, 6, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 6, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 5, 8 ], [ 34, 1, 6, 8 ], [ 34, 2, 4, 4 ], [ 34, 2, 8, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 1, 2, 16 ], [ 36, 1, 17, 16 ], [ 36, 2, 2, 8 ], [ 36, 2, 13, 8 ], [ 36, 3, 2, 8 ], [ 36, 3, 13, 8 ], [ 36, 4, 2, 8 ], [ 36, 4, 13, 8 ], [ 36, 5, 2, 8 ], [ 36, 5, 17, 8 ], [ 36, 6, 2, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 10, 8 ], [ 36, 6, 11, 8 ], [ 37, 1, 4, 16 ], [ 37, 2, 4, 8 ], [ 38, 1, 10, 16 ], [ 38, 1, 13, 16 ], [ 38, 2, 10, 8 ], [ 38, 2, 13, 8 ], [ 38, 3, 10, 8 ], [ 38, 3, 11, 8 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 16 ], [ 39, 2, 9, 8 ], [ 39, 2, 17, 8 ], [ 39, 3, 9, 8 ], [ 39, 3, 17, 8 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 8 ], [ 39, 5, 10, 8 ], [ 39, 5, 16, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 18, 32 ], [ 41, 2, 4, 8 ], [ 41, 2, 18, 16 ], [ 41, 3, 4, 8 ], [ 41, 3, 18, 16 ], [ 41, 4, 18, 16 ], [ 41, 4, 21, 16 ], [ 41, 5, 16, 16 ], [ 41, 5, 18, 16 ], [ 41, 6, 16, 16 ], [ 41, 6, 18, 16 ], [ 41, 7, 16, 16 ], [ 41, 7, 18, 16 ], [ 42, 1, 16, 32 ], [ 42, 2, 3, 16 ], [ 42, 3, 4, 16 ], [ 42, 4, 13, 16 ], [ 43, 2, 39, 16 ], [ 43, 3, 30, 16 ], [ 43, 4, 4, 16 ], [ 43, 4, 22, 16 ], [ 43, 5, 3, 16 ], [ 43, 5, 20, 16 ] ] k = 34: F-action on Pi is () [43,1,34] 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^2-2 ) q congruent 2 modulo 12: 1/32 q^5 ( q-2 ) q congruent 3 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2-2 ) q congruent 4 modulo 12: 1/32 q^5 ( q-2 ) q congruent 5 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2-2 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2-2 ) q congruent 8 modulo 12: 1/32 q^5 ( q-2 ) q congruent 9 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2-2 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 ( q^3-q^2-2 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 14, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 19, 1, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 4, 8 ], [ 23, 2, 4, 4 ], [ 24, 1, 3, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 1, 11, 16 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 27, 2, 11, 8 ], [ 27, 3, 7, 8 ], [ 27, 3, 8, 8 ], [ 30, 1, 8, 16 ], [ 30, 2, 8, 8 ], [ 31, 1, 4, 8 ], [ 31, 1, 7, 8 ], [ 31, 2, 4, 4 ], [ 31, 2, 7, 4 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 34, 1, 7, 8 ], [ 34, 1, 8, 8 ], [ 34, 2, 3, 4 ], [ 34, 2, 5, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 8, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 1, 5, 16 ], [ 36, 1, 10, 16 ], [ 36, 2, 5, 8 ], [ 36, 2, 16, 8 ], [ 36, 3, 5, 8 ], [ 36, 3, 16, 8 ], [ 36, 4, 5, 8 ], [ 36, 4, 16, 8 ], [ 36, 5, 5, 8 ], [ 36, 5, 10, 8 ], [ 36, 6, 6, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 14, 8 ], [ 36, 6, 15, 8 ], [ 37, 1, 10, 16 ], [ 37, 2, 10, 8 ], [ 38, 1, 12, 16 ], [ 38, 1, 16, 16 ], [ 38, 2, 12, 8 ], [ 38, 2, 16, 8 ], [ 38, 3, 14, 8 ], [ 38, 3, 15, 8 ], [ 39, 1, 6, 16 ], [ 39, 1, 14, 16 ], [ 39, 2, 6, 8 ], [ 39, 2, 14, 8 ], [ 39, 3, 6, 8 ], [ 39, 3, 14, 8 ], [ 39, 4, 4, 8 ], [ 39, 4, 14, 8 ], [ 39, 5, 4, 8 ], [ 39, 5, 14, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 1, 9, 16 ], [ 41, 1, 12, 32 ], [ 41, 2, 9, 8 ], [ 41, 2, 12, 16 ], [ 41, 3, 9, 8 ], [ 41, 3, 12, 16 ], [ 41, 4, 6, 16 ], [ 41, 4, 8, 16 ], [ 41, 5, 6, 16 ], [ 41, 5, 11, 16 ], [ 41, 6, 6, 16 ], [ 41, 6, 11, 16 ], [ 41, 7, 6, 16 ], [ 41, 7, 11, 16 ], [ 42, 1, 14, 32 ], [ 42, 2, 18, 16 ], [ 42, 3, 20, 16 ], [ 42, 4, 15, 16 ], [ 43, 2, 41, 16 ], [ 43, 3, 31, 16 ], [ 43, 4, 38, 16 ], [ 43, 4, 41, 16 ], [ 43, 5, 30, 16 ], [ 43, 5, 35, 16 ] ] k = 35: F-action on Pi is () [43,1,35] 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+2*q-2 ) 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+2*q-2 ) 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+2*q-2 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 ( q^3-3*q^2+2*q-2 ) 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+2*q-2 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 ( q^3-3*q^2+2*q-2 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 4 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 12, 2, 4, 8 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 20, 1, 3, 16 ], [ 20, 2, 3, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 8 ], [ 23, 2, 2, 4 ], [ 24, 1, 4, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 6, 16 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 6, 8 ], [ 27, 2, 7, 4 ], [ 27, 3, 4, 8 ], [ 27, 3, 13, 8 ], [ 30, 1, 7, 16 ], [ 30, 2, 7, 8 ], [ 31, 1, 3, 8 ], [ 31, 1, 8, 8 ], [ 31, 2, 3, 4 ], [ 31, 2, 8, 4 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 34, 1, 5, 8 ], [ 34, 1, 6, 8 ], [ 34, 2, 4, 4 ], [ 34, 2, 8, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 1, 2, 16 ], [ 36, 1, 17, 16 ], [ 36, 2, 2, 8 ], [ 36, 2, 13, 8 ], [ 36, 3, 2, 8 ], [ 36, 3, 13, 8 ], [ 36, 4, 2, 8 ], [ 36, 4, 13, 8 ], [ 36, 5, 2, 8 ], [ 36, 5, 17, 8 ], [ 36, 6, 2, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 10, 8 ], [ 36, 6, 11, 8 ], [ 37, 1, 10, 16 ], [ 37, 2, 10, 8 ], [ 38, 1, 11, 16 ], [ 38, 1, 15, 16 ], [ 38, 2, 11, 8 ], [ 38, 2, 15, 8 ], [ 38, 3, 13, 8 ], [ 38, 3, 16, 8 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 16 ], [ 39, 2, 9, 8 ], [ 39, 2, 17, 8 ], [ 39, 3, 9, 8 ], [ 39, 3, 17, 8 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 8 ], [ 39, 5, 10, 8 ], [ 39, 5, 16, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 1, 9, 16 ], [ 41, 1, 18, 32 ], [ 41, 2, 9, 8 ], [ 41, 2, 18, 16 ], [ 41, 3, 9, 8 ], [ 41, 3, 18, 16 ], [ 41, 4, 18, 16 ], [ 41, 4, 21, 16 ], [ 41, 5, 16, 16 ], [ 41, 5, 18, 16 ], [ 41, 6, 16, 16 ], [ 41, 6, 18, 16 ], [ 41, 7, 16, 16 ], [ 41, 7, 18, 16 ], [ 42, 1, 13, 32 ], [ 42, 2, 14, 16 ], [ 42, 3, 15, 16 ], [ 42, 4, 16, 16 ], [ 43, 2, 42, 16 ], [ 43, 3, 33, 16 ], [ 43, 4, 15, 16 ], [ 43, 4, 48, 16 ], [ 43, 5, 6, 16 ], [ 43, 5, 15, 16 ] ] k = 36: F-action on Pi is () [43,1,36] 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+q^2+4*q+6 ) 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+q^2+4*q+6 ) 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+q^2+4*q+6 ) q congruent 7 modulo 12: 1/32 phi1 phi2 ( q^4-4*q^3+q^2+4*q+6 ) 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+q^2+4*q+6 ) q congruent 11 modulo 12: 1/32 phi1 phi2 ( q^4-4*q^3+q^2+4*q+6 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 3, 4 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 12, 2, 2, 8 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 20, 1, 4, 16 ], [ 20, 2, 4, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 1, 3, 8 ], [ 23, 2, 3, 4 ], [ 24, 1, 2, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 4, 16 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 4, 8 ], [ 27, 2, 7, 4 ], [ 27, 3, 3, 8 ], [ 27, 3, 14, 8 ], [ 30, 1, 3, 16 ], [ 30, 2, 3, 8 ], [ 31, 1, 2, 8 ], [ 31, 1, 5, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 5, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 8, 8 ], [ 34, 1, 7, 8 ], [ 34, 1, 8, 8 ], [ 34, 2, 3, 4 ], [ 34, 2, 5, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 8, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 1, 5, 16 ], [ 36, 1, 10, 16 ], [ 36, 2, 5, 8 ], [ 36, 2, 16, 8 ], [ 36, 3, 5, 8 ], [ 36, 3, 16, 8 ], [ 36, 4, 5, 8 ], [ 36, 4, 16, 8 ], [ 36, 5, 5, 8 ], [ 36, 5, 10, 8 ], [ 36, 6, 6, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 14, 8 ], [ 36, 6, 15, 8 ], [ 37, 1, 4, 16 ], [ 37, 2, 4, 8 ], [ 38, 1, 9, 16 ], [ 38, 1, 14, 16 ], [ 38, 2, 9, 8 ], [ 38, 2, 14, 8 ], [ 38, 3, 9, 8 ], [ 38, 3, 12, 8 ], [ 39, 1, 6, 16 ], [ 39, 1, 14, 16 ], [ 39, 2, 6, 8 ], [ 39, 2, 14, 8 ], [ 39, 3, 6, 8 ], [ 39, 3, 14, 8 ], [ 39, 4, 4, 8 ], [ 39, 4, 14, 8 ], [ 39, 5, 4, 8 ], [ 39, 5, 14, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 12, 32 ], [ 41, 2, 4, 8 ], [ 41, 2, 12, 16 ], [ 41, 3, 4, 8 ], [ 41, 3, 12, 16 ], [ 41, 4, 6, 16 ], [ 41, 4, 8, 16 ], [ 41, 5, 6, 16 ], [ 41, 5, 11, 16 ], [ 41, 6, 6, 16 ], [ 41, 6, 11, 16 ], [ 41, 7, 6, 16 ], [ 41, 7, 11, 16 ], [ 42, 1, 15, 32 ], [ 42, 2, 7, 16 ], [ 42, 3, 9, 16 ], [ 42, 4, 14, 16 ], [ 43, 2, 40, 16 ], [ 43, 3, 32, 16 ], [ 43, 4, 12, 16 ], [ 43, 4, 30, 16 ], [ 43, 5, 28, 16 ], [ 43, 5, 32, 16 ] ] 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+11*q^3+43*q^2+112*q-574 ) 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 ( q^6-10*q^5+20*q^4+32*q^3+69*q^2-622*q+462 ) 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+11*q^3+43*q^2+112*q-510 ) q congruent 7 modulo 12: 1/384 ( q^6-10*q^5+20*q^4+32*q^3+69*q^2-686*q+526 ) 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+11*q^3+43*q^2+112*q-510 ) q congruent 11 modulo 12: 1/384 ( q^6-10*q^5+20*q^4+32*q^3+69*q^2-622*q+462 ) 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 ], [ 4, 2, 1, 12 ], [ 4, 2, 2, 12 ], [ 4, 2, 3, 8 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 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 ], [ 12, 2, 2, 32 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 3, 48 ], [ 15, 1, 4, 48 ], [ 15, 2, 3, 24 ], [ 15, 2, 4, 24 ], [ 15, 3, 3, 24 ], [ 15, 3, 4, 24 ], [ 15, 4, 3, 24 ], [ 15, 4, 4, 24 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 36 ], [ 17, 1, 2, 48 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 18 ], [ 17, 2, 2, 24 ], [ 17, 2, 3, 18 ], [ 18, 1, 2, 24 ], [ 18, 1, 3, 24 ], [ 18, 2, 2, 12 ], [ 18, 2, 3, 12 ], [ 20, 1, 4, 64 ], [ 20, 2, 4, 32 ], [ 21, 1, 1, 48 ], [ 21, 1, 2, 96 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 48 ], [ 22, 1, 3, 72 ], [ 23, 1, 3, 48 ], [ 23, 2, 3, 24 ], [ 24, 1, 2, 48 ], [ 25, 1, 5, 96 ], [ 25, 1, 6, 96 ], [ 25, 1, 7, 96 ], [ 25, 1, 8, 96 ], [ 25, 2, 5, 48 ], [ 25, 2, 6, 48 ], [ 25, 2, 7, 48 ], [ 25, 2, 8, 48 ], [ 25, 3, 5, 48 ], [ 25, 3, 6, 48 ], [ 25, 3, 7, 48 ], [ 25, 3, 8, 48 ], [ 25, 4, 5, 48 ], [ 25, 4, 6, 48 ], [ 25, 4, 7, 48 ], [ 25, 4, 8, 48 ], [ 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 ], [ 27, 2, 1, 48 ], [ 27, 2, 2, 48 ], [ 27, 2, 4, 48 ], [ 27, 2, 8, 72 ], [ 27, 2, 12, 48 ], [ 27, 3, 1, 48 ], [ 27, 3, 3, 48 ], [ 27, 3, 5, 72 ], [ 27, 3, 9, 72 ], [ 27, 3, 11, 48 ], [ 27, 3, 14, 48 ], [ 30, 1, 2, 96 ], [ 30, 1, 3, 192 ], [ 30, 2, 2, 48 ], [ 30, 2, 3, 96 ], [ 31, 1, 2, 48 ], [ 31, 1, 4, 96 ], [ 31, 1, 5, 144 ], [ 31, 2, 2, 24 ], [ 31, 2, 4, 48 ], [ 31, 2, 5, 72 ], [ 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 ], [ 34, 2, 2, 24 ], [ 34, 2, 3, 48 ], [ 34, 2, 10, 24 ], [ 34, 3, 2, 24 ], [ 34, 3, 3, 48 ], [ 34, 3, 5, 24 ], [ 34, 3, 8, 48 ], [ 35, 1, 3, 96 ], [ 35, 1, 5, 96 ], [ 35, 2, 3, 48 ], [ 35, 2, 5, 48 ], [ 36, 1, 4, 192 ], [ 36, 1, 5, 192 ], [ 36, 1, 20, 192 ], [ 36, 2, 4, 96 ], [ 36, 2, 5, 96 ], [ 36, 2, 14, 96 ], [ 36, 2, 25, 96 ], [ 36, 3, 4, 96 ], [ 36, 3, 5, 96 ], [ 36, 3, 14, 96 ], [ 36, 3, 25, 96 ], [ 36, 4, 4, 96 ], [ 36, 4, 5, 96 ], [ 36, 4, 14, 96 ], [ 36, 4, 25, 96 ], [ 36, 5, 4, 96 ], [ 36, 5, 5, 96 ], [ 36, 5, 20, 96 ], [ 36, 6, 5, 96 ], [ 36, 6, 6, 96 ], [ 36, 6, 8, 96 ], [ 36, 6, 13, 96 ], [ 36, 6, 14, 96 ], [ 36, 6, 15, 96 ], [ 37, 1, 5, 192 ], [ 37, 2, 5, 96 ], [ 38, 1, 2, 96 ], [ 38, 1, 3, 288 ], [ 38, 1, 5, 192 ], [ 38, 1, 9, 192 ], [ 38, 2, 2, 48 ], [ 38, 2, 3, 144 ], [ 38, 2, 5, 96 ], [ 38, 2, 9, 96 ], [ 38, 3, 2, 48 ], [ 38, 3, 3, 144 ], [ 38, 3, 8, 96 ], [ 38, 3, 9, 96 ], [ 38, 3, 12, 96 ], [ 39, 1, 4, 192 ], [ 39, 1, 13, 192 ], [ 39, 2, 4, 96 ], [ 39, 2, 13, 96 ], [ 39, 3, 4, 96 ], [ 39, 3, 13, 96 ], [ 39, 4, 3, 96 ], [ 39, 4, 5, 96 ], [ 39, 4, 12, 96 ], [ 39, 4, 13, 96 ], [ 39, 5, 3, 96 ], [ 39, 5, 5, 96 ], [ 39, 5, 12, 96 ], [ 39, 5, 13, 96 ], [ 40, 1, 3, 192 ], [ 40, 2, 16, 96 ], [ 40, 3, 2, 96 ], [ 40, 3, 17, 96 ], [ 41, 1, 5, 192 ], [ 41, 1, 10, 384 ], [ 41, 2, 5, 96 ], [ 41, 2, 10, 192 ], [ 41, 3, 5, 96 ], [ 41, 3, 10, 192 ], [ 41, 4, 3, 96 ], [ 41, 4, 5, 192 ], [ 41, 4, 9, 192 ], [ 41, 4, 14, 192 ], [ 41, 5, 4, 192 ], [ 41, 5, 10, 192 ], [ 41, 6, 4, 192 ], [ 41, 6, 10, 192 ], [ 41, 7, 4, 192 ], [ 41, 7, 10, 192 ], [ 42, 1, 19, 384 ], [ 42, 2, 6, 192 ], [ 42, 2, 10, 192 ], [ 42, 3, 10, 192 ], [ 42, 4, 19, 192 ], [ 43, 2, 36, 192 ], [ 43, 3, 37, 192 ], [ 43, 4, 10, 192 ], [ 43, 4, 31, 192 ], [ 43, 5, 8, 192 ], [ 43, 5, 27, 192 ], [ 43, 5, 37, 192 ] ] j = 5: Omega of order 2, action on Pi: <()> k = 1: F-action on Pi is () [43,5,1] Dynkin type is (A_1(q) + T(phi1^6)).2 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^3-25*q^2+199*q-559 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 ( q^3-25*q^2+187*q-363 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 7 modulo 12: 1/192 ( q^3-25*q^2+187*q-427 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 11 modulo 12: 1/192 ( q^3-25*q^2+187*q-363 ) 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, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 4, 2, 1, 20 ], [ 5, 2, 1, 4 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 12, 2, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 2, 1, 24 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 17, 2, 1, 42 ], [ 18, 2, 1, 12 ], [ 20, 2, 1, 32 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 23, 2, 1, 24 ], [ 25, 2, 1, 48 ], [ 25, 3, 1, 48 ], [ 25, 4, 1, 48 ], [ 26, 1, 1, 24 ], [ 27, 1, 1, 96 ], [ 27, 2, 1, 48 ], [ 27, 3, 1, 96 ], [ 30, 2, 1, 96 ], [ 31, 2, 1, 72 ], [ 32, 1, 1, 48 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 48 ], [ 36, 5, 1, 96 ], [ 36, 6, 1, 96 ], [ 38, 2, 1, 144 ], [ 38, 3, 1, 96 ], [ 39, 4, 1, 96 ], [ 39, 5, 1, 96 ], [ 41, 4, 1, 192 ], [ 42, 2, 1, 192 ] ] k = 2: F-action on Pi is () [43,5,2] Dynkin type is (A_1(q) + T(phi1^5 phi2)).2 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^2-12*q+35 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1 ( q^2-12*q+35 ) q congruent 7 modulo 12: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1 ( q^2-12*q+35 ) q congruent 11 modulo 12: 1/64 ( q^3-13*q^2+51*q-63 ) 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, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 4, 2, 1, 12 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 15, 2, 3, 8 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 8 ], [ 18, 2, 2, 4 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 25, 2, 5, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 24 ], [ 27, 1, 1, 96 ], [ 27, 2, 1, 48 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 16 ], [ 30, 2, 2, 32 ], [ 31, 2, 2, 24 ], [ 32, 1, 1, 48 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 16 ], [ 36, 5, 4, 32 ], [ 36, 6, 5, 32 ], [ 38, 2, 2, 48 ], [ 38, 3, 2, 32 ], [ 39, 4, 7, 32 ], [ 39, 5, 2, 32 ], [ 39, 5, 7, 32 ], [ 41, 4, 2, 64 ], [ 41, 4, 16, 64 ], [ 42, 2, 2, 64 ] ] k = 3: F-action on Pi is () [43,5,3] Dynkin type is (A_1(q) + T(phi1^3 phi2 phi4)).2 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 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 ] 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, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 32, 1, 2, 8 ], [ 34, 2, 8, 4 ], [ 36, 5, 17, 8 ], [ 38, 2, 13, 8 ], [ 39, 5, 10, 8 ], [ 39, 5, 16, 8 ], [ 41, 4, 18, 16 ], [ 42, 2, 3, 16 ] ] k = 4: F-action on Pi is () [43,5,4] Dynkin type is (A_1(q) + T(phi1^4 phi2^2)).2 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^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 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: 0 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: [ 4, 35 ] 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, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 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, 2, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 6 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 20, 2, 1, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 2, 1, 4 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 27, 3, 1, 8 ], [ 27, 3, 16, 8 ], [ 30, 2, 1, 8 ], [ 30, 2, 4, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 6, 4 ], [ 32, 1, 2, 8 ], [ 34, 2, 4, 4 ], [ 34, 3, 1, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 6, 4 ], [ 34, 3, 7, 4 ], [ 36, 5, 2, 8 ], [ 36, 6, 1, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 9, 8 ], [ 36, 6, 11, 8 ], [ 38, 2, 10, 8 ], [ 38, 3, 1, 8 ], [ 38, 3, 4, 8 ], [ 38, 3, 10, 8 ], [ 38, 3, 11, 8 ], [ 39, 4, 9, 8 ], [ 39, 4, 17, 8 ], [ 39, 5, 9, 8 ], [ 39, 5, 17, 8 ], [ 41, 4, 19, 16 ], [ 42, 2, 4, 16 ] ] k = 5: F-action on Pi is () [43,5,5] Dynkin type is (A_1(q) + T(phi1^4 phi2^2)).2 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^2-12*q+35 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1 ( q^2-12*q+35 ) q congruent 7 modulo 12: 1/64 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1 ( q^2-12*q+35 ) q congruent 11 modulo 12: 1/64 ( q^3-13*q^2+51*q-63 ) 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, 8 ], [ 4, 1, 1, 24 ], [ 4, 2, 1, 12 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 15, 2, 2, 8 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 17, 2, 1, 18 ], [ 17, 2, 4, 8 ], [ 18, 2, 4, 4 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 25, 2, 2, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 3, 16 ], [ 26, 1, 1, 24 ], [ 27, 1, 1, 96 ], [ 27, 2, 1, 48 ], [ 27, 3, 1, 48 ], [ 27, 3, 16, 16 ], [ 30, 2, 4, 32 ], [ 31, 2, 6, 24 ], [ 32, 1, 1, 48 ], [ 34, 2, 9, 8 ], [ 34, 3, 7, 16 ], [ 36, 5, 18, 32 ], [ 36, 6, 4, 32 ], [ 38, 2, 4, 48 ], [ 38, 3, 11, 32 ], [ 39, 4, 18, 32 ], [ 39, 5, 6, 32 ], [ 39, 5, 8, 32 ], [ 41, 4, 15, 64 ], [ 41, 4, 22, 64 ], [ 42, 2, 5, 64 ] ] k = 6: F-action on Pi is () [43,5,6] Dynkin type is (A_1(q) + T(phi1^2 phi2^2 phi4)).2 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: [ 13, 40 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 23, 2, 2, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 31, 2, 3, 4 ], [ 31, 2, 8, 4 ], [ 32, 1, 4, 8 ], [ 34, 2, 4, 4 ], [ 36, 5, 2, 8 ], [ 38, 2, 15, 8 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 8 ], [ 41, 4, 21, 16 ] ] k = 7: F-action on Pi is () [43,5,7] Dynkin type is (A_1(q) + T(phi1 phi2 phi4^2)).2 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: [ 42, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 27, 3, 3, 8 ], [ 27, 3, 10, 8 ], [ 32, 1, 4, 8 ], [ 34, 2, 8, 4 ], [ 36, 5, 17, 8 ], [ 38, 2, 11, 8 ], [ 41, 4, 20, 16 ] ] k = 8: F-action on Pi is () [43,5,8] Dynkin type is (A_1(q) + T(phi1^3 phi2^3)).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: [ 33, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 4, 2, 3, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 15, 2, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 12 ], [ 18, 2, 2, 4 ], [ 22, 1, 3, 8 ], [ 25, 2, 7, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 6, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ], [ 27, 2, 8, 16 ], [ 27, 2, 12, 16 ], [ 27, 3, 3, 32 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 11, 16 ], [ 27, 3, 14, 16 ], [ 31, 2, 2, 8 ], [ 31, 2, 4, 16 ], [ 32, 1, 3, 16 ], [ 34, 2, 2, 8 ], [ 34, 3, 3, 16 ], [ 36, 5, 4, 32 ], [ 36, 6, 15, 32 ], [ 38, 2, 2, 16 ], [ 38, 2, 5, 32 ], [ 38, 3, 9, 32 ], [ 39, 4, 5, 32 ], [ 39, 5, 12, 32 ], [ 41, 4, 3, 32 ], [ 41, 4, 9, 64 ] ] k = 9: F-action on Pi is () [43,5,9] Dynkin type is (A_1(q) + T(phi1^2 phi2^4)).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, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 15, 2, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 18, 2, 4, 4 ], [ 22, 1, 3, 8 ], [ 25, 3, 4, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ], [ 27, 2, 8, 16 ], [ 27, 2, 12, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 7, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 11, 16 ], [ 31, 2, 6, 8 ], [ 31, 2, 8, 16 ], [ 32, 1, 3, 16 ], [ 34, 2, 9, 8 ], [ 36, 5, 18, 32 ], [ 38, 2, 4, 16 ], [ 38, 2, 6, 32 ], [ 39, 4, 19, 16 ], [ 39, 5, 11, 16 ], [ 41, 4, 10, 32 ], [ 41, 4, 12, 16 ], [ 41, 4, 23, 32 ] ] k = 10: F-action on Pi is () [43,5,10] Dynkin type is (A_1(q) + T(phi1^4 phi2^2)).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 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 5, 2, 1, 4 ], [ 6, 2, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 14, 2, 1, 16 ], [ 15, 2, 1, 24 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 17, 2, 4, 8 ], [ 18, 2, 1, 12 ], [ 22, 1, 3, 8 ], [ 23, 2, 1, 8 ], [ 23, 2, 2, 16 ], [ 25, 2, 3, 16 ], [ 25, 3, 1, 48 ], [ 25, 4, 2, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ], [ 27, 2, 8, 16 ], [ 27, 2, 12, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 11, 16 ], [ 27, 3, 16, 16 ], [ 31, 2, 1, 24 ], [ 31, 2, 3, 48 ], [ 32, 1, 3, 16 ], [ 34, 2, 1, 24 ], [ 34, 3, 4, 16 ], [ 36, 5, 1, 96 ], [ 36, 6, 11, 32 ], [ 38, 2, 1, 48 ], [ 38, 2, 8, 96 ], [ 38, 3, 10, 32 ], [ 39, 4, 2, 32 ], [ 39, 4, 8, 32 ], [ 39, 5, 18, 32 ], [ 41, 4, 4, 64 ], [ 41, 4, 24, 64 ] ] k = 11: F-action on Pi is () [43,5,11] Dynkin type is (A_1(q) + T(phi1^3 phi2^3)).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: [ 35, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 15, 2, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 18, 2, 2, 4 ], [ 22, 1, 3, 8 ], [ 25, 3, 5, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ], [ 27, 2, 8, 16 ], [ 27, 2, 12, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 10, 16 ], [ 27, 3, 11, 16 ], [ 31, 2, 2, 8 ], [ 31, 2, 4, 16 ], [ 32, 1, 3, 16 ], [ 34, 2, 2, 8 ], [ 36, 5, 4, 32 ], [ 38, 2, 2, 16 ], [ 38, 2, 5, 32 ], [ 39, 4, 6, 16 ], [ 39, 5, 19, 16 ], [ 41, 4, 3, 16 ], [ 41, 4, 11, 32 ], [ 41, 4, 25, 32 ] ] k = 12: F-action on Pi is () [43,5,12] Dynkin type is (A_1(q) + T(phi1^3 phi2^3)).2 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: [ 35, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 4, 2, 4, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 15, 2, 2, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 6 ], [ 17, 2, 4, 8 ], [ 18, 2, 4, 4 ], [ 22, 1, 2, 8 ], [ 25, 2, 2, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 3, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 4, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 13, 32 ], [ 31, 2, 6, 16 ], [ 31, 2, 8, 8 ], [ 32, 1, 6, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 7, 16 ], [ 36, 5, 18, 32 ], [ 36, 6, 4, 32 ], [ 38, 2, 4, 32 ], [ 38, 2, 6, 16 ], [ 38, 3, 13, 32 ], [ 39, 4, 18, 32 ], [ 39, 5, 8, 32 ], [ 41, 4, 12, 32 ], [ 41, 4, 22, 64 ] ] k = 13: F-action on Pi is () [43,5,13] Dynkin type is (A_1(q) + T(phi1^4 phi2^2)).2 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: [ 4, 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 15, 2, 3, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 6 ], [ 18, 2, 2, 4 ], [ 22, 1, 2, 8 ], [ 25, 3, 5, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 15, 16 ], [ 31, 2, 2, 16 ], [ 31, 2, 4, 8 ], [ 32, 1, 6, 16 ], [ 34, 2, 2, 8 ], [ 36, 5, 4, 32 ], [ 38, 2, 2, 32 ], [ 38, 2, 5, 16 ], [ 39, 4, 6, 16 ], [ 39, 5, 2, 16 ], [ 41, 4, 2, 32 ], [ 41, 4, 3, 16 ], [ 41, 4, 11, 32 ] ] k = 14: F-action on Pi is () [43,5,14] Dynkin type is (A_1(q) + T(phi1^3 phi2^3)).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 ( 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: [ 35, 3 ] 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, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 4 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 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, 2, 4, 8 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 20, 2, 3, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 2, 2, 4 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 27, 3, 4, 8 ], [ 27, 3, 9, 8 ], [ 30, 2, 6, 8 ], [ 30, 2, 7, 8 ], [ 31, 2, 3, 4 ], [ 31, 2, 8, 4 ], [ 32, 1, 5, 8 ], [ 34, 2, 4, 4 ], [ 34, 3, 1, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 6, 4 ], [ 34, 3, 7, 4 ], [ 36, 5, 2, 8 ], [ 36, 6, 1, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 9, 8 ], [ 36, 6, 11, 8 ], [ 38, 2, 15, 8 ], [ 38, 3, 6, 8 ], [ 38, 3, 7, 8 ], [ 38, 3, 13, 8 ], [ 38, 3, 16, 8 ], [ 39, 4, 9, 8 ], [ 39, 4, 17, 8 ], [ 39, 5, 9, 8 ], [ 39, 5, 17, 8 ], [ 41, 4, 19, 16 ], [ 42, 2, 13, 16 ] ] k = 15: F-action on Pi is () [43,5,15] Dynkin type is (A_1(q) + T(phi1^2 phi2^2 phi4)).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 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, 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, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 3, 2 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 32, 1, 5, 8 ], [ 34, 2, 8, 4 ], [ 36, 5, 17, 8 ], [ 38, 2, 11, 8 ], [ 39, 5, 10, 8 ], [ 39, 5, 16, 8 ], [ 41, 4, 18, 16 ], [ 42, 2, 14, 16 ] ] k = 16: F-action on Pi is () [43,5,16] Dynkin type is (A_1(q) + T(phi1^5 phi2)).2 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 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 5, 2, 1, 4 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 14, 2, 1, 16 ], [ 15, 2, 1, 24 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 20 ], [ 17, 2, 3, 6 ], [ 18, 2, 1, 12 ], [ 22, 1, 2, 8 ], [ 23, 2, 1, 16 ], [ 23, 2, 2, 8 ], [ 25, 2, 1, 16 ], [ 25, 3, 1, 48 ], [ 25, 4, 1, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 32 ], [ 31, 2, 1, 48 ], [ 31, 2, 3, 24 ], [ 32, 1, 6, 16 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 16 ], [ 36, 5, 1, 96 ], [ 36, 6, 1, 32 ], [ 38, 2, 1, 96 ], [ 38, 2, 8, 48 ], [ 38, 3, 7, 32 ], [ 39, 4, 1, 32 ], [ 39, 4, 2, 32 ], [ 39, 5, 1, 32 ], [ 41, 4, 1, 64 ], [ 41, 4, 4, 64 ] ] k = 17: F-action on Pi is () [43,5,17] Dynkin type is (A_1(q) + T(phi1 phi2^5)).2 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 phi1^2 ( 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: [ 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 ], [ 4, 2, 2, 12 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 15, 2, 2, 8 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 8 ], [ 17, 2, 3, 18 ], [ 18, 2, 4, 4 ], [ 21, 1, 6, 48 ], [ 22, 1, 4, 24 ], [ 25, 2, 4, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 4, 16 ], [ 26, 1, 3, 24 ], [ 27, 1, 12, 96 ], [ 27, 2, 12, 48 ], [ 27, 3, 9, 16 ], [ 27, 3, 11, 48 ], [ 30, 2, 6, 32 ], [ 31, 2, 8, 24 ], [ 32, 1, 7, 48 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 16 ], [ 36, 5, 18, 32 ], [ 36, 6, 9, 32 ], [ 38, 2, 6, 48 ], [ 38, 3, 6, 32 ], [ 39, 4, 20, 32 ], [ 39, 5, 11, 32 ], [ 39, 5, 20, 32 ], [ 41, 4, 10, 64 ], [ 41, 4, 26, 64 ], [ 42, 2, 11, 64 ] ] k = 18: F-action on Pi is () [43,5,18] Dynkin type is (A_1(q) + T(phi1^2 phi2^4)).2 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 phi1^2 ( 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: [ 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 24 ], [ 4, 2, 2, 12 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 15, 2, 3, 8 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 36 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 18 ], [ 18, 2, 2, 4 ], [ 21, 1, 6, 48 ], [ 22, 1, 4, 24 ], [ 25, 2, 7, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 6, 16 ], [ 26, 1, 3, 24 ], [ 27, 1, 12, 96 ], [ 27, 2, 12, 48 ], [ 27, 3, 8, 16 ], [ 27, 3, 11, 48 ], [ 30, 2, 8, 32 ], [ 31, 2, 4, 24 ], [ 32, 1, 7, 48 ], [ 34, 2, 2, 8 ], [ 34, 3, 3, 16 ], [ 36, 5, 4, 32 ], [ 36, 6, 15, 32 ], [ 38, 2, 5, 48 ], [ 38, 3, 15, 32 ], [ 39, 4, 5, 32 ], [ 39, 5, 12, 32 ], [ 39, 5, 19, 32 ], [ 41, 4, 9, 64 ], [ 41, 4, 25, 64 ], [ 42, 2, 12, 64 ] ] k = 19: F-action on Pi is () [43,5,19] Dynkin type is (A_1(q) + T(phi1^3 phi2^3)).2 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^2-18*q+81 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 ( q^3-19*q^2+99*q-145 ) q congruent 7 modulo 12: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1 ( q^2-18*q+81 ) q congruent 11 modulo 12: 1/192 ( q^3-19*q^2+111*q-253 ) 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, 2, 24 ], [ 4, 2, 2, 12 ], [ 4, 2, 4, 8 ], [ 5, 2, 1, 4 ], [ 6, 2, 1, 4 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 12, 2, 4, 32 ], [ 14, 2, 1, 16 ], [ 15, 2, 1, 24 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 36 ], [ 17, 2, 3, 18 ], [ 17, 2, 4, 24 ], [ 18, 2, 1, 12 ], [ 20, 2, 3, 32 ], [ 21, 1, 6, 48 ], [ 22, 1, 4, 24 ], [ 23, 2, 2, 24 ], [ 25, 2, 3, 48 ], [ 25, 3, 1, 48 ], [ 25, 4, 2, 48 ], [ 26, 1, 3, 24 ], [ 27, 1, 12, 96 ], [ 27, 2, 12, 48 ], [ 27, 3, 4, 48 ], [ 27, 3, 11, 48 ], [ 30, 2, 7, 96 ], [ 31, 2, 3, 72 ], [ 32, 1, 7, 48 ], [ 34, 2, 1, 24 ], [ 34, 3, 4, 48 ], [ 36, 5, 1, 96 ], [ 36, 6, 11, 96 ], [ 38, 2, 8, 144 ], [ 38, 3, 16, 96 ], [ 39, 4, 8, 96 ], [ 39, 5, 18, 96 ], [ 41, 4, 24, 192 ], [ 42, 2, 15, 192 ] ] k = 20: F-action on Pi is () [43,5,20] Dynkin type is (A_1(q) + T(phi1^3 phi2 phi4)).2 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 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 23, 2, 1, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 31, 2, 1, 4 ], [ 31, 2, 6, 4 ], [ 32, 1, 8, 8 ], [ 34, 2, 4, 4 ], [ 36, 5, 2, 8 ], [ 38, 2, 10, 8 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 8 ], [ 41, 4, 21, 16 ] ] k = 21: F-action on Pi is () [43,5,21] Dynkin type is (A_1(q) + T(phi1^2 phi4^2)).2 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: [ 9, 42 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 27, 3, 2, 8 ], [ 27, 3, 15, 8 ], [ 32, 1, 8, 8 ], [ 34, 2, 8, 4 ], [ 36, 5, 17, 8 ], [ 38, 2, 13, 8 ], [ 41, 4, 20, 16 ] ] k = 22: F-action on Pi is () [43,5,22] Dynkin type is (A_1(q) + T(phi1^3 phi2^3)).2 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, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 15, 2, 2, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 6 ], [ 18, 2, 4, 4 ], [ 22, 1, 2, 8 ], [ 25, 3, 4, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 6, 16 ], [ 27, 3, 9, 16 ], [ 31, 2, 6, 16 ], [ 31, 2, 8, 8 ], [ 32, 1, 6, 16 ], [ 34, 2, 9, 8 ], [ 36, 5, 18, 32 ], [ 38, 2, 4, 32 ], [ 38, 2, 6, 16 ], [ 39, 4, 19, 16 ], [ 39, 5, 6, 16 ], [ 41, 4, 12, 16 ], [ 41, 4, 15, 32 ], [ 41, 4, 23, 32 ] ] k = 23: F-action on Pi is () [43,5,23] Dynkin type is (A_1(q) + T(phi1^4 phi2^2)).2 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: [ 4, 33 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 15, 2, 3, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 14 ], [ 18, 2, 2, 4 ], [ 22, 1, 2, 8 ], [ 25, 2, 5, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 2, 32 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 11, 16 ], [ 31, 2, 2, 16 ], [ 31, 2, 4, 8 ], [ 32, 1, 6, 16 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 16 ], [ 36, 5, 4, 32 ], [ 36, 6, 5, 32 ], [ 38, 2, 2, 32 ], [ 38, 2, 5, 16 ], [ 38, 3, 8, 32 ], [ 39, 4, 7, 32 ], [ 39, 5, 7, 32 ], [ 41, 4, 3, 32 ], [ 41, 4, 16, 64 ] ] k = 24: F-action on Pi is () [43,5,24] Dynkin type is (A_1(q) + T(phi1^2 phi2^4)).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, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 8 ], [ 4, 2, 1, 8 ], [ 4, 2, 2, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 15, 2, 2, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 14 ], [ 17, 2, 3, 12 ], [ 18, 2, 4, 4 ], [ 22, 1, 3, 8 ], [ 25, 2, 4, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 4, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ], [ 27, 2, 8, 16 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 9, 16 ], [ 27, 3, 11, 16 ], [ 27, 3, 12, 32 ], [ 31, 2, 6, 8 ], [ 31, 2, 8, 16 ], [ 32, 1, 3, 16 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 16 ], [ 36, 5, 18, 32 ], [ 36, 6, 9, 32 ], [ 38, 2, 4, 16 ], [ 38, 2, 6, 32 ], [ 38, 3, 4, 32 ], [ 39, 4, 20, 32 ], [ 39, 5, 20, 32 ], [ 41, 4, 12, 32 ], [ 41, 4, 26, 64 ] ] k = 25: F-action on Pi is () [43,5,25] Dynkin type is (A_1(q) + T(phi1 phi2 phi3 phi6)).2 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 phi1 ( q^2-2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 12: 1/6 q phi2 ( q-2 ) 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, 2, 3, 2 ], [ 5, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 2 ], [ 12, 2, 2, 2 ], [ 14, 2, 2, 1 ], [ 20, 2, 4, 2 ], [ 21, 1, 5, 6 ], [ 32, 1, 9, 6 ], [ 34, 2, 6, 3 ], [ 36, 5, 7, 3 ], [ 42, 2, 8, 6 ] ] k = 26: F-action on Pi is () [43,5,26] Dynkin type is (A_1(q) + T(phi1^2 phi3^2)).2 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 phi1 ( q^2-2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 12: 1/6 q phi2 ( q-2 ) 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, 2 ], [ 4, 2, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 11, 1, 1, 2 ], [ 12, 2, 1, 2 ], [ 14, 2, 1, 1 ], [ 20, 2, 1, 2 ], [ 21, 1, 5, 6 ], [ 32, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 36, 5, 9, 3 ], [ 42, 2, 9, 6 ] ] k = 27: F-action on Pi is () [43,5,27] Dynkin type is (A_1(q) + T(phi1^3 phi2^3)).2 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^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 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: 0 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: [ 33, 5 ] 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, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 3, 4 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 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, 2, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 20, 2, 4, 8 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 23, 2, 3, 4 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 27, 3, 5, 8 ], [ 27, 3, 14, 8 ], [ 30, 2, 2, 8 ], [ 30, 2, 3, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 5, 4 ], [ 32, 1, 2, 8 ], [ 34, 2, 3, 4 ], [ 34, 3, 2, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 5, 4 ], [ 34, 3, 8, 4 ], [ 36, 5, 5, 8 ], [ 36, 6, 5, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 13, 8 ], [ 36, 6, 15, 8 ], [ 38, 2, 9, 8 ], [ 38, 3, 2, 8 ], [ 38, 3, 3, 8 ], [ 38, 3, 9, 8 ], [ 38, 3, 12, 8 ], [ 39, 4, 3, 8 ], [ 39, 4, 13, 8 ], [ 39, 5, 3, 8 ], [ 39, 5, 13, 8 ], [ 41, 4, 5, 16 ], [ 42, 2, 6, 16 ] ] k = 28: F-action on Pi is () [43,5,28] Dynkin type is (A_1(q) + T(phi1^2 phi2^2 phi4)).2 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 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: [ 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, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 32, 1, 2, 8 ], [ 34, 2, 5, 4 ], [ 36, 5, 10, 8 ], [ 38, 2, 14, 8 ], [ 39, 5, 4, 8 ], [ 39, 5, 14, 8 ], [ 41, 4, 6, 16 ], [ 42, 2, 7, 16 ] ] k = 29: F-action on Pi is () [43,5,29] Dynkin type is (A_1(q) + T(phi2^2 phi4^2)).2 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, 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 27, 3, 7, 8 ], [ 27, 3, 12, 8 ], [ 32, 1, 4, 8 ], [ 34, 2, 5, 4 ], [ 36, 5, 10, 8 ], [ 38, 2, 12, 8 ], [ 41, 4, 7, 16 ] ] k = 30: F-action on Pi is () [43,5,30] Dynkin type is (A_1(q) + T(phi1 phi2^3 phi4)).2 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: [ 43, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 23, 2, 4, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 31, 2, 4, 4 ], [ 31, 2, 7, 4 ], [ 32, 1, 4, 8 ], [ 34, 2, 3, 4 ], [ 36, 5, 5, 8 ], [ 38, 2, 16, 8 ], [ 39, 4, 4, 8 ], [ 39, 4, 14, 8 ], [ 41, 4, 8, 16 ] ] k = 31: F-action on Pi is () [43,5,31] Dynkin type is (A_1(q) + T(phi1 phi2 phi4^2)).2 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, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 27, 3, 6, 8 ], [ 27, 3, 13, 8 ], [ 32, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 36, 5, 10, 8 ], [ 38, 2, 14, 8 ], [ 41, 4, 7, 16 ] ] k = 32: F-action on Pi is () [43,5,32] Dynkin type is (A_1(q) + T(phi1^2 phi2^2 phi4)).2 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: [ 10, 43 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 23, 2, 3, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 2, 7, 4 ], [ 31, 2, 2, 4 ], [ 31, 2, 5, 4 ], [ 32, 1, 8, 8 ], [ 34, 2, 3, 4 ], [ 36, 5, 5, 8 ], [ 38, 2, 9, 8 ], [ 39, 4, 4, 8 ], [ 39, 4, 14, 8 ], [ 41, 4, 8, 16 ] ] k = 33: F-action on Pi is () [43,5,33] Dynkin type is (A_1(q) + T(phi2^2 phi6^2)).2 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^2 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q^2 phi1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/6 q^2 phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q^2 phi1 q congruent 11 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) 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, 2 ], [ 4, 2, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 11, 1, 2, 2 ], [ 12, 2, 3, 2 ], [ 14, 2, 2, 1 ], [ 20, 2, 2, 2 ], [ 21, 1, 4, 6 ], [ 32, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 36, 5, 7, 3 ], [ 42, 2, 16, 6 ] ] k = 34: F-action on Pi is () [43,5,34] Dynkin type is (A_1(q) + T(phi1 phi2 phi3 phi6)).2 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^2 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/6 q^2 phi1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/6 q^2 phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/6 q^2 phi1 q congruent 11 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) 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, 2, 4, 2 ], [ 5, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 2 ], [ 12, 2, 4, 2 ], [ 14, 2, 1, 1 ], [ 20, 2, 3, 2 ], [ 21, 1, 4, 6 ], [ 32, 1, 10, 6 ], [ 34, 2, 7, 3 ], [ 36, 5, 9, 3 ], [ 42, 2, 17, 6 ] ] k = 35: F-action on Pi is () [43,5,35] Dynkin type is (A_1(q) + T(phi1 phi2^3 phi4)).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 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: [ 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 3, 2 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 32, 1, 5, 8 ], [ 34, 2, 5, 4 ], [ 36, 5, 10, 8 ], [ 38, 2, 12, 8 ], [ 39, 5, 4, 8 ], [ 39, 5, 14, 8 ], [ 41, 4, 6, 16 ], [ 42, 2, 18, 16 ] ] k = 36: F-action on Pi is () [43,5,36] Dynkin type is (A_1(q) + T(phi1^2 phi2^4)).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 ( 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: [ 5, 34 ] 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, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 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, 2, 3, 8 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 3, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 6 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 20, 2, 2, 8 ], [ 21, 1, 3, 8 ], [ 22, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 23, 2, 4, 4 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 2, 2, 4 ], [ 27, 3, 8, 8 ], [ 27, 3, 11, 8 ], [ 30, 2, 5, 8 ], [ 30, 2, 8, 8 ], [ 31, 2, 4, 4 ], [ 31, 2, 7, 4 ], [ 32, 1, 5, 8 ], [ 34, 2, 3, 4 ], [ 34, 3, 2, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 5, 4 ], [ 34, 3, 8, 4 ], [ 36, 5, 5, 8 ], [ 36, 6, 5, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 13, 8 ], [ 36, 6, 15, 8 ], [ 38, 2, 16, 8 ], [ 38, 3, 5, 8 ], [ 38, 3, 8, 8 ], [ 38, 3, 14, 8 ], [ 38, 3, 15, 8 ], [ 39, 4, 3, 8 ], [ 39, 4, 13, 8 ], [ 39, 5, 3, 8 ], [ 39, 5, 13, 8 ], [ 41, 4, 5, 16 ], [ 42, 2, 19, 16 ] ] k = 37: F-action on Pi is () [43,5,37] Dynkin type is (A_1(q) + T(phi1^3 phi2^3)).2 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^3-25*q^2+199*q-559 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 ( q^3-25*q^2+187*q-363 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 7 modulo 12: 1/192 ( q^3-25*q^2+187*q-427 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 ( q^3-25*q^2+199*q-495 ) q congruent 11 modulo 12: 1/192 ( q^3-25*q^2+187*q-363 ) 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, 2, 1, 12 ], [ 4, 2, 3, 8 ], [ 5, 2, 2, 4 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 12, 2, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 2, 4, 24 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 36 ], [ 17, 2, 1, 18 ], [ 17, 2, 2, 24 ], [ 18, 2, 3, 12 ], [ 20, 2, 4, 32 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 23, 2, 3, 24 ], [ 25, 2, 6, 48 ], [ 25, 3, 8, 48 ], [ 25, 4, 7, 48 ], [ 26, 1, 1, 24 ], [ 27, 1, 1, 96 ], [ 27, 2, 1, 48 ], [ 27, 3, 1, 48 ], [ 27, 3, 14, 48 ], [ 30, 2, 3, 96 ], [ 31, 2, 5, 72 ], [ 32, 1, 1, 48 ], [ 34, 2, 10, 24 ], [ 34, 3, 8, 48 ], [ 36, 5, 20, 96 ], [ 36, 6, 8, 96 ], [ 38, 2, 3, 144 ], [ 38, 3, 12, 96 ], [ 39, 4, 12, 96 ], [ 39, 5, 5, 96 ], [ 41, 4, 14, 192 ], [ 42, 2, 10, 192 ] ] k = 38: F-action on Pi is () [43,5,38] Dynkin type is (A_1(q) + T(phi1 phi2^5)).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: [ 34, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 5, 2, 2, 4 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 4, 16 ], [ 14, 2, 2, 16 ], [ 15, 2, 4, 24 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 20 ], [ 18, 2, 3, 12 ], [ 22, 1, 3, 8 ], [ 23, 2, 3, 8 ], [ 23, 2, 4, 16 ], [ 25, 2, 8, 16 ], [ 25, 3, 8, 48 ], [ 25, 4, 8, 16 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 8, 32 ], [ 27, 1, 12, 32 ], [ 27, 2, 8, 16 ], [ 27, 2, 12, 16 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 16 ], [ 27, 3, 11, 16 ], [ 31, 2, 5, 24 ], [ 31, 2, 7, 48 ], [ 32, 1, 3, 16 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 16 ], [ 36, 5, 20, 96 ], [ 36, 6, 13, 32 ], [ 38, 2, 3, 48 ], [ 38, 2, 7, 96 ], [ 38, 3, 3, 32 ], [ 39, 4, 11, 32 ], [ 39, 4, 15, 32 ], [ 39, 5, 15, 32 ], [ 41, 4, 13, 64 ], [ 41, 4, 17, 64 ] ] k = 39: F-action on Pi is () [43,5,39] Dynkin type is (A_1(q) + T(phi1^2 phi2^4)).2 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: [ 5, 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 5, 2, 2, 4 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 1, 16 ], [ 14, 2, 2, 16 ], [ 15, 2, 4, 24 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 6 ], [ 18, 2, 3, 12 ], [ 22, 1, 2, 8 ], [ 23, 2, 3, 16 ], [ 23, 2, 4, 8 ], [ 25, 2, 6, 16 ], [ 25, 3, 8, 48 ], [ 25, 4, 7, 16 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 27, 1, 1, 32 ], [ 27, 1, 8, 32 ], [ 27, 2, 1, 16 ], [ 27, 2, 8, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 16 ], [ 27, 3, 8, 16 ], [ 27, 3, 9, 16 ], [ 31, 2, 5, 48 ], [ 31, 2, 7, 24 ], [ 32, 1, 6, 16 ], [ 34, 2, 10, 24 ], [ 34, 3, 8, 16 ], [ 36, 5, 20, 96 ], [ 36, 6, 8, 32 ], [ 38, 2, 3, 96 ], [ 38, 2, 7, 48 ], [ 38, 3, 14, 32 ], [ 39, 4, 11, 32 ], [ 39, 4, 12, 32 ], [ 39, 5, 5, 32 ], [ 41, 4, 13, 64 ], [ 41, 4, 14, 64 ] ] k = 40: F-action on Pi is () [43,5,40] Dynkin type is (A_1(q) + T(phi2^6)).2 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^2-18*q+81 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 ( q^3-19*q^2+99*q-145 ) q congruent 7 modulo 12: 1/192 ( q^3-19*q^2+111*q-189 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1 ( q^2-18*q+81 ) q congruent 11 modulo 12: 1/192 ( q^3-19*q^2+111*q-253 ) 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, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 24 ], [ 4, 2, 2, 20 ], [ 5, 2, 2, 4 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 12, 2, 3, 32 ], [ 14, 2, 2, 16 ], [ 15, 2, 4, 24 ], [ 16, 1, 2, 6 ], [ 17, 1, 3, 36 ], [ 17, 2, 3, 42 ], [ 18, 2, 3, 12 ], [ 20, 2, 2, 32 ], [ 21, 1, 6, 48 ], [ 22, 1, 4, 24 ], [ 23, 2, 4, 24 ], [ 25, 2, 8, 48 ], [ 25, 3, 8, 48 ], [ 25, 4, 8, 48 ], [ 26, 1, 3, 24 ], [ 27, 1, 12, 96 ], [ 27, 2, 12, 48 ], [ 27, 3, 11, 96 ], [ 30, 2, 5, 96 ], [ 31, 2, 7, 72 ], [ 32, 1, 7, 48 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 48 ], [ 36, 5, 20, 96 ], [ 36, 6, 13, 96 ], [ 38, 2, 7, 144 ], [ 38, 3, 5, 96 ], [ 39, 4, 15, 96 ], [ 39, 5, 15, 96 ], [ 41, 4, 17, 192 ], [ 42, 2, 20, 192 ] ] 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 ], [ 4, 2, 1, 1260 ], [ 5, 1, 1, 72 ], [ 5, 2, 1, 36 ], [ 6, 1, 1, 56 ], [ 6, 2, 1, 28 ], [ 7, 1, 1, 756 ], [ 8, 1, 1, 4032 ], [ 9, 1, 1, 10080 ], [ 10, 1, 1, 15120 ], [ 11, 1, 1, 2016 ], [ 12, 1, 1, 13440 ], [ 12, 2, 1, 6720 ], [ 13, 1, 1, 576 ], [ 14, 1, 1, 2016 ], [ 14, 2, 1, 1008 ], [ 15, 1, 1, 5040 ], [ 15, 2, 1, 2520 ], [ 15, 3, 1, 2520 ], [ 15, 4, 1, 2520 ], [ 16, 1, 1, 126 ], [ 17, 1, 1, 3780 ], [ 17, 2, 1, 1890 ], [ 18, 1, 1, 1512 ], [ 18, 2, 1, 756 ], [ 19, 1, 1, 12096 ], [ 20, 1, 1, 40320 ], [ 20, 2, 1, 20160 ], [ 21, 1, 1, 60480 ], [ 22, 1, 1, 30240 ], [ 23, 1, 1, 4032 ], [ 23, 2, 1, 2016 ], [ 24, 1, 1, 20160 ], [ 25, 1, 1, 30240 ], [ 25, 2, 1, 15120 ], [ 25, 3, 1, 15120 ], [ 25, 4, 1, 15120 ], [ 26, 1, 1, 7560 ], [ 27, 1, 1, 90720 ], [ 27, 2, 1, 45360 ], [ 27, 3, 1, 45360 ], [ 28, 1, 1, 4032 ], [ 28, 2, 1, 2016 ], [ 29, 1, 1, 24192 ], [ 29, 2, 1, 12096 ], [ 30, 1, 1, 120960 ], [ 30, 2, 1, 60480 ], [ 31, 1, 1, 60480 ], [ 31, 2, 1, 30240 ], [ 32, 1, 1, 181440 ], [ 33, 1, 1, 80640 ], [ 33, 2, 1, 40320 ], [ 33, 3, 1, 40320 ], [ 33, 4, 1, 40320 ], [ 34, 1, 1, 15120 ], [ 34, 2, 1, 7560 ], [ 34, 3, 1, 7560 ], [ 35, 1, 1, 60480 ], [ 35, 2, 1, 30240 ], [ 36, 1, 1, 181440 ], [ 36, 2, 1, 90720 ], [ 36, 3, 1, 90720 ], [ 36, 4, 1, 90720 ], [ 36, 5, 1, 90720 ], [ 36, 6, 1, 90720 ], [ 37, 1, 1, 241920 ], [ 37, 2, 1, 120960 ], [ 38, 1, 1, 362880 ], [ 38, 2, 1, 181440 ], [ 38, 3, 1, 181440 ], [ 39, 1, 1, 120960 ], [ 39, 2, 1, 60480 ], [ 39, 3, 1, 60480 ], [ 39, 4, 1, 60480 ], [ 39, 5, 1, 60480 ], [ 40, 1, 1, 362880 ], [ 40, 2, 1, 181440 ], [ 40, 3, 1, 181440 ], [ 41, 1, 1, 725760 ], [ 41, 2, 1, 362880 ], [ 41, 3, 1, 362880 ], [ 41, 4, 1, 362880 ], [ 41, 5, 1, 362880 ], [ 41, 6, 1, 362880 ], [ 41, 7, 1, 362880 ], [ 42, 1, 1, 483840 ], [ 42, 2, 1, 241920 ], [ 42, 3, 1, 241920 ], [ 42, 4, 1, 241920 ], [ 43, 1, 1, 1451520 ], [ 43, 2, 1, 725760 ], [ 43, 3, 1, 725760 ], [ 43, 4, 1, 725760 ], [ 43, 5, 1, 725760 ], [ 44, 2, 1, 1451520 ], [ 44, 3, 1, 1451520 ], [ 44, 4, 1, 1451520 ], [ 44, 5, 1, 1451520 ], [ 44, 6, 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 ], [ 4, 2, 2, 260 ], [ 5, 1, 2, 32 ], [ 5, 2, 2, 16 ], [ 6, 1, 2, 32 ], [ 6, 2, 2, 16 ], [ 7, 1, 2, 252 ], [ 8, 1, 2, 832 ], [ 9, 1, 2, 1600 ], [ 10, 1, 4, 2160 ], [ 11, 1, 2, 512 ], [ 12, 1, 6, 1920 ], [ 12, 2, 3, 960 ], [ 13, 1, 2, 192 ], [ 14, 1, 2, 512 ], [ 14, 2, 2, 256 ], [ 15, 1, 2, 80 ], [ 15, 1, 4, 960 ], [ 15, 2, 2, 40 ], [ 15, 2, 4, 480 ], [ 15, 3, 2, 40 ], [ 15, 3, 4, 480 ], [ 15, 4, 2, 40 ], [ 15, 4, 4, 480 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 60 ], [ 17, 1, 1, 60 ], [ 17, 1, 3, 840 ], [ 17, 2, 1, 30 ], [ 17, 2, 3, 420 ], [ 18, 1, 3, 480 ], [ 18, 1, 4, 24 ], [ 18, 2, 3, 240 ], [ 18, 2, 4, 12 ], [ 19, 1, 2, 2112 ], [ 20, 1, 2, 4480 ], [ 20, 2, 2, 2240 ], [ 21, 1, 6, 5760 ], [ 22, 1, 3, 480 ], [ 22, 1, 4, 3840 ], [ 23, 1, 3, 64 ], [ 23, 1, 4, 960 ], [ 23, 2, 3, 32 ], [ 23, 2, 4, 480 ], [ 24, 1, 3, 2880 ], [ 24, 1, 4, 320 ], [ 25, 1, 4, 480 ], [ 25, 1, 8, 3840 ], [ 25, 2, 4, 240 ], [ 25, 2, 8, 1920 ], [ 25, 3, 4, 240 ], [ 25, 3, 8, 1920 ], [ 25, 4, 4, 240 ], [ 25, 4, 8, 1920 ], [ 26, 1, 2, 120 ], [ 26, 1, 3, 1560 ], [ 27, 1, 8, 1440 ], [ 27, 1, 12, 7200 ], [ 27, 2, 8, 720 ], [ 27, 2, 12, 3600 ], [ 27, 3, 5, 720 ], [ 27, 3, 9, 720 ], [ 27, 3, 11, 3600 ], [ 28, 1, 2, 64 ], [ 28, 1, 6, 960 ], [ 28, 2, 2, 32 ], [ 28, 2, 6, 480 ], [ 29, 1, 4, 3840 ], [ 29, 1, 5, 384 ], [ 29, 2, 4, 1920 ], [ 29, 2, 5, 192 ], [ 30, 1, 5, 9600 ], [ 30, 1, 6, 1920 ], [ 30, 2, 5, 4800 ], [ 30, 2, 6, 960 ], [ 31, 1, 5, 960 ], [ 31, 1, 7, 6720 ], [ 31, 1, 8, 960 ], [ 31, 2, 5, 480 ], [ 31, 2, 7, 3360 ], [ 31, 2, 8, 480 ], [ 32, 1, 3, 2880 ], [ 32, 1, 7, 11520 ], [ 33, 1, 4, 1280 ], [ 33, 1, 6, 7680 ], [ 33, 2, 4, 640 ], [ 33, 2, 6, 3840 ], [ 33, 3, 4, 640 ], [ 33, 3, 6, 3840 ], [ 33, 4, 4, 640 ], [ 33, 4, 6, 3840 ], [ 34, 1, 3, 240 ], [ 34, 1, 4, 2880 ], [ 34, 2, 9, 120 ], [ 34, 2, 10, 1440 ], [ 34, 3, 5, 1440 ], [ 34, 3, 6, 120 ], [ 35, 1, 4, 960 ], [ 35, 1, 10, 6720 ], [ 35, 2, 4, 480 ], [ 35, 2, 10, 3360 ], [ 36, 1, 18, 2880 ], [ 36, 1, 20, 11520 ], [ 36, 2, 17, 1440 ], [ 36, 2, 23, 1440 ], [ 36, 2, 25, 5760 ], [ 36, 3, 17, 1440 ], [ 36, 3, 23, 1440 ], [ 36, 3, 25, 5760 ], [ 36, 4, 17, 1440 ], [ 36, 4, 23, 1440 ], [ 36, 4, 25, 5760 ], [ 36, 5, 18, 1440 ], [ 36, 5, 20, 5760 ], [ 36, 6, 9, 1440 ], [ 36, 6, 13, 5760 ], [ 37, 1, 6, 15360 ], [ 37, 1, 7, 3840 ], [ 37, 2, 6, 7680 ], [ 37, 2, 7, 1920 ], [ 38, 1, 3, 5760 ], [ 38, 1, 6, 5760 ], [ 38, 1, 7, 17280 ], [ 38, 2, 3, 2880 ], [ 38, 2, 6, 2880 ], [ 38, 2, 7, 8640 ], [ 38, 3, 3, 2880 ], [ 38, 3, 5, 8640 ], [ 38, 3, 6, 2880 ], [ 39, 1, 11, 1920 ], [ 39, 1, 15, 11520 ], [ 39, 1, 20, 1920 ], [ 39, 2, 11, 960 ], [ 39, 2, 15, 5760 ], [ 39, 2, 20, 960 ], [ 39, 3, 11, 960 ], [ 39, 3, 15, 5760 ], [ 39, 3, 20, 960 ], [ 39, 4, 11, 960 ], [ 39, 4, 15, 5760 ], [ 39, 4, 20, 960 ], [ 39, 5, 11, 960 ], [ 39, 5, 15, 5760 ], [ 39, 5, 20, 960 ], [ 40, 1, 2, 17280 ], [ 40, 1, 18, 5760 ], [ 40, 2, 13, 8640 ], [ 40, 2, 23, 2880 ], [ 40, 3, 3, 2880 ], [ 40, 3, 19, 8640 ], [ 41, 1, 6, 11520 ], [ 41, 1, 16, 23040 ], [ 41, 1, 22, 11520 ], [ 41, 2, 6, 5760 ], [ 41, 2, 16, 11520 ], [ 41, 2, 22, 5760 ], [ 41, 3, 6, 5760 ], [ 41, 3, 16, 11520 ], [ 41, 3, 22, 5760 ], [ 41, 4, 10, 5760 ], [ 41, 4, 13, 5760 ], [ 41, 4, 17, 11520 ], [ 41, 4, 26, 5760 ], [ 41, 5, 8, 5760 ], [ 41, 5, 13, 11520 ], [ 41, 5, 20, 5760 ], [ 41, 6, 8, 5760 ], [ 41, 6, 13, 11520 ], [ 41, 6, 20, 5760 ], [ 41, 7, 8, 5760 ], [ 41, 7, 13, 11520 ], [ 41, 7, 20, 5760 ], [ 42, 1, 21, 7680 ], [ 42, 1, 22, 23040 ], [ 42, 2, 11, 3840 ], [ 42, 2, 20, 11520 ], [ 42, 3, 11, 3840 ], [ 42, 3, 16, 11520 ], [ 42, 3, 17, 3840 ], [ 42, 4, 21, 3840 ], [ 42, 4, 22, 11520 ], [ 43, 1, 26, 23040 ], [ 43, 1, 27, 23040 ], [ 43, 2, 22, 11520 ], [ 43, 2, 34, 11520 ], [ 43, 2, 45, 11520 ], [ 43, 3, 26, 11520 ], [ 43, 3, 28, 11520 ], [ 43, 4, 18, 11520 ], [ 43, 4, 32, 11520 ], [ 43, 4, 44, 11520 ], [ 43, 4, 52, 11520 ], [ 43, 5, 17, 11520 ], [ 43, 5, 38, 11520 ], [ 43, 5, 40, 11520 ], [ 44, 2, 49, 23040 ], [ 44, 2, 56, 23040 ], [ 44, 3, 48, 23040 ], [ 44, 3, 82, 23040 ], [ 44, 4, 2, 23040 ], [ 44, 5, 49, 23040 ], [ 44, 5, 81, 23040 ], [ 44, 6, 33, 23040 ], [ 44, 6, 63, 23040 ], [ 44, 6, 87, 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+185*q^2-1731*q+1899 ) 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^5-43*q^4+185*q^3-1916*q^2+3774*q-1179 ) 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^5-43*q^4+185*q^3-1916*q^2+4142*q-3435 ) q congruent 7 modulo 12: 1/9216 ( q^7-14*q^6+56*q^5-43*q^4+185*q^3-1916*q^2+3774*q-1179 ) 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+185*q^2-1731*q+1899 ) q congruent 11 modulo 12: 1/9216 ( q^7-14*q^6+56*q^5-43*q^4+185*q^3-1916*q^2+4286*q-2715 ) 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 ], [ 4, 2, 1, 36 ], [ 4, 2, 2, 24 ], [ 4, 2, 4, 96 ], [ 5, 1, 1, 24 ], [ 5, 2, 1, 12 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 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 ], [ 12, 2, 4, 128 ], [ 14, 1, 1, 96 ], [ 14, 2, 1, 48 ], [ 15, 1, 1, 144 ], [ 15, 1, 2, 96 ], [ 15, 1, 8, 384 ], [ 15, 2, 1, 72 ], [ 15, 2, 2, 48 ], [ 15, 2, 8, 192 ], [ 15, 3, 1, 72 ], [ 15, 3, 2, 48 ], [ 15, 3, 8, 192 ], [ 15, 4, 1, 72 ], [ 15, 4, 2, 48 ], [ 15, 4, 8, 192 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 24 ], [ 17, 1, 1, 84 ], [ 17, 1, 3, 144 ], [ 17, 1, 4, 96 ], [ 17, 2, 1, 42 ], [ 17, 2, 3, 72 ], [ 17, 2, 4, 48 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 48 ], [ 18, 2, 1, 12 ], [ 18, 2, 4, 24 ], [ 20, 1, 3, 768 ], [ 20, 2, 3, 384 ], [ 21, 1, 3, 384 ], [ 21, 1, 6, 192 ], [ 22, 1, 2, 288 ], [ 22, 1, 3, 96 ], [ 22, 1, 4, 288 ], [ 23, 1, 2, 192 ], [ 23, 2, 2, 96 ], [ 24, 1, 4, 192 ], [ 25, 1, 1, 288 ], [ 25, 1, 2, 576 ], [ 25, 1, 3, 192 ], [ 25, 1, 4, 384 ], [ 25, 2, 1, 144 ], [ 25, 2, 2, 288 ], [ 25, 2, 3, 96 ], [ 25, 2, 4, 192 ], [ 25, 3, 1, 144 ], [ 25, 3, 2, 288 ], [ 25, 3, 3, 96 ], [ 25, 3, 4, 192 ], [ 25, 4, 1, 144 ], [ 25, 4, 2, 288 ], [ 25, 4, 3, 96 ], [ 25, 4, 4, 192 ], [ 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 ], [ 27, 2, 1, 144 ], [ 27, 2, 2, 288 ], [ 27, 2, 6, 576 ], [ 27, 2, 8, 288 ], [ 27, 2, 12, 288 ], [ 27, 2, 13, 576 ], [ 27, 3, 1, 144 ], [ 27, 3, 4, 576 ], [ 27, 3, 5, 288 ], [ 27, 3, 9, 288 ], [ 27, 3, 11, 288 ], [ 27, 3, 12, 576 ], [ 27, 3, 13, 576 ], [ 28, 1, 6, 192 ], [ 28, 2, 6, 96 ], [ 30, 1, 6, 384 ], [ 30, 1, 7, 768 ], [ 30, 2, 6, 192 ], [ 30, 2, 7, 384 ], [ 31, 1, 3, 576 ], [ 31, 1, 6, 192 ], [ 31, 1, 8, 576 ], [ 31, 2, 3, 288 ], [ 31, 2, 6, 96 ], [ 31, 2, 8, 288 ], [ 32, 1, 3, 576 ], [ 32, 1, 5, 1152 ], [ 32, 1, 6, 576 ], [ 32, 1, 7, 576 ], [ 33, 1, 9, 1536 ], [ 33, 2, 9, 768 ], [ 33, 3, 9, 768 ], [ 33, 4, 9, 768 ], [ 34, 1, 1, 48 ], [ 34, 1, 3, 288 ], [ 34, 1, 5, 192 ], [ 34, 2, 1, 24 ], [ 34, 2, 4, 96 ], [ 34, 2, 9, 144 ], [ 34, 3, 1, 24 ], [ 34, 3, 4, 96 ], [ 34, 3, 6, 144 ], [ 34, 3, 7, 96 ], [ 35, 1, 3, 192 ], [ 35, 1, 5, 576 ], [ 35, 1, 10, 576 ], [ 35, 2, 3, 96 ], [ 35, 2, 5, 288 ], [ 35, 2, 10, 288 ], [ 36, 1, 1, 576 ], [ 36, 1, 2, 1152 ], [ 36, 1, 15, 2304 ], [ 36, 1, 18, 1152 ], [ 36, 2, 1, 288 ], [ 36, 2, 2, 576 ], [ 36, 2, 12, 1152 ], [ 36, 2, 17, 576 ], [ 36, 2, 23, 576 ], [ 36, 2, 24, 1152 ], [ 36, 3, 1, 288 ], [ 36, 3, 2, 576 ], [ 36, 3, 12, 1152 ], [ 36, 3, 17, 576 ], [ 36, 3, 23, 576 ], [ 36, 3, 24, 1152 ], [ 36, 4, 1, 288 ], [ 36, 4, 2, 576 ], [ 36, 4, 12, 1152 ], [ 36, 4, 17, 576 ], [ 36, 4, 23, 576 ], [ 36, 4, 24, 1152 ], [ 36, 5, 1, 288 ], [ 36, 5, 2, 576 ], [ 36, 5, 15, 1152 ], [ 36, 5, 18, 576 ], [ 36, 6, 1, 288 ], [ 36, 6, 2, 576 ], [ 36, 6, 4, 576 ], [ 36, 6, 9, 576 ], [ 36, 6, 10, 576 ], [ 36, 6, 11, 576 ], [ 36, 6, 12, 1152 ], [ 37, 1, 9, 768 ], [ 37, 2, 9, 384 ], [ 38, 1, 4, 1152 ], [ 38, 1, 6, 1152 ], [ 38, 1, 8, 1152 ], [ 38, 1, 15, 2304 ], [ 38, 2, 4, 576 ], [ 38, 2, 6, 576 ], [ 38, 2, 8, 576 ], [ 38, 2, 15, 1152 ], [ 38, 3, 4, 576 ], [ 38, 3, 6, 576 ], [ 38, 3, 7, 576 ], [ 38, 3, 13, 1152 ], [ 38, 3, 16, 1152 ], [ 39, 1, 10, 1152 ], [ 39, 1, 18, 384 ], [ 39, 1, 20, 1152 ], [ 39, 2, 10, 576 ], [ 39, 2, 18, 192 ], [ 39, 2, 20, 576 ], [ 39, 3, 10, 576 ], [ 39, 3, 18, 192 ], [ 39, 3, 20, 576 ], [ 39, 4, 8, 576 ], [ 39, 4, 9, 576 ], [ 39, 4, 17, 192 ], [ 39, 4, 18, 192 ], [ 39, 4, 20, 576 ], [ 39, 5, 8, 576 ], [ 39, 5, 9, 576 ], [ 39, 5, 17, 192 ], [ 39, 5, 18, 192 ], [ 39, 5, 20, 576 ], [ 40, 1, 2, 1152 ], [ 40, 1, 3, 1152 ], [ 40, 1, 13, 2304 ], [ 40, 2, 13, 576 ], [ 40, 2, 16, 576 ], [ 40, 2, 24, 1152 ], [ 40, 3, 2, 576 ], [ 40, 3, 17, 576 ], [ 40, 3, 18, 1152 ], [ 40, 3, 19, 576 ], [ 40, 3, 20, 1152 ], [ 41, 1, 7, 2304 ], [ 41, 1, 19, 2304 ], [ 41, 1, 22, 2304 ], [ 41, 1, 40, 4608 ], [ 41, 2, 7, 1152 ], [ 41, 2, 19, 1152 ], [ 41, 2, 22, 1152 ], [ 41, 2, 40, 2304 ], [ 41, 3, 7, 1152 ], [ 41, 3, 19, 1152 ], [ 41, 3, 22, 1152 ], [ 41, 3, 40, 2304 ], [ 41, 4, 12, 1152 ], [ 41, 4, 19, 1152 ], [ 41, 4, 22, 1152 ], [ 41, 4, 24, 1152 ], [ 41, 4, 26, 1152 ], [ 41, 4, 47, 2304 ], [ 41, 4, 50, 2304 ], [ 41, 5, 14, 1152 ], [ 41, 5, 19, 1152 ], [ 41, 5, 20, 1152 ], [ 41, 5, 39, 2304 ], [ 41, 5, 40, 2304 ], [ 41, 6, 14, 1152 ], [ 41, 6, 19, 1152 ], [ 41, 6, 20, 1152 ], [ 41, 6, 39, 2304 ], [ 41, 6, 40, 2304 ], [ 41, 7, 14, 1152 ], [ 41, 7, 19, 1152 ], [ 41, 7, 20, 1152 ], [ 41, 7, 39, 2304 ], [ 41, 7, 40, 2304 ], [ 42, 1, 20, 1536 ], [ 42, 2, 13, 768 ], [ 42, 2, 15, 768 ], [ 42, 3, 14, 768 ], [ 42, 4, 18, 768 ], [ 43, 1, 16, 4608 ], [ 43, 1, 31, 4608 ], [ 43, 2, 12, 2304 ], [ 43, 2, 23, 2304 ], [ 43, 2, 46, 2304 ], [ 43, 2, 52, 2304 ], [ 43, 3, 16, 2304 ], [ 43, 3, 34, 2304 ], [ 43, 4, 16, 2304 ], [ 43, 4, 26, 2304 ], [ 43, 4, 33, 2304 ], [ 43, 4, 49, 2304 ], [ 43, 5, 12, 2304 ], [ 43, 5, 14, 2304 ], [ 43, 5, 19, 2304 ], [ 43, 5, 24, 2304 ], [ 44, 2, 30, 4608 ], [ 44, 2, 74, 4608 ], [ 44, 3, 32, 4608 ], [ 44, 3, 66, 4608 ], [ 44, 3, 88, 4608 ], [ 44, 4, 3, 4608 ], [ 44, 5, 32, 4608 ], [ 44, 5, 68, 4608 ], [ 44, 5, 86, 4608 ], [ 44, 6, 22, 4608 ], [ 44, 6, 64, 4608 ], [ 44, 6, 93, 4608 ], [ 44, 6, 98, 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^4-224*q^3+225*q^2-703*q+1515 ) 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 ( q^7-18*q^6+116*q^5-323*q^4+449*q^3-928*q^2+2362*q-1947 ) 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^4-224*q^3+225*q^2-703*q+1515 ) q congruent 7 modulo 12: 1/3072 ( q^7-18*q^6+116*q^5-323*q^4+449*q^3-928*q^2+2362*q-1947 ) 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^4-224*q^3+225*q^2-703*q+1515 ) q congruent 11 modulo 12: 1/3072 ( q^7-18*q^6+116*q^5-323*q^4+449*q^3-928*q^2+2362*q-1947 ) 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 ], [ 4, 2, 1, 72 ], [ 4, 2, 2, 12 ], [ 5, 1, 1, 16 ], [ 5, 2, 1, 8 ], [ 6, 1, 1, 16 ], [ 6, 2, 1, 8 ], [ 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 ], [ 12, 2, 1, 192 ], [ 13, 1, 1, 64 ], [ 14, 1, 1, 128 ], [ 14, 2, 1, 64 ], [ 15, 1, 1, 224 ], [ 15, 1, 2, 48 ], [ 15, 1, 3, 64 ], [ 15, 2, 1, 112 ], [ 15, 2, 2, 24 ], [ 15, 2, 3, 32 ], [ 15, 3, 1, 112 ], [ 15, 3, 2, 24 ], [ 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41, 3, 11, 384 ], [ 41, 3, 15, 768 ], [ 41, 3, 19, 384 ], [ 41, 3, 36, 768 ], [ 41, 4, 1, 384 ], [ 41, 4, 2, 768 ], [ 41, 4, 3, 384 ], [ 41, 4, 4, 768 ], [ 41, 4, 11, 384 ], [ 41, 4, 15, 384 ], [ 41, 4, 16, 768 ], [ 41, 4, 19, 384 ], [ 41, 4, 22, 384 ], [ 41, 4, 24, 384 ], [ 41, 4, 41, 768 ], [ 41, 4, 44, 768 ], [ 41, 5, 1, 384 ], [ 41, 5, 2, 768 ], [ 41, 5, 5, 384 ], [ 41, 5, 12, 768 ], [ 41, 5, 14, 384 ], [ 41, 5, 19, 384 ], [ 41, 5, 33, 768 ], [ 41, 5, 35, 768 ], [ 41, 6, 1, 384 ], [ 41, 6, 2, 768 ], [ 41, 6, 5, 384 ], [ 41, 6, 12, 768 ], [ 41, 6, 14, 384 ], [ 41, 6, 19, 384 ], [ 41, 6, 33, 768 ], [ 41, 6, 35, 768 ], [ 41, 7, 1, 384 ], [ 41, 7, 2, 768 ], [ 41, 7, 5, 384 ], [ 41, 7, 12, 768 ], [ 41, 7, 14, 384 ], [ 41, 7, 19, 384 ], [ 41, 7, 33, 768 ], [ 41, 7, 35, 768 ], [ 42, 1, 12, 512 ], [ 42, 1, 18, 1536 ], [ 42, 2, 2, 768 ], [ 42, 2, 4, 256 ], [ 42, 2, 5, 256 ], [ 42, 3, 2, 768 ], [ 42, 3, 5, 256 ], [ 42, 3, 6, 768 ], [ 42, 3, 7, 256 ], [ 42, 4, 12, 256 ], [ 42, 4, 20, 768 ], [ 43, 1, 22, 1536 ], [ 43, 1, 28, 1536 ], [ 43, 1, 32, 1536 ], [ 43, 2, 18, 768 ], [ 43, 2, 27, 768 ], [ 43, 2, 35, 768 ], [ 43, 2, 38, 768 ], [ 43, 2, 43, 768 ], [ 43, 2, 49, 768 ], [ 43, 2, 50, 768 ], [ 43, 3, 22, 768 ], [ 43, 3, 27, 768 ], [ 43, 3, 29, 768 ], [ 43, 4, 2, 768 ], [ 43, 4, 5, 768 ], [ 43, 4, 11, 768 ], [ 43, 4, 17, 768 ], [ 43, 4, 19, 768 ], [ 43, 4, 23, 768 ], [ 43, 4, 27, 768 ], [ 43, 4, 28, 768 ], [ 43, 4, 43, 768 ], [ 43, 5, 2, 768 ], [ 43, 5, 4, 768 ], [ 43, 5, 5, 768 ], [ 43, 5, 10, 768 ], [ 43, 5, 13, 768 ], [ 43, 5, 16, 768 ], [ 43, 5, 23, 768 ], [ 44, 2, 42, 1536 ], [ 44, 2, 54, 1536 ], [ 44, 2, 57, 1536 ], [ 44, 3, 41, 1536 ], [ 44, 3, 53, 1536 ], [ 44, 3, 79, 1536 ], [ 44, 3, 87, 1536 ], [ 44, 4, 4, 1536 ], [ 44, 5, 42, 1536 ], [ 44, 5, 53, 1536 ], [ 44, 5, 80, 1536 ], [ 44, 5, 85, 1536 ], [ 44, 6, 34, 1536 ], [ 44, 6, 45, 1536 ], [ 44, 6, 60, 1536 ], [ 44, 6, 71, 1536 ], [ 44, 6, 91, 1536 ], [ 44, 6, 99, 1536 ], [ 44, 6, 103, 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 ( q^5-4*q^4-9*q^3+7*q^2+128*q-75 ) 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 ( q^7-6*q^6+21*q^4+105*q^3-324*q^2+230*q-123 ) 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 ( q^5-4*q^4-9*q^3+7*q^2+128*q-75 ) q congruent 7 modulo 12: 1/768 ( q^7-6*q^6+21*q^4+105*q^3-324*q^2+230*q-123 ) 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 ( q^5-4*q^4-9*q^3+7*q^2+128*q-75 ) q congruent 11 modulo 12: 1/768 ( q^7-6*q^6+21*q^4+105*q^3-324*q^2+230*q-123 ) 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 ], [ 4, 2, 1, 12 ], [ 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39, 3, 13, 96 ], [ 39, 3, 19, 96 ], [ 39, 4, 3, 96 ], [ 39, 4, 5, 96 ], [ 39, 4, 6, 48 ], [ 39, 4, 11, 48 ], [ 39, 4, 12, 96 ], [ 39, 4, 13, 96 ], [ 39, 4, 19, 96 ], [ 39, 5, 3, 96 ], [ 39, 5, 5, 96 ], [ 39, 5, 6, 48 ], [ 39, 5, 11, 48 ], [ 39, 5, 12, 96 ], [ 39, 5, 13, 96 ], [ 39, 5, 19, 96 ], [ 40, 1, 3, 192 ], [ 40, 1, 17, 96 ], [ 40, 1, 18, 288 ], [ 40, 1, 22, 192 ], [ 40, 2, 16, 96 ], [ 40, 2, 22, 48 ], [ 40, 2, 23, 144 ], [ 40, 2, 25, 96 ], [ 40, 3, 2, 96 ], [ 40, 3, 3, 144 ], [ 40, 3, 4, 48 ], [ 40, 3, 7, 96 ], [ 40, 3, 8, 96 ], [ 40, 3, 17, 96 ], [ 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 ], [ 41, 2, 5, 96 ], [ 41, 2, 6, 96 ], [ 41, 2, 7, 96 ], [ 41, 2, 10, 192 ], [ 41, 2, 11, 96 ], [ 41, 2, 20, 192 ], [ 41, 2, 24, 192 ], [ 41, 3, 5, 96 ], [ 41, 3, 6, 96 ], [ 41, 3, 7, 96 ], [ 41, 3, 10, 192 ], [ 41, 3, 11, 96 ], [ 41, 3, 20, 192 ], [ 41, 3, 24, 192 ], [ 41, 4, 3, 96 ], [ 41, 4, 5, 192 ], [ 41, 4, 9, 192 ], [ 41, 4, 10, 96 ], [ 41, 4, 11, 96 ], [ 41, 4, 12, 96 ], [ 41, 4, 13, 96 ], [ 41, 4, 14, 192 ], [ 41, 4, 15, 96 ], [ 41, 4, 23, 192 ], [ 41, 4, 25, 192 ], [ 41, 4, 28, 192 ], [ 41, 4, 34, 192 ], [ 41, 5, 4, 192 ], [ 41, 5, 5, 96 ], [ 41, 5, 8, 96 ], [ 41, 5, 10, 192 ], [ 41, 5, 15, 192 ], [ 41, 5, 22, 192 ], [ 41, 5, 26, 192 ], [ 41, 6, 4, 192 ], [ 41, 6, 5, 96 ], [ 41, 6, 8, 96 ], [ 41, 6, 10, 192 ], [ 41, 6, 15, 192 ], [ 41, 6, 22, 192 ], [ 41, 6, 26, 192 ], [ 41, 7, 4, 192 ], [ 41, 7, 5, 96 ], [ 41, 7, 8, 96 ], [ 41, 7, 10, 192 ], [ 41, 7, 15, 192 ], [ 41, 7, 22, 192 ], [ 41, 7, 26, 192 ], [ 42, 1, 17, 384 ], [ 42, 1, 19, 384 ], [ 42, 2, 6, 192 ], [ 42, 2, 10, 192 ], [ 42, 2, 12, 192 ], [ 42, 2, 19, 192 ], [ 42, 3, 10, 192 ], [ 42, 3, 12, 192 ], [ 42, 3, 19, 192 ], [ 42, 4, 17, 192 ], [ 42, 4, 19, 192 ], [ 43, 1, 29, 384 ], [ 43, 1, 30, 384 ], [ 43, 1, 37, 384 ], [ 43, 2, 36, 192 ], [ 43, 2, 37, 192 ], [ 43, 2, 44, 192 ], [ 43, 2, 47, 192 ], [ 43, 2, 48, 192 ], [ 43, 2, 51, 192 ], [ 43, 2, 53, 192 ], [ 43, 3, 35, 192 ], [ 43, 3, 36, 192 ], [ 43, 3, 37, 192 ], [ 43, 4, 6, 192 ], [ 43, 4, 7, 192 ], [ 43, 4, 10, 192 ], [ 43, 4, 24, 192 ], [ 43, 4, 31, 192 ], [ 43, 4, 36, 192 ], [ 43, 4, 37, 192 ], [ 43, 4, 42, 192 ], [ 43, 4, 45, 192 ], [ 43, 4, 50, 192 ], [ 43, 5, 8, 192 ], [ 43, 5, 9, 192 ], [ 43, 5, 11, 192 ], [ 43, 5, 18, 192 ], [ 43, 5, 22, 192 ], [ 43, 5, 27, 192 ], [ 43, 5, 36, 192 ], [ 43, 5, 37, 192 ], [ 43, 5, 39, 192 ], [ 44, 2, 67, 384 ], [ 44, 2, 69, 384 ], [ 44, 2, 70, 384 ], [ 44, 3, 77, 384 ], [ 44, 3, 78, 384 ], [ 44, 3, 84, 384 ], [ 44, 3, 89, 384 ], [ 44, 4, 5, 384 ], [ 44, 5, 75, 384 ], [ 44, 5, 83, 384 ], [ 44, 5, 84, 384 ], [ 44, 5, 90, 384 ], [ 44, 6, 80, 384 ], [ 44, 6, 85, 384 ], [ 44, 6, 88, 384 ], [ 44, 6, 89, 384 ], [ 44, 6, 96, 384 ], [ 44, 6, 102, 384 ], [ 44, 6, 106, 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 ], [ 4, 2, 1, 30 ], [ 5, 1, 1, 12 ], [ 5, 2, 1, 6 ], [ 6, 1, 1, 20 ], [ 6, 2, 1, 10 ], [ 7, 1, 1, 90 ], [ 8, 1, 1, 132 ], [ 9, 1, 1, 150 ], [ 10, 1, 1, 180 ], [ 11, 1, 1, 120 ], [ 12, 1, 1, 120 ], [ 12, 2, 1, 60 ], [ 13, 1, 1, 60 ], [ 14, 1, 1, 120 ], [ 14, 2, 1, 60 ], [ 15, 1, 1, 120 ], [ 15, 2, 1, 60 ], [ 15, 3, 1, 60 ], [ 15, 4, 1, 60 ], [ 16, 1, 1, 30 ], [ 17, 1, 1, 180 ], [ 17, 2, 1, 90 ], [ 18, 1, 1, 180 ], [ 18, 2, 1, 90 ], [ 19, 1, 1, 360 ], [ 20, 1, 1, 240 ], [ 20, 2, 1, 120 ], [ 21, 1, 1, 180 ], [ 22, 1, 1, 360 ], [ 23, 1, 1, 240 ], [ 23, 2, 1, 120 ], [ 24, 1, 1, 300 ], [ 25, 1, 1, 360 ], [ 25, 2, 1, 180 ], [ 25, 3, 1, 180 ], [ 25, 4, 1, 180 ], [ 26, 1, 1, 360 ], [ 28, 1, 1, 240 ], [ 28, 1, 5, 6 ], [ 28, 2, 1, 120 ], [ 28, 2, 3, 3 ], [ 29, 1, 1, 720 ], [ 29, 1, 3, 36 ], [ 29, 2, 1, 360 ], [ 29, 2, 3, 18 ], [ 30, 1, 1, 360 ], [ 30, 2, 1, 180 ], [ 31, 1, 1, 720 ], [ 31, 2, 1, 360 ], [ 33, 1, 1, 480 ], [ 33, 1, 2, 120 ], [ 33, 2, 1, 240 ], [ 33, 2, 2, 60 ], [ 33, 3, 1, 240 ], [ 33, 3, 2, 60 ], [ 33, 4, 1, 240 ], [ 33, 4, 2, 60 ], [ 34, 1, 1, 720 ], [ 34, 2, 1, 360 ], [ 34, 3, 1, 360 ], [ 35, 1, 1, 720 ], [ 35, 1, 8, 90 ], [ 35, 2, 1, 360 ], [ 35, 2, 8, 45 ], [ 37, 1, 1, 720 ], [ 37, 1, 3, 360 ], [ 37, 2, 1, 360 ], [ 37, 2, 3, 180 ], [ 39, 1, 1, 1440 ], [ 39, 1, 3, 180 ], [ 39, 2, 1, 720 ], [ 39, 2, 3, 90 ], [ 39, 3, 1, 720 ], [ 39, 3, 3, 90 ], [ 39, 4, 1, 720 ], [ 39, 5, 1, 720 ], [ 40, 1, 7, 540 ], [ 40, 2, 2, 270 ], [ 40, 3, 10, 270 ], [ 41, 1, 3, 1080 ], [ 41, 2, 3, 540 ], [ 41, 3, 3, 540 ], [ 41, 5, 3, 540 ], [ 41, 6, 3, 540 ], [ 41, 7, 3, 540 ], [ 42, 1, 1, 1440 ], [ 42, 1, 4, 720 ], [ 42, 2, 1, 720 ], [ 42, 3, 1, 720 ], [ 42, 3, 3, 360 ], [ 42, 4, 1, 720 ], [ 42, 4, 4, 360 ], [ 43, 1, 4, 2160 ], [ 43, 2, 2, 1080 ], [ 43, 3, 4, 1080 ], [ 43, 4, 3, 1080 ], [ 44, 2, 6, 2160 ], [ 44, 3, 2, 2160 ], [ 44, 4, 6, 2160 ], [ 44, 5, 2, 2160 ], [ 44, 6, 2, 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 ], [ 6, 2, 1, 1 ], [ 12, 1, 1, 48 ], [ 12, 2, 1, 24 ], [ 21, 1, 5, 216 ], [ 28, 1, 5, 72 ], [ 28, 2, 3, 36 ], [ 33, 1, 2, 144 ], [ 33, 2, 2, 72 ], [ 33, 3, 2, 72 ], [ 33, 4, 2, 72 ], [ 34, 1, 9, 54 ], [ 34, 2, 7, 27 ], [ 40, 1, 9, 648 ], [ 40, 2, 4, 324 ], [ 42, 1, 5, 432 ], [ 42, 2, 9, 216 ], [ 42, 4, 5, 216 ], [ 44, 3, 4, 648 ], [ 44, 4, 7, 648 ], [ 44, 5, 4, 648 ] ] 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 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 6 ], [ 5, 2, 1, 3 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 12 ], [ 11, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 12, 1, 3, 36 ], [ 12, 2, 1, 6 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 3 ], [ 15, 1, 1, 24 ], [ 15, 2, 1, 12 ], [ 15, 3, 1, 12 ], [ 15, 4, 1, 12 ], [ 16, 1, 1, 6 ], [ 20, 1, 1, 12 ], [ 20, 2, 1, 6 ], [ 21, 1, 5, 18 ], [ 23, 1, 1, 12 ], [ 23, 2, 1, 6 ], [ 24, 1, 1, 24 ], [ 28, 1, 1, 12 ], [ 28, 1, 5, 12 ], [ 28, 2, 1, 6 ], [ 28, 2, 3, 6 ], [ 29, 1, 3, 36 ], [ 29, 2, 3, 18 ], [ 32, 1, 9, 54 ], [ 33, 1, 1, 24 ], [ 33, 1, 2, 24 ], [ 33, 2, 1, 12 ], [ 33, 2, 2, 12 ], [ 33, 3, 1, 12 ], [ 33, 3, 2, 12 ], [ 33, 4, 1, 12 ], [ 33, 4, 2, 12 ], [ 34, 1, 9, 18 ], [ 34, 2, 7, 9 ], [ 35, 1, 8, 36 ], [ 35, 2, 8, 18 ], [ 36, 1, 9, 54 ], [ 36, 5, 9, 27 ], [ 37, 1, 3, 36 ], [ 37, 2, 3, 18 ], [ 38, 1, 20, 108 ], [ 38, 2, 20, 54 ], [ 39, 1, 3, 72 ], [ 39, 2, 3, 36 ], [ 39, 3, 3, 36 ], [ 40, 1, 4, 108 ], [ 40, 2, 3, 54 ], [ 42, 1, 4, 72 ], [ 42, 1, 5, 36 ], [ 42, 2, 9, 18 ], [ 42, 3, 3, 36 ], [ 42, 4, 4, 36 ], [ 42, 4, 5, 18 ], [ 43, 1, 5, 108 ], [ 43, 3, 5, 54 ], [ 43, 5, 26, 54 ], [ 44, 2, 7, 108 ], [ 44, 3, 3, 108 ], [ 44, 4, 8, 108 ], [ 44, 5, 3, 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+3*q^2-18*q+27 ) 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+3*q^2-18*q+27 ) 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+3*q^2-18*q+27 ) q congruent 7 modulo 12: 1/768 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-18*q+27 ) 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+3*q^2-18*q+27 ) q congruent 11 modulo 12: 1/768 phi1 phi2 ( q^5-6*q^4+9*q^3+3*q^2-18*q+27 ) 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 ], [ 4, 2, 2, 12 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 10, 1, 3, 48 ], [ 15, 1, 2, 48 ], [ 15, 2, 2, 24 ], [ 15, 3, 2, 24 ], [ 15, 4, 2, 24 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 4, 12 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 25, 1, 3, 96 ], [ 25, 2, 3, 48 ], [ 25, 3, 3, 48 ], [ 25, 4, 3, 48 ], [ 26, 1, 1, 24 ], [ 26, 1, 5, 24 ], [ 27, 1, 3, 96 ], [ 27, 1, 7, 48 ], [ 27, 1, 14, 96 ], [ 27, 2, 3, 48 ], [ 27, 2, 7, 24 ], [ 27, 2, 14, 48 ], [ 27, 3, 2, 48 ], [ 27, 3, 15, 48 ], [ 27, 3, 16, 48 ], [ 32, 1, 8, 96 ], [ 34, 1, 1, 48 ], [ 34, 1, 6, 48 ], [ 34, 2, 1, 24 ], [ 34, 2, 8, 24 ], [ 34, 3, 1, 24 ], [ 35, 1, 7, 96 ], [ 35, 2, 7, 48 ], [ 36, 1, 3, 192 ], [ 36, 1, 17, 96 ], [ 36, 2, 3, 96 ], [ 36, 2, 13, 48 ], [ 36, 2, 27, 96 ], [ 36, 3, 3, 96 ], [ 36, 3, 13, 48 ], [ 36, 3, 27, 96 ], [ 36, 4, 3, 96 ], [ 36, 4, 13, 48 ], [ 36, 4, 27, 96 ], [ 36, 5, 3, 96 ], [ 36, 5, 17, 48 ], [ 36, 6, 3, 96 ], [ 38, 1, 13, 192 ], [ 38, 2, 13, 96 ], [ 39, 1, 17, 192 ], [ 39, 2, 17, 96 ], [ 39, 3, 17, 96 ], [ 39, 4, 16, 96 ], [ 39, 5, 16, 96 ], [ 40, 1, 6, 96 ], [ 40, 1, 23, 192 ], [ 40, 2, 14, 48 ], [ 40, 2, 17, 96 ], [ 40, 3, 16, 96 ], [ 41, 1, 21, 192 ], [ 41, 1, 34, 384 ], [ 41, 2, 21, 96 ], [ 41, 2, 34, 192 ], [ 41, 3, 21, 96 ], [ 41, 3, 34, 192 ], [ 41, 4, 20, 96 ], [ 41, 4, 40, 192 ], [ 41, 4, 43, 192 ], [ 41, 5, 32, 192 ], [ 41, 6, 32, 192 ], [ 41, 7, 32, 192 ], [ 43, 1, 19, 384 ], [ 43, 2, 13, 192 ], [ 43, 2, 25, 192 ], [ 43, 3, 19, 192 ], [ 43, 4, 25, 192 ], [ 43, 5, 21, 192 ], [ 44, 2, 32, 384 ], [ 44, 3, 35, 384 ], [ 44, 3, 67, 384 ], [ 44, 4, 9, 384 ], [ 44, 5, 34, 384 ], [ 44, 5, 69, 384 ], [ 44, 6, 23, 384 ], [ 44, 6, 67, 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+5*q^2+8*q-69 ) 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+5*q^2+8*q-69 ) 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+5*q^2+8*q-69 ) q congruent 7 modulo 12: 1/384 phi1 phi2 ( q^5-8*q^4+15*q^3+5*q^2+8*q-69 ) 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+5*q^2+8*q-69 ) q congruent 11 modulo 12: 1/384 phi1 phi2 ( q^5-8*q^4+15*q^3+5*q^2+8*q-69 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 4, 2, 3, 24 ], [ 5, 1, 2, 12 ], [ 5, 2, 2, 6 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 12, 2, 2, 16 ], [ 14, 1, 2, 24 ], [ 14, 2, 2, 12 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 24 ], [ 15, 1, 5, 96 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 12 ], [ 15, 2, 5, 48 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 12 ], [ 15, 3, 5, 48 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 12 ], [ 15, 4, 5, 48 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 6 ], [ 18, 1, 2, 12 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 6 ], [ 18, 2, 3, 2 ], [ 20, 1, 4, 96 ], [ 20, 2, 4, 48 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 1, 3, 48 ], [ 23, 2, 3, 24 ], [ 24, 1, 2, 16 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 72 ], [ 25, 1, 8, 24 ], [ 25, 2, 5, 12 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 36 ], [ 25, 2, 8, 12 ], [ 25, 3, 5, 12 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 36 ], [ 25, 3, 8, 12 ], [ 25, 4, 5, 12 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 36 ], [ 25, 4, 8, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 2, 4, 48 ], [ 27, 2, 7, 12 ], [ 27, 3, 2, 48 ], [ 27, 3, 3, 48 ], [ 27, 3, 14, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 30, 1, 3, 32 ], [ 30, 2, 3, 16 ], [ 31, 1, 2, 48 ], [ 31, 1, 5, 48 ], [ 31, 2, 2, 24 ], [ 31, 2, 5, 24 ], [ 32, 1, 2, 48 ], [ 32, 1, 8, 48 ], [ 33, 1, 10, 192 ], [ 33, 2, 10, 96 ], [ 33, 3, 10, 96 ], [ 33, 4, 10, 96 ], [ 34, 1, 2, 48 ], [ 34, 1, 7, 24 ], [ 34, 1, 8, 8 ], [ 34, 2, 2, 24 ], [ 34, 2, 3, 12 ], [ 34, 2, 5, 4 ], [ 34, 3, 2, 24 ], [ 34, 3, 3, 12 ], [ 34, 3, 8, 12 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 24 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 12 ], [ 36, 1, 5, 48 ], [ 36, 1, 6, 192 ], [ 36, 1, 10, 48 ], [ 36, 2, 5, 24 ], [ 36, 2, 6, 96 ], [ 36, 2, 7, 96 ], [ 36, 2, 16, 24 ], [ 36, 3, 5, 24 ], [ 36, 3, 6, 96 ], [ 36, 3, 7, 96 ], [ 36, 3, 16, 24 ], [ 36, 4, 5, 24 ], [ 36, 4, 6, 96 ], [ 36, 4, 7, 96 ], [ 36, 4, 16, 24 ], [ 36, 5, 5, 24 ], [ 36, 5, 6, 96 ], [ 36, 5, 10, 24 ], [ 36, 6, 6, 24 ], [ 36, 6, 7, 96 ], [ 36, 6, 8, 24 ], [ 36, 6, 14, 24 ], [ 36, 6, 15, 24 ], [ 37, 1, 4, 32 ], [ 37, 2, 4, 16 ], [ 38, 1, 9, 96 ], [ 38, 1, 14, 96 ], [ 38, 2, 9, 48 ], [ 38, 2, 14, 48 ], [ 38, 3, 9, 48 ], [ 38, 3, 12, 48 ], [ 39, 1, 6, 16 ], [ 39, 1, 8, 96 ], [ 39, 1, 13, 96 ], [ 39, 1, 14, 48 ], [ 39, 2, 6, 8 ], [ 39, 2, 8, 48 ], [ 39, 2, 13, 48 ], [ 39, 2, 14, 24 ], [ 39, 3, 6, 8 ], [ 39, 3, 8, 48 ], [ 39, 3, 13, 48 ], [ 39, 3, 14, 24 ], [ 39, 4, 4, 8 ], [ 39, 4, 7, 48 ], [ 39, 4, 12, 48 ], [ 39, 4, 13, 48 ], [ 39, 4, 14, 24 ], [ 39, 5, 4, 8 ], [ 39, 5, 7, 48 ], [ 39, 5, 12, 48 ], [ 39, 5, 13, 48 ], [ 39, 5, 14, 24 ], [ 40, 1, 12, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 23, 96 ], [ 40, 2, 17, 48 ], [ 40, 2, 20, 24 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 48 ], [ 40, 3, 11, 24 ], [ 40, 3, 15, 24 ], [ 40, 3, 16, 48 ], [ 41, 1, 4, 96 ], [ 41, 1, 12, 96 ], [ 41, 1, 30, 192 ], [ 41, 1, 31, 192 ], [ 41, 2, 4, 48 ], [ 41, 2, 12, 48 ], [ 41, 2, 30, 96 ], [ 41, 2, 31, 96 ], [ 41, 3, 4, 48 ], [ 41, 3, 12, 48 ], [ 41, 3, 30, 96 ], [ 41, 3, 31, 96 ], [ 41, 4, 6, 48 ], [ 41, 4, 8, 48 ], [ 41, 4, 35, 96 ], [ 41, 4, 36, 96 ], [ 41, 4, 37, 96 ], [ 41, 4, 38, 96 ], [ 41, 5, 6, 48 ], [ 41, 5, 11, 48 ], [ 41, 5, 28, 96 ], [ 41, 5, 29, 96 ], [ 41, 5, 30, 96 ], [ 41, 6, 6, 48 ], [ 41, 6, 11, 48 ], [ 41, 6, 28, 96 ], [ 41, 6, 29, 96 ], [ 41, 6, 30, 96 ], [ 41, 7, 6, 48 ], [ 41, 7, 11, 48 ], [ 41, 7, 28, 96 ], [ 41, 7, 29, 96 ], [ 41, 7, 30, 96 ], [ 42, 1, 15, 64 ], [ 42, 2, 7, 32 ], [ 42, 3, 9, 32 ], [ 42, 4, 14, 32 ], [ 43, 1, 24, 192 ], [ 43, 1, 36, 192 ], [ 43, 2, 20, 96 ], [ 43, 2, 28, 96 ], [ 43, 2, 31, 96 ], [ 43, 2, 40, 96 ], [ 43, 3, 24, 96 ], [ 43, 3, 32, 96 ], [ 43, 4, 12, 96 ], [ 43, 4, 20, 96 ], [ 43, 4, 30, 96 ], [ 43, 5, 28, 96 ], [ 43, 5, 32, 96 ], [ 44, 2, 46, 192 ], [ 44, 2, 65, 192 ], [ 44, 3, 42, 192 ], [ 44, 3, 56, 192 ], [ 44, 3, 58, 192 ], [ 44, 4, 10, 192 ], [ 44, 5, 46, 192 ], [ 44, 5, 57, 192 ], [ 44, 5, 60, 192 ], [ 44, 6, 37, 192 ], [ 44, 6, 47, 192 ], [ 44, 6, 49, 192 ], [ 44, 6, 78, 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 ( q^4-3*q^3-7*q+21 ) 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 ( q^4-3*q^3-7*q+21 ) 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 ( q^4-3*q^3-7*q+21 ) q congruent 7 modulo 12: 1/384 phi1^2 phi2 ( q^4-3*q^3-7*q+21 ) 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 ( q^4-3*q^3-7*q+21 ) q congruent 11 modulo 12: 1/384 phi1^2 phi2 ( q^4-3*q^3-7*q+21 ) 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 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 12 ], [ 6, 2, 2, 6 ], [ 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 ], [ 14, 2, 2, 12 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 8 ], [ 15, 2, 3, 12 ], [ 15, 2, 4, 4 ], [ 15, 3, 3, 12 ], [ 15, 3, 4, 4 ], [ 15, 4, 3, 12 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 14 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 36 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 18 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 60 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 30 ], [ 19, 1, 2, 48 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 1, 4, 48 ], [ 23, 2, 4, 24 ], [ 24, 1, 3, 16 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 72 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 24 ], [ 25, 2, 5, 12 ], [ 25, 2, 6, 36 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 12 ], [ 25, 3, 5, 12 ], [ 25, 3, 6, 36 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 12 ], [ 25, 4, 5, 12 ], [ 25, 4, 6, 36 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 7, 12 ], [ 27, 2, 11, 48 ], [ 27, 2, 13, 48 ], [ 27, 3, 7, 48 ], [ 27, 3, 8, 48 ], [ 27, 3, 12, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 29, 1, 4, 96 ], [ 29, 2, 4, 48 ], [ 30, 1, 8, 32 ], [ 30, 2, 8, 16 ], [ 31, 1, 4, 48 ], [ 31, 1, 7, 48 ], [ 31, 2, 4, 24 ], [ 31, 2, 7, 24 ], [ 32, 1, 4, 48 ], [ 32, 1, 5, 48 ], [ 34, 1, 4, 144 ], [ 34, 1, 7, 24 ], [ 34, 1, 8, 8 ], [ 34, 2, 3, 12 ], [ 34, 2, 5, 4 ], [ 34, 2, 10, 72 ], [ 34, 3, 3, 12 ], [ 34, 3, 5, 72 ], [ 34, 3, 8, 12 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 8 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 6, 12 ], [ 35, 2, 7, 4 ], [ 35, 2, 10, 24 ], [ 36, 1, 5, 48 ], [ 36, 1, 10, 48 ], [ 36, 1, 19, 192 ], [ 36, 2, 5, 24 ], [ 36, 2, 16, 24 ], [ 36, 2, 22, 96 ], [ 36, 2, 26, 96 ], [ 36, 3, 5, 24 ], [ 36, 3, 16, 24 ], [ 36, 3, 22, 96 ], [ 36, 3, 26, 96 ], [ 36, 4, 5, 24 ], [ 36, 4, 16, 24 ], [ 36, 4, 22, 96 ], [ 36, 4, 26, 96 ], [ 36, 5, 5, 24 ], [ 36, 5, 10, 24 ], [ 36, 5, 19, 96 ], [ 36, 6, 6, 24 ], [ 36, 6, 8, 24 ], [ 36, 6, 14, 24 ], [ 36, 6, 15, 24 ], [ 36, 6, 16, 96 ], [ 37, 1, 10, 32 ], [ 37, 2, 10, 16 ], [ 38, 1, 12, 96 ], [ 38, 1, 16, 96 ], [ 38, 2, 12, 48 ], [ 38, 2, 16, 48 ], [ 38, 3, 14, 48 ], [ 38, 3, 15, 48 ], [ 39, 1, 4, 96 ], [ 39, 1, 6, 48 ], [ 39, 1, 14, 16 ], [ 39, 1, 15, 96 ], [ 39, 2, 4, 48 ], [ 39, 2, 6, 24 ], [ 39, 2, 14, 8 ], [ 39, 2, 15, 48 ], [ 39, 3, 4, 48 ], [ 39, 3, 6, 24 ], [ 39, 3, 14, 8 ], [ 39, 3, 15, 48 ], [ 39, 4, 3, 48 ], [ 39, 4, 4, 24 ], [ 39, 4, 5, 48 ], [ 39, 4, 14, 8 ], [ 39, 4, 15, 48 ], [ 39, 5, 3, 48 ], [ 39, 5, 4, 24 ], [ 39, 5, 5, 48 ], [ 39, 5, 14, 8 ], [ 39, 5, 15, 48 ], [ 40, 1, 13, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 24, 96 ], [ 40, 2, 18, 48 ], [ 40, 2, 20, 24 ], [ 40, 2, 24, 48 ], [ 40, 3, 11, 24 ], [ 40, 3, 14, 48 ], [ 40, 3, 15, 24 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 48 ], [ 41, 1, 9, 96 ], [ 41, 1, 12, 96 ], [ 41, 1, 23, 192 ], [ 41, 1, 26, 192 ], [ 41, 2, 9, 48 ], [ 41, 2, 12, 48 ], [ 41, 2, 23, 96 ], [ 41, 2, 26, 96 ], [ 41, 3, 9, 48 ], [ 41, 3, 12, 48 ], [ 41, 3, 23, 96 ], [ 41, 3, 26, 96 ], [ 41, 4, 6, 48 ], [ 41, 4, 8, 48 ], [ 41, 4, 27, 96 ], [ 41, 4, 30, 96 ], [ 41, 4, 31, 96 ], [ 41, 4, 32, 96 ], [ 41, 5, 6, 48 ], [ 41, 5, 11, 48 ], [ 41, 5, 21, 96 ], [ 41, 5, 23, 96 ], [ 41, 5, 25, 96 ], [ 41, 6, 6, 48 ], [ 41, 6, 11, 48 ], [ 41, 6, 21, 96 ], [ 41, 6, 23, 96 ], [ 41, 6, 25, 96 ], [ 41, 7, 6, 48 ], [ 41, 7, 11, 48 ], [ 41, 7, 21, 96 ], [ 41, 7, 23, 96 ], [ 41, 7, 25, 96 ], [ 42, 1, 14, 64 ], [ 42, 2, 18, 32 ], [ 42, 3, 20, 32 ], [ 42, 4, 15, 32 ], [ 43, 1, 23, 192 ], [ 43, 1, 34, 192 ], [ 43, 2, 19, 96 ], [ 43, 2, 29, 96 ], [ 43, 2, 30, 96 ], [ 43, 2, 41, 96 ], [ 43, 3, 23, 96 ], [ 43, 3, 31, 96 ], [ 43, 4, 35, 96 ], [ 43, 4, 38, 96 ], [ 43, 4, 41, 96 ], [ 43, 5, 30, 96 ], [ 43, 5, 35, 96 ], [ 44, 2, 44, 192 ], [ 44, 2, 63, 192 ], [ 44, 3, 45, 192 ], [ 44, 3, 57, 192 ], [ 44, 3, 59, 192 ], [ 44, 4, 11, 192 ], [ 44, 5, 44, 192 ], [ 44, 5, 58, 192 ], [ 44, 5, 61, 192 ], [ 44, 6, 36, 192 ], [ 44, 6, 46, 192 ], [ 44, 6, 53, 192 ], [ 44, 6, 75, 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-q^2-6*q+27 ) 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-q^2-6*q+27 ) 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-q^2-6*q+27 ) q congruent 7 modulo 12: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3-q^2-6*q+27 ) 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-q^2-6*q+27 ) q congruent 11 modulo 12: 1/256 phi1 phi2 ( q^5-2*q^4-3*q^3-q^2-6*q+27 ) 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 ], [ 4, 2, 1, 4 ], [ 4, 2, 3, 8 ], [ 4, 2, 4, 8 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 7, 32 ], [ 15, 1, 8, 32 ], [ 15, 2, 1, 8 ], [ 15, 2, 7, 16 ], [ 15, 2, 8, 16 ], [ 15, 3, 1, 8 ], [ 15, 3, 7, 16 ], [ 15, 3, 8, 16 ], [ 15, 4, 1, 8 ], [ 15, 4, 7, 16 ], [ 15, 4, 8, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 4, 4 ], [ 25, 1, 2, 32 ], [ 25, 2, 2, 16 ], [ 25, 3, 2, 16 ], [ 25, 4, 2, 16 ], [ 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 ], [ 27, 2, 4, 16 ], [ 27, 2, 5, 32 ], [ 27, 2, 6, 16 ], [ 27, 2, 7, 24 ], [ 27, 2, 9, 16 ], [ 27, 2, 11, 16 ], [ 27, 2, 13, 16 ], [ 27, 3, 3, 16 ], [ 27, 3, 4, 16 ], [ 27, 3, 6, 16 ], [ 27, 3, 7, 16 ], [ 27, 3, 8, 16 ], [ 27, 3, 10, 16 ], [ 27, 3, 12, 16 ], [ 27, 3, 13, 16 ], [ 27, 3, 14, 16 ], [ 32, 1, 4, 64 ], [ 32, 1, 8, 32 ], [ 34, 1, 3, 16 ], [ 34, 1, 6, 16 ], [ 34, 1, 8, 32 ], [ 34, 2, 5, 16 ], [ 34, 2, 8, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 35, 1, 6, 32 ], [ 35, 2, 6, 16 ], [ 36, 1, 10, 64 ], [ 36, 1, 11, 128 ], [ 36, 1, 14, 64 ], [ 36, 1, 15, 64 ], [ 36, 1, 17, 32 ], [ 36, 2, 10, 32 ], [ 36, 2, 11, 64 ], [ 36, 2, 12, 32 ], [ 36, 2, 13, 16 ], [ 36, 2, 16, 32 ], [ 36, 2, 18, 32 ], [ 36, 2, 20, 32 ], [ 36, 2, 24, 32 ], [ 36, 3, 10, 32 ], [ 36, 3, 11, 64 ], [ 36, 3, 12, 32 ], [ 36, 3, 13, 16 ], [ 36, 3, 16, 32 ], [ 36, 3, 18, 32 ], [ 36, 3, 20, 32 ], [ 36, 3, 24, 32 ], [ 36, 4, 10, 32 ], [ 36, 4, 11, 64 ], [ 36, 4, 12, 32 ], [ 36, 4, 13, 16 ], [ 36, 4, 16, 32 ], [ 36, 4, 18, 32 ], [ 36, 4, 20, 32 ], [ 36, 4, 24, 32 ], [ 36, 5, 10, 32 ], [ 36, 5, 11, 64 ], [ 36, 5, 14, 32 ], [ 36, 5, 15, 32 ], [ 36, 5, 17, 16 ], [ 36, 6, 12, 32 ], [ 38, 1, 11, 64 ], [ 38, 1, 12, 64 ], [ 38, 1, 14, 64 ], [ 38, 2, 11, 32 ], [ 38, 2, 12, 32 ], [ 38, 2, 14, 32 ], [ 39, 1, 9, 64 ], [ 39, 2, 9, 32 ], [ 39, 3, 9, 32 ], [ 39, 4, 10, 32 ], [ 39, 5, 10, 32 ], [ 40, 1, 6, 96 ], [ 40, 1, 16, 64 ], [ 40, 1, 24, 64 ], [ 40, 2, 14, 48 ], [ 40, 2, 18, 32 ], [ 40, 2, 19, 32 ], [ 40, 3, 14, 32 ], [ 41, 1, 14, 128 ], [ 41, 1, 21, 64 ], [ 41, 1, 27, 128 ], [ 41, 1, 39, 128 ], [ 41, 2, 14, 64 ], [ 41, 2, 21, 32 ], [ 41, 2, 27, 64 ], [ 41, 2, 39, 64 ], [ 41, 3, 14, 64 ], [ 41, 3, 21, 32 ], [ 41, 3, 27, 64 ], [ 41, 3, 39, 64 ], [ 41, 4, 7, 64 ], [ 41, 4, 20, 32 ], [ 41, 4, 29, 64 ], [ 41, 4, 33, 64 ], [ 41, 4, 48, 64 ], [ 41, 4, 49, 64 ], [ 41, 5, 38, 64 ], [ 41, 6, 38, 64 ], [ 41, 7, 38, 64 ], [ 43, 1, 17, 128 ], [ 43, 1, 21, 128 ], [ 43, 2, 15, 64 ], [ 43, 2, 17, 64 ], [ 43, 2, 24, 64 ], [ 43, 2, 26, 64 ], [ 43, 3, 17, 64 ], [ 43, 3, 21, 64 ], [ 43, 4, 14, 64 ], [ 43, 4, 40, 64 ], [ 43, 4, 51, 64 ], [ 43, 5, 7, 64 ], [ 43, 5, 29, 64 ], [ 43, 5, 31, 64 ], [ 44, 2, 36, 128 ], [ 44, 2, 40, 128 ], [ 44, 3, 38, 128 ], [ 44, 3, 69, 128 ], [ 44, 3, 72, 128 ], [ 44, 4, 12, 128 ], [ 44, 5, 37, 128 ], [ 44, 5, 70, 128 ], [ 44, 5, 73, 128 ], [ 44, 6, 26, 128 ], [ 44, 6, 32, 128 ], [ 44, 6, 65, 128 ], [ 44, 6, 70, 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 phi2 ( q^5-4*q^4+3*q^3+q^2-4*q+11 ) 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 phi2 ( q^5-4*q^4+3*q^3+q^2-4*q+11 ) 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 phi2 ( q^5-4*q^4+3*q^3+q^2-4*q+11 ) q congruent 7 modulo 12: 1/64 phi1 phi2 ( q^5-4*q^4+3*q^3+q^2-4*q+11 ) 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 phi2 ( q^5-4*q^4+3*q^3+q^2-4*q+11 ) q congruent 11 modulo 12: 1/64 phi1 phi2 ( q^5-4*q^4+3*q^3+q^2-4*q+11 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 4 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 12, 2, 4, 8 ], [ 13, 1, 1, 8 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 15, 1, 6, 16 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 2, 6, 8 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 4 ], [ 15, 3, 6, 8 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 4 ], [ 15, 4, 6, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 2, 4 ], [ 18, 2, 4, 2 ], [ 19, 1, 1, 8 ], [ 20, 1, 3, 16 ], [ 20, 2, 3, 8 ], [ 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 ], [ 23, 2, 1, 4 ], [ 23, 2, 2, 4 ], [ 24, 1, 1, 8 ], [ 24, 1, 4, 8 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 8 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 6, 8 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 2, 10, 8 ], [ 27, 2, 14, 8 ], [ 27, 3, 4, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 13, 8 ], [ 27, 3, 15, 8 ], [ 27, 3, 16, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 29, 1, 2, 16 ], [ 29, 2, 2, 8 ], [ 30, 1, 4, 16 ], [ 30, 1, 7, 16 ], [ 30, 2, 4, 8 ], [ 30, 2, 7, 8 ], [ 31, 1, 1, 8 ], [ 31, 1, 3, 8 ], [ 31, 1, 6, 8 ], [ 31, 1, 8, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 3, 4 ], [ 31, 2, 6, 4 ], [ 31, 2, 8, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 32, 1, 8, 8 ], [ 33, 1, 7, 32 ], [ 33, 2, 7, 16 ], [ 33, 3, 7, 16 ], [ 33, 4, 7, 16 ], [ 34, 1, 2, 16 ], [ 34, 1, 5, 8 ], [ 34, 1, 6, 8 ], [ 34, 2, 2, 8 ], [ 34, 2, 4, 4 ], [ 34, 2, 8, 4 ], [ 34, 3, 2, 8 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 1, 2, 16 ], [ 36, 1, 13, 32 ], [ 36, 1, 16, 32 ], [ 36, 1, 17, 16 ], [ 36, 2, 2, 8 ], [ 36, 2, 9, 16 ], [ 36, 2, 13, 8 ], [ 36, 2, 15, 16 ], [ 36, 2, 19, 16 ], [ 36, 2, 28, 16 ], [ 36, 3, 2, 8 ], [ 36, 3, 9, 16 ], [ 36, 3, 13, 8 ], [ 36, 3, 15, 16 ], [ 36, 3, 19, 16 ], [ 36, 3, 28, 16 ], [ 36, 4, 2, 8 ], [ 36, 4, 9, 16 ], [ 36, 4, 13, 8 ], [ 36, 4, 15, 16 ], [ 36, 4, 19, 16 ], [ 36, 4, 28, 16 ], [ 36, 5, 2, 8 ], [ 36, 5, 13, 16 ], [ 36, 5, 16, 16 ], [ 36, 5, 17, 8 ], [ 36, 6, 2, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 10, 8 ], [ 36, 6, 11, 8 ], [ 37, 1, 4, 16 ], [ 37, 1, 10, 16 ], [ 37, 2, 4, 8 ], [ 37, 2, 10, 8 ], [ 38, 1, 10, 16 ], [ 38, 1, 11, 16 ], [ 38, 1, 13, 16 ], [ 38, 1, 15, 16 ], [ 38, 2, 10, 8 ], [ 38, 2, 11, 8 ], [ 38, 2, 13, 8 ], [ 38, 2, 15, 8 ], [ 38, 3, 10, 8 ], [ 38, 3, 11, 8 ], [ 38, 3, 13, 8 ], [ 38, 3, 16, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 16 ], [ 39, 1, 19, 16 ], [ 39, 2, 2, 8 ], [ 39, 2, 9, 8 ], [ 39, 2, 17, 8 ], [ 39, 2, 19, 8 ], [ 39, 3, 2, 8 ], [ 39, 3, 9, 8 ], [ 39, 3, 17, 8 ], [ 39, 3, 19, 8 ], [ 39, 4, 2, 8 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 8 ], [ 39, 4, 19, 8 ], [ 39, 5, 2, 8 ], [ 39, 5, 10, 8 ], [ 39, 5, 16, 8 ], [ 39, 5, 19, 8 ], [ 40, 1, 16, 16 ], [ 40, 1, 21, 16 ], [ 40, 1, 22, 16 ], [ 40, 2, 19, 8 ], [ 40, 2, 20, 8 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 18, 32 ], [ 41, 1, 35, 32 ], [ 41, 1, 37, 32 ], [ 41, 2, 4, 8 ], [ 41, 2, 9, 8 ], [ 41, 2, 18, 16 ], [ 41, 2, 35, 16 ], [ 41, 2, 37, 16 ], [ 41, 3, 4, 8 ], [ 41, 3, 9, 8 ], [ 41, 3, 18, 16 ], [ 41, 3, 35, 16 ], [ 41, 3, 37, 16 ], [ 41, 4, 18, 16 ], [ 41, 4, 21, 16 ], [ 41, 4, 39, 16 ], [ 41, 4, 42, 16 ], [ 41, 4, 45, 16 ], [ 41, 4, 46, 16 ], [ 41, 5, 16, 16 ], [ 41, 5, 18, 16 ], [ 41, 5, 34, 16 ], [ 41, 5, 36, 16 ], [ 41, 6, 16, 16 ], [ 41, 6, 18, 16 ], [ 41, 6, 34, 16 ], [ 41, 6, 36, 16 ], [ 41, 7, 16, 16 ], [ 41, 7, 18, 16 ], [ 41, 7, 34, 16 ], [ 41, 7, 36, 16 ], [ 42, 1, 13, 32 ], [ 42, 1, 16, 32 ], [ 42, 2, 3, 16 ], [ 42, 2, 14, 16 ], [ 42, 3, 4, 16 ], [ 42, 3, 15, 16 ], [ 42, 4, 13, 16 ], [ 42, 4, 16, 16 ], [ 43, 1, 25, 32 ], [ 43, 1, 33, 32 ], [ 43, 1, 35, 32 ], [ 43, 2, 21, 16 ], [ 43, 2, 32, 16 ], [ 43, 2, 33, 16 ], [ 43, 2, 39, 16 ], [ 43, 2, 42, 16 ], [ 43, 3, 25, 16 ], [ 43, 3, 30, 16 ], [ 43, 3, 33, 16 ], [ 43, 4, 4, 16 ], [ 43, 4, 9, 16 ], [ 43, 4, 15, 16 ], [ 43, 4, 22, 16 ], [ 43, 4, 46, 16 ], [ 43, 4, 48, 16 ], [ 43, 5, 3, 16 ], [ 43, 5, 6, 16 ], [ 43, 5, 15, 16 ], [ 43, 5, 20, 16 ], [ 44, 2, 47, 32 ], [ 44, 2, 58, 32 ], [ 44, 2, 64, 32 ], [ 44, 3, 47, 32 ], [ 44, 3, 62, 32 ], [ 44, 3, 63, 32 ], [ 44, 4, 13, 32 ], [ 44, 5, 47, 32 ], [ 44, 5, 63, 32 ], [ 44, 5, 65, 32 ], [ 44, 6, 39, 32 ], [ 44, 6, 54, 32 ], [ 44, 6, 57, 32 ], [ 44, 6, 74, 32 ], [ 44, 6, 76, 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 6 ], [ 6, 2, 1, 3 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 6 ], [ 13, 1, 1, 6 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 3 ], [ 16, 1, 1, 6 ], [ 18, 1, 1, 12 ], [ 18, 2, 1, 6 ], [ 19, 1, 1, 6 ], [ 23, 1, 1, 12 ], [ 23, 2, 1, 6 ], [ 28, 1, 1, 12 ], [ 28, 2, 1, 6 ], [ 29, 1, 1, 12 ], [ 29, 2, 1, 6 ], [ 42, 1, 2, 10 ], [ 42, 4, 2, 5 ], [ 43, 1, 2, 30 ], [ 43, 3, 2, 15 ], [ 44, 2, 2, 30 ], [ 44, 4, 14, 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 ], [ 4, 2, 2, 14 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 18 ], [ 8, 1, 2, 40 ], [ 9, 1, 2, 46 ], [ 10, 1, 4, 36 ], [ 11, 1, 2, 32 ], [ 12, 1, 6, 48 ], [ 12, 2, 3, 24 ], [ 13, 1, 2, 24 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 2, 8 ], [ 15, 1, 4, 48 ], [ 15, 2, 2, 4 ], [ 15, 2, 4, 24 ], [ 15, 3, 2, 4 ], [ 15, 3, 4, 24 ], [ 15, 4, 2, 4 ], [ 15, 4, 4, 24 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 18, 1, 3, 24 ], [ 18, 1, 4, 12 ], [ 18, 2, 3, 12 ], [ 18, 2, 4, 6 ], [ 19, 1, 2, 48 ], [ 20, 1, 2, 64 ], [ 20, 2, 2, 32 ], [ 21, 1, 6, 36 ], [ 22, 1, 3, 24 ], [ 22, 1, 4, 48 ], [ 23, 1, 3, 16 ], [ 23, 1, 4, 48 ], [ 23, 2, 3, 8 ], [ 23, 2, 4, 24 ], [ 24, 1, 3, 72 ], [ 24, 1, 4, 20 ], [ 25, 1, 4, 24 ], [ 25, 1, 8, 48 ], [ 25, 2, 4, 12 ], [ 25, 2, 8, 24 ], [ 25, 3, 4, 12 ], [ 25, 3, 8, 24 ], [ 25, 4, 4, 12 ], [ 25, 4, 8, 24 ], [ 26, 1, 2, 24 ], [ 26, 1, 3, 24 ], [ 28, 1, 2, 16 ], [ 28, 1, 4, 6 ], [ 28, 1, 6, 48 ], [ 28, 2, 2, 8 ], [ 28, 2, 5, 3 ], [ 28, 2, 6, 24 ], [ 29, 1, 4, 48 ], [ 29, 1, 5, 48 ], [ 29, 1, 6, 24 ], [ 29, 2, 4, 24 ], [ 29, 2, 5, 24 ], [ 29, 2, 6, 12 ], [ 30, 1, 5, 48 ], [ 30, 1, 6, 24 ], [ 30, 2, 5, 24 ], [ 30, 2, 6, 12 ], [ 31, 1, 5, 48 ], [ 31, 1, 7, 48 ], [ 31, 1, 8, 48 ], [ 31, 2, 5, 24 ], [ 31, 2, 7, 24 ], [ 31, 2, 8, 24 ], [ 33, 1, 4, 32 ], [ 33, 1, 5, 48 ], [ 33, 1, 6, 96 ], [ 33, 2, 4, 16 ], [ 33, 2, 5, 24 ], [ 33, 2, 6, 48 ], [ 33, 3, 4, 16 ], [ 33, 3, 5, 24 ], [ 33, 3, 6, 48 ], [ 33, 4, 4, 16 ], [ 33, 4, 5, 24 ], [ 33, 4, 6, 48 ], [ 34, 1, 3, 48 ], [ 34, 2, 9, 24 ], [ 34, 3, 6, 24 ], [ 35, 1, 4, 48 ], [ 35, 1, 9, 42 ], [ 35, 1, 10, 48 ], [ 35, 2, 4, 24 ], [ 35, 2, 9, 21 ], [ 35, 2, 10, 24 ], [ 37, 1, 6, 48 ], [ 37, 1, 7, 48 ], [ 37, 1, 8, 96 ], [ 37, 2, 6, 24 ], [ 37, 2, 7, 24 ], [ 37, 2, 8, 48 ], [ 39, 1, 11, 96 ], [ 39, 1, 12, 72 ], [ 39, 1, 16, 12 ], [ 39, 1, 20, 96 ], [ 39, 2, 11, 48 ], [ 39, 2, 12, 36 ], [ 39, 2, 16, 6 ], [ 39, 2, 20, 48 ], [ 39, 3, 11, 48 ], [ 39, 3, 12, 36 ], [ 39, 3, 16, 6 ], [ 39, 3, 20, 48 ], [ 39, 4, 11, 48 ], [ 39, 4, 20, 48 ], [ 39, 5, 11, 48 ], [ 39, 5, 20, 48 ], [ 40, 1, 8, 108 ], [ 40, 2, 5, 54 ], [ 40, 3, 9, 54 ], [ 41, 1, 8, 144 ], [ 41, 1, 17, 72 ], [ 41, 2, 8, 72 ], [ 41, 2, 17, 36 ], [ 41, 3, 8, 72 ], [ 41, 3, 17, 36 ], [ 41, 5, 9, 72 ], [ 41, 5, 17, 36 ], [ 41, 6, 9, 72 ], [ 41, 6, 17, 36 ], [ 41, 7, 9, 72 ], [ 41, 7, 17, 36 ], [ 42, 1, 6, 144 ], [ 42, 1, 8, 48 ], [ 42, 1, 21, 96 ], [ 42, 2, 11, 48 ], [ 42, 3, 11, 48 ], [ 42, 3, 13, 24 ], [ 42, 3, 17, 48 ], [ 42, 3, 18, 72 ], [ 42, 4, 7, 24 ], [ 42, 4, 8, 72 ], [ 42, 4, 21, 48 ], [ 43, 1, 9, 144 ], [ 43, 1, 12, 144 ], [ 43, 2, 7, 72 ], [ 43, 2, 11, 72 ], [ 43, 3, 9, 72 ], [ 43, 3, 11, 72 ], [ 43, 4, 8, 72 ], [ 43, 4, 34, 72 ], [ 43, 4, 47, 72 ], [ 44, 2, 17, 144 ], [ 44, 2, 20, 144 ], [ 44, 3, 13, 144 ], [ 44, 4, 15, 144 ], [ 44, 5, 11, 144 ], [ 44, 6, 11, 144 ], [ 44, 6, 20, 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 phi1^2 ( q^4-3*q^3-8*q^2+13*q+33 ) 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 phi1^2 ( q^4-3*q^3-8*q^2+13*q+33 ) 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+21*q^3-22*q^2-31*q+48 ) q congruent 7 modulo 12: 1/288 q phi1^2 ( q^4-3*q^3-8*q^2+13*q+33 ) 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 phi1^2 ( q^4-3*q^3-8*q^2+13*q+33 ) q congruent 11 modulo 12: 1/288 phi2 ( q^6-6*q^5+5*q^4+21*q^3-22*q^2-31*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 ], [ 4, 2, 2, 6 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 3, 24 ], [ 10, 1, 4, 12 ], [ 12, 1, 5, 16 ], [ 12, 2, 4, 8 ], [ 15, 1, 2, 24 ], [ 15, 2, 2, 12 ], [ 15, 3, 2, 12 ], [ 15, 4, 2, 12 ], [ 16, 1, 1, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 4, 24 ], [ 17, 2, 1, 6 ], [ 17, 2, 4, 12 ], [ 18, 1, 1, 24 ], [ 18, 1, 4, 12 ], [ 18, 2, 1, 12 ], [ 18, 2, 4, 6 ], [ 21, 1, 3, 24 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 24 ], [ 24, 1, 4, 12 ], [ 25, 1, 3, 48 ], [ 25, 1, 4, 24 ], [ 25, 2, 3, 24 ], [ 25, 2, 4, 12 ], [ 25, 3, 3, 24 ], [ 25, 3, 4, 12 ], [ 25, 4, 3, 24 ], [ 25, 4, 4, 12 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 24 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 1, 6, 24 ], [ 30, 1, 7, 48 ], [ 30, 2, 6, 12 ], [ 30, 2, 7, 24 ], [ 31, 1, 6, 48 ], [ 31, 2, 6, 24 ], [ 33, 1, 8, 48 ], [ 33, 2, 8, 24 ], [ 33, 3, 8, 24 ], [ 33, 4, 8, 24 ], [ 34, 1, 1, 48 ], [ 34, 1, 5, 48 ], [ 34, 2, 1, 24 ], [ 34, 2, 4, 24 ], [ 34, 3, 1, 24 ], [ 34, 3, 4, 24 ], [ 34, 3, 7, 24 ], [ 35, 1, 3, 48 ], [ 35, 1, 9, 18 ], [ 35, 2, 3, 24 ], [ 35, 2, 9, 9 ], [ 37, 1, 9, 48 ], [ 37, 2, 9, 24 ], [ 39, 1, 16, 36 ], [ 39, 1, 18, 96 ], [ 39, 2, 16, 18 ], [ 39, 2, 18, 48 ], [ 39, 3, 16, 18 ], [ 39, 3, 18, 48 ], [ 39, 4, 17, 48 ], [ 39, 4, 18, 48 ], [ 39, 5, 17, 48 ], [ 39, 5, 18, 48 ], [ 40, 1, 8, 36 ], [ 40, 1, 15, 72 ], [ 40, 2, 5, 18 ], [ 40, 2, 6, 36 ], [ 40, 3, 9, 18 ], [ 40, 3, 12, 36 ], [ 41, 1, 17, 72 ], [ 41, 1, 33, 144 ], [ 41, 2, 17, 36 ], [ 41, 2, 33, 72 ], [ 41, 3, 17, 36 ], [ 41, 3, 33, 72 ], [ 41, 5, 17, 36 ], [ 41, 5, 31, 72 ], [ 41, 6, 17, 36 ], [ 41, 6, 31, 72 ], [ 41, 7, 17, 36 ], [ 41, 7, 31, 72 ], [ 42, 1, 20, 96 ], [ 42, 2, 13, 48 ], [ 42, 2, 15, 48 ], [ 42, 3, 14, 48 ], [ 42, 4, 18, 48 ], [ 43, 1, 10, 144 ], [ 43, 2, 6, 72 ], [ 43, 2, 9, 72 ], [ 43, 3, 10, 72 ], [ 43, 4, 21, 72 ], [ 44, 2, 18, 144 ], [ 44, 3, 14, 144 ], [ 44, 3, 18, 144 ], [ 44, 4, 16, 144 ], [ 44, 5, 10, 144 ], [ 44, 5, 17, 144 ], [ 44, 6, 10, 144 ], [ 44, 6, 16, 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 ], [ 6, 2, 1, 1 ], [ 12, 1, 5, 16 ], [ 12, 2, 4, 8 ], [ 21, 1, 4, 24 ], [ 28, 1, 4, 24 ], [ 28, 2, 5, 12 ], [ 33, 1, 8, 48 ], [ 33, 2, 8, 24 ], [ 33, 3, 8, 24 ], [ 33, 4, 8, 24 ], [ 34, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 40, 1, 10, 72 ], [ 40, 2, 11, 36 ], [ 42, 1, 10, 48 ], [ 42, 2, 17, 24 ], [ 42, 4, 11, 24 ], [ 44, 3, 28, 72 ], [ 44, 4, 17, 72 ], [ 44, 5, 29, 72 ] ] 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 ( q^4-3*q^3+q+5 ) 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 ( q^4-3*q^3+q+5 ) 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 ( q^4-3*q^3+q+5 ) q congruent 7 modulo 12: 1/96 q phi1 phi2 ( q^4-3*q^3+q+5 ) 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 ( q^4-3*q^3+q+5 ) q congruent 11 modulo 12: 1/96 q phi1 phi2 ( q^4-3*q^3+q+5 ) 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 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 12, 2, 1, 12 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 8 ], [ 14, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 3, 16 ], [ 15, 2, 1, 4 ], [ 15, 2, 3, 8 ], [ 15, 3, 1, 4 ], [ 15, 3, 3, 8 ], [ 15, 4, 1, 4 ], [ 15, 4, 3, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 8 ], [ 17, 1, 4, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 8 ], [ 18, 2, 1, 2 ], [ 18, 2, 2, 4 ], [ 18, 2, 4, 4 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 16 ], [ 20, 2, 1, 8 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 8 ], [ 22, 1, 1, 8 ], [ 22, 1, 2, 16 ], [ 23, 1, 2, 16 ], [ 23, 2, 2, 8 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 24 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 5, 16 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 8 ], [ 25, 2, 5, 8 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 8 ], [ 25, 3, 5, 8 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 8 ], [ 25, 4, 5, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 3, 16 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 28, 2, 4, 8 ], [ 29, 1, 2, 16 ], [ 29, 1, 3, 12 ], [ 29, 2, 2, 8 ], [ 29, 2, 3, 6 ], [ 30, 1, 1, 8 ], [ 30, 1, 2, 16 ], [ 30, 1, 4, 16 ], [ 30, 2, 1, 4 ], [ 30, 2, 2, 8 ], [ 30, 2, 4, 8 ], [ 31, 1, 2, 16 ], [ 31, 1, 3, 16 ], [ 31, 1, 4, 16 ], [ 31, 2, 2, 8 ], [ 31, 2, 3, 8 ], [ 31, 2, 4, 8 ], [ 33, 1, 2, 24 ], [ 33, 1, 3, 32 ], [ 33, 2, 2, 12 ], [ 33, 2, 3, 16 ], [ 33, 3, 2, 12 ], [ 33, 3, 3, 16 ], [ 33, 4, 2, 12 ], [ 33, 4, 3, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 5, 16 ], [ 34, 2, 4, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 4, 8 ], [ 34, 3, 6, 8 ], [ 34, 3, 7, 8 ], [ 35, 1, 2, 16 ], [ 35, 1, 5, 16 ], [ 35, 1, 8, 18 ], [ 35, 2, 2, 8 ], [ 35, 2, 5, 8 ], [ 35, 2, 8, 9 ], [ 37, 1, 2, 16 ], [ 37, 1, 3, 24 ], [ 37, 1, 5, 16 ], [ 37, 2, 2, 8 ], [ 37, 2, 3, 12 ], [ 37, 2, 5, 8 ], [ 39, 1, 3, 12 ], [ 39, 1, 5, 32 ], [ 39, 1, 7, 24 ], [ 39, 1, 10, 32 ], [ 39, 2, 3, 6 ], [ 39, 2, 5, 16 ], [ 39, 2, 7, 12 ], [ 39, 2, 10, 16 ], [ 39, 3, 3, 6 ], [ 39, 3, 5, 16 ], [ 39, 3, 7, 12 ], [ 39, 3, 10, 16 ], [ 39, 4, 6, 16 ], [ 39, 4, 8, 16 ], [ 39, 4, 9, 16 ], [ 39, 5, 6, 16 ], [ 39, 5, 8, 16 ], [ 39, 5, 9, 16 ], [ 40, 1, 7, 36 ], [ 40, 1, 14, 24 ], [ 40, 2, 2, 18 ], [ 40, 2, 7, 12 ], [ 40, 3, 10, 18 ], [ 40, 3, 13, 12 ], [ 41, 1, 3, 24 ], [ 41, 1, 13, 48 ], [ 41, 1, 38, 48 ], [ 41, 2, 3, 12 ], [ 41, 2, 13, 24 ], [ 41, 2, 38, 24 ], [ 41, 3, 3, 12 ], [ 41, 3, 13, 24 ], [ 41, 3, 38, 24 ], [ 41, 5, 3, 12 ], [ 41, 5, 7, 24 ], [ 41, 5, 37, 24 ], [ 41, 6, 3, 12 ], [ 41, 6, 7, 24 ], [ 41, 6, 37, 24 ], [ 41, 7, 3, 12 ], [ 41, 7, 7, 24 ], [ 41, 7, 37, 24 ], [ 42, 1, 7, 48 ], [ 42, 1, 12, 32 ], [ 42, 2, 4, 16 ], [ 42, 2, 5, 16 ], [ 42, 3, 5, 16 ], [ 42, 3, 7, 16 ], [ 42, 3, 8, 24 ], [ 42, 4, 6, 24 ], [ 42, 4, 12, 16 ], [ 43, 1, 6, 48 ], [ 43, 1, 11, 48 ], [ 43, 2, 3, 24 ], [ 43, 2, 8, 24 ], [ 43, 2, 10, 24 ], [ 43, 3, 6, 24 ], [ 43, 3, 12, 24 ], [ 43, 4, 13, 24 ], [ 43, 4, 29, 24 ], [ 43, 4, 39, 24 ], [ 44, 2, 8, 48 ], [ 44, 2, 22, 48 ], [ 44, 3, 7, 48 ], [ 44, 3, 16, 48 ], [ 44, 4, 18, 48 ], [ 44, 5, 5, 48 ], [ 44, 5, 18, 48 ], [ 44, 6, 3, 48 ], [ 44, 6, 15, 48 ], [ 44, 6, 19, 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 21, 1, 4, 18 ], [ 23, 1, 3, 4 ], [ 23, 2, 3, 2 ], [ 24, 1, 4, 8 ], [ 28, 1, 2, 4 ], [ 28, 1, 4, 12 ], [ 28, 2, 2, 2 ], [ 28, 2, 5, 6 ], [ 29, 1, 6, 12 ], [ 29, 2, 6, 6 ], [ 32, 1, 10, 18 ], [ 33, 1, 4, 8 ], [ 33, 1, 5, 24 ], [ 33, 2, 4, 4 ], [ 33, 2, 5, 12 ], [ 33, 3, 4, 4 ], [ 33, 3, 5, 12 ], [ 33, 4, 4, 4 ], [ 33, 4, 5, 12 ], [ 34, 1, 10, 18 ], [ 34, 2, 6, 9 ], [ 35, 1, 9, 12 ], [ 35, 2, 9, 6 ], [ 36, 1, 7, 18 ], [ 36, 5, 7, 9 ], [ 37, 1, 8, 12 ], [ 37, 2, 8, 6 ], [ 38, 1, 19, 36 ], [ 38, 2, 19, 18 ], [ 39, 1, 16, 24 ], [ 39, 2, 16, 12 ], [ 39, 3, 16, 12 ], [ 40, 1, 20, 36 ], [ 40, 2, 9, 18 ], [ 42, 1, 8, 24 ], [ 42, 1, 11, 36 ], [ 42, 2, 16, 18 ], [ 42, 3, 13, 12 ], [ 42, 4, 7, 12 ], [ 42, 4, 9, 18 ], [ 43, 1, 13, 36 ], [ 43, 3, 13, 18 ], [ 43, 5, 33, 18 ], [ 44, 2, 26, 36 ], [ 44, 3, 21, 36 ], [ 44, 4, 19, 36 ], [ 44, 5, 22, 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 ], [ 4, 2, 4, 6 ], [ 5, 1, 1, 6 ], [ 5, 2, 1, 3 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 6 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 3 ], [ 15, 1, 8, 24 ], [ 15, 2, 8, 12 ], [ 15, 3, 8, 12 ], [ 15, 4, 8, 12 ], [ 16, 1, 2, 6 ], [ 20, 1, 3, 12 ], [ 20, 2, 3, 6 ], [ 21, 1, 4, 6 ], [ 23, 1, 2, 12 ], [ 23, 2, 2, 6 ], [ 28, 1, 6, 12 ], [ 28, 2, 6, 6 ], [ 32, 1, 10, 18 ], [ 33, 1, 9, 24 ], [ 33, 2, 9, 12 ], [ 33, 3, 9, 12 ], [ 33, 4, 9, 12 ], [ 34, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 36, 1, 9, 18 ], [ 36, 5, 9, 9 ], [ 38, 1, 17, 36 ], [ 38, 2, 17, 18 ], [ 40, 1, 5, 36 ], [ 40, 2, 8, 18 ], [ 42, 1, 10, 12 ], [ 42, 2, 17, 6 ], [ 42, 4, 11, 6 ], [ 43, 1, 15, 36 ], [ 43, 3, 15, 18 ], [ 43, 5, 34, 18 ], [ 44, 2, 25, 36 ], [ 44, 3, 23, 36 ], [ 44, 4, 20, 36 ], [ 44, 5, 24, 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 ], [ 4, 2, 3, 2 ], [ 5, 1, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 12, 1, 4, 12 ], [ 12, 2, 2, 2 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 15, 1, 7, 8 ], [ 15, 2, 7, 4 ], [ 15, 3, 7, 4 ], [ 15, 4, 7, 4 ], [ 16, 1, 2, 2 ], [ 20, 1, 4, 4 ], [ 20, 2, 4, 2 ], [ 21, 1, 5, 6 ], [ 23, 1, 4, 4 ], [ 23, 2, 4, 2 ], [ 28, 1, 3, 4 ], [ 28, 2, 4, 2 ], [ 32, 1, 9, 6 ], [ 33, 1, 12, 8 ], [ 33, 2, 12, 4 ], [ 33, 3, 12, 4 ], [ 33, 4, 12, 4 ], [ 34, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 36, 1, 7, 6 ], [ 36, 5, 7, 3 ], [ 38, 1, 18, 12 ], [ 38, 2, 18, 6 ], [ 40, 1, 19, 12 ], [ 40, 2, 10, 6 ], [ 42, 1, 9, 12 ], [ 42, 2, 8, 6 ], [ 42, 4, 10, 6 ], [ 43, 1, 14, 12 ], [ 43, 3, 14, 6 ], [ 43, 5, 25, 6 ], [ 44, 2, 29, 12 ], [ 44, 3, 25, 12 ], [ 44, 4, 21, 12 ], [ 44, 5, 25, 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 ], [ 5, 2, 1, 1 ], [ 13, 1, 1, 2 ], [ 44, 4, 22, 7 ] ] 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 phi2^2 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 phi2^2 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 phi2^2 phi4 ( q^2-q-1 ) q congruent 7 modulo 12: 1/32 phi1 phi2^2 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 phi2^2 phi4 ( q^2-q-1 ) q congruent 11 modulo 12: 1/32 phi1 phi2^2 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 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 26, 1, 4, 4 ], [ 27, 1, 10, 8 ], [ 27, 2, 10, 4 ], [ 34, 1, 7, 8 ], [ 34, 2, 3, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 8, 4 ], [ 36, 1, 8, 16 ], [ 36, 2, 21, 8 ], [ 36, 3, 21, 8 ], [ 36, 4, 21, 8 ], [ 36, 5, 8, 8 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ], [ 41, 1, 29, 16 ], [ 41, 2, 29, 8 ], [ 41, 3, 29, 8 ], [ 43, 1, 20, 16 ], [ 43, 2, 14, 8 ], [ 43, 3, 20, 8 ], [ 44, 2, 34, 16 ], [ 44, 3, 37, 16 ], [ 44, 4, 23, 16 ], [ 44, 5, 35, 16 ], [ 44, 6, 24, 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 phi2 phi4 ( q^3-2*q^2-1 ) q congruent 2 modulo 12: 1/32 q^6 ( q-2 ) q congruent 3 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-1 ) q congruent 4 modulo 12: 1/32 q^6 ( q-2 ) q congruent 5 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-1 ) q congruent 7 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-1 ) q congruent 8 modulo 12: 1/32 q^6 ( q-2 ) q congruent 9 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-1 ) q congruent 11 modulo 12: 1/32 phi1 phi2 phi4 ( q^3-2*q^2-1 ) 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 ], [ 4, 2, 3, 2 ], [ 4, 2, 4, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 15, 1, 5, 8 ], [ 15, 1, 6, 8 ], [ 15, 2, 5, 4 ], [ 15, 2, 6, 4 ], [ 15, 3, 5, 4 ], [ 15, 3, 6, 4 ], [ 15, 4, 5, 4 ], [ 15, 4, 6, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 27, 2, 5, 4 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 36, 1, 12, 16 ], [ 36, 2, 8, 8 ], [ 36, 3, 8, 8 ], [ 36, 4, 8, 8 ], [ 36, 5, 12, 8 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ], [ 41, 1, 32, 16 ], [ 41, 2, 32, 8 ], [ 41, 3, 32, 8 ], [ 43, 1, 18, 16 ], [ 43, 2, 16, 8 ], [ 43, 3, 18, 8 ], [ 44, 2, 37, 16 ], [ 44, 3, 40, 16 ], [ 44, 4, 24, 16 ], [ 44, 5, 39, 16 ], [ 44, 6, 28, 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 ], [ 6, 2, 1, 1 ], [ 12, 1, 3, 6 ], [ 44, 4, 25, 9 ] ] 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 13, 1, 2, 2 ], [ 14, 1, 2, 2 ], [ 14, 2, 2, 1 ], [ 16, 1, 1, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 19, 1, 2, 2 ], [ 23, 1, 3, 4 ], [ 23, 2, 3, 2 ], [ 28, 1, 2, 4 ], [ 28, 2, 2, 2 ], [ 29, 1, 5, 4 ], [ 29, 2, 5, 2 ], [ 42, 1, 3, 10 ], [ 42, 4, 3, 5 ], [ 43, 1, 3, 10 ], [ 43, 3, 3, 5 ], [ 44, 2, 3, 10 ], [ 44, 4, 26, 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 phi1^2 phi2^2 phi3 q congruent 2 modulo 12: 1/48 q^4 phi1 phi2^2 q congruent 3 modulo 12: 1/48 q phi1^2 phi2^2 phi3 q congruent 4 modulo 12: 1/48 q^4 phi1 phi2^2 q congruent 5 modulo 12: 1/48 q phi1^2 phi2^2 phi3 q congruent 7 modulo 12: 1/48 q phi1^2 phi2^2 phi3 q congruent 8 modulo 12: 1/48 q^4 phi1 phi2^2 q congruent 9 modulo 12: 1/48 q phi1^2 phi2^2 phi3 q congruent 11 modulo 12: 1/48 q phi1^2 phi2^2 phi3 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 ], [ 4, 2, 1, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 21, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 6, 8 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ], [ 25, 4, 6, 4 ], [ 26, 1, 5, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 1, 3, 8 ], [ 30, 2, 3, 4 ], [ 33, 1, 11, 24 ], [ 33, 2, 11, 12 ], [ 33, 3, 11, 12 ], [ 33, 4, 11, 12 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 6 ], [ 35, 2, 6, 4 ], [ 35, 2, 8, 3 ], [ 37, 1, 4, 8 ], [ 37, 2, 4, 4 ], [ 39, 1, 6, 16 ], [ 39, 1, 7, 12 ], [ 39, 2, 6, 8 ], [ 39, 2, 7, 6 ], [ 39, 3, 6, 8 ], [ 39, 3, 7, 6 ], [ 39, 4, 4, 8 ], [ 39, 5, 4, 8 ], [ 40, 1, 14, 12 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 6 ], [ 41, 1, 28, 24 ], [ 41, 2, 28, 12 ], [ 41, 3, 28, 12 ], [ 41, 5, 24, 12 ], [ 41, 6, 24, 12 ], [ 41, 7, 24, 12 ], [ 42, 1, 15, 16 ], [ 42, 2, 7, 8 ], [ 42, 3, 9, 8 ], [ 42, 4, 14, 8 ], [ 43, 1, 8, 24 ], [ 43, 2, 5, 12 ], [ 43, 3, 7, 12 ], [ 44, 2, 12, 24 ], [ 44, 3, 9, 24 ], [ 44, 4, 27, 24 ], [ 44, 5, 8, 24 ], [ 44, 6, 4, 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 phi1^3 phi2 phi3 q congruent 2 modulo 12: 1/48 q^4 phi1^2 phi2 q congruent 3 modulo 12: 1/48 q phi1^3 phi2 phi3 q congruent 4 modulo 12: 1/48 q^4 phi1^2 phi2 q congruent 5 modulo 12: 1/48 q phi1^3 phi2 phi3 q congruent 7 modulo 12: 1/48 q phi1^3 phi2 phi3 q congruent 8 modulo 12: 1/48 q^4 phi1^2 phi2 q congruent 9 modulo 12: 1/48 q phi1^3 phi2 phi3 q congruent 11 modulo 12: 1/48 q phi1^3 phi2 phi3 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 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 13, 1, 2, 4 ], [ 15, 1, 4, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 4, 4 ], [ 15, 4, 4, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 21, 1, 3, 4 ], [ 24, 1, 3, 4 ], [ 25, 1, 7, 8 ], [ 25, 2, 7, 4 ], [ 25, 3, 7, 4 ], [ 25, 4, 7, 4 ], [ 26, 1, 5, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 29, 1, 6, 12 ], [ 29, 2, 6, 6 ], [ 30, 1, 8, 8 ], [ 30, 2, 8, 4 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 35, 1, 7, 8 ], [ 35, 1, 9, 6 ], [ 35, 2, 7, 4 ], [ 35, 2, 9, 3 ], [ 37, 1, 10, 8 ], [ 37, 2, 10, 4 ], [ 39, 1, 12, 12 ], [ 39, 1, 14, 16 ], [ 39, 2, 12, 6 ], [ 39, 2, 14, 8 ], [ 39, 3, 12, 6 ], [ 39, 3, 14, 8 ], [ 39, 4, 14, 8 ], [ 39, 5, 14, 8 ], [ 40, 1, 15, 12 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 6 ], [ 41, 1, 25, 24 ], [ 41, 2, 25, 12 ], [ 41, 3, 25, 12 ], [ 41, 5, 27, 12 ], [ 41, 6, 27, 12 ], [ 41, 7, 27, 12 ], [ 42, 1, 14, 16 ], [ 42, 2, 18, 8 ], [ 42, 3, 20, 8 ], [ 42, 4, 15, 8 ], [ 43, 1, 7, 24 ], [ 43, 2, 4, 12 ], [ 43, 3, 8, 12 ], [ 44, 2, 10, 24 ], [ 44, 3, 11, 24 ], [ 44, 4, 28, 24 ], [ 44, 5, 6, 24 ], [ 44, 6, 7, 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 ], [ 6, 2, 1, 1 ], [ 34, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 40, 1, 11, 12 ], [ 40, 2, 12, 6 ], [ 44, 3, 29, 12 ], [ 44, 4, 29, 12 ], [ 44, 5, 30, 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 ], [ 5, 2, 1, 1 ], [ 8, 1, 1, 2 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 29, 1, 3, 6 ], [ 29, 2, 3, 3 ], [ 42, 1, 2, 10 ], [ 42, 4, 2, 5 ], [ 44, 4, 30, 15 ] ] 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 ], [ 4, 2, 2, 1260 ], [ 5, 1, 2, 72 ], [ 5, 2, 2, 36 ], [ 6, 1, 2, 56 ], [ 6, 2, 2, 28 ], [ 7, 1, 2, 756 ], [ 8, 1, 2, 4032 ], [ 9, 1, 2, 10080 ], [ 10, 1, 4, 15120 ], [ 11, 1, 2, 2016 ], [ 12, 1, 6, 13440 ], [ 12, 2, 3, 6720 ], [ 13, 1, 2, 576 ], [ 14, 1, 2, 2016 ], [ 14, 2, 2, 1008 ], [ 15, 1, 4, 5040 ], [ 15, 2, 4, 2520 ], [ 15, 3, 4, 2520 ], [ 15, 4, 4, 2520 ], [ 16, 1, 2, 126 ], [ 17, 1, 3, 3780 ], [ 17, 2, 3, 1890 ], [ 18, 1, 3, 1512 ], [ 18, 2, 3, 756 ], [ 19, 1, 2, 12096 ], [ 20, 1, 2, 40320 ], [ 20, 2, 2, 20160 ], [ 21, 1, 6, 60480 ], [ 22, 1, 4, 30240 ], [ 23, 1, 4, 4032 ], [ 23, 2, 4, 2016 ], [ 24, 1, 3, 20160 ], [ 25, 1, 8, 30240 ], [ 25, 2, 8, 15120 ], [ 25, 3, 8, 15120 ], [ 25, 4, 8, 15120 ], [ 26, 1, 3, 7560 ], [ 27, 1, 12, 90720 ], [ 27, 2, 12, 45360 ], [ 27, 3, 11, 45360 ], [ 28, 1, 6, 4032 ], [ 28, 2, 6, 2016 ], [ 29, 1, 4, 24192 ], [ 29, 2, 4, 12096 ], [ 30, 1, 5, 120960 ], [ 30, 2, 5, 60480 ], [ 31, 1, 7, 60480 ], [ 31, 2, 7, 30240 ], [ 32, 1, 7, 181440 ], [ 33, 1, 6, 80640 ], [ 33, 2, 6, 40320 ], [ 33, 3, 6, 40320 ], [ 33, 4, 6, 40320 ], [ 34, 1, 4, 15120 ], [ 34, 2, 10, 7560 ], [ 34, 3, 5, 7560 ], [ 35, 1, 10, 60480 ], [ 35, 2, 10, 30240 ], [ 36, 1, 20, 181440 ], [ 36, 2, 25, 90720 ], [ 36, 3, 25, 90720 ], [ 36, 4, 25, 90720 ], [ 36, 5, 20, 90720 ], [ 36, 6, 13, 90720 ], [ 37, 1, 6, 241920 ], [ 37, 2, 6, 120960 ], [ 38, 1, 7, 362880 ], [ 38, 2, 7, 181440 ], [ 38, 3, 5, 181440 ], [ 39, 1, 15, 120960 ], [ 39, 2, 15, 60480 ], [ 39, 3, 15, 60480 ], [ 39, 4, 15, 60480 ], [ 39, 5, 15, 60480 ], [ 40, 1, 2, 362880 ], [ 40, 2, 13, 181440 ], [ 40, 3, 19, 181440 ], [ 41, 1, 16, 725760 ], [ 41, 2, 16, 362880 ], [ 41, 3, 16, 362880 ], [ 41, 4, 17, 362880 ], [ 41, 5, 13, 362880 ], [ 41, 6, 13, 362880 ], [ 41, 7, 13, 362880 ], [ 42, 1, 22, 483840 ], [ 42, 2, 20, 241920 ], [ 42, 3, 16, 241920 ], [ 42, 4, 22, 241920 ], [ 43, 1, 26, 1451520 ], [ 43, 2, 22, 725760 ], [ 43, 3, 26, 725760 ], [ 43, 4, 44, 725760 ], [ 43, 5, 40, 725760 ], [ 44, 2, 52, 1451520 ], [ 44, 3, 51, 1451520 ], [ 44, 4, 31, 1451520 ], [ 44, 5, 50, 1451520 ], [ 44, 6, 42, 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 ], [ 4, 2, 1, 260 ], [ 5, 1, 1, 32 ], [ 5, 2, 1, 16 ], [ 6, 1, 1, 32 ], [ 6, 2, 1, 16 ], [ 7, 1, 1, 252 ], [ 8, 1, 1, 832 ], [ 9, 1, 1, 1600 ], [ 10, 1, 1, 2160 ], [ 11, 1, 1, 512 ], [ 12, 1, 1, 1920 ], [ 12, 2, 1, 960 ], [ 13, 1, 1, 192 ], [ 14, 1, 1, 512 ], [ 14, 2, 1, 256 ], [ 15, 1, 1, 960 ], [ 15, 1, 3, 80 ], [ 15, 2, 1, 480 ], [ 15, 2, 3, 40 ], [ 15, 3, 1, 480 ], [ 15, 3, 3, 40 ], [ 15, 4, 1, 480 ], [ 15, 4, 3, 40 ], [ 16, 1, 1, 60 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 840 ], [ 17, 1, 3, 60 ], [ 17, 2, 1, 420 ], [ 17, 2, 3, 30 ], [ 18, 1, 1, 480 ], [ 18, 1, 2, 24 ], [ 18, 2, 1, 240 ], [ 18, 2, 2, 12 ], [ 19, 1, 1, 2112 ], [ 20, 1, 1, 4480 ], [ 20, 2, 1, 2240 ], [ 21, 1, 1, 5760 ], [ 22, 1, 1, 3840 ], [ 22, 1, 2, 480 ], [ 23, 1, 1, 960 ], [ 23, 1, 2, 64 ], [ 23, 2, 1, 480 ], [ 23, 2, 2, 32 ], [ 24, 1, 1, 2880 ], [ 24, 1, 2, 320 ], [ 25, 1, 1, 3840 ], [ 25, 1, 5, 480 ], [ 25, 2, 1, 1920 ], [ 25, 2, 5, 240 ], [ 25, 3, 1, 1920 ], [ 25, 3, 5, 240 ], [ 25, 4, 1, 1920 ], [ 25, 4, 5, 240 ], [ 26, 1, 1, 1560 ], [ 26, 1, 2, 120 ], [ 27, 1, 1, 7200 ], [ 27, 1, 8, 1440 ], [ 27, 2, 1, 3600 ], [ 27, 2, 8, 720 ], [ 27, 3, 1, 3600 ], [ 27, 3, 5, 720 ], [ 27, 3, 9, 720 ], [ 28, 1, 1, 960 ], [ 28, 1, 3, 64 ], [ 28, 2, 1, 480 ], [ 28, 2, 4, 32 ], [ 29, 1, 1, 3840 ], [ 29, 1, 2, 384 ], [ 29, 2, 1, 1920 ], [ 29, 2, 2, 192 ], [ 30, 1, 1, 9600 ], [ 30, 1, 2, 1920 ], [ 30, 2, 1, 4800 ], [ 30, 2, 2, 960 ], [ 31, 1, 1, 6720 ], [ 31, 1, 2, 960 ], [ 31, 1, 3, 960 ], [ 31, 2, 1, 3360 ], [ 31, 2, 2, 480 ], [ 31, 2, 3, 480 ], [ 32, 1, 1, 11520 ], [ 32, 1, 6, 2880 ], [ 33, 1, 1, 7680 ], [ 33, 1, 3, 1280 ], [ 33, 2, 1, 3840 ], [ 33, 2, 3, 640 ], [ 33, 3, 1, 3840 ], [ 33, 3, 3, 640 ], [ 33, 4, 1, 3840 ], [ 33, 4, 3, 640 ], [ 34, 1, 1, 2880 ], [ 34, 1, 2, 240 ], [ 34, 2, 1, 1440 ], [ 34, 2, 2, 120 ], [ 34, 3, 1, 1440 ], [ 34, 3, 2, 120 ], [ 35, 1, 1, 6720 ], [ 35, 1, 2, 960 ], [ 35, 2, 1, 3360 ], [ 35, 2, 2, 480 ], [ 36, 1, 1, 11520 ], [ 36, 1, 4, 2880 ], [ 36, 2, 1, 5760 ], [ 36, 2, 4, 1440 ], [ 36, 2, 14, 1440 ], [ 36, 3, 1, 5760 ], [ 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], [ 44, 6, 94, 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+74*q^3-37*q^2-3363*q+7127 ) 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 ( q^7-16*q^6+68*q^5+21*q^4-111*q^3-3326*q^2+9834*q-5319 ) 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+74*q^3-37*q^2-3363*q+6615 ) q congruent 7 modulo 12: 1/9216 ( q^7-16*q^6+68*q^5+21*q^4-111*q^3-3326*q^2+10346*q-5831 ) 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+74*q^3-37*q^2-3363*q+6615 ) q congruent 11 modulo 12: 1/9216 ( q^7-16*q^6+68*q^5+21*q^4-111*q^3-3326*q^2+9834*q-5319 ) 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 ], [ 4, 2, 1, 24 ], [ 4, 2, 2, 36 ], [ 4, 2, 3, 96 ], [ 5, 1, 2, 24 ], [ 5, 2, 2, 12 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 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 ], [ 12, 2, 2, 128 ], [ 14, 1, 2, 96 ], [ 14, 2, 2, 48 ], [ 15, 1, 3, 96 ], [ 15, 1, 4, 144 ], [ 15, 1, 5, 384 ], [ 15, 2, 3, 48 ], [ 15, 2, 4, 72 ], [ 15, 2, 5, 192 ], [ 15, 3, 3, 48 ], [ 15, 3, 4, 72 ], [ 15, 3, 5, 192 ], [ 15, 4, 3, 48 ], [ 15, 4, 4, 72 ], [ 15, 4, 5, 192 ], [ 16, 1, 1, 24 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 144 ], [ 17, 1, 2, 96 ], [ 17, 1, 3, 84 ], [ 17, 2, 1, 72 ], [ 17, 2, 2, 48 ], [ 17, 2, 3, 42 ], [ 18, 1, 2, 48 ], [ 18, 1, 3, 24 ], [ 18, 2, 2, 24 ], [ 18, 2, 3, 12 ], [ 20, 1, 4, 768 ], [ 20, 2, 4, 384 ], [ 21, 1, 1, 192 ], [ 21, 1, 2, 384 ], [ 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576 ], [ 40, 3, 5, 1152 ], [ 40, 3, 6, 1152 ], [ 40, 3, 17, 576 ], [ 41, 1, 5, 2304 ], [ 41, 1, 10, 2304 ], [ 41, 1, 15, 2304 ], [ 41, 1, 30, 4608 ], [ 41, 2, 5, 1152 ], [ 41, 2, 10, 1152 ], [ 41, 2, 15, 1152 ], [ 41, 2, 30, 2304 ], [ 41, 3, 5, 1152 ], [ 41, 3, 10, 1152 ], [ 41, 3, 15, 1152 ], [ 41, 3, 30, 2304 ], [ 41, 4, 3, 1152 ], [ 41, 4, 5, 1152 ], [ 41, 4, 9, 1152 ], [ 41, 4, 14, 1152 ], [ 41, 4, 16, 1152 ], [ 41, 4, 35, 2304 ], [ 41, 4, 37, 2304 ], [ 41, 5, 4, 1152 ], [ 41, 5, 10, 1152 ], [ 41, 5, 12, 1152 ], [ 41, 5, 28, 2304 ], [ 41, 5, 30, 2304 ], [ 41, 6, 4, 1152 ], [ 41, 6, 10, 1152 ], [ 41, 6, 12, 1152 ], [ 41, 6, 28, 2304 ], [ 41, 6, 30, 2304 ], [ 41, 7, 4, 1152 ], [ 41, 7, 10, 1152 ], [ 41, 7, 12, 1152 ], [ 41, 7, 28, 2304 ], [ 41, 7, 30, 2304 ], [ 42, 1, 19, 1536 ], [ 42, 2, 6, 768 ], [ 42, 2, 10, 768 ], [ 42, 3, 10, 768 ], [ 42, 4, 19, 768 ], [ 43, 1, 22, 4608 ], [ 43, 1, 37, 4608 ], [ 43, 2, 18, 2304 ], [ 43, 2, 27, 2304 ], [ 43, 2, 36, 2304 ], [ 43, 2, 50, 2304 ], [ 43, 3, 22, 2304 ], [ 43, 3, 37, 2304 ], [ 43, 4, 10, 2304 ], [ 43, 4, 19, 2304 ], [ 43, 4, 31, 2304 ], [ 43, 4, 43, 2304 ], [ 43, 5, 8, 2304 ], [ 43, 5, 23, 2304 ], [ 43, 5, 27, 2304 ], [ 43, 5, 37, 2304 ], [ 44, 2, 41, 4608 ], [ 44, 2, 72, 4608 ], [ 44, 3, 50, 4608 ], [ 44, 3, 73, 4608 ], [ 44, 3, 86, 4608 ], [ 44, 4, 33, 4608 ], [ 44, 5, 52, 4608 ], [ 44, 5, 67, 4608 ], [ 44, 5, 88, 4608 ], [ 44, 6, 43, 4608 ], [ 44, 6, 62, 4608 ], [ 44, 6, 86, 4608 ], [ 44, 6, 104, 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 ( q^6-11*q^5+37*q^4-54*q^3+195*q^2-647*q+735 ) 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 ( q^6-11*q^5+37*q^4-54*q^3+195*q^2-647*q+591 ) 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 ( q^6-11*q^5+37*q^4-54*q^3+195*q^2-647*q+735 ) q congruent 7 modulo 12: 1/3072 phi1 ( q^6-11*q^5+37*q^4-54*q^3+195*q^2-647*q+591 ) 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 ( q^6-11*q^5+37*q^4-54*q^3+195*q^2-647*q+735 ) q congruent 11 modulo 12: 1/3072 phi1 ( q^6-11*q^5+37*q^4-54*q^3+195*q^2-647*q+591 ) 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 ], [ 4, 2, 1, 12 ], [ 4, 2, 2, 72 ], [ 5, 1, 2, 16 ], [ 5, 2, 2, 8 ], [ 6, 1, 2, 16 ], [ 6, 2, 2, 8 ], [ 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 ], [ 12, 2, 3, 192 ], [ 13, 1, 2, 64 ], [ 14, 1, 2, 128 ], [ 14, 2, 2, 64 ], [ 15, 1, 2, 64 ], [ 15, 1, 3, 48 ], [ 15, 1, 4, 224 ], [ 15, 2, 2, 32 ], [ 15, 2, 3, 24 ], [ 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1536 ], [ 44, 6, 82, 1536 ], [ 44, 6, 84, 1536 ], [ 44, 6, 97, 1536 ], [ 44, 6, 101, 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+26*q^3+59*q^2-251*q+39 ) 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 ( q^6-7*q^5+5*q^4+26*q^3+59*q^2-251*q+87 ) 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+26*q^3+59*q^2-251*q+39 ) q congruent 7 modulo 12: 1/768 phi1 ( q^6-7*q^5+5*q^4+26*q^3+59*q^2-251*q+87 ) 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+26*q^3+59*q^2-251*q+39 ) q congruent 11 modulo 12: 1/768 phi1 ( q^6-7*q^5+5*q^4+26*q^3+59*q^2-251*q+87 ) Fusion of maximal tori of C^F in those of G^F: [ 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4, 18, 192 ], [ 43, 1, 29, 384 ], [ 43, 1, 31, 384 ], [ 43, 1, 32, 384 ], [ 43, 2, 38, 192 ], [ 43, 2, 44, 192 ], [ 43, 2, 46, 192 ], [ 43, 2, 47, 192 ], [ 43, 2, 48, 192 ], [ 43, 2, 49, 192 ], [ 43, 2, 53, 192 ], [ 43, 3, 29, 192 ], [ 43, 3, 34, 192 ], [ 43, 3, 36, 192 ], [ 43, 4, 5, 192 ], [ 43, 4, 7, 192 ], [ 43, 4, 11, 192 ], [ 43, 4, 16, 192 ], [ 43, 4, 23, 192 ], [ 43, 4, 24, 192 ], [ 43, 4, 28, 192 ], [ 43, 4, 37, 192 ], [ 43, 4, 45, 192 ], [ 43, 4, 49, 192 ], [ 43, 5, 4, 192 ], [ 43, 5, 5, 192 ], [ 43, 5, 10, 192 ], [ 43, 5, 11, 192 ], [ 43, 5, 12, 192 ], [ 43, 5, 13, 192 ], [ 43, 5, 14, 192 ], [ 43, 5, 19, 192 ], [ 43, 5, 22, 192 ], [ 44, 2, 66, 384 ], [ 44, 2, 68, 384 ], [ 44, 2, 73, 384 ], [ 44, 3, 76, 384 ], [ 44, 3, 80, 384 ], [ 44, 3, 83, 384 ], [ 44, 3, 90, 384 ], [ 44, 4, 35, 384 ], [ 44, 5, 78, 384 ], [ 44, 5, 79, 384 ], [ 44, 5, 82, 384 ], [ 44, 5, 89, 384 ], [ 44, 6, 81, 384 ], [ 44, 6, 83, 384 ], [ 44, 6, 90, 384 ], [ 44, 6, 92, 384 ], [ 44, 6, 95, 384 ], [ 44, 6, 100, 384 ], [ 44, 6, 105, 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 ], [ 4, 2, 2, 30 ], [ 5, 1, 2, 12 ], [ 5, 2, 2, 6 ], [ 6, 1, 2, 20 ], [ 6, 2, 2, 10 ], [ 7, 1, 2, 90 ], [ 8, 1, 2, 132 ], [ 9, 1, 2, 150 ], [ 10, 1, 4, 180 ], [ 11, 1, 2, 120 ], [ 12, 1, 6, 120 ], [ 12, 2, 3, 60 ], [ 13, 1, 2, 60 ], [ 14, 1, 2, 120 ], [ 14, 2, 2, 60 ], [ 15, 1, 4, 120 ], [ 15, 2, 4, 60 ], [ 15, 3, 4, 60 ], [ 15, 4, 4, 60 ], [ 16, 1, 2, 30 ], [ 17, 1, 3, 180 ], [ 17, 2, 3, 90 ], [ 18, 1, 3, 180 ], [ 18, 2, 3, 90 ], [ 19, 1, 2, 360 ], [ 20, 1, 2, 240 ], [ 20, 2, 2, 120 ], [ 21, 1, 6, 180 ], [ 22, 1, 4, 360 ], [ 23, 1, 4, 240 ], [ 23, 2, 4, 120 ], [ 24, 1, 3, 300 ], [ 25, 1, 8, 360 ], [ 25, 2, 8, 180 ], [ 25, 3, 8, 180 ], [ 25, 4, 8, 180 ], [ 26, 1, 3, 360 ], [ 28, 1, 4, 6 ], [ 28, 1, 6, 240 ], [ 28, 2, 5, 3 ], [ 28, 2, 6, 120 ], [ 29, 1, 4, 720 ], [ 29, 1, 6, 36 ], [ 29, 2, 4, 360 ], [ 29, 2, 6, 18 ], [ 30, 1, 5, 360 ], [ 30, 2, 5, 180 ], [ 31, 1, 7, 720 ], [ 31, 2, 7, 360 ], [ 33, 1, 5, 120 ], [ 33, 1, 6, 480 ], [ 33, 2, 5, 60 ], [ 33, 2, 6, 240 ], [ 33, 3, 5, 60 ], [ 33, 3, 6, 240 ], [ 33, 4, 5, 60 ], [ 33, 4, 6, 240 ], [ 34, 1, 4, 720 ], [ 34, 2, 10, 360 ], [ 34, 3, 5, 360 ], [ 35, 1, 9, 90 ], [ 35, 1, 10, 720 ], [ 35, 2, 9, 45 ], [ 35, 2, 10, 360 ], [ 37, 1, 6, 720 ], [ 37, 1, 8, 360 ], [ 37, 2, 6, 360 ], [ 37, 2, 8, 180 ], [ 39, 1, 12, 180 ], [ 39, 1, 15, 1440 ], [ 39, 2, 12, 90 ], [ 39, 2, 15, 720 ], [ 39, 3, 12, 90 ], [ 39, 3, 15, 720 ], [ 39, 4, 15, 720 ], [ 39, 5, 15, 720 ], [ 40, 1, 8, 540 ], [ 40, 2, 5, 270 ], [ 40, 3, 9, 270 ], [ 41, 1, 8, 1080 ], [ 41, 2, 8, 540 ], [ 41, 3, 8, 540 ], [ 41, 5, 9, 540 ], [ 41, 6, 9, 540 ], [ 41, 7, 9, 540 ], [ 42, 1, 6, 720 ], [ 42, 1, 22, 1440 ], [ 42, 2, 20, 720 ], [ 42, 3, 16, 720 ], [ 42, 3, 18, 360 ], [ 42, 4, 8, 360 ], [ 42, 4, 22, 720 ], [ 43, 1, 9, 2160 ], [ 43, 2, 7, 1080 ], [ 43, 3, 9, 1080 ], [ 43, 4, 34, 1080 ], [ 44, 2, 13, 2160 ], [ 44, 3, 15, 2160 ], [ 44, 4, 36, 2160 ], [ 44, 5, 13, 2160 ], [ 44, 6, 13, 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 ], [ 6, 2, 2, 1 ], [ 12, 1, 6, 48 ], [ 12, 2, 3, 24 ], [ 21, 1, 4, 216 ], [ 28, 1, 4, 72 ], [ 28, 2, 5, 36 ], [ 33, 1, 5, 144 ], [ 33, 2, 5, 72 ], [ 33, 3, 5, 72 ], [ 33, 4, 5, 72 ], [ 34, 1, 10, 54 ], [ 34, 2, 6, 27 ], [ 40, 1, 10, 648 ], [ 40, 2, 11, 324 ], [ 42, 1, 11, 432 ], [ 42, 2, 16, 216 ], [ 42, 4, 9, 216 ], [ 44, 3, 31, 648 ], [ 44, 4, 37, 648 ], [ 44, 5, 27, 648 ] ] 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 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 6 ], [ 5, 2, 2, 3 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 12 ], [ 11, 1, 2, 6 ], [ 12, 1, 4, 36 ], [ 12, 1, 6, 12 ], [ 12, 2, 3, 6 ], [ 13, 1, 2, 12 ], [ 14, 1, 2, 6 ], [ 14, 2, 2, 3 ], [ 15, 1, 4, 24 ], [ 15, 2, 4, 12 ], [ 15, 3, 4, 12 ], [ 15, 4, 4, 12 ], [ 16, 1, 2, 6 ], [ 20, 1, 2, 12 ], [ 20, 2, 2, 6 ], [ 21, 1, 4, 18 ], [ 23, 1, 4, 12 ], [ 23, 2, 4, 6 ], [ 24, 1, 3, 24 ], [ 28, 1, 4, 12 ], [ 28, 1, 6, 12 ], [ 28, 2, 5, 6 ], [ 28, 2, 6, 6 ], [ 29, 1, 6, 36 ], [ 29, 2, 6, 18 ], [ 32, 1, 10, 54 ], [ 33, 1, 5, 24 ], [ 33, 1, 6, 24 ], [ 33, 2, 5, 12 ], [ 33, 2, 6, 12 ], [ 33, 3, 5, 12 ], [ 33, 3, 6, 12 ], [ 33, 4, 5, 12 ], [ 33, 4, 6, 12 ], [ 34, 1, 10, 18 ], [ 34, 2, 6, 9 ], [ 35, 1, 9, 36 ], [ 35, 2, 9, 18 ], [ 36, 1, 7, 54 ], [ 36, 5, 7, 27 ], [ 37, 1, 8, 36 ], [ 37, 2, 8, 18 ], [ 38, 1, 18, 108 ], [ 38, 2, 18, 54 ], [ 39, 1, 12, 72 ], [ 39, 2, 12, 36 ], [ 39, 3, 12, 36 ], [ 40, 1, 5, 108 ], [ 40, 2, 8, 54 ], [ 42, 1, 6, 72 ], [ 42, 1, 11, 36 ], [ 42, 2, 16, 18 ], [ 42, 3, 18, 36 ], [ 42, 4, 8, 36 ], [ 42, 4, 9, 18 ], [ 43, 1, 13, 108 ], [ 43, 3, 13, 54 ], [ 43, 5, 33, 54 ], [ 44, 2, 23, 108 ], [ 44, 3, 24, 108 ], [ 44, 4, 38, 108 ], [ 44, 5, 20, 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 phi1^2 phi2 ( q^4+q^3-2*q^2-9*q-15 ) q congruent 2 modulo 12: 1/768 q^5 ( q^2-4 ) q congruent 3 modulo 12: 1/768 phi1^2 phi2 ( q^4+q^3-2*q^2-9*q-15 ) q congruent 4 modulo 12: 1/768 q^5 ( q^2-4 ) q congruent 5 modulo 12: 1/768 phi1^2 phi2 ( q^4+q^3-2*q^2-9*q-15 ) q congruent 7 modulo 12: 1/768 phi1^2 phi2 ( q^4+q^3-2*q^2-9*q-15 ) q congruent 8 modulo 12: 1/768 q^5 ( q^2-4 ) q congruent 9 modulo 12: 1/768 phi1^2 phi2 ( q^4+q^3-2*q^2-9*q-15 ) q congruent 11 modulo 12: 1/768 phi1^2 phi2 ( q^4+q^3-2*q^2-9*q-15 ) 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 ], [ 4, 2, 1, 12 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 12 ], [ 10, 1, 2, 48 ], [ 15, 1, 3, 48 ], [ 15, 2, 3, 24 ], [ 15, 3, 3, 24 ], [ 15, 4, 3, 24 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 2, 12 ], [ 17, 2, 3, 6 ], [ 18, 1, 3, 24 ], [ 18, 2, 3, 12 ], [ 25, 1, 6, 96 ], [ 25, 2, 6, 48 ], [ 25, 3, 6, 48 ], [ 25, 4, 6, 48 ], [ 26, 1, 3, 24 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 1, 11, 96 ], [ 27, 1, 13, 96 ], [ 27, 2, 7, 24 ], [ 27, 2, 11, 48 ], [ 27, 2, 13, 48 ], [ 27, 3, 7, 48 ], [ 27, 3, 8, 48 ], [ 27, 3, 12, 48 ], [ 32, 1, 4, 96 ], [ 34, 1, 4, 48 ], [ 34, 1, 8, 48 ], [ 34, 2, 5, 24 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 24 ], [ 35, 1, 6, 96 ], [ 35, 2, 6, 48 ], [ 36, 1, 10, 96 ], [ 36, 1, 19, 192 ], [ 36, 2, 16, 48 ], [ 36, 2, 22, 96 ], [ 36, 2, 26, 96 ], [ 36, 3, 16, 48 ], [ 36, 3, 22, 96 ], [ 36, 3, 26, 96 ], [ 36, 4, 16, 48 ], [ 36, 4, 22, 96 ], [ 36, 4, 26, 96 ], [ 36, 5, 10, 48 ], [ 36, 5, 19, 96 ], [ 36, 6, 16, 96 ], [ 38, 1, 12, 192 ], [ 38, 2, 12, 96 ], [ 39, 1, 6, 192 ], [ 39, 2, 6, 96 ], [ 39, 3, 6, 96 ], [ 39, 4, 4, 96 ], [ 39, 5, 4, 96 ], [ 40, 1, 6, 96 ], [ 40, 1, 24, 192 ], [ 40, 2, 14, 48 ], [ 40, 2, 18, 96 ], [ 40, 3, 14, 96 ], [ 41, 1, 14, 192 ], [ 41, 1, 26, 384 ], [ 41, 2, 14, 96 ], [ 41, 2, 26, 192 ], [ 41, 3, 14, 96 ], [ 41, 3, 26, 192 ], [ 41, 4, 7, 96 ], [ 41, 4, 30, 192 ], [ 41, 4, 32, 192 ], [ 41, 5, 23, 192 ], [ 41, 6, 23, 192 ], [ 41, 7, 23, 192 ], [ 43, 1, 17, 384 ], [ 43, 2, 15, 192 ], [ 43, 2, 24, 192 ], [ 43, 3, 17, 192 ], [ 43, 4, 40, 192 ], [ 43, 5, 29, 192 ], [ 44, 2, 35, 384 ], [ 44, 3, 33, 384 ], [ 44, 3, 70, 384 ], [ 44, 4, 39, 384 ], [ 44, 5, 33, 384 ], [ 44, 5, 71, 384 ], [ 44, 6, 30, 384 ], [ 44, 6, 66, 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 phi1^2 phi2 ( q^4-5*q^3+6*q^2-7*q+21 ) 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 phi1^2 phi2 ( q^4-5*q^3+6*q^2-7*q+21 ) 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 phi1^2 phi2 ( q^4-5*q^3+6*q^2-7*q+21 ) q congruent 7 modulo 12: 1/384 phi1^2 phi2 ( q^4-5*q^3+6*q^2-7*q+21 ) 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 phi1^2 phi2 ( q^4-5*q^3+6*q^2-7*q+21 ) q congruent 11 modulo 12: 1/384 phi1^2 phi2 ( q^4-5*q^3+6*q^2-7*q+21 ) 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 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 24 ], [ 5, 1, 1, 12 ], [ 5, 2, 1, 6 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 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 ], [ 12, 2, 4, 16 ], [ 14, 1, 1, 24 ], [ 14, 2, 1, 12 ], [ 15, 1, 1, 24 ], [ 15, 1, 2, 8 ], [ 15, 1, 8, 96 ], [ 15, 2, 1, 12 ], [ 15, 2, 2, 4 ], [ 15, 2, 8, 48 ], [ 15, 3, 1, 12 ], [ 15, 3, 2, 4 ], [ 15, 3, 8, 48 ], [ 15, 4, 1, 12 ], [ 15, 4, 2, 4 ], [ 15, 4, 8, 48 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 12 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 24 ], [ 17, 1, 4, 16 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 12 ], [ 17, 2, 4, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 12 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 6 ], [ 20, 1, 3, 96 ], [ 20, 2, 3, 48 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 1, 2, 48 ], [ 23, 2, 2, 24 ], [ 24, 1, 4, 16 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 72 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 24 ], [ 25, 2, 1, 12 ], [ 25, 2, 2, 36 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 12 ], [ 25, 3, 1, 12 ], [ 25, 3, 2, 36 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 12 ], [ 25, 4, 1, 12 ], [ 25, 4, 2, 36 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 6, 48 ], [ 27, 2, 7, 12 ], [ 27, 2, 13, 48 ], [ 27, 3, 4, 48 ], [ 27, 3, 12, 48 ], [ 27, 3, 13, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 30, 1, 7, 32 ], [ 30, 2, 7, 16 ], [ 31, 1, 3, 48 ], [ 31, 1, 8, 48 ], [ 31, 2, 3, 24 ], [ 31, 2, 8, 24 ], [ 32, 1, 4, 48 ], [ 32, 1, 5, 48 ], [ 33, 1, 9, 192 ], [ 33, 2, 9, 96 ], [ 33, 3, 9, 96 ], [ 33, 4, 9, 96 ], [ 34, 1, 3, 48 ], [ 34, 1, 5, 24 ], [ 34, 1, 6, 8 ], [ 34, 2, 4, 12 ], [ 34, 2, 8, 4 ], [ 34, 2, 9, 24 ], [ 34, 3, 4, 12 ], [ 34, 3, 6, 24 ], [ 34, 3, 7, 12 ], [ 35, 1, 5, 48 ], [ 35, 1, 6, 24 ], [ 35, 1, 7, 8 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 6, 12 ], [ 35, 2, 7, 4 ], [ 35, 2, 10, 24 ], [ 36, 1, 2, 48 ], [ 36, 1, 15, 192 ], [ 36, 1, 17, 48 ], [ 36, 2, 2, 24 ], [ 36, 2, 12, 96 ], [ 36, 2, 13, 24 ], [ 36, 2, 24, 96 ], [ 36, 3, 2, 24 ], [ 36, 3, 12, 96 ], [ 36, 3, 13, 24 ], [ 36, 3, 24, 96 ], [ 36, 4, 2, 24 ], [ 36, 4, 12, 96 ], [ 36, 4, 13, 24 ], [ 36, 4, 24, 96 ], [ 36, 5, 2, 24 ], [ 36, 5, 15, 96 ], [ 36, 5, 17, 24 ], [ 36, 6, 2, 24 ], [ 36, 6, 4, 24 ], [ 36, 6, 10, 24 ], [ 36, 6, 11, 24 ], [ 36, 6, 12, 96 ], [ 37, 1, 10, 32 ], [ 37, 2, 10, 16 ], [ 38, 1, 11, 96 ], [ 38, 1, 15, 96 ], [ 38, 2, 11, 48 ], [ 38, 2, 15, 48 ], [ 38, 3, 13, 48 ], [ 38, 3, 16, 48 ], [ 39, 1, 9, 48 ], [ 39, 1, 10, 96 ], [ 39, 1, 17, 16 ], [ 39, 1, 20, 96 ], [ 39, 2, 9, 24 ], [ 39, 2, 10, 48 ], [ 39, 2, 17, 8 ], [ 39, 2, 20, 48 ], [ 39, 3, 9, 24 ], [ 39, 3, 10, 48 ], [ 39, 3, 17, 8 ], [ 39, 3, 20, 48 ], [ 39, 4, 8, 48 ], [ 39, 4, 9, 48 ], [ 39, 4, 10, 24 ], [ 39, 4, 16, 8 ], [ 39, 4, 20, 48 ], [ 39, 5, 8, 48 ], [ 39, 5, 9, 48 ], [ 39, 5, 10, 24 ], [ 39, 5, 16, 8 ], [ 39, 5, 20, 48 ], [ 40, 1, 13, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 24, 96 ], [ 40, 2, 18, 48 ], [ 40, 2, 20, 24 ], [ 40, 2, 24, 48 ], [ 40, 3, 11, 24 ], [ 40, 3, 14, 48 ], [ 40, 3, 15, 24 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 48 ], [ 41, 1, 9, 96 ], [ 41, 1, 18, 96 ], [ 41, 1, 39, 192 ], [ 41, 1, 40, 192 ], [ 41, 2, 9, 48 ], [ 41, 2, 18, 48 ], [ 41, 2, 39, 96 ], [ 41, 2, 40, 96 ], [ 41, 3, 9, 48 ], [ 41, 3, 18, 48 ], [ 41, 3, 39, 96 ], [ 41, 3, 40, 96 ], [ 41, 4, 18, 48 ], [ 41, 4, 21, 48 ], [ 41, 4, 47, 96 ], [ 41, 4, 48, 96 ], [ 41, 4, 49, 96 ], [ 41, 4, 50, 96 ], [ 41, 5, 16, 48 ], [ 41, 5, 18, 48 ], [ 41, 5, 38, 96 ], [ 41, 5, 39, 96 ], [ 41, 5, 40, 96 ], [ 41, 6, 16, 48 ], [ 41, 6, 18, 48 ], [ 41, 6, 38, 96 ], [ 41, 6, 39, 96 ], [ 41, 6, 40, 96 ], [ 41, 7, 16, 48 ], [ 41, 7, 18, 48 ], [ 41, 7, 38, 96 ], [ 41, 7, 39, 96 ], [ 41, 7, 40, 96 ], [ 42, 1, 13, 64 ], [ 42, 2, 14, 32 ], [ 42, 3, 15, 32 ], [ 42, 4, 16, 32 ], [ 43, 1, 23, 192 ], [ 43, 1, 35, 192 ], [ 43, 2, 19, 96 ], [ 43, 2, 29, 96 ], [ 43, 2, 30, 96 ], [ 43, 2, 42, 96 ], [ 43, 3, 23, 96 ], [ 43, 3, 33, 96 ], [ 43, 4, 15, 96 ], [ 43, 4, 35, 96 ], [ 43, 4, 48, 96 ], [ 43, 5, 6, 96 ], [ 43, 5, 15, 96 ], [ 44, 2, 45, 192 ], [ 44, 2, 60, 192 ], [ 44, 3, 43, 192 ], [ 44, 3, 55, 192 ], [ 44, 3, 60, 192 ], [ 44, 4, 40, 192 ], [ 44, 5, 43, 192 ], [ 44, 5, 55, 192 ], [ 44, 5, 59, 192 ], [ 44, 6, 38, 192 ], [ 44, 6, 48, 192 ], [ 44, 6, 51, 192 ], [ 44, 6, 77, 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^3-25*q^2-16*q+3 ) 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^3-25*q^2-16*q+3 ) 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^3-25*q^2-16*q+3 ) q congruent 7 modulo 12: 1/384 phi1 phi2 ( q^5-10*q^4+31*q^3-25*q^2-16*q+3 ) 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^3-25*q^2-16*q+3 ) q congruent 11 modulo 12: 1/384 phi1 phi2 ( q^5-10*q^4+31*q^3-25*q^2-16*q+3 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 1, 1, 12 ], [ 6, 2, 1, 6 ], [ 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 ], [ 14, 2, 1, 12 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 24 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 12 ], [ 15, 3, 1, 4 ], [ 15, 3, 2, 12 ], [ 15, 4, 1, 4 ], [ 15, 4, 2, 12 ], [ 16, 1, 1, 14 ], [ 17, 1, 1, 36 ], [ 17, 1, 4, 16 ], [ 17, 2, 1, 18 ], [ 17, 2, 4, 8 ], [ 18, 1, 1, 60 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 30 ], [ 18, 2, 4, 2 ], [ 19, 1, 1, 48 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 1, 1, 48 ], [ 23, 2, 1, 24 ], [ 24, 1, 1, 16 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 72 ], [ 25, 1, 4, 24 ], [ 25, 2, 1, 12 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 36 ], [ 25, 2, 4, 12 ], [ 25, 3, 1, 12 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 36 ], [ 25, 3, 4, 12 ], [ 25, 4, 1, 12 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 36 ], [ 25, 4, 4, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 2, 7, 12 ], [ 27, 2, 14, 48 ], [ 27, 3, 2, 48 ], [ 27, 3, 15, 48 ], [ 27, 3, 16, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 29, 1, 1, 96 ], [ 29, 2, 1, 48 ], [ 30, 1, 4, 32 ], [ 30, 2, 4, 16 ], [ 31, 1, 1, 48 ], [ 31, 1, 6, 48 ], [ 31, 2, 1, 24 ], [ 31, 2, 6, 24 ], [ 32, 1, 2, 48 ], [ 32, 1, 8, 48 ], [ 34, 1, 1, 144 ], [ 34, 1, 5, 24 ], [ 34, 1, 6, 8 ], [ 34, 2, 1, 72 ], [ 34, 2, 4, 12 ], [ 34, 2, 8, 4 ], [ 34, 3, 1, 72 ], [ 34, 3, 4, 12 ], [ 34, 3, 7, 12 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 24 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 12 ], [ 36, 1, 2, 48 ], [ 36, 1, 3, 192 ], [ 36, 1, 17, 48 ], [ 36, 2, 2, 24 ], [ 36, 2, 3, 96 ], [ 36, 2, 13, 24 ], [ 36, 2, 27, 96 ], [ 36, 3, 2, 24 ], [ 36, 3, 3, 96 ], [ 36, 3, 13, 24 ], [ 36, 3, 27, 96 ], [ 36, 4, 2, 24 ], [ 36, 4, 3, 96 ], [ 36, 4, 13, 24 ], [ 36, 4, 27, 96 ], [ 36, 5, 2, 24 ], [ 36, 5, 3, 96 ], [ 36, 5, 17, 24 ], [ 36, 6, 2, 24 ], [ 36, 6, 3, 96 ], [ 36, 6, 4, 24 ], [ 36, 6, 10, 24 ], [ 36, 6, 11, 24 ], [ 37, 1, 4, 32 ], [ 37, 2, 4, 16 ], [ 38, 1, 10, 96 ], [ 38, 1, 13, 96 ], [ 38, 2, 10, 48 ], [ 38, 2, 13, 48 ], [ 38, 3, 10, 48 ], [ 38, 3, 11, 48 ], [ 39, 1, 1, 96 ], [ 39, 1, 9, 16 ], [ 39, 1, 17, 48 ], [ 39, 1, 18, 96 ], [ 39, 2, 1, 48 ], [ 39, 2, 9, 8 ], [ 39, 2, 17, 24 ], [ 39, 2, 18, 48 ], [ 39, 3, 1, 48 ], [ 39, 3, 9, 8 ], [ 39, 3, 17, 24 ], [ 39, 3, 18, 48 ], [ 39, 4, 1, 48 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 24 ], [ 39, 4, 17, 48 ], [ 39, 4, 18, 48 ], [ 39, 5, 1, 48 ], [ 39, 5, 10, 8 ], [ 39, 5, 16, 24 ], [ 39, 5, 17, 48 ], [ 39, 5, 18, 48 ], [ 40, 1, 12, 96 ], [ 40, 1, 21, 48 ], [ 40, 1, 23, 96 ], [ 40, 2, 17, 48 ], [ 40, 2, 20, 24 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 48 ], [ 40, 3, 11, 24 ], [ 40, 3, 15, 24 ], [ 40, 3, 16, 48 ], [ 41, 1, 4, 96 ], [ 41, 1, 18, 96 ], [ 41, 1, 34, 192 ], [ 41, 1, 36, 192 ], [ 41, 2, 4, 48 ], [ 41, 2, 18, 48 ], [ 41, 2, 34, 96 ], [ 41, 2, 36, 96 ], [ 41, 3, 4, 48 ], [ 41, 3, 18, 48 ], [ 41, 3, 34, 96 ], [ 41, 3, 36, 96 ], [ 41, 4, 18, 48 ], [ 41, 4, 21, 48 ], [ 41, 4, 40, 96 ], [ 41, 4, 41, 96 ], [ 41, 4, 43, 96 ], [ 41, 4, 44, 96 ], [ 41, 5, 16, 48 ], [ 41, 5, 18, 48 ], [ 41, 5, 32, 96 ], [ 41, 5, 33, 96 ], [ 41, 5, 35, 96 ], [ 41, 6, 16, 48 ], [ 41, 6, 18, 48 ], [ 41, 6, 32, 96 ], [ 41, 6, 33, 96 ], [ 41, 6, 35, 96 ], [ 41, 7, 16, 48 ], [ 41, 7, 18, 48 ], [ 41, 7, 32, 96 ], [ 41, 7, 33, 96 ], [ 41, 7, 35, 96 ], [ 42, 1, 16, 64 ], [ 42, 2, 3, 32 ], [ 42, 3, 4, 32 ], [ 42, 4, 13, 32 ], [ 43, 1, 24, 192 ], [ 43, 1, 33, 192 ], [ 43, 2, 20, 96 ], [ 43, 2, 28, 96 ], [ 43, 2, 31, 96 ], [ 43, 2, 39, 96 ], [ 43, 3, 24, 96 ], [ 43, 3, 30, 96 ], [ 43, 4, 4, 96 ], [ 43, 4, 20, 96 ], [ 43, 4, 22, 96 ], [ 43, 5, 3, 96 ], [ 43, 5, 20, 96 ], [ 44, 2, 43, 192 ], [ 44, 2, 61, 192 ], [ 44, 3, 44, 192 ], [ 44, 3, 54, 192 ], [ 44, 3, 61, 192 ], [ 44, 4, 41, 192 ], [ 44, 5, 45, 192 ], [ 44, 5, 54, 192 ], [ 44, 5, 56, 192 ], [ 44, 6, 35, 192 ], [ 44, 6, 50, 192 ], [ 44, 6, 52, 192 ], [ 44, 6, 79, 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 phi2 ( q^5-4*q^4+q^3+5*q^2-10*q+39 ) 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 phi2 ( q^5-4*q^4+q^3+5*q^2-10*q+39 ) 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 phi2 ( q^5-4*q^4+q^3+5*q^2-10*q+39 ) q congruent 7 modulo 12: 1/256 phi1 phi2 ( q^5-4*q^4+q^3+5*q^2-10*q+39 ) 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 phi2 ( q^5-4*q^4+q^3+5*q^2-10*q+39 ) q congruent 11 modulo 12: 1/256 phi1 phi2 ( q^5-4*q^4+q^3+5*q^2-10*q+39 ) 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 ], [ 4, 2, 2, 4 ], [ 4, 2, 3, 8 ], [ 4, 2, 4, 8 ], [ 5, 1, 2, 8 ], [ 5, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 15, 1, 4, 16 ], [ 15, 1, 5, 32 ], [ 15, 1, 6, 32 ], [ 15, 2, 4, 8 ], [ 15, 2, 5, 16 ], [ 15, 2, 6, 16 ], [ 15, 3, 4, 8 ], [ 15, 3, 5, 16 ], [ 15, 3, 6, 16 ], [ 15, 4, 4, 8 ], [ 15, 4, 5, 16 ], [ 15, 4, 6, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 1, 4, 16 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 8 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 25, 1, 7, 32 ], [ 25, 2, 7, 16 ], [ 25, 3, 7, 16 ], [ 25, 4, 7, 16 ], [ 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 ], [ 27, 2, 3, 16 ], [ 27, 2, 4, 16 ], [ 27, 2, 5, 32 ], [ 27, 2, 6, 16 ], [ 27, 2, 7, 24 ], [ 27, 2, 9, 16 ], [ 27, 2, 14, 16 ], [ 27, 3, 2, 16 ], [ 27, 3, 3, 16 ], [ 27, 3, 4, 16 ], [ 27, 3, 6, 16 ], [ 27, 3, 10, 16 ], [ 27, 3, 13, 16 ], [ 27, 3, 14, 16 ], [ 27, 3, 15, 16 ], [ 27, 3, 16, 16 ], [ 32, 1, 4, 32 ], [ 32, 1, 8, 64 ], [ 34, 1, 2, 16 ], [ 34, 1, 6, 32 ], [ 34, 1, 8, 16 ], [ 34, 2, 2, 8 ], [ 34, 2, 5, 8 ], [ 34, 2, 8, 16 ], [ 34, 3, 2, 8 ], [ 35, 1, 7, 32 ], [ 35, 2, 7, 16 ], [ 36, 1, 6, 64 ], [ 36, 1, 10, 32 ], [ 36, 1, 12, 128 ], [ 36, 1, 13, 64 ], [ 36, 1, 17, 64 ], [ 36, 2, 6, 32 ], [ 36, 2, 7, 32 ], [ 36, 2, 8, 64 ], [ 36, 2, 9, 32 ], [ 36, 2, 13, 32 ], [ 36, 2, 15, 32 ], [ 36, 2, 16, 16 ], [ 36, 2, 28, 32 ], [ 36, 3, 6, 32 ], [ 36, 3, 7, 32 ], [ 36, 3, 8, 64 ], [ 36, 3, 9, 32 ], [ 36, 3, 13, 32 ], [ 36, 3, 15, 32 ], [ 36, 3, 16, 16 ], [ 36, 3, 28, 32 ], [ 36, 4, 6, 32 ], [ 36, 4, 7, 32 ], [ 36, 4, 8, 64 ], [ 36, 4, 9, 32 ], [ 36, 4, 13, 32 ], [ 36, 4, 15, 32 ], [ 36, 4, 16, 16 ], [ 36, 4, 28, 32 ], [ 36, 5, 6, 32 ], [ 36, 5, 10, 16 ], [ 36, 5, 12, 64 ], [ 36, 5, 13, 32 ], [ 36, 5, 17, 32 ], [ 36, 6, 7, 32 ], [ 38, 1, 11, 64 ], [ 38, 1, 13, 64 ], [ 38, 1, 14, 64 ], [ 38, 2, 11, 32 ], [ 38, 2, 13, 32 ], [ 38, 2, 14, 32 ], [ 39, 1, 14, 64 ], [ 39, 2, 14, 32 ], [ 39, 3, 14, 32 ], [ 39, 4, 14, 32 ], [ 39, 5, 14, 32 ], [ 40, 1, 6, 96 ], [ 40, 1, 16, 64 ], [ 40, 1, 23, 64 ], [ 40, 2, 14, 48 ], [ 40, 2, 17, 32 ], [ 40, 2, 19, 32 ], [ 40, 3, 16, 32 ], [ 41, 1, 14, 64 ], [ 41, 1, 21, 128 ], [ 41, 1, 31, 128 ], [ 41, 1, 35, 128 ], [ 41, 2, 14, 32 ], [ 41, 2, 21, 64 ], [ 41, 2, 31, 64 ], [ 41, 2, 35, 64 ], [ 41, 3, 14, 32 ], [ 41, 3, 21, 64 ], [ 41, 3, 31, 64 ], [ 41, 3, 35, 64 ], [ 41, 4, 7, 32 ], [ 41, 4, 20, 64 ], [ 41, 4, 36, 64 ], [ 41, 4, 38, 64 ], [ 41, 4, 39, 64 ], [ 41, 4, 45, 64 ], [ 41, 5, 29, 64 ], [ 41, 6, 29, 64 ], [ 41, 7, 29, 64 ], [ 43, 1, 19, 128 ], [ 43, 1, 21, 128 ], [ 43, 2, 13, 64 ], [ 43, 2, 17, 64 ], [ 43, 2, 25, 64 ], [ 43, 2, 26, 64 ], [ 43, 3, 19, 64 ], [ 43, 3, 21, 64 ], [ 43, 4, 14, 64 ], [ 43, 4, 25, 64 ], [ 43, 4, 51, 64 ], [ 43, 5, 7, 64 ], [ 43, 5, 21, 64 ], [ 43, 5, 31, 64 ], [ 44, 2, 31, 128 ], [ 44, 2, 39, 128 ], [ 44, 3, 34, 128 ], [ 44, 3, 68, 128 ], [ 44, 3, 71, 128 ], [ 44, 4, 42, 128 ], [ 44, 5, 40, 128 ], [ 44, 5, 72, 128 ], [ 44, 5, 74, 128 ], [ 44, 6, 29, 128 ], [ 44, 6, 31, 128 ], [ 44, 6, 68, 128 ], [ 44, 6, 69, 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 phi1^2 phi2^2 ( q^3-2*q^2-3 ) q congruent 2 modulo 12: 1/64 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 3 modulo 12: 1/64 phi1^2 phi2^2 ( q^3-2*q^2-3 ) q congruent 4 modulo 12: 1/64 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 5 modulo 12: 1/64 phi1^2 phi2^2 ( q^3-2*q^2-3 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2^2 ( q^3-2*q^2-3 ) q congruent 8 modulo 12: 1/64 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 9 modulo 12: 1/64 phi1^2 phi2^2 ( q^3-2*q^2-3 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2^2 ( q^3-2*q^2-3 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 4, 2, 3, 4 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 12, 2, 2, 8 ], [ 13, 1, 2, 8 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 15, 1, 7, 16 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 15, 2, 7, 8 ], [ 15, 3, 3, 4 ], [ 15, 3, 4, 4 ], [ 15, 3, 7, 8 ], [ 15, 4, 3, 4 ], [ 15, 4, 4, 4 ], [ 15, 4, 7, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 4 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 18, 2, 4, 4 ], [ 19, 1, 2, 8 ], [ 20, 1, 4, 16 ], [ 20, 2, 4, 8 ], [ 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 ], [ 23, 2, 3, 4 ], [ 23, 2, 4, 4 ], [ 24, 1, 2, 8 ], [ 24, 1, 3, 8 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 4, 8 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 2, 10, 8 ], [ 27, 2, 11, 8 ], [ 27, 3, 3, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 7, 8 ], [ 27, 3, 8, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 14, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 29, 1, 5, 16 ], [ 29, 2, 5, 8 ], [ 30, 1, 3, 16 ], [ 30, 1, 8, 16 ], [ 30, 2, 3, 8 ], [ 30, 2, 8, 8 ], [ 31, 1, 2, 8 ], [ 31, 1, 4, 8 ], [ 31, 1, 5, 8 ], [ 31, 1, 7, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 4, 4 ], [ 31, 2, 5, 4 ], [ 31, 2, 7, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 5, 8 ], [ 32, 1, 8, 8 ], [ 33, 1, 12, 32 ], [ 33, 2, 12, 16 ], [ 33, 3, 12, 16 ], [ 33, 4, 12, 16 ], [ 34, 1, 3, 16 ], [ 34, 1, 7, 8 ], [ 34, 1, 8, 8 ], [ 34, 2, 3, 4 ], [ 34, 2, 5, 4 ], [ 34, 2, 9, 8 ], [ 34, 3, 3, 4 ], [ 34, 3, 6, 8 ], [ 34, 3, 8, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 1, 5, 16 ], [ 36, 1, 8, 32 ], [ 36, 1, 10, 16 ], [ 36, 1, 14, 32 ], [ 36, 2, 5, 8 ], [ 36, 2, 10, 16 ], [ 36, 2, 16, 8 ], [ 36, 2, 18, 16 ], [ 36, 2, 20, 16 ], [ 36, 2, 21, 16 ], [ 36, 3, 5, 8 ], [ 36, 3, 10, 16 ], [ 36, 3, 16, 8 ], [ 36, 3, 18, 16 ], [ 36, 3, 20, 16 ], [ 36, 3, 21, 16 ], [ 36, 4, 5, 8 ], [ 36, 4, 10, 16 ], [ 36, 4, 16, 8 ], [ 36, 4, 18, 16 ], [ 36, 4, 20, 16 ], [ 36, 4, 21, 16 ], [ 36, 5, 5, 8 ], [ 36, 5, 8, 16 ], [ 36, 5, 10, 8 ], [ 36, 5, 14, 16 ], [ 36, 6, 6, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 14, 8 ], [ 36, 6, 15, 8 ], [ 37, 1, 4, 16 ], [ 37, 1, 10, 16 ], [ 37, 2, 4, 8 ], [ 37, 2, 10, 8 ], [ 38, 1, 9, 16 ], [ 38, 1, 12, 16 ], [ 38, 1, 14, 16 ], [ 38, 1, 16, 16 ], [ 38, 2, 9, 8 ], [ 38, 2, 12, 8 ], [ 38, 2, 14, 8 ], [ 38, 2, 16, 8 ], [ 38, 3, 9, 8 ], [ 38, 3, 12, 8 ], [ 38, 3, 14, 8 ], [ 38, 3, 15, 8 ], [ 39, 1, 5, 16 ], [ 39, 1, 6, 16 ], [ 39, 1, 11, 16 ], [ 39, 1, 14, 16 ], [ 39, 2, 5, 8 ], [ 39, 2, 6, 8 ], [ 39, 2, 11, 8 ], [ 39, 2, 14, 8 ], [ 39, 3, 5, 8 ], [ 39, 3, 6, 8 ], [ 39, 3, 11, 8 ], [ 39, 3, 14, 8 ], [ 39, 4, 4, 8 ], [ 39, 4, 6, 8 ], [ 39, 4, 11, 8 ], [ 39, 4, 14, 8 ], [ 39, 5, 4, 8 ], [ 39, 5, 6, 8 ], [ 39, 5, 11, 8 ], [ 39, 5, 14, 8 ], [ 40, 1, 16, 16 ], [ 40, 1, 21, 16 ], [ 40, 1, 22, 16 ], [ 40, 2, 19, 8 ], [ 40, 2, 20, 8 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 12, 32 ], [ 41, 1, 24, 32 ], [ 41, 1, 27, 32 ], [ 41, 2, 4, 8 ], [ 41, 2, 9, 8 ], [ 41, 2, 12, 16 ], [ 41, 2, 24, 16 ], [ 41, 2, 27, 16 ], [ 41, 3, 4, 8 ], [ 41, 3, 9, 8 ], [ 41, 3, 12, 16 ], [ 41, 3, 24, 16 ], [ 41, 3, 27, 16 ], [ 41, 4, 6, 16 ], [ 41, 4, 8, 16 ], [ 41, 4, 28, 16 ], [ 41, 4, 29, 16 ], [ 41, 4, 33, 16 ], [ 41, 4, 34, 16 ], [ 41, 5, 6, 16 ], [ 41, 5, 11, 16 ], [ 41, 5, 22, 16 ], [ 41, 5, 26, 16 ], [ 41, 6, 6, 16 ], [ 41, 6, 11, 16 ], [ 41, 6, 22, 16 ], [ 41, 6, 26, 16 ], [ 41, 7, 6, 16 ], [ 41, 7, 11, 16 ], [ 41, 7, 22, 16 ], [ 41, 7, 26, 16 ], [ 42, 1, 14, 32 ], [ 42, 1, 15, 32 ], [ 42, 2, 7, 16 ], [ 42, 2, 18, 16 ], [ 42, 3, 9, 16 ], [ 42, 3, 20, 16 ], [ 42, 4, 14, 16 ], [ 42, 4, 15, 16 ], [ 43, 1, 25, 32 ], [ 43, 1, 34, 32 ], [ 43, 1, 36, 32 ], [ 43, 2, 21, 16 ], [ 43, 2, 32, 16 ], [ 43, 2, 33, 16 ], [ 43, 2, 40, 16 ], [ 43, 2, 41, 16 ], [ 43, 3, 25, 16 ], [ 43, 3, 31, 16 ], [ 43, 3, 32, 16 ], [ 43, 4, 9, 16 ], [ 43, 4, 12, 16 ], [ 43, 4, 30, 16 ], [ 43, 4, 38, 16 ], [ 43, 4, 41, 16 ], [ 43, 4, 46, 16 ], [ 43, 5, 28, 16 ], [ 43, 5, 30, 16 ], [ 43, 5, 32, 16 ], [ 43, 5, 35, 16 ], [ 44, 2, 48, 32 ], [ 44, 2, 59, 32 ], [ 44, 2, 62, 32 ], [ 44, 3, 46, 32 ], [ 44, 3, 64, 32 ], [ 44, 3, 65, 32 ], [ 44, 4, 43, 32 ], [ 44, 5, 48, 32 ], [ 44, 5, 62, 32 ], [ 44, 5, 64, 32 ], [ 44, 6, 40, 32 ], [ 44, 6, 55, 32 ], [ 44, 6, 56, 32 ], [ 44, 6, 72, 32 ], [ 44, 6, 73, 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 ], [ 5, 2, 2, 1 ], [ 6, 1, 2, 6 ], [ 6, 2, 2, 3 ], [ 7, 1, 2, 6 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 6 ], [ 13, 1, 2, 6 ], [ 14, 1, 2, 6 ], [ 14, 2, 2, 3 ], [ 16, 1, 2, 6 ], [ 18, 1, 3, 12 ], [ 18, 2, 3, 6 ], [ 19, 1, 2, 6 ], [ 23, 1, 4, 12 ], [ 23, 2, 4, 6 ], [ 28, 1, 6, 12 ], [ 28, 2, 6, 6 ], [ 29, 1, 4, 12 ], [ 29, 2, 4, 6 ], [ 42, 1, 3, 10 ], [ 42, 4, 3, 5 ], [ 43, 1, 3, 30 ], [ 43, 3, 3, 15 ], [ 44, 2, 5, 30 ], [ 44, 4, 44, 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 ], [ 4, 2, 1, 14 ], [ 5, 1, 1, 8 ], [ 5, 2, 1, 4 ], [ 6, 1, 1, 8 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 40 ], [ 9, 1, 1, 46 ], [ 10, 1, 1, 36 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 48 ], [ 12, 2, 1, 24 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 48 ], [ 15, 1, 3, 8 ], [ 15, 2, 1, 24 ], [ 15, 2, 3, 4 ], [ 15, 3, 1, 24 ], [ 15, 3, 3, 4 ], [ 15, 4, 1, 24 ], [ 15, 4, 3, 4 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 6 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 12 ], [ 18, 2, 1, 12 ], [ 18, 2, 2, 6 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 64 ], [ 20, 2, 1, 32 ], [ 21, 1, 1, 36 ], [ 22, 1, 1, 48 ], [ 22, 1, 2, 24 ], [ 23, 1, 1, 48 ], [ 23, 1, 2, 16 ], [ 23, 2, 1, 24 ], [ 23, 2, 2, 8 ], [ 24, 1, 1, 72 ], [ 24, 1, 2, 20 ], [ 25, 1, 1, 48 ], [ 25, 1, 5, 24 ], [ 25, 2, 1, 24 ], [ 25, 2, 5, 12 ], [ 25, 3, 1, 24 ], [ 25, 3, 5, 12 ], [ 25, 4, 1, 24 ], [ 25, 4, 5, 12 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 24 ], [ 28, 1, 1, 48 ], [ 28, 1, 3, 16 ], [ 28, 1, 5, 6 ], [ 28, 2, 1, 24 ], [ 28, 2, 3, 3 ], [ 28, 2, 4, 8 ], [ 29, 1, 1, 48 ], [ 29, 1, 2, 48 ], [ 29, 1, 3, 24 ], [ 29, 2, 1, 24 ], [ 29, 2, 2, 24 ], [ 29, 2, 3, 12 ], [ 30, 1, 1, 48 ], [ 30, 1, 2, 24 ], [ 30, 2, 1, 24 ], [ 30, 2, 2, 12 ], [ 31, 1, 1, 48 ], [ 31, 1, 2, 48 ], [ 31, 1, 3, 48 ], [ 31, 2, 1, 24 ], [ 31, 2, 2, 24 ], [ 31, 2, 3, 24 ], [ 33, 1, 1, 96 ], [ 33, 1, 2, 48 ], [ 33, 1, 3, 32 ], [ 33, 2, 1, 48 ], [ 33, 2, 2, 24 ], [ 33, 2, 3, 16 ], [ 33, 3, 1, 48 ], [ 33, 3, 2, 24 ], [ 33, 3, 3, 16 ], [ 33, 4, 1, 48 ], [ 33, 4, 2, 24 ], [ 33, 4, 3, 16 ], [ 34, 1, 2, 48 ], [ 34, 2, 2, 24 ], [ 34, 3, 2, 24 ], [ 35, 1, 1, 48 ], [ 35, 1, 2, 48 ], [ 35, 1, 8, 42 ], [ 35, 2, 1, 24 ], [ 35, 2, 2, 24 ], [ 35, 2, 8, 21 ], [ 37, 1, 1, 48 ], [ 37, 1, 2, 48 ], [ 37, 1, 3, 96 ], [ 37, 2, 1, 24 ], [ 37, 2, 2, 24 ], [ 37, 2, 3, 48 ], [ 39, 1, 2, 96 ], [ 39, 1, 3, 72 ], [ 39, 1, 7, 12 ], [ 39, 1, 8, 96 ], [ 39, 2, 2, 48 ], [ 39, 2, 3, 36 ], [ 39, 2, 7, 6 ], [ 39, 2, 8, 48 ], [ 39, 3, 2, 48 ], [ 39, 3, 3, 36 ], [ 39, 3, 7, 6 ], [ 39, 3, 8, 48 ], [ 39, 4, 2, 48 ], [ 39, 4, 7, 48 ], [ 39, 5, 2, 48 ], [ 39, 5, 7, 48 ], [ 40, 1, 7, 108 ], [ 40, 2, 2, 54 ], [ 40, 3, 10, 54 ], [ 41, 1, 3, 144 ], [ 41, 1, 13, 72 ], [ 41, 2, 3, 72 ], [ 41, 2, 13, 36 ], [ 41, 3, 3, 72 ], [ 41, 3, 13, 36 ], [ 41, 5, 3, 72 ], [ 41, 5, 7, 36 ], [ 41, 6, 3, 72 ], [ 41, 6, 7, 36 ], [ 41, 7, 3, 72 ], [ 41, 7, 7, 36 ], [ 42, 1, 4, 144 ], [ 42, 1, 7, 48 ], [ 42, 1, 18, 96 ], [ 42, 2, 2, 48 ], [ 42, 3, 2, 48 ], [ 42, 3, 3, 72 ], [ 42, 3, 6, 48 ], [ 42, 3, 8, 24 ], [ 42, 4, 4, 72 ], [ 42, 4, 6, 24 ], [ 42, 4, 20, 48 ], [ 43, 1, 4, 144 ], [ 43, 1, 11, 144 ], [ 43, 2, 2, 72 ], [ 43, 2, 8, 72 ], [ 43, 3, 4, 72 ], [ 43, 3, 12, 72 ], [ 43, 4, 3, 72 ], [ 43, 4, 13, 72 ], [ 43, 4, 29, 72 ], [ 44, 2, 15, 144 ], [ 44, 2, 19, 144 ], [ 44, 3, 6, 144 ], [ 44, 4, 45, 144 ], [ 44, 5, 14, 144 ], [ 44, 6, 8, 144 ], [ 44, 6, 18, 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^3-19*q^2-5*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 ( q^4-q^3-6*q^2-7*q+21 ) 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 ( q^4-q^3-6*q^2-7*q+21 ) q congruent 7 modulo 12: 1/288 phi1^2 ( q^5+q^4-6*q^3-19*q^2-5*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 ( q^4-q^3-6*q^2-7*q+21 ) q congruent 11 modulo 12: 1/288 q phi1 phi2 ( q^4-q^3-6*q^2-7*q+21 ) 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 ], [ 4, 2, 1, 6 ], [ 6, 1, 2, 8 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 12 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 24 ], [ 12, 1, 2, 16 ], [ 12, 2, 2, 8 ], [ 15, 1, 3, 24 ], [ 15, 2, 3, 12 ], [ 15, 3, 3, 12 ], [ 15, 4, 3, 12 ], [ 16, 1, 2, 6 ], [ 17, 1, 2, 24 ], [ 17, 1, 3, 12 ], [ 17, 2, 2, 12 ], [ 17, 2, 3, 6 ], [ 18, 1, 2, 12 ], [ 18, 1, 3, 24 ], [ 18, 2, 2, 6 ], [ 18, 2, 3, 12 ], [ 21, 1, 1, 12 ], [ 21, 1, 2, 24 ], [ 22, 1, 2, 24 ], [ 24, 1, 2, 12 ], [ 25, 1, 5, 24 ], [ 25, 1, 6, 48 ], [ 25, 2, 5, 12 ], [ 25, 2, 6, 24 ], [ 25, 3, 5, 12 ], [ 25, 3, 6, 24 ], [ 25, 4, 5, 12 ], [ 25, 4, 6, 24 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 24 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 1, 2, 24 ], [ 30, 1, 3, 48 ], [ 30, 2, 2, 12 ], [ 30, 2, 3, 24 ], [ 31, 1, 4, 48 ], [ 31, 2, 4, 24 ], [ 33, 1, 11, 48 ], [ 33, 2, 11, 24 ], [ 33, 3, 11, 24 ], [ 33, 4, 11, 24 ], [ 34, 1, 4, 48 ], [ 34, 1, 7, 48 ], [ 34, 2, 3, 24 ], [ 34, 2, 10, 24 ], [ 34, 3, 3, 24 ], [ 34, 3, 5, 24 ], [ 34, 3, 8, 24 ], [ 35, 1, 5, 48 ], [ 35, 1, 8, 18 ], [ 35, 2, 5, 24 ], [ 35, 2, 8, 9 ], [ 37, 1, 5, 48 ], [ 37, 2, 5, 24 ], [ 39, 1, 4, 96 ], [ 39, 1, 7, 36 ], [ 39, 2, 4, 48 ], [ 39, 2, 7, 18 ], [ 39, 3, 4, 48 ], [ 39, 3, 7, 18 ], [ 39, 4, 3, 48 ], [ 39, 4, 5, 48 ], [ 39, 5, 3, 48 ], [ 39, 5, 5, 48 ], [ 40, 1, 7, 36 ], [ 40, 1, 14, 72 ], [ 40, 2, 2, 18 ], [ 40, 2, 7, 36 ], [ 40, 3, 10, 18 ], [ 40, 3, 13, 36 ], [ 41, 1, 13, 72 ], [ 41, 1, 28, 144 ], [ 41, 2, 13, 36 ], [ 41, 2, 28, 72 ], [ 41, 3, 13, 36 ], [ 41, 3, 28, 72 ], [ 41, 5, 7, 36 ], [ 41, 5, 24, 72 ], [ 41, 6, 7, 36 ], [ 41, 6, 24, 72 ], [ 41, 7, 7, 36 ], [ 41, 7, 24, 72 ], [ 42, 1, 19, 96 ], [ 42, 2, 6, 48 ], [ 42, 2, 10, 48 ], [ 42, 3, 10, 48 ], [ 42, 4, 19, 48 ], [ 43, 1, 6, 144 ], [ 43, 2, 3, 72 ], [ 43, 2, 10, 72 ], [ 43, 3, 6, 72 ], [ 43, 4, 39, 72 ], [ 44, 2, 16, 144 ], [ 44, 3, 5, 144 ], [ 44, 3, 17, 144 ], [ 44, 4, 46, 144 ], [ 44, 5, 15, 144 ], [ 44, 5, 19, 144 ], [ 44, 6, 9, 144 ], [ 44, 6, 14, 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 ], [ 6, 2, 2, 1 ], [ 12, 1, 2, 16 ], [ 12, 2, 2, 8 ], [ 21, 1, 5, 24 ], [ 28, 1, 5, 24 ], [ 28, 2, 3, 12 ], [ 33, 1, 11, 48 ], [ 33, 2, 11, 24 ], [ 33, 3, 11, 24 ], [ 33, 4, 11, 24 ], [ 34, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 40, 1, 9, 72 ], [ 40, 2, 4, 36 ], [ 42, 1, 9, 48 ], [ 42, 2, 8, 24 ], [ 42, 4, 10, 24 ], [ 44, 3, 27, 72 ], [ 44, 4, 47, 72 ], [ 44, 5, 28, 72 ] ] 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 phi2 ( q^4-3*q^3-2*q^2+5*q+7 ) 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 phi2 ( q^4-3*q^3-2*q^2+5*q+7 ) 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 phi2 ( q^4-3*q^3-2*q^2+5*q+7 ) q congruent 7 modulo 12: 1/96 q phi1 phi2 ( q^4-3*q^3-2*q^2+5*q+7 ) 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 phi2 ( q^4-3*q^3-2*q^2+5*q+7 ) q congruent 11 modulo 12: 1/96 q phi1 phi2 ( q^4-3*q^3-2*q^2+5*q+7 ) 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 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 1, 2, 4 ], [ 6, 2, 2, 2 ], [ 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 ], [ 12, 2, 3, 12 ], [ 13, 1, 2, 4 ], [ 14, 1, 2, 8 ], [ 14, 2, 2, 4 ], [ 15, 1, 2, 16 ], [ 15, 1, 4, 8 ], [ 15, 2, 2, 8 ], [ 15, 2, 4, 4 ], [ 15, 3, 2, 8 ], [ 15, 3, 4, 4 ], [ 15, 4, 2, 8 ], [ 15, 4, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 2 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 8 ], [ 18, 2, 2, 4 ], [ 18, 2, 3, 2 ], [ 18, 2, 4, 4 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 16 ], [ 20, 2, 2, 8 ], [ 21, 1, 3, 8 ], [ 21, 1, 6, 12 ], [ 22, 1, 3, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 3, 16 ], [ 23, 2, 3, 8 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 24 ], [ 25, 1, 4, 16 ], [ 25, 1, 7, 16 ], [ 25, 1, 8, 8 ], [ 25, 2, 4, 8 ], [ 25, 2, 7, 8 ], [ 25, 2, 8, 4 ], [ 25, 3, 4, 8 ], [ 25, 3, 7, 8 ], [ 25, 3, 8, 4 ], [ 25, 4, 4, 8 ], [ 25, 4, 7, 8 ], [ 25, 4, 8, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 2, 8 ], [ 26, 1, 4, 8 ], [ 28, 1, 2, 16 ], [ 28, 1, 4, 6 ], [ 28, 2, 2, 8 ], [ 28, 2, 5, 3 ], [ 29, 1, 5, 16 ], [ 29, 1, 6, 12 ], [ 29, 2, 5, 8 ], [ 29, 2, 6, 6 ], [ 30, 1, 5, 8 ], [ 30, 1, 6, 16 ], [ 30, 1, 8, 16 ], [ 30, 2, 5, 4 ], [ 30, 2, 6, 8 ], [ 30, 2, 8, 8 ], [ 31, 1, 5, 16 ], [ 31, 1, 6, 16 ], [ 31, 1, 8, 16 ], [ 31, 2, 5, 8 ], [ 31, 2, 6, 8 ], [ 31, 2, 8, 8 ], [ 33, 1, 4, 32 ], [ 33, 1, 5, 24 ], [ 33, 2, 4, 16 ], [ 33, 2, 5, 12 ], [ 33, 3, 4, 16 ], [ 33, 3, 5, 12 ], [ 33, 4, 4, 16 ], [ 33, 4, 5, 12 ], [ 34, 1, 2, 16 ], [ 34, 1, 7, 16 ], [ 34, 2, 2, 8 ], [ 34, 2, 3, 8 ], [ 34, 3, 2, 8 ], [ 34, 3, 3, 8 ], [ 34, 3, 8, 8 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 1, 9, 18 ], [ 35, 2, 3, 8 ], [ 35, 2, 4, 8 ], [ 35, 2, 9, 9 ], [ 37, 1, 7, 16 ], [ 37, 1, 8, 24 ], [ 37, 1, 9, 16 ], [ 37, 2, 7, 8 ], [ 37, 2, 8, 12 ], [ 37, 2, 9, 8 ], [ 39, 1, 12, 12 ], [ 39, 1, 13, 32 ], [ 39, 1, 16, 24 ], [ 39, 1, 19, 32 ], [ 39, 2, 12, 6 ], [ 39, 2, 13, 16 ], [ 39, 2, 16, 12 ], [ 39, 2, 19, 16 ], [ 39, 3, 12, 6 ], [ 39, 3, 13, 16 ], [ 39, 3, 16, 12 ], [ 39, 3, 19, 16 ], [ 39, 4, 12, 16 ], [ 39, 4, 13, 16 ], [ 39, 4, 19, 16 ], [ 39, 5, 12, 16 ], [ 39, 5, 13, 16 ], [ 39, 5, 19, 16 ], [ 40, 1, 8, 36 ], [ 40, 1, 15, 24 ], [ 40, 2, 5, 18 ], [ 40, 2, 6, 12 ], [ 40, 3, 9, 18 ], [ 40, 3, 12, 12 ], [ 41, 1, 8, 24 ], [ 41, 1, 17, 48 ], [ 41, 1, 25, 48 ], [ 41, 2, 8, 12 ], [ 41, 2, 17, 24 ], [ 41, 2, 25, 24 ], [ 41, 3, 8, 12 ], [ 41, 3, 17, 24 ], [ 41, 3, 25, 24 ], [ 41, 5, 9, 12 ], [ 41, 5, 17, 24 ], [ 41, 5, 27, 24 ], [ 41, 6, 9, 12 ], [ 41, 6, 17, 24 ], [ 41, 6, 27, 24 ], [ 41, 7, 9, 12 ], [ 41, 7, 17, 24 ], [ 41, 7, 27, 24 ], [ 42, 1, 8, 48 ], [ 42, 1, 17, 32 ], [ 42, 2, 12, 16 ], [ 42, 2, 19, 16 ], [ 42, 3, 12, 16 ], [ 42, 3, 13, 24 ], [ 42, 3, 19, 16 ], [ 42, 4, 7, 24 ], [ 42, 4, 17, 16 ], [ 43, 1, 10, 48 ], [ 43, 1, 12, 48 ], [ 43, 2, 6, 24 ], [ 43, 2, 9, 24 ], [ 43, 2, 11, 24 ], [ 43, 3, 10, 24 ], [ 43, 3, 11, 24 ], [ 43, 4, 8, 24 ], [ 43, 4, 21, 24 ], [ 43, 4, 47, 24 ], [ 44, 2, 14, 48 ], [ 44, 2, 21, 48 ], [ 44, 3, 12, 48 ], [ 44, 3, 19, 48 ], [ 44, 4, 48, 48 ], [ 44, 5, 12, 48 ], [ 44, 5, 16, 48 ], [ 44, 6, 12, 48 ], [ 44, 6, 17, 48 ], [ 44, 6, 21, 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 12 ], [ 12, 2, 1, 6 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 15, 1, 3, 8 ], [ 15, 2, 3, 4 ], [ 15, 3, 3, 4 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 20, 1, 1, 4 ], [ 20, 2, 1, 2 ], [ 21, 1, 5, 18 ], [ 23, 1, 2, 4 ], [ 23, 2, 2, 2 ], [ 24, 1, 2, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 5, 12 ], [ 28, 2, 3, 6 ], [ 28, 2, 4, 2 ], [ 29, 1, 3, 12 ], [ 29, 2, 3, 6 ], [ 32, 1, 9, 18 ], [ 33, 1, 2, 24 ], [ 33, 1, 3, 8 ], [ 33, 2, 2, 12 ], [ 33, 2, 3, 4 ], [ 33, 3, 2, 12 ], [ 33, 3, 3, 4 ], [ 33, 4, 2, 12 ], [ 33, 4, 3, 4 ], [ 34, 1, 9, 18 ], [ 34, 2, 7, 9 ], [ 35, 1, 8, 12 ], [ 35, 2, 8, 6 ], [ 36, 1, 9, 18 ], [ 36, 5, 9, 9 ], [ 37, 1, 3, 12 ], [ 37, 2, 3, 6 ], [ 38, 1, 17, 36 ], [ 38, 2, 17, 18 ], [ 39, 1, 7, 24 ], [ 39, 2, 7, 12 ], [ 39, 3, 7, 12 ], [ 40, 1, 19, 36 ], [ 40, 2, 10, 18 ], [ 42, 1, 5, 36 ], [ 42, 1, 7, 24 ], [ 42, 2, 9, 18 ], [ 42, 3, 8, 12 ], [ 42, 4, 5, 18 ], [ 42, 4, 6, 12 ], [ 43, 1, 5, 36 ], [ 43, 3, 5, 18 ], [ 43, 5, 26, 18 ], [ 44, 2, 27, 36 ], [ 44, 3, 26, 36 ], [ 44, 4, 49, 36 ], [ 44, 5, 21, 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 ], [ 4, 2, 3, 6 ], [ 5, 1, 2, 6 ], [ 5, 2, 2, 3 ], [ 6, 1, 2, 2 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 6 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 14, 1, 2, 6 ], [ 14, 2, 2, 3 ], [ 15, 1, 5, 24 ], [ 15, 2, 5, 12 ], [ 15, 3, 5, 12 ], [ 15, 4, 5, 12 ], [ 16, 1, 1, 6 ], [ 20, 1, 4, 12 ], [ 20, 2, 4, 6 ], [ 21, 1, 5, 6 ], [ 23, 1, 3, 12 ], [ 23, 2, 3, 6 ], [ 28, 1, 1, 12 ], [ 28, 2, 1, 6 ], [ 32, 1, 9, 18 ], [ 33, 1, 10, 24 ], [ 33, 2, 10, 12 ], [ 33, 3, 10, 12 ], [ 33, 4, 10, 12 ], [ 34, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 36, 1, 7, 18 ], [ 36, 5, 7, 9 ], [ 38, 1, 19, 36 ], [ 38, 2, 19, 18 ], [ 40, 1, 4, 36 ], [ 40, 2, 3, 18 ], [ 42, 1, 9, 12 ], [ 42, 2, 8, 6 ], [ 42, 4, 10, 6 ], [ 43, 1, 14, 36 ], [ 43, 3, 14, 18 ], [ 43, 5, 25, 18 ], [ 44, 2, 24, 36 ], [ 44, 3, 20, 36 ], [ 44, 4, 50, 36 ], [ 44, 5, 23, 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 ], [ 4, 2, 4, 2 ], [ 5, 1, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 2 ], [ 12, 1, 3, 12 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 15, 1, 6, 8 ], [ 15, 2, 6, 4 ], [ 15, 3, 6, 4 ], [ 15, 4, 6, 4 ], [ 16, 1, 1, 2 ], [ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ], [ 21, 1, 4, 6 ], [ 23, 1, 1, 4 ], [ 23, 2, 1, 2 ], [ 28, 1, 2, 4 ], [ 28, 2, 2, 2 ], [ 32, 1, 10, 6 ], [ 33, 1, 7, 8 ], [ 33, 2, 7, 4 ], [ 33, 3, 7, 4 ], [ 33, 4, 7, 4 ], [ 34, 1, 9, 6 ], [ 34, 2, 7, 3 ], [ 36, 1, 9, 6 ], [ 36, 5, 9, 3 ], [ 38, 1, 20, 12 ], [ 38, 2, 20, 6 ], [ 40, 1, 20, 12 ], [ 40, 2, 9, 6 ], [ 42, 1, 10, 12 ], [ 42, 2, 17, 6 ], [ 42, 4, 11, 6 ], [ 43, 1, 15, 12 ], [ 43, 3, 15, 6 ], [ 43, 5, 34, 6 ], [ 44, 2, 28, 12 ], [ 44, 3, 22, 12 ], [ 44, 4, 51, 12 ], [ 44, 5, 26, 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 ], [ 5, 2, 2, 1 ], [ 13, 1, 2, 2 ], [ 44, 4, 52, 7 ] ] 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 phi1^2 phi2 phi4 ( q^2-q-3 ) q congruent 2 modulo 12: 1/32 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 3 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-3 ) q congruent 4 modulo 12: 1/32 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 5 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-3 ) q congruent 7 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-3 ) q congruent 8 modulo 12: 1/32 q^4 ( q^3-2*q^2-2*q+4 ) q congruent 9 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-3 ) q congruent 11 modulo 12: 1/32 phi1^2 phi2 phi4 ( q^2-q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 53 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 1, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 26, 1, 4, 4 ], [ 27, 1, 10, 8 ], [ 27, 2, 10, 4 ], [ 34, 1, 5, 8 ], [ 34, 2, 4, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 7, 4 ], [ 36, 1, 16, 16 ], [ 36, 2, 19, 8 ], [ 36, 3, 19, 8 ], [ 36, 4, 19, 8 ], [ 36, 5, 16, 8 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ], [ 41, 1, 32, 16 ], [ 41, 2, 32, 8 ], [ 41, 3, 32, 8 ], [ 43, 1, 20, 16 ], [ 43, 2, 14, 8 ], [ 43, 3, 20, 8 ], [ 44, 2, 33, 16 ], [ 44, 3, 36, 16 ], [ 44, 4, 53, 16 ], [ 44, 5, 36, 16 ], [ 44, 6, 25, 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 phi1^2 phi2 phi3 phi4 q congruent 2 modulo 12: 1/32 q^7 q congruent 3 modulo 12: 1/32 phi1^2 phi2 phi3 phi4 q congruent 4 modulo 12: 1/32 q^7 q congruent 5 modulo 12: 1/32 phi1^2 phi2 phi3 phi4 q congruent 7 modulo 12: 1/32 phi1^2 phi2 phi3 phi4 q congruent 8 modulo 12: 1/32 q^7 q congruent 9 modulo 12: 1/32 phi1^2 phi2 phi3 phi4 q congruent 11 modulo 12: 1/32 phi1^2 phi2 phi3 phi4 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 ], [ 4, 2, 3, 2 ], [ 4, 2, 4, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 15, 1, 7, 8 ], [ 15, 1, 8, 8 ], [ 15, 2, 7, 4 ], [ 15, 2, 8, 4 ], [ 15, 3, 7, 4 ], [ 15, 3, 8, 4 ], [ 15, 4, 7, 4 ], [ 15, 4, 8, 4 ], [ 16, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 26, 1, 5, 4 ], [ 27, 1, 5, 8 ], [ 27, 2, 5, 4 ], [ 34, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 36, 1, 11, 16 ], [ 36, 2, 11, 8 ], [ 36, 3, 11, 8 ], [ 36, 4, 11, 8 ], [ 36, 5, 11, 8 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ], [ 41, 1, 29, 16 ], [ 41, 2, 29, 8 ], [ 41, 3, 29, 8 ], [ 43, 1, 18, 16 ], [ 43, 2, 16, 8 ], [ 43, 3, 18, 8 ], [ 44, 2, 38, 16 ], [ 44, 3, 39, 16 ], [ 44, 4, 54, 16 ], [ 44, 5, 38, 16 ], [ 44, 6, 27, 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 ], [ 6, 2, 2, 1 ], [ 12, 1, 4, 6 ], [ 44, 4, 55, 9 ] ] 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 ], [ 5, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 2, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 1, 2 ], [ 14, 1, 1, 2 ], [ 14, 2, 1, 1 ], [ 16, 1, 2, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 19, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 23, 2, 2, 2 ], [ 28, 1, 3, 4 ], [ 28, 2, 4, 2 ], [ 29, 1, 2, 4 ], [ 29, 2, 2, 2 ], [ 42, 1, 2, 10 ], [ 42, 4, 2, 5 ], [ 43, 1, 2, 10 ], [ 43, 3, 2, 5 ], [ 44, 2, 4, 10 ], [ 44, 4, 56, 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 phi1^2 phi2 ( q^3-2*q^2-1 ) q congruent 2 modulo 12: 1/48 q^3 phi1^2 phi2 ( q-2 ) q congruent 3 modulo 12: 1/48 q phi1^2 phi2 ( q^3-2*q^2-1 ) q congruent 4 modulo 12: 1/48 q^3 phi1^2 phi2 ( q-2 ) q congruent 5 modulo 12: 1/48 q phi1^2 phi2 ( q^3-2*q^2-1 ) q congruent 7 modulo 12: 1/48 q phi1^2 phi2 ( q^3-2*q^2-1 ) q congruent 8 modulo 12: 1/48 q^3 phi1^2 phi2 ( q-2 ) q congruent 9 modulo 12: 1/48 q phi1^2 phi2 ( q^3-2*q^2-1 ) q congruent 11 modulo 12: 1/48 q phi1^2 phi2 ( q^3-2*q^2-1 ) 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 ], [ 4, 2, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 1, 5, 8 ], [ 12, 2, 4, 4 ], [ 15, 1, 2, 8 ], [ 15, 2, 2, 4 ], [ 15, 3, 2, 4 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 21, 1, 3, 4 ], [ 24, 1, 4, 4 ], [ 25, 1, 3, 8 ], [ 25, 2, 3, 4 ], [ 25, 3, 3, 4 ], [ 25, 4, 3, 4 ], [ 26, 1, 5, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 1, 7, 8 ], [ 30, 2, 7, 4 ], [ 33, 1, 8, 24 ], [ 33, 2, 8, 12 ], [ 33, 3, 8, 12 ], [ 33, 4, 8, 12 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 35, 1, 7, 8 ], [ 35, 1, 9, 6 ], [ 35, 2, 7, 4 ], [ 35, 2, 9, 3 ], [ 37, 1, 10, 8 ], [ 37, 2, 10, 4 ], [ 39, 1, 16, 12 ], [ 39, 1, 17, 16 ], [ 39, 2, 16, 6 ], [ 39, 2, 17, 8 ], [ 39, 3, 16, 6 ], [ 39, 3, 17, 8 ], [ 39, 4, 16, 8 ], [ 39, 5, 16, 8 ], [ 40, 1, 15, 12 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 6 ], [ 41, 1, 33, 24 ], [ 41, 2, 33, 12 ], [ 41, 3, 33, 12 ], [ 41, 5, 31, 12 ], [ 41, 6, 31, 12 ], [ 41, 7, 31, 12 ], [ 42, 1, 13, 16 ], [ 42, 2, 14, 8 ], [ 42, 3, 15, 8 ], [ 42, 4, 16, 8 ], [ 43, 1, 7, 24 ], [ 43, 2, 4, 12 ], [ 43, 3, 8, 12 ], [ 44, 2, 11, 24 ], [ 44, 3, 10, 24 ], [ 44, 4, 57, 24 ], [ 44, 5, 7, 24 ], [ 44, 6, 6, 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 phi2^2 ( q^3-2*q^2-1 ) q congruent 2 modulo 12: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 3 modulo 12: 1/48 q phi1 phi2^2 ( q^3-2*q^2-1 ) q congruent 4 modulo 12: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 5 modulo 12: 1/48 q phi1 phi2^2 ( q^3-2*q^2-1 ) q congruent 7 modulo 12: 1/48 q phi1 phi2^2 ( q^3-2*q^2-1 ) q congruent 8 modulo 12: 1/48 q^3 phi1 phi2^2 ( q-2 ) q congruent 9 modulo 12: 1/48 q phi1 phi2^2 ( q^3-2*q^2-1 ) q congruent 11 modulo 12: 1/48 q phi1 phi2^2 ( q^3-2*q^2-1 ) 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 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 2, 1, 4 ], [ 15, 3, 1, 4 ], [ 15, 4, 1, 4 ], [ 16, 1, 1, 2 ], [ 17, 1, 4, 4 ], [ 17, 2, 4, 2 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 21, 1, 2, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 2, 2, 4 ], [ 25, 3, 2, 4 ], [ 25, 4, 2, 4 ], [ 26, 1, 5, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 29, 1, 3, 12 ], [ 29, 2, 3, 6 ], [ 30, 1, 4, 8 ], [ 30, 2, 4, 4 ], [ 34, 1, 6, 8 ], [ 34, 2, 8, 4 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 6 ], [ 35, 2, 6, 4 ], [ 35, 2, 8, 3 ], [ 37, 1, 4, 8 ], [ 37, 2, 4, 4 ], [ 39, 1, 3, 12 ], [ 39, 1, 9, 16 ], [ 39, 2, 3, 6 ], [ 39, 2, 9, 8 ], [ 39, 3, 3, 6 ], [ 39, 3, 9, 8 ], [ 39, 4, 10, 8 ], [ 39, 5, 10, 8 ], [ 40, 1, 14, 12 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 6 ], [ 41, 1, 38, 24 ], [ 41, 2, 38, 12 ], [ 41, 3, 38, 12 ], [ 41, 5, 37, 12 ], [ 41, 6, 37, 12 ], [ 41, 7, 37, 12 ], [ 42, 1, 16, 16 ], [ 42, 2, 3, 8 ], [ 42, 3, 4, 8 ], [ 42, 4, 13, 8 ], [ 43, 1, 8, 24 ], [ 43, 2, 5, 12 ], [ 43, 3, 7, 12 ], [ 44, 2, 9, 24 ], [ 44, 3, 8, 24 ], [ 44, 4, 58, 24 ], [ 44, 5, 9, 24 ], [ 44, 6, 5, 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 ], [ 6, 2, 2, 1 ], [ 34, 1, 10, 6 ], [ 34, 2, 6, 3 ], [ 40, 1, 11, 12 ], [ 40, 2, 12, 6 ], [ 44, 3, 30, 12 ], [ 44, 4, 59, 12 ], [ 44, 5, 31, 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 ], [ 5, 2, 2, 1 ], [ 8, 1, 2, 2 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 29, 1, 6, 6 ], [ 29, 2, 6, 3 ], [ 42, 1, 3, 10 ], [ 42, 4, 3, 5 ], [ 44, 4, 60, 15 ] ] j = 5: Omega of order 2, action on Pi: <()> k = 1: F-action on Pi is () [44,5,1] Dynkin type is (A_0(q) + T(phi1^7)).2 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: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 7 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 11 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) Fusion of maximal tori of C^F in those of G^F: [ 1 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 48 ], [ 4, 2, 1, 120 ], [ 5, 2, 1, 12 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 11, 1, 1, 96 ], [ 12, 2, 1, 128 ], [ 14, 2, 1, 48 ], [ 15, 2, 1, 72 ], [ 15, 4, 1, 192 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 144 ], [ 17, 2, 1, 120 ], [ 18, 2, 1, 12 ], [ 20, 2, 1, 384 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 288 ], [ 23, 2, 1, 96 ], [ 25, 2, 1, 96 ], [ 25, 3, 1, 144 ], [ 25, 4, 1, 288 ], [ 26, 1, 1, 144 ], [ 27, 1, 1, 576 ], [ 27, 2, 1, 288 ], [ 27, 3, 1, 864 ], [ 28, 1, 1, 192 ], [ 28, 2, 1, 96 ], [ 30, 2, 1, 384 ], [ 31, 2, 1, 288 ], [ 32, 1, 1, 576 ], [ 33, 4, 1, 768 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 96 ], [ 35, 1, 1, 576 ], [ 35, 2, 1, 288 ], [ 36, 3, 1, 1152 ], [ 36, 5, 1, 288 ], [ 36, 6, 1, 576 ], [ 38, 2, 1, 576 ], [ 38, 3, 1, 1152 ], [ 39, 4, 1, 576 ], [ 39, 5, 1, 192 ], [ 40, 1, 1, 1152 ], [ 40, 2, 1, 576 ], [ 40, 3, 1, 576 ], [ 41, 4, 1, 1152 ], [ 41, 5, 1, 2304 ], [ 42, 2, 1, 768 ], [ 43, 5, 1, 2304 ] ] k = 2: F-action on Pi is () [44,5,2] Dynkin type is (A_0(q) + T(phi1^5 phi3)).2 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: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/144 q phi2 ( q^2-8*q+15 ) 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, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 4, 2, 1, 6 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 12, 2, 1, 8 ], [ 17, 2, 1, 12 ], [ 18, 2, 1, 12 ], [ 21, 1, 1, 12 ], [ 25, 2, 1, 24 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 1, 24 ], [ 33, 4, 2, 24 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 24 ], [ 35, 1, 8, 18 ], [ 35, 2, 8, 9 ], [ 39, 5, 1, 48 ], [ 40, 1, 7, 36 ], [ 40, 2, 2, 18 ], [ 40, 3, 10, 18 ], [ 41, 5, 3, 72 ], [ 42, 2, 1, 48 ] ] k = 3: F-action on Pi is () [44,5,3] Dynkin type is (A_0(q) + T(phi1^3 phi3^2)).2 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: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) 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, 2 ], [ 4, 2, 1, 6 ], [ 5, 2, 1, 3 ], [ 6, 2, 1, 1 ], [ 11, 1, 1, 6 ], [ 12, 2, 1, 2 ], [ 14, 2, 1, 3 ], [ 15, 4, 1, 12 ], [ 16, 1, 1, 6 ], [ 20, 2, 1, 6 ], [ 21, 1, 5, 6 ], [ 23, 2, 1, 6 ], [ 28, 1, 1, 12 ], [ 28, 2, 1, 6 ], [ 32, 1, 9, 18 ], [ 33, 4, 1, 12 ], [ 34, 2, 7, 3 ], [ 36, 5, 9, 9 ], [ 38, 2, 20, 18 ], [ 40, 1, 4, 36 ], [ 40, 2, 3, 18 ], [ 42, 2, 9, 6 ], [ 43, 5, 26, 18 ] ] k = 4: F-action on Pi is () [44,5,4] Dynkin type is (A_0(q) + T(phi1 phi3^3)).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: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 7 modulo 12: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 11 modulo 12: 1/72 q phi2 ( q^2+q-6 ) 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, 8 ], [ 6, 2, 1, 1 ], [ 12, 2, 1, 8 ], [ 21, 1, 5, 24 ], [ 28, 1, 5, 24 ], [ 28, 2, 3, 12 ], [ 33, 4, 2, 24 ], [ 34, 2, 7, 3 ], [ 40, 1, 9, 72 ], [ 40, 2, 4, 36 ], [ 42, 2, 9, 24 ] ] k = 5: F-action on Pi is () [44,5,5] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi3)).2 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: 1/48 q phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/48 q phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/48 q phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/48 q phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/48 q phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/48 q phi1 phi2 ( q-3 ) 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, 2 ], [ 4, 1, 1, 12 ], [ 4, 2, 1, 6 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 17, 2, 4, 4 ], [ 18, 2, 4, 4 ], [ 21, 1, 1, 12 ], [ 25, 2, 2, 8 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 4, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 7, 8 ], [ 35, 1, 8, 18 ], [ 35, 2, 8, 9 ], [ 39, 5, 6, 16 ], [ 39, 5, 8, 16 ], [ 40, 1, 7, 36 ], [ 40, 2, 2, 18 ], [ 40, 3, 10, 18 ], [ 41, 5, 37, 24 ], [ 42, 2, 5, 16 ] ] k = 6: F-action on Pi is () [44,5,6] Dynkin type is (A_0(q) + T(phi1 phi2^2 phi4 phi6)).2 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: 1/24 q phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/24 q phi1^2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/24 q phi1^2 phi2 q congruent 7 modulo 12: 1/24 q phi1^2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/24 q phi1^2 phi2 q congruent 11 modulo 12: 1/24 q phi1^2 phi2 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 34, 2, 5, 4 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 39, 5, 14, 8 ], [ 40, 1, 15, 12 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 6 ], [ 42, 2, 18, 8 ] ] k = 7: F-action on Pi is () [44,5,7] Dynkin type is (A_0(q) + T(phi1^2 phi2 phi4 phi6)).2 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: 1/24 q phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/24 q phi1^2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/24 q phi1^2 phi2 q congruent 7 modulo 12: 1/24 q phi1^2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/24 q phi1^2 phi2 q congruent 11 modulo 12: 1/24 q phi1^2 phi2 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 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 21, 1, 3, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 34, 2, 8, 4 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 39, 5, 16, 8 ], [ 40, 1, 15, 12 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 6 ], [ 42, 2, 14, 8 ] ] k = 8: F-action on Pi is () [44,5,8] Dynkin type is (A_0(q) + T(phi1 phi2^2 phi3 phi4)).2 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: 1/24 q phi1 phi2^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/24 q phi1 phi2^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/24 q phi1 phi2^2 q congruent 7 modulo 12: 1/24 q phi1 phi2^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/24 q phi1 phi2^2 q congruent 11 modulo 12: 1/24 q phi1 phi2^2 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 34, 2, 5, 4 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 39, 5, 4, 8 ], [ 40, 1, 14, 12 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 6 ], [ 42, 2, 7, 8 ] ] k = 9: F-action on Pi is () [44,5,9] Dynkin type is (A_0(q) + T(phi1^2 phi2 phi3 phi4)).2 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: 1/24 q phi1 phi2^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/24 q phi1 phi2^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/24 q phi1 phi2^2 q congruent 7 modulo 12: 1/24 q phi1 phi2^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/24 q phi1 phi2^2 q congruent 11 modulo 12: 1/24 q phi1 phi2^2 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 ], [ 4, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 21, 1, 2, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 34, 2, 8, 4 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 39, 5, 10, 8 ], [ 40, 1, 14, 12 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 6 ], [ 42, 2, 3, 8 ] ] k = 10: F-action on Pi is () [44,5,10] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi6)).2 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: 1/144 q phi1^2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/144 q phi1^2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 7 modulo 12: 1/144 q phi1^2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/144 q phi1^2 ( q-3 ) q congruent 11 modulo 12: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) 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 ], [ 4, 2, 2, 6 ], [ 6, 2, 1, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 12, 2, 4, 8 ], [ 17, 2, 4, 12 ], [ 18, 2, 1, 12 ], [ 21, 1, 6, 12 ], [ 25, 2, 3, 24 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 7, 24 ], [ 33, 4, 8, 24 ], [ 34, 2, 1, 24 ], [ 34, 3, 4, 24 ], [ 35, 1, 9, 18 ], [ 35, 2, 9, 9 ], [ 39, 5, 18, 48 ], [ 40, 1, 8, 36 ], [ 40, 2, 5, 18 ], [ 40, 3, 9, 18 ], [ 41, 5, 31, 72 ], [ 42, 2, 15, 48 ] ] k = 11: F-action on Pi is () [44,5,11] Dynkin type is (A_0(q) + T(phi1 phi2^4 phi6)).2 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: 1/48 q phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/48 q phi1^2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/48 q phi1^2 phi2 q congruent 7 modulo 12: 1/48 q phi1^2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/48 q phi1^2 phi2 q congruent 11 modulo 12: 1/48 q phi1^2 phi2 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, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 4, 2, 2, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 17, 2, 1, 4 ], [ 18, 2, 4, 4 ], [ 21, 1, 6, 12 ], [ 25, 2, 4, 8 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 6, 8 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 35, 1, 9, 18 ], [ 35, 2, 9, 9 ], [ 39, 5, 11, 16 ], [ 39, 5, 20, 16 ], [ 40, 1, 8, 36 ], [ 40, 2, 5, 18 ], [ 40, 3, 9, 18 ], [ 41, 5, 17, 24 ], [ 42, 2, 11, 16 ] ] k = 12: F-action on Pi is () [44,5,12] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi6)).2 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: 1/48 q phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/48 q phi1^2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/48 q phi1^2 phi2 q congruent 7 modulo 12: 1/48 q phi1^2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/48 q phi1^2 phi2 q congruent 11 modulo 12: 1/48 q phi1^2 phi2 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, 2 ], [ 4, 1, 2, 12 ], [ 4, 2, 2, 6 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 17, 2, 2, 4 ], [ 18, 2, 2, 4 ], [ 21, 1, 6, 12 ], [ 25, 2, 7, 8 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 8, 8 ], [ 34, 2, 2, 8 ], [ 34, 3, 3, 8 ], [ 35, 1, 9, 18 ], [ 35, 2, 9, 9 ], [ 39, 5, 12, 16 ], [ 39, 5, 19, 16 ], [ 40, 1, 8, 36 ], [ 40, 2, 5, 18 ], [ 40, 3, 9, 18 ], [ 41, 5, 27, 24 ], [ 42, 2, 12, 16 ] ] k = 13: F-action on Pi is () [44,5,13] Dynkin type is (A_0(q) + T(phi2^5 phi6)).2 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: 1/144 q phi1^2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/144 q phi1^2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) q congruent 7 modulo 12: 1/144 q phi1^2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/144 q phi1^2 ( q-3 ) q congruent 11 modulo 12: 1/144 phi2 ( q^3-6*q^2+13*q-16 ) 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, 3 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], [ 4, 2, 2, 6 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 4, 12 ], [ 12, 2, 3, 8 ], [ 17, 2, 3, 12 ], [ 18, 2, 3, 12 ], [ 21, 1, 6, 12 ], [ 25, 2, 8, 24 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 5, 24 ], [ 33, 4, 5, 24 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 24 ], [ 35, 1, 9, 18 ], [ 35, 2, 9, 9 ], [ 39, 5, 15, 48 ], [ 40, 1, 8, 36 ], [ 40, 2, 5, 18 ], [ 40, 3, 9, 18 ], [ 41, 5, 9, 72 ], [ 42, 2, 20, 48 ] ] k = 14: F-action on Pi is () [44,5,14] Dynkin type is (A_0(q) + T(phi1^4 phi2 phi3)).2 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: 1/48 q phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/48 q phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/48 q phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/48 q phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/48 q phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/48 q phi1 phi2 ( q-3 ) 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, 3 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], [ 4, 2, 1, 6 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 17, 2, 3, 4 ], [ 18, 2, 2, 4 ], [ 21, 1, 1, 12 ], [ 25, 2, 5, 8 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 2, 8 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 35, 1, 8, 18 ], [ 35, 2, 8, 9 ], [ 39, 5, 2, 16 ], [ 39, 5, 7, 16 ], [ 40, 1, 7, 36 ], [ 40, 2, 2, 18 ], [ 40, 3, 10, 18 ], [ 41, 5, 7, 24 ], [ 42, 2, 2, 16 ] ] k = 15: F-action on Pi is () [44,5,15] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi3)).2 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: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/144 phi1 ( q^3-6*q^2+q+16 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/144 q phi2 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/144 q phi2 ( q^2-8*q+15 ) 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 ], [ 4, 2, 1, 6 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 12 ], [ 12, 2, 2, 8 ], [ 17, 2, 2, 12 ], [ 18, 2, 3, 12 ], [ 21, 1, 1, 12 ], [ 25, 2, 6, 24 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 3, 24 ], [ 33, 4, 11, 24 ], [ 34, 2, 10, 24 ], [ 34, 3, 8, 24 ], [ 35, 1, 8, 18 ], [ 35, 2, 8, 9 ], [ 39, 5, 5, 48 ], [ 40, 1, 7, 36 ], [ 40, 2, 2, 18 ], [ 40, 3, 10, 18 ], [ 41, 5, 24, 72 ], [ 42, 2, 10, 48 ] ] k = 16: F-action on Pi is () [44,5,16] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi6)).2 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: 1/24 q phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/24 q phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/24 q phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/24 q phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/24 q phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/24 q phi1 phi2 ( q-3 ) 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, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 2, 3, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 21, 1, 3, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 5, 4 ], [ 30, 2, 8, 4 ], [ 33, 4, 5, 12 ], [ 34, 2, 3, 4 ], [ 34, 3, 2, 4 ], [ 34, 3, 8, 4 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 39, 5, 13, 8 ], [ 40, 1, 15, 12 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 6 ], [ 41, 5, 9, 12 ], [ 41, 5, 27, 12 ], [ 42, 2, 19, 8 ] ] k = 17: F-action on Pi is () [44,5,17] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi6)).2 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: 1/24 q phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/24 q phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/24 q phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/24 q phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/24 q phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/24 q phi1 phi2 ( q-3 ) 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, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 3, 4 ], [ 12, 2, 4, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 21, 1, 3, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 28, 1, 4, 6 ], [ 28, 2, 5, 3 ], [ 30, 2, 6, 4 ], [ 30, 2, 7, 4 ], [ 33, 4, 8, 12 ], [ 34, 2, 4, 4 ], [ 34, 3, 1, 4 ], [ 34, 3, 7, 4 ], [ 35, 1, 9, 6 ], [ 35, 2, 9, 3 ], [ 39, 5, 17, 8 ], [ 40, 1, 15, 12 ], [ 40, 2, 6, 6 ], [ 40, 3, 12, 6 ], [ 41, 5, 17, 12 ], [ 41, 5, 31, 12 ], [ 42, 2, 13, 8 ] ] k = 18: F-action on Pi is () [44,5,18] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi3)).2 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: 1/24 q phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/24 q phi1^2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/24 q phi1^2 phi2 q congruent 7 modulo 12: 1/24 q phi1^2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/24 q phi1^2 phi2 q congruent 11 modulo 12: 1/24 q phi1^2 phi2 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, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 2, 1, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 4, 2 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 21, 1, 2, 4 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 1, 4 ], [ 30, 2, 4, 4 ], [ 33, 4, 2, 12 ], [ 34, 2, 4, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 6, 4 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 39, 5, 9, 8 ], [ 40, 1, 14, 12 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 6 ], [ 41, 5, 3, 12 ], [ 41, 5, 37, 12 ], [ 42, 2, 4, 8 ] ] k = 19: F-action on Pi is () [44,5,19] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi3)).2 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: 1/24 q phi1^2 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/24 q phi1^2 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/24 q phi1^2 phi2 q congruent 7 modulo 12: 1/24 q phi1^2 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/24 q phi1^2 phi2 q congruent 11 modulo 12: 1/24 q phi1^2 phi2 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, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 12, 2, 2, 4 ], [ 17, 2, 2, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 21, 1, 2, 4 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 28, 1, 5, 6 ], [ 28, 2, 3, 3 ], [ 30, 2, 2, 4 ], [ 30, 2, 3, 4 ], [ 33, 4, 11, 12 ], [ 34, 2, 3, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 5, 4 ], [ 35, 1, 8, 6 ], [ 35, 2, 8, 3 ], [ 39, 5, 3, 8 ], [ 40, 1, 14, 12 ], [ 40, 2, 7, 6 ], [ 40, 3, 13, 6 ], [ 41, 5, 7, 12 ], [ 41, 5, 24, 12 ], [ 42, 2, 6, 8 ] ] k = 20: F-action on Pi is () [44,5,20] Dynkin type is (A_0(q) + T(phi2^3 phi6^2)).2 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: 1/36 q^2 phi1^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/36 q^2 phi1^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 12: 1/36 q^2 phi1^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/36 q^2 phi1^2 q congruent 11 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) 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, 2 ], [ 4, 2, 2, 6 ], [ 5, 2, 2, 3 ], [ 6, 2, 2, 1 ], [ 11, 1, 2, 6 ], [ 12, 2, 3, 2 ], [ 14, 2, 2, 3 ], [ 15, 4, 4, 12 ], [ 16, 1, 2, 6 ], [ 20, 2, 2, 6 ], [ 21, 1, 4, 6 ], [ 23, 2, 4, 6 ], [ 28, 1, 6, 12 ], [ 28, 2, 6, 6 ], [ 32, 1, 10, 18 ], [ 33, 4, 6, 12 ], [ 34, 2, 6, 3 ], [ 36, 5, 7, 9 ], [ 38, 2, 18, 18 ], [ 40, 1, 5, 36 ], [ 40, 2, 8, 18 ], [ 42, 2, 16, 6 ], [ 43, 5, 33, 18 ] ] k = 21: F-action on Pi is () [44,5,21] Dynkin type is (A_0(q) + T(phi1^2 phi2 phi3^2)).2 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: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 q^2 phi1 phi2 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, 2 ], [ 4, 2, 1, 2 ], [ 5, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 11, 1, 1, 2 ], [ 12, 2, 1, 2 ], [ 14, 2, 1, 1 ], [ 15, 4, 3, 4 ], [ 16, 1, 2, 2 ], [ 20, 2, 1, 2 ], [ 21, 1, 5, 6 ], [ 23, 2, 2, 2 ], [ 28, 1, 3, 4 ], [ 28, 2, 4, 2 ], [ 32, 1, 9, 6 ], [ 33, 4, 3, 4 ], [ 34, 2, 7, 3 ], [ 36, 5, 9, 3 ], [ 38, 2, 17, 6 ], [ 40, 1, 19, 12 ], [ 40, 2, 10, 6 ], [ 42, 2, 9, 6 ], [ 43, 5, 26, 6 ] ] k = 22: F-action on Pi is () [44,5,22] Dynkin type is (A_0(q) + T(phi1 phi2^2 phi6^2)).2 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: 1/12 q phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/12 q phi1 phi2 ( q-2 ) 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, 2 ], [ 4, 2, 2, 2 ], [ 5, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 11, 1, 2, 2 ], [ 12, 2, 3, 2 ], [ 14, 2, 2, 1 ], [ 15, 4, 2, 4 ], [ 16, 1, 1, 2 ], [ 20, 2, 2, 2 ], [ 21, 1, 4, 6 ], [ 23, 2, 3, 2 ], [ 28, 1, 2, 4 ], [ 28, 2, 2, 2 ], [ 32, 1, 10, 6 ], [ 33, 4, 4, 4 ], [ 34, 2, 6, 3 ], [ 36, 5, 7, 3 ], [ 38, 2, 19, 6 ], [ 40, 1, 20, 12 ], [ 40, 2, 9, 6 ], [ 42, 2, 16, 6 ], [ 43, 5, 33, 6 ] ] k = 23: F-action on Pi is () [44,5,23] Dynkin type is (A_0(q) + T(phi1^2 phi2 phi3 phi6)).2 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: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) 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, 2, 3, 6 ], [ 5, 2, 2, 3 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 6 ], [ 12, 2, 2, 2 ], [ 14, 2, 2, 3 ], [ 15, 4, 5, 12 ], [ 16, 1, 1, 6 ], [ 20, 2, 4, 6 ], [ 21, 1, 5, 6 ], [ 23, 2, 3, 6 ], [ 28, 1, 1, 12 ], [ 28, 2, 1, 6 ], [ 32, 1, 9, 18 ], [ 33, 4, 10, 12 ], [ 34, 2, 6, 3 ], [ 36, 5, 7, 9 ], [ 38, 2, 19, 18 ], [ 40, 1, 4, 36 ], [ 40, 2, 3, 18 ], [ 42, 2, 8, 6 ], [ 43, 5, 25, 18 ] ] k = 24: F-action on Pi is () [44,5,24] Dynkin type is (A_0(q) + T(phi1 phi2^2 phi3 phi6)).2 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: 1/36 q^2 phi1^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/36 q^2 phi1^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 12: 1/36 q^2 phi1^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/36 q^2 phi1^2 q congruent 11 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) 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, 2, 4, 6 ], [ 5, 2, 1, 3 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 6 ], [ 12, 2, 4, 2 ], [ 14, 2, 1, 3 ], [ 15, 4, 8, 12 ], [ 16, 1, 2, 6 ], [ 20, 2, 3, 6 ], [ 21, 1, 4, 6 ], [ 23, 2, 2, 6 ], [ 28, 1, 6, 12 ], [ 28, 2, 6, 6 ], [ 32, 1, 10, 18 ], [ 33, 4, 9, 12 ], [ 34, 2, 7, 3 ], [ 36, 5, 9, 9 ], [ 38, 2, 17, 18 ], [ 40, 1, 5, 36 ], [ 40, 2, 8, 18 ], [ 42, 2, 17, 6 ], [ 43, 5, 34, 18 ] ] k = 25: F-action on Pi is () [44,5,25] Dynkin type is (A_0(q) + T(phi1 phi2^2 phi3 phi6)).2 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: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 q^2 phi1 phi2 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, 2, 3, 2 ], [ 5, 2, 2, 1 ], [ 6, 2, 2, 1 ], [ 11, 1, 1, 2 ], [ 12, 2, 2, 2 ], [ 14, 2, 2, 1 ], [ 15, 4, 7, 4 ], [ 16, 1, 2, 2 ], [ 20, 2, 4, 2 ], [ 21, 1, 5, 6 ], [ 23, 2, 4, 2 ], [ 28, 1, 3, 4 ], [ 28, 2, 4, 2 ], [ 32, 1, 9, 6 ], [ 33, 4, 12, 4 ], [ 34, 2, 6, 3 ], [ 36, 5, 7, 3 ], [ 38, 2, 18, 6 ], [ 40, 1, 19, 12 ], [ 40, 2, 10, 6 ], [ 42, 2, 8, 6 ], [ 43, 5, 25, 6 ] ] k = 26: F-action on Pi is () [44,5,26] Dynkin type is (A_0(q) + T(phi1^2 phi2 phi3 phi6)).2 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: 1/12 q phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/12 q phi1 phi2 ( q-2 ) 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, 2, 4, 2 ], [ 5, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 11, 1, 2, 2 ], [ 12, 2, 4, 2 ], [ 14, 2, 1, 1 ], [ 15, 4, 6, 4 ], [ 16, 1, 1, 2 ], [ 20, 2, 3, 2 ], [ 21, 1, 4, 6 ], [ 23, 2, 1, 2 ], [ 28, 1, 2, 4 ], [ 28, 2, 2, 2 ], [ 32, 1, 10, 6 ], [ 33, 4, 7, 4 ], [ 34, 2, 7, 3 ], [ 36, 5, 9, 3 ], [ 38, 2, 20, 6 ], [ 40, 1, 20, 12 ], [ 40, 2, 9, 6 ], [ 42, 2, 17, 6 ], [ 43, 5, 34, 6 ] ] k = 27: F-action on Pi is () [44,5,27] Dynkin type is (A_0(q) + T(phi2 phi6^3)).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: 1/72 q phi1 ( q^2-q-6 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 7 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 11 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) 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, 8 ], [ 6, 2, 2, 1 ], [ 12, 2, 3, 8 ], [ 21, 1, 4, 24 ], [ 28, 1, 4, 24 ], [ 28, 2, 5, 12 ], [ 33, 4, 5, 24 ], [ 34, 2, 6, 3 ], [ 40, 1, 10, 72 ], [ 40, 2, 11, 36 ], [ 42, 2, 16, 24 ] ] k = 28: F-action on Pi is () [44,5,28] Dynkin type is (A_0(q) + T(phi2 phi3^2 phi6)).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: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 7 modulo 12: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 11 modulo 12: 1/72 q phi2 ( q^2+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, 2, 2, 1 ], [ 12, 2, 2, 8 ], [ 21, 1, 5, 24 ], [ 28, 1, 5, 24 ], [ 28, 2, 3, 12 ], [ 33, 4, 11, 24 ], [ 34, 2, 6, 3 ], [ 40, 1, 9, 72 ], [ 40, 2, 4, 36 ], [ 42, 2, 8, 24 ] ] k = 29: F-action on Pi is () [44,5,29] Dynkin type is (A_0(q) + T(phi1 phi3 phi6^2)).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: 1/72 q phi1 ( q^2-q-6 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 7 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 11 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) 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, 2, 1, 1 ], [ 12, 2, 4, 8 ], [ 21, 1, 4, 24 ], [ 28, 1, 4, 24 ], [ 28, 2, 5, 12 ], [ 33, 4, 8, 24 ], [ 34, 2, 7, 3 ], [ 40, 1, 10, 72 ], [ 40, 2, 11, 36 ], [ 42, 2, 17, 24 ] ] k = 30: F-action on Pi is () [44,5,30] Dynkin type is (A_0(q) + T(phi1 phi3 phi12)).2 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: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 q^2 phi1 phi2 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, 2, 1, 1 ], [ 34, 2, 7, 3 ], [ 40, 1, 11, 12 ], [ 40, 2, 12, 6 ] ] k = 31: F-action on Pi is () [44,5,31] Dynkin type is (A_0(q) + T(phi2 phi6 phi12)).2 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: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 q^2 phi1 phi2 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, 2, 2, 1 ], [ 34, 2, 6, 3 ], [ 40, 1, 11, 12 ], [ 40, 2, 12, 6 ] ] k = 32: F-action on Pi is () [44,5,32] Dynkin type is (A_0(q) + T(phi1^3 phi2^4)).2 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: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 ) q congruent 7 modulo 12: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 11 modulo 12: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 ) Fusion of maximal tori of C^F in those of G^F: [ 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 48 ], [ 4, 2, 2, 24 ], [ 4, 2, 4, 96 ], [ 5, 2, 1, 12 ], [ 6, 2, 1, 4 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 12, 2, 4, 128 ], [ 14, 2, 1, 48 ], [ 15, 2, 1, 72 ], [ 15, 4, 8, 192 ], [ 16, 1, 2, 24 ], [ 17, 1, 3, 144 ], [ 17, 2, 3, 72 ], [ 17, 2, 4, 48 ], [ 18, 2, 1, 12 ], [ 20, 2, 3, 384 ], [ 21, 1, 6, 192 ], [ 22, 1, 4, 288 ], [ 23, 2, 2, 96 ], [ 25, 2, 3, 96 ], [ 25, 3, 1, 144 ], [ 25, 4, 2, 288 ], [ 26, 1, 3, 144 ], [ 27, 1, 12, 576 ], [ 27, 2, 12, 288 ], [ 27, 3, 4, 576 ], [ 27, 3, 11, 288 ], [ 28, 1, 6, 192 ], [ 28, 2, 6, 96 ], [ 30, 2, 7, 384 ], [ 31, 2, 3, 288 ], [ 32, 1, 7, 576 ], [ 33, 4, 9, 768 ], [ 34, 2, 1, 24 ], [ 34, 3, 4, 96 ], [ 35, 1, 10, 576 ], [ 35, 2, 10, 288 ], [ 36, 3, 24, 1152 ], [ 36, 5, 1, 288 ], [ 36, 6, 11, 576 ], [ 38, 2, 8, 576 ], [ 38, 3, 16, 1152 ], [ 39, 4, 8, 576 ], [ 39, 5, 18, 192 ], [ 40, 1, 2, 1152 ], [ 40, 2, 13, 576 ], [ 40, 3, 19, 576 ], [ 41, 4, 24, 1152 ], [ 41, 5, 40, 2304 ], [ 42, 2, 15, 768 ], [ 43, 5, 19, 2304 ] ] k = 33: F-action on Pi is () [44,5,33] Dynkin type is (A_0(q) + T(phi2^3 phi4^2)).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: 1/384 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) 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 ], [ 6, 2, 2, 4 ], [ 15, 2, 3, 24 ], [ 18, 2, 3, 12 ], [ 25, 3, 6, 48 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 2, 7, 24 ], [ 34, 2, 10, 24 ], [ 36, 5, 19, 96 ], [ 39, 4, 4, 96 ], [ 40, 1, 6, 96 ], [ 40, 2, 14, 48 ], [ 41, 4, 30, 192 ] ] k = 34: F-action on Pi is () [44,5,34] Dynkin type is (A_0(q) + T(phi1^3 phi4^2)).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: 1/384 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 12: 1/384 phi1 phi2 ( q^2-9 ) 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 ], [ 6, 2, 1, 4 ], [ 15, 2, 2, 24 ], [ 18, 2, 1, 12 ], [ 25, 3, 3, 48 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 2, 7, 24 ], [ 34, 2, 1, 24 ], [ 36, 5, 3, 96 ], [ 39, 4, 16, 96 ], [ 40, 1, 6, 96 ], [ 40, 2, 14, 48 ], [ 41, 4, 40, 192 ] ] k = 35: F-action on Pi is () [44,5,35] Dynkin type is (A_0(q) + T(phi1 phi2^2 phi8)).2 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: 1/16 phi1 phi2 phi4 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 phi2 phi4 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 phi2 phi4 q congruent 7 modulo 12: 1/16 phi1 phi2 phi4 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 phi2 phi4 q congruent 11 modulo 12: 1/16 phi1 phi2 phi4 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, 2, 2, 2 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 34, 2, 3, 4 ], [ 36, 5, 8, 8 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ] ] k = 36: F-action on Pi is () [44,5,36] Dynkin type is (A_0(q) + T(phi1^2 phi2 phi8)).2 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: 1/16 phi1 phi2 phi4 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 phi2 phi4 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 phi2 phi4 q congruent 7 modulo 12: 1/16 phi1 phi2 phi4 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 phi2 phi4 q congruent 11 modulo 12: 1/16 phi1 phi2 phi4 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, 2, 1, 2 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 34, 2, 4, 4 ], [ 36, 5, 16, 8 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ] ] k = 37: F-action on Pi is () [44,5,37] Dynkin type is (A_0(q) + T(phi1 phi2^2 phi4^2)).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: 1/128 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) 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 ], [ 5, 2, 1, 4 ], [ 15, 2, 1, 8 ], [ 15, 2, 7, 16 ], [ 15, 2, 8, 16 ], [ 18, 2, 4, 4 ], [ 25, 3, 2, 16 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 2, 7, 24 ], [ 34, 2, 9, 8 ], [ 36, 3, 11, 64 ], [ 36, 5, 14, 32 ], [ 36, 5, 15, 32 ], [ 39, 4, 10, 32 ], [ 40, 1, 6, 96 ], [ 40, 2, 14, 48 ], [ 41, 4, 29, 64 ], [ 41, 4, 48, 64 ] ] k = 38: F-action on Pi is () [44,5,38] Dynkin type is (A_0(q) + T(phi2 phi4 phi8)).2 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: 1/16 phi1 phi2 phi4 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 phi2 phi4 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 phi2 phi4 q congruent 7 modulo 12: 1/16 phi1 phi2 phi4 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 phi2 phi4 q congruent 11 modulo 12: 1/16 phi1 phi2 phi4 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 ], [ 5, 2, 1, 2 ], [ 15, 2, 7, 4 ], [ 15, 2, 8, 4 ], [ 34, 2, 5, 4 ], [ 36, 5, 11, 8 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ] ] k = 39: F-action on Pi is () [44,5,39] Dynkin type is (A_0(q) + T(phi1 phi4 phi8)).2 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: 1/16 phi1 phi2 phi4 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi1 phi2 phi4 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 phi2 phi4 q congruent 7 modulo 12: 1/16 phi1 phi2 phi4 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 phi2 phi4 q congruent 11 modulo 12: 1/16 phi1 phi2 phi4 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 ], [ 5, 2, 2, 2 ], [ 15, 2, 5, 4 ], [ 15, 2, 6, 4 ], [ 34, 2, 8, 4 ], [ 36, 5, 12, 8 ], [ 40, 1, 25, 8 ], [ 40, 2, 15, 4 ] ] k = 40: F-action on Pi is () [44,5,40] Dynkin type is (A_0(q) + T(phi1^2 phi2 phi4^2)).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: 1/128 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 12: 1/128 phi1 phi2 ( q^2-9 ) 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 ], [ 5, 2, 2, 4 ], [ 15, 2, 4, 8 ], [ 15, 2, 5, 16 ], [ 15, 2, 6, 16 ], [ 18, 2, 2, 4 ], [ 25, 3, 7, 16 ], [ 26, 1, 5, 24 ], [ 27, 1, 7, 48 ], [ 27, 2, 7, 24 ], [ 34, 2, 2, 8 ], [ 36, 3, 8, 64 ], [ 36, 5, 6, 32 ], [ 36, 5, 13, 32 ], [ 39, 4, 14, 32 ], [ 40, 1, 6, 96 ], [ 40, 2, 14, 48 ], [ 41, 4, 36, 64 ], [ 41, 4, 39, 64 ] ] k = 41: F-action on Pi is () [44,5,41] Dynkin type is (A_0(q) + T(phi1^2 phi2^5)).2 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: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) 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, 32 ], [ 4, 1, 2, 48 ], [ 4, 2, 2, 24 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 15, 2, 3, 24 ], [ 16, 1, 2, 24 ], [ 17, 1, 3, 144 ], [ 17, 2, 2, 16 ], [ 17, 2, 3, 72 ], [ 18, 2, 2, 4 ], [ 21, 1, 6, 192 ], [ 22, 1, 4, 288 ], [ 25, 2, 7, 32 ], [ 25, 3, 5, 48 ], [ 25, 4, 6, 96 ], [ 26, 1, 3, 144 ], [ 27, 1, 12, 576 ], [ 27, 2, 12, 288 ], [ 27, 3, 8, 192 ], [ 27, 3, 11, 288 ], [ 28, 1, 6, 192 ], [ 28, 2, 6, 96 ], [ 30, 2, 8, 128 ], [ 31, 2, 4, 96 ], [ 32, 1, 7, 576 ], [ 34, 2, 2, 8 ], [ 34, 3, 3, 32 ], [ 35, 1, 10, 576 ], [ 35, 2, 10, 288 ], [ 36, 3, 26, 384 ], [ 36, 5, 4, 96 ], [ 36, 6, 15, 192 ], [ 38, 2, 5, 192 ], [ 38, 3, 15, 384 ], [ 39, 4, 5, 192 ], [ 39, 5, 12, 64 ], [ 39, 5, 19, 64 ], [ 40, 1, 2, 1152 ], [ 40, 2, 13, 576 ], [ 40, 3, 19, 576 ], [ 41, 4, 9, 384 ], [ 41, 4, 25, 384 ], [ 41, 5, 25, 768 ], [ 42, 2, 12, 256 ], [ 43, 5, 18, 768 ] ] k = 42: F-action on Pi is () [44,5,42] Dynkin type is (A_0(q) + T(phi1^5 phi2^2)).2 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: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 7 modulo 12: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 11 modulo 12: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) Fusion of maximal tori of C^F in those of G^F: [ 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 48 ], [ 4, 2, 1, 24 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 11, 1, 1, 96 ], [ 15, 2, 2, 24 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 144 ], [ 17, 2, 1, 72 ], [ 17, 2, 4, 16 ], [ 18, 2, 4, 4 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 288 ], [ 25, 2, 2, 32 ], [ 25, 3, 4, 48 ], [ 25, 4, 3, 96 ], [ 26, 1, 1, 144 ], [ 27, 1, 1, 576 ], [ 27, 2, 1, 288 ], [ 27, 3, 1, 288 ], [ 27, 3, 16, 192 ], [ 28, 1, 1, 192 ], [ 28, 2, 1, 96 ], [ 30, 2, 4, 128 ], [ 31, 2, 6, 96 ], [ 32, 1, 1, 576 ], [ 34, 2, 9, 8 ], [ 34, 3, 7, 32 ], [ 35, 1, 1, 576 ], [ 35, 2, 1, 288 ], [ 36, 3, 3, 384 ], [ 36, 5, 18, 96 ], [ 36, 6, 4, 192 ], [ 38, 2, 4, 192 ], [ 38, 3, 11, 384 ], [ 39, 4, 18, 192 ], [ 39, 5, 6, 64 ], [ 39, 5, 8, 64 ], [ 40, 1, 1, 1152 ], [ 40, 2, 1, 576 ], [ 40, 3, 1, 576 ], [ 41, 4, 15, 384 ], [ 41, 4, 22, 384 ], [ 41, 5, 35, 768 ], [ 42, 2, 5, 256 ], [ 43, 5, 5, 768 ] ] k = 43: F-action on Pi is () [44,5,43] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi4)).2 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: 1/192 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/192 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/192 phi1^2 phi2 ( 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, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 3, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 13, 48 ], [ 27, 3, 12, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 32, 1, 5, 48 ], [ 34, 2, 8, 4 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 10, 24 ], [ 36, 5, 17, 24 ], [ 38, 2, 11, 48 ], [ 39, 5, 10, 24 ], [ 39, 5, 16, 8 ], [ 40, 1, 13, 96 ], [ 40, 2, 24, 48 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 48 ], [ 41, 4, 18, 48 ], [ 41, 4, 49, 96 ], [ 42, 2, 14, 32 ], [ 43, 5, 15, 96 ] ] k = 44: F-action on Pi is () [44,5,44] Dynkin type is (A_0(q) + T(phi1 phi2^4 phi4)).2 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: 1/192 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/192 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/192 phi1^2 phi2 ( 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 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 3, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 13, 48 ], [ 27, 3, 12, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 32, 1, 5, 48 ], [ 34, 2, 5, 4 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 10, 24 ], [ 36, 5, 10, 24 ], [ 38, 2, 12, 48 ], [ 39, 5, 4, 24 ], [ 39, 5, 14, 8 ], [ 40, 1, 13, 96 ], [ 40, 2, 24, 48 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 48 ], [ 41, 4, 6, 48 ], [ 41, 4, 32, 96 ], [ 42, 2, 18, 32 ], [ 43, 5, 35, 96 ] ] k = 45: F-action on Pi is () [44,5,45] Dynkin type is (A_0(q) + T(phi1^4 phi2 phi4)).2 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: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) 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 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 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 ], [ 17, 2, 1, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 3, 2, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 32, 1, 2, 48 ], [ 34, 2, 8, 4 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 36, 5, 17, 24 ], [ 38, 2, 13, 48 ], [ 39, 5, 10, 8 ], [ 39, 5, 16, 24 ], [ 40, 1, 12, 96 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 48 ], [ 41, 4, 18, 48 ], [ 41, 4, 43, 96 ], [ 42, 2, 3, 32 ], [ 43, 5, 3, 96 ] ] k = 46: F-action on Pi is () [44,5,46] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi4)).2 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: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/192 phi1 phi2 ( q^2-8*q+15 ) 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, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 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 ], [ 17, 2, 1, 12 ], [ 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 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 3, 2, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 32, 1, 2, 48 ], [ 34, 2, 5, 4 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 36, 5, 10, 24 ], [ 38, 2, 14, 48 ], [ 39, 5, 4, 8 ], [ 39, 5, 14, 24 ], [ 40, 1, 12, 96 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 48 ], [ 41, 4, 6, 48 ], [ 41, 4, 38, 96 ], [ 42, 2, 7, 32 ], [ 43, 5, 28, 96 ] ] k = 47: F-action on Pi is () [44,5,47] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi4)).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 phi2^2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 7 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 11 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) 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, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 34, 2, 8, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 36, 3, 19, 16 ], [ 36, 5, 17, 8 ], [ 38, 2, 11, 8 ], [ 38, 2, 13, 8 ], [ 39, 5, 10, 8 ], [ 39, 5, 16, 8 ], [ 40, 1, 22, 16 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 8 ], [ 41, 4, 18, 16 ], [ 41, 4, 45, 16 ], [ 42, 2, 3, 16 ], [ 42, 2, 14, 16 ], [ 43, 5, 3, 16 ], [ 43, 5, 15, 16 ] ] k = 48: F-action on Pi is () [44,5,48] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi4)).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 phi2^2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 7 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 11 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) 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, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 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 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 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 ], [ 27, 2, 2, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 34, 2, 5, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 36, 3, 21, 16 ], [ 36, 5, 10, 8 ], [ 38, 2, 12, 8 ], [ 38, 2, 14, 8 ], [ 39, 5, 4, 8 ], [ 39, 5, 14, 8 ], [ 40, 1, 22, 16 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 8 ], [ 41, 4, 6, 16 ], [ 41, 4, 33, 16 ], [ 42, 2, 7, 16 ], [ 42, 2, 18, 16 ], [ 43, 5, 28, 16 ], [ 43, 5, 35, 16 ] ] k = 49: F-action on Pi is () [44,5,49] Dynkin type is (A_0(q) + T(phi1 phi2^6)).2 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: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 7 modulo 12: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/1536 phi1^2 ( q^2-14*q+45 ) q congruent 11 modulo 12: 1/1536 phi2 ( q^3-17*q^2+91*q-147 ) 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, 15 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 48 ], [ 4, 2, 2, 24 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 15, 2, 2, 24 ], [ 16, 1, 2, 24 ], [ 17, 1, 3, 144 ], [ 17, 2, 1, 16 ], [ 17, 2, 3, 72 ], [ 18, 2, 4, 4 ], [ 21, 1, 6, 192 ], [ 22, 1, 4, 288 ], [ 25, 2, 4, 32 ], [ 25, 3, 4, 48 ], [ 25, 4, 4, 96 ], [ 26, 1, 3, 144 ], [ 27, 1, 12, 576 ], [ 27, 2, 12, 288 ], [ 27, 3, 9, 192 ], [ 27, 3, 11, 288 ], [ 28, 1, 6, 192 ], [ 28, 2, 6, 96 ], [ 30, 2, 6, 128 ], [ 31, 2, 8, 96 ], [ 32, 1, 7, 576 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 32 ], [ 35, 1, 10, 576 ], [ 35, 2, 10, 288 ], [ 36, 3, 23, 384 ], [ 36, 5, 18, 96 ], [ 36, 6, 9, 192 ], [ 38, 2, 6, 192 ], [ 38, 3, 6, 384 ], [ 39, 4, 20, 192 ], [ 39, 5, 11, 64 ], [ 39, 5, 20, 64 ], [ 40, 1, 2, 1152 ], [ 40, 2, 13, 576 ], [ 40, 3, 19, 576 ], [ 41, 4, 10, 384 ], [ 41, 4, 26, 384 ], [ 41, 5, 20, 768 ], [ 42, 2, 11, 256 ], [ 43, 5, 17, 768 ] ] k = 50: F-action on Pi is () [44,5,50] Dynkin type is (A_0(q) + T(phi2^7)).2 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: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 ) q congruent 7 modulo 12: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4608 phi1 ( q^3-31*q^2+315*q-1053 ) q congruent 11 modulo 12: 1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 ) Fusion of maximal tori of C^F in those of G^F: [ 31 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 48 ], [ 4, 2, 2, 120 ], [ 5, 2, 2, 12 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 24 ], [ 9, 1, 2, 96 ], [ 10, 1, 4, 192 ], [ 11, 1, 2, 96 ], [ 12, 2, 3, 128 ], [ 14, 2, 2, 48 ], [ 15, 2, 4, 72 ], [ 15, 4, 4, 192 ], [ 16, 1, 2, 24 ], [ 17, 1, 3, 144 ], [ 17, 2, 3, 120 ], [ 18, 2, 3, 12 ], [ 20, 2, 2, 384 ], [ 21, 1, 6, 192 ], [ 22, 1, 4, 288 ], [ 23, 2, 4, 96 ], [ 25, 2, 8, 96 ], [ 25, 3, 8, 144 ], [ 25, 4, 8, 288 ], [ 26, 1, 3, 144 ], [ 27, 1, 12, 576 ], [ 27, 2, 12, 288 ], [ 27, 3, 11, 864 ], [ 28, 1, 6, 192 ], [ 28, 2, 6, 96 ], [ 30, 2, 5, 384 ], [ 31, 2, 7, 288 ], [ 32, 1, 7, 576 ], [ 33, 4, 6, 768 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 96 ], [ 35, 1, 10, 576 ], [ 35, 2, 10, 288 ], [ 36, 3, 25, 1152 ], [ 36, 5, 20, 288 ], [ 36, 6, 13, 576 ], [ 38, 2, 7, 576 ], [ 38, 3, 5, 1152 ], [ 39, 4, 15, 576 ], [ 39, 5, 15, 192 ], [ 40, 1, 2, 1152 ], [ 40, 2, 13, 576 ], [ 40, 3, 19, 576 ], [ 41, 4, 17, 1152 ], [ 41, 5, 13, 2304 ], [ 42, 2, 20, 768 ], [ 43, 5, 40, 2304 ] ] k = 51: F-action on Pi is () [44,5,51] Dynkin type is (A_0(q) + T(phi1^6 phi2)).2 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: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 7 modulo 12: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/1536 phi1 ( q^3-23*q^2+171*q-405 ) q congruent 11 modulo 12: 1/1536 ( q^4-24*q^3+194*q^2-624*q+693 ) Fusion of maximal tori of C^F in those of G^F: [ 32 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 15 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 48 ], [ 4, 2, 1, 24 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 11, 1, 1, 96 ], [ 15, 2, 3, 24 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 144 ], [ 17, 2, 1, 72 ], [ 17, 2, 3, 16 ], [ 18, 2, 2, 4 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 288 ], [ 25, 2, 5, 32 ], [ 25, 3, 5, 48 ], [ 25, 4, 5, 96 ], [ 26, 1, 1, 144 ], [ 27, 1, 1, 576 ], [ 27, 2, 1, 288 ], [ 27, 3, 1, 288 ], [ 27, 3, 5, 192 ], [ 28, 1, 1, 192 ], [ 28, 2, 1, 96 ], [ 30, 2, 2, 128 ], [ 31, 2, 2, 96 ], [ 32, 1, 1, 576 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 32 ], [ 35, 1, 1, 576 ], [ 35, 2, 1, 288 ], [ 36, 3, 4, 384 ], [ 36, 5, 4, 96 ], [ 36, 6, 5, 192 ], [ 38, 2, 2, 192 ], [ 38, 3, 2, 384 ], [ 39, 4, 7, 192 ], [ 39, 5, 2, 64 ], [ 39, 5, 7, 64 ], [ 40, 1, 1, 1152 ], [ 40, 2, 1, 576 ], [ 40, 3, 1, 576 ], [ 41, 4, 2, 384 ], [ 41, 4, 16, 384 ], [ 41, 5, 12, 768 ], [ 42, 2, 2, 256 ], [ 43, 5, 2, 768 ] ] k = 52: F-action on Pi is () [44,5,52] Dynkin type is (A_0(q) + T(phi1^4 phi2^3)).2 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: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 7 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 ) q congruent 11 modulo 12: 1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 ) Fusion of maximal tori of C^F in those of G^F: [ 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, 2, 1, 24 ], [ 4, 2, 3, 96 ], [ 5, 2, 2, 12 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 192 ], [ 11, 1, 1, 96 ], [ 12, 2, 2, 128 ], [ 14, 2, 2, 48 ], [ 15, 2, 4, 72 ], [ 15, 4, 5, 192 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 144 ], [ 17, 2, 1, 72 ], [ 17, 2, 2, 48 ], [ 18, 2, 3, 12 ], [ 20, 2, 4, 384 ], [ 21, 1, 1, 192 ], [ 22, 1, 1, 288 ], [ 23, 2, 3, 96 ], [ 25, 2, 6, 96 ], [ 25, 3, 8, 144 ], [ 25, 4, 7, 288 ], [ 26, 1, 1, 144 ], [ 27, 1, 1, 576 ], [ 27, 2, 1, 288 ], [ 27, 3, 1, 288 ], [ 27, 3, 14, 576 ], [ 28, 1, 1, 192 ], [ 28, 2, 1, 96 ], [ 30, 2, 3, 384 ], [ 31, 2, 5, 288 ], [ 32, 1, 1, 576 ], [ 33, 4, 10, 768 ], [ 34, 2, 10, 24 ], [ 34, 3, 8, 96 ], [ 35, 1, 1, 576 ], [ 35, 2, 1, 288 ], [ 36, 3, 6, 1152 ], [ 36, 5, 20, 288 ], [ 36, 6, 8, 576 ], [ 38, 2, 3, 576 ], [ 38, 3, 12, 1152 ], [ 39, 4, 12, 576 ], [ 39, 5, 5, 192 ], [ 40, 1, 1, 1152 ], [ 40, 2, 1, 576 ], [ 40, 3, 1, 576 ], [ 41, 4, 14, 1152 ], [ 41, 5, 30, 2304 ], [ 42, 2, 10, 768 ], [ 43, 5, 37, 2304 ] ] k = 53: F-action on Pi is () [44,5,53] Dynkin type is (A_0(q) + T(phi1^5 phi2^2)).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: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 7 modulo 12: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 11 modulo 12: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) Fusion of maximal tori of C^F in those of G^F: [ 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 8 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 4 ], [ 5, 2, 1, 4 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 16 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 16 ], [ 14, 2, 1, 16 ], [ 15, 2, 1, 24 ], [ 15, 2, 2, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 20 ], [ 17, 2, 3, 12 ], [ 17, 2, 4, 8 ], [ 18, 2, 1, 12 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 16 ], [ 23, 2, 1, 16 ], [ 23, 2, 2, 16 ], [ 25, 2, 1, 16 ], [ 25, 2, 3, 16 ], [ 25, 3, 1, 48 ], [ 25, 3, 3, 32 ], [ 25, 4, 1, 16 ], [ 25, 4, 2, 16 ], [ 25, 4, 3, 32 ], [ 25, 4, 4, 32 ], [ 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 64 ], [ 27, 3, 11, 16 ], [ 27, 3, 16, 32 ], [ 31, 2, 1, 48 ], [ 31, 2, 3, 48 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 32 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 16 ], [ 34, 3, 4, 16 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 3, 2, 64 ], [ 36, 3, 3, 64 ], [ 36, 3, 23, 64 ], [ 36, 5, 1, 96 ], [ 36, 5, 3, 64 ], [ 36, 6, 1, 32 ], [ 36, 6, 3, 64 ], [ 36, 6, 10, 64 ], [ 36, 6, 11, 32 ], [ 38, 2, 1, 96 ], [ 38, 2, 8, 96 ], [ 38, 3, 7, 64 ], [ 38, 3, 10, 64 ], [ 39, 4, 1, 32 ], [ 39, 4, 2, 64 ], [ 39, 4, 8, 32 ], [ 39, 4, 17, 64 ], [ 39, 5, 1, 32 ], [ 39, 5, 18, 32 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 4, 1, 64 ], [ 41, 4, 4, 128 ], [ 41, 4, 24, 64 ], [ 41, 4, 41, 128 ], [ 41, 5, 19, 128 ], [ 41, 5, 33, 128 ], [ 43, 5, 10, 128 ], [ 43, 5, 16, 128 ] ] k = 54: F-action on Pi is () [44,5,54] Dynkin type is (A_0(q) + T(phi1^4 phi2 phi4)).2 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: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) 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, 3 ], [ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 8 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 23, 2, 1, 8 ], [ 25, 2, 3, 8 ], [ 25, 2, 4, 8 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 8 ], [ 25, 4, 3, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 8 ], [ 27, 2, 3, 16 ], [ 27, 2, 7, 4 ], [ 27, 3, 2, 16 ], [ 31, 2, 1, 8 ], [ 31, 2, 6, 8 ], [ 32, 1, 8, 16 ], [ 34, 2, 4, 4 ], [ 34, 3, 1, 8 ], [ 34, 3, 7, 8 ], [ 35, 1, 7, 16 ], [ 35, 2, 7, 8 ], [ 36, 3, 13, 16 ], [ 36, 5, 2, 8 ], [ 36, 6, 2, 16 ], [ 36, 6, 3, 16 ], [ 38, 2, 10, 16 ], [ 39, 4, 1, 16 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 8 ], [ 39, 4, 18, 16 ], [ 39, 5, 17, 16 ], [ 40, 1, 23, 32 ], [ 40, 2, 17, 16 ], [ 40, 3, 16, 16 ], [ 41, 4, 21, 16 ], [ 41, 4, 44, 32 ], [ 41, 5, 16, 32 ], [ 41, 5, 32, 32 ], [ 43, 5, 20, 32 ] ] k = 55: F-action on Pi is () [44,5,55] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi4)).2 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: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( 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, 3 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 3, 4 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 23, 2, 2, 8 ], [ 25, 2, 1, 8 ], [ 25, 2, 2, 8 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 2, 8 ], [ 25, 4, 4, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 13, 32 ], [ 27, 2, 7, 4 ], [ 27, 2, 13, 16 ], [ 27, 3, 12, 16 ], [ 31, 2, 3, 8 ], [ 31, 2, 8, 8 ], [ 32, 1, 4, 16 ], [ 34, 2, 4, 4 ], [ 34, 3, 4, 8 ], [ 34, 3, 6, 8 ], [ 35, 1, 6, 16 ], [ 35, 2, 6, 8 ], [ 36, 3, 13, 16 ], [ 36, 5, 2, 8 ], [ 36, 6, 10, 16 ], [ 36, 6, 12, 16 ], [ 38, 2, 15, 16 ], [ 39, 4, 8, 16 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 8 ], [ 39, 4, 20, 16 ], [ 39, 5, 9, 16 ], [ 40, 1, 24, 32 ], [ 40, 2, 18, 16 ], [ 40, 3, 14, 16 ], [ 41, 4, 21, 16 ], [ 41, 4, 50, 32 ], [ 41, 5, 18, 32 ], [ 41, 5, 38, 32 ], [ 43, 5, 6, 32 ] ] k = 56: F-action on Pi is () [44,5,56] Dynkin type is (A_0(q) + T(phi1^4 phi2 phi4)).2 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: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) 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, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 6, 2, 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 ], [ 15, 2, 2, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 12 ], [ 25, 2, 1, 8 ], [ 25, 2, 3, 8 ], [ 25, 3, 3, 16 ], [ 25, 4, 3, 8 ], [ 25, 4, 4, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 8 ], [ 34, 3, 4, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 3, 13, 16 ], [ 36, 5, 3, 32 ], [ 36, 6, 3, 16 ], [ 36, 6, 10, 16 ], [ 39, 4, 16, 16 ], [ 39, 4, 17, 16 ], [ 39, 5, 1, 16 ], [ 39, 5, 18, 16 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 4, 40, 32 ], [ 41, 4, 41, 32 ], [ 41, 5, 18, 32 ], [ 41, 5, 32, 32 ] ] k = 57: F-action on Pi is () [44,5,57] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi4)).2 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: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) 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, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 2, 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 ], [ 15, 2, 4, 8 ], [ 15, 2, 5, 16 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 2, 2, 4 ], [ 25, 2, 5, 8 ], [ 25, 2, 7, 8 ], [ 25, 3, 7, 16 ], [ 25, 4, 7, 8 ], [ 25, 4, 8, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 8 ], [ 34, 3, 3, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 3, 16, 16 ], [ 36, 5, 6, 32 ], [ 36, 6, 7, 16 ], [ 36, 6, 14, 16 ], [ 39, 4, 13, 16 ], [ 39, 4, 14, 16 ], [ 39, 5, 7, 16 ], [ 39, 5, 12, 16 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 4, 35, 32 ], [ 41, 4, 36, 32 ], [ 41, 5, 6, 32 ], [ 41, 5, 29, 32 ] ] k = 58: F-action on Pi is () [44,5,58] Dynkin type is (A_0(q) + T(phi1 phi2^4 phi4)).2 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: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( 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, 3 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 8 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 23, 2, 4, 8 ], [ 25, 2, 5, 8 ], [ 25, 2, 6, 8 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 6, 8 ], [ 25, 4, 8, 8 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 13, 32 ], [ 27, 2, 7, 4 ], [ 27, 2, 13, 16 ], [ 27, 3, 12, 16 ], [ 31, 2, 4, 8 ], [ 31, 2, 7, 8 ], [ 32, 1, 4, 16 ], [ 34, 2, 3, 4 ], [ 34, 3, 3, 8 ], [ 34, 3, 5, 8 ], [ 35, 1, 6, 16 ], [ 35, 2, 6, 8 ], [ 36, 3, 16, 16 ], [ 36, 5, 5, 8 ], [ 36, 6, 14, 16 ], [ 36, 6, 16, 16 ], [ 38, 2, 16, 16 ], [ 39, 4, 4, 8 ], [ 39, 4, 5, 16 ], [ 39, 4, 14, 8 ], [ 39, 4, 15, 16 ], [ 39, 5, 3, 16 ], [ 40, 1, 24, 32 ], [ 40, 2, 18, 16 ], [ 40, 3, 14, 16 ], [ 41, 4, 8, 16 ], [ 41, 4, 31, 32 ], [ 41, 5, 6, 32 ], [ 41, 5, 23, 32 ], [ 43, 5, 30, 32 ] ] k = 59: F-action on Pi is () [44,5,59] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi4)).2 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: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( 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, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 2, 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 ], [ 15, 2, 1, 8 ], [ 15, 2, 8, 16 ], [ 17, 2, 1, 4 ], [ 17, 2, 4, 4 ], [ 18, 2, 4, 4 ], [ 25, 2, 2, 8 ], [ 25, 2, 4, 8 ], [ 25, 3, 2, 16 ], [ 25, 4, 1, 8 ], [ 25, 4, 2, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 8 ], [ 34, 3, 7, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 3, 13, 16 ], [ 36, 5, 15, 32 ], [ 36, 6, 2, 16 ], [ 36, 6, 12, 16 ], [ 39, 4, 9, 16 ], [ 39, 4, 10, 16 ], [ 39, 5, 8, 16 ], [ 39, 5, 20, 16 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 4, 47, 32 ], [ 41, 4, 48, 32 ], [ 41, 5, 16, 32 ], [ 41, 5, 38, 32 ] ] k = 60: F-action on Pi is () [44,5,60] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi4)).2 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: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/64 phi1 phi2 ( q^2-8*q+15 ) 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, 3 ], [ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 23, 2, 3, 8 ], [ 25, 2, 7, 8 ], [ 25, 2, 8, 8 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 8 ], [ 25, 4, 7, 8 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 8 ], [ 27, 2, 3, 16 ], [ 27, 2, 7, 4 ], [ 27, 3, 2, 16 ], [ 31, 2, 2, 8 ], [ 31, 2, 5, 8 ], [ 32, 1, 8, 16 ], [ 34, 2, 3, 4 ], [ 34, 3, 2, 8 ], [ 34, 3, 8, 8 ], [ 35, 1, 7, 16 ], [ 35, 2, 7, 8 ], [ 36, 3, 16, 16 ], [ 36, 5, 5, 8 ], [ 36, 6, 6, 16 ], [ 36, 6, 7, 16 ], [ 38, 2, 9, 16 ], [ 39, 4, 4, 8 ], [ 39, 4, 7, 16 ], [ 39, 4, 12, 16 ], [ 39, 4, 14, 8 ], [ 39, 5, 13, 16 ], [ 40, 1, 23, 32 ], [ 40, 2, 17, 16 ], [ 40, 3, 16, 16 ], [ 41, 4, 8, 16 ], [ 41, 4, 37, 32 ], [ 41, 5, 11, 32 ], [ 41, 5, 29, 32 ], [ 43, 5, 32, 32 ] ] k = 61: F-action on Pi is () [44,5,61] Dynkin type is (A_0(q) + T(phi1 phi2^4 phi4)).2 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: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( 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, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 6, 2, 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 ], [ 15, 2, 3, 8 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 4 ], [ 18, 2, 3, 12 ], [ 25, 2, 6, 8 ], [ 25, 2, 8, 8 ], [ 25, 3, 6, 16 ], [ 25, 4, 5, 8 ], [ 25, 4, 6, 8 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 8 ], [ 34, 3, 8, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 3, 16, 16 ], [ 36, 5, 19, 32 ], [ 36, 6, 6, 16 ], [ 36, 6, 16, 16 ], [ 39, 4, 3, 16 ], [ 39, 4, 4, 16 ], [ 39, 5, 5, 16 ], [ 39, 5, 15, 16 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 4, 27, 32 ], [ 41, 4, 30, 32 ], [ 41, 5, 11, 32 ], [ 41, 5, 23, 32 ] ] k = 62: F-action on Pi is () [44,5,62] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi4)).2 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: 1/32 phi1^2 phi2^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1^2 phi2^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^2 phi2^2 q congruent 7 modulo 12: 1/32 phi1^2 phi2^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^2 phi2^2 q congruent 11 modulo 12: 1/32 phi1^2 phi2^2 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 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 15, 2, 7, 8 ], [ 18, 2, 4, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 34, 2, 9, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 3, 21, 16 ], [ 36, 5, 14, 16 ], [ 39, 5, 6, 8 ], [ 39, 5, 11, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 4, 28, 16 ], [ 41, 4, 29, 16 ] ] k = 63: F-action on Pi is () [44,5,63] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi4)).2 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: 1/32 phi1^3 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1^3 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^3 phi2 q congruent 7 modulo 12: 1/32 phi1^3 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^3 phi2 q congruent 11 modulo 12: 1/32 phi1^3 phi2 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 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 23, 2, 1, 4 ], [ 23, 2, 2, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 3, 4 ], [ 31, 2, 6, 4 ], [ 31, 2, 8, 4 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ], [ 34, 2, 4, 4 ], [ 36, 5, 2, 8 ], [ 36, 5, 16, 16 ], [ 38, 2, 10, 8 ], [ 38, 2, 15, 8 ], [ 39, 4, 2, 8 ], [ 39, 4, 10, 8 ], [ 39, 4, 16, 8 ], [ 39, 4, 19, 8 ], [ 40, 1, 16, 16 ], [ 40, 2, 19, 8 ], [ 41, 4, 21, 16 ], [ 41, 4, 46, 16 ], [ 43, 5, 6, 16 ], [ 43, 5, 20, 16 ] ] k = 64: F-action on Pi is () [44,5,64] Dynkin type is (A_0(q) + T(phi1^2 phi2^3 phi4)).2 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: 1/32 phi1^3 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1^3 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^3 phi2 q congruent 7 modulo 12: 1/32 phi1^3 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^3 phi2 q congruent 11 modulo 12: 1/32 phi1^3 phi2 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 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 23, 2, 3, 4 ], [ 23, 2, 4, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 4, 4 ], [ 31, 2, 5, 4 ], [ 31, 2, 7, 4 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ], [ 34, 2, 3, 4 ], [ 36, 5, 5, 8 ], [ 36, 5, 8, 16 ], [ 38, 2, 9, 8 ], [ 38, 2, 16, 8 ], [ 39, 4, 4, 8 ], [ 39, 4, 6, 8 ], [ 39, 4, 11, 8 ], [ 39, 4, 14, 8 ], [ 40, 1, 16, 16 ], [ 40, 2, 19, 8 ], [ 41, 4, 8, 16 ], [ 41, 4, 34, 16 ], [ 43, 5, 30, 16 ], [ 43, 5, 32, 16 ] ] k = 65: F-action on Pi is () [44,5,65] Dynkin type is (A_0(q) + T(phi1^3 phi2^2 phi4)).2 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: 1/32 phi1^2 phi2^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1^2 phi2^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^2 phi2^2 q congruent 7 modulo 12: 1/32 phi1^2 phi2^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^2 phi2^2 q congruent 11 modulo 12: 1/32 phi1^2 phi2^2 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 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 10, 1, 3, 4 ], [ 10, 1, 4, 4 ], [ 15, 2, 6, 8 ], [ 18, 2, 2, 4 ], [ 26, 1, 4, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 7, 8 ], [ 27, 2, 2, 4 ], [ 27, 2, 7, 4 ], [ 34, 2, 2, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 2, 6, 4 ], [ 35, 2, 7, 4 ], [ 36, 3, 19, 16 ], [ 36, 5, 13, 16 ], [ 39, 5, 2, 8 ], [ 39, 5, 19, 8 ], [ 40, 1, 21, 16 ], [ 40, 2, 20, 8 ], [ 40, 3, 11, 8 ], [ 40, 3, 15, 8 ], [ 41, 4, 39, 16 ], [ 41, 4, 42, 16 ] ] k = 66: F-action on Pi is () [44,5,66] Dynkin type is (A_0(q) + T(phi1^2 phi2^5)).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: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 7 modulo 12: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/256 phi1 ( q^3-11*q^2+43*q-65 ) q congruent 11 modulo 12: 1/256 ( q^4-12*q^3+54*q^2-108*q+81 ) Fusion of maximal tori of C^F in those of G^F: [ 34 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 8 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 4 ], [ 5, 2, 2, 4 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 16 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 16 ], [ 14, 2, 2, 16 ], [ 15, 2, 3, 16 ], [ 15, 2, 4, 24 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 20 ], [ 18, 2, 3, 12 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 16 ], [ 23, 2, 3, 16 ], [ 23, 2, 4, 16 ], [ 25, 2, 6, 16 ], [ 25, 2, 8, 16 ], [ 25, 3, 6, 32 ], [ 25, 3, 8, 48 ], [ 25, 4, 5, 32 ], [ 25, 4, 6, 32 ], [ 25, 4, 7, 16 ], [ 25, 4, 8, 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 64 ], [ 27, 3, 8, 32 ], [ 27, 3, 9, 32 ], [ 27, 3, 11, 16 ], [ 31, 2, 5, 48 ], [ 31, 2, 7, 48 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 32 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 16 ], [ 34, 3, 8, 16 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 3, 4, 64 ], [ 36, 3, 5, 64 ], [ 36, 3, 26, 64 ], [ 36, 5, 19, 64 ], [ 36, 5, 20, 96 ], [ 36, 6, 6, 64 ], [ 36, 6, 8, 32 ], [ 36, 6, 13, 32 ], [ 36, 6, 16, 64 ], [ 38, 2, 3, 96 ], [ 38, 2, 7, 96 ], [ 38, 3, 3, 64 ], [ 38, 3, 14, 64 ], [ 39, 4, 3, 64 ], [ 39, 4, 11, 64 ], [ 39, 4, 12, 32 ], [ 39, 4, 15, 32 ], [ 39, 5, 5, 32 ], [ 39, 5, 15, 32 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 4, 13, 128 ], [ 41, 4, 14, 64 ], [ 41, 4, 17, 64 ], [ 41, 4, 27, 128 ], [ 41, 5, 10, 128 ], [ 41, 5, 21, 128 ], [ 43, 5, 38, 128 ], [ 43, 5, 39, 128 ] ] k = 67: F-action on Pi is () [44,5,67] Dynkin type is (A_0(q) + T(phi1^4 phi2^3)).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: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 7 modulo 12: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 11 modulo 12: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) 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, 7 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 8 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 20 ], [ 4, 2, 3, 16 ], [ 5, 2, 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 ], [ 15, 2, 3, 8 ], [ 15, 2, 4, 16 ], [ 15, 2, 5, 32 ], [ 15, 4, 4, 32 ], [ 15, 4, 5, 32 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 20 ], [ 18, 2, 2, 4 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 16 ], [ 25, 2, 5, 16 ], [ 25, 2, 7, 16 ], [ 25, 3, 5, 16 ], [ 25, 3, 7, 32 ], [ 25, 4, 5, 16 ], [ 25, 4, 6, 16 ], [ 25, 4, 7, 32 ], [ 25, 4, 8, 32 ], [ 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 2, 64 ], [ 27, 3, 3, 64 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 32 ], [ 27, 3, 11, 48 ], [ 27, 3, 14, 32 ], [ 31, 2, 2, 16 ], [ 31, 2, 4, 16 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 32 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 16 ], [ 34, 3, 3, 16 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 3, 5, 64 ], [ 36, 3, 6, 64 ], [ 36, 3, 7, 128 ], [ 36, 3, 25, 64 ], [ 36, 5, 4, 32 ], [ 36, 5, 6, 64 ], [ 36, 6, 5, 32 ], [ 36, 6, 7, 64 ], [ 36, 6, 14, 64 ], [ 36, 6, 15, 32 ], [ 38, 2, 2, 32 ], [ 38, 2, 5, 32 ], [ 38, 3, 8, 64 ], [ 38, 3, 9, 64 ], [ 39, 4, 5, 32 ], [ 39, 4, 7, 32 ], [ 39, 4, 13, 64 ], [ 39, 5, 7, 32 ], [ 39, 5, 12, 32 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 4, 3, 64 ], [ 41, 4, 9, 64 ], [ 41, 4, 16, 64 ], [ 41, 4, 35, 128 ], [ 41, 5, 4, 128 ], [ 41, 5, 28, 128 ], [ 43, 5, 8, 128 ], [ 43, 5, 23, 128 ] ] k = 68: F-action on Pi is () [44,5,68] Dynkin type is (A_0(q) + T(phi1^3 phi2^4)).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: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 7 modulo 12: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/256 phi1 ( q^3-11*q^2+27*q+15 ) q congruent 11 modulo 12: 1/256 phi2 ( q^3-13*q^2+51*q-63 ) 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, 7 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 8 ], [ 4, 2, 1, 20 ], [ 4, 2, 2, 4 ], [ 4, 2, 4, 16 ], [ 5, 2, 1, 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 ], [ 15, 2, 1, 16 ], [ 15, 2, 2, 8 ], [ 15, 2, 8, 32 ], [ 15, 4, 1, 32 ], [ 15, 4, 8, 32 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 20 ], [ 17, 2, 3, 12 ], [ 17, 2, 4, 8 ], [ 18, 2, 4, 4 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 16 ], [ 25, 2, 2, 16 ], [ 25, 2, 4, 16 ], [ 25, 3, 2, 32 ], [ 25, 3, 4, 16 ], [ 25, 4, 1, 32 ], [ 25, 4, 2, 32 ], [ 25, 4, 3, 16 ], [ 25, 4, 4, 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 48 ], [ 27, 3, 4, 32 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 32 ], [ 27, 3, 11, 16 ], [ 27, 3, 12, 64 ], [ 27, 3, 13, 64 ], [ 31, 2, 6, 16 ], [ 31, 2, 8, 16 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 32 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 16 ], [ 34, 3, 7, 16 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 3, 1, 64 ], [ 36, 3, 2, 64 ], [ 36, 3, 12, 128 ], [ 36, 3, 24, 64 ], [ 36, 5, 15, 64 ], [ 36, 5, 18, 32 ], [ 36, 6, 2, 64 ], [ 36, 6, 4, 32 ], [ 36, 6, 9, 32 ], [ 36, 6, 12, 64 ], [ 38, 2, 4, 32 ], [ 38, 2, 6, 32 ], [ 38, 3, 4, 64 ], [ 38, 3, 13, 64 ], [ 39, 4, 9, 64 ], [ 39, 4, 18, 32 ], [ 39, 4, 20, 32 ], [ 39, 5, 8, 32 ], [ 39, 5, 20, 32 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 4, 12, 64 ], [ 41, 4, 22, 64 ], [ 41, 4, 26, 64 ], [ 41, 4, 47, 128 ], [ 41, 5, 14, 128 ], [ 41, 5, 39, 128 ], [ 43, 5, 12, 128 ], [ 43, 5, 24, 128 ] ] k = 69: F-action on Pi is () [44,5,69] Dynkin type is (A_0(q) + T(phi1^3 phi4^2)).2 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: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) 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, 8 ], [ 4, 2, 2, 12 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 15, 4, 2, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 8 ], [ 27, 2, 3, 16 ], [ 27, 2, 7, 4 ], [ 27, 3, 2, 32 ], [ 27, 3, 15, 16 ], [ 32, 1, 8, 16 ], [ 34, 2, 8, 4 ], [ 35, 1, 7, 16 ], [ 35, 2, 7, 8 ], [ 36, 3, 27, 32 ], [ 36, 5, 17, 8 ], [ 38, 2, 13, 16 ], [ 39, 5, 16, 16 ], [ 40, 1, 23, 32 ], [ 40, 2, 17, 16 ], [ 40, 3, 16, 16 ], [ 41, 4, 20, 16 ], [ 41, 4, 43, 32 ], [ 43, 5, 21, 32 ] ] k = 70: F-action on Pi is () [44,5,70] Dynkin type is (A_0(q) + T(phi1 phi2^2 phi4^2)).2 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: 1/64 phi1^2 phi2^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2^2 q congruent 7 modulo 12: 1/64 phi1^2 phi2^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2^2 q congruent 11 modulo 12: 1/64 phi1^2 phi2^2 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, 2, 1, 4 ], [ 4, 2, 3, 8 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 15, 4, 7, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 13, 32 ], [ 27, 2, 7, 4 ], [ 27, 2, 13, 16 ], [ 27, 3, 3, 16 ], [ 27, 3, 10, 16 ], [ 27, 3, 12, 16 ], [ 32, 1, 4, 16 ], [ 34, 2, 8, 4 ], [ 35, 1, 6, 16 ], [ 35, 2, 6, 8 ], [ 36, 3, 20, 32 ], [ 36, 5, 17, 8 ], [ 38, 2, 11, 16 ], [ 39, 5, 10, 16 ], [ 40, 1, 24, 32 ], [ 40, 2, 18, 16 ], [ 40, 3, 14, 16 ], [ 41, 4, 20, 16 ], [ 41, 4, 49, 32 ], [ 43, 5, 7, 32 ] ] k = 71: F-action on Pi is () [44,5,71] Dynkin type is (A_0(q) + T(phi2^3 phi4^2)).2 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: 1/64 phi1^2 phi2^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2^2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2^2 q congruent 7 modulo 12: 1/64 phi1^2 phi2^2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2^2 q congruent 11 modulo 12: 1/64 phi1^2 phi2^2 Fusion of maximal tori of C^F in those of G^F: [ 39 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 4, 1, 1, 8 ], [ 4, 2, 1, 12 ], [ 7, 1, 2, 4 ], [ 10, 1, 2, 16 ], [ 15, 4, 3, 16 ], [ 16, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 17, 2, 3, 4 ], [ 26, 1, 3, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 13, 32 ], [ 27, 2, 7, 4 ], [ 27, 2, 13, 16 ], [ 27, 3, 7, 16 ], [ 27, 3, 12, 32 ], [ 32, 1, 4, 16 ], [ 34, 2, 5, 4 ], [ 35, 1, 6, 16 ], [ 35, 2, 6, 8 ], [ 36, 3, 22, 32 ], [ 36, 5, 10, 8 ], [ 38, 2, 12, 16 ], [ 39, 5, 4, 16 ], [ 40, 1, 24, 32 ], [ 40, 2, 18, 16 ], [ 40, 3, 14, 16 ], [ 41, 4, 7, 16 ], [ 41, 4, 32, 32 ], [ 43, 5, 29, 32 ] ] k = 72: F-action on Pi is () [44,5,72] Dynkin type is (A_0(q) + T(phi1^2 phi2 phi4^2)).2 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: 1/64 phi1^2 phi2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 7 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) q congruent 11 modulo 12: 1/64 phi1^2 phi2 ( q-3 ) 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, 2, 2, 4 ], [ 4, 2, 4, 8 ], [ 7, 1, 1, 4 ], [ 10, 1, 3, 16 ], [ 15, 4, 6, 16 ], [ 16, 1, 1, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ], [ 26, 1, 1, 8 ], [ 26, 1, 5, 4 ], [ 27, 1, 3, 32 ], [ 27, 1, 7, 8 ], [ 27, 2, 3, 16 ], [ 27, 2, 7, 4 ], [ 27, 3, 2, 16 ], [ 27, 3, 6, 16 ], [ 27, 3, 13, 16 ], [ 32, 1, 8, 16 ], [ 34, 2, 5, 4 ], [ 35, 1, 7, 16 ], [ 35, 2, 7, 8 ], [ 36, 3, 28, 32 ], [ 36, 5, 10, 8 ], [ 38, 2, 14, 16 ], [ 39, 5, 14, 16 ], [ 40, 1, 23, 32 ], [ 40, 2, 17, 16 ], [ 40, 3, 16, 16 ], [ 41, 4, 7, 16 ], [ 41, 4, 38, 32 ], [ 43, 5, 31, 32 ] ] k = 73: F-action on Pi is () [44,5,73] Dynkin type is (A_0(q) + T(phi1 phi2^2 phi4^2)).2 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: 1/32 phi1 phi2^2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 7 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 11 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) 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, 2, 1, 4 ], [ 4, 2, 4, 4 ], [ 5, 2, 1, 4 ], [ 15, 2, 7, 8 ], [ 15, 2, 8, 8 ], [ 15, 4, 1, 8 ], [ 15, 4, 8, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 6, 16 ], [ 27, 3, 7, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 12, 8 ], [ 27, 3, 13, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ], [ 34, 2, 5, 4 ], [ 36, 3, 10, 16 ], [ 36, 3, 11, 16 ], [ 36, 3, 12, 16 ], [ 36, 5, 10, 8 ], [ 36, 5, 11, 16 ], [ 38, 2, 12, 8 ], [ 38, 2, 14, 8 ], [ 40, 1, 16, 16 ], [ 40, 2, 19, 8 ], [ 41, 4, 7, 16 ], [ 41, 4, 33, 16 ], [ 43, 5, 29, 16 ], [ 43, 5, 31, 16 ] ] k = 74: F-action on Pi is () [44,5,74] Dynkin type is (A_0(q) + T(phi1^2 phi2 phi4^2)).2 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: 1/32 phi1 phi2^2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 7 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) q congruent 11 modulo 12: 1/32 phi1 phi2^2 ( q-3 ) 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, 2, 2, 4 ], [ 4, 2, 3, 4 ], [ 5, 2, 2, 4 ], [ 15, 2, 5, 8 ], [ 15, 2, 6, 8 ], [ 15, 4, 4, 8 ], [ 15, 4, 5, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 3, 2 ], [ 26, 1, 2, 4 ], [ 26, 1, 5, 4 ], [ 27, 1, 7, 8 ], [ 27, 1, 9, 16 ], [ 27, 2, 7, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 2, 8 ], [ 27, 3, 3, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 10, 16 ], [ 27, 3, 15, 8 ], [ 32, 1, 4, 8 ], [ 32, 1, 8, 8 ], [ 34, 2, 8, 4 ], [ 36, 3, 7, 16 ], [ 36, 3, 8, 16 ], [ 36, 3, 9, 16 ], [ 36, 5, 12, 16 ], [ 36, 5, 17, 8 ], [ 38, 2, 11, 8 ], [ 38, 2, 13, 8 ], [ 40, 1, 16, 16 ], [ 40, 2, 19, 8 ], [ 41, 4, 20, 16 ], [ 41, 4, 45, 16 ], [ 43, 5, 7, 16 ], [ 43, 5, 21, 16 ] ] k = 75: F-action on Pi is () [44,5,75] Dynkin type is (A_0(q) + T(phi1^3 phi2^4)).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: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 7 modulo 12: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 11 modulo 12: 1/128 phi2^2 ( q^2-6*q+9 ) 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 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 8 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 16 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 16 ], [ 15, 2, 2, 8 ], [ 15, 2, 7, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 12 ], [ 18, 2, 4, 4 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 16 ], [ 25, 3, 4, 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 32 ], [ 27, 3, 6, 32 ], [ 27, 3, 7, 32 ], [ 27, 3, 9, 32 ], [ 27, 3, 11, 16 ], [ 31, 2, 6, 16 ], [ 31, 2, 8, 16 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 32 ], [ 34, 2, 9, 8 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 3, 10, 64 ], [ 36, 5, 14, 32 ], [ 36, 5, 18, 32 ], [ 38, 2, 4, 32 ], [ 38, 2, 6, 32 ], [ 39, 4, 19, 32 ], [ 39, 5, 6, 16 ], [ 39, 5, 11, 16 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 4, 10, 32 ], [ 41, 4, 12, 32 ], [ 41, 4, 15, 32 ], [ 41, 4, 23, 64 ], [ 41, 4, 28, 64 ], [ 43, 5, 9, 64 ], [ 43, 5, 22, 64 ] ] k = 76: F-action on Pi is () [44,5,76] Dynkin type is (A_0(q) + T(phi1^2 phi2^5)).2 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: 1/128 phi1^2 phi2 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/128 phi1^2 phi2 ( q-5 ) q congruent 7 modulo 12: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/128 phi1^2 phi2 ( q-5 ) q congruent 11 modulo 12: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) 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, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 24 ], [ 4, 2, 1, 8 ], [ 4, 2, 2, 12 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 15, 2, 2, 8 ], [ 15, 4, 3, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 14 ], [ 17, 2, 3, 18 ], [ 18, 2, 4, 4 ], [ 21, 1, 6, 48 ], [ 22, 1, 3, 24 ], [ 22, 1, 4, 24 ], [ 25, 2, 4, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 4, 16 ], [ 26, 1, 2, 12 ], [ 26, 1, 3, 24 ], [ 27, 1, 8, 48 ], [ 27, 1, 12, 96 ], [ 27, 2, 8, 24 ], [ 27, 2, 12, 48 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 24 ], [ 27, 3, 7, 32 ], [ 27, 3, 9, 40 ], [ 27, 3, 11, 48 ], [ 27, 3, 12, 32 ], [ 28, 1, 2, 16 ], [ 28, 2, 2, 8 ], [ 30, 2, 6, 32 ], [ 31, 2, 6, 8 ], [ 31, 2, 8, 24 ], [ 32, 1, 3, 48 ], [ 32, 1, 7, 48 ], [ 34, 2, 9, 8 ], [ 34, 3, 6, 16 ], [ 35, 1, 4, 48 ], [ 35, 2, 4, 24 ], [ 36, 3, 14, 32 ], [ 36, 3, 22, 64 ], [ 36, 5, 18, 32 ], [ 36, 6, 9, 32 ], [ 38, 2, 4, 16 ], [ 38, 2, 6, 48 ], [ 38, 3, 4, 32 ], [ 38, 3, 6, 32 ], [ 39, 4, 19, 16 ], [ 39, 4, 20, 32 ], [ 39, 5, 11, 32 ], [ 39, 5, 20, 32 ], [ 40, 1, 18, 96 ], [ 40, 2, 23, 48 ], [ 40, 3, 3, 48 ], [ 41, 4, 10, 64 ], [ 41, 4, 12, 32 ], [ 41, 4, 23, 32 ], [ 41, 4, 26, 64 ], [ 41, 5, 15, 64 ], [ 42, 2, 11, 64 ], [ 43, 5, 9, 64 ], [ 43, 5, 17, 64 ], [ 43, 5, 24, 64 ] ] k = 77: F-action on Pi is () [44,5,77] Dynkin type is (A_0(q) + T(phi1^6 phi2)).2 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: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 7 modulo 12: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 11 modulo 12: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) Fusion of maximal tori of C^F in those of G^F: [ 32 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 4, 2, 1, 20 ], [ 5, 2, 1, 4 ], [ 6, 2, 1, 4 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 12, 2, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 2, 1, 24 ], [ 15, 4, 3, 16 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 42 ], [ 17, 2, 3, 6 ], [ 18, 2, 1, 12 ], [ 20, 2, 1, 32 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 24 ], [ 23, 2, 1, 24 ], [ 23, 2, 2, 8 ], [ 25, 2, 1, 48 ], [ 25, 3, 1, 48 ], [ 25, 4, 1, 48 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 48 ], [ 27, 2, 1, 48 ], [ 27, 2, 8, 24 ], [ 27, 3, 1, 96 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 72 ], [ 28, 1, 3, 16 ], [ 28, 2, 4, 8 ], [ 30, 2, 1, 96 ], [ 31, 2, 1, 72 ], [ 31, 2, 3, 24 ], [ 32, 1, 1, 48 ], [ 32, 1, 6, 48 ], [ 33, 4, 3, 64 ], [ 34, 2, 1, 24 ], [ 34, 3, 1, 48 ], [ 35, 1, 2, 48 ], [ 35, 2, 2, 24 ], [ 36, 3, 14, 96 ], [ 36, 5, 1, 96 ], [ 36, 6, 1, 96 ], [ 38, 2, 1, 144 ], [ 38, 2, 8, 48 ], [ 38, 3, 1, 96 ], [ 38, 3, 7, 96 ], [ 39, 4, 1, 96 ], [ 39, 4, 2, 48 ], [ 39, 5, 1, 96 ], [ 40, 1, 17, 96 ], [ 40, 2, 22, 48 ], [ 40, 3, 4, 48 ], [ 41, 4, 1, 192 ], [ 41, 4, 4, 96 ], [ 41, 5, 2, 192 ], [ 42, 2, 1, 192 ], [ 43, 5, 1, 192 ], [ 43, 5, 16, 192 ] ] k = 78: F-action on Pi is () [44,5,78] Dynkin type is (A_0(q) + T(phi1^4 phi2^3)).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: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 7 modulo 12: 1/128 phi2^2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/128 phi1^2 ( q^2-2*q-7 ) q congruent 11 modulo 12: 1/128 phi2^2 ( q^2-6*q+9 ) 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 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 8 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 10, 1, 1, 16 ], [ 10, 1, 2, 16 ], [ 10, 1, 3, 16 ], [ 10, 1, 4, 16 ], [ 15, 2, 3, 8 ], [ 15, 2, 6, 16 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 17, 1, 1, 24 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 3, 12 ], [ 18, 2, 2, 4 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 16 ], [ 25, 3, 5, 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 ], [ 27, 2, 1, 16 ], [ 27, 2, 2, 16 ], [ 27, 2, 8, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 1, 16 ], [ 27, 3, 5, 32 ], [ 27, 3, 9, 32 ], [ 27, 3, 10, 32 ], [ 27, 3, 11, 16 ], [ 27, 3, 15, 32 ], [ 31, 2, 2, 16 ], [ 31, 2, 4, 16 ], [ 32, 1, 3, 32 ], [ 32, 1, 6, 32 ], [ 34, 2, 2, 8 ], [ 35, 1, 3, 32 ], [ 35, 1, 5, 32 ], [ 35, 2, 3, 16 ], [ 35, 2, 5, 16 ], [ 36, 3, 9, 64 ], [ 36, 5, 4, 32 ], [ 36, 5, 13, 32 ], [ 38, 2, 2, 32 ], [ 38, 2, 5, 32 ], [ 39, 4, 6, 32 ], [ 39, 5, 2, 16 ], [ 39, 5, 19, 16 ], [ 40, 1, 3, 64 ], [ 40, 2, 16, 32 ], [ 40, 3, 2, 32 ], [ 40, 3, 17, 32 ], [ 41, 4, 2, 32 ], [ 41, 4, 3, 32 ], [ 41, 4, 11, 64 ], [ 41, 4, 25, 32 ], [ 41, 4, 42, 64 ], [ 43, 5, 11, 64 ], [ 43, 5, 13, 64 ] ] k = 79: F-action on Pi is () [44,5,79] Dynkin type is (A_0(q) + T(phi1^4 phi2^3)).2 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: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 7 modulo 12: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 11 modulo 12: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) Fusion of maximal tori of C^F in those of G^F: [ 35 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 24 ], [ 4, 2, 2, 12 ], [ 4, 2, 4, 8 ], [ 5, 2, 1, 4 ], [ 6, 2, 1, 4 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 12, 2, 4, 32 ], [ 14, 2, 1, 16 ], [ 15, 2, 1, 24 ], [ 15, 4, 6, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 18 ], [ 17, 2, 4, 24 ], [ 18, 2, 1, 12 ], [ 20, 2, 3, 32 ], [ 21, 1, 6, 48 ], [ 22, 1, 3, 24 ], [ 22, 1, 4, 24 ], [ 23, 2, 1, 8 ], [ 23, 2, 2, 24 ], [ 25, 2, 3, 48 ], [ 25, 3, 1, 48 ], [ 25, 4, 2, 48 ], [ 26, 1, 2, 12 ], [ 26, 1, 3, 24 ], [ 27, 1, 8, 48 ], [ 27, 1, 12, 96 ], [ 27, 2, 8, 24 ], [ 27, 2, 12, 48 ], [ 27, 3, 4, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 24 ], [ 27, 3, 11, 48 ], [ 27, 3, 16, 48 ], [ 28, 1, 2, 16 ], [ 28, 2, 2, 8 ], [ 30, 2, 7, 96 ], [ 31, 2, 1, 24 ], [ 31, 2, 3, 72 ], [ 32, 1, 3, 48 ], [ 32, 1, 7, 48 ], [ 33, 4, 7, 64 ], [ 34, 2, 1, 24 ], [ 34, 3, 4, 48 ], [ 35, 1, 4, 48 ], [ 35, 2, 4, 24 ], [ 36, 3, 15, 96 ], [ 36, 5, 1, 96 ], [ 36, 6, 11, 96 ], [ 38, 2, 1, 48 ], [ 38, 2, 8, 144 ], [ 38, 3, 10, 96 ], [ 38, 3, 16, 96 ], [ 39, 4, 2, 48 ], [ 39, 4, 8, 96 ], [ 39, 5, 18, 96 ], [ 40, 1, 18, 96 ], [ 40, 2, 23, 48 ], [ 40, 3, 3, 48 ], [ 41, 4, 4, 96 ], [ 41, 4, 24, 192 ], [ 41, 5, 34, 192 ], [ 42, 2, 15, 192 ], [ 43, 5, 10, 192 ], [ 43, 5, 19, 192 ] ] k = 80: F-action on Pi is () [44,5,80] Dynkin type is (A_0(q) + T(phi1^5 phi2^2)).2 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: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 11 modulo 12: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) 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, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 24 ], [ 4, 2, 1, 12 ], [ 4, 2, 2, 8 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 15, 2, 3, 8 ], [ 15, 4, 2, 16 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 14 ], [ 18, 2, 2, 4 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 24 ], [ 25, 2, 5, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 5, 16 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 48 ], [ 27, 2, 1, 48 ], [ 27, 2, 8, 24 ], [ 27, 3, 1, 48 ], [ 27, 3, 2, 32 ], [ 27, 3, 5, 40 ], [ 27, 3, 9, 24 ], [ 27, 3, 11, 16 ], [ 27, 3, 15, 32 ], [ 28, 1, 3, 16 ], [ 28, 2, 4, 8 ], [ 30, 2, 2, 32 ], [ 31, 2, 2, 24 ], [ 31, 2, 4, 8 ], [ 32, 1, 1, 48 ], [ 32, 1, 6, 48 ], [ 34, 2, 2, 8 ], [ 34, 3, 2, 16 ], [ 35, 1, 2, 48 ], [ 35, 2, 2, 24 ], [ 36, 3, 17, 32 ], [ 36, 3, 27, 64 ], [ 36, 5, 4, 32 ], [ 36, 6, 5, 32 ], [ 38, 2, 2, 48 ], [ 38, 2, 5, 16 ], [ 38, 3, 2, 32 ], [ 38, 3, 8, 32 ], [ 39, 4, 6, 16 ], [ 39, 4, 7, 32 ], [ 39, 5, 2, 32 ], [ 39, 5, 7, 32 ], [ 40, 1, 17, 96 ], [ 40, 2, 22, 48 ], [ 40, 3, 4, 48 ], [ 41, 4, 2, 64 ], [ 41, 4, 3, 32 ], [ 41, 4, 11, 32 ], [ 41, 4, 16, 64 ], [ 41, 5, 5, 64 ], [ 42, 2, 2, 64 ], [ 43, 5, 2, 64 ], [ 43, 5, 13, 64 ], [ 43, 5, 23, 64 ] ] k = 81: F-action on Pi is () [44,5,81] Dynkin type is (A_0(q) + T(phi1 phi2^6)).2 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: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 7 modulo 12: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/384 phi1 ( q^3-13*q^2+55*q-75 ) q congruent 11 modulo 12: 1/384 ( q^4-14*q^3+68*q^2-154*q+147 ) Fusion of maximal tori of C^F in those of G^F: [ 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 24 ], [ 4, 2, 2, 20 ], [ 5, 2, 2, 4 ], [ 6, 2, 2, 4 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 12, 2, 3, 32 ], [ 14, 2, 2, 16 ], [ 15, 2, 4, 24 ], [ 15, 4, 2, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 42 ], [ 18, 2, 3, 12 ], [ 20, 2, 2, 32 ], [ 21, 1, 6, 48 ], [ 22, 1, 3, 24 ], [ 22, 1, 4, 24 ], [ 23, 2, 3, 8 ], [ 23, 2, 4, 24 ], [ 25, 2, 8, 48 ], [ 25, 3, 8, 48 ], [ 25, 4, 8, 48 ], [ 26, 1, 2, 12 ], [ 26, 1, 3, 24 ], [ 27, 1, 8, 48 ], [ 27, 1, 12, 96 ], [ 27, 2, 8, 24 ], [ 27, 2, 12, 48 ], [ 27, 3, 5, 72 ], [ 27, 3, 9, 24 ], [ 27, 3, 11, 96 ], [ 28, 1, 2, 16 ], [ 28, 2, 2, 8 ], [ 30, 2, 5, 96 ], [ 31, 2, 5, 24 ], [ 31, 2, 7, 72 ], [ 32, 1, 3, 48 ], [ 32, 1, 7, 48 ], [ 33, 4, 4, 64 ], [ 34, 2, 10, 24 ], [ 34, 3, 5, 48 ], [ 35, 1, 4, 48 ], [ 35, 2, 4, 24 ], [ 36, 3, 17, 96 ], [ 36, 5, 20, 96 ], [ 36, 6, 13, 96 ], [ 38, 2, 3, 48 ], [ 38, 2, 7, 144 ], [ 38, 3, 3, 96 ], [ 38, 3, 5, 96 ], [ 39, 4, 11, 48 ], [ 39, 4, 15, 96 ], [ 39, 5, 15, 96 ], [ 40, 1, 18, 96 ], [ 40, 2, 23, 48 ], [ 40, 3, 3, 48 ], [ 41, 4, 13, 96 ], [ 41, 4, 17, 192 ], [ 41, 5, 8, 192 ], [ 42, 2, 20, 192 ], [ 43, 5, 38, 192 ], [ 43, 5, 40, 192 ] ] k = 82: F-action on Pi is () [44,5,82] Dynkin type is (A_0(q) + T(phi1^4 phi2^3)).2 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: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/128 phi1 phi2 ( q^2-10*q+25 ) q congruent 11 modulo 12: 1/128 phi2 ( q^3-11*q^2+35*q-33 ) 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, 8 ], [ 4, 1, 1, 24 ], [ 4, 2, 1, 12 ], [ 4, 2, 4, 8 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 15, 2, 2, 8 ], [ 15, 4, 6, 16 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 18 ], [ 17, 2, 3, 6 ], [ 17, 2, 4, 8 ], [ 18, 2, 4, 4 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 24 ], [ 25, 2, 2, 16 ], [ 25, 3, 4, 16 ], [ 25, 4, 3, 16 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 48 ], [ 27, 2, 1, 48 ], [ 27, 2, 8, 24 ], [ 27, 3, 1, 48 ], [ 27, 3, 4, 16 ], [ 27, 3, 5, 24 ], [ 27, 3, 6, 32 ], [ 27, 3, 9, 24 ], [ 27, 3, 13, 32 ], [ 27, 3, 16, 16 ], [ 28, 1, 3, 16 ], [ 28, 2, 4, 8 ], [ 30, 2, 4, 32 ], [ 31, 2, 6, 24 ], [ 31, 2, 8, 8 ], [ 32, 1, 1, 48 ], [ 32, 1, 6, 48 ], [ 34, 2, 9, 8 ], [ 34, 3, 7, 16 ], [ 35, 1, 2, 48 ], [ 35, 2, 2, 24 ], [ 36, 3, 15, 32 ], [ 36, 3, 28, 64 ], [ 36, 5, 18, 32 ], [ 36, 6, 4, 32 ], [ 38, 2, 4, 48 ], [ 38, 2, 6, 16 ], [ 38, 3, 11, 32 ], [ 38, 3, 13, 32 ], [ 39, 4, 18, 32 ], [ 39, 4, 19, 16 ], [ 39, 5, 6, 32 ], [ 39, 5, 8, 32 ], [ 40, 1, 17, 96 ], [ 40, 2, 22, 48 ], [ 40, 3, 4, 48 ], [ 41, 4, 12, 32 ], [ 41, 4, 15, 64 ], [ 41, 4, 22, 64 ], [ 41, 4, 23, 32 ], [ 41, 5, 36, 64 ], [ 42, 2, 5, 64 ], [ 43, 5, 5, 64 ], [ 43, 5, 12, 64 ], [ 43, 5, 22, 64 ] ] k = 83: F-action on Pi is () [44,5,83] Dynkin type is (A_0(q) + T(phi1^3 phi2^4)).2 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: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 7 modulo 12: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/384 phi1 ( q^3-17*q^2+87*q-135 ) q congruent 11 modulo 12: 1/384 ( q^4-18*q^3+104*q^2-198*q+63 ) Fusion of maximal tori of C^F in those of G^F: [ 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, 2, 1, 12 ], [ 4, 2, 3, 8 ], [ 5, 2, 2, 4 ], [ 6, 2, 2, 4 ], [ 7, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 48 ], [ 11, 1, 1, 8 ], [ 12, 2, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 2, 4, 24 ], [ 15, 4, 7, 16 ], [ 16, 1, 1, 6 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 36 ], [ 17, 1, 3, 12 ], [ 17, 2, 1, 18 ], [ 17, 2, 2, 24 ], [ 17, 2, 3, 6 ], [ 18, 2, 3, 12 ], [ 20, 2, 4, 32 ], [ 21, 1, 1, 48 ], [ 22, 1, 1, 24 ], [ 22, 1, 2, 24 ], [ 23, 2, 3, 24 ], [ 23, 2, 4, 8 ], [ 25, 2, 6, 48 ], [ 25, 3, 8, 48 ], [ 25, 4, 7, 48 ], [ 26, 1, 1, 24 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 96 ], [ 27, 1, 8, 48 ], [ 27, 2, 1, 48 ], [ 27, 2, 8, 24 ], [ 27, 3, 1, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 8, 48 ], [ 27, 3, 9, 24 ], [ 27, 3, 14, 48 ], [ 28, 1, 3, 16 ], [ 28, 2, 4, 8 ], [ 30, 2, 3, 96 ], [ 31, 2, 5, 72 ], [ 31, 2, 7, 24 ], [ 32, 1, 1, 48 ], [ 32, 1, 6, 48 ], [ 33, 4, 12, 64 ], [ 34, 2, 10, 24 ], [ 34, 3, 8, 48 ], [ 35, 1, 2, 48 ], [ 35, 2, 2, 24 ], [ 36, 3, 18, 96 ], [ 36, 5, 20, 96 ], [ 36, 6, 8, 96 ], [ 38, 2, 3, 144 ], [ 38, 2, 7, 48 ], [ 38, 3, 12, 96 ], [ 38, 3, 14, 96 ], [ 39, 4, 11, 48 ], [ 39, 4, 12, 96 ], [ 39, 5, 5, 96 ], [ 40, 1, 17, 96 ], [ 40, 2, 22, 48 ], [ 40, 3, 4, 48 ], [ 41, 4, 13, 96 ], [ 41, 4, 14, 192 ], [ 41, 5, 22, 192 ], [ 42, 2, 10, 192 ], [ 43, 5, 37, 192 ], [ 43, 5, 39, 192 ] ] k = 84: F-action on Pi is () [44,5,84] Dynkin type is (A_0(q) + T(phi1^3 phi2^4)).2 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: 1/128 phi1^2 phi2 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/128 phi1^2 phi2 ( q-5 ) q congruent 7 modulo 12: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/128 phi1^2 phi2 ( q-5 ) q congruent 11 modulo 12: 1/128 phi2 ( q^3-7*q^2+11*q+3 ) 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, 2, 8 ], [ 4, 1, 2, 24 ], [ 4, 2, 2, 12 ], [ 4, 2, 3, 8 ], [ 7, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 10, 1, 4, 48 ], [ 11, 1, 2, 8 ], [ 15, 2, 3, 8 ], [ 15, 4, 7, 16 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 6 ], [ 17, 1, 1, 12 ], [ 17, 1, 3, 36 ], [ 17, 2, 1, 6 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 18 ], [ 18, 2, 2, 4 ], [ 21, 1, 6, 48 ], [ 22, 1, 3, 24 ], [ 22, 1, 4, 24 ], [ 25, 2, 7, 16 ], [ 25, 3, 5, 16 ], [ 25, 4, 6, 16 ], [ 26, 1, 2, 12 ], [ 26, 1, 3, 24 ], [ 27, 1, 8, 48 ], [ 27, 1, 12, 96 ], [ 27, 2, 8, 24 ], [ 27, 2, 12, 48 ], [ 27, 3, 3, 32 ], [ 27, 3, 5, 24 ], [ 27, 3, 8, 16 ], [ 27, 3, 9, 24 ], [ 27, 3, 10, 32 ], [ 27, 3, 11, 48 ], [ 27, 3, 14, 16 ], [ 28, 1, 2, 16 ], [ 28, 2, 2, 8 ], [ 30, 2, 8, 32 ], [ 31, 2, 2, 8 ], [ 31, 2, 4, 24 ], [ 32, 1, 3, 48 ], [ 32, 1, 7, 48 ], [ 34, 2, 2, 8 ], [ 34, 3, 3, 16 ], [ 35, 1, 4, 48 ], [ 35, 2, 4, 24 ], [ 36, 3, 18, 32 ], [ 36, 3, 20, 64 ], [ 36, 5, 4, 32 ], [ 36, 6, 15, 32 ], [ 38, 2, 2, 16 ], [ 38, 2, 5, 48 ], [ 38, 3, 9, 32 ], [ 38, 3, 15, 32 ], [ 39, 4, 5, 32 ], [ 39, 4, 6, 16 ], [ 39, 5, 12, 32 ], [ 39, 5, 19, 32 ], [ 40, 1, 18, 96 ], [ 40, 2, 23, 48 ], [ 40, 3, 3, 48 ], [ 41, 4, 3, 32 ], [ 41, 4, 9, 64 ], [ 41, 4, 11, 32 ], [ 41, 4, 25, 64 ], [ 41, 5, 26, 64 ], [ 42, 2, 12, 64 ], [ 43, 5, 8, 64 ], [ 43, 5, 11, 64 ], [ 43, 5, 18, 64 ] ] k = 85: F-action on Pi is () [44,5,85] Dynkin type is (A_0(q) + T(phi1^5 phi2^2)).2 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: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 7 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 11 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) 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, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 12 ], [ 4, 2, 1, 26 ], [ 4, 2, 2, 6 ], [ 5, 2, 1, 6 ], [ 6, 2, 1, 2 ], [ 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, 2, 1, 16 ], [ 14, 2, 1, 12 ], [ 15, 2, 1, 12 ], [ 15, 2, 2, 12 ], [ 15, 4, 1, 48 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 20 ], [ 17, 2, 4, 8 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 20, 2, 1, 48 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 2, 1, 24 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 12 ], [ 25, 2, 4, 12 ], [ 25, 3, 1, 12 ], [ 25, 3, 2, 12 ], [ 25, 3, 3, 12 ], [ 25, 3, 4, 12 ], [ 25, 4, 1, 36 ], [ 25, 4, 2, 12 ], [ 25, 4, 3, 36 ], [ 25, 4, 4, 12 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 3, 1, 48 ], [ 27, 3, 2, 48 ], [ 27, 3, 16, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 30, 2, 1, 16 ], [ 30, 2, 4, 16 ], [ 31, 2, 1, 24 ], [ 31, 2, 6, 24 ], [ 32, 1, 2, 48 ], [ 33, 4, 1, 96 ], [ 34, 2, 4, 4 ], [ 34, 3, 1, 12 ], [ 34, 3, 4, 4 ], [ 34, 3, 6, 4 ], [ 34, 3, 7, 12 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 36, 3, 1, 96 ], [ 36, 3, 2, 48 ], [ 36, 3, 3, 96 ], [ 36, 5, 2, 24 ], [ 36, 6, 1, 24 ], [ 36, 6, 2, 48 ], [ 36, 6, 3, 48 ], [ 36, 6, 4, 24 ], [ 36, 6, 9, 24 ], [ 36, 6, 11, 24 ], [ 38, 2, 10, 48 ], [ 38, 3, 1, 48 ], [ 38, 3, 4, 48 ], [ 38, 3, 10, 48 ], [ 38, 3, 11, 48 ], [ 39, 4, 1, 48 ], [ 39, 4, 9, 24 ], [ 39, 4, 17, 24 ], [ 39, 4, 18, 48 ], [ 39, 5, 9, 8 ], [ 39, 5, 17, 24 ], [ 40, 1, 12, 96 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 48 ], [ 41, 4, 19, 48 ], [ 41, 4, 44, 96 ], [ 41, 5, 1, 96 ], [ 41, 5, 14, 96 ], [ 41, 5, 33, 96 ], [ 41, 5, 35, 96 ], [ 42, 2, 4, 32 ], [ 43, 5, 4, 96 ] ] k = 86: F-action on Pi is () [44,5,86] Dynkin type is (A_0(q) + T(phi1^3 phi2^4)).2 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: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) 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, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 24 ], [ 5, 2, 1, 6 ], [ 6, 2, 1, 2 ], [ 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, 2, 4, 16 ], [ 14, 2, 1, 12 ], [ 15, 2, 1, 12 ], [ 15, 2, 2, 12 ], [ 15, 4, 8, 48 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 1, 8 ], [ 17, 2, 3, 12 ], [ 17, 2, 4, 8 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 20, 2, 3, 48 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 2, 2, 24 ], [ 25, 2, 1, 12 ], [ 25, 2, 2, 12 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 12 ], [ 25, 3, 2, 12 ], [ 25, 3, 3, 12 ], [ 25, 3, 4, 12 ], [ 25, 4, 1, 12 ], [ 25, 4, 2, 36 ], [ 25, 4, 3, 12 ], [ 25, 4, 4, 36 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 13, 96 ], [ 27, 2, 2, 12 ], [ 27, 2, 13, 48 ], [ 27, 3, 4, 48 ], [ 27, 3, 9, 48 ], [ 27, 3, 12, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 30, 2, 6, 16 ], [ 30, 2, 7, 16 ], [ 31, 2, 3, 24 ], [ 31, 2, 8, 24 ], [ 32, 1, 5, 48 ], [ 33, 4, 9, 96 ], [ 34, 2, 4, 4 ], [ 34, 3, 1, 4 ], [ 34, 3, 4, 12 ], [ 34, 3, 6, 12 ], [ 34, 3, 7, 4 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 10, 24 ], [ 36, 3, 2, 48 ], [ 36, 3, 23, 96 ], [ 36, 3, 24, 96 ], [ 36, 5, 2, 24 ], [ 36, 6, 1, 24 ], [ 36, 6, 4, 24 ], [ 36, 6, 9, 24 ], [ 36, 6, 10, 48 ], [ 36, 6, 11, 24 ], [ 36, 6, 12, 48 ], [ 38, 2, 15, 48 ], [ 38, 3, 6, 48 ], [ 38, 3, 7, 48 ], [ 38, 3, 13, 48 ], [ 38, 3, 16, 48 ], [ 39, 4, 8, 48 ], [ 39, 4, 9, 24 ], [ 39, 4, 17, 24 ], [ 39, 4, 20, 48 ], [ 39, 5, 9, 24 ], [ 39, 5, 17, 8 ], [ 40, 1, 13, 96 ], [ 40, 2, 24, 48 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 48 ], [ 41, 4, 19, 48 ], [ 41, 4, 50, 96 ], [ 41, 5, 19, 96 ], [ 41, 5, 20, 96 ], [ 41, 5, 39, 96 ], [ 41, 5, 40, 96 ], [ 42, 2, 13, 32 ], [ 43, 5, 14, 96 ] ] k = 87: F-action on Pi is () [44,5,87] Dynkin type is (A_0(q) + T(phi1^2 phi2^5)).2 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: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 12: 1/192 phi1 ( q^3-11*q^2+39*q-45 ) 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, 7 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 26 ], [ 5, 2, 2, 6 ], [ 6, 2, 2, 2 ], [ 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, 2, 3, 16 ], [ 14, 2, 2, 12 ], [ 15, 2, 3, 12 ], [ 15, 2, 4, 12 ], [ 15, 4, 4, 48 ], [ 16, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 20 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 20, 2, 2, 48 ], [ 21, 1, 3, 16 ], [ 22, 1, 2, 24 ], [ 22, 1, 4, 24 ], [ 23, 2, 4, 24 ], [ 25, 2, 5, 12 ], [ 25, 2, 6, 12 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 12 ], [ 25, 3, 6, 12 ], [ 25, 3, 7, 12 ], [ 25, 3, 8, 12 ], [ 25, 4, 5, 12 ], [ 25, 4, 6, 36 ], [ 25, 4, 7, 12 ], [ 25, 4, 8, 36 ], [ 26, 1, 3, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 13, 96 ], [ 27, 2, 2, 12 ], [ 27, 2, 13, 48 ], [ 27, 3, 8, 48 ], [ 27, 3, 11, 48 ], [ 27, 3, 12, 48 ], [ 28, 1, 6, 48 ], [ 28, 2, 6, 24 ], [ 30, 2, 5, 16 ], [ 30, 2, 8, 16 ], [ 31, 2, 4, 24 ], [ 31, 2, 7, 24 ], [ 32, 1, 5, 48 ], [ 33, 4, 6, 96 ], [ 34, 2, 3, 4 ], [ 34, 3, 2, 4 ], [ 34, 3, 3, 12 ], [ 34, 3, 5, 12 ], [ 34, 3, 8, 4 ], [ 35, 1, 5, 48 ], [ 35, 1, 10, 48 ], [ 35, 2, 5, 24 ], [ 35, 2, 10, 24 ], [ 36, 3, 5, 48 ], [ 36, 3, 25, 96 ], [ 36, 3, 26, 96 ], [ 36, 5, 5, 24 ], [ 36, 6, 5, 24 ], [ 36, 6, 8, 24 ], [ 36, 6, 13, 24 ], [ 36, 6, 14, 48 ], [ 36, 6, 15, 24 ], [ 36, 6, 16, 48 ], [ 38, 2, 16, 48 ], [ 38, 3, 5, 48 ], [ 38, 3, 8, 48 ], [ 38, 3, 14, 48 ], [ 38, 3, 15, 48 ], [ 39, 4, 3, 24 ], [ 39, 4, 5, 48 ], [ 39, 4, 13, 24 ], [ 39, 4, 15, 48 ], [ 39, 5, 3, 24 ], [ 39, 5, 13, 8 ], [ 40, 1, 13, 96 ], [ 40, 2, 24, 48 ], [ 40, 3, 18, 48 ], [ 40, 3, 20, 48 ], [ 41, 4, 5, 48 ], [ 41, 4, 31, 96 ], [ 41, 5, 4, 96 ], [ 41, 5, 13, 96 ], [ 41, 5, 21, 96 ], [ 41, 5, 25, 96 ], [ 42, 2, 19, 32 ], [ 43, 5, 36, 96 ] ] k = 88: F-action on Pi is () [44,5,88] Dynkin type is (A_0(q) + T(phi1^4 phi2^3)).2 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: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 7 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) q congruent 11 modulo 12: 1/192 phi1 ( q^3-15*q^2+71*q-105 ) 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, 7 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 12 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 4, 2, 3, 24 ], [ 5, 2, 2, 6 ], [ 6, 2, 2, 2 ], [ 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, 2, 2, 16 ], [ 14, 2, 2, 12 ], [ 15, 2, 3, 12 ], [ 15, 2, 4, 12 ], [ 15, 4, 5, 48 ], [ 16, 1, 1, 12 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ], [ 17, 2, 2, 8 ], [ 17, 2, 3, 8 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 20, 2, 4, 48 ], [ 21, 1, 2, 16 ], [ 22, 1, 1, 24 ], [ 22, 1, 3, 24 ], [ 23, 2, 3, 24 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 12 ], [ 25, 2, 8, 12 ], [ 25, 3, 5, 12 ], [ 25, 3, 6, 12 ], [ 25, 3, 7, 12 ], [ 25, 3, 8, 12 ], [ 25, 4, 5, 36 ], [ 25, 4, 6, 12 ], [ 25, 4, 7, 36 ], [ 25, 4, 8, 12 ], [ 26, 1, 1, 24 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 24 ], [ 27, 1, 3, 96 ], [ 27, 2, 2, 12 ], [ 27, 2, 3, 48 ], [ 27, 3, 2, 48 ], [ 27, 3, 5, 48 ], [ 27, 3, 14, 48 ], [ 28, 1, 1, 48 ], [ 28, 2, 1, 24 ], [ 30, 2, 2, 16 ], [ 30, 2, 3, 16 ], [ 31, 2, 2, 24 ], [ 31, 2, 5, 24 ], [ 32, 1, 2, 48 ], [ 33, 4, 10, 96 ], [ 34, 2, 3, 4 ], [ 34, 3, 2, 12 ], [ 34, 3, 3, 4 ], [ 34, 3, 5, 4 ], [ 34, 3, 8, 12 ], [ 35, 1, 1, 48 ], [ 35, 1, 3, 48 ], [ 35, 2, 1, 24 ], [ 35, 2, 3, 24 ], [ 36, 3, 4, 96 ], [ 36, 3, 5, 48 ], [ 36, 3, 6, 96 ], [ 36, 5, 5, 24 ], [ 36, 6, 5, 24 ], [ 36, 6, 6, 48 ], [ 36, 6, 7, 48 ], [ 36, 6, 8, 24 ], [ 36, 6, 13, 24 ], [ 36, 6, 15, 24 ], [ 38, 2, 9, 48 ], [ 38, 3, 2, 48 ], [ 38, 3, 3, 48 ], [ 38, 3, 9, 48 ], [ 38, 3, 12, 48 ], [ 39, 4, 3, 24 ], [ 39, 4, 7, 48 ], [ 39, 4, 12, 48 ], [ 39, 4, 13, 24 ], [ 39, 5, 3, 8 ], [ 39, 5, 13, 24 ], [ 40, 1, 12, 96 ], [ 40, 2, 21, 48 ], [ 40, 3, 5, 48 ], [ 40, 3, 6, 48 ], [ 41, 4, 5, 48 ], [ 41, 4, 37, 96 ], [ 41, 5, 10, 96 ], [ 41, 5, 12, 96 ], [ 41, 5, 28, 96 ], [ 41, 5, 30, 96 ], [ 42, 2, 6, 32 ], [ 43, 5, 27, 96 ] ] k = 89: F-action on Pi is () [44,5,89] Dynkin type is (A_0(q) + T(phi1^4 phi2^3)).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 phi1^3 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1^3 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^3 ( q-3 ) q congruent 7 modulo 12: 1/32 phi1^3 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^3 ( q-3 ) q congruent 11 modulo 12: 1/32 phi1^3 ( q-3 ) 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, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 6 ], [ 4, 2, 2, 2 ], [ 4, 2, 4, 4 ], [ 5, 2, 1, 2 ], [ 6, 2, 1, 2 ], [ 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 ], [ 12, 2, 1, 8 ], [ 12, 2, 4, 8 ], [ 14, 2, 1, 4 ], [ 15, 2, 1, 4 ], [ 15, 2, 2, 4 ], [ 15, 4, 3, 8 ], [ 15, 4, 6, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 6 ], [ 17, 2, 3, 2 ], [ 17, 2, 4, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 4, 2 ], [ 20, 2, 1, 8 ], [ 20, 2, 3, 8 ], [ 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, 2, 1, 4 ], [ 23, 2, 2, 4 ], [ 25, 2, 1, 4 ], [ 25, 2, 2, 4 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 25, 4, 1, 4 ], [ 25, 4, 2, 4 ], [ 25, 4, 3, 4 ], [ 25, 4, 4, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 9, 16 ], [ 27, 2, 2, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 1, 8 ], [ 27, 3, 4, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 9, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 16, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 30, 2, 1, 8 ], [ 30, 2, 4, 8 ], [ 30, 2, 6, 8 ], [ 30, 2, 7, 8 ], [ 31, 2, 1, 4 ], [ 31, 2, 3, 4 ], [ 31, 2, 6, 4 ], [ 31, 2, 8, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 33, 4, 3, 16 ], [ 33, 4, 7, 16 ], [ 34, 2, 4, 4 ], [ 34, 3, 1, 4 ], [ 34, 3, 4, 4 ], [ 34, 3, 6, 4 ], [ 34, 3, 7, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 36, 3, 14, 16 ], [ 36, 3, 15, 16 ], [ 36, 5, 2, 8 ], [ 36, 6, 1, 8 ], [ 36, 6, 4, 8 ], [ 36, 6, 9, 8 ], [ 36, 6, 11, 8 ], [ 38, 2, 10, 8 ], [ 38, 2, 15, 8 ], [ 38, 3, 1, 8 ], [ 38, 3, 4, 8 ], [ 38, 3, 6, 8 ], [ 38, 3, 7, 8 ], [ 38, 3, 10, 8 ], [ 38, 3, 11, 8 ], [ 38, 3, 13, 8 ], [ 38, 3, 16, 8 ], [ 39, 4, 2, 8 ], [ 39, 4, 9, 8 ], [ 39, 4, 17, 8 ], [ 39, 4, 19, 8 ], [ 39, 5, 9, 8 ], [ 39, 5, 17, 8 ], [ 40, 1, 22, 16 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 8 ], [ 41, 4, 19, 16 ], [ 41, 4, 46, 16 ], [ 41, 5, 2, 16 ], [ 41, 5, 15, 16 ], [ 41, 5, 34, 16 ], [ 41, 5, 36, 16 ], [ 42, 2, 4, 16 ], [ 42, 2, 13, 16 ], [ 43, 5, 4, 16 ], [ 43, 5, 14, 16 ] ] k = 90: F-action on Pi is () [44,5,90] Dynkin type is (A_0(q) + T(phi1^3 phi2^4)).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 phi1^3 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/32 phi1^3 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/32 phi1^3 ( q-3 ) q congruent 7 modulo 12: 1/32 phi1^3 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/32 phi1^3 ( q-3 ) q congruent 11 modulo 12: 1/32 phi1^3 ( q-3 ) 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, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 6 ], [ 4, 2, 3, 4 ], [ 5, 2, 2, 2 ], [ 6, 2, 2, 2 ], [ 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 ], [ 12, 2, 2, 8 ], [ 12, 2, 3, 8 ], [ 14, 2, 2, 4 ], [ 15, 2, 3, 4 ], [ 15, 2, 4, 4 ], [ 15, 4, 2, 8 ], [ 15, 4, 7, 8 ], [ 16, 1, 1, 2 ], [ 16, 1, 2, 2 ], [ 17, 1, 1, 4 ], [ 17, 1, 3, 4 ], [ 17, 2, 1, 2 ], [ 17, 2, 2, 4 ], [ 17, 2, 3, 6 ], [ 18, 2, 2, 2 ], [ 18, 2, 3, 2 ], [ 20, 2, 2, 8 ], [ 20, 2, 4, 8 ], [ 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, 2, 3, 4 ], [ 23, 2, 4, 4 ], [ 25, 2, 5, 4 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 2, 8, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 25, 4, 5, 4 ], [ 25, 4, 6, 4 ], [ 25, 4, 7, 4 ], [ 25, 4, 8, 4 ], [ 26, 1, 2, 4 ], [ 26, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 9, 16 ], [ 27, 2, 2, 4 ], [ 27, 2, 9, 8 ], [ 27, 3, 5, 8 ], [ 27, 3, 6, 8 ], [ 27, 3, 8, 8 ], [ 27, 3, 10, 8 ], [ 27, 3, 11, 8 ], [ 27, 3, 14, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 2, 2, 4 ], [ 28, 2, 4, 4 ], [ 30, 2, 2, 8 ], [ 30, 2, 3, 8 ], [ 30, 2, 5, 8 ], [ 30, 2, 8, 8 ], [ 31, 2, 2, 4 ], [ 31, 2, 4, 4 ], [ 31, 2, 5, 4 ], [ 31, 2, 7, 4 ], [ 32, 1, 2, 8 ], [ 32, 1, 5, 8 ], [ 33, 4, 4, 16 ], [ 33, 4, 12, 16 ], [ 34, 2, 3, 4 ], [ 34, 3, 2, 4 ], [ 34, 3, 3, 4 ], [ 34, 3, 5, 4 ], [ 34, 3, 8, 4 ], [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 35, 2, 2, 4 ], [ 35, 2, 4, 4 ], [ 36, 3, 17, 16 ], [ 36, 3, 18, 16 ], [ 36, 5, 5, 8 ], [ 36, 6, 5, 8 ], [ 36, 6, 8, 8 ], [ 36, 6, 13, 8 ], [ 36, 6, 15, 8 ], [ 38, 2, 9, 8 ], [ 38, 2, 16, 8 ], [ 38, 3, 2, 8 ], [ 38, 3, 3, 8 ], [ 38, 3, 5, 8 ], [ 38, 3, 8, 8 ], [ 38, 3, 9, 8 ], [ 38, 3, 12, 8 ], [ 38, 3, 14, 8 ], [ 38, 3, 15, 8 ], [ 39, 4, 3, 8 ], [ 39, 4, 6, 8 ], [ 39, 4, 11, 8 ], [ 39, 4, 13, 8 ], [ 39, 5, 3, 8 ], [ 39, 5, 13, 8 ], [ 40, 1, 22, 16 ], [ 40, 2, 25, 8 ], [ 40, 3, 7, 8 ], [ 40, 3, 8, 8 ], [ 41, 4, 5, 16 ], [ 41, 4, 34, 16 ], [ 41, 5, 5, 16 ], [ 41, 5, 8, 16 ], [ 41, 5, 22, 16 ], [ 41, 5, 26, 16 ], [ 42, 2, 6, 16 ], [ 42, 2, 19, 16 ], [ 43, 5, 27, 16 ], [ 43, 5, 36, 16 ] ]