Centralizers of semisimple elements in F4(q) -------------------------------------------- |G(q)| = q^24 phi1^4 phi2^4 phi3^2 phi4^2 phi6^2 phi8 phi12 Semisimple class types: i = 1: Pi = [ 1, 2, 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [1,1,1] Dynkin type is F_4(q) Order of center |Z^F|: 1 Numbers of classes in class type: q congruent 1 modulo 12: 1 q congruent 2 modulo 12: 1 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 1 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 1 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 1 Fusion of maximal tori of C^F in those of G^F: [ 1 .. 25 ] elements of other class types in center: [ ] i = 2: Pi = [ 1, 2, 3, 48 ] j = 1: Omega trivial k = 1: F-action on Pi is () [2,1,1] Dynkin type is B_4(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 1 Fusion of maximal tori of C^F in those of G^F: [ 1, 17, 3, 18, 2, 12, 23, 22, 16, 13, 24, 3, 21, 6, 4, 20, 19, 5, 16, 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 3: Pi = [ 1, 2, 4, 48 ] j = 1: Omega trivial k = 1: F-action on Pi is () [3,1,1] Dynkin type is A_3(q) + ~A_1(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 4 4, q congruent 1 modulo 4 1, q congruent 2 modulo 4 2, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 12: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 17, 12, 22, 3, 18, 4, 19, 16, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 2,48) [3,1,2] Dynkin type is ^2A_3(q) + ~A_1(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 4 2, q congruent 1 modulo 4 1, q congruent 2 modulo 4 4, q congruent 3 modulo 4 Numbers of classes in class type: q congruent 1 modulo 12: 0 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1 Fusion of maximal tori of C^F in those of G^F: [ 18, 2, 22, 13, 17, 3, 20, 5, 23, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 4: Pi = [ 1, 3, 4, 48 ] j = 1: Omega trivial k = 1: F-action on Pi is () [4,1,1] Dynkin type is A_2(q) + ~A_2(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 3 3, q congruent 1 modulo 3 1, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 12: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 1 q congruent 5 modulo 12: 0 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 0 Fusion of maximal tori of C^F in those of G^F: [ 1, 17, 7, 12, 22, 14, 4, 19, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 2: F-action on Pi is ( 1,48)( 3, 4) [4,1,2] Dynkin type is ^2A_2(q) + ^2~A_2(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 3 1, q congruent 1 modulo 3 3, q congruent 2 modulo 3 Numbers of classes in class type: q congruent 1 modulo 12: 0 q congruent 2 modulo 12: 1 q congruent 3 modulo 12: 0 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 0 q congruent 8 modulo 12: 1 q congruent 9 modulo 12: 0 q congruent 11 modulo 12: 1 Fusion of maximal tori of C^F in those of G^F: [ 2, 18, 8, 13, 22, 15, 5, 20, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 5: Pi = [ 2, 3, 4, 48 ] j = 1: Omega trivial k = 1: F-action on Pi is () [5,1,1] Dynkin type is C_3(q) + A_1(q) Order of center |Z^F|: 1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1 q congruent 7 modulo 12: 1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1 q congruent 11 modulo 12: 1 Fusion of maximal tori of C^F in those of G^F: [ 1, 12, 12, 3, 3, 13, 13, 2, 17, 22, 23, 21, 22, 18, 21, 24, 7, 14, 15, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] i = 6: Pi = [ 1, 2, 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [6,1,1] Dynkin type is B_3(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-3 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-2 ) q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 ( q-3 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 17, 3, 18, 12, 23, 22, 16, 4, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] k = 2: F-action on Pi is () [6,1,2] Dynkin type is B_3(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 1/2 q q congruent 3 modulo 12: 1/2 phi1 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 phi1 q congruent 8 modulo 12: 1/2 q q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 17, 3, 18, 2, 22, 16, 13, 24, 19, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 7: Pi = [ 1, 2, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [7,1,1] Dynkin type is A_2(q) + ~A_1(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-7 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-4 ) q congruent 5 modulo 12: 1/2 ( q-5 ) q congruent 7 modulo 12: 1/2 ( q-5 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 ( q-5 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 17, 12, 22, 4, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ] ] k = 2: F-action on Pi is (1,2) [7,1,2] Dynkin type is ^2A_2(q) + ~A_1(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 ( q-5 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 2, 22, 13, 20, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ] ] i = 8: Pi = [ 1, 2, 48 ] j = 1: Omega trivial k = 1: F-action on Pi is () [8,1,1] Dynkin type is A_3(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 12, 3, 4, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ] ] k = 2: F-action on Pi is () [8,1,2] Dynkin type is A_3(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 17, 22, 18, 19, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 2, 2 ] ] k = 3: F-action on Pi is ( 2,48) [8,1,3] Dynkin type is ^2A_3(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 22, 17, 20, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ] ] k = 4: F-action on Pi is ( 2,48) [8,1,4] Dynkin type is ^2A_3(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 13, 3, 5, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ] ] i = 9: Pi = [ 1, 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [9,1,1] Dynkin type is ~A_2(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-5 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-4 ) q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 ( q-5 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 ( q-3 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 12, 17, 22, 7, 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 1 ] ] k = 2: F-action on Pi is (3,4) [9,1,2] Dynkin type is ^2~A_2(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 phi1 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 phi1 q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 13, 2, 22, 18, 15, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 1 ] ] i = 10: Pi = [ 2, 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [10,1,1] Dynkin type is C_3(q) + T(phi1) Order of center |Z^F|: phi1 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-3 ) q congruent 2 modulo 12: 1/2 ( q-2 ) q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 1/2 ( q-2 ) q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 1/2 ( q-2 ) q congruent 9 modulo 12: 1/2 ( q-3 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 12, 3, 13, 17, 23, 22, 21, 7, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 1, 1 ] ] k = 2: F-action on Pi is () [10,1,2] Dynkin type is C_3(q) + T(phi2) Order of center |Z^F|: phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 1/2 q q congruent 3 modulo 12: 1/2 phi1 q congruent 4 modulo 12: 1/2 q q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 phi1 q congruent 8 modulo 12: 1/2 q q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 12, 3, 13, 2, 22, 21, 18, 24, 14, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 5, 1, 1, 1 ] ] i = 11: Pi = [ 2, 3, 48 ] j = 1: Omega trivial k = 1: F-action on Pi is () [11,1,1] Dynkin type is C_2(q) + A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 ( q-3 ) q congruent 7 modulo 12: 1/2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 ( q-3 ) q congruent 11 modulo 12: 1/2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 12, 12, 3, 3, 13, 17, 22, 23, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 10, 1, 1, 2 ] ] k = 2: F-action on Pi is () [11,1,2] Dynkin type is C_2(q) + A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/2 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/2 phi1 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/2 phi1 q congruent 7 modulo 12: 1/2 phi1 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/2 phi1 q congruent 11 modulo 12: 1/2 phi1 Fusion of maximal tori of C^F in those of G^F: [ 12, 3, 3, 13, 13, 2, 22, 18, 21, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 10, 1, 2, 2 ] ] i = 12: Pi = [ 2, 4, 48 ] j = 1: Omega trivial k = 1: F-action on Pi is () [12,1,1] Dynkin type is A_1(q) + A_1(q) + ~A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 ( q-5 ) q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 17, 12, 22, 12, 22, 3, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ] ] k = 2: F-action on Pi is ( 2,48) [12,1,2] Dynkin type is A_1(q^2) + ~A_1(q) + T(phi1) Order of center |Z^F|: phi1 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 3, 23, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ] ] k = 3: F-action on Pi is () [12,1,3] Dynkin type is A_1(q) + A_1(q) + ~A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 3, 22, 13, 22, 13, 18, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 2 ] ] k = 4: F-action on Pi is ( 2,48) [12,1,4] Dynkin type is A_1(q^2) + ~A_1(q) + T(phi2) Order of center |Z^F|: phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/4 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/4 phi1 q congruent 7 modulo 12: 1/4 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/4 phi1 q congruent 11 modulo 12: 1/4 phi2 Fusion of maximal tori of C^F in those of G^F: [ 3, 18, 16, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 2, 2 ] ] i = 13: Pi = [ 1, 2 ] j = 1: Omega trivial k = 1: F-action on Pi is () [13,1,1] Dynkin type is A_2(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 ( q^2-11*q+34 ) q congruent 2 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/12 ( q^2-11*q+24 ) q congruent 4 modulo 12: 1/12 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/12 ( q^2-11*q+30 ) q congruent 7 modulo 12: 1/12 ( q^2-11*q+28 ) q congruent 8 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/12 ( q^2-11*q+30 ) q congruent 11 modulo 12: 1/12 ( q^2-11*q+24 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 12, 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 2 ], [ 6, 1, 1, 6 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ] ] k = 2: F-action on Pi is () [13,1,2] Dynkin type is A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-2 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 q ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 q ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 q ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 22, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ] ] k = 3: F-action on Pi is (1,2) [13,1,3] Dynkin type is ^2A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-2 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-2 ) q congruent 7 modulo 12: 1/4 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-2 ) q congruent 11 modulo 12: 1/4 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 22, 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 3, 4 ] ] k = 4: F-action on Pi is (1,2) [13,1,4] Dynkin type is ^2A_2(q) + T(phi6) Order of center |Z^F|: phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q phi1 q congruent 2 modulo 12: 1/6 phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi1 q congruent 4 modulo 12: 1/6 q phi1 q congruent 5 modulo 12: 1/6 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 q congruent 8 modulo 12: 1/6 phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi1 q congruent 11 modulo 12: 1/6 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 8, 15, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ] ] k = 5: F-action on Pi is () [13,1,5] Dynkin type is A_2(q) + T(phi3) Order of center |Z^F|: phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 phi1 ( q+2 ) q congruent 2 modulo 12: 1/6 q phi2 q congruent 3 modulo 12: 1/6 q phi2 q congruent 4 modulo 12: 1/6 phi1 ( q+2 ) q congruent 5 modulo 12: 1/6 q phi2 q congruent 7 modulo 12: 1/6 phi1 ( q+2 ) q congruent 8 modulo 12: 1/6 q phi2 q congruent 9 modulo 12: 1/6 q phi2 q congruent 11 modulo 12: 1/6 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 7, 14, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ] ] k = 6: F-action on Pi is (1,2) [13,1,6] Dynkin type is ^2A_2(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 phi1 ( q-6 ) q congruent 2 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/12 ( q^2-7*q+12 ) q congruent 4 modulo 12: 1/12 q ( q-4 ) q congruent 5 modulo 12: 1/12 ( q^2-7*q+10 ) q congruent 7 modulo 12: 1/12 ( q^2-7*q+12 ) q congruent 8 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/12 phi1 ( q-6 ) q congruent 11 modulo 12: 1/12 ( q^2-7*q+16 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 13, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 2, 6 ], [ 8, 1, 4, 12 ] ] i = 14: Pi = [ 1, 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [14,1,1] Dynkin type is A_1(q) + ~A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 ( q^2-10*q+29 ) q congruent 2 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/4 ( q^2-10*q+21 ) q congruent 4 modulo 12: 1/4 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/4 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/4 ( q^2-10*q+25 ) q congruent 8 modulo 12: 1/4 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/4 ( q^2-10*q+25 ) q congruent 11 modulo 12: 1/4 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 17, 12, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 4 ] ] k = 2: F-action on Pi is () [14,1,2] Dynkin type is A_1(q) + ~A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 3, 22, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 12, 1, 3, 4 ] ] k = 3: F-action on Pi is () [14,1,3] Dynkin type is A_1(q) + ~A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 22, 3, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 1, 4 ] ] k = 4: F-action on Pi is () [14,1,4] Dynkin type is A_1(q) + ~A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-5 ) q congruent 2 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/4 q ( q-4 ) q congruent 5 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/4 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/4 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/4 phi1 ( q-5 ) q congruent 11 modulo 12: 1/4 ( q^2-6*q+13 ) Fusion of maximal tori of C^F in those of G^F: [ 22, 13, 18, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 3, 4 ] ] i = 15: Pi = [ 2, 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [15,1,1] Dynkin type is C_2(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/8 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/8 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/8 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/8 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 12, 3, 17, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ] ] k = 2: F-action on Pi is () [15,1,2] Dynkin type is C_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 ( q-3 ) q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1 ( q-3 ) q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1 ( q-3 ) q congruent 7 modulo 12: 1/4 phi1 ( q-3 ) q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1 ( q-3 ) q congruent 11 modulo 12: 1/4 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 3, 13, 22, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ] ] k = 3: F-action on Pi is () [15,1,3] Dynkin type is C_2(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q-3 ) q congruent 2 modulo 12: 1/8 q ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 ( q-3 ) q congruent 4 modulo 12: 1/8 q ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 ( q-3 ) q congruent 8 modulo 12: 1/8 q ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 13, 2, 18, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 4 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 4 ] ] k = 4: F-action on Pi is () [15,1,4] Dynkin type is C_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^2 q congruent 7 modulo 12: 1/4 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^2 q congruent 11 modulo 12: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 17, 22, 18, 3, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ] ] k = 5: F-action on Pi is () [15,1,5] Dynkin type is C_2(q) + T(phi4) Order of center |Z^F|: phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1 phi2 q congruent 2 modulo 12: 1/4 q^2 q congruent 3 modulo 12: 1/4 phi1 phi2 q congruent 4 modulo 12: 1/4 q^2 q congruent 5 modulo 12: 1/4 phi1 phi2 q congruent 7 modulo 12: 1/4 phi1 phi2 q congruent 8 modulo 12: 1/4 q^2 q congruent 9 modulo 12: 1/4 phi1 phi2 q congruent 11 modulo 12: 1/4 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 23, 21, 24, 16, 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ] i = 16: Pi = [ 2, 48 ] j = 1: Omega trivial k = 1: F-action on Pi is () [16,1,1] Dynkin type is A_1(q) + A_1(q) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 ( q^2-10*q+25 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^2-10*q+21 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 ( q^2-10*q+25 ) q congruent 7 modulo 12: 1/16 ( q^2-10*q+21 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 ( q^2-10*q+25 ) q congruent 11 modulo 12: 1/16 ( q^2-10*q+21 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 12, 12, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 8, 1, 1, 8 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 8 ], [ 15, 1, 1, 8 ] ] k = 2: F-action on Pi is () [16,1,2] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 22, 22, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 8, 1, 3, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 3, 4 ], [ 15, 1, 4, 4 ] ] k = 3: F-action on Pi is ( 2,48) [16,1,3] Dynkin type is A_1(q^2) + T(phi1^2) Order of center |Z^F|: phi1^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 ( q-5 ) q congruent 7 modulo 12: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q-5 ) q congruent 11 modulo 12: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 8, 1, 3, 8 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 2, 8 ], [ 15, 1, 1, 8 ] ] k = 4: F-action on Pi is ( 2,48) [16,1,4] Dynkin type is A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 8, 1, 4, 4 ], [ 12, 1, 2, 4 ], [ 12, 1, 4, 4 ], [ 15, 1, 4, 4 ] ] k = 5: F-action on Pi is () [16,1,5] Dynkin type is A_1(q) + A_1(q) + T(phi4) Order of center |Z^F|: phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 phi2 q congruent 7 modulo 12: 1/8 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 phi2 q congruent 11 modulo 12: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 23, 21, 21, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 15, 1, 5, 4 ] ] k = 6: F-action on Pi is () [16,1,6] Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q-3 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 3, 3, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 5, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 6 ], [ 15, 1, 2, 4 ] ] k = 7: F-action on Pi is ( 2,48) [16,1,7] Dynkin type is A_1(q^2) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 phi2 q congruent 7 modulo 12: 1/8 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 phi2 q congruent 11 modulo 12: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 22, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 15, 1, 2, 4 ] ] k = 8: F-action on Pi is ( 2,48) [16,1,8] Dynkin type is A_1(q^2) + T(phi4) Order of center |Z^F|: phi4 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/8 phi1 phi2 q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/8 phi1 phi2 q congruent 7 modulo 12: 1/8 phi1 phi2 q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/8 phi1 phi2 q congruent 11 modulo 12: 1/8 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 16, 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 15, 1, 5, 4 ] ] k = 9: F-action on Pi is () [16,1,9] Dynkin type is A_1(q) + A_1(q) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q-5 ) q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 ( q^2-6*q+9 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1 ( q-5 ) q congruent 7 modulo 12: 1/16 ( q^2-6*q+9 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1 ( q-5 ) q congruent 11 modulo 12: 1/16 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 13, 13, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 8, 1, 4, 8 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 12 ], [ 12, 1, 3, 8 ], [ 15, 1, 3, 8 ] ] k = 10: F-action on Pi is ( 2,48) [16,1,10] Dynkin type is A_1(q^2) + T(phi2^2) Order of center |Z^F|: phi2^2 times 1, q congruent 0 modulo 2 2, q congruent 1 modulo 2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^2 q congruent 2 modulo 12: 0 q congruent 3 modulo 12: 1/16 phi2 ( q-3 ) q congruent 4 modulo 12: 0 q congruent 5 modulo 12: 1/16 phi1^2 q congruent 7 modulo 12: 1/16 phi2 ( q-3 ) q congruent 8 modulo 12: 0 q congruent 9 modulo 12: 1/16 phi1^2 q congruent 11 modulo 12: 1/16 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 4 ], [ 8, 1, 2, 8 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 4, 8 ], [ 15, 1, 3, 8 ] ] i = 17: Pi = [ 3, 4 ] j = 1: Omega trivial k = 1: F-action on Pi is () [17,1,1] Dynkin type is ~A_2(q) + T(phi1^2) Order of center |Z^F|: phi1^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 ( q^2-8*q+19 ) q congruent 2 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 3 modulo 12: 1/12 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/12 ( q^2-8*q+16 ) q congruent 5 modulo 12: 1/12 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/12 ( q^2-8*q+19 ) q congruent 8 modulo 12: 1/12 ( q^2-8*q+12 ) q congruent 9 modulo 12: 1/12 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/12 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 17, 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 3 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 6 ] ] k = 2: F-action on Pi is (3,4) [17,1,2] Dynkin type is ^2~A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^2 q congruent 7 modulo 12: 1/4 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^2 q congruent 11 modulo 12: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 13, 22, 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 1 ], [ 9, 1, 2, 2 ], [ 10, 1, 1, 2 ] ] k = 3: F-action on Pi is () [17,1,3] Dynkin type is ~A_2(q) + T(phi1 phi2) Order of center |Z^F|: phi1 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/4 phi1^2 q congruent 2 modulo 12: 1/4 q ( q-2 ) q congruent 3 modulo 12: 1/4 phi1^2 q congruent 4 modulo 12: 1/4 q ( q-2 ) q congruent 5 modulo 12: 1/4 phi1^2 q congruent 7 modulo 12: 1/4 phi1^2 q congruent 8 modulo 12: 1/4 q ( q-2 ) q congruent 9 modulo 12: 1/4 phi1^2 q congruent 11 modulo 12: 1/4 phi1^2 Fusion of maximal tori of C^F in those of G^F: [ 12, 22, 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 1 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ] ] k = 4: F-action on Pi is (3,4) [17,1,4] Dynkin type is ^2~A_2(q) + T(phi6) Order of center |Z^F|: phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q phi1 q congruent 2 modulo 12: 1/6 phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi1 q congruent 4 modulo 12: 1/6 q phi1 q congruent 5 modulo 12: 1/6 phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 q phi1 q congruent 8 modulo 12: 1/6 phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi1 q congruent 11 modulo 12: 1/6 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 5, 20, 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ] ] k = 5: F-action on Pi is () [17,1,5] Dynkin type is ~A_2(q) + T(phi3) Order of center |Z^F|: phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 phi1 ( q+2 ) q congruent 2 modulo 12: 1/6 q phi2 q congruent 3 modulo 12: 1/6 q phi2 q congruent 4 modulo 12: 1/6 phi1 ( q+2 ) q congruent 5 modulo 12: 1/6 q phi2 q congruent 7 modulo 12: 1/6 phi1 ( q+2 ) q congruent 8 modulo 12: 1/6 q phi2 q congruent 9 modulo 12: 1/6 q phi2 q congruent 11 modulo 12: 1/6 q phi2 Fusion of maximal tori of C^F in those of G^F: [ 4, 19, 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ] ] k = 6: F-action on Pi is (3,4) [17,1,6] Dynkin type is ^2~A_2(q) + T(phi2^2) Order of center |Z^F|: phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 phi1 ( q-3 ) q congruent 2 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/12 phi1 ( q-3 ) q congruent 4 modulo 12: 1/12 q ( q-4 ) q congruent 5 modulo 12: 1/12 ( q^2-4*q+7 ) q congruent 7 modulo 12: 1/12 phi1 ( q-3 ) q congruent 8 modulo 12: 1/12 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/12 phi1 ( q-3 ) q congruent 11 modulo 12: 1/12 ( q^2-4*q+7 ) Fusion of maximal tori of C^F in those of G^F: [ 2, 18, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 3 ], [ 9, 1, 2, 6 ], [ 10, 1, 2, 6 ] ] i = 18: Pi = [ 1 ] j = 1: Omega trivial k = 1: F-action on Pi is () [18,1,1] Dynkin type is A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 ( q^3-19*q^2+115*q-241 ) q congruent 2 modulo 12: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 12: 1/48 ( q^3-19*q^2+115*q-201 ) q congruent 4 modulo 12: 1/48 ( q^3-16*q^2+76*q-112 ) q congruent 5 modulo 12: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 7 modulo 12: 1/48 ( q^3-19*q^2+115*q-217 ) q congruent 8 modulo 12: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 12: 1/48 ( q^3-19*q^2+115*q-225 ) q congruent 11 modulo 12: 1/48 ( q^3-19*q^2+115*q-201 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 12 ], [ 4, 1, 1, 8 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 24 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 18 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 48 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 48 ] ] k = 2: F-action on Pi is () [18,1,2] Dynkin type is A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q^2-6*q+7 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 4 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-6*q+7 ) q congruent 7 modulo 12: 1/8 ( q^3-7*q^2+13*q-3 ) q congruent 8 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-6*q+7 ) q congruent 11 modulo 12: 1/8 ( q^3-7*q^2+13*q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 8, 1, 3, 4 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 12, 1, 1, 4 ], [ 12, 1, 3, 4 ], [ 13, 1, 2, 8 ], [ 14, 1, 1, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 4, 4 ], [ 16, 1, 2, 8 ] ] k = 3: F-action on Pi is () [18,1,3] Dynkin type is A_1(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 2 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 12: 1/6 q phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 7, 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 1 ], [ 9, 1, 1, 2 ], [ 13, 1, 5, 6 ] ] k = 4: F-action on Pi is () [18,1,4] Dynkin type is A_1(q) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1^2 phi2 q congruent 2 modulo 12: 1/8 q^3 q congruent 3 modulo 12: 1/8 phi1^2 phi2 q congruent 4 modulo 12: 1/8 q^3 q congruent 5 modulo 12: 1/8 phi1^2 phi2 q congruent 7 modulo 12: 1/8 phi1^2 phi2 q congruent 8 modulo 12: 1/8 q^3 q congruent 9 modulo 12: 1/8 phi1^2 phi2 q congruent 11 modulo 12: 1/8 phi1^2 phi2 Fusion of maximal tori of C^F in those of G^F: [ 21, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 15, 1, 5, 4 ], [ 16, 1, 5, 8 ] ] k = 5: F-action on Pi is () [18,1,5] Dynkin type is A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/16 phi1 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 8, 1, 4, 8 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 12 ], [ 12, 1, 3, 8 ], [ 14, 1, 2, 8 ], [ 15, 1, 2, 8 ], [ 15, 1, 3, 8 ], [ 16, 1, 6, 16 ], [ 16, 1, 9, 16 ] ] k = 6: F-action on Pi is () [18,1,6] Dynkin type is A_1(q) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 7 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 phi2 ( q-3 ) q congruent 11 modulo 12: 1/8 phi1 phi2 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 23, 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 2 ], [ 15, 1, 5, 4 ], [ 16, 1, 5, 8 ] ] k = 7: F-action on Pi is () [18,1,7] Dynkin type is A_1(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q^2 phi1 q congruent 2 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/6 q^2 phi1 q congruent 4 modulo 12: 1/6 q^2 phi1 q congruent 5 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/6 q^2 phi1 q congruent 8 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/6 q^2 phi1 q congruent 11 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 15, 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 1 ], [ 9, 1, 2, 2 ], [ 13, 1, 4, 6 ] ] k = 8: F-action on Pi is () [18,1,8] Dynkin type is A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q^2-4*q+5 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-4*q+5 ) q congruent 7 modulo 12: 1/8 ( q^3-5*q^2+9*q-9 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-4*q+5 ) q congruent 11 modulo 12: 1/8 ( q^3-5*q^2+9*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 22, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 8, 1, 3, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 1, 4 ], [ 12, 1, 3, 4 ], [ 13, 1, 3, 8 ], [ 14, 1, 3, 4 ], [ 14, 1, 4, 4 ], [ 15, 1, 4, 4 ], [ 16, 1, 2, 8 ] ] k = 9: F-action on Pi is () [18,1,9] Dynkin type is A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 2 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 4 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 7 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 8 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) q congruent 11 modulo 12: 1/16 phi1 ( q^2-8*q+15 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 8, 1, 1, 8 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 12 ], [ 11, 1, 2, 6 ], [ 12, 1, 1, 8 ], [ 14, 1, 3, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 8 ], [ 16, 1, 1, 16 ], [ 16, 1, 6, 16 ] ] k = 10: F-action on Pi is () [18,1,10] Dynkin type is A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 phi1 ( q^2-12*q+39 ) q congruent 2 modulo 12: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 3 modulo 12: 1/48 ( q^3-13*q^2+51*q-63 ) q congruent 4 modulo 12: 1/48 q ( q^2-10*q+24 ) q congruent 5 modulo 12: 1/48 ( q^3-13*q^2+51*q-55 ) q congruent 7 modulo 12: 1/48 ( q^3-13*q^2+51*q-63 ) q congruent 8 modulo 12: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 9 modulo 12: 1/48 phi1 ( q^2-12*q+39 ) q congruent 11 modulo 12: 1/48 ( q^3-13*q^2+51*q-79 ) Fusion of maximal tori of C^F in those of G^F: [ 13, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 12 ], [ 4, 1, 2, 8 ], [ 5, 1, 1, 4 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 24 ], [ 8, 1, 4, 24 ], [ 9, 1, 2, 8 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 18 ], [ 12, 1, 3, 24 ], [ 13, 1, 6, 48 ], [ 14, 1, 4, 24 ], [ 15, 1, 3, 24 ], [ 16, 1, 9, 48 ] ] i = 19: Pi = [ 3 ] j = 1: Omega trivial k = 1: F-action on Pi is () [19,1,1] Dynkin type is ~A_1(q) + T(phi1^3) Order of center |Z^F|: phi1^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 ( q^3-16*q^2+85*q-166 ) q congruent 2 modulo 12: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 3 modulo 12: 1/48 ( q^3-16*q^2+85*q-138 ) q congruent 4 modulo 12: 1/48 ( q^3-16*q^2+76*q-112 ) q congruent 5 modulo 12: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 7 modulo 12: 1/48 ( q^3-16*q^2+85*q-154 ) q congruent 8 modulo 12: 1/48 ( q^3-16*q^2+76*q-96 ) q congruent 9 modulo 12: 1/48 ( q^3-16*q^2+85*q-150 ) q congruent 11 modulo 12: 1/48 ( q^3-16*q^2+85*q-138 ) Fusion of maximal tori of C^F in those of G^F: [ 1, 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 8 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 6 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 12 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 17, 1, 1, 48 ] ] k = 2: F-action on Pi is () [19,1,2] Dynkin type is ~A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^2 ( q-4 ) q congruent 2 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/16 q ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/16 phi1^2 ( q-4 ) q congruent 7 modulo 12: 1/16 q ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/16 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/16 phi1^2 ( q-4 ) q congruent 11 modulo 12: 1/16 q ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 17, 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 6, 1, 2, 2 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 2, 8 ], [ 12, 1, 3, 4 ], [ 14, 1, 2, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ] ] k = 3: F-action on Pi is () [19,1,3] Dynkin type is ~A_1(q) + T(phi1^2 phi2) Order of center |Z^F|: phi1^2 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 2 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 8 modulo 12: 1/8 q ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 12, 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 1, 4 ], [ 14, 1, 1, 4 ], [ 14, 1, 3, 4 ], [ 15, 1, 2, 4 ], [ 17, 1, 3, 8 ] ] k = 4: F-action on Pi is () [19,1,4] Dynkin type is ~A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 2 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 4 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 7 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 8 modulo 12: 1/8 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) q congruent 11 modulo 12: 1/8 phi1 ( q^2-3*q+4 ) Fusion of maximal tori of C^F in those of G^F: [ 22, 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 14, 1, 4, 4 ], [ 15, 1, 2, 4 ], [ 17, 1, 2, 8 ] ] k = 5: F-action on Pi is () [19,1,5] Dynkin type is ~A_1(q) + T(phi1 phi2^2) Order of center |Z^F|: phi1 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^2 ( q-2 ) q congruent 2 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 4 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1^2 ( q-2 ) q congruent 7 modulo 12: 1/16 ( q^3-4*q^2+5*q-6 ) q congruent 8 modulo 12: 1/16 q ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1^2 ( q-2 ) q congruent 11 modulo 12: 1/16 ( q^3-4*q^2+5*q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 3, 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 4 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 4, 8 ], [ 14, 1, 3, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ] ] k = 6: F-action on Pi is () [19,1,6] Dynkin type is ~A_1(q) + T(phi1 phi4) Order of center |Z^F|: phi1 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/8 q^2 ( q-2 ) q congruent 3 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/8 q^2 ( q-2 ) q congruent 5 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/8 q^2 ( q-2 ) q congruent 9 modulo 12: 1/8 phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/8 phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 23, 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 12, 1, 2, 4 ], [ 15, 1, 5, 4 ] ] k = 7: F-action on Pi is () [19,1,7] Dynkin type is ~A_1(q) + T(phi2 phi4) Order of center |Z^F|: phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 q phi1 phi2 q congruent 2 modulo 12: 1/8 q^3 q congruent 3 modulo 12: 1/8 q phi1 phi2 q congruent 4 modulo 12: 1/8 q^3 q congruent 5 modulo 12: 1/8 q phi1 phi2 q congruent 7 modulo 12: 1/8 q phi1 phi2 q congruent 8 modulo 12: 1/8 q^3 q congruent 9 modulo 12: 1/8 q phi1 phi2 q congruent 11 modulo 12: 1/8 q phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 16, 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 12, 1, 4, 4 ], [ 15, 1, 5, 4 ] ] k = 8: F-action on Pi is () [19,1,8] Dynkin type is ~A_1(q) + T(phi1 phi3) Order of center |Z^F|: phi1 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 2 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 3 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 4 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 5 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 7 modulo 12: 1/6 phi1 ( q^2-2 ) q congruent 8 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 9 modulo 12: 1/6 q phi2 ( q-2 ) q congruent 11 modulo 12: 1/6 q phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 4, 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 17, 1, 5, 6 ] ] k = 9: F-action on Pi is () [19,1,9] Dynkin type is ~A_1(q) + T(phi2 phi6) Order of center |Z^F|: phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/6 q^2 phi1 q congruent 2 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 3 modulo 12: 1/6 q^2 phi1 q congruent 4 modulo 12: 1/6 q^2 phi1 q congruent 5 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 7 modulo 12: 1/6 q^2 phi1 q congruent 8 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) q congruent 9 modulo 12: 1/6 q^2 phi1 q congruent 11 modulo 12: 1/6 phi2 ( q^2-2*q+2 ) Fusion of maximal tori of C^F in those of G^F: [ 20, 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 17, 1, 4, 6 ] ] k = 10: F-action on Pi is () [19,1,10] Dynkin type is ~A_1(q) + T(phi2^3) Order of center |Z^F|: phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/48 phi1 ( q^2-9*q+24 ) q congruent 2 modulo 12: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 3 modulo 12: 1/48 ( q^3-10*q^2+33*q-36 ) q congruent 4 modulo 12: 1/48 q ( q^2-10*q+24 ) q congruent 5 modulo 12: 1/48 ( q^3-10*q^2+33*q-40 ) q congruent 7 modulo 12: 1/48 ( q^3-10*q^2+33*q-36 ) q congruent 8 modulo 12: 1/48 ( q^3-10*q^2+24*q-16 ) q congruent 9 modulo 12: 1/48 phi1 ( q^2-9*q+24 ) q congruent 11 modulo 12: 1/48 ( q^3-10*q^2+33*q-52 ) Fusion of maximal tori of C^F in those of G^F: [ 18, 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 8 ], [ 5, 1, 1, 6 ], [ 6, 1, 2, 6 ], [ 7, 1, 2, 8 ], [ 9, 1, 2, 24 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 12 ], [ 12, 1, 3, 12 ], [ 14, 1, 4, 24 ], [ 15, 1, 3, 24 ], [ 17, 1, 6, 48 ] ] i = 20: Pi = [ ] j = 1: Omega trivial k = 1: F-action on Pi is () [20,1,1] Dynkin type is A_0(q) + T(phi1^4) Order of center |Z^F|: phi1^4 Numbers of classes in class type: q congruent 1 modulo 12: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 ) q congruent 2 modulo 12: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 3 modulo 12: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 ) q congruent 4 modulo 12: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1280 ) q congruent 5 modulo 12: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 7 modulo 12: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2009 ) q congruent 8 modulo 12: 1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 ) q congruent 9 modulo 12: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 ) q congruent 11 modulo 12: 1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 ) Fusion of maximal tori of C^F in those of G^F: [ 1 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 24 ], [ 4, 1, 1, 32 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 24 ], [ 7, 1, 1, 96 ], [ 8, 1, 1, 48 ], [ 9, 1, 1, 96 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 72 ], [ 12, 1, 1, 144 ], [ 13, 1, 1, 192 ], [ 14, 1, 1, 288 ], [ 15, 1, 1, 144 ], [ 16, 1, 1, 288 ], [ 17, 1, 1, 192 ], [ 18, 1, 1, 576 ], [ 19, 1, 1, 576 ] ] k = 2: F-action on Pi is () [20,1,2] Dynkin type is A_0(q) + T(phi2^4) Order of center |Z^F|: phi2^4 Numbers of classes in class type: q congruent 1 modulo 12: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 2 modulo 12: 1/1152 ( q^4-20*q^3+124*q^2-240*q+128 ) q congruent 3 modulo 12: 1/1152 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 4 modulo 12: 1/1152 q ( q^3-20*q^2+124*q-240 ) q congruent 5 modulo 12: 1/1152 ( q^4-20*q^3+142*q^2-420*q+425 ) q congruent 7 modulo 12: 1/1152 ( q^4-20*q^3+142*q^2-420*q+441 ) q congruent 8 modulo 12: 1/1152 ( q^4-20*q^3+124*q^2-240*q+128 ) q congruent 9 modulo 12: 1/1152 phi1 ( q^3-19*q^2+123*q-297 ) q congruent 11 modulo 12: 1/1152 ( q^4-20*q^3+142*q^2-420*q+569 ) Fusion of maximal tori of C^F in those of G^F: [ 2 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 24 ], [ 4, 1, 2, 32 ], [ 5, 1, 1, 12 ], [ 6, 1, 2, 24 ], [ 7, 1, 2, 96 ], [ 8, 1, 4, 48 ], [ 9, 1, 2, 96 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 72 ], [ 12, 1, 3, 144 ], [ 13, 1, 6, 192 ], [ 14, 1, 4, 288 ], [ 15, 1, 3, 144 ], [ 16, 1, 9, 288 ], [ 17, 1, 6, 192 ], [ 18, 1, 10, 576 ], [ 19, 1, 10, 576 ] ] k = 3: F-action on Pi is () [20,1,3] Dynkin type is A_0(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/64 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/64 phi1^2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/64 phi1^2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 3 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 8, 1, 1, 8 ], [ 8, 1, 4, 8 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 12 ], [ 11, 1, 2, 12 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 16 ], [ 12, 1, 3, 8 ], [ 12, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 14, 1, 3, 16 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 16 ], [ 16, 1, 1, 16 ], [ 16, 1, 4, 32 ], [ 16, 1, 6, 32 ], [ 16, 1, 9, 16 ], [ 18, 1, 5, 32 ], [ 18, 1, 9, 32 ], [ 19, 1, 2, 32 ], [ 19, 1, 5, 32 ] ] k = 4: F-action on Pi is () [20,1,4] Dynkin type is A_0(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 4 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 6 ], [ 4, 1, 1, 2 ], [ 6, 1, 1, 6 ], [ 7, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 13, 1, 1, 12 ], [ 17, 1, 5, 6 ], [ 19, 1, 8, 18 ] ] k = 5: F-action on Pi is () [20,1,5] Dynkin type is A_0(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 q^2 phi1^2 q congruent 2 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 12: 1/36 q^2 phi1^2 q congruent 4 modulo 12: 1/36 q^2 phi1^2 q congruent 5 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 12: 1/36 q^2 phi1^2 q congruent 8 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 9 modulo 12: 1/36 q^2 phi1^2 q congruent 11 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 5 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 6 ], [ 4, 1, 2, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 2, 6 ], [ 8, 1, 4, 12 ], [ 13, 1, 6, 12 ], [ 17, 1, 4, 6 ], [ 19, 1, 9, 18 ] ] k = 6: F-action on Pi is () [20,1,6] Dynkin type is A_0(q) + T(phi4^2) Order of center |Z^F|: phi4^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 2 modulo 12: 1/96 q^2 ( q^2-4 ) q congruent 3 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 4 modulo 12: 1/96 q^2 ( q^2-4 ) q congruent 5 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 7 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 8 modulo 12: 1/96 q^2 ( q^2-4 ) q congruent 9 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) q congruent 11 modulo 12: 1/96 phi1 phi2 ( q^2-9 ) Fusion of maximal tori of C^F in those of G^F: [ 6 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 15, 1, 5, 24 ], [ 16, 1, 8, 48 ] ] k = 7: F-action on Pi is () [20,1,7] Dynkin type is A_0(q) + T(phi1^2 phi3) Order of center |Z^F|: phi1^2 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 2 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 3 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 4 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 5 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 7 modulo 12: 1/36 phi1^2 ( q^2-2*q-4 ) q congruent 8 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 9 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) q congruent 11 modulo 12: 1/36 q phi2 ( q^2-5*q+6 ) Fusion of maximal tori of C^F in those of G^F: [ 7 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 3 ], [ 9, 1, 1, 6 ], [ 10, 1, 1, 6 ], [ 13, 1, 5, 6 ], [ 17, 1, 1, 12 ], [ 18, 1, 3, 18 ] ] k = 8: F-action on Pi is () [20,1,8] Dynkin type is A_0(q) + T(phi2^2 phi6) Order of center |Z^F|: phi2^2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/36 q^2 phi1^2 q congruent 2 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 3 modulo 12: 1/36 q^2 phi1^2 q congruent 4 modulo 12: 1/36 q^2 phi1^2 q congruent 5 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 7 modulo 12: 1/36 q^2 phi1^2 q congruent 8 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) q congruent 9 modulo 12: 1/36 q^2 phi1^2 q congruent 11 modulo 12: 1/36 phi2 ( q^3-3*q^2+4*q-4 ) Fusion of maximal tori of C^F in those of G^F: [ 8 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 3 ], [ 9, 1, 2, 6 ], [ 10, 1, 2, 6 ], [ 13, 1, 4, 6 ], [ 17, 1, 6, 12 ], [ 18, 1, 7, 18 ] ] k = 9: F-action on Pi is () [20,1,9] Dynkin type is A_0(q) + T(phi3^2) Order of center |Z^F|: phi3^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 2 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 3 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 4 modulo 12: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 5 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 7 modulo 12: 1/72 phi1 ( q^3+3*q^2-2*q-8 ) q congruent 8 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 9 modulo 12: 1/72 q phi2 ( q^2+q-6 ) q congruent 11 modulo 12: 1/72 q phi2 ( q^2+q-6 ) Fusion of maximal tori of C^F in those of G^F: [ 9 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 8 ], [ 13, 1, 5, 24 ], [ 17, 1, 5, 24 ] ] k = 10: F-action on Pi is () [20,1,10] Dynkin type is A_0(q) + T(phi6^2) Order of center |Z^F|: phi6^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 2 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 3 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 4 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 5 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 7 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 8 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) q congruent 9 modulo 12: 1/72 q phi1 ( q^2-q-6 ) q congruent 11 modulo 12: 1/72 phi2 ( q^3-3*q^2-2*q+8 ) Fusion of maximal tori of C^F in those of G^F: [ 10 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 8 ], [ 13, 1, 4, 24 ], [ 17, 1, 4, 24 ] ] k = 11: F-action on Pi is () [20,1,11] Dynkin type is A_0(q) + T(phi12) Order of center |Z^F|: phi12 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 11 ] elements of other class types in center: [ [ 1, 1, 1, 1 ] ] k = 12: F-action on Pi is () [20,1,12] Dynkin type is A_0(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 2 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 4 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 7 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 8 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) q congruent 11 modulo 12: 1/96 phi1 ( q^3-11*q^2+39*q-45 ) Fusion of maximal tori of C^F in those of G^F: [ 12 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 12 ], [ 4, 1, 1, 8 ], [ 5, 1, 1, 4 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 24 ], [ 8, 1, 1, 24 ], [ 9, 1, 1, 8 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 18 ], [ 11, 1, 2, 6 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 48 ], [ 14, 1, 1, 24 ], [ 14, 1, 3, 24 ], [ 15, 1, 1, 24 ], [ 15, 1, 2, 12 ], [ 16, 1, 1, 48 ], [ 16, 1, 6, 24 ], [ 17, 1, 3, 16 ], [ 18, 1, 1, 48 ], [ 18, 1, 9, 48 ], [ 19, 1, 3, 48 ] ] k = 13: F-action on Pi is () [20,1,13] Dynkin type is A_0(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 2 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 4 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 7 modulo 12: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 8 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) q congruent 11 modulo 12: 1/96 phi1 ( q^3-7*q^2+19*q-21 ) Fusion of maximal tori of C^F in those of G^F: [ 13 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 12 ], [ 4, 1, 2, 8 ], [ 5, 1, 1, 4 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 24 ], [ 8, 1, 4, 24 ], [ 9, 1, 2, 8 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 18 ], [ 12, 1, 3, 24 ], [ 13, 1, 6, 48 ], [ 14, 1, 2, 24 ], [ 14, 1, 4, 24 ], [ 15, 1, 2, 12 ], [ 15, 1, 3, 24 ], [ 16, 1, 6, 24 ], [ 16, 1, 9, 48 ], [ 17, 1, 2, 16 ], [ 18, 1, 5, 48 ], [ 18, 1, 10, 48 ], [ 19, 1, 4, 48 ] ] k = 14: F-action on Pi is () [20,1,14] Dynkin type is A_0(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 14 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 1 ], [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 13, 1, 5, 6 ], [ 17, 1, 3, 4 ], [ 18, 1, 3, 6 ] ] k = 15: F-action on Pi is () [20,1,15] Dynkin type is A_0(q) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/12 q phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 15 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 1 ], [ 9, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 13, 1, 4, 6 ], [ 17, 1, 2, 4 ], [ 18, 1, 7, 6 ] ] k = 16: F-action on Pi is () [20,1,16] Dynkin type is A_0(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 7 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) q congruent 11 modulo 12: 1/16 phi1 phi2 ( q^2-2*q-1 ) Fusion of maximal tori of C^F in those of G^F: [ 16 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 8, 1, 4, 4 ], [ 12, 1, 2, 4 ], [ 12, 1, 4, 4 ], [ 15, 1, 4, 4 ], [ 15, 1, 5, 4 ], [ 16, 1, 4, 8 ], [ 16, 1, 8, 8 ], [ 19, 1, 6, 8 ], [ 19, 1, 7, 8 ] ] k = 17: F-action on Pi is () [20,1,17] Dynkin type is A_0(q) + T(phi1^3 phi2) Order of center |Z^F|: phi1^3 phi2 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 2 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 3 modulo 12: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 4 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 5 modulo 12: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 7 modulo 12: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) q congruent 8 modulo 12: 1/96 q ( q^3-12*q^2+44*q-48 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-11*q^2+33*q-15 ) q congruent 11 modulo 12: 1/96 ( q^4-12*q^3+44*q^2-48*q-9 ) Fusion of maximal tori of C^F in those of G^F: [ 17 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 6 ], [ 4, 1, 1, 8 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 6 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 8 ], [ 8, 1, 2, 4 ], [ 8, 1, 3, 12 ], [ 9, 1, 1, 24 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 12 ], [ 12, 1, 2, 24 ], [ 12, 1, 3, 12 ], [ 13, 1, 2, 16 ], [ 14, 1, 1, 24 ], [ 14, 1, 2, 24 ], [ 15, 1, 1, 24 ], [ 15, 1, 4, 12 ], [ 16, 1, 2, 24 ], [ 16, 1, 3, 48 ], [ 17, 1, 1, 48 ], [ 18, 1, 2, 48 ], [ 19, 1, 1, 48 ], [ 19, 1, 2, 48 ] ] k = 18: F-action on Pi is () [20,1,18] Dynkin type is A_0(q) + T(phi1 phi2^3) Order of center |Z^F|: phi1 phi2^3 Numbers of classes in class type: q congruent 1 modulo 12: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 2 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 3 modulo 12: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 4 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 5 modulo 12: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 7 modulo 12: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) q congruent 8 modulo 12: 1/96 q ( q^3-8*q^2+20*q-16 ) q congruent 9 modulo 12: 1/96 phi1 ( q^3-7*q^2+13*q-15 ) q congruent 11 modulo 12: 1/96 ( q^4-8*q^3+20*q^2-28*q+39 ) Fusion of maximal tori of C^F in those of G^F: [ 18 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 6 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 8 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 12 ], [ 8, 1, 3, 4 ], [ 9, 1, 2, 24 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 12 ], [ 12, 1, 1, 12 ], [ 12, 1, 3, 12 ], [ 12, 1, 4, 24 ], [ 13, 1, 3, 16 ], [ 14, 1, 3, 24 ], [ 14, 1, 4, 24 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 12 ], [ 16, 1, 2, 24 ], [ 16, 1, 10, 48 ], [ 17, 1, 6, 48 ], [ 18, 1, 8, 48 ], [ 19, 1, 5, 48 ], [ 19, 1, 10, 48 ] ] k = 19: F-action on Pi is () [20,1,19] Dynkin type is A_0(q) + T(phi1 phi2 phi3) Order of center |Z^F|: phi1 phi2 phi3 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q^2 phi1 phi2 q congruent 2 modulo 12: 1/12 q^2 phi1 phi2 q congruent 3 modulo 12: 1/12 q^2 phi1 phi2 q congruent 4 modulo 12: 1/12 q^2 phi1 phi2 q congruent 5 modulo 12: 1/12 q^2 phi1 phi2 q congruent 7 modulo 12: 1/12 q^2 phi1 phi2 q congruent 8 modulo 12: 1/12 q^2 phi1 phi2 q congruent 9 modulo 12: 1/12 q^2 phi1 phi2 q congruent 11 modulo 12: 1/12 q^2 phi1 phi2 Fusion of maximal tori of C^F in those of G^F: [ 19 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 17, 1, 5, 6 ], [ 19, 1, 8, 6 ] ] k = 20: F-action on Pi is () [20,1,20] Dynkin type is A_0(q) + T(phi1 phi2 phi6) Order of center |Z^F|: phi1 phi2 phi6 Numbers of classes in class type: q congruent 1 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 2 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 3 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 4 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 5 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 7 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 8 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 9 modulo 12: 1/12 q phi1 phi2 ( q-2 ) q congruent 11 modulo 12: 1/12 q phi1 phi2 ( q-2 ) Fusion of maximal tori of C^F in those of G^F: [ 20 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 3, 4 ], [ 13, 1, 3, 4 ], [ 17, 1, 4, 6 ], [ 19, 1, 9, 6 ] ] k = 21: F-action on Pi is () [20,1,21] Dynkin type is A_0(q) + T(phi1 phi2 phi4) Order of center |Z^F|: phi1 phi2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1^3 phi2 q congruent 2 modulo 12: 1/16 q^3 ( q-2 ) q congruent 3 modulo 12: 1/16 phi1^3 phi2 q congruent 4 modulo 12: 1/16 q^3 ( q-2 ) q congruent 5 modulo 12: 1/16 phi1^3 phi2 q congruent 7 modulo 12: 1/16 phi1^3 phi2 q congruent 8 modulo 12: 1/16 q^3 ( q-2 ) q congruent 9 modulo 12: 1/16 phi1^3 phi2 q congruent 11 modulo 12: 1/16 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 21 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 5, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 16, 1, 5, 8 ], [ 16, 1, 7, 8 ], [ 18, 1, 4, 8 ], [ 18, 1, 6, 8 ] ] k = 22: F-action on Pi is () [20,1,22] Dynkin type is A_0(q) + T(phi1^2 phi2^2) Order of center |Z^F|: phi1^2 phi2^2 Numbers of classes in class type: q congruent 1 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 2 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 3 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 4 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 5 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 7 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 8 modulo 12: 1/16 q^2 ( q^2-4*q+4 ) q congruent 9 modulo 12: 1/16 phi1 phi4 ( q-3 ) q congruent 11 modulo 12: 1/16 phi1 phi4 ( q-3 ) Fusion of maximal tori of C^F in those of G^F: [ 22 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 8, 1, 3, 4 ], [ 9, 1, 1, 4 ], [ 9, 1, 2, 4 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 12, 1, 1, 4 ], [ 12, 1, 3, 4 ], [ 13, 1, 2, 8 ], [ 13, 1, 3, 8 ], [ 14, 1, 1, 4 ], [ 14, 1, 2, 4 ], [ 14, 1, 3, 4 ], [ 14, 1, 4, 4 ], [ 15, 1, 2, 4 ], [ 15, 1, 4, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 7, 8 ], [ 17, 1, 2, 8 ], [ 17, 1, 3, 8 ], [ 18, 1, 2, 8 ], [ 18, 1, 8, 8 ], [ 19, 1, 3, 8 ], [ 19, 1, 4, 8 ] ] k = 23: F-action on Pi is () [20,1,23] Dynkin type is A_0(q) + T(phi1^2 phi4) Order of center |Z^F|: phi1^2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 2 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 3 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 4 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 5 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 7 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 8 modulo 12: 1/32 q^2 ( q^2-6*q+8 ) q congruent 9 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) q congruent 11 modulo 12: 1/32 phi1 phi2 ( q^2-6*q+9 ) Fusion of maximal tori of C^F in those of G^F: [ 23 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ], [ 8, 1, 3, 8 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 2, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 5, 4 ], [ 16, 1, 3, 16 ], [ 16, 1, 5, 8 ], [ 18, 1, 6, 16 ], [ 19, 1, 6, 16 ] ] k = 24: F-action on Pi is () [20,1,24] Dynkin type is A_0(q) + T(phi2^2 phi4) Order of center |Z^F|: phi2^2 phi4 Numbers of classes in class type: q congruent 1 modulo 12: 1/32 phi1^3 phi2 q congruent 2 modulo 12: 1/32 q^3 ( q-2 ) q congruent 3 modulo 12: 1/32 phi1^3 phi2 q congruent 4 modulo 12: 1/32 q^3 ( q-2 ) q congruent 5 modulo 12: 1/32 phi1^3 phi2 q congruent 7 modulo 12: 1/32 phi1^3 phi2 q congruent 8 modulo 12: 1/32 q^3 ( q-2 ) q congruent 9 modulo 12: 1/32 phi1^3 phi2 q congruent 11 modulo 12: 1/32 phi1^3 phi2 Fusion of maximal tori of C^F in those of G^F: [ 24 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 4 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 4 ], [ 8, 1, 2, 8 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 4, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 5, 4 ], [ 16, 1, 5, 8 ], [ 16, 1, 10, 16 ], [ 18, 1, 4, 16 ], [ 19, 1, 7, 16 ] ] k = 25: F-action on Pi is () [20,1,25] Dynkin type is A_0(q) + T(phi8) Order of center |Z^F|: phi8 Numbers of classes in class type: q congruent 1 modulo 12: 1/8 phi1 phi2 phi4 q congruent 2 modulo 12: 1/8 q^4 q congruent 3 modulo 12: 1/8 phi1 phi2 phi4 q congruent 4 modulo 12: 1/8 q^4 q congruent 5 modulo 12: 1/8 phi1 phi2 phi4 q congruent 7 modulo 12: 1/8 phi1 phi2 phi4 q congruent 8 modulo 12: 1/8 q^4 q congruent 9 modulo 12: 1/8 phi1 phi2 phi4 q congruent 11 modulo 12: 1/8 phi1 phi2 phi4 Fusion of maximal tori of C^F in those of G^F: [ 25 ] elements of other class types in center: [ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ]