Centralizers of semisimple elements in E6(q)_ad -------------------------------------------- |G(q)| = q^36 phi1^6 phi2^4 phi3^3 phi4^2 phi5 phi6^2 phi8 phi9 phi12 Semisimple class types: i = 1: Pi = [ 1, 2, 3, 4, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [1,1,1] Dynkin type is E_6(q) Order of center |Z^F|: 1 Numbers of classes in class type: q congruent 1 modulo 6: 1 q congruent 2 modulo 6: 1 q congruent 3 modulo 6: 1 q congruent 4 modulo 6: 1 q congruent 5 modulo 6: 1 Fusion of maximal tori of C^F in those of G^F: [ 1 .. 25 ] elements of other class types in center: [ ] i = 2: Pi = [ 1, 2, 3, 4, 6, 72 ] j = 1: Omega trivial k = 1: F-action on Pi is () [2,1,1] Dynkin type is A_5(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 6: 1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 1 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1 Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 3, 17, 17, 2, 5, 20, 20, 13, 6, 21, 19, 8, 8, 18, 9, 24, 22, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 3: Pi = [ 1, 2, 3, 5, 6, 72 ] j = 2: Omega of order 3, action on Pi: <( 1,72, 6)( 2, 5, 3)> k = 1: F-action on Pi is () [3,2,1] Dynkin type is (A_2(q) + A_2(q) + A_2(q)).3 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 6: 1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 5, 16, 3, 20, 5, 20, 6, 16, 3, 20, 3, 17, 13, 20, 13, 21, 5, 20, 6, 20, 13, 21, 6, 21, 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 1, 2)( 3,72)( 5, 6) [3,2,2] Dynkin type is A_2(q^2) + ^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 6: 0 q congruent 2 modulo 6: 1 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1 Fusion of maximal tori of C^F in those of G^F: [ 2, 17, 11, 18, 8, 25, 12, 22, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 3: F-action on Pi is ( 1, 6,72)( 2, 3, 5) [3,2,3] Dynkin type is A_2(q^3).3 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 6: 2 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 2 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 6, 22, 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 4: Pi = [ 1, 2, 3, 4, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [4,1,1] Dynkin type is D_5(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 6: ( q-2 ) q congruent 2 modulo 6: ( q-2 ) q congruent 3 modulo 6: ( q-2 ) q congruent 4 modulo 6: ( q-2 ) q congruent 5 modulo 6: ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 3, 2, 16, 19, 17, 18, 3, 7, 8, 5, 11, 13, 20, 25, 19, 23, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 5: Pi = [ 1, 2, 3, 4, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [5,1,1] Dynkin type is A_4(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 6: ( q-3 ) q congruent 2 modulo 6: ( q-2 ) q congruent 3 modulo 6: ( q-3 ) q congruent 4 modulo 6: ( q-2 ) q congruent 5 modulo 6: ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 3, 17, 5, 20, 20, 13, 19, 8, 9, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 6: Pi = [ 1, 2, 3, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [6,1,1] Dynkin type is A_2(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 6: 1/2 ( q-5 ) q congruent 2 modulo 6: 1/2 ( q-2 ) q congruent 3 modulo 6: 1/2 ( q-3 ) q congruent 4 modulo 6: 1/2 ( q-4 ) q congruent 5 modulo 6: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 5, 20, 16, 3, 3, 17, 20, 13, 5, 20, 20, 13, 6, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ] ] k = 2: F-action on Pi is (1,5)(3,6) [6,1,2] Dynkin type is A_2(q^2) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 phi1 q congruent 2 modulo 6: 1/2 ( q-2 ) q congruent 3 modulo 6: 1/2 phi1 q congruent 4 modulo 6: 1/2 q q congruent 5 modulo 6: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 2, 8, 18, 22, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ] ] i = 7: Pi = [ 1, 2, 4, 6, 72 ] j = 1: Omega trivial k = 1: F-action on Pi is () [7,1,1] Dynkin type is A_3(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 6: 1/2 ( q-3 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 1/2 ( q-3 ) q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 16, 3, 3, 17, 3, 17, 17, 2, 5, 20, 20, 13, 19, 8, 8, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 1, 6)( 4,72) [7,1,2] Dynkin type is ^2A_3(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 6: 1/2 phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 1/2 phi1 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 2, 18, 17, 8, 3, 19, 11, 25, 19, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 1 ] ] i = 8: Pi = [ 1, 3, 4, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [8,1,1] Dynkin type is A_5(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 ( q-3 ) q congruent 2 modulo 6: 1/2 ( q-2 ) q congruent 3 modulo 6: 1/2 ( q-3 ) q congruent 4 modulo 6: 1/2 ( q-2 ) q congruent 5 modulo 6: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 3, 17, 5, 20, 6, 19, 8, 9, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 2: F-action on Pi is () [8,1,2] Dynkin type is A_5(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 phi1 q congruent 2 modulo 6: 1/2 q q congruent 3 modulo 6: 1/2 phi1 q congruent 4 modulo 6: 1/2 q q congruent 5 modulo 6: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 17, 2, 20, 13, 21, 8, 18, 24, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 9: Pi = [ 1, 2, 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [9,1,1] Dynkin type is A_4(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 ( q^2-6*q+9 ) q congruent 2 modulo 6: 1/2 ( q^2-6*q+8 ) q congruent 3 modulo 6: 1/2 ( q^2-6*q+9 ) q congruent 4 modulo 6: 1/2 ( q^2-6*q+8 ) q congruent 5 modulo 6: 1/2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 3, 5, 20, 19, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 1 ], [ 8, 1, 1, 2 ] ] k = 2: F-action on Pi is () [9,1,2] Dynkin type is A_4(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 phi1^2 q congruent 2 modulo 6: 1/2 q ( q-2 ) q congruent 3 modulo 6: 1/2 phi1^2 q congruent 4 modulo 6: 1/2 q ( q-2 ) q congruent 5 modulo 6: 1/2 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 17, 20, 13, 8, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 1 ], [ 8, 1, 2, 2 ] ] i = 10: Pi = [ 1, 2, 3, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [10,1,1] Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 ( q^2-8*q+17 ) q congruent 2 modulo 6: 1/2 ( q^2-7*q+10 ) q congruent 3 modulo 6: 1/2 ( q^2-8*q+15 ) q congruent 4 modulo 6: 1/2 ( q^2-7*q+12 ) q congruent 5 modulo 6: 1/2 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 16, 3, 3, 17, 5, 20, 20, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ] ] k = 2: F-action on Pi is (1,3)(2,5) [10,1,2] Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 phi1^2 q congruent 2 modulo 6: 1/2 phi2 ( q-2 ) q congruent 3 modulo 6: 1/2 phi1^2 q congruent 4 modulo 6: 1/2 q phi1 q congruent 5 modulo 6: 1/2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 18, 17, 8, 11, 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 4, 1, 1, 1 ], [ 7, 1, 2, 2 ] ] i = 11: Pi = [ 1, 2, 4, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [11,1,1] Dynkin type is A_3(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 ( q^2-7*q+12 ) q congruent 2 modulo 6: 1/2 ( q^2-6*q+8 ) q congruent 3 modulo 6: 1/2 ( q^2-7*q+12 ) q congruent 4 modulo 6: 1/2 ( q^2-6*q+8 ) q congruent 5 modulo 6: 1/2 ( q^2-7*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 3, 17, 5, 20, 19, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ] ] k = 2: F-action on Pi is () [11,1,2] Dynkin type is A_3(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 phi1 ( q-2 ) q congruent 2 modulo 6: 1/2 q ( q-2 ) q congruent 3 modulo 6: 1/2 phi1 ( q-2 ) q congruent 4 modulo 6: 1/2 q ( q-2 ) q congruent 5 modulo 6: 1/2 phi1 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 3, 17, 17, 2, 20, 13, 8, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 2 ] ] i = 12: Pi = [ 1, 3, 5, 6 ] j = 1: Omega trivial k = 1: F-action on Pi is () [12,1,1] Dynkin type is A_2(q) + A_2(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/12 ( q^2-8*q+19 ) q congruent 2 modulo 6: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 6: 1/12 ( q^2-8*q+15 ) q congruent 4 modulo 6: 1/12 ( q^2-8*q+16 ) q congruent 5 modulo 6: 1/12 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 5, 16, 3, 20, 5, 20, 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 6 ], [ 8, 1, 1, 6 ] ] k = 2: F-action on Pi is (1,5)(3,6) [12,1,2] Dynkin type is A_2(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/4 phi1^2 q congruent 2 modulo 6: 1/4 q ( q-2 ) q congruent 3 modulo 6: 1/4 phi1^2 q congruent 4 modulo 6: 1/4 q ( q-2 ) q congruent 5 modulo 6: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 17, 8, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 1, 2 ] ] k = 3: F-action on Pi is () [12,1,3] Dynkin type is A_2(q) + A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/4 phi1^2 q congruent 2 modulo 6: 1/4 q ( q-2 ) q congruent 3 modulo 6: 1/4 phi1^2 q congruent 4 modulo 6: 1/4 q ( q-2 ) q congruent 5 modulo 6: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 20, 3, 17, 13, 20, 13, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 2, 2 ] ] k = 4: F-action on Pi is (1,5)(3,6) [12,1,4] Dynkin type is A_2(q^2) + T(phi6) Order of center |Z^F|: phi6 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 q phi1 q congruent 2 modulo 6: 1/6 phi2 ( q-2 ) q congruent 3 modulo 6: 1/6 q phi1 q congruent 4 modulo 6: 1/6 q phi1 q congruent 5 modulo 6: 1/6 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 11, 25, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ] ] k = 5: F-action on Pi is () [12,1,5] Dynkin type is A_2(q) + A_2(q) + T(phi3) Order of center |Z^F|: phi3 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 phi1 ( q+2 ) q congruent 2 modulo 6: 1/6 q phi2 q congruent 3 modulo 6: 1/6 q phi2 q congruent 4 modulo 6: 1/6 phi1 ( q+2 ) q congruent 5 modulo 6: 1/6 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 5, 20, 6, 20, 13, 21, 6, 21, 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ] ] k = 6: F-action on Pi is (1,5)(3,6) [12,1,6] Dynkin type is A_2(q^2) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/12 phi1 ( q-3 ) q congruent 2 modulo 6: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 6: 1/12 phi1 ( q-3 ) q congruent 4 modulo 6: 1/12 q ( q-4 ) q congruent 5 modulo 6: 1/12 ( q^2-4*q+7 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 18, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 6 ], [ 8, 1, 2, 6 ] ] i = 13: Pi = [ 1, 4, 6, 72 ] j = 1: Omega trivial k = 1: F-action on Pi is () [13,1,1] Dynkin type is 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 6: 1/24 phi1 ( q-7 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 1/24 ( q^2-8*q+15 ) q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/24 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 16, 3, 3, 17, 16, 3, 3, 17, 3, 17, 17, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 3 ], [ 7, 1, 1, 12 ], [ 13, 2, 1, 8 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 2 ] ] k = 2: F-action on Pi is ( 4, 6,72) [13,1,2] Dynkin type is A_1(q) + A_1(q^3) + T(phi3) Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 6: 1/3 phi1 ( q+2 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 1/3 q phi2 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/3 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 6, 22, 21, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 13, 2, 2, 1 ], [ 14, 1, 3, 3 ], [ 14, 2, 2, 1 ] ] k = 3: F-action on Pi is (4,6) [13,1,3] Dynkin type is 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 6: 1/4 phi1^2 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 1/4 phi1^2 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/4 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 17, 19, 8, 17, 2, 8, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ] ] k = 4: F-action on Pi is ( 1, 4,72, 6) [13,1,4] Dynkin type is 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 6: 1/4 phi1 phi2 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 1/4 phi1 phi2 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/4 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 8, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 1 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ] ] k = 5: F-action on Pi is ( 1, 4)( 6,72) [13,1,5] Dynkin type is 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 6: 1/8 phi1 ( q-3 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 1/8 phi1 ( q-3 ) q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 19, 19, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 3 ], [ 7, 1, 2, 4 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 2 ] ] j = 2: Omega of order 3, action on Pi: <( 4,72, 6)> k = 1: F-action on Pi is () [13,2,1] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2)).3 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 6: 1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 16, 3, 3, 17, 16, 3, 3, 17, 3, 17, 17, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 14, 2, 1, 2 ] ] k = 2: F-action on Pi is ( 4, 6,72) [13,2,2] Dynkin type is (A_1(q) + A_1(q^3) + T(phi3)).3 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 6: 2 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 6, 22, 21, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 14, 2, 2, 1 ] ] k = 3: F-action on Pi is (4,6) [13,2,3] Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2) 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 6: 0 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1 Fusion of maximal tori of C^F in those of G^F: [ 3, 17, 19, 8, 17, 2, 8, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 14, 2, 3, 2 ] ] i = 14: Pi = [ 2, 3, 4, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [14,1,1] Dynkin type is D_4(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 phi1 ( q-4 ) q congruent 2 modulo 6: 1/6 ( q^2-5*q+6 ) q congruent 3 modulo 6: 1/6 ( q^2-5*q+6 ) q congruent 4 modulo 6: 1/6 phi1 ( q-4 ) q congruent 5 modulo 6: 1/6 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 3, 2, 16, 19, 17, 3, 3, 7, 5, 11, 19, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 3 ], [ 14, 2, 1, 2 ] ] k = 2: F-action on Pi is (2,5) [14,1,2] Dynkin type is ^2D_4(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 q phi1 q congruent 2 modulo 6: 1/2 phi2 ( q-2 ) q congruent 3 modulo 6: 1/2 q phi1 q congruent 4 modulo 6: 1/2 q phi1 q congruent 5 modulo 6: 1/2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 2, 19, 17, 18, 8, 11, 13, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 1 ], [ 14, 2, 3, 2 ] ] k = 3: F-action on Pi is (2,5,3) [14,1,3] Dynkin type is ^3D_4(q) + T(phi3) Order of center |Z^F|: phi3 Numbers of classes in class type: q congruent 1 modulo 6: 1/3 phi1 ( q+2 ) q congruent 2 modulo 6: 1/3 q phi2 q congruent 3 modulo 6: 1/3 q phi2 q congruent 4 modulo 6: 1/3 phi1 ( q+2 ) q congruent 5 modulo 6: 1/3 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 6, 22, 21, 12, 4, 15, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 14, 2, 2, 1 ] ] j = 2: Omega of order 3, action on Pi: <(2,5,3)> k = 1: F-action on Pi is () [14,2,1] Dynkin type is (D_4(q) + T(phi1^2)).3 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 6: 1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 3, 2, 16, 19, 17, 3, 3, 7, 5, 11, 19, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 2: F-action on Pi is (2,3,5) [14,2,2] Dynkin type is (^3D_4(q) + T(phi3)).3 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 6: 2 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 2 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 6, 22, 21, 12, 4, 15, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 3: F-action on Pi is (2,3) [14,2,3] Dynkin type is ^2D_4(q) + T(phi1 phi2) 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 6: 0 q congruent 2 modulo 6: 1 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1 Fusion of maximal tori of C^F in those of G^F: [ 3, 2, 19, 17, 18, 8, 11, 13, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 15: Pi = [ 1, 2, 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [15,1,1] Dynkin type is A_2(q) + A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 ( q^3-13*q^2+55*q-79 ) q congruent 2 modulo 6: 1/6 ( q^3-13*q^2+52*q-60 ) q congruent 3 modulo 6: 1/6 ( q^3-13*q^2+55*q-75 ) q congruent 4 modulo 6: 1/6 ( q^3-13*q^2+52*q-64 ) q congruent 5 modulo 6: 1/6 ( q^3-13*q^2+55*q-75 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 5, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 3 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 12, 1, 1, 12 ] ] k = 2: F-action on Pi is () [15,1,2] Dynkin type is A_2(q) + A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 phi1^2 ( q-3 ) q congruent 2 modulo 6: 1/2 q ( q^2-5*q+6 ) q congruent 3 modulo 6: 1/2 phi1^2 ( q-3 ) q congruent 4 modulo 6: 1/2 q ( q^2-5*q+6 ) q congruent 5 modulo 6: 1/2 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 3, 17, 20, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 3, 4 ] ] k = 3: F-action on Pi is () [15,1,3] Dynkin type is A_2(q) + A_1(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 6: 1/3 phi1 ( q^2-2 ) q congruent 2 modulo 6: 1/3 q phi2 ( q-2 ) q congruent 3 modulo 6: 1/3 q phi2 ( q-2 ) q congruent 4 modulo 6: 1/3 phi1 ( q^2-2 ) q congruent 5 modulo 6: 1/3 q phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 20, 20, 13, 6, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 12, 1, 5, 6 ] ] i = 16: Pi = [ 1, 2, 5 ] j = 1: Omega trivial k = 1: F-action on Pi is () [16,1,1] Dynkin type is 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 6: 1/12 ( q^3-14*q^2+61*q-84 ) q congruent 2 modulo 6: 1/12 ( q^3-13*q^2+52*q-60 ) q congruent 3 modulo 6: 1/12 ( q^3-14*q^2+63*q-90 ) q congruent 4 modulo 6: 1/12 ( q^3-13*q^2+50*q-56 ) q congruent 5 modulo 6: 1/12 ( q^3-14*q^2+63*q-90 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 16, 3, 3, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 12 ], [ 3, 2, 1, 4 ], [ 4, 1, 1, 3 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 2 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 6 ], [ 13, 1, 1, 24 ], [ 13, 2, 1, 8 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 2 ], [ 16, 2, 1, 4 ] ] k = 2: F-action on Pi is () [16,1,2] Dynkin type is 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 6: 1/12 phi1^2 ( q-4 ) q congruent 2 modulo 6: 1/12 q ( q^2-5*q+6 ) q congruent 3 modulo 6: 1/12 phi1 ( q^2-5*q+6 ) q congruent 4 modulo 6: 1/12 q phi1 ( q-4 ) q congruent 5 modulo 6: 1/12 phi1 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 3, 17, 3, 17, 17, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 3 ], [ 7, 1, 1, 12 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 6 ], [ 13, 1, 1, 24 ], [ 13, 2, 1, 8 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 2 ], [ 16, 2, 2, 4 ] ] k = 3: F-action on Pi is (2,5) [16,1,3] Dynkin type is 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 6: 1/4 q phi1 ( q-3 ) q congruent 2 modulo 6: 1/4 phi2 ( q^2-4*q+4 ) q congruent 3 modulo 6: 1/4 q phi1 ( q-3 ) q congruent 4 modulo 6: 1/4 q phi1 ( q-2 ) q congruent 5 modulo 6: 1/4 phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 19, 17, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 3, 4 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ], [ 16, 2, 3, 4 ] ] k = 4: F-action on Pi is (2,5) [16,1,4] Dynkin type is 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 6: 1/4 q phi1 ( q-3 ) q congruent 2 modulo 6: 1/4 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 6: 1/4 q phi1 ( q-3 ) q congruent 4 modulo 6: 1/4 q^2 ( q-3 ) q congruent 5 modulo 6: 1/4 ( q^3-4*q^2+q+10 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 8, 2, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 4 ], [ 4, 1, 1, 1 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 13, 1, 3, 4 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ], [ 16, 2, 4, 4 ] ] k = 5: F-action on Pi is (1,2,5) [16,1,5] Dynkin type is A_1(q^3) + T(phi2 phi3) Order of center |Z^F|: phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 phi1^2 ( q+2 ) q congruent 2 modulo 6: 1/6 q^2 phi2 q congruent 3 modulo 6: 1/6 q phi1 phi2 q congruent 4 modulo 6: 1/6 q phi1 ( q+2 ) q congruent 5 modulo 6: 1/6 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 21, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 8, 1, 2, 2 ], [ 13, 1, 2, 3 ], [ 13, 2, 2, 1 ], [ 14, 1, 3, 3 ], [ 14, 2, 2, 1 ], [ 16, 2, 5, 2 ] ] k = 6: F-action on Pi is (1,2,5) [16,1,6] Dynkin type is A_1(q^3) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 phi1 ( q^2-q-6 ) q congruent 2 modulo 6: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 6: 1/6 q phi2 ( q-3 ) q congruent 4 modulo 6: 1/6 phi1 ( q^2-4 ) q congruent 5 modulo 6: 1/6 q phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 3, 6 ], [ 3, 2, 3, 2 ], [ 8, 1, 1, 2 ], [ 13, 1, 2, 3 ], [ 13, 2, 2, 1 ], [ 14, 1, 3, 3 ], [ 14, 2, 2, 1 ], [ 16, 2, 6, 2 ] ] j = 2: Omega of order 3, action on Pi: <(1,5,2)> k = 1: F-action on Pi is () [16,2,1] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^3)).3 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 6: 1/2 ( q-5 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/2 ( q-4 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3, 16, 3, 3, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 2, 1, 4 ], [ 8, 1, 1, 2 ], [ 13, 2, 1, 2 ], [ 14, 2, 1, 2 ] ] k = 2: F-action on Pi is () [16,2,2] Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)).3 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 6: 1/2 phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/2 q q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 3, 17, 3, 17, 17, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 8, 1, 2, 2 ], [ 13, 2, 1, 2 ], [ 14, 2, 1, 2 ] ] k = 3: F-action on Pi is (2,5) [16,2,3] Dynkin type is A_1(q) + A_1(q^2) + T(phi1^2 phi2) 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 6: 0 q congruent 2 modulo 6: 1/2 ( q-2 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 19, 17, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 8, 1, 1, 2 ], [ 13, 2, 3, 2 ], [ 14, 2, 3, 2 ] ] k = 4: F-action on Pi is (2,5) [16,2,4] Dynkin type is A_1(q) + A_1(q^2) + T(phi1 phi2^2) 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 6: 0 q congruent 2 modulo 6: 1/2 ( q-2 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 8, 2, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 2, 2, 4 ], [ 8, 1, 2, 2 ], [ 13, 2, 3, 2 ], [ 14, 2, 3, 2 ] ] k = 5: F-action on Pi is (1,2,5) [16,2,5] Dynkin type is (A_1(q^3) + T(phi2 phi3)).3 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 6: phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: q q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 21, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 8, 1, 2, 2 ], [ 13, 2, 2, 1 ], [ 14, 2, 2, 1 ] ] k = 6: F-action on Pi is (1,2,5) [16,2,6] Dynkin type is (A_1(q^3) + T(phi1 phi3)).3 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 6: ( q-5 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: ( q-4 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 6, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 2, 3, 2 ], [ 8, 1, 1, 2 ], [ 13, 2, 2, 1 ], [ 14, 2, 2, 1 ] ] i = 17: Pi = [ 1, 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [17,1,1] Dynkin type is A_3(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 6: 1/8 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 6: 1/8 ( q^3-11*q^2+38*q-40 ) q congruent 3 modulo 6: 1/8 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 6: 1/8 ( q^3-11*q^2+38*q-40 ) q congruent 5 modulo 6: 1/8 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 3, 5, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 5 ], [ 5, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 8 ], [ 11, 1, 1, 4 ], [ 14, 1, 1, 12 ], [ 14, 2, 1, 4 ] ] k = 2: F-action on Pi is () [17,1,2] Dynkin type is A_3(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/4 phi1^2 ( q-3 ) q congruent 2 modulo 6: 1/4 q ( q^2-5*q+6 ) q congruent 3 modulo 6: 1/4 phi1^2 ( q-3 ) q congruent 4 modulo 6: 1/4 q ( q^2-5*q+6 ) q congruent 5 modulo 6: 1/4 phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 17, 20, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ] ] k = 3: F-action on Pi is () [17,1,3] Dynkin type is A_3(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/8 phi1^3 q congruent 2 modulo 6: 1/8 q phi1 ( q-2 ) q congruent 3 modulo 6: 1/8 phi1^3 q congruent 4 modulo 6: 1/8 q phi1 ( q-2 ) q congruent 5 modulo 6: 1/8 phi1^3 Fusion of maximal tori of C^F in those of G^F: [ 3, 17, 2, 13, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 11, 1, 2, 4 ], [ 14, 1, 2, 4 ], [ 14, 2, 3, 4 ] ] k = 4: F-action on Pi is (1,4) [17,1,4] Dynkin type is ^2A_3(q) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 Numbers of classes in class type: q congruent 1 modulo 6: 1/4 phi1^2 phi2 q congruent 2 modulo 6: 1/4 q^2 phi1 q congruent 3 modulo 6: 1/4 phi1^2 phi2 q congruent 4 modulo 6: 1/4 q^2 phi1 q congruent 5 modulo 6: 1/4 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 18, 8, 19, 25, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 1 ], [ 7, 1, 2, 2 ] ] k = 5: F-action on Pi is (1,4) [17,1,5] Dynkin type is ^2A_3(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/4 phi1 ( q^2-2*q-1 ) q congruent 2 modulo 6: 1/4 q phi1 ( q-2 ) q congruent 3 modulo 6: 1/4 phi1 ( q^2-2*q-1 ) q congruent 4 modulo 6: 1/4 q phi1 ( q-2 ) q congruent 5 modulo 6: 1/4 phi1 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 17, 3, 11, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 3 ], [ 7, 1, 2, 2 ], [ 14, 1, 1, 6 ], [ 14, 1, 2, 2 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 2 ] ] i = 18: Pi = [ 1, 2 ] j = 1: Omega trivial k = 1: F-action on Pi is () [18,1,1] Dynkin type is 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 6: 1/48 ( q^4-21*q^3+159*q^2-515*q+616 ) q congruent 2 modulo 6: 1/48 ( q^4-21*q^3+156*q^2-476*q+480 ) q congruent 3 modulo 6: 1/48 ( q^4-21*q^3+159*q^2-515*q+600 ) q congruent 4 modulo 6: 1/48 ( q^4-21*q^3+156*q^2-476*q+496 ) q congruent 5 modulo 6: 1/48 ( q^4-21*q^3+159*q^2-515*q+600 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 16, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 24 ], [ 3, 2, 1, 8 ], [ 4, 1, 1, 7 ], [ 5, 1, 1, 20 ], [ 6, 1, 1, 40 ], [ 7, 1, 1, 32 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 56 ], [ 11, 1, 1, 36 ], [ 12, 1, 1, 48 ], [ 13, 1, 1, 72 ], [ 13, 2, 1, 24 ], [ 14, 1, 1, 18 ], [ 14, 2, 1, 6 ], [ 15, 1, 1, 48 ], [ 16, 1, 1, 72 ], [ 16, 2, 1, 24 ], [ 17, 1, 1, 24 ] ] k = 2: F-action on Pi is () [18,1,2] Dynkin type is 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 6: 1/8 phi1^2 ( q^2-7*q+12 ) q congruent 2 modulo 6: 1/8 q ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 6: 1/8 phi1^2 ( q^2-7*q+12 ) q congruent 4 modulo 6: 1/8 q ( q^3-9*q^2+26*q-24 ) q congruent 5 modulo 6: 1/8 phi1^2 ( q^2-7*q+12 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 3, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 12 ], [ 3, 2, 1, 4 ], [ 4, 1, 1, 3 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 6 ], [ 12, 1, 3, 8 ], [ 13, 1, 1, 24 ], [ 13, 2, 1, 8 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 2 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 12 ], [ 16, 2, 1, 4 ], [ 16, 2, 2, 4 ], [ 17, 1, 2, 4 ] ] k = 3: F-action on Pi is () [18,1,3] Dynkin type is 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 6: 1/6 phi1 ( q^3-2*q^2-2*q+2 ) q congruent 2 modulo 6: 1/6 q phi2 ( q^2-4*q+4 ) q congruent 3 modulo 6: 1/6 q phi2 ( q^2-4*q+4 ) q congruent 4 modulo 6: 1/6 phi1 ( q^3-2*q^2-2*q+2 ) q congruent 5 modulo 6: 1/6 q phi2 ( q^2-4*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 20, 20, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 12, 1, 5, 6 ], [ 15, 1, 3, 6 ] ] k = 4: F-action on Pi is () [18,1,4] Dynkin type is 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 6: 1/8 q phi1^2 phi2 q congruent 2 modulo 6: 1/8 q^3 phi1 q congruent 3 modulo 6: 1/8 q phi1^2 phi2 q congruent 4 modulo 6: 1/8 q^3 phi1 q congruent 5 modulo 6: 1/8 q phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 19, 8, 8, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 13, 1, 3, 4 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ], [ 17, 1, 4, 4 ] ] k = 5: F-action on Pi is () [18,1,5] Dynkin type is 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 6: 1/16 q phi1^2 ( q-3 ) q congruent 2 modulo 6: 1/16 q phi1 ( q^2-4*q+4 ) q congruent 3 modulo 6: 1/16 q phi1^2 ( q-3 ) q congruent 4 modulo 6: 1/16 q phi1 ( q^2-4*q+4 ) q congruent 5 modulo 6: 1/16 q phi1^2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 17, 17, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 3 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 11, 1, 2, 12 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 8 ], [ 13, 2, 1, 8 ], [ 13, 2, 3, 8 ], [ 14, 1, 1, 6 ], [ 14, 1, 2, 4 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 4 ], [ 16, 1, 2, 24 ], [ 16, 2, 2, 8 ], [ 17, 1, 3, 8 ], [ 17, 1, 5, 8 ] ] k = 6: F-action on Pi is (1,2) [18,1,6] Dynkin type is A_1(q^2) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 q phi1 ( q^2-2 ) q congruent 2 modulo 6: 1/6 phi2 ( q^3-2*q^2+2 ) q congruent 3 modulo 6: 1/6 q phi1 ( q^2-2 ) q congruent 4 modulo 6: 1/6 q phi1 ( q^2-2 ) q congruent 5 modulo 6: 1/6 phi2 ( q^3-2*q^2+2 ) Fusion of maximal tori of C^F in those of G^F: [ 11, 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 4, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 4, 6 ] ] k = 7: F-action on Pi is (1,2) [18,1,7] Dynkin type is 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 6: 1/8 phi1^2 phi2 ( q-2 ) q congruent 2 modulo 6: 1/8 q^2 phi1 ( q-2 ) q congruent 3 modulo 6: 1/8 phi1^2 phi2 ( q-2 ) q congruent 4 modulo 6: 1/8 q^2 phi1 ( q-2 ) q congruent 5 modulo 6: 1/8 phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 3 ], [ 7, 1, 2, 4 ], [ 13, 1, 5, 8 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 2 ], [ 17, 1, 4, 4 ] ] k = 8: F-action on Pi is (1,2) [18,1,8] Dynkin type is 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 6: 1/16 phi1 ( q^3-6*q^2+7*q+6 ) q congruent 2 modulo 6: 1/16 q phi1 ( q^2-6*q+8 ) q congruent 3 modulo 6: 1/16 phi1 ( q^3-6*q^2+7*q+6 ) q congruent 4 modulo 6: 1/16 q phi1 ( q^2-6*q+8 ) q congruent 5 modulo 6: 1/16 phi1 ( q^3-6*q^2+7*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 5 ], [ 5, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 8 ], [ 11, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 5, 16 ], [ 13, 2, 3, 4 ], [ 14, 1, 1, 12 ], [ 14, 1, 2, 2 ], [ 14, 2, 1, 4 ], [ 14, 2, 3, 2 ], [ 16, 1, 3, 8 ], [ 16, 2, 3, 8 ], [ 17, 1, 1, 8 ], [ 17, 1, 5, 8 ] ] k = 9: F-action on Pi is (1,2) [18,1,9] Dynkin type is 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 6: 1/8 phi1^2 phi2 ( q-2 ) q congruent 2 modulo 6: 1/8 q phi2 ( q^2-4*q+4 ) q congruent 3 modulo 6: 1/8 phi1^2 phi2 ( q-2 ) q congruent 4 modulo 6: 1/8 q phi2 ( q^2-4*q+4 ) q congruent 5 modulo 6: 1/8 phi1^2 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 4 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 2, 8 ], [ 13, 1, 3, 4 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 16, 2, 3, 4 ], [ 16, 2, 4, 4 ], [ 17, 1, 2, 4 ] ] k = 10: F-action on Pi is (1,2) [18,1,10] Dynkin type is 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 6: 1/48 phi1 ( q^3-6*q^2+7*q+6 ) q congruent 2 modulo 6: 1/48 ( q^4-7*q^3+10*q^2+8*q-16 ) q congruent 3 modulo 6: 1/48 phi1 ( q^3-6*q^2+7*q+6 ) q congruent 4 modulo 6: 1/48 q ( q^3-7*q^2+10*q+8 ) q congruent 5 modulo 6: 1/48 phi2 ( q^3-8*q^2+21*q-22 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 3, 2, 2, 8 ], [ 4, 1, 1, 1 ], [ 6, 1, 2, 24 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 12 ], [ 10, 1, 2, 8 ], [ 11, 1, 2, 12 ], [ 12, 1, 6, 48 ], [ 13, 1, 3, 12 ], [ 13, 2, 3, 12 ], [ 14, 1, 2, 6 ], [ 14, 2, 3, 6 ], [ 16, 1, 4, 24 ], [ 16, 2, 4, 24 ], [ 17, 1, 3, 24 ] ] i = 19: Pi = [ 1, 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [19,1,1] Dynkin type is A_2(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 6: 1/72 ( q^4-19*q^3+130*q^2-381*q+413 ) q congruent 2 modulo 6: 1/72 ( q^4-19*q^3+130*q^2-372*q+360 ) q congruent 3 modulo 6: 1/72 ( q^4-19*q^3+130*q^2-381*q+405 ) q congruent 4 modulo 6: 1/72 ( q^4-19*q^3+130*q^2-372*q+368 ) q congruent 5 modulo 6: 1/72 ( q^4-19*q^3+130*q^2-381*q+405 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 9 ], [ 5, 1, 1, 18 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 36 ], [ 10, 1, 1, 18 ], [ 11, 1, 1, 36 ], [ 12, 1, 1, 24 ], [ 14, 1, 1, 36 ], [ 14, 2, 1, 12 ], [ 15, 1, 1, 36 ], [ 17, 1, 1, 72 ], [ 19, 2, 1, 24 ] ] k = 2: F-action on Pi is () [19,1,2] Dynkin type is A_2(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/12 phi1 ( q^3-8*q^2+18*q-9 ) q congruent 2 modulo 6: 1/12 q ( q^3-9*q^2+26*q-24 ) q congruent 3 modulo 6: 1/12 phi1 ( q^3-8*q^2+18*q-9 ) q congruent 4 modulo 6: 1/12 q ( q^3-9*q^2+26*q-24 ) q congruent 5 modulo 6: 1/12 phi1 ( q^3-8*q^2+18*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 3, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 3 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 6 ], [ 12, 1, 1, 12 ], [ 12, 1, 3, 4 ], [ 15, 1, 1, 6 ], [ 15, 1, 2, 6 ], [ 17, 1, 2, 12 ] ] k = 3: F-action on Pi is () [19,1,3] Dynkin type is A_2(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 6: 1/18 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 6: 1/18 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 6: 1/18 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 6: 1/18 phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 6: 1/18 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 20, 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 12, 1, 5, 6 ], [ 15, 1, 3, 9 ], [ 19, 2, 2, 6 ] ] k = 4: F-action on Pi is () [19,1,4] Dynkin type is A_2(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 q^2 phi1 phi2 q congruent 2 modulo 6: 1/6 q^2 phi1 phi2 q congruent 3 modulo 6: 1/6 q^2 phi1 phi2 q congruent 4 modulo 6: 1/6 q^2 phi1 phi2 q congruent 5 modulo 6: 1/6 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 20, 13, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 1, 3, 4 ], [ 12, 1, 5, 6 ], [ 15, 1, 3, 3 ] ] k = 5: F-action on Pi is () [19,1,5] Dynkin type is A_2(q) + T(phi3^2) Order of center |Z^F|: phi3^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/18 phi1 ( q^3+3*q^2+q-2 ) q congruent 2 modulo 6: 1/18 q phi2 ( q^2+q-3 ) q congruent 3 modulo 6: 1/18 q phi2 ( q^2+q-3 ) q congruent 4 modulo 6: 1/18 phi1 ( q^3+3*q^2+q-2 ) q congruent 5 modulo 6: 1/18 q phi2 ( q^2+q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 21, 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 12, 1, 5, 12 ], [ 14, 1, 3, 9 ], [ 14, 2, 2, 3 ], [ 19, 2, 3, 6 ], [ 19, 2, 4, 6 ] ] k = 6: F-action on Pi is () [19,1,6] Dynkin type is A_2(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/8 phi1 ( q^3-2*q^2-1 ) q congruent 2 modulo 6: 1/8 q^2 phi1 ( q-2 ) q congruent 3 modulo 6: 1/8 phi1 ( q^3-2*q^2-1 ) q congruent 4 modulo 6: 1/8 q^2 phi1 ( q-2 ) q congruent 5 modulo 6: 1/8 phi1 ( q^3-2*q^2-1 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 17, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 3, 8 ], [ 14, 1, 2, 4 ], [ 14, 2, 3, 4 ], [ 15, 1, 2, 4 ], [ 17, 1, 3, 8 ], [ 19, 2, 5, 8 ] ] k = 7: F-action on Pi is (1,3) [19,1,7] Dynkin type is ^2A_2(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 6: 1/4 phi1 phi2 phi6 q congruent 2 modulo 6: 1/4 q^3 phi1 q congruent 3 modulo 6: 1/4 phi1 phi2 phi6 q congruent 4 modulo 6: 1/4 q^3 phi1 q congruent 5 modulo 6: 1/4 phi1 phi2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 18, 8, 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 4, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 2 ], [ 17, 1, 4, 4 ] ] k = 8: F-action on Pi is (1,3) [19,1,8] Dynkin type is ^2A_2(q) + T(phi3 phi6) Order of center |Z^F|: phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 q phi1 phi3 q congruent 2 modulo 6: 1/6 phi2 ( q^3-q^2+q-2 ) q congruent 3 modulo 6: 1/6 q phi1 phi3 q congruent 4 modulo 6: 1/6 q phi1 phi3 q congruent 5 modulo 6: 1/6 phi2 ( q^3-q^2+q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 22, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 14, 1, 3, 3 ], [ 14, 2, 2, 1 ], [ 19, 2, 6, 6 ], [ 19, 2, 8, 2 ] ] k = 9: F-action on Pi is (1,3) [19,1,9] Dynkin type is ^2A_2(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/12 phi1^2 ( q^2-q-3 ) q congruent 2 modulo 6: 1/12 ( q^4-3*q^3+2*q+4 ) q congruent 3 modulo 6: 1/12 phi1^2 ( q^2-q-3 ) q congruent 4 modulo 6: 1/12 q phi1 ( q^2-2*q-2 ) q congruent 5 modulo 6: 1/12 phi2 ( q^3-4*q^2+4*q+1 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 17, 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 4, 1, 1, 3 ], [ 7, 1, 2, 6 ], [ 10, 1, 2, 6 ], [ 14, 1, 1, 6 ], [ 14, 1, 2, 6 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 6 ], [ 17, 1, 5, 12 ], [ 19, 2, 7, 12 ], [ 19, 2, 9, 4 ] ] i = 20: Pi = [ 1 ] j = 1: Omega trivial k = 1: F-action on Pi is () [20,1,1] Dynkin type is A_1(q) + T(phi1^5) Order of center |Z^F|: phi1^5 Numbers of classes in class type: q congruent 1 modulo 6: 1/720 ( q^5-30*q^4+345*q^3-1895*q^2+4934*q-4795 ) q congruent 2 modulo 6: 1/720 ( q^5-30*q^4+345*q^3-1880*q^2+4764*q-4320 ) q congruent 3 modulo 6: 1/720 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) q congruent 4 modulo 6: 1/720 ( q^5-30*q^4+345*q^3-1880*q^2+4724*q-4240 ) q congruent 5 modulo 6: 1/720 ( q^5-30*q^4+345*q^3-1895*q^2+4974*q-4995 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 60 ], [ 3, 2, 1, 20 ], [ 4, 1, 1, 15 ], [ 5, 1, 1, 66 ], [ 6, 1, 1, 140 ], [ 7, 1, 1, 120 ], [ 8, 1, 1, 30 ], [ 9, 1, 1, 120 ], [ 10, 1, 1, 300 ], [ 11, 1, 1, 210 ], [ 12, 1, 1, 240 ], [ 13, 1, 1, 360 ], [ 13, 2, 1, 120 ], [ 14, 1, 1, 90 ], [ 14, 2, 1, 30 ], [ 15, 1, 1, 480 ], [ 16, 1, 1, 540 ], [ 16, 2, 1, 180 ], [ 17, 1, 1, 360 ], [ 18, 1, 1, 720 ], [ 19, 1, 1, 720 ], [ 19, 2, 1, 240 ], [ 20, 2, 1, 240 ] ] k = 2: F-action on Pi is () [20,1,2] Dynkin type is 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 6: 1/48 phi1 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 2 modulo 6: 1/48 q ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 3 modulo 6: 1/48 phi1 ( q^4-13*q^3+58*q^2-99*q+45 ) q congruent 4 modulo 6: 1/48 q ( q^4-14*q^3+71*q^2-154*q+120 ) q congruent 5 modulo 6: 1/48 phi1 ( q^4-13*q^3+58*q^2-99*q+45 ) Fusion of maximal tori of C^F in those of G^F: [ 16, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 24 ], [ 3, 2, 1, 8 ], [ 4, 1, 1, 7 ], [ 5, 1, 1, 20 ], [ 6, 1, 1, 40 ], [ 7, 1, 1, 32 ], [ 8, 1, 1, 12 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 24 ], [ 9, 1, 2, 8 ], [ 10, 1, 1, 56 ], [ 11, 1, 1, 36 ], [ 11, 1, 2, 14 ], [ 12, 1, 1, 48 ], [ 12, 1, 3, 16 ], [ 13, 1, 1, 72 ], [ 13, 2, 1, 24 ], [ 14, 1, 1, 18 ], [ 14, 2, 1, 6 ], [ 15, 1, 1, 48 ], [ 15, 1, 2, 32 ], [ 16, 1, 1, 72 ], [ 16, 1, 2, 36 ], [ 16, 2, 1, 24 ], [ 16, 2, 2, 12 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 24 ], [ 18, 1, 1, 48 ], [ 18, 1, 2, 48 ], [ 19, 1, 2, 48 ] ] k = 3: F-action on Pi is () [20,1,3] Dynkin type is 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 6: 1/18 phi1^2 ( q^3-4*q^2+8 ) q congruent 2 modulo 6: 1/18 q phi2 ( q^3-7*q^2+16*q-12 ) q congruent 3 modulo 6: 1/18 q phi2 ( q^3-7*q^2+16*q-12 ) q congruent 4 modulo 6: 1/18 phi1^2 ( q^3-4*q^2+8 ) q congruent 5 modulo 6: 1/18 q phi2 ( q^3-7*q^2+16*q-12 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 3 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 12, 1, 5, 6 ], [ 15, 1, 1, 6 ], [ 15, 1, 3, 12 ], [ 18, 1, 3, 18 ], [ 19, 1, 3, 18 ], [ 19, 2, 2, 6 ], [ 20, 2, 2, 6 ] ] k = 4: F-action on Pi is () [20,1,4] Dynkin type is 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 6: 1/8 phi1^2 phi2 ( q^2-q-1 ) q congruent 2 modulo 6: 1/8 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 6: 1/8 phi1^2 phi2 ( q^2-q-1 ) q congruent 4 modulo 6: 1/8 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 6: 1/8 phi1^2 phi2 ( q^2-q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 19, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 13, 1, 3, 4 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ], [ 16, 1, 3, 4 ], [ 16, 2, 3, 4 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 8 ] ] k = 5: F-action on Pi is () [20,1,5] Dynkin type is 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 6: 1/16 phi1 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 2 modulo 6: 1/16 ( q^5-6*q^4+9*q^3-12*q+16 ) q congruent 3 modulo 6: 1/16 phi1 ( q^4-5*q^3+4*q^2+5*q+3 ) q congruent 4 modulo 6: 1/16 q phi1 ( q^3-5*q^2+4*q+4 ) q congruent 5 modulo 6: 1/16 ( q^5-6*q^4+9*q^3+q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 12 ], [ 3, 2, 1, 4 ], [ 4, 1, 1, 3 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 4 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 8 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 12 ], [ 12, 1, 3, 16 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 8 ], [ 13, 2, 1, 8 ], [ 13, 2, 3, 8 ], [ 14, 1, 1, 6 ], [ 14, 1, 2, 4 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 4 ], [ 15, 1, 2, 16 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 24 ], [ 16, 1, 3, 8 ], [ 16, 2, 1, 4 ], [ 16, 2, 2, 8 ], [ 16, 2, 3, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 17, 1, 5, 8 ], [ 18, 1, 2, 16 ], [ 18, 1, 5, 16 ], [ 19, 1, 6, 16 ], [ 19, 2, 5, 16 ], [ 20, 2, 9, 16 ] ] k = 6: F-action on Pi is () [20,1,6] Dynkin type is A_1(q) + T(phi1 phi5) Order of center |Z^F|: phi1 phi5 Numbers of classes in class type: q congruent 1 modulo 6: 1/5 q phi1 phi2 phi4 q congruent 2 modulo 6: 1/5 q phi1 phi2 phi4 q congruent 3 modulo 6: 1/5 q phi1 phi2 phi4 q congruent 4 modulo 6: 1/5 q phi1 phi2 phi4 q congruent 5 modulo 6: 1/5 q phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 9, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 1 ] ] k = 7: F-action on Pi is () [20,1,7] Dynkin type is 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 6: 1/6 q^2 phi1 phi2 ( q-2 ) q congruent 2 modulo 6: 1/6 q^2 phi1 phi2 ( q-2 ) q congruent 3 modulo 6: 1/6 q^2 phi1 phi2 ( q-2 ) q congruent 4 modulo 6: 1/6 q^2 phi1 phi2 ( q-2 ) q congruent 5 modulo 6: 1/6 q^2 phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 3, 4 ], [ 12, 1, 5, 6 ], [ 15, 1, 2, 2 ], [ 15, 1, 3, 6 ], [ 18, 1, 3, 6 ], [ 19, 1, 4, 6 ] ] k = 8: F-action on Pi is () [20,1,8] Dynkin type is A_1(q) + T(phi2 phi3 phi6) Order of center |Z^F|: phi2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 phi1 ( q^4+q^3+2*q^2+q-2 ) q congruent 2 modulo 6: 1/6 q phi1 phi2 ( q^2+2 ) q congruent 3 modulo 6: 1/6 q phi1 ( q^3+q^2+2*q+1 ) q congruent 4 modulo 6: 1/6 q phi1 phi2 ( q^2+2 ) q congruent 5 modulo 6: 1/6 q phi2 ( q^3-q^2+2*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 22, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 2 ], [ 13, 1, 2, 3 ], [ 13, 2, 2, 1 ], [ 14, 1, 3, 3 ], [ 14, 2, 2, 1 ], [ 19, 1, 8, 6 ], [ 19, 2, 6, 6 ], [ 19, 2, 8, 2 ], [ 20, 2, 3, 6 ], [ 20, 2, 5, 2 ] ] k = 9: F-action on Pi is () [20,1,9] Dynkin type is 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 6: 1/8 phi1^2 phi2 phi6 q congruent 2 modulo 6: 1/8 q^3 phi1^2 q congruent 3 modulo 6: 1/8 phi1^2 phi2 phi6 q congruent 4 modulo 6: 1/8 q^3 phi1^2 q congruent 5 modulo 6: 1/8 phi1^2 phi2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 8, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 4 ], [ 4, 1, 1, 1 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 2 ], [ 13, 1, 3, 4 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ], [ 16, 1, 4, 4 ], [ 16, 2, 4, 4 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 8 ], [ 19, 1, 7, 8 ] ] k = 10: F-action on Pi is () [20,1,10] Dynkin type is A_1(q) + T(phi1 phi3^2) Order of center |Z^F|: phi1 phi3^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/18 phi1 ( q^4+q^3-2*q^2-7*q-14 ) q congruent 2 modulo 6: 1/18 q^2 phi2^2 ( q-2 ) q congruent 3 modulo 6: 1/18 q phi2 ( q^3-q^2-2*q-3 ) q congruent 4 modulo 6: 1/18 phi1 ( q^4+q^3-2*q^2-4*q-8 ) q congruent 5 modulo 6: 1/18 q phi2 ( q^3-q^2-2*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 6, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 12, 1, 5, 12 ], [ 13, 1, 2, 9 ], [ 13, 2, 2, 3 ], [ 14, 1, 3, 9 ], [ 14, 2, 2, 3 ], [ 15, 1, 3, 6 ], [ 19, 1, 5, 18 ], [ 19, 2, 3, 6 ], [ 19, 2, 4, 6 ], [ 20, 2, 7, 6 ], [ 20, 2, 8, 6 ] ] k = 11: F-action on Pi is () [20,1,11] Dynkin type is 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 6: 1/48 phi1^2 ( q^3-4*q^2-2*q+11 ) q congruent 2 modulo 6: 1/48 q phi1 phi2 ( q^2-6*q+8 ) q congruent 3 modulo 6: 1/48 phi1 ( q^4-5*q^3+2*q^2+13*q-3 ) q congruent 4 modulo 6: 1/48 q phi1 phi2 ( q^2-6*q+8 ) q congruent 5 modulo 6: 1/48 ( q^5-6*q^4+7*q^3+11*q^2-24*q+27 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 3, 2, 2, 8 ], [ 4, 1, 1, 3 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 6 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 18 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 24 ], [ 13, 2, 1, 8 ], [ 13, 2, 3, 24 ], [ 14, 1, 1, 6 ], [ 14, 1, 2, 12 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 12 ], [ 16, 1, 2, 36 ], [ 16, 1, 4, 24 ], [ 16, 2, 2, 12 ], [ 16, 2, 4, 24 ], [ 17, 1, 3, 24 ], [ 17, 1, 5, 24 ], [ 18, 1, 5, 48 ], [ 19, 1, 9, 48 ], [ 19, 2, 7, 48 ], [ 19, 2, 9, 16 ], [ 20, 2, 4, 48 ], [ 20, 2, 6, 16 ] ] j = 2: Omega of order 3, action on Pi: <()> k = 1: F-action on Pi is () [20,2,1] Dynkin type is (A_1(q) + T(phi1^5)).3 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 6: 1/6 ( q-7 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/6 ( q-4 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 13, 2, 1, 6 ], [ 14, 2, 1, 6 ], [ 19, 2, 1, 12 ] ] k = 2: F-action on Pi is () [20,2,2] Dynkin type is (A_1(q) + T(phi1^3 phi3)).3 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 6: 2/3 phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 2/3 phi1 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 5, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 19, 2, 2, 3 ] ] k = 3: F-action on Pi is () [20,2,3] Dynkin type is A_1(q) + T(phi2 phi3 phi6) 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 6: 0 q congruent 2 modulo 6: 1/3 phi2 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 22, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 2 ], [ 19, 2, 6, 6 ] ] k = 4: F-action on Pi is () [20,2,4] Dynkin type is A_1(q) + T(phi1^2 phi2^3) 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 6: 0 q congruent 2 modulo 6: 1/6 ( q-2 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/6 ( q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 2 ], [ 13, 2, 3, 6 ], [ 14, 2, 3, 6 ], [ 19, 2, 7, 12 ] ] k = 5: F-action on Pi is () [20,2,5] Dynkin type is (A_1(q) + T(phi2 phi3 phi6)).3 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 6: phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: q q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 22, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 2 ], [ 13, 2, 2, 1 ], [ 14, 2, 2, 1 ], [ 19, 2, 8, 2 ] ] k = 6: F-action on Pi is () [20,2,6] Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).3 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 6: 1/2 phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/2 q q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 17, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 2 ], [ 13, 2, 1, 2 ], [ 14, 2, 1, 2 ], [ 19, 2, 9, 4 ] ] k = 7: F-action on Pi is () [20,2,7] Dynkin type is (A_1(q) + T(phi1 phi3^2)).3 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 6: 1/3 ( q-7 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/3 ( q-4 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 6, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 13, 2, 2, 3 ], [ 14, 2, 2, 3 ], [ 19, 2, 3, 6 ] ] k = 8: F-action on Pi is () [20,2,8] Dynkin type is (A_1(q) + T(phi1 phi3^2)).3 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 6: 1/3 phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/3 phi1 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 6, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 19, 2, 4, 6 ] ] k = 9: F-action on Pi is () [20,2,9] Dynkin type is A_1(q) + T(phi1^3 phi2^2) 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 6: 0 q congruent 2 modulo 6: 1/2 ( q-2 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 13, 2, 3, 2 ], [ 14, 2, 3, 2 ], [ 19, 2, 5, 4 ] ] i = 21: Pi = [ ] j = 1: Omega trivial k = 1: F-action on Pi is () [21,1,1] Dynkin type is A_0(q) + T(phi1^6) Order of center |Z^F|: phi1^6 Numbers of classes in class type: q congruent 1 modulo 6: 1/51840 phi1 ( q^5-41*q^4+664*q^3-5356*q^2+21623*q-35035 ) q congruent 2 modulo 6: 1/51840 ( q^6-42*q^5+705*q^4-6020*q^3+27324*q^2-61488*q+51840 ) q congruent 3 modulo 6: 1/51840 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) q congruent 4 modulo 6: 1/51840 phi1 ( q^5-41*q^4+664*q^3-5356*q^2+21488*q-33280 ) q congruent 5 modulo 6: 1/51840 ( q^6-42*q^5+705*q^4-6020*q^3+27459*q^2-63378*q+57915 ) Fusion of maximal tori of C^F in those of G^F: [ 1 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 36 ], [ 3, 1, 1, 240 ], [ 3, 2, 1, 80 ], [ 4, 1, 1, 27 ], [ 5, 1, 1, 216 ], [ 6, 1, 1, 720 ], [ 7, 1, 1, 540 ], [ 8, 1, 1, 72 ], [ 9, 1, 1, 432 ], [ 10, 1, 1, 2160 ], [ 11, 1, 1, 1080 ], [ 12, 1, 1, 1440 ], [ 13, 1, 1, 3240 ], [ 13, 2, 1, 1080 ], [ 14, 1, 1, 270 ], [ 14, 2, 1, 90 ], [ 15, 1, 1, 4320 ], [ 16, 1, 1, 6480 ], [ 16, 2, 1, 2160 ], [ 17, 1, 1, 2160 ], [ 18, 1, 1, 12960 ], [ 19, 1, 1, 8640 ], [ 19, 2, 1, 2880 ], [ 20, 1, 1, 25920 ], [ 20, 2, 1, 8640 ], [ 21, 2, 1, 17280 ], [ 21, 3, 1, 17280 ] ] k = 2: F-action on Pi is () [21,1,2] Dynkin type is A_0(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 6: 1/1152 phi1^2 ( q^4-8*q^3+8*q^2+44*q-69 ) q congruent 2 modulo 6: 1/1152 ( q^6-10*q^5+25*q^4+20*q^3-116*q^2+272*q-384 ) q congruent 3 modulo 6: 1/1152 phi1 ( q^5-9*q^4+16*q^3+36*q^2-81*q-27 ) q congruent 4 modulo 6: 1/1152 q phi1 ( q^4-9*q^3+16*q^2+36*q-80 ) q congruent 5 modulo 6: 1/1152 ( q^6-10*q^5+25*q^4+20*q^3-149*q^2+374*q-645 ) 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, 12 ], [ 3, 1, 2, 32 ], [ 3, 2, 2, 32 ], [ 4, 1, 1, 3 ], [ 6, 1, 2, 96 ], [ 7, 1, 1, 36 ], [ 7, 1, 2, 24 ], [ 8, 1, 2, 24 ], [ 10, 1, 2, 96 ], [ 11, 1, 2, 72 ], [ 12, 1, 6, 192 ], [ 13, 1, 1, 72 ], [ 13, 1, 3, 144 ], [ 13, 2, 1, 24 ], [ 13, 2, 3, 144 ], [ 14, 1, 1, 6 ], [ 14, 1, 2, 24 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 24 ], [ 16, 1, 2, 144 ], [ 16, 1, 4, 288 ], [ 16, 2, 2, 48 ], [ 16, 2, 4, 288 ], [ 17, 1, 3, 144 ], [ 17, 1, 5, 48 ], [ 18, 1, 5, 288 ], [ 18, 1, 10, 576 ], [ 19, 1, 9, 192 ], [ 19, 2, 7, 192 ], [ 19, 2, 9, 64 ], [ 20, 1, 11, 576 ], [ 20, 2, 4, 576 ], [ 20, 2, 6, 192 ], [ 21, 2, 14, 384 ], [ 21, 3, 18, 384 ], [ 21, 3, 27, 1152 ] ] k = 3: F-action on Pi is () [21,1,3] Dynkin type is A_0(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 6: 1/192 phi1 phi2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 2 modulo 6: 1/192 ( q^6-10*q^5+29*q^4-8*q^3-76*q^2+176*q-192 ) q congruent 3 modulo 6: 1/192 phi1 phi2 ( q^4-10*q^3+30*q^2-18*q-27 ) q congruent 4 modulo 6: 1/192 q phi1 ( q^4-9*q^3+20*q^2+12*q-48 ) q congruent 5 modulo 6: 1/192 ( q^6-10*q^5+29*q^4-8*q^3-73*q^2+146*q-213 ) 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, 8 ], [ 3, 1, 1, 24 ], [ 3, 2, 1, 8 ], [ 4, 1, 1, 7 ], [ 5, 1, 1, 20 ], [ 6, 1, 1, 40 ], [ 7, 1, 1, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 1, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 24 ], [ 9, 1, 2, 16 ], [ 10, 1, 1, 56 ], [ 11, 1, 1, 36 ], [ 11, 1, 2, 28 ], [ 12, 1, 1, 48 ], [ 12, 1, 3, 32 ], [ 13, 1, 1, 72 ], [ 13, 1, 3, 24 ], [ 13, 1, 5, 48 ], [ 13, 2, 1, 24 ], [ 13, 2, 3, 24 ], [ 14, 1, 1, 18 ], [ 14, 1, 2, 4 ], [ 14, 2, 1, 6 ], [ 14, 2, 3, 4 ], [ 15, 1, 1, 48 ], [ 15, 1, 2, 64 ], [ 16, 1, 1, 72 ], [ 16, 1, 2, 72 ], [ 16, 1, 3, 48 ], [ 16, 2, 1, 24 ], [ 16, 2, 2, 24 ], [ 16, 2, 3, 48 ], [ 17, 1, 1, 24 ], [ 17, 1, 2, 48 ], [ 17, 1, 3, 8 ], [ 17, 1, 5, 24 ], [ 18, 1, 1, 48 ], [ 18, 1, 2, 96 ], [ 18, 1, 5, 48 ], [ 18, 1, 8, 96 ], [ 19, 1, 2, 96 ], [ 19, 1, 6, 32 ], [ 19, 2, 5, 32 ], [ 20, 1, 2, 96 ], [ 20, 1, 5, 96 ], [ 20, 2, 9, 96 ], [ 21, 3, 19, 192 ] ] k = 4: F-action on Pi is () [21,1,4] Dynkin type is A_0(q) + T(phi3^3) Order of center |Z^F|: phi3^3 Numbers of classes in class type: q congruent 1 modulo 6: 1/648 phi1 ( q^5+4*q^4-2*q^3-19*q^2-58*q-88 ) q congruent 2 modulo 6: 1/648 q phi2 ( q^4+2*q^3-8*q^2-9*q+18 ) q congruent 3 modulo 6: 1/648 q phi2 ( q^4+2*q^3-8*q^2-9*q+18 ) q congruent 4 modulo 6: 1/648 phi1 ( q^5+4*q^4-2*q^3-19*q^2-58*q-88 ) q congruent 5 modulo 6: 1/648 q phi2 ( q^4+2*q^3-8*q^2-9*q+18 ) Fusion of maximal tori of C^F in those of G^F: [ 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 24 ], [ 3, 2, 1, 8 ], [ 12, 1, 5, 72 ], [ 14, 1, 3, 27 ], [ 14, 2, 2, 9 ], [ 19, 1, 5, 216 ], [ 19, 2, 3, 72 ], [ 19, 2, 4, 72 ], [ 21, 2, 2, 216 ], [ 21, 2, 6, 216 ], [ 21, 3, 9, 216 ], [ 21, 3, 10, 216 ] ] k = 5: F-action on Pi is () [21,1,5] Dynkin type is A_0(q) + T(phi1^4 phi3) Order of center |Z^F|: phi1^4 phi3 Numbers of classes in class type: q congruent 1 modulo 6: 1/216 phi1^2 ( q^4-7*q^3+12*q^2+8*q-32 ) q congruent 2 modulo 6: 1/216 q phi2 ( q^4-10*q^3+37*q^2-60*q+36 ) q congruent 3 modulo 6: 1/216 q phi2 ( q^4-10*q^3+37*q^2-60*q+36 ) q congruent 4 modulo 6: 1/216 phi1^2 ( q^4-7*q^3+12*q^2+8*q-32 ) q congruent 5 modulo 6: 1/216 q phi2 ( q^4-10*q^3+37*q^2-60*q+36 ) 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, 6 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 9 ], [ 5, 1, 1, 18 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 18 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 36 ], [ 10, 1, 1, 18 ], [ 11, 1, 1, 36 ], [ 12, 1, 1, 24 ], [ 12, 1, 5, 6 ], [ 14, 1, 1, 36 ], [ 14, 2, 1, 12 ], [ 15, 1, 1, 36 ], [ 15, 1, 3, 18 ], [ 17, 1, 1, 72 ], [ 18, 1, 3, 54 ], [ 19, 1, 1, 72 ], [ 19, 1, 3, 36 ], [ 19, 2, 1, 24 ], [ 19, 2, 2, 12 ], [ 20, 1, 3, 108 ], [ 20, 2, 2, 36 ], [ 21, 2, 5, 72 ], [ 21, 3, 2, 72 ], [ 21, 3, 4, 72 ] ] k = 6: F-action on Pi is () [21,1,6] Dynkin type is A_0(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 6: 1/108 phi1 ( q^5-2*q^4-5*q^3-7*q^2+5*q+62 ) q congruent 2 modulo 6: 1/108 q phi2 ( q^4-4*q^3+q^2-3*q+18 ) q congruent 3 modulo 6: 1/108 q phi2 ( q^4-4*q^3+q^2-3*q+27 ) q congruent 4 modulo 6: 1/108 phi1 ( q^5-2*q^4-5*q^3-7*q^2-4*q+44 ) q congruent 5 modulo 6: 1/108 q phi2 ( q^4-4*q^3+q^2-3*q+27 ) 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, 6 ], [ 3, 1, 3, 18 ], [ 3, 2, 1, 2 ], [ 3, 2, 3, 6 ], [ 6, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 12, 1, 5, 12 ], [ 13, 1, 2, 27 ], [ 13, 2, 2, 9 ], [ 14, 1, 3, 9 ], [ 14, 2, 2, 3 ], [ 15, 1, 3, 18 ], [ 16, 1, 6, 54 ], [ 16, 2, 6, 18 ], [ 19, 1, 3, 36 ], [ 19, 1, 5, 18 ], [ 19, 2, 2, 12 ], [ 19, 2, 3, 6 ], [ 19, 2, 4, 6 ], [ 20, 1, 10, 54 ], [ 20, 2, 7, 18 ], [ 20, 2, 8, 18 ], [ 21, 2, 4, 36 ], [ 21, 2, 7, 36 ], [ 21, 3, 3, 36 ], [ 21, 3, 7, 36 ], [ 21, 3, 8, 36 ] ] k = 7: F-action on Pi is () [21,1,7] Dynkin type is A_0(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 6: 1/96 phi1^3 phi2 ( q^2-3 ) q congruent 2 modulo 6: 1/96 q^2 phi1^2 ( q^2-4 ) q congruent 3 modulo 6: 1/96 phi1^3 phi2 ( q^2-3 ) q congruent 4 modulo 6: 1/96 q^2 phi1^2 ( q^2-4 ) q congruent 5 modulo 6: 1/96 phi1^3 phi2 ( q^2-3 ) Fusion of maximal tori of C^F in those of G^F: [ 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 3 ], [ 7, 1, 2, 12 ], [ 13, 1, 5, 24 ], [ 14, 1, 1, 6 ], [ 14, 2, 1, 2 ], [ 17, 1, 4, 24 ], [ 18, 1, 7, 48 ], [ 21, 2, 15, 32 ] ] k = 8: F-action on Pi is () [21,1,8] Dynkin type is A_0(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 6: 1/16 phi1 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 2 modulo 6: 1/16 q^3 phi1 phi2 ( q-2 ) q congruent 3 modulo 6: 1/16 phi1 phi2^2 ( q^3-3*q^2+3*q-3 ) q congruent 4 modulo 6: 1/16 q^3 phi1 phi2 ( q-2 ) q congruent 5 modulo 6: 1/16 phi1 phi2^2 ( q^3-3*q^2+3*q-3 ) 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, 2 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 4 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 2, 4 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 2, 8 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 16, 2, 3, 4 ], [ 16, 2, 4, 4 ], [ 17, 1, 2, 4 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 8 ], [ 18, 1, 9, 8 ], [ 19, 1, 7, 8 ], [ 20, 1, 4, 8 ], [ 20, 1, 9, 8 ] ] k = 9: F-action on Pi is () [21,1,9] Dynkin type is A_0(q) + T(phi1^2 phi5) Order of center |Z^F|: phi1^2 phi5 Numbers of classes in class type: q congruent 1 modulo 6: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 2 modulo 6: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 3 modulo 6: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 4 modulo 6: 1/10 q phi1 phi2 phi4 ( q-2 ) q congruent 5 modulo 6: 1/10 q phi1 phi2 phi4 ( q-2 ) 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, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 1 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 2 ], [ 20, 1, 6, 5 ] ] k = 10: F-action on Pi is () [21,1,10] Dynkin type is A_0(q) + T(phi3 phi6^2) Order of center |Z^F|: phi3 phi6^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/72 q phi1 ( q^4-2*q^2-3*q-14 ) q congruent 2 modulo 6: 1/72 phi2 ( q^5-2*q^4-q^2-10*q+24 ) q congruent 3 modulo 6: 1/72 q phi1 ( q^4-2*q^2-3*q-6 ) q congruent 4 modulo 6: 1/72 q phi1 ( q^4-2*q^2-3*q-14 ) q congruent 5 modulo 6: 1/72 phi2 ( q^5-2*q^4-q^2-10*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 3, 2, 2, 8 ], [ 12, 1, 4, 24 ], [ 14, 1, 3, 3 ], [ 14, 2, 2, 1 ], [ 19, 1, 8, 24 ], [ 19, 2, 6, 24 ], [ 19, 2, 8, 8 ], [ 21, 2, 8, 24 ], [ 21, 2, 12, 24 ], [ 21, 3, 15, 24 ], [ 21, 3, 24, 72 ] ] k = 11: F-action on Pi is () [21,1,11] Dynkin type is A_0(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 6: 1/36 q phi1^2 phi2 ( q^2-4 ) q congruent 2 modulo 6: 1/36 q phi1^2 phi2 ( q^2-4 ) q congruent 3 modulo 6: 1/36 q phi1 ( q^4-5*q^2+6 ) q congruent 4 modulo 6: 1/36 q phi1^2 phi2 ( q^2-4 ) q congruent 5 modulo 6: 1/36 q phi1^2 phi2 ( q^2-4 ) Fusion of maximal tori of C^F in those of G^F: [ 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 4, 1, 1, 3 ], [ 7, 1, 2, 6 ], [ 10, 1, 2, 6 ], [ 12, 1, 4, 6 ], [ 14, 1, 1, 6 ], [ 14, 1, 2, 6 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 6 ], [ 17, 1, 5, 12 ], [ 18, 1, 6, 18 ], [ 19, 1, 9, 12 ], [ 19, 2, 7, 12 ], [ 19, 2, 9, 4 ], [ 21, 2, 11, 12 ], [ 21, 3, 16, 12 ], [ 21, 3, 25, 36 ] ] k = 12: F-action on Pi is () [21,1,12] Dynkin type is A_0(q) + T(phi2^2 phi3 phi6) Order of center |Z^F|: phi2^2 phi3 phi6 Numbers of classes in class type: q congruent 1 modulo 6: 1/36 phi1^2 ( q^4+q^3+2*q^2-q-6 ) q congruent 2 modulo 6: 1/36 q phi2 ( q^4-2*q^3+3*q^2-7*q+2 ) q congruent 3 modulo 6: 1/36 q phi1 ( q^4+q^2-3*q-3 ) q congruent 4 modulo 6: 1/36 q phi1 ( q^4+q^2-3*q-8 ) q congruent 5 modulo 6: 1/36 q phi1 phi2 ( q^3-q^2+2*q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 6 ], [ 8, 1, 2, 6 ], [ 12, 1, 6, 12 ], [ 13, 1, 2, 9 ], [ 13, 2, 2, 3 ], [ 14, 1, 3, 3 ], [ 14, 2, 2, 1 ], [ 16, 1, 5, 18 ], [ 16, 2, 5, 6 ], [ 19, 1, 8, 6 ], [ 19, 2, 6, 6 ], [ 19, 2, 8, 2 ], [ 20, 1, 8, 18 ], [ 20, 2, 3, 18 ], [ 20, 2, 5, 6 ], [ 21, 2, 13, 12 ], [ 21, 3, 17, 12 ], [ 21, 3, 26, 36 ] ] k = 13: F-action on Pi is () [21,1,13] Dynkin type is A_0(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 6: 1/24 q^3 phi1^2 phi2 q congruent 2 modulo 6: 1/24 q phi2^2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 6: 1/24 q^3 phi1^2 phi2 q congruent 4 modulo 6: 1/24 q^3 phi1^2 phi2 q congruent 5 modulo 6: 1/24 q phi2^2 ( q^3-3*q^2+4*q-4 ) 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, 2 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 3, 8 ], [ 12, 1, 5, 6 ], [ 14, 1, 2, 4 ], [ 14, 2, 3, 4 ], [ 15, 1, 2, 4 ], [ 15, 1, 3, 6 ], [ 17, 1, 3, 8 ], [ 18, 1, 3, 6 ], [ 19, 1, 4, 12 ], [ 19, 1, 6, 8 ], [ 19, 2, 5, 8 ], [ 20, 1, 7, 12 ], [ 21, 3, 20, 24 ] ] k = 14: F-action on Pi is () [21,1,14] Dynkin type is A_0(q) + T(phi9) Order of center |Z^F|: phi9 Numbers of classes in class type: q congruent 1 modulo 6: 1/9 phi1 phi3 ( q^3+2 ) q congruent 2 modulo 6: 1/9 q^3 phi2 phi6 q congruent 3 modulo 6: 1/9 q^3 phi2 phi6 q congruent 4 modulo 6: 1/9 phi1 phi3 ( q^3+2 ) q congruent 5 modulo 6: 1/9 q^3 phi2 phi6 Fusion of maximal tori of C^F in those of G^F: [ 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 3, 3 ], [ 3, 2, 3, 1 ], [ 21, 2, 3, 3 ] ] k = 15: F-action on Pi is () [21,1,15] Dynkin type is A_0(q) + T(phi3 phi12) Order of center |Z^F|: phi3 phi12 Numbers of classes in class type: q congruent 1 modulo 6: 1/12 q^2 phi1 phi2 phi3 q congruent 2 modulo 6: 1/12 q^2 phi1 phi2 phi3 q congruent 3 modulo 6: 1/12 q^2 phi1 phi2 phi3 q congruent 4 modulo 6: 1/12 q^2 phi1 phi2 phi3 q congruent 5 modulo 6: 1/12 q^2 phi1 phi2 phi3 Fusion of maximal tori of C^F in those of G^F: [ 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 14, 1, 3, 3 ], [ 14, 2, 2, 1 ], [ 21, 2, 9, 4 ] ] k = 16: F-action on Pi is () [21,1,16] Dynkin type is A_0(q) + T(phi1^5 phi2) Order of center |Z^F|: phi1^5 phi2 Numbers of classes in class type: q congruent 1 modulo 6: 1/1440 phi1 ( q^5-19*q^4+136*q^3-444*q^2+575*q-105 ) q congruent 2 modulo 6: 1/1440 q ( q^5-20*q^4+155*q^3-580*q^2+1044*q-720 ) q congruent 3 modulo 6: 1/1440 phi1 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) q congruent 4 modulo 6: 1/1440 q phi1 ( q^4-19*q^3+136*q^2-444*q+560 ) q congruent 5 modulo 6: 1/1440 phi1 ( q^5-19*q^4+136*q^3-444*q^2+615*q-225 ) Fusion of maximal tori of C^F in those of G^F: [ 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 60 ], [ 3, 2, 1, 20 ], [ 4, 1, 1, 15 ], [ 5, 1, 1, 66 ], [ 6, 1, 1, 140 ], [ 7, 1, 1, 120 ], [ 8, 1, 1, 30 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 120 ], [ 9, 1, 2, 12 ], [ 10, 1, 1, 300 ], [ 11, 1, 1, 210 ], [ 11, 1, 2, 30 ], [ 12, 1, 1, 240 ], [ 12, 1, 3, 40 ], [ 13, 1, 1, 360 ], [ 13, 2, 1, 120 ], [ 14, 1, 1, 90 ], [ 14, 2, 1, 30 ], [ 15, 1, 1, 480 ], [ 15, 1, 2, 120 ], [ 16, 1, 1, 540 ], [ 16, 1, 2, 180 ], [ 16, 2, 1, 180 ], [ 16, 2, 2, 60 ], [ 17, 1, 1, 360 ], [ 17, 1, 2, 60 ], [ 18, 1, 1, 720 ], [ 18, 1, 2, 360 ], [ 19, 1, 1, 720 ], [ 19, 1, 2, 240 ], [ 19, 2, 1, 240 ], [ 20, 1, 1, 720 ], [ 20, 1, 2, 720 ], [ 20, 2, 1, 240 ], [ 21, 3, 6, 480 ] ] k = 17: F-action on Pi is () [21,1,17] Dynkin type is A_0(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 6: 1/96 phi1^3 ( q^3-q^2-7*q-1 ) q congruent 2 modulo 6: 1/96 ( q^6-4*q^5-q^4+16*q^3-36*q^2+64*q-32 ) q congruent 3 modulo 6: 1/96 phi1^2 phi2 ( q^3-3*q^2-3*q+9 ) q congruent 4 modulo 6: 1/96 q^2 phi1 ( q^3-3*q^2-4*q+12 ) q congruent 5 modulo 6: 1/96 ( q^6-4*q^5-q^4+16*q^3-41*q^2+68*q-71 ) Fusion of maximal tori of C^F in those of G^F: [ 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 12 ], [ 3, 1, 2, 8 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 8 ], [ 4, 1, 1, 3 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 12 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 12 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 6 ], [ 9, 1, 2, 12 ], [ 10, 1, 1, 12 ], [ 10, 1, 2, 24 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 18 ], [ 12, 1, 2, 16 ], [ 12, 1, 3, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 24 ], [ 13, 2, 1, 8 ], [ 13, 2, 3, 24 ], [ 14, 1, 1, 6 ], [ 14, 1, 2, 12 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 12 ], [ 15, 1, 2, 24 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 36 ], [ 16, 1, 3, 24 ], [ 16, 1, 4, 24 ], [ 16, 2, 1, 4 ], [ 16, 2, 2, 12 ], [ 16, 2, 3, 24 ], [ 16, 2, 4, 24 ], [ 17, 1, 2, 12 ], [ 17, 1, 3, 24 ], [ 17, 1, 5, 24 ], [ 18, 1, 2, 24 ], [ 18, 1, 5, 48 ], [ 18, 1, 9, 48 ], [ 19, 1, 6, 48 ], [ 19, 1, 9, 48 ], [ 19, 2, 5, 48 ], [ 19, 2, 7, 48 ], [ 19, 2, 9, 16 ], [ 20, 1, 5, 48 ], [ 20, 1, 11, 48 ], [ 20, 2, 4, 48 ], [ 20, 2, 6, 16 ], [ 20, 2, 9, 48 ], [ 21, 2, 18, 96 ], [ 21, 3, 14, 32 ], [ 21, 3, 21, 96 ], [ 21, 3, 23, 96 ] ] k = 18: F-action on Pi is () [21,1,18] Dynkin type is A_0(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 6: 1/96 phi1^2 phi2 ( q^3-3*q^2+3*q-3 ) q congruent 2 modulo 6: 1/96 q^3 phi1^2 ( q-2 ) q congruent 3 modulo 6: 1/96 phi1^2 phi2 ( q^3-3*q^2+3*q-3 ) q congruent 4 modulo 6: 1/96 q^3 phi1^2 ( q-2 ) q congruent 5 modulo 6: 1/96 phi1^2 phi2 ( q^3-3*q^2+3*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, 6 ], [ 3, 1, 2, 8 ], [ 3, 2, 2, 8 ], [ 4, 1, 1, 1 ], [ 6, 1, 2, 24 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 12 ], [ 10, 1, 2, 8 ], [ 11, 1, 2, 12 ], [ 12, 1, 6, 48 ], [ 13, 1, 3, 12 ], [ 13, 2, 3, 12 ], [ 14, 1, 2, 6 ], [ 14, 2, 3, 6 ], [ 16, 1, 4, 24 ], [ 16, 2, 4, 24 ], [ 17, 1, 3, 24 ], [ 17, 1, 4, 4 ], [ 18, 1, 4, 24 ], [ 18, 1, 10, 48 ], [ 19, 1, 7, 16 ], [ 20, 1, 9, 48 ] ] k = 19: F-action on Pi is () [21,1,19] Dynkin type is A_0(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 6: 1/32 phi1^2 phi2 ( q^3-3*q^2-q+5 ) q congruent 2 modulo 6: 1/32 q^2 phi1 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 6: 1/32 phi1^2 phi2 ( q^3-3*q^2-q+5 ) q congruent 4 modulo 6: 1/32 q^2 phi1 ( q^3-3*q^2-2*q+8 ) q congruent 5 modulo 6: 1/32 phi1^2 phi2 ( q^3-3*q^2-q+5 ) 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, 2 ], [ 4, 1, 1, 5 ], [ 5, 1, 1, 4 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 6 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 8 ], [ 11, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 5, 16 ], [ 13, 2, 3, 4 ], [ 14, 1, 1, 12 ], [ 14, 1, 2, 2 ], [ 14, 2, 1, 4 ], [ 14, 2, 3, 2 ], [ 16, 1, 3, 8 ], [ 16, 2, 3, 8 ], [ 17, 1, 1, 8 ], [ 17, 1, 4, 4 ], [ 17, 1, 5, 8 ], [ 18, 1, 4, 8 ], [ 18, 1, 7, 16 ], [ 18, 1, 8, 16 ], [ 20, 1, 4, 16 ] ] k = 20: F-action on Pi is () [21,1,20] Dynkin type is A_0(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 6: 1/36 q phi1^3 ( q^2-2*q-4 ) q congruent 2 modulo 6: 1/36 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 3 modulo 6: 1/36 q^2 phi1 phi2 ( q^2-5*q+6 ) q congruent 4 modulo 6: 1/36 q phi1^3 ( q^2-2*q-4 ) q congruent 5 modulo 6: 1/36 q^2 phi1 phi2 ( q^2-5*q+6 ) 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, 4 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 3 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 6 ], [ 9, 1, 2, 6 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 6 ], [ 12, 1, 1, 12 ], [ 12, 1, 3, 4 ], [ 12, 1, 5, 6 ], [ 15, 1, 1, 6 ], [ 15, 1, 2, 6 ], [ 15, 1, 3, 12 ], [ 17, 1, 2, 12 ], [ 18, 1, 3, 18 ], [ 19, 1, 2, 12 ], [ 19, 1, 3, 18 ], [ 19, 1, 4, 6 ], [ 19, 2, 2, 6 ], [ 20, 1, 3, 18 ], [ 20, 1, 7, 18 ], [ 20, 2, 2, 6 ], [ 21, 3, 5, 12 ] ] k = 21: F-action on Pi is () [21,1,21] Dynkin type is A_0(q) + T(phi1 phi2 phi3^2) Order of center |Z^F|: phi1 phi2 phi3^2 Numbers of classes in class type: q congruent 1 modulo 6: 1/36 phi1^2 ( q^4+3*q^3+4*q^2+q-6 ) q congruent 2 modulo 6: 1/36 q^2 phi2 ( q^3-q-3 ) q congruent 3 modulo 6: 1/36 q phi1 phi2 ( q^3+q^2-3 ) q congruent 4 modulo 6: 1/36 q phi1 ( q^4+2*q^3+q^2-3*q-10 ) q congruent 5 modulo 6: 1/36 q phi1 phi2 ( q^3+q^2-3 ) 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, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 1, 3, 4 ], [ 12, 1, 5, 12 ], [ 13, 1, 2, 9 ], [ 13, 2, 2, 3 ], [ 14, 1, 3, 9 ], [ 14, 2, 2, 3 ], [ 15, 1, 3, 6 ], [ 16, 1, 5, 18 ], [ 16, 2, 5, 6 ], [ 19, 1, 4, 12 ], [ 19, 1, 5, 18 ], [ 19, 2, 3, 6 ], [ 19, 2, 4, 6 ], [ 20, 1, 10, 18 ], [ 20, 2, 7, 6 ], [ 20, 2, 8, 6 ], [ 21, 3, 11, 12 ], [ 21, 3, 12, 12 ] ] k = 22: F-action on Pi is () [21,1,22] Dynkin type is A_0(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 6: 1/12 phi1 ( q^5-q^3-3*q^2-5*q+2 ) q congruent 2 modulo 6: 1/12 phi2 ( q^5-2*q^4+q^3-3*q^2+4 ) q congruent 3 modulo 6: 1/12 q phi1 phi2 ( q^3-q^2-3 ) q congruent 4 modulo 6: 1/12 q phi1 ( q^4-q^2-3*q-6 ) q congruent 5 modulo 6: 1/12 phi2 ( q^5-2*q^4+q^3-3*q^2+q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 1, 3, 6 ], [ 3, 2, 2, 2 ], [ 3, 2, 3, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 3 ], [ 13, 2, 2, 1 ], [ 14, 1, 3, 3 ], [ 14, 2, 2, 1 ], [ 16, 1, 6, 6 ], [ 16, 2, 6, 2 ], [ 19, 1, 8, 6 ], [ 19, 2, 6, 6 ], [ 19, 2, 8, 2 ], [ 20, 1, 8, 6 ], [ 20, 2, 3, 6 ], [ 20, 2, 5, 2 ], [ 21, 2, 10, 12 ], [ 21, 3, 13, 4 ], [ 21, 3, 22, 12 ] ] k = 23: F-action on Pi is () [21,1,23] Dynkin type is A_0(q) + T(phi1 phi2 phi8) Order of center |Z^F|: phi1 phi2 phi8 Numbers of classes in class type: q congruent 1 modulo 6: 1/8 phi1^2 phi2^2 phi4 q congruent 2 modulo 6: 1/8 q^4 phi1 phi2 q congruent 3 modulo 6: 1/8 phi1^2 phi2^2 phi4 q congruent 4 modulo 6: 1/8 q^4 phi1 phi2 q congruent 5 modulo 6: 1/8 phi1^2 phi2^2 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 ], [ 4, 1, 1, 1 ], [ 13, 1, 4, 4 ], [ 14, 1, 2, 2 ], [ 14, 2, 3, 2 ], [ 21, 2, 16, 8 ], [ 21, 2, 17, 8 ] ] k = 24: F-action on Pi is () [21,1,24] Dynkin type is A_0(q) + T(phi1 phi2 phi5) Order of center |Z^F|: phi1 phi2 phi5 Numbers of classes in class type: q congruent 1 modulo 6: 1/10 q^2 phi1 phi2 phi4 q congruent 2 modulo 6: 1/10 q^2 phi1 phi2 phi4 q congruent 3 modulo 6: 1/10 q^2 phi1 phi2 phi4 q congruent 4 modulo 6: 1/10 q^2 phi1 phi2 phi4 q congruent 5 modulo 6: 1/10 q^2 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, 1, 1, 1 ], [ 8, 1, 2, 2 ], [ 9, 1, 2, 2 ], [ 20, 1, 6, 5 ] ] k = 25: F-action on Pi is () [21,1,25] Dynkin type is A_0(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 6: 1/12 q^3 phi1^2 phi2 q congruent 2 modulo 6: 1/12 q^3 phi1^2 phi2 q congruent 3 modulo 6: 1/12 q^3 phi1^2 phi2 q congruent 4 modulo 6: 1/12 q^3 phi1^2 phi2 q congruent 5 modulo 6: 1/12 q^3 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 4, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 4, 6 ], [ 17, 1, 4, 4 ], [ 18, 1, 6, 6 ], [ 19, 1, 7, 4 ] ] j = 3: Omega of order 3, action on Pi: <()> k = 1: F-action on Pi is () [21,3,1] Dynkin type is (A_0(q) + T(phi1^6)).3 Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/36 ( q^2-14*q+49 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/36 ( q^2-14*q+40 ) q congruent 5 modulo 6: 0 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, 3 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 14 ], [ 6, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 13, 2, 1, 18 ], [ 14, 2, 1, 6 ], [ 16, 2, 1, 36 ], [ 19, 2, 1, 12 ], [ 20, 2, 1, 36 ] ] k = 2: F-action on Pi is () [21,3,2] Dynkin type is (A_0(q) + T(phi1^4 phi3)).3 Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/9 phi1 ( q-4 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/9 phi1 ( q-4 ) q congruent 5 modulo 6: 0 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, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 19, 2, 2, 3 ], [ 20, 2, 2, 9 ] ] k = 3: F-action on Pi is () [21,3,3] Dynkin type is (A_0(q) + T(phi1^2 phi3^2)).3 Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 2/9 phi1 ( q+2 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 2/9 phi1 ( q+2 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 3, 2, 3, 3 ], [ 12, 1, 5, 6 ], [ 19, 2, 2, 3 ] ] k = 4: F-action on Pi is () [21,3,4] Dynkin type is (A_0(q) + T(phi1^4 phi3)).3 Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/18 phi1 ( q+2 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/18 phi1 ( q+2 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 12, 1, 5, 6 ], [ 14, 2, 1, 6 ], [ 19, 2, 1, 12 ] ] k = 5: F-action on Pi is () [21,3,5] Dynkin type is (A_0(q) + T(phi1^3 phi2 phi3)).3 Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/3 q phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/3 q phi1 q congruent 5 modulo 6: 0 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, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 1, 3, 4 ], [ 19, 2, 2, 3 ], [ 20, 2, 2, 3 ] ] k = 6: F-action on Pi is () [21,3,6] Dynkin type is (A_0(q) + T(phi1^5 phi2)).3 Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/12 phi1 ( q-3 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/12 q ( q-4 ) q congruent 5 modulo 6: 0 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, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 1, 3, 4 ], [ 13, 2, 1, 6 ], [ 14, 2, 1, 6 ], [ 16, 2, 2, 12 ], [ 19, 2, 1, 12 ], [ 20, 2, 1, 12 ] ] k = 7: F-action on Pi is () [21,3,7] Dynkin type is (A_0(q) + T(phi1^2 phi3^2)).3 Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/18 ( q^2-14*q+49 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/18 ( q^2-14*q+40 ) q congruent 5 modulo 6: 0 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, 6 ], [ 3, 2, 1, 2 ], [ 3, 2, 3, 6 ], [ 6, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 13, 2, 2, 9 ], [ 14, 2, 2, 3 ], [ 16, 2, 6, 18 ], [ 19, 2, 3, 6 ], [ 20, 2, 7, 18 ] ] k = 8: F-action on Pi is () [21,3,8] Dynkin type is (A_0(q) + T(phi1^2 phi3^2)).3 Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/18 phi1 ( q-4 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/18 phi1 ( q-4 ) q congruent 5 modulo 6: 0 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, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 19, 2, 4, 6 ], [ 20, 2, 8, 18 ] ] k = 9: F-action on Pi is () [21,3,9] Dynkin type is (A_0(q) + T(phi3^3)).3 Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/9 phi1 ( q+2 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/9 phi1 ( q+2 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 8 ], [ 12, 1, 5, 6 ], [ 19, 2, 4, 6 ] ] k = 10: F-action on Pi is () [21,3,10] Dynkin type is (A_0(q) + T(phi3^3)).3 Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/9 phi1 ( q+2 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/9 phi1 ( q+2 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 12, 1, 5, 6 ], [ 14, 2, 2, 3 ], [ 19, 2, 3, 6 ] ] k = 11: F-action on Pi is () [21,3,11] Dynkin type is (A_0(q) + T(phi1 phi2 phi3^2)).3 Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 q phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/6 q phi1 q congruent 5 modulo 6: 0 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, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 1, 3, 4 ], [ 19, 2, 4, 6 ], [ 20, 2, 8, 6 ] ] k = 12: F-action on Pi is () [21,3,12] Dynkin type is (A_0(q) + T(phi1 phi2 phi3^2)).3 Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 phi1 ( q-3 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/6 q ( q-4 ) q congruent 5 modulo 6: 0 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, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 1, 3, 4 ], [ 13, 2, 2, 3 ], [ 14, 2, 2, 3 ], [ 16, 2, 5, 6 ], [ 19, 2, 3, 6 ], [ 20, 2, 7, 6 ] ] k = 13: F-action on Pi is () [21,3,13] Dynkin type is (A_0(q) + T(phi1 phi2 phi3 phi6)).3 Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/2 phi1^2 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/2 q ( q-2 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 3, 2, 3, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 2, 2, 1 ], [ 14, 2, 2, 1 ], [ 16, 2, 6, 2 ], [ 19, 2, 8, 2 ], [ 20, 2, 5, 2 ] ] k = 14: F-action on Pi is () [21,3,14] Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).3 Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/4 phi1^2 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/4 q ( q-2 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 2, 1, 2 ], [ 14, 2, 1, 2 ], [ 16, 2, 1, 4 ], [ 19, 2, 9, 4 ], [ 20, 2, 6, 4 ] ] k = 15: F-action on Pi is () [21,3,15] Dynkin type is (A_0(q) + T(phi3 phi6^2)).3 Order of center |Z^F|: phi6 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/3 q phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/3 q phi1 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 12, 1, 4, 6 ], [ 14, 2, 2, 1 ], [ 19, 2, 8, 2 ] ] k = 16: F-action on Pi is () [21,3,16] Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi6)).3 Order of center |Z^F|: phi6 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 q phi1 q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/6 q phi1 q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 12, 1, 4, 6 ], [ 14, 2, 1, 2 ], [ 19, 2, 9, 4 ] ] k = 17: F-action on Pi is () [21,3,17] Dynkin type is (A_0(q) + T(phi2^2 phi3 phi6)).3 Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/6 phi1 ( q-3 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/6 q ( q-4 ) q congruent 5 modulo 6: 0 Fusion of maximal tori of C^F in those of G^F: [ 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 6 ], [ 8, 1, 2, 6 ], [ 12, 1, 6, 12 ], [ 13, 2, 2, 3 ], [ 14, 2, 2, 1 ], [ 16, 2, 5, 6 ], [ 19, 2, 8, 2 ], [ 20, 2, 5, 6 ] ] k = 18: F-action on Pi is () [21,3,18] Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).3 Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 1/12 phi1 ( q-3 ) q congruent 2 modulo 6: 0 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 1/12 q ( q-4 ) q congruent 5 modulo 6: 0 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, 3 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 6 ], [ 8, 1, 2, 6 ], [ 12, 1, 6, 12 ], [ 13, 2, 1, 6 ], [ 14, 2, 1, 2 ], [ 16, 2, 2, 12 ], [ 19, 2, 9, 4 ], [ 20, 2, 6, 12 ] ] k = 19: F-action on Pi is () [21,3,19] Dynkin type is A_0(q) + T(phi1^4 phi2^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 0 q congruent 2 modulo 6: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/12 ( q^2-8*q+15 ) 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, 3 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 6, 1, 1, 6 ], [ 8, 1, 1, 6 ], [ 12, 1, 1, 12 ], [ 13, 2, 3, 6 ], [ 14, 2, 3, 2 ], [ 16, 2, 3, 12 ], [ 19, 2, 5, 4 ], [ 20, 2, 9, 12 ] ] k = 20: F-action on Pi is () [21,3,20] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi3) Order of center |Z^F|: phi3 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 0 q congruent 2 modulo 6: 1/6 q phi2 q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/6 q 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 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 12, 1, 5, 6 ], [ 14, 2, 3, 2 ], [ 19, 2, 5, 4 ] ] k = 21: F-action on Pi is () [21,3,21] Dynkin type is A_0(q) + T(phi1^3 phi2^3) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 0 q congruent 2 modulo 6: 1/4 q ( q-2 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 4 ], [ 6, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 1, 3, 4 ], [ 13, 2, 3, 2 ], [ 14, 2, 3, 2 ], [ 16, 2, 4, 4 ], [ 19, 2, 5, 4 ], [ 20, 2, 9, 4 ] ] k = 22: F-action on Pi is () [21,3,22] Dynkin type is A_0(q) + T(phi1 phi2 phi3 phi6) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 0 q congruent 2 modulo 6: 1/6 phi2 ( q-2 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/6 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 19, 2, 6, 6 ], [ 20, 2, 3, 6 ] ] k = 23: F-action on Pi is () [21,3,23] Dynkin type is A_0(q) + T(phi1^3 phi2^3) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 0 q congruent 2 modulo 6: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/12 ( q^2-4*q+7 ) Fusion of maximal tori of C^F in those of G^F: [ 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 13, 2, 3, 6 ], [ 14, 2, 3, 6 ], [ 16, 2, 3, 12 ], [ 19, 2, 7, 12 ], [ 20, 2, 4, 12 ] ] k = 24: F-action on Pi is () [21,3,24] Dynkin type is A_0(q) + T(phi3 phi6^2) Order of center |Z^F|: phi6 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 0 q congruent 2 modulo 6: 1/9 phi2 ( q-2 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/9 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 8 ], [ 12, 1, 4, 6 ], [ 19, 2, 6, 6 ] ] k = 25: F-action on Pi is () [21,3,25] Dynkin type is A_0(q) + T(phi1^2 phi2^2 phi6) Order of center |Z^F|: phi6 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 0 q congruent 2 modulo 6: 1/18 phi2 ( q-2 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/18 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 12, 1, 4, 6 ], [ 14, 2, 3, 6 ], [ 19, 2, 7, 12 ] ] k = 26: F-action on Pi is () [21,3,26] Dynkin type is A_0(q) + T(phi2^2 phi3 phi6) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 0 q congruent 2 modulo 6: 1/18 phi2 ( q-2 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/18 phi2 ( q-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 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 2 ], [ 6, 1, 2, 6 ], [ 8, 1, 2, 6 ], [ 12, 1, 6, 12 ], [ 19, 2, 6, 6 ], [ 20, 2, 3, 18 ] ] k = 27: F-action on Pi is () [21,3,27] Dynkin type is A_0(q) + T(phi1^2 phi2^4) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 6: 0 q congruent 2 modulo 6: 1/36 ( q^2-10*q+16 ) q congruent 3 modulo 6: 0 q congruent 4 modulo 6: 0 q congruent 5 modulo 6: 1/36 ( q^2-10*q+25 ) 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, 3 ], [ 3, 1, 2, 2 ], [ 3, 2, 2, 14 ], [ 6, 1, 2, 6 ], [ 8, 1, 2, 6 ], [ 12, 1, 6, 12 ], [ 13, 2, 3, 18 ], [ 14, 2, 3, 6 ], [ 16, 2, 4, 36 ], [ 19, 2, 7, 12 ], [ 20, 2, 4, 36 ] ]