Centralizers of semisimple elements in D6(q)_ad
--------------------------------------------
|G(q)| = q^30 phi1^6 phi2^6 phi3^2 phi4^2 phi5 phi6^2 phi8 phi10
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 D_6(q)
Order of center |Z^F|: 1
Numbers of classes in class type:
q congruent 0 modulo 4: 1
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 1
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 1 .. 37 ]
elements of other class types in center:
[ ]
i = 2: Pi = [ 1, 2, 3, 4, 6, 60 ]
j = 2: Omega of order 2, action on Pi: <( 1, 2)( 6,60)>
k = 1: F-action on Pi is () [2,2,1]
Dynkin type is (D_4(q) + A_1(q) + A_1(q)).2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2, 2, 7, 7, 3, 3, 9, 9, 4, 5, 10, 10, 7, 6, 12, 12, 8, 7,
13, 13, 9, 10, 16, 15, 13, 10, 15, 16, 13, 11, 17, 17, 14, 18, 22, 22, 20,
19, 24, 24, 21, 28, 32, 31, 30, 28, 31, 32, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
k = 2: F-action on Pi is ( 1, 2)( 6,60) [2,2,2]
Dynkin type is (^2D_4(q) + A_1(q^2)).2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6, 3, 8, 6, 11, 7, 12, 8, 14, 12, 17, 19, 23, 20, 25, 29, 33 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
i = 3: Pi = [ 1, 2, 3, 5, 6, 60 ]
j = 5: Omega of order 4, action on Pi: <( 1, 2)( 6,60), ( 1, 2)( 6,60)>
k = 1: F-action on Pi is () [3,5,1]
Dynkin type is (A_3(q) + A_3(q)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 2, 18, 6, 5, 10, 7, 22, 12, 2, 7, 3, 20, 8, 18, 22, 20, 26,
25, 6, 12, 8, 25, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
k = 2: F-action on Pi is ( 1, 2)( 6,60) [3,5,2]
Dynkin type is (^2A_3(q) + ^2A_3(q)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 3, 21, 8, 9, 13, 7, 24, 12, 3, 7, 2, 19, 6, 21, 24, 19, 27,
23, 8, 12, 6, 23, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
k = 3: F-action on Pi is ( 1, 6)( 2,60)( 3, 5) [3,5,3]
Dynkin type is A_3(q^2).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 17, 37, 33 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
k = 4: F-action on Pi is ( 1,60)( 2, 6)( 3, 5) [3,5,4]
Dynkin type is A_3(q^2).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 17, 36, 33 ]
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 0 modulo 4: 1/2 ( q-2 )
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 1/2 ( q-2 )
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 18, 19, 20, 22, 23, 28, 29, 34 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 2, 1, 1 ] ]
k = 2: F-action on Pi is (1,2) [4,1,2]
Dynkin type is ^2D_5(q) + T(phi2)
Order of center |Z^F|: phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 q
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 1/2 q
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 19, 20, 21, 24, 25, 29, 30, 35 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 2, 2, 1 ] ]
j = 2: Omega of order 2, action on Pi: <(1,2)>
k = 1: F-action on Pi is () [4,2,1]
Dynkin type is (D_5(q) + T(phi1)).2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 18, 19, 20, 22, 23, 28, 29, 34 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
k = 2: F-action on Pi is (1,2) [4,2,2]
Dynkin type is (^2D_5(q) + T(phi2)).2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 19, 20, 21, 24, 25, 29, 30, 35 ]
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 D_4(q) + A_1(q) + T(phi1)
Order of center |Z^F|: phi1
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 ( q-2 )
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 1/2 ( q-2 )
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 2, 7, 3, 9, 5, 10, 6, 12, 7, 13, 10, 15, 10, 16, 11, 17, 18,
22, 19, 24, 28, 31, 28, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 2: F-action on Pi is () [5,1,2]
Dynkin type is D_4(q) + A_1(q) + T(phi2)
Order of center |Z^F|: phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 q
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 1/2 q
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 7, 3, 9, 4, 10, 7, 12, 8, 13, 9, 16, 13, 15, 13, 17, 14, 22,
20, 24, 21, 32, 30, 31, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 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_3(q) + A_2(q) + T(phi1)
Order of center |Z^F|: phi1
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 ( q-2 )
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 1/2 ( q-2 )
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 18, 5, 10, 22, 2, 7, 20, 18, 22, 26, 6, 12, 25 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ] ]
k = 2: F-action on Pi is (1,2)(5,6) [6,1,2]
Dynkin type is ^2A_3(q) + ^2A_2(q) + T(phi2)
Order of center |Z^F|: phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 q
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 1/2 q
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 21, 9, 13, 24, 3, 7, 19, 21, 24, 27, 8, 12, 23 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ] ]
i = 7: Pi = [ 1, 2, 3, 6, 60 ]
j = 4: Omega of order 2, action on Pi: <( 1, 2)( 6,60)>
k = 1: F-action on Pi is () [7,4,1]
Dynkin type is (A_3(q) + A_1(q) + A_1(q) + T(phi1)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2, 5, 10, 10, 7, 2, 7, 7, 3, 18, 22, 22, 20, 6, 12, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 1, 1 ], [ 3, 2, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 7, 5, 1, 1 ] ]
k = 2: F-action on Pi is ( 6,60) [7,4,2]
Dynkin type is (A_3(q) + A_1(q^2) + T(phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6, 7, 12, 3, 8, 20, 25, 8, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 2, 1 ], [ 3, 2, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 7, 5, 2, 1 ] ]
k = 3: F-action on Pi is ( 1, 2)( 6,60) [7,4,3]
Dynkin type is (^2A_3(q) + A_1(q^2) + T(phi1)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 8, 7, 12, 2, 6, 19, 23, 6, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 2, 1 ], [ 3, 2, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 7, 5, 3, 1 ] ]
k = 4: F-action on Pi is (1,2) [7,4,4]
Dynkin type is (^2A_3(q) + A_1(q) + A_1(q) + T(phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 9, 4, 7, 13, 13, 9, 2, 7, 7, 3, 19, 24, 24, 21, 6, 12, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 1, 1 ], [ 3, 2, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 7, 5, 4, 1 ] ]
i = 8: Pi = [ 1, 2, 4, 5, 6 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [8,1,1]
Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1)
Order of center |Z^F|: phi1
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 ( q-2 )
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 1/2 ( q-2 )
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2, 5, 10, 10, 7, 10, 16, 15, 13, 18, 22, 22, 20, 28, 32,
31, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 2: F-action on Pi is (4,6) [8,1,2]
Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi2)
Order of center |Z^F|: phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 q
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 1/2 q
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 9, 4, 7, 13, 13, 9, 10, 16, 15, 13, 19, 24, 24, 21, 28, 32,
31, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
i = 9: Pi = [ 1, 2, 4, 6, 60 ]
j = 2: Omega of order 2, action on Pi: <( 1, 2)( 6,60)>
k = 1: F-action on Pi is () [9,2,1]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2, 5, 10, 10, 7, 5, 10, 10, 7, 10, 15, 16, 13, 5, 10, 10,
7, 10, 16, 15, 13, 2, 7, 7, 3, 7, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 5, 1, 2 ] ]
k = 2: F-action on Pi is () [9,2,2]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 7, 2, 7, 7, 3, 10, 16, 15, 13, 7, 13, 13, 9, 10, 15, 16,
13, 7, 13, 13, 9, 7, 13, 13, 9, 3, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 5, 2, 2 ] ]
k = 3: F-action on Pi is ( 1, 2)( 6,60) [9,2,3]
Dynkin type is (A_1(q^2) + A_1(q) + A_1(q^2) + T(phi1)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6, 7, 12, 6, 11, 12, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 5, 1, 1, 2 ], [ 9, 5, 3, 2 ] ]
k = 4: F-action on Pi is ( 1, 2)( 6,60) [9,2,4]
Dynkin type is (A_1(q^2) + A_1(q) + A_1(q^2) + T(phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 12, 3, 8, 12, 17, 8, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 5, 1, 2, 2 ], [ 9, 5, 4, 2 ] ]
k = 5: F-action on Pi is ( 1, 6)( 2,60) [9,2,5]
Dynkin type is (A_1(q^2) + A_1(q^2) + A_1(q) + T(phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13, 32, 30, 32, 30, 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 5, 5, 2 ] ]
k = 6: F-action on Pi is ( 1, 6)( 2,60) [9,2,6]
Dynkin type is (A_1(q^2) + A_1(q^2) + A_1(q) + T(phi1)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15, 28, 31, 28, 31, 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 5, 6, 2 ] ]
k = 7: F-action on Pi is ( 1,60)( 2, 6) [9,2,7]
Dynkin type is (A_1(q^2) + A_1(q^2) + A_1(q) + T(phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13, 31, 30, 31, 30, 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 5, 7, 2 ] ]
k = 8: F-action on Pi is ( 1,60)( 2, 6) [9,2,8]
Dynkin type is (A_1(q^2) + A_1(q^2) + A_1(q) + T(phi1)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16, 28, 32, 28, 32, 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 5, 8, 2 ] ]
j = 5: Omega of order 4, action on Pi: <( 1, 2)( 6,60), ( 1, 2)( 6,60)>
k = 1: F-action on Pi is () [9,5,1]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1)).2.2
Order of center |Z^F|: 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 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2, 5, 10, 10, 7, 5, 10, 10, 7, 10, 15, 16, 13, 5, 10, 10,
7, 10, 16, 15, 13, 2, 7, 7, 3, 7, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 2: F-action on Pi is () [9,5,2]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2)).2.2
Order of center |Z^F|: 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 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 7, 2, 7, 7, 3, 10, 16, 15, 13, 7, 13, 13, 9, 10, 15, 16,
13, 7, 13, 13, 9, 7, 13, 13, 9, 3, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 3: F-action on Pi is ( 1, 2)( 6,60) [9,5,3]
Dynkin type is (A_1(q^2) + A_1(q) + A_1(q^2) + T(phi1)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6, 7, 12, 6, 11, 12, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 4: F-action on Pi is ( 1, 2)( 6,60) [9,5,4]
Dynkin type is (A_1(q^2) + A_1(q) + A_1(q^2) + T(phi2)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 7, 12, 3, 8, 12, 17, 8, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 5: F-action on Pi is ( 1, 6)( 2,60) [9,5,5]
Dynkin type is (A_1(q^2) + A_1(q^2) + A_1(q) + T(phi2)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13, 32, 30, 32, 30, 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 6: F-action on Pi is ( 1, 6)( 2,60) [9,5,6]
Dynkin type is (A_1(q^2) + A_1(q^2) + A_1(q) + T(phi1)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15, 28, 31, 28, 31, 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 7: F-action on Pi is ( 1,60)( 2, 6) [9,5,7]
Dynkin type is (A_1(q^2) + A_1(q^2) + A_1(q) + T(phi2)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13, 31, 30, 31, 30, 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 8: F-action on Pi is ( 1,60)( 2, 6) [9,5,8]
Dynkin type is (A_1(q^2) + A_1(q^2) + A_1(q) + T(phi1)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16, 28, 32, 28, 32, 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
i = 10: Pi = [ 1, 3, 4, 5, 6 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [10,1,1]
Dynkin type is A_5(q) + T(phi1)
Order of center |Z^F|: phi1
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 ( q-2 )
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 1/2 ( q-2 )
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 15, 18, 22, 26, 28, 31, 34, 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 10, 2, 1, 1 ] ]
k = 2: F-action on Pi is (1,6)(3,5) [10,1,2]
Dynkin type is ^2A_5(q) + T(phi2)
Order of center |Z^F|: phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 q
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 1/2 q
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 16, 21, 24, 27, 30, 32, 35, 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 10, 2, 2, 1 ] ]
j = 2: Omega of order 2, action on Pi: <(1,6)(3,5)>
k = 1: F-action on Pi is () [10,2,1]
Dynkin type is (A_5(q) + T(phi1)).2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 15, 18, 22, 26, 28, 31, 34, 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
k = 2: F-action on Pi is (1,6)(3,5) [10,2,2]
Dynkin type is (^2A_5(q) + T(phi2)).2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 16, 21, 24, 27, 30, 32, 35, 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
i = 11: Pi = [ 2, 3, 4, 5, 6 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [11,1,1]
Dynkin type is A_5(q) + T(phi1)
Order of center |Z^F|: phi1
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 ( q-2 )
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 1/2 ( q-2 )
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 16, 18, 22, 26, 28, 32, 34, 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 11, 2, 1, 1 ] ]
k = 2: F-action on Pi is (2,6)(3,5) [11,1,2]
Dynkin type is ^2A_5(q) + T(phi2)
Order of center |Z^F|: phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 q
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 1/2 q
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 15, 21, 24, 27, 30, 31, 35, 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 11, 2, 2, 1 ] ]
j = 2: Omega of order 2, action on Pi: <(2,6)(3,5)>
k = 1: F-action on Pi is () [11,2,1]
Dynkin type is (A_5(q) + T(phi1)).2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 16, 18, 22, 26, 28, 32, 34, 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
k = 2: F-action on Pi is (2,6)(3,5) [11,2,2]
Dynkin type is (^2A_5(q) + T(phi2)).2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 15, 21, 24, 27, 30, 31, 35, 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]
i = 12: Pi = [ 1, 2, 3, 4 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [12,1,1]
Dynkin type is D_4(q) + T(phi1^2)
Order of center |Z^F|: phi1^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/8 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/8 ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/8 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 2, 3, 5, 6, 7, 10, 10, 11, 18, 19, 28, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ],
[ 12, 4, 1, 2 ] ]
k = 2: F-action on Pi is () [12,1,2]
Dynkin type is D_4(q) + T(phi1 phi2)
Order of center |Z^F|: phi1 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 5, 7, 9, 10, 12, 13, 15, 16, 17, 22, 24, 31, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ] ]
k = 3: F-action on Pi is () [12,1,3]
Dynkin type is D_4(q) + T(phi2^2)
Order of center |Z^F|: phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 1/8 q ( q-2 )
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 3, 4, 7, 8, 9, 13, 13, 14, 20, 21, 30, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 2, 4 ],
[ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ],
[ 12, 4, 3, 2 ] ]
k = 4: F-action on Pi is (1,2) [12,1,4]
Dynkin type is ^2D_4(q) + T(phi1 phi2)
Order of center |Z^F|: phi1 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 3, 6, 7, 8, 12, 19, 20, 29 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 12, 2, 4, 2 ],
[ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ] ]
k = 5: F-action on Pi is (1,2) [12,1,5]
Dynkin type is ^2D_4(q) + T(phi4)
Order of center |Z^F|: phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q^2
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 1/4 q^2
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 6, 8, 11, 12, 14, 17, 23, 25, 33 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 12, 2, 5, 2 ],
[ 12, 4, 5, 2 ] ]
j = 3: Omega of order 2, action on Pi: <(1,2)>
k = 1: F-action on Pi is () [12,3,1]
Dynkin type is (D_4(q) + T(phi1^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 2, 3, 5, 6, 7, 10, 10, 11, 18, 19, 28, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 2, 1, 2 ],
[ 12, 4, 1, 2 ] ]
k = 2: F-action on Pi is () [12,3,2]
Dynkin type is (D_4(q) + T(phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 2, 3, 4, 7, 8, 9, 13, 13, 14, 20, 21, 30, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 1, 1 ], [ 4, 1, 2, 2 ], [ 4, 2, 2, 2 ],
[ 12, 4, 3, 2 ] ]
k = 3: F-action on Pi is (1,2) [12,3,3]
Dynkin type is (^2D_4(q) + T(phi1 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 2, 3, 6, 7, 8, 12, 19, 20, 29 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 2, 1 ], [ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ],
[ 4, 2, 2, 1 ], [ 12, 4, 4, 1 ] ]
k = 4: F-action on Pi is (1,2) [12,3,4]
Dynkin type is (^2D_4(q) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 3, 6, 7, 8, 12, 19, 20, 29 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 2, 1 ], [ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ],
[ 4, 2, 2, 1 ], [ 12, 4, 4, 1 ] ]
i = 13: Pi = [ 1, 2, 3, 5 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [13,1,1]
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 0 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/4 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/4 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 2, 7, 18, 22, 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ],
[ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ],
[ 7, 5, 1, 1 ], [ 13, 2, 1, 2 ] ]
k = 2: F-action on Pi is () [13,1,2]
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 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 10, 7, 7, 3, 22, 20, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 5, 1, 2, 2 ], [ 7, 1, 1, 4 ],
[ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ],
[ 13, 2, 2, 2 ] ]
k = 3: F-action on Pi is (1,2) [13,1,3]
Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2)
Order of center |Z^F|: phi1 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 7, 13, 2, 7, 19, 24, 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 7, 1, 4, 4 ],
[ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 4, 1 ],
[ 13, 2, 3, 2 ] ]
k = 4: F-action on Pi is (1,2) [13,1,4]
Dynkin type is ^2A_3(q) + A_1(q) + T(phi2^2)
Order of center |Z^F|: phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4, 13, 9, 7, 3, 24, 21, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ],
[ 7, 5, 4, 1 ], [ 13, 2, 4, 2 ] ]
j = 2: Omega of order 2, action on Pi: <(1,2)>
k = 1: F-action on Pi is () [13,2,1]
Dynkin type is (A_3(q) + A_1(q) + T(phi1^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 2, 7, 18, 22, 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 1, 2 ],
[ 3, 5, 1, 1 ], [ 4, 2, 1, 1 ], [ 5, 1, 1, 2 ], [ 7, 3, 1, 2 ],
[ 7, 5, 1, 1 ] ]
k = 2: F-action on Pi is () [13,2,2]
Dynkin type is (A_3(q) + A_1(q) + T(phi1 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 10, 7, 7, 3, 22, 20, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 1, 2 ],
[ 3, 5, 1, 1 ], [ 4, 2, 1, 1 ], [ 5, 1, 2, 2 ], [ 7, 3, 1, 2 ],
[ 7, 5, 1, 1 ] ]
k = 3: F-action on Pi is (1,2) [13,2,3]
Dynkin type is (^2A_3(q) + A_1(q) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 7, 13, 2, 7, 19, 24, 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 2, 2 ],
[ 3, 5, 2, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 7, 3, 4, 2 ],
[ 7, 5, 4, 1 ] ]
k = 4: F-action on Pi is (1,2) [13,2,4]
Dynkin type is (^2A_3(q) + A_1(q) + T(phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4, 13, 9, 7, 3, 24, 21, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 2, 2 ],
[ 3, 5, 2, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ], [ 7, 3, 4, 2 ],
[ 7, 5, 4, 1 ] ]
i = 14: Pi = [ 1, 2, 4, 5 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [14,1,1]
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 0 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/4 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/4 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2, 5, 10, 10, 7, 18, 22, 22, 20 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ],
[ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ],
[ 8, 1, 1, 4 ], [ 14, 2, 1, 2 ] ]
k = 2: F-action on Pi is (4,5) [14,1,2]
Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi2^2)
Order of center |Z^F|: phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 9, 4, 7, 13, 13, 9, 19, 24, 24, 21 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 4, 4 ],
[ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 4, 1 ],
[ 8, 1, 2, 4 ], [ 14, 2, 2, 2 ] ]
k = 3: F-action on Pi is (1,2) [14,1,3]
Dynkin type is A_2(q) + A_1(q^2) + T(phi1 phi2)
Order of center |Z^F|: phi1 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6, 7, 12, 20, 25 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 2, 4 ],
[ 7, 2, 2, 2 ], [ 7, 3, 2, 2 ], [ 7, 4, 2, 2 ], [ 7, 5, 2, 1 ],
[ 14, 2, 3, 2 ] ]
k = 4: F-action on Pi is (1,2)(4,5) [14,1,4]
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 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 8, 7, 12, 19, 23 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 3, 4 ],
[ 7, 2, 3, 2 ], [ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 3, 1 ],
[ 14, 2, 4, 2 ] ]
j = 2: Omega of order 2, action on Pi: <(1,2)>
k = 1: F-action on Pi is () [14,2,1]
Dynkin type is (A_2(q) + A_1(q) + A_1(q) + T(phi1^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2, 5, 10, 10, 7, 18, 22, 22, 20 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ],
[ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 4, 2, 1, 1 ],
[ 6, 1, 1, 2 ], [ 7, 2, 1, 2 ], [ 7, 5, 1, 1 ] ]
k = 2: F-action on Pi is (4,5) [14,2,2]
Dynkin type is (^2A_2(q) + A_1(q) + A_1(q) + T(phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 9, 4, 7, 13, 13, 9, 19, 24, 24, 21 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ],
[ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 4, 2, 2, 1 ],
[ 6, 1, 2, 2 ], [ 7, 2, 4, 2 ], [ 7, 5, 4, 1 ] ]
k = 3: F-action on Pi is (1,2) [14,2,3]
Dynkin type is (A_2(q) + A_1(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6, 7, 12, 20, 25 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ],
[ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 4, 2, 2, 1 ],
[ 6, 1, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 5, 2, 1 ] ]
k = 4: F-action on Pi is (1,2)(4,5) [14,2,4]
Dynkin type is (^2A_2(q) + A_1(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 3, 8, 7, 12, 19, 23 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 2, 1 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ],
[ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 4, 2, 1, 1 ],
[ 6, 1, 2, 2 ], [ 7, 2, 3, 2 ], [ 7, 5, 3, 1 ] ]
i = 15: Pi = [ 1, 2, 4, 6 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [15,1,1]
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
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/8 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/8 ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/8 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 5, 10, 10, 16, 5, 10, 10, 15, 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ] ]
k = 2: F-action on Pi is (4,6) [15,1,2]
Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1 phi2)
Order of center |Z^F|: phi1 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28, 16, 32, 15, 31, 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ] ]
k = 3: F-action on Pi is () [15,1,3]
Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2)
Order of center |Z^F|: phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 1/8 q ( q-2 )
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 7, 3, 16, 13, 13, 9, 15, 13, 13, 9, 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ] ]
k = 4: F-action on Pi is () [15,1,4]
Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2)
Order of center |Z^F|: phi1 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 2, 7, 10, 15, 7, 13, 10, 16, 7, 13, 7, 13, 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ] ]
k = 5: F-action on Pi is (4,6) [15,1,5]
Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi4)
Order of center |Z^F|: phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q^2
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 1/4 q^2
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 28, 11, 32, 17, 31, 17, 30, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
i = 16: Pi = [ 1, 2, 6, 60 ]
j = 4: Omega of order 2, action on Pi: <( 1, 2)( 6,60)>
k = 1: F-action on Pi is () [16,4,1]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2, 5, 10, 10, 7, 5, 10, 10, 7, 2, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 2, 1, 4 ],
[ 3, 5, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ],
[ 7, 4, 1, 8 ], [ 7, 5, 1, 4 ], [ 9, 2, 1, 8 ], [ 9, 5, 1, 4 ],
[ 12, 1, 1, 8 ], [ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ],
[ 16, 9, 1, 8 ], [ 16, 12, 1, 8 ], [ 16, 13, 1, 8 ], [ 16, 14, 1, 8 ] ]
k = 2: F-action on Pi is ( 6,60) [16,4,2]
Dynkin type is (A_1(q) + A_1(q) + A_1(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6, 7, 12, 7, 12, 3, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ],
[ 7, 4, 1, 2 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ], [ 7, 4, 4, 2 ],
[ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ],
[ 12, 1, 4, 4 ], [ 12, 2, 4, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ],
[ 12, 4, 4, 1 ], [ 16, 9, 2, 2 ], [ 16, 13, 2, 4 ], [ 16, 14, 2, 2 ],
[ 16, 14, 3, 2 ] ]
k = 3: F-action on Pi is () [16,4,3]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 7, 10, 15, 16, 13, 10, 16, 15, 13, 7, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 4 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ],
[ 16, 9, 3, 4 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ] ]
k = 4: F-action on Pi is ( 6,60) [16,4,4]
Dynkin type is (A_1(q) + A_1(q) + A_1(q^2) + T(phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 6, 11, 12, 17, 12, 17, 8, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 16, 9, 4, 2 ],
[ 16, 13, 4, 4 ] ]
k = 5: F-action on Pi is () [16,4,5]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 3, 7, 13, 13, 9, 7, 13, 13, 9, 3, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 2, 2, 4 ],
[ 3, 5, 2, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ],
[ 7, 4, 4, 8 ], [ 7, 5, 4, 4 ], [ 9, 2, 2, 8 ], [ 9, 5, 2, 4 ],
[ 12, 1, 3, 8 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ],
[ 16, 9, 5, 8 ], [ 16, 12, 3, 8 ], [ 16, 13, 5, 8 ], [ 16, 14, 4, 8 ] ]
k = 6: F-action on Pi is ( 1, 2)( 6,60) [16,4,6]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6, 6, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 2, 2, 4 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ],
[ 5, 1, 1, 4 ], [ 7, 4, 3, 8 ], [ 7, 5, 3, 4 ], [ 9, 2, 3, 8 ],
[ 9, 5, 3, 4 ], [ 12, 1, 1, 8 ], [ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ],
[ 12, 4, 1, 2 ], [ 16, 9, 6, 8 ], [ 16, 12, 5, 8 ], [ 16, 13, 6, 8 ],
[ 16, 14, 5, 8 ] ]
k = 7: F-action on Pi is ( 1, 2)( 6,60) [16,4,7]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 12, 12, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 2, 3, 4 ], [ 9, 2, 4, 4 ],
[ 9, 5, 3, 2 ], [ 9, 5, 4, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 16, 9, 7, 4 ], [ 16, 12, 6, 4 ], [ 16, 12, 8, 4 ],
[ 16, 13, 7, 4 ] ]
k = 8: F-action on Pi is ( 1, 2)( 6,60) [16,4,8]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 8, 8, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 2, 1, 4 ], [ 3, 5, 1, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ],
[ 5, 1, 2, 4 ], [ 7, 4, 2, 8 ], [ 7, 5, 2, 4 ], [ 9, 2, 4, 8 ],
[ 9, 5, 4, 4 ], [ 12, 1, 3, 8 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ],
[ 12, 4, 3, 2 ], [ 16, 9, 8, 8 ], [ 16, 12, 7, 8 ], [ 16, 13, 8, 8 ],
[ 16, 14, 6, 8 ] ]
k = 9: F-action on Pi is ( 1, 6)( 2,60) [16,4,9]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 32, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 3, 4 ],
[ 3, 5, 3, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 2, 5, 4 ],
[ 9, 2, 8, 4 ], [ 9, 5, 5, 2 ], [ 9, 5, 8, 2 ], [ 12, 1, 2, 4 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 16, 9, 9, 4 ], [ 16, 12, 9, 4 ],
[ 16, 12, 16, 4 ], [ 16, 13, 9, 4 ] ]
k = 10: F-action on Pi is ( 1, 6, 2,60) [16,4,10]
Dynkin type is (A_1(q^4) + T(phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 17, 33 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 2, 3, 2 ],
[ 3, 2, 4, 2 ], [ 3, 5, 3, 1 ], [ 3, 5, 4, 1 ], [ 12, 1, 5, 4 ],
[ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 16, 9, 10, 2 ], [ 16, 13, 10, 4 ] ]
k = 11: F-action on Pi is ( 1, 6, 2,60) [16,4,11]
Dynkin type is (A_1(q^4) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 12, 29 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 12, 1, 4, 4 ],
[ 12, 2, 4, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ],
[ 16, 9, 11, 2 ], [ 16, 13, 11, 4 ], [ 16, 14, 7, 4 ], [ 16, 14, 10, 4 ] ]
k = 12: F-action on Pi is ( 1, 6)( 2,60) [16,4,12]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30, 30, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 2, 4 ],
[ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 9, 2, 5, 4 ], [ 9, 2, 7, 4 ],
[ 9, 5, 5, 2 ], [ 9, 5, 7, 2 ], [ 12, 1, 3, 8 ], [ 12, 2, 3, 4 ],
[ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ], [ 16, 9, 12, 4 ], [ 16, 12, 10, 4 ],
[ 16, 12, 14, 4 ], [ 16, 13, 12, 4 ], [ 16, 14, 8, 8 ] ]
k = 13: F-action on Pi is ( 1, 6)( 2,60) [16,4,13]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28, 28, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 9, 2, 6, 4 ], [ 9, 2, 8, 4 ],
[ 9, 5, 6, 2 ], [ 9, 5, 8, 2 ], [ 12, 1, 1, 8 ], [ 12, 2, 1, 4 ],
[ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 16, 9, 13, 4 ], [ 16, 12, 11, 4 ],
[ 16, 12, 15, 4 ], [ 16, 13, 13, 4 ], [ 16, 14, 9, 8 ] ]
k = 14: F-action on Pi is ( 1, 6)( 2,60) [16,4,14]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 31, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 4, 4 ],
[ 3, 5, 4, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 2, 6, 4 ],
[ 9, 2, 7, 4 ], [ 9, 5, 6, 2 ], [ 9, 5, 7, 2 ], [ 12, 1, 2, 4 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 16, 9, 14, 4 ], [ 16, 12, 12, 4 ],
[ 16, 12, 13, 4 ], [ 16, 13, 14, 4 ] ]
j = 12: Omega of order 4, action on Pi: <( 1, 2)( 6,60), ( 1, 2)( 6,60)>
k = 1: F-action on Pi is () [16,12,1]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2, 5, 10, 10, 7, 5, 10, 10, 7, 2, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 1, 2 ],
[ 5, 1, 1, 2 ], [ 9, 5, 1, 2 ] ]
k = 2: F-action on Pi is () [16,12,2]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 7, 10, 15, 16, 13, 10, 16, 15, 13, 7, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 5, 2, 2 ] ]
k = 3: F-action on Pi is () [16,12,3]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 3, 7, 13, 13, 9, 7, 13, 13, 9, 3, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 2, 2 ],
[ 5, 1, 2, 2 ], [ 9, 5, 2, 2 ] ]
k = 4: F-action on Pi is () [16,12,4]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 7, 10, 16, 15, 13, 10, 15, 16, 13, 7, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 5, 1, 2 ] ]
k = 5: F-action on Pi is ( 1, 2)( 6,60) [16,12,5]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6, 6, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 2, 2 ],
[ 5, 1, 1, 2 ], [ 9, 5, 3, 2 ] ]
k = 6: F-action on Pi is ( 1, 2)( 6,60) [16,12,6]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 12, 12, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 5, 4, 2 ] ]
k = 7: F-action on Pi is ( 1, 2)( 6,60) [16,12,7]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 8, 8, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 5, 4, 2 ] ]
k = 8: F-action on Pi is ( 1, 2)( 6,60) [16,12,8]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 7, 12, 12, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 5, 3, 2 ] ]
k = 9: F-action on Pi is ( 1, 6)( 2,60) [16,12,9]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 32, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 3, 2 ],
[ 5, 1, 2, 2 ], [ 9, 5, 8, 2 ] ]
k = 10: F-action on Pi is ( 1, 6)( 2,60) [16,12,10]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30, 30, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 5, 7, 2 ] ]
k = 11: F-action on Pi is ( 1, 6)( 2,60) [16,12,11]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28, 28, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 5, 8, 2 ] ]
k = 12: F-action on Pi is ( 1, 6)( 2,60) [16,12,12]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 31, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 4, 2 ],
[ 5, 1, 1, 2 ], [ 9, 5, 7, 2 ] ]
k = 13: F-action on Pi is ( 1,60)( 2, 6) [16,12,13]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 31, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 4, 2 ],
[ 5, 1, 2, 2 ], [ 9, 5, 6, 2 ] ]
k = 14: F-action on Pi is ( 1,60)( 2, 6) [16,12,14]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30, 30, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 5, 5, 2 ] ]
k = 15: F-action on Pi is ( 1,60)( 2, 6) [16,12,15]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28, 28, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 5, 6, 2 ] ]
k = 16: F-action on Pi is ( 1,60)( 2, 6) [16,12,16]
Dynkin type is (A_1(q^2) + A_1(q^2) + T(phi1 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 32, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 3, 2 ],
[ 5, 1, 1, 2 ], [ 9, 5, 5, 2 ] ]
i = 17: Pi = [ 1, 3, 4, 5 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [17,1,1]
Dynkin type is A_4(q) + T(phi1^2)
Order of center |Z^F|: phi1^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 ( q^2-5*q+6 )
q congruent 1 modulo 4: 1/2 ( q^2-5*q+6 )
q congruent 2 modulo 4: 1/2 ( q^2-5*q+6 )
q congruent 3 modulo 4: 1/2 ( q^2-5*q+6 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 18, 22, 28, 34 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 10, 1, 1, 2 ],
[ 10, 2, 1, 1 ], [ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 17, 2, 1, 1 ] ]
k = 2: F-action on Pi is (1,5)(3,4) [17,1,2]
Dynkin type is ^2A_4(q) + T(phi2^2)
Order of center |Z^F|: phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/2 q phi1
q congruent 1 modulo 4: 1/2 q phi1
q congruent 2 modulo 4: 1/2 q phi1
q congruent 3 modulo 4: 1/2 q phi1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 21, 24, 30, 35 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 10, 1, 2, 2 ],
[ 10, 2, 2, 1 ], [ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 17, 2, 2, 1 ] ]
i = 18: Pi = [ 1, 3, 4, 6 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [18,1,1]
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 0 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/4 ( q^2-6*q+9 )
q congruent 2 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/4 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 10, 15, 18, 22, 28, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ], [ 18, 2, 1, 2 ] ]
k = 2: F-action on Pi is () [18,1,2]
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 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 10, 7, 16, 13, 22, 20, 32, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 18, 2, 2, 2 ] ]
k = 3: F-action on Pi is (1,4) [18,1,3]
Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2)
Order of center |Z^F|: phi1 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 7, 13, 10, 15, 19, 24, 28, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 18, 2, 3, 2 ] ]
k = 4: F-action on Pi is (1,4) [18,1,4]
Dynkin type is ^2A_3(q) + A_1(q) + T(phi2^2)
Order of center |Z^F|: phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4, 13, 9, 16, 13, 24, 21, 32, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ], [ 18, 2, 4, 2 ] ]
i = 19: Pi = [ 1, 3, 5, 6 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [19,1,1]
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 0 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/4 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/4 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 18, 5, 10, 22, 18, 22, 26 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 6, 1, 1, 4 ], [ 10, 1, 1, 2 ],
[ 10, 2, 1, 1 ], [ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 19, 2, 1, 2 ],
[ 19, 3, 1, 2 ], [ 19, 4, 1, 2 ], [ 19, 5, 1, 1 ] ]
k = 2: F-action on Pi is (1,3)(5,6) [19,1,2]
Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi2^2)
Order of center |Z^F|: phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 21, 9, 13, 24, 21, 24, 27 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 6, 1, 2, 4 ], [ 10, 1, 2, 2 ],
[ 10, 2, 2, 1 ], [ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 19, 2, 2, 2 ],
[ 19, 3, 2, 2 ], [ 19, 4, 2, 2 ], [ 19, 5, 2, 1 ] ]
k = 3: F-action on Pi is (1,5)(3,6) [19,1,3]
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 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 4, 4 ], [ 3, 2, 4, 2 ], [ 3, 3, 4, 2 ],
[ 3, 4, 4, 2 ], [ 3, 5, 4, 1 ], [ 10, 1, 1, 2 ], [ 10, 2, 1, 1 ],
[ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 19, 2, 3, 2 ], [ 19, 3, 3, 2 ],
[ 19, 4, 3, 2 ], [ 19, 5, 3, 1 ] ]
k = 4: F-action on Pi is (1,6)(3,5) [19,1,4]
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 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 3, 4 ], [ 3, 2, 3, 2 ], [ 3, 3, 3, 2 ],
[ 3, 4, 3, 2 ], [ 3, 5, 3, 1 ], [ 10, 1, 2, 2 ], [ 10, 2, 2, 1 ],
[ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 19, 2, 4, 2 ], [ 19, 3, 4, 2 ],
[ 19, 4, 4, 2 ], [ 19, 5, 4, 1 ] ]
j = 3: Omega of order 2, action on Pi: <(1,5)(3,6)>
k = 1: F-action on Pi is () [19,3,1]
Dynkin type is (A_2(q) + A_2(q) + T(phi1^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 18, 5, 10, 22, 18, 22, 26 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 10, 1, 1, 2 ],
[ 10, 2, 1, 1 ], [ 11, 2, 1, 1 ], [ 19, 5, 1, 1 ] ]
k = 2: F-action on Pi is (1,3)(5,6) [19,3,2]
Dynkin type is (^2A_2(q) + ^2A_2(q) + T(phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 21, 9, 13, 24, 21, 24, 27 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 10, 1, 2, 2 ],
[ 10, 2, 2, 1 ], [ 11, 2, 2, 1 ], [ 19, 5, 2, 1 ] ]
k = 3: F-action on Pi is (1,5)(3,6) [19,3,3]
Dynkin type is (A_2(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 4, 4, 2 ], [ 3, 5, 4, 1 ], [ 10, 1, 1, 2 ],
[ 10, 2, 1, 1 ], [ 11, 2, 2, 1 ], [ 19, 5, 3, 1 ] ]
k = 4: F-action on Pi is (1,6)(3,5) [19,3,4]
Dynkin type is (A_2(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 4, 3, 2 ], [ 3, 5, 3, 1 ], [ 10, 1, 2, 2 ],
[ 10, 2, 2, 1 ], [ 11, 2, 1, 1 ], [ 19, 5, 4, 1 ] ]
j = 4: Omega of order 2, action on Pi: <(1,6)(3,5)>
k = 1: F-action on Pi is () [19,4,1]
Dynkin type is (A_2(q) + A_2(q) + T(phi1^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 18, 5, 10, 22, 18, 22, 26 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 3, 1, 2 ], [ 3, 5, 1, 1 ], [ 10, 2, 1, 1 ],
[ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 19, 5, 1, 1 ] ]
k = 2: F-action on Pi is (1,3)(5,6) [19,4,2]
Dynkin type is (^2A_2(q) + ^2A_2(q) + T(phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 21, 9, 13, 24, 21, 24, 27 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 3, 2, 2 ], [ 3, 5, 2, 1 ], [ 10, 2, 2, 1 ],
[ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 19, 5, 2, 1 ] ]
k = 3: F-action on Pi is (1,5)(3,6) [19,4,3]
Dynkin type is (A_2(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 phi1
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 3, 4, 2 ], [ 3, 5, 4, 1 ], [ 10, 2, 1, 1 ],
[ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 19, 5, 3, 1 ] ]
k = 4: F-action on Pi is (1,6)(3,5) [19,4,4]
Dynkin type is (A_2(q^2) + T(phi1 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 3, 3, 2 ], [ 3, 5, 3, 1 ], [ 10, 2, 2, 1 ],
[ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 19, 5, 4, 1 ] ]
i = 20: Pi = [ 2, 3, 4, 6 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [20,1,1]
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 0 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/4 ( q^2-6*q+9 )
q congruent 2 modulo 4: 1/4 ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/4 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 10, 16, 18, 22, 28, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 20, 2, 1, 2 ] ]
k = 2: F-action on Pi is () [20,1,2]
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 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 10, 7, 15, 13, 22, 20, 31, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 20, 2, 2, 2 ] ]
k = 3: F-action on Pi is (2,4) [20,1,3]
Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2)
Order of center |Z^F|: phi1 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 7, 13, 10, 16, 19, 24, 28, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 20, 2, 3, 2 ] ]
k = 4: F-action on Pi is (2,4) [20,1,4]
Dynkin type is ^2A_3(q) + A_1(q) + T(phi2^2)
Order of center |Z^F|: phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q-2 )
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 1/4 q ( q-2 )
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4, 13, 9, 15, 13, 24, 21, 31, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 20, 2, 4, 2 ] ]
i = 21: Pi = [ 1, 2, 3 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [21,1,1]
Dynkin type is A_3(q) + T(phi1^3)
Order of center |Z^F|: phi1^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/48 ( q^3-12*q^2+44*q-48 )
q congruent 1 modulo 4: 1/48 ( q^3-15*q^2+71*q-105 )
q congruent 2 modulo 4: 1/48 ( q^3-12*q^2+44*q-48 )
q congruent 3 modulo 4: 1/48 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 2, 18, 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 6 ], [ 4, 2, 1, 3 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 8 ],
[ 7, 1, 1, 12 ], [ 7, 2, 1, 6 ], [ 7, 3, 1, 6 ], [ 7, 4, 1, 6 ],
[ 7, 5, 1, 3 ], [ 12, 1, 1, 24 ], [ 12, 2, 1, 12 ], [ 12, 3, 1, 12 ],
[ 12, 4, 1, 6 ], [ 13, 1, 1, 24 ], [ 13, 2, 1, 12 ], [ 21, 2, 1, 24 ],
[ 21, 3, 1, 24 ], [ 21, 4, 1, 24 ], [ 21, 5, 1, 12 ], [ 21, 6, 1, 12 ],
[ 21, 7, 1, 12 ] ]
k = 2: F-action on Pi is (1,2) [21,1,2]
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 0 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 2, 19, 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 4 ], [ 7, 1, 3, 8 ],
[ 7, 1, 4, 4 ], [ 7, 2, 3, 4 ], [ 7, 2, 4, 2 ], [ 7, 3, 3, 4 ],
[ 7, 3, 4, 2 ], [ 7, 4, 3, 4 ], [ 7, 4, 4, 2 ], [ 7, 5, 3, 2 ],
[ 7, 5, 4, 1 ], [ 12, 1, 1, 8 ], [ 12, 1, 4, 8 ], [ 12, 2, 1, 4 ],
[ 12, 2, 4, 4 ], [ 12, 3, 1, 4 ], [ 12, 3, 3, 4 ], [ 12, 3, 4, 4 ],
[ 12, 4, 1, 2 ], [ 12, 4, 4, 2 ], [ 13, 1, 3, 8 ], [ 13, 2, 3, 4 ],
[ 21, 2, 6, 8 ], [ 21, 2, 8, 8 ], [ 21, 3, 6, 8 ], [ 21, 3, 7, 8 ],
[ 21, 4, 6, 8 ], [ 21, 5, 6, 4 ], [ 21, 5, 8, 4 ], [ 21, 6, 6, 4 ],
[ 21, 6, 7, 4 ], [ 21, 7, 6, 4 ] ]
k = 3: F-action on Pi is () [21,1,3]
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 0 modulo 4: 1/16 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 1/16 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 3, 20, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 7, 1, 1, 4 ],
[ 7, 1, 2, 8 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 4 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 4 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 4 ], [ 7, 5, 1, 1 ],
[ 7, 5, 2, 2 ], [ 12, 1, 3, 8 ], [ 12, 1, 4, 8 ], [ 12, 2, 3, 4 ],
[ 12, 2, 4, 4 ], [ 12, 3, 2, 4 ], [ 12, 3, 3, 4 ], [ 12, 3, 4, 4 ],
[ 12, 4, 3, 2 ], [ 12, 4, 4, 2 ], [ 13, 1, 2, 8 ], [ 13, 2, 2, 4 ],
[ 21, 2, 3, 8 ], [ 21, 2, 4, 8 ], [ 21, 3, 2, 8 ], [ 21, 3, 5, 8 ],
[ 21, 4, 3, 8 ], [ 21, 5, 3, 4 ], [ 21, 5, 4, 4 ], [ 21, 6, 2, 4 ],
[ 21, 6, 5, 4 ], [ 21, 7, 3, 4 ] ]
k = 4: F-action on Pi is (1,2) [21,1,4]
Dynkin type is ^2A_3(q) + T(phi2^3)
Order of center |Z^F|: phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/48 q ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/48 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/48 q ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/48 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 3, 21, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 6 ], [ 4, 2, 2, 3 ], [ 5, 1, 2, 12 ], [ 6, 1, 2, 8 ],
[ 7, 1, 4, 12 ], [ 7, 2, 4, 6 ], [ 7, 3, 4, 6 ], [ 7, 4, 4, 6 ],
[ 7, 5, 4, 3 ], [ 12, 1, 3, 24 ], [ 12, 2, 3, 12 ], [ 12, 3, 2, 12 ],
[ 12, 4, 3, 6 ], [ 13, 1, 4, 24 ], [ 13, 2, 4, 12 ], [ 21, 2, 10, 24 ],
[ 21, 3, 10, 24 ], [ 21, 4, 10, 24 ], [ 21, 5, 10, 12 ], [ 21, 6, 10, 12 ],
[ 21, 7, 10, 12 ] ]
k = 5: F-action on Pi is () [21,1,5]
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 0 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/8 phi1^2 ( q-3 )
q congruent 2 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/8 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 7, 22, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ],
[ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 4 ], [ 13, 2, 1, 2 ],
[ 13, 2, 2, 2 ], [ 21, 2, 2, 4 ], [ 21, 3, 3, 4 ], [ 21, 4, 2, 4 ],
[ 21, 5, 2, 2 ], [ 21, 6, 3, 4 ], [ 21, 7, 2, 4 ] ]
k = 6: F-action on Pi is (1,2) [21,1,6]
Dynkin type is ^2A_3(q) + T(phi1 phi4)
Order of center |Z^F|: phi1 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 8, 12, 6, 23, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 7, 1, 3, 4 ], [ 7, 2, 3, 2 ],
[ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 3, 1 ], [ 12, 1, 5, 4 ],
[ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 21, 2, 7, 4 ], [ 21, 3, 9, 4 ],
[ 21, 4, 7, 4 ], [ 21, 5, 7, 2 ], [ 21, 6, 8, 4 ], [ 21, 7, 7, 4 ] ]
k = 7: F-action on Pi is (1,2) [21,1,7]
Dynkin type is ^2A_3(q) + T(phi1 phi2^2)
Order of center |Z^F|: phi1 phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1^3
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 phi1^3
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 7, 24, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 2, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 4, 1 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 4 ], [ 13, 2, 3, 2 ],
[ 13, 2, 4, 2 ], [ 21, 2, 9, 4 ], [ 21, 3, 8, 4 ], [ 21, 4, 9, 4 ],
[ 21, 5, 9, 2 ], [ 21, 6, 9, 4 ], [ 21, 7, 9, 4 ] ]
k = 8: F-action on Pi is () [21,1,8]
Dynkin type is A_3(q) + T(phi2 phi4)
Order of center |Z^F|: phi2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^3
q congruent 1 modulo 4: 1/8 phi1^2 phi2
q congruent 2 modulo 4: 1/8 q^3
q congruent 3 modulo 4: 1/8 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12, 8, 25, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 7, 1, 2, 4 ], [ 7, 2, 2, 2 ],
[ 7, 3, 2, 2 ], [ 7, 4, 2, 2 ], [ 7, 5, 2, 1 ], [ 12, 1, 5, 4 ],
[ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 21, 2, 5, 4 ], [ 21, 3, 4, 4 ],
[ 21, 4, 5, 4 ], [ 21, 5, 5, 2 ], [ 21, 6, 4, 4 ], [ 21, 7, 5, 4 ] ]
k = 9: F-action on Pi is () [21,1,9]
Dynkin type is A_3(q) + T(phi1 phi3)
Order of center |Z^F|: phi1 phi3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/6 q phi1 phi2
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 1/6 q phi1 phi2
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 18, 22, 20, 26, 25 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 6, 1, 1, 2 ], [ 21, 4, 4, 3 ],
[ 21, 7, 4, 6 ] ]
k = 10: F-action on Pi is (1,2) [21,1,10]
Dynkin type is ^2A_3(q) + T(phi2 phi6)
Order of center |Z^F|: phi2 phi6
Numbers of classes in class type:
q congruent 0 modulo 4: 1/6 q phi1 phi2
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 1/6 q phi1 phi2
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 21, 24, 19, 27, 23 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 6, 1, 2, 2 ], [ 21, 4, 8, 3 ],
[ 21, 7, 8, 6 ] ]
j = 2: Omega of order 2, action on Pi: <(1,2)>
k = 1: F-action on Pi is () [21,2,1]
Dynkin type is (A_3(q) + T(phi1^3)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 2, 18, 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 2, 1, 2 ],
[ 3, 5, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 7, 3, 1, 2 ], [ 7, 4, 1, 4 ], [ 7, 5, 1, 3 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 3, 1, 8 ], [ 12, 4, 1, 6 ], [ 13, 2, 1, 4 ],
[ 21, 5, 1, 4 ], [ 21, 6, 1, 8 ] ]
k = 2: F-action on Pi is () [21,2,2]
Dynkin type is (A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 7, 22, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 1, 2 ],
[ 3, 5, 1, 1 ], [ 4, 2, 1, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 7, 3, 1, 2 ], [ 7, 5, 1, 1 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 13, 2, 1, 2 ], [ 13, 2, 2, 2 ], [ 21, 5, 2, 2 ] ]
k = 3: F-action on Pi is () [21,2,3]
Dynkin type is (A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 3, 20, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 2, 1, 2 ], [ 3, 5, 1, 1 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 1 ],
[ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 7, 3, 1, 2 ], [ 7, 4, 2, 4 ],
[ 7, 5, 1, 1 ], [ 7, 5, 2, 2 ], [ 12, 1, 3, 8 ], [ 12, 2, 3, 4 ],
[ 12, 3, 2, 4 ], [ 12, 3, 3, 4 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 2 ],
[ 13, 2, 2, 4 ], [ 21, 5, 3, 4 ], [ 21, 6, 2, 4 ] ]
k = 4: F-action on Pi is () [21,2,4]
Dynkin type is (A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 3, 20, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 2, 1, 2 ], [ 3, 5, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 2 ], [ 7, 3, 2, 2 ], [ 7, 4, 1, 2 ],
[ 7, 4, 2, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 2 ], [ 12, 1, 4, 4 ],
[ 12, 2, 4, 2 ], [ 12, 3, 2, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 4 ],
[ 12, 4, 3, 2 ], [ 12, 4, 4, 2 ], [ 21, 5, 4, 2 ], [ 21, 6, 2, 2 ],
[ 21, 6, 5, 4 ] ]
k = 5: F-action on Pi is () [21,2,5]
Dynkin type is (A_3(q) + T(phi2 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12, 8, 25, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 2, 1, 2 ],
[ 3, 5, 1, 1 ], [ 4, 2, 2, 1 ], [ 7, 3, 2, 2 ], [ 7, 5, 2, 1 ],
[ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 21, 5, 5, 2 ] ]
k = 6: F-action on Pi is (1,2) [21,2,6]
Dynkin type is (^2A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 2, 19, 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 2, 2, 2 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 1 ], [ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 3, 2 ], [ 7, 5, 4, 1 ], [ 12, 1, 4, 4 ],
[ 12, 2, 4, 2 ], [ 12, 3, 1, 2 ], [ 12, 3, 3, 4 ], [ 12, 3, 4, 2 ],
[ 12, 4, 1, 2 ], [ 12, 4, 4, 2 ], [ 21, 5, 6, 2 ], [ 21, 6, 6, 2 ],
[ 21, 6, 7, 4 ] ]
k = 7: F-action on Pi is (1,2) [21,2,7]
Dynkin type is (^2A_3(q) + T(phi1 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 8, 12, 6, 23, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 2, 2, 2 ],
[ 3, 5, 2, 1 ], [ 4, 2, 1, 1 ], [ 7, 3, 3, 2 ], [ 7, 5, 3, 1 ],
[ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 21, 5, 7, 2 ] ]
k = 8: F-action on Pi is (1,2) [21,2,8]
Dynkin type is (^2A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 2, 19, 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 2, 2, 2 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ],
[ 4, 2, 2, 1 ], [ 5, 1, 1, 4 ], [ 7, 3, 4, 2 ], [ 7, 4, 3, 4 ],
[ 7, 5, 3, 2 ], [ 7, 5, 4, 1 ], [ 12, 1, 1, 8 ], [ 12, 2, 1, 4 ],
[ 12, 3, 1, 4 ], [ 12, 3, 4, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 4, 2 ],
[ 13, 2, 3, 4 ], [ 21, 5, 8, 4 ], [ 21, 6, 6, 4 ] ]
k = 9: F-action on Pi is (1,2) [21,2,9]
Dynkin type is (^2A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1^2
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 7, 24, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 2, 2 ],
[ 3, 5, 2, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 7, 3, 4, 2 ], [ 7, 5, 4, 1 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 13, 2, 3, 2 ], [ 13, 2, 4, 2 ], [ 21, 5, 9, 2 ] ]
k = 10: F-action on Pi is (1,2) [21,2,10]
Dynkin type is (^2A_3(q) + T(phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 3, 21, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 2, 2, 2 ],
[ 3, 5, 2, 1 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 3 ], [ 5, 1, 2, 4 ],
[ 7, 3, 4, 2 ], [ 7, 4, 4, 4 ], [ 7, 5, 4, 3 ], [ 12, 1, 3, 8 ],
[ 12, 2, 3, 4 ], [ 12, 3, 2, 8 ], [ 12, 4, 3, 6 ], [ 13, 2, 4, 4 ],
[ 21, 5, 10, 4 ], [ 21, 6, 10, 8 ] ]
i = 22: Pi = [ 1, 2, 4 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [22,1,1]
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 0 modulo 4: 1/16 ( q^3-12*q^2+44*q-48 )
q congruent 1 modulo 4: 1/16 ( q^3-15*q^2+71*q-105 )
q congruent 2 modulo 4: 1/16 ( q^3-12*q^2+44*q-48 )
q congruent 3 modulo 4: 1/16 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 5, 10, 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 8 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ], [ 7, 4, 1, 8 ],
[ 7, 5, 1, 4 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 24 ], [ 9, 2, 1, 12 ],
[ 9, 3, 1, 12 ], [ 9, 4, 1, 12 ], [ 9, 5, 1, 6 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 13, 1, 1, 8 ],
[ 13, 2, 1, 4 ], [ 14, 1, 1, 16 ], [ 14, 2, 1, 8 ], [ 15, 1, 1, 16 ],
[ 16, 1, 1, 32 ], [ 16, 2, 1, 16 ], [ 16, 3, 1, 16 ], [ 16, 4, 1, 16 ],
[ 16, 5, 1, 16 ], [ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ], [ 16, 8, 1, 16 ],
[ 16, 9, 1, 8 ], [ 16, 10, 1, 8 ], [ 16, 11, 1, 8 ], [ 16, 12, 1, 8 ],
[ 16, 13, 1, 8 ], [ 16, 14, 1, 8 ], [ 16, 15, 1, 8 ], [ 16, 16, 1, 8 ],
[ 16, 17, 1, 8 ], [ 22, 2, 1, 8 ], [ 22, 3, 1, 8 ], [ 22, 4, 1, 4 ] ]
k = 2: F-action on Pi is () [22,1,2]
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 0 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/8 phi1^2 ( q-3 )
q congruent 2 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/8 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 16, 10, 15, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 2 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 15, 1, 1, 8 ],
[ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ], [ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ],
[ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ], [ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ],
[ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ], [ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ],
[ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 16, 12, 2, 4 ],
[ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ], [ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ],
[ 22, 2, 2, 4 ], [ 22, 4, 2, 4 ] ]
k = 3: F-action on Pi is () [22,1,3]
Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
Order of center |Z^F|: phi1 phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 1/16 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 13, 7, 13, 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ],
[ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 4, 8 ],
[ 7, 5, 4, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 4 ], [ 12, 1, 3, 8 ],
[ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ], [ 13, 1, 3, 8 ],
[ 13, 2, 3, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 5, 32 ], [ 16, 2, 5, 16 ],
[ 16, 3, 5, 16 ], [ 16, 4, 5, 16 ], [ 16, 5, 3, 16 ], [ 16, 6, 3, 16 ],
[ 16, 7, 3, 16 ], [ 16, 8, 4, 16 ], [ 16, 9, 5, 8 ], [ 16, 10, 3, 8 ],
[ 16, 11, 5, 8 ], [ 16, 12, 3, 8 ], [ 16, 13, 5, 8 ], [ 16, 14, 4, 8 ],
[ 16, 15, 5, 8 ], [ 16, 16, 5, 8 ], [ 16, 17, 4, 8 ], [ 22, 2, 3, 8 ],
[ 22, 3, 2, 8 ], [ 22, 4, 3, 4 ] ]
k = 4: F-action on Pi is () [22,1,4]
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 0 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 10, 7, 10, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ], [ 7, 4, 1, 8 ],
[ 7, 5, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 2 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 13, 1, 2, 8 ],
[ 13, 2, 2, 4 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 32 ], [ 16, 2, 1, 16 ],
[ 16, 3, 1, 16 ], [ 16, 4, 1, 16 ], [ 16, 5, 1, 16 ], [ 16, 6, 1, 16 ],
[ 16, 7, 1, 16 ], [ 16, 8, 1, 16 ], [ 16, 9, 1, 8 ], [ 16, 10, 1, 8 ],
[ 16, 11, 1, 8 ], [ 16, 12, 1, 8 ], [ 16, 13, 1, 8 ], [ 16, 14, 1, 8 ],
[ 16, 15, 1, 8 ], [ 16, 16, 1, 8 ], [ 16, 17, 1, 8 ], [ 22, 2, 4, 8 ],
[ 22, 3, 3, 8 ], [ 22, 4, 4, 4 ] ]
k = 5: F-action on Pi is () [22,1,5]
Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
Order of center |Z^F|: phi1 phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1^3
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 phi1^3
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 15, 13, 16, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 4 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 15, 1, 3, 8 ],
[ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ], [ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ],
[ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ], [ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ],
[ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ], [ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ],
[ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 16, 12, 2, 4 ],
[ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ], [ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ],
[ 22, 2, 5, 4 ], [ 22, 4, 5, 4 ] ]
k = 6: F-action on Pi is () [22,1,6]
Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi2^3)
Order of center |Z^F|: phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3, 13, 9, 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 6 ], [ 6, 1, 2, 8 ],
[ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 4, 8 ],
[ 7, 5, 4, 4 ], [ 8, 1, 2, 8 ], [ 9, 1, 2, 24 ], [ 9, 2, 2, 12 ],
[ 9, 3, 2, 12 ], [ 9, 4, 2, 12 ], [ 9, 5, 2, 6 ], [ 12, 1, 3, 8 ],
[ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ], [ 13, 1, 4, 8 ],
[ 13, 2, 4, 4 ], [ 14, 1, 2, 16 ], [ 14, 2, 2, 8 ], [ 15, 1, 3, 16 ],
[ 16, 1, 5, 32 ], [ 16, 2, 5, 16 ], [ 16, 3, 5, 16 ], [ 16, 4, 5, 16 ],
[ 16, 5, 3, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ], [ 16, 8, 4, 16 ],
[ 16, 9, 5, 8 ], [ 16, 10, 3, 8 ], [ 16, 11, 5, 8 ], [ 16, 12, 3, 8 ],
[ 16, 13, 5, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 5, 8 ], [ 16, 16, 5, 8 ],
[ 16, 17, 4, 8 ], [ 22, 2, 6, 8 ], [ 22, 3, 4, 8 ], [ 22, 4, 6, 4 ] ]
k = 7: F-action on Pi is (1,2) [22,1,7]
Dynkin type is A_1(q^2) + A_1(q) + T(phi1^2 phi2)
Order of center |Z^F|: phi1^2 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/8 q ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/8 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ],
[ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 1 ], [ 9, 1, 3, 8 ], [ 9, 2, 3, 4 ], [ 9, 3, 3, 4 ],
[ 9, 4, 3, 4 ], [ 9, 5, 3, 2 ], [ 12, 1, 4, 4 ], [ 12, 2, 4, 2 ],
[ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ], [ 13, 1, 1, 4 ],
[ 13, 1, 3, 4 ], [ 13, 2, 1, 2 ], [ 13, 2, 3, 2 ], [ 14, 1, 3, 8 ],
[ 14, 2, 3, 4 ], [ 16, 1, 2, 8 ], [ 16, 2, 2, 4 ], [ 16, 3, 2, 4 ],
[ 16, 4, 2, 4 ], [ 16, 8, 2, 4 ], [ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ],
[ 16, 8, 7, 4 ], [ 16, 9, 2, 2 ], [ 16, 11, 2, 2 ], [ 16, 11, 7, 2 ],
[ 16, 13, 2, 4 ], [ 16, 14, 2, 2 ], [ 16, 14, 3, 2 ], [ 16, 15, 2, 4 ],
[ 16, 16, 2, 4 ], [ 16, 17, 2, 2 ], [ 16, 17, 3, 2 ], [ 22, 2, 7, 4 ],
[ 22, 3, 5, 4 ], [ 22, 3, 6, 4 ], [ 22, 4, 7, 2 ] ]
k = 8: F-action on Pi is (1,2) [22,1,8]
Dynkin type is A_1(q^2) + A_1(q) + T(phi1 phi4)
Order of center |Z^F|: phi1 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12, 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 9, 1, 3, 8 ], [ 9, 2, 3, 4 ],
[ 9, 3, 3, 4 ], [ 9, 4, 3, 4 ], [ 9, 5, 3, 2 ], [ 12, 1, 5, 4 ],
[ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 16, 1, 4, 8 ], [ 16, 2, 4, 4 ],
[ 16, 3, 4, 4 ], [ 16, 4, 4, 4 ], [ 16, 9, 4, 2 ], [ 16, 11, 4, 4 ],
[ 16, 11, 9, 4 ], [ 16, 13, 4, 4 ], [ 16, 15, 4, 4 ], [ 16, 16, 4, 4 ],
[ 22, 2, 8, 4 ], [ 22, 4, 8, 4 ] ]
k = 9: F-action on Pi is (1,2) [22,1,9]
Dynkin type is A_1(q^2) + A_1(q) + T(phi1 phi2^2)
Order of center |Z^F|: phi1 phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/8 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ],
[ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 1 ], [ 9, 1, 4, 8 ], [ 9, 2, 4, 4 ], [ 9, 3, 4, 4 ],
[ 9, 4, 4, 4 ], [ 9, 5, 4, 2 ], [ 12, 1, 4, 4 ], [ 12, 2, 4, 2 ],
[ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ], [ 13, 1, 2, 4 ],
[ 13, 1, 4, 4 ], [ 13, 2, 2, 2 ], [ 13, 2, 4, 2 ], [ 14, 1, 4, 8 ],
[ 14, 2, 4, 4 ], [ 16, 1, 2, 8 ], [ 16, 2, 2, 4 ], [ 16, 3, 2, 4 ],
[ 16, 4, 2, 4 ], [ 16, 8, 2, 4 ], [ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ],
[ 16, 8, 7, 4 ], [ 16, 9, 2, 2 ], [ 16, 11, 2, 2 ], [ 16, 11, 7, 2 ],
[ 16, 13, 2, 4 ], [ 16, 14, 2, 2 ], [ 16, 14, 3, 2 ], [ 16, 15, 2, 4 ],
[ 16, 16, 2, 4 ], [ 16, 17, 2, 2 ], [ 16, 17, 3, 2 ], [ 22, 2, 9, 4 ],
[ 22, 3, 7, 4 ], [ 22, 3, 8, 4 ], [ 22, 4, 9, 2 ] ]
k = 10: F-action on Pi is (1,2) [22,1,10]
Dynkin type is A_1(q^2) + A_1(q) + T(phi2 phi4)
Order of center |Z^F|: phi2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^3
q congruent 1 modulo 4: 1/8 phi1^2 phi2
q congruent 2 modulo 4: 1/8 q^3
q congruent 3 modulo 4: 1/8 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 12, 8, 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 4, 8 ], [ 9, 2, 4, 4 ],
[ 9, 3, 4, 4 ], [ 9, 4, 4, 4 ], [ 9, 5, 4, 2 ], [ 12, 1, 5, 4 ],
[ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 16, 1, 4, 8 ], [ 16, 2, 4, 4 ],
[ 16, 3, 4, 4 ], [ 16, 4, 4, 4 ], [ 16, 9, 4, 2 ], [ 16, 11, 4, 4 ],
[ 16, 11, 9, 4 ], [ 16, 13, 4, 4 ], [ 16, 15, 4, 4 ], [ 16, 16, 4, 4 ],
[ 22, 2, 10, 4 ], [ 22, 4, 10, 4 ] ]
j = 3: Omega of order 2, action on Pi: <(1,2)>
k = 1: F-action on Pi is () [22,3,1]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^3)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 5, 10, 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ],
[ 7, 1, 1, 4 ], [ 7, 2, 1, 4 ], [ 7, 3, 1, 4 ], [ 7, 4, 1, 4 ],
[ 7, 5, 1, 4 ], [ 9, 2, 1, 4 ], [ 9, 5, 1, 2 ], [ 12, 3, 1, 2 ],
[ 12, 4, 1, 2 ], [ 13, 1, 1, 4 ], [ 13, 2, 1, 4 ], [ 14, 2, 1, 4 ],
[ 16, 8, 1, 4 ], [ 16, 11, 1, 4 ], [ 16, 14, 1, 4 ], [ 16, 17, 1, 4 ],
[ 22, 4, 1, 4 ] ]
k = 2: F-action on Pi is () [22,3,2]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 13, 7, 13, 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 7, 1, 4, 4 ],
[ 7, 2, 4, 4 ], [ 7, 3, 4, 4 ], [ 7, 4, 4, 4 ], [ 7, 5, 4, 4 ],
[ 9, 2, 1, 4 ], [ 9, 5, 1, 2 ], [ 12, 3, 2, 2 ], [ 12, 4, 3, 2 ],
[ 13, 1, 3, 4 ], [ 13, 2, 3, 4 ], [ 16, 8, 4, 4 ], [ 16, 11, 5, 4 ],
[ 16, 14, 4, 4 ], [ 16, 17, 4, 4 ], [ 22, 4, 3, 4 ] ]
k = 3: F-action on Pi is () [22,3,3]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 10, 7, 10, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 2 ], [ 5, 1, 2, 2 ], [ 7, 1, 1, 4 ],
[ 7, 2, 1, 4 ], [ 7, 3, 1, 4 ], [ 7, 4, 1, 4 ], [ 7, 5, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 5, 2, 2 ], [ 12, 3, 1, 2 ], [ 12, 4, 1, 2 ],
[ 13, 1, 2, 4 ], [ 13, 2, 2, 4 ], [ 16, 8, 1, 4 ], [ 16, 11, 1, 4 ],
[ 16, 14, 1, 4 ], [ 16, 17, 1, 4 ], [ 22, 4, 4, 4 ] ]
k = 4: F-action on Pi is () [22,3,4]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3, 13, 9, 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 4, 4 ], [ 7, 3, 4, 4 ], [ 7, 4, 4, 4 ],
[ 7, 5, 4, 4 ], [ 9, 2, 2, 4 ], [ 9, 5, 2, 2 ], [ 12, 3, 2, 2 ],
[ 12, 4, 3, 2 ], [ 13, 1, 4, 4 ], [ 13, 2, 4, 4 ], [ 14, 2, 2, 4 ],
[ 16, 8, 4, 4 ], [ 16, 11, 5, 4 ], [ 16, 14, 4, 4 ], [ 16, 17, 4, 4 ],
[ 22, 4, 6, 4 ] ]
k = 5: F-action on Pi is (1,2) [22,3,5]
Dynkin type is (A_1(q^2) + A_1(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 4 ],
[ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 3, 1, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 1, 1 ],
[ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ], [ 9, 2, 3, 4 ],
[ 9, 5, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ], [ 13, 1, 1, 4 ],
[ 13, 2, 1, 2 ], [ 13, 2, 3, 2 ], [ 14, 2, 3, 4 ], [ 16, 8, 2, 4 ],
[ 16, 11, 2, 2 ], [ 16, 14, 3, 2 ], [ 16, 17, 3, 2 ], [ 22, 4, 7, 2 ] ]
k = 6: F-action on Pi is (1,2) [22,3,6]
Dynkin type is (A_1(q^2) + A_1(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 2, 2 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 7, 1, 4, 4 ],
[ 7, 2, 3, 2 ], [ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 4, 2 ],
[ 7, 4, 2, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ],
[ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ], [ 9, 2, 3, 4 ], [ 9, 5, 3, 2 ],
[ 12, 3, 3, 2 ], [ 12, 4, 4, 1 ], [ 13, 1, 3, 4 ], [ 13, 2, 1, 2 ],
[ 13, 2, 3, 2 ], [ 16, 8, 3, 4 ], [ 16, 11, 2, 2 ], [ 16, 14, 2, 2 ],
[ 16, 17, 2, 2 ], [ 22, 4, 7, 2 ] ]
k = 7: F-action on Pi is (1,2) [22,3,7]
Dynkin type is (A_1(q^2) + A_1(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ], [ 7, 1, 1, 4 ],
[ 7, 2, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 4, 2 ],
[ 7, 4, 1, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ],
[ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ], [ 9, 2, 4, 4 ], [ 9, 5, 4, 2 ],
[ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ], [ 13, 1, 2, 4 ], [ 13, 2, 2, 2 ],
[ 13, 2, 4, 2 ], [ 16, 8, 2, 4 ], [ 16, 11, 2, 2 ], [ 16, 14, 3, 2 ],
[ 16, 17, 3, 2 ], [ 22, 4, 9, 2 ] ]
k = 8: F-action on Pi is (1,2) [22,3,8]
Dynkin type is (A_1(q^2) + A_1(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 2, 2 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 3, 2 ], [ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 2, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ],
[ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ], [ 9, 2, 4, 4 ],
[ 9, 5, 4, 2 ], [ 12, 3, 3, 2 ], [ 12, 4, 4, 1 ], [ 13, 1, 4, 4 ],
[ 13, 2, 2, 2 ], [ 13, 2, 4, 2 ], [ 14, 2, 4, 4 ], [ 16, 8, 3, 4 ],
[ 16, 11, 2, 2 ], [ 16, 14, 2, 2 ], [ 16, 17, 2, 2 ], [ 22, 4, 9, 2 ] ]
i = 23: Pi = [ 1, 3, 4 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [23,1,1]
Dynkin type is A_3(q) + T(phi1^3)
Order of center |Z^F|: phi1^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 ( q^3-10*q^2+32*q-32 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-9*q+20 )
q congruent 2 modulo 4: 1/8 ( q^3-10*q^2+32*q-32 )
q congruent 3 modulo 4: 1/8 ( q^3-10*q^2+29*q-24 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 18, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 10, 1, 1, 4 ],
[ 10, 2, 1, 2 ], [ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 17, 1, 1, 8 ],
[ 17, 2, 1, 4 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 20, 1, 1, 4 ],
[ 20, 2, 1, 2 ], [ 23, 2, 1, 4 ], [ 23, 3, 1, 4 ], [ 23, 4, 1, 4 ],
[ 23, 5, 1, 4 ], [ 23, 6, 1, 2 ] ]
k = 2: F-action on Pi is () [23,1,2]
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 0 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-3*q-2 )
q congruent 2 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/8 phi2 ( q^2-5*q+6 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 15, 22, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 18, 1, 1, 4 ],
[ 18, 2, 1, 2 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 23, 2, 2, 4 ],
[ 23, 3, 2, 4 ], [ 23, 4, 2, 4 ], [ 23, 5, 2, 4 ], [ 23, 6, 2, 2 ] ]
k = 3: F-action on Pi is () [23,1,3]
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 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-q-4 )
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 q phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 13, 20, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 2, 4 ],
[ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 1, 2 ], [ 12, 1, 3, 8 ],
[ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ], [ 18, 1, 2, 4 ],
[ 18, 2, 2, 2 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 23, 2, 3, 4 ],
[ 23, 3, 3, 4 ], [ 23, 4, 3, 4 ], [ 23, 5, 3, 4 ], [ 23, 6, 3, 2 ] ]
k = 4: F-action on Pi is () [23,1,4]
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 0 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-3*q-2 )
q congruent 2 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/8 phi2 ( q^2-5*q+6 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 16, 22, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 18, 1, 2, 4 ],
[ 18, 2, 2, 2 ], [ 20, 1, 1, 4 ], [ 20, 2, 1, 2 ], [ 23, 2, 4, 4 ],
[ 23, 3, 4, 4 ], [ 23, 4, 4, 4 ], [ 23, 5, 4, 4 ], [ 23, 6, 4, 2 ] ]
k = 5: F-action on Pi is (1,4) [23,1,5]
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 0 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-3*q-2 )
q congruent 2 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/8 phi2 ( q^2-5*q+6 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 10, 19, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 2, 2 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 18, 1, 3, 4 ],
[ 18, 2, 3, 2 ], [ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ], [ 23, 2, 5, 4 ],
[ 23, 3, 5, 4 ], [ 23, 4, 5, 4 ], [ 23, 5, 5, 4 ], [ 23, 6, 5, 2 ] ]
k = 6: F-action on Pi is (1,4) [23,1,6]
Dynkin type is ^2A_3(q) + T(phi1 phi2^2)
Order of center |Z^F|: phi1 phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-q-4 )
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 q phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 15, 24, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 18, 1, 3, 4 ],
[ 18, 2, 3, 2 ], [ 20, 1, 4, 4 ], [ 20, 2, 4, 2 ], [ 23, 2, 6, 4 ],
[ 23, 3, 6, 4 ], [ 23, 4, 6, 4 ], [ 23, 5, 6, 4 ], [ 23, 6, 6, 2 ] ]
k = 7: F-action on Pi is (1,4) [23,1,7]
Dynkin type is ^2A_3(q) + T(phi2^3)
Order of center |Z^F|: phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-3*q-2 )
q congruent 2 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/8 phi2 ( q^2-5*q+6 )
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 21, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 2, 4 ],
[ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], [ 10, 1, 2, 4 ],
[ 10, 2, 2, 2 ], [ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 12, 1, 3, 8 ],
[ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ], [ 17, 1, 2, 8 ],
[ 17, 2, 2, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 20, 1, 4, 4 ],
[ 20, 2, 4, 2 ], [ 23, 2, 7, 4 ], [ 23, 3, 7, 4 ], [ 23, 4, 7, 4 ],
[ 23, 5, 7, 4 ], [ 23, 6, 7, 2 ] ]
k = 8: F-action on Pi is (1,4) [23,1,8]
Dynkin type is ^2A_3(q) + T(phi1 phi2^2)
Order of center |Z^F|: phi1 phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-q-4 )
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 q phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 16, 24, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 18, 1, 4, 4 ],
[ 18, 2, 4, 2 ], [ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ], [ 23, 2, 8, 4 ],
[ 23, 3, 8, 4 ], [ 23, 4, 8, 4 ], [ 23, 5, 8, 4 ], [ 23, 6, 8, 2 ] ]
j = 2: Omega of order 2, action on Pi: <()>
k = 1: F-action on Pi is () [23,2,1]
Dynkin type is (A_3(q) + T(phi1^3)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 18, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 1, 2 ],
[ 8, 1, 1, 2 ], [ 12, 2, 1, 4 ], [ 12, 4, 1, 2 ], [ 23, 6, 1, 2 ] ]
k = 2: F-action on Pi is () [23,2,2]
Dynkin type is (A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 15, 22, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 23, 6, 2, 2 ] ]
k = 3: F-action on Pi is () [23,2,3]
Dynkin type is (A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 13, 20, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 2, 2 ],
[ 8, 1, 1, 2 ], [ 12, 2, 3, 4 ], [ 12, 4, 3, 2 ], [ 23, 6, 3, 2 ] ]
k = 4: F-action on Pi is () [23,2,4]
Dynkin type is (A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 16, 22, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 23, 6, 4, 2 ] ]
k = 5: F-action on Pi is (1,4) [23,2,5]
Dynkin type is (^2A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 10, 19, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 1, 2 ],
[ 8, 1, 2, 2 ], [ 12, 2, 1, 4 ], [ 12, 4, 1, 2 ], [ 23, 6, 5, 2 ] ]
k = 6: F-action on Pi is (1,4) [23,2,6]
Dynkin type is (^2A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 15, 24, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 23, 6, 6, 2 ] ]
k = 7: F-action on Pi is (1,4) [23,2,7]
Dynkin type is (^2A_3(q) + T(phi2^3)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 21, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 2, 2 ],
[ 8, 1, 2, 2 ], [ 12, 2, 3, 4 ], [ 12, 4, 3, 2 ], [ 23, 6, 7, 2 ] ]
k = 8: F-action on Pi is (1,4) [23,2,8]
Dynkin type is (^2A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 16, 24, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 23, 6, 8, 2 ] ]
j = 3: Omega of order 2, action on Pi: <(1,4)>
k = 1: F-action on Pi is () [23,3,1]
Dynkin type is (A_3(q) + T(phi1^3)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 18, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 11, 2, 1, 2 ], [ 20, 2, 1, 2 ], [ 23, 6, 1, 2 ] ]
k = 2: F-action on Pi is () [23,3,2]
Dynkin type is (A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 15, 22, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 20, 2, 2, 2 ], [ 23, 6, 2, 2 ] ]
k = 3: F-action on Pi is () [23,3,3]
Dynkin type is (A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 13, 20, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 20, 2, 2, 2 ], [ 23, 6, 3, 2 ] ]
k = 4: F-action on Pi is () [23,3,4]
Dynkin type is (A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 16, 22, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 11, 2, 1, 2 ], [ 20, 2, 1, 2 ], [ 23, 6, 4, 2 ] ]
k = 5: F-action on Pi is (1,4) [23,3,5]
Dynkin type is (^2A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 10, 19, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 20, 2, 3, 2 ], [ 23, 6, 5, 2 ] ]
k = 6: F-action on Pi is (1,4) [23,3,6]
Dynkin type is (^2A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 15, 24, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 11, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 23, 6, 6, 2 ] ]
k = 7: F-action on Pi is (1,4) [23,3,7]
Dynkin type is (^2A_3(q) + T(phi2^3)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 21, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 11, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 23, 6, 7, 2 ] ]
k = 8: F-action on Pi is (1,4) [23,3,8]
Dynkin type is (^2A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 16, 24, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 20, 2, 3, 2 ], [ 23, 6, 8, 2 ] ]
j = 4: Omega of order 2, action on Pi: <(1,4)>
k = 1: F-action on Pi is () [23,4,1]
Dynkin type is (A_3(q) + T(phi1^3)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 18, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 10, 2, 1, 2 ], [ 18, 2, 1, 2 ], [ 23, 6, 1, 2 ] ]
k = 2: F-action on Pi is () [23,4,2]
Dynkin type is (A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 15, 22, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 10, 2, 1, 2 ], [ 18, 2, 1, 2 ], [ 23, 6, 2, 2 ] ]
k = 3: F-action on Pi is () [23,4,3]
Dynkin type is (A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 13, 20, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 18, 2, 2, 2 ], [ 23, 6, 3, 2 ] ]
k = 4: F-action on Pi is () [23,4,4]
Dynkin type is (A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 16, 22, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 18, 2, 2, 2 ], [ 23, 6, 4, 2 ] ]
k = 5: F-action on Pi is (1,4) [23,4,5]
Dynkin type is (^2A_3(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 10, 19, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 18, 2, 3, 2 ], [ 23, 6, 5, 2 ] ]
k = 6: F-action on Pi is (1,4) [23,4,6]
Dynkin type is (^2A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 15, 24, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 18, 2, 3, 2 ], [ 23, 6, 6, 2 ] ]
k = 7: F-action on Pi is (1,4) [23,4,7]
Dynkin type is (^2A_3(q) + T(phi2^3)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 21, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 10, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 23, 6, 7, 2 ] ]
k = 8: F-action on Pi is (1,4) [23,4,8]
Dynkin type is (^2A_3(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 16, 24, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 10, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 23, 6, 8, 2 ] ]
j = 6: Omega of order 4, action on Pi: <(), ()>
k = 1: F-action on Pi is () [23,6,1]
Dynkin type is (A_3(q) + T(phi1^3)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 10, 18, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 2: F-action on Pi is () [23,6,2]
Dynkin type is (A_3(q) + T(phi1^2 phi2)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 15, 22, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 3: F-action on Pi is () [23,6,3]
Dynkin type is (A_3(q) + T(phi1 phi2^2)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 13, 20, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 4: F-action on Pi is () [23,6,4]
Dynkin type is (A_3(q) + T(phi1^2 phi2)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 16, 22, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 5: F-action on Pi is (1,4) [23,6,5]
Dynkin type is (^2A_3(q) + T(phi1^2 phi2)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 10, 19, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 6: F-action on Pi is (1,4) [23,6,6]
Dynkin type is (^2A_3(q) + T(phi1 phi2^2)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 15, 24, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 7: F-action on Pi is (1,4) [23,6,7]
Dynkin type is (^2A_3(q) + T(phi2^3)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 13, 21, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
k = 8: F-action on Pi is (1,4) [23,6,8]
Dynkin type is (^2A_3(q) + T(phi1 phi2^2)).2.2
Order of center |Z^F|: 1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 16, 24, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ] ]
i = 24: Pi = [ 1, 3, 5 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [24,1,1]
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 0 modulo 4: 1/4 ( q^3-11*q^2+38*q-40 )
q congruent 1 modulo 4: 1/4 ( q^3-11*q^2+39*q-45 )
q congruent 2 modulo 4: 1/4 ( q^3-11*q^2+38*q-40 )
q congruent 3 modulo 4: 1/4 ( q^3-11*q^2+39*q-45 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 18, 22 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 6 ],
[ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ],
[ 7, 5, 1, 1 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ],
[ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 13, 1, 1, 4 ], [ 13, 2, 1, 2 ],
[ 14, 1, 1, 4 ], [ 14, 2, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ],
[ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 19, 1, 1, 8 ], [ 19, 2, 1, 4 ],
[ 19, 3, 1, 4 ], [ 19, 4, 1, 4 ], [ 19, 5, 1, 2 ], [ 20, 1, 1, 4 ],
[ 20, 2, 1, 2 ], [ 24, 2, 1, 2 ] ]
k = 2: F-action on Pi is () [24,1,2]
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 0 modulo 4: 1/4 q ( q^2-5*q+6 )
q congruent 1 modulo 4: 1/4 phi1^2 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q^2-5*q+6 )
q congruent 3 modulo 4: 1/4 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 10, 7, 22, 20 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 1, 2 ],
[ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ],
[ 7, 5, 1, 1 ], [ 8, 1, 1, 4 ], [ 13, 1, 2, 4 ], [ 13, 2, 2, 2 ],
[ 14, 1, 1, 4 ], [ 14, 2, 1, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ],
[ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 24, 2, 2, 2 ] ]
k = 3: F-action on Pi is (1,3) [24,1,3]
Dynkin type is ^2A_2(q) + A_1(q) + T(phi1 phi2^2)
Order of center |Z^F|: phi1 phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q phi1 ( q-2 )
q congruent 1 modulo 4: 1/4 phi1^3
q congruent 2 modulo 4: 1/4 q phi1 ( q-2 )
q congruent 3 modulo 4: 1/4 phi1^3
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 7, 13, 19, 24 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 2 ],
[ 7, 1, 4, 4 ], [ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ],
[ 7, 5, 4, 1 ], [ 8, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 2, 3, 2 ],
[ 14, 1, 2, 4 ], [ 14, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ],
[ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ], [ 24, 2, 3, 2 ] ]
k = 4: F-action on Pi is (1,3) [24,1,4]
Dynkin type is ^2A_2(q) + A_1(q) + T(phi2^3)
Order of center |Z^F|: phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/4 q ( q^2-5*q+6 )
q congruent 1 modulo 4: 1/4 phi1^2 ( q-3 )
q congruent 2 modulo 4: 1/4 q ( q^2-5*q+6 )
q congruent 3 modulo 4: 1/4 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4, 13, 9, 24, 21 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 6 ],
[ 7, 1, 4, 4 ], [ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ],
[ 7, 5, 4, 1 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ],
[ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 13, 1, 4, 4 ], [ 13, 2, 4, 2 ],
[ 14, 1, 2, 4 ], [ 14, 2, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ],
[ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 19, 1, 2, 8 ], [ 19, 2, 2, 4 ],
[ 19, 3, 2, 4 ], [ 19, 4, 2, 4 ], [ 19, 5, 2, 2 ], [ 20, 1, 4, 4 ],
[ 20, 2, 4, 2 ], [ 24, 2, 4, 2 ] ]
i = 25: Pi = [ 1, 4, 6 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [25,1,1]
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 0 modulo 4: 1/48 ( q^3-12*q^2+44*q-48 )
q congruent 1 modulo 4: 1/48 phi1 ( q^2-11*q+30 )
q congruent 2 modulo 4: 1/48 ( q^3-12*q^2+44*q-48 )
q congruent 3 modulo 4: 1/48 ( q^3-12*q^2+41*q-42 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 5, 10, 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 9, 2, 1, 12 ], [ 9, 3, 1, 12 ],
[ 9, 4, 1, 12 ], [ 9, 5, 1, 6 ], [ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ],
[ 15, 1, 1, 24 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 25, 2, 1, 24 ],
[ 25, 3, 1, 24 ] ]
k = 2: F-action on Pi is () [25,1,2]
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 0 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/16 phi1^2 ( q-4 )
q congruent 2 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/16 q ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 16, 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 2 ],
[ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ],
[ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ] ]
k = 3: F-action on Pi is () [25,1,3]
Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
Order of center |Z^F|: phi1 phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/16 phi1^2 ( q-2 )
q congruent 2 modulo 4: 1/16 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/16 ( q^3-4*q^2+5*q-6 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15, 7, 13, 7, 13, 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 4 ],
[ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ],
[ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ] ]
k = 4: F-action on Pi is () [25,1,4]
Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi2^3)
Order of center |Z^F|: phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/48 q ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/48 q phi1 ( q-5 )
q congruent 2 modulo 4: 1/48 q ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/48 phi2 ( q^2-7*q+12 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13, 13, 9, 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 6 ],
[ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 9, 2, 2, 12 ], [ 9, 3, 2, 12 ],
[ 9, 4, 2, 12 ], [ 9, 5, 2, 6 ], [ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ],
[ 15, 1, 3, 24 ], [ 18, 1, 4, 24 ], [ 18, 2, 4, 12 ], [ 25, 2, 8, 24 ],
[ 25, 3, 7, 24 ] ]
k = 5: F-action on Pi is (1,4) [25,1,5]
Dynkin type is A_1(q^2) + A_1(q) + T(phi1^2 phi2)
Order of center |Z^F|: phi1^2 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-3*q-2 )
q congruent 2 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/8 phi2 ( q^2-5*q+6 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15, 28, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ],
[ 9, 3, 6, 4 ], [ 9, 4, 6, 4 ], [ 9, 5, 6, 2 ], [ 10, 1, 1, 4 ],
[ 10, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 3, 4 ],
[ 18, 2, 1, 2 ], [ 18, 2, 3, 2 ], [ 25, 2, 3, 4 ], [ 25, 3, 2, 4 ],
[ 25, 3, 4, 4 ] ]
k = 6: F-action on Pi is (1,4) [25,1,6]
Dynkin type is A_1(q^2) + A_1(q) + T(phi1 phi4)
Order of center |Z^F|: phi1 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 phi2 ( q-2 )
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 phi1 phi2 ( q-2 )
Fusion of maximal tori of C^F in those of G^F:
[ 28, 31, 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ], [ 9, 3, 6, 4 ], [ 9, 4, 6, 4 ],
[ 9, 5, 6, 2 ], [ 15, 1, 5, 4 ], [ 25, 2, 4, 4 ] ]
k = 7: F-action on Pi is (4,6) [25,1,7]
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 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-q-4 )
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 q phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ],
[ 9, 3, 5, 4 ], [ 9, 4, 5, 4 ], [ 9, 5, 5, 2 ], [ 10, 1, 2, 4 ],
[ 10, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 4 ],
[ 18, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ],
[ 25, 3, 8, 4 ] ]
k = 8: F-action on Pi is (4,6) [25,1,8]
Dynkin type is A_1(q) + A_1(q^2) + T(phi2 phi4)
Order of center |Z^F|: phi2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^3
q congruent 1 modulo 4: 1/8 q phi1 phi2
q congruent 2 modulo 4: 1/8 q^3
q congruent 3 modulo 4: 1/8 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 32, 17, 30, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ], [ 9, 3, 5, 4 ], [ 9, 4, 5, 4 ],
[ 9, 5, 5, 2 ], [ 15, 1, 5, 4 ], [ 25, 2, 7, 4 ] ]
k = 9: F-action on Pi is (1,6,4) [25,1,9]
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 0 modulo 4: 1/6 q phi1 phi2
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 1/6 q phi1 phi2
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 26, 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 2, 1, 1 ], [ 25, 2, 9, 3 ] ]
k = 10: F-action on Pi is (1,6,4) [25,1,10]
Dynkin type is A_1(q^3) + T(phi2 phi6)
Order of center |Z^F|: phi2 phi6
Numbers of classes in class type:
q congruent 0 modulo 4: 1/6 q phi1 phi2
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 1/6 q phi1 phi2
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 37, 27 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 10, 2, 2, 1 ], [ 25, 2, 10, 3 ] ]
j = 3: Omega of order 2, action on Pi: <(4,6)>
k = 1: F-action on Pi is () [25,3,1]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^3)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 5, 10, 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 9, 3, 1, 4 ], [ 9, 5, 1, 2 ], [ 10, 2, 1, 2 ], [ 18, 2, 1, 2 ] ]
k = 2: F-action on Pi is (4,6) [25,3,2]
Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28, 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 9, 3, 6, 4 ], [ 9, 5, 6, 2 ], [ 18, 2, 3, 2 ] ]
k = 3: F-action on Pi is () [25,3,3]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 7, 3, 15, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 9, 3, 1, 4 ], [ 9, 5, 1, 2 ], [ 18, 2, 3, 2 ] ]
k = 4: F-action on Pi is (4,6) [25,3,4]
Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28, 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 9, 3, 6, 4 ], [ 9, 5, 6, 2 ], [ 10, 2, 1, 2 ], [ 18, 2, 1, 2 ] ]
k = 5: F-action on Pi is () [25,3,5]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 16, 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 9, 3, 2, 4 ], [ 9, 5, 2, 2 ], [ 18, 2, 2, 2 ] ]
k = 6: F-action on Pi is (4,6) [25,3,6]
Dynkin type is (A_1(q) + A_1(q^2) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 9, 3, 5, 4 ], [ 9, 5, 5, 2 ], [ 10, 2, 2, 2 ], [ 18, 2, 4, 2 ] ]
k = 7: F-action on Pi is () [25,3,7]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi2^3)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13, 13, 9, 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 9, 3, 2, 4 ], [ 9, 5, 2, 2 ], [ 10, 2, 2, 2 ], [ 18, 2, 4, 2 ] ]
k = 8: F-action on Pi is (4,6) [25,3,8]
Dynkin type is (A_1(q) + A_1(q^2) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32, 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 9, 3, 5, 4 ], [ 9, 5, 5, 2 ], [ 18, 2, 2, 2 ] ]
i = 26: Pi = [ 2, 4, 6 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [26,1,1]
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 0 modulo 4: 1/48 ( q^3-12*q^2+44*q-48 )
q congruent 1 modulo 4: 1/48 phi1 ( q^2-11*q+30 )
q congruent 2 modulo 4: 1/48 ( q^3-12*q^2+44*q-48 )
q congruent 3 modulo 4: 1/48 ( q^3-12*q^2+41*q-42 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 5, 10, 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 9, 2, 1, 12 ], [ 9, 3, 1, 12 ],
[ 9, 4, 1, 12 ], [ 9, 5, 1, 6 ], [ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ],
[ 15, 1, 1, 24 ], [ 20, 1, 1, 24 ], [ 20, 2, 1, 12 ], [ 26, 2, 1, 24 ],
[ 26, 3, 1, 24 ] ]
k = 2: F-action on Pi is () [26,1,2]
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 0 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/16 phi1^2 ( q-4 )
q congruent 2 modulo 4: 1/16 q ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/16 q ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 15, 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 2 ],
[ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ], [ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ],
[ 26, 2, 2, 8 ], [ 26, 3, 5, 8 ] ]
k = 3: F-action on Pi is () [26,1,3]
Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
Order of center |Z^F|: phi1 phi2^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/16 phi1^2 ( q-2 )
q congruent 2 modulo 4: 1/16 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/16 ( q^3-4*q^2+5*q-6 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16, 7, 13, 7, 13, 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 4 ],
[ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ],
[ 26, 2, 5, 8 ], [ 26, 3, 3, 8 ] ]
k = 4: F-action on Pi is () [26,1,4]
Dynkin type is A_1(q) + A_1(q) + A_1(q) + T(phi2^3)
Order of center |Z^F|: phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/48 q ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/48 q phi1 ( q-5 )
q congruent 2 modulo 4: 1/48 q ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/48 phi2 ( q^2-7*q+12 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13, 13, 9, 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 6 ],
[ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 9, 2, 2, 12 ], [ 9, 3, 2, 12 ],
[ 9, 4, 2, 12 ], [ 9, 5, 2, 6 ], [ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ],
[ 15, 1, 3, 24 ], [ 20, 1, 4, 24 ], [ 20, 2, 4, 12 ], [ 26, 2, 10, 24 ],
[ 26, 3, 7, 24 ] ]
k = 5: F-action on Pi is (2,4) [26,1,5]
Dynkin type is A_1(q^2) + A_1(q) + T(phi1^2 phi2)
Order of center |Z^F|: phi1^2 phi2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-3*q-2 )
q congruent 2 modulo 4: 1/8 q ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/8 phi2 ( q^2-5*q+6 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16, 28, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ],
[ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 8, 2 ], [ 11, 1, 1, 4 ],
[ 11, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 20, 1, 1, 4 ], [ 20, 1, 3, 4 ],
[ 20, 2, 1, 2 ], [ 20, 2, 3, 2 ], [ 26, 2, 3, 4 ], [ 26, 3, 2, 4 ],
[ 26, 3, 4, 4 ] ]
k = 6: F-action on Pi is (2,4) [26,1,6]
Dynkin type is A_1(q^2) + A_1(q) + T(phi1 phi4)
Order of center |Z^F|: phi1 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 phi2 ( q-2 )
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 phi1 phi2 ( q-2 )
Fusion of maximal tori of C^F in those of G^F:
[ 28, 32, 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ],
[ 9, 5, 8, 2 ], [ 15, 1, 5, 4 ], [ 26, 2, 4, 4 ] ]
k = 7: F-action on Pi is (4,6) [26,1,7]
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 0 modulo 4: 1/8 q^2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 ( q^2-q-4 )
q congruent 2 modulo 4: 1/8 q^2 ( q-2 )
q congruent 3 modulo 4: 1/8 q phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ],
[ 9, 3, 7, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 7, 2 ], [ 11, 1, 2, 4 ],
[ 11, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 20, 1, 2, 4 ], [ 20, 1, 4, 4 ],
[ 20, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 26, 2, 8, 4 ], [ 26, 3, 6, 4 ],
[ 26, 3, 8, 4 ] ]
k = 8: F-action on Pi is (4,6) [26,1,8]
Dynkin type is A_1(q) + A_1(q^2) + T(phi2 phi4)
Order of center |Z^F|: phi2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^3
q congruent 1 modulo 4: 1/8 q phi1 phi2
q congruent 2 modulo 4: 1/8 q^3
q congruent 3 modulo 4: 1/8 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 31, 17, 30, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ], [ 9, 3, 7, 4 ], [ 9, 4, 7, 4 ],
[ 9, 5, 7, 2 ], [ 15, 1, 5, 4 ], [ 26, 2, 9, 4 ] ]
k = 9: F-action on Pi is (2,6,4) [26,1,9]
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 0 modulo 4: 1/6 q phi1 phi2
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 1/6 q phi1 phi2
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 26, 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 26, 2, 6, 3 ] ]
k = 10: F-action on Pi is (2,6,4) [26,1,10]
Dynkin type is A_1(q^3) + T(phi2 phi6)
Order of center |Z^F|: phi2 phi6
Numbers of classes in class type:
q congruent 0 modulo 4: 1/6 q phi1 phi2
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 1/6 q phi1 phi2
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 36, 27 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 26, 2, 7, 3 ] ]
j = 3: Omega of order 2, action on Pi: <(4,6)>
k = 1: F-action on Pi is () [26,3,1]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^3)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10, 5, 10, 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 9, 4, 1, 4 ], [ 9, 5, 1, 2 ], [ 11, 2, 1, 2 ], [ 20, 2, 1, 2 ] ]
k = 2: F-action on Pi is (4,6) [26,3,2]
Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28, 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 9, 4, 8, 4 ], [ 9, 5, 8, 2 ], [ 20, 2, 3, 2 ] ]
k = 3: F-action on Pi is () [26,3,3]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 7, 3, 16, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 9, 4, 1, 4 ], [ 9, 5, 1, 2 ], [ 20, 2, 3, 2 ] ]
k = 4: F-action on Pi is (4,6) [26,3,4]
Dynkin type is (A_1(q) + A_1(q^2) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28, 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 9, 4, 8, 4 ], [ 9, 5, 8, 2 ], [ 11, 2, 1, 2 ], [ 20, 2, 1, 2 ] ]
k = 5: F-action on Pi is () [26,3,5]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 15, 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 9, 4, 2, 4 ], [ 9, 5, 2, 2 ], [ 20, 2, 2, 2 ] ]
k = 6: F-action on Pi is (4,6) [26,3,6]
Dynkin type is (A_1(q) + A_1(q^2) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 9, 4, 7, 4 ], [ 9, 5, 7, 2 ], [ 11, 2, 2, 2 ], [ 20, 2, 4, 2 ] ]
k = 7: F-action on Pi is () [26,3,7]
Dynkin type is (A_1(q) + A_1(q) + A_1(q) + T(phi2^3)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13, 13, 9, 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 9, 4, 2, 4 ], [ 9, 5, 2, 2 ], [ 11, 2, 2, 2 ], [ 20, 2, 4, 2 ] ]
k = 8: F-action on Pi is (4,6) [26,3,8]
Dynkin type is (A_1(q) + A_1(q^2) + T(phi1 phi2^2)).2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31, 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 9, 4, 7, 4 ], [ 9, 5, 7, 2 ], [ 20, 2, 2, 2 ] ]
i = 27: Pi = [ 1, 2 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [27,1,1]
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 0 modulo 4: 1/384 ( q^4-20*q^3+140*q^2-400*q+384 )
q congruent 1 modulo 4: 1/384 ( q^4-24*q^3+206*q^2-744*q+945 )
q congruent 2 modulo 4: 1/384 ( q^4-20*q^3+140*q^2-400*q+384 )
q congruent 3 modulo 4: 1/384 ( q^4-24*q^3+206*q^2-744*q+945 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 1, 16 ],
[ 3, 2, 1, 8 ], [ 3, 3, 1, 8 ], [ 3, 4, 1, 8 ], [ 3, 5, 1, 4 ],
[ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ],
[ 7, 1, 1, 64 ], [ 7, 2, 1, 32 ], [ 7, 3, 1, 32 ], [ 7, 4, 1, 32 ],
[ 7, 5, 1, 16 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 96 ], [ 9, 2, 1, 48 ],
[ 9, 3, 1, 48 ], [ 9, 4, 1, 48 ], [ 9, 5, 1, 24 ], [ 12, 1, 1, 48 ],
[ 12, 2, 1, 24 ], [ 12, 3, 1, 24 ], [ 12, 4, 1, 12 ], [ 13, 1, 1, 96 ],
[ 13, 2, 1, 48 ], [ 14, 1, 1, 64 ], [ 14, 2, 1, 32 ], [ 15, 1, 1, 96 ],
[ 16, 1, 1, 192 ], [ 16, 2, 1, 96 ], [ 16, 3, 1, 96 ], [ 16, 4, 1, 96 ],
[ 16, 5, 1, 96 ], [ 16, 6, 1, 96 ], [ 16, 7, 1, 96 ], [ 16, 8, 1, 96 ],
[ 16, 9, 1, 48 ], [ 16, 10, 1, 48 ], [ 16, 11, 1, 48 ], [ 16, 12, 1, 48 ],
[ 16, 13, 1, 48 ], [ 16, 14, 1, 48 ], [ 16, 15, 1, 48 ], [ 16, 16, 1, 48 ],
[ 16, 17, 1, 48 ], [ 21, 1, 1, 192 ], [ 21, 2, 1, 96 ], [ 21, 3, 1, 96 ],
[ 21, 4, 1, 96 ], [ 21, 5, 1, 48 ], [ 21, 6, 1, 48 ], [ 21, 7, 1, 48 ],
[ 22, 1, 1, 192 ], [ 22, 2, 1, 96 ], [ 22, 3, 1, 96 ], [ 22, 4, 1, 48 ],
[ 27, 2, 1, 192 ], [ 27, 3, 1, 192 ], [ 27, 4, 1, 192 ], [ 27, 5, 1, 192 ],
[ 27, 6, 1, 96 ], [ 27, 7, 1, 96 ], [ 27, 8, 1, 96 ], [ 27, 9, 1, 96 ],
[ 27, 10, 1, 96 ], [ 27, 11, 1, 96 ], [ 27, 12, 1, 96 ], [ 27, 13, 1, 96 ],
[ 27, 14, 1, 96 ] ]
k = 2: F-action on Pi is (1,2) [27,1,2]
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 0 modulo 4: 1/96 q ( q^3-12*q^2+44*q-48 )
q congruent 1 modulo 4: 1/96 phi1 ( q^3-15*q^2+71*q-105 )
q congruent 2 modulo 4: 1/96 q ( q^3-12*q^2+44*q-48 )
q congruent 3 modulo 4: 1/96 phi1 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 12 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 6 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 6 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 6 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 3 ], [ 4, 1, 1, 6 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 3 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 12 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 36 ],
[ 7, 1, 4, 12 ], [ 7, 2, 1, 6 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 18 ],
[ 7, 2, 4, 6 ], [ 7, 3, 1, 6 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 18 ],
[ 7, 3, 4, 6 ], [ 7, 4, 1, 6 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 18 ],
[ 7, 4, 4, 6 ], [ 7, 5, 1, 3 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 9 ],
[ 7, 5, 4, 3 ], [ 9, 1, 3, 48 ], [ 9, 2, 3, 24 ], [ 9, 3, 3, 24 ],
[ 9, 4, 3, 24 ], [ 9, 5, 3, 12 ], [ 12, 1, 1, 24 ], [ 12, 1, 4, 12 ],
[ 12, 2, 1, 12 ], [ 12, 2, 4, 6 ], [ 12, 3, 1, 12 ], [ 12, 3, 3, 6 ],
[ 12, 3, 4, 6 ], [ 12, 4, 1, 6 ], [ 12, 4, 4, 3 ], [ 13, 1, 1, 24 ],
[ 13, 1, 3, 24 ], [ 13, 2, 1, 12 ], [ 13, 2, 3, 12 ], [ 14, 1, 3, 16 ],
[ 14, 2, 3, 8 ], [ 16, 1, 2, 24 ], [ 16, 1, 6, 96 ], [ 16, 2, 2, 12 ],
[ 16, 2, 6, 48 ], [ 16, 3, 2, 12 ], [ 16, 3, 6, 48 ], [ 16, 4, 2, 12 ],
[ 16, 4, 6, 48 ], [ 16, 5, 5, 48 ], [ 16, 6, 5, 48 ], [ 16, 7, 5, 48 ],
[ 16, 8, 2, 12 ], [ 16, 8, 3, 12 ], [ 16, 8, 5, 48 ], [ 16, 8, 6, 12 ],
[ 16, 8, 7, 12 ], [ 16, 9, 2, 6 ], [ 16, 9, 6, 24 ], [ 16, 10, 5, 24 ],
[ 16, 11, 2, 6 ], [ 16, 11, 6, 24 ], [ 16, 11, 7, 6 ], [ 16, 12, 5, 24 ],
[ 16, 13, 2, 12 ], [ 16, 13, 6, 24 ], [ 16, 14, 2, 6 ], [ 16, 14, 3, 6 ],
[ 16, 14, 5, 24 ], [ 16, 15, 2, 12 ], [ 16, 15, 6, 24 ], [ 16, 16, 2, 12 ],
[ 16, 16, 6, 24 ], [ 16, 17, 2, 6 ], [ 16, 17, 3, 6 ], [ 16, 17, 5, 24 ],
[ 21, 1, 1, 48 ], [ 21, 1, 2, 48 ], [ 21, 2, 1, 24 ], [ 21, 2, 6, 24 ],
[ 21, 2, 8, 24 ], [ 21, 3, 1, 24 ], [ 21, 3, 6, 24 ], [ 21, 3, 7, 24 ],
[ 21, 4, 1, 24 ], [ 21, 4, 6, 24 ], [ 21, 5, 1, 12 ], [ 21, 5, 6, 12 ],
[ 21, 5, 8, 12 ], [ 21, 6, 1, 12 ], [ 21, 6, 6, 12 ], [ 21, 6, 7, 12 ],
[ 21, 7, 1, 12 ], [ 21, 7, 6, 12 ], [ 22, 1, 7, 48 ], [ 22, 2, 7, 24 ],
[ 22, 3, 5, 24 ], [ 22, 3, 6, 24 ], [ 22, 4, 7, 12 ], [ 27, 2, 11, 48 ],
[ 27, 2, 16, 48 ], [ 27, 3, 14, 48 ], [ 27, 3, 16, 48 ], [ 27, 4, 11, 48 ],
[ 27, 4, 12, 48 ], [ 27, 5, 12, 48 ], [ 27, 6, 11, 24 ], [ 27, 6, 13, 24 ],
[ 27, 6, 16, 24 ], [ 27, 7, 11, 24 ], [ 27, 7, 16, 24 ], [ 27, 8, 14, 24 ],
[ 27, 8, 16, 24 ], [ 27, 9, 13, 24 ], [ 27, 10, 11, 24 ],
[ 27, 10, 12, 24 ], [ 27, 10, 13, 24 ], [ 27, 11, 14, 24 ],
[ 27, 11, 16, 24 ], [ 27, 12, 11, 24 ], [ 27, 12, 12, 24 ],
[ 27, 13, 11, 24 ], [ 27, 13, 12, 24 ], [ 27, 13, 16, 24 ],
[ 27, 14, 14, 24 ], [ 27, 14, 15, 24 ] ]
k = 3: F-action on Pi is () [27,1,3]
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 0 modulo 4: 1/64 q ( q^3-8*q^2+20*q-16 )
q congruent 1 modulo 4: 1/64 phi1 ( q^3-11*q^2+39*q-45 )
q congruent 2 modulo 4: 1/64 q ( q^3-8*q^2+20*q-16 )
q congruent 3 modulo 4: 1/64 phi1 ( q^3-11*q^2+39*q-45 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 3, 2, 1, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 1, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 1, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 4 ], [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ], [ 7, 1, 3, 16 ],
[ 7, 1, 4, 16 ], [ 7, 2, 1, 8 ], [ 7, 2, 2, 8 ], [ 7, 2, 3, 8 ],
[ 7, 2, 4, 8 ], [ 7, 3, 1, 8 ], [ 7, 3, 2, 8 ], [ 7, 3, 3, 8 ],
[ 7, 3, 4, 8 ], [ 7, 4, 1, 8 ], [ 7, 4, 2, 8 ], [ 7, 4, 3, 8 ],
[ 7, 4, 4, 8 ], [ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ],
[ 7, 5, 4, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ],
[ 9, 2, 2, 8 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ], [ 12, 1, 1, 8 ],
[ 12, 1, 3, 8 ], [ 12, 1, 4, 16 ], [ 12, 2, 1, 4 ], [ 12, 2, 3, 4 ],
[ 12, 2, 4, 8 ], [ 12, 3, 1, 4 ], [ 12, 3, 2, 4 ], [ 12, 3, 3, 8 ],
[ 12, 3, 4, 8 ], [ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ],
[ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 2, 2, 8 ], [ 13, 2, 3, 8 ],
[ 15, 1, 4, 16 ], [ 16, 1, 1, 32 ], [ 16, 1, 2, 32 ], [ 16, 1, 5, 32 ],
[ 16, 2, 1, 16 ], [ 16, 2, 2, 16 ], [ 16, 2, 5, 16 ], [ 16, 3, 1, 16 ],
[ 16, 3, 2, 16 ], [ 16, 3, 5, 16 ], [ 16, 4, 1, 16 ], [ 16, 4, 2, 16 ],
[ 16, 4, 5, 16 ], [ 16, 5, 1, 16 ], [ 16, 5, 3, 16 ], [ 16, 6, 1, 16 ],
[ 16, 6, 3, 16 ], [ 16, 7, 1, 16 ], [ 16, 7, 3, 16 ], [ 16, 8, 1, 16 ],
[ 16, 8, 2, 16 ], [ 16, 8, 3, 16 ], [ 16, 8, 4, 16 ], [ 16, 8, 6, 16 ],
[ 16, 8, 7, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 2, 8 ], [ 16, 9, 5, 8 ],
[ 16, 10, 1, 8 ], [ 16, 10, 3, 8 ], [ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ],
[ 16, 11, 5, 8 ], [ 16, 11, 7, 8 ], [ 16, 12, 1, 8 ], [ 16, 12, 3, 8 ],
[ 16, 13, 1, 8 ], [ 16, 13, 2, 16 ], [ 16, 13, 5, 8 ], [ 16, 14, 1, 8 ],
[ 16, 14, 2, 8 ], [ 16, 14, 3, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 1, 8 ],
[ 16, 15, 2, 16 ], [ 16, 15, 5, 8 ], [ 16, 16, 1, 8 ], [ 16, 16, 2, 16 ],
[ 16, 16, 5, 8 ], [ 16, 17, 1, 8 ], [ 16, 17, 2, 8 ], [ 16, 17, 3, 8 ],
[ 16, 17, 4, 8 ], [ 21, 1, 2, 32 ], [ 21, 1, 3, 32 ], [ 21, 2, 3, 16 ],
[ 21, 2, 4, 16 ], [ 21, 2, 6, 16 ], [ 21, 2, 8, 16 ], [ 21, 3, 2, 16 ],
[ 21, 3, 5, 16 ], [ 21, 3, 6, 16 ], [ 21, 3, 7, 16 ], [ 21, 4, 3, 16 ],
[ 21, 4, 6, 16 ], [ 21, 5, 3, 8 ], [ 21, 5, 4, 8 ], [ 21, 5, 6, 8 ],
[ 21, 5, 8, 8 ], [ 21, 6, 2, 8 ], [ 21, 6, 5, 8 ], [ 21, 6, 6, 8 ],
[ 21, 6, 7, 8 ], [ 21, 7, 3, 8 ], [ 21, 7, 6, 8 ], [ 22, 1, 3, 32 ],
[ 22, 1, 4, 32 ], [ 22, 2, 3, 16 ], [ 22, 2, 4, 16 ], [ 22, 3, 2, 16 ],
[ 22, 3, 3, 16 ], [ 22, 4, 3, 8 ], [ 22, 4, 4, 8 ], [ 27, 2, 3, 32 ],
[ 27, 2, 6, 32 ], [ 27, 3, 3, 32 ], [ 27, 3, 4, 32 ], [ 27, 3, 11, 32 ],
[ 27, 4, 2, 32 ], [ 27, 4, 5, 32 ], [ 27, 5, 3, 32 ], [ 27, 6, 3, 16 ],
[ 27, 6, 4, 16 ], [ 27, 6, 6, 16 ], [ 27, 6, 8, 16 ], [ 27, 7, 3, 16 ],
[ 27, 7, 6, 16 ], [ 27, 8, 3, 16 ], [ 27, 8, 4, 16 ], [ 27, 8, 11, 16 ],
[ 27, 9, 3, 16 ], [ 27, 9, 4, 16 ], [ 27, 10, 2, 16 ], [ 27, 10, 3, 16 ],
[ 27, 10, 4, 16 ], [ 27, 10, 9, 16 ], [ 27, 11, 3, 16 ], [ 27, 11, 4, 16 ],
[ 27, 11, 11, 16 ], [ 27, 12, 2, 16 ], [ 27, 12, 5, 16 ], [ 27, 13, 2, 16 ],
[ 27, 13, 5, 16 ], [ 27, 13, 6, 16 ], [ 27, 13, 7, 16 ], [ 27, 14, 2, 16 ],
[ 27, 14, 5, 16 ], [ 27, 14, 11, 16 ] ]
k = 4: F-action on Pi is (1,2) [27,1,4]
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 0 modulo 4: 1/96 q ( q^3-8*q^2+20*q-16 )
q congruent 1 modulo 4: 1/96 phi1 ( q^3-11*q^2+39*q-45 )
q congruent 2 modulo 4: 1/96 q ( q^3-8*q^2+20*q-16 )
q congruent 3 modulo 4: 1/96 phi1 ( q^3-11*q^2+39*q-45 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 12 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 6 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 6 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 6 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 3 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 6 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 3 ], [ 5, 1, 2, 12 ],
[ 6, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 36 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 12 ], [ 7, 2, 1, 6 ], [ 7, 2, 2, 18 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 6 ], [ 7, 3, 1, 6 ], [ 7, 3, 2, 18 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 6 ], [ 7, 4, 1, 6 ], [ 7, 4, 2, 18 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 6 ], [ 7, 5, 1, 3 ], [ 7, 5, 2, 9 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 3 ], [ 9, 1, 4, 48 ], [ 9, 2, 4, 24 ], [ 9, 3, 4, 24 ],
[ 9, 4, 4, 24 ], [ 9, 5, 4, 12 ], [ 12, 1, 3, 24 ], [ 12, 1, 4, 12 ],
[ 12, 2, 3, 12 ], [ 12, 2, 4, 6 ], [ 12, 3, 2, 12 ], [ 12, 3, 3, 6 ],
[ 12, 3, 4, 6 ], [ 12, 4, 3, 6 ], [ 12, 4, 4, 3 ], [ 13, 1, 2, 24 ],
[ 13, 1, 4, 24 ], [ 13, 2, 2, 12 ], [ 13, 2, 4, 12 ], [ 14, 1, 4, 16 ],
[ 14, 2, 4, 8 ], [ 16, 1, 2, 24 ], [ 16, 1, 8, 96 ], [ 16, 2, 2, 12 ],
[ 16, 2, 8, 48 ], [ 16, 3, 2, 12 ], [ 16, 3, 8, 48 ], [ 16, 4, 2, 12 ],
[ 16, 4, 8, 48 ], [ 16, 5, 7, 48 ], [ 16, 6, 7, 48 ], [ 16, 7, 7, 48 ],
[ 16, 8, 2, 12 ], [ 16, 8, 3, 12 ], [ 16, 8, 6, 12 ], [ 16, 8, 7, 12 ],
[ 16, 8, 8, 48 ], [ 16, 9, 2, 6 ], [ 16, 9, 8, 24 ], [ 16, 10, 7, 24 ],
[ 16, 11, 2, 6 ], [ 16, 11, 7, 6 ], [ 16, 11, 10, 24 ], [ 16, 12, 7, 24 ],
[ 16, 13, 2, 12 ], [ 16, 13, 8, 24 ], [ 16, 14, 2, 6 ], [ 16, 14, 3, 6 ],
[ 16, 14, 6, 24 ], [ 16, 15, 2, 12 ], [ 16, 15, 8, 24 ], [ 16, 16, 2, 12 ],
[ 16, 16, 8, 24 ], [ 16, 17, 2, 6 ], [ 16, 17, 3, 6 ], [ 16, 17, 6, 24 ],
[ 21, 1, 3, 48 ], [ 21, 1, 4, 48 ], [ 21, 2, 3, 24 ], [ 21, 2, 4, 24 ],
[ 21, 2, 10, 24 ], [ 21, 3, 2, 24 ], [ 21, 3, 5, 24 ], [ 21, 3, 10, 24 ],
[ 21, 4, 3, 24 ], [ 21, 4, 10, 24 ], [ 21, 5, 3, 12 ], [ 21, 5, 4, 12 ],
[ 21, 5, 10, 12 ], [ 21, 6, 2, 12 ], [ 21, 6, 5, 12 ], [ 21, 6, 10, 12 ],
[ 21, 7, 3, 12 ], [ 21, 7, 10, 12 ], [ 22, 1, 9, 48 ], [ 22, 2, 9, 24 ],
[ 22, 3, 7, 24 ], [ 22, 3, 8, 24 ], [ 22, 4, 9, 12 ], [ 27, 2, 15, 48 ],
[ 27, 2, 18, 48 ], [ 27, 3, 18, 48 ], [ 27, 3, 24, 48 ], [ 27, 4, 15, 48 ],
[ 27, 4, 20, 48 ], [ 27, 5, 16, 48 ], [ 27, 6, 15, 24 ], [ 27, 6, 18, 24 ],
[ 27, 6, 19, 24 ], [ 27, 7, 15, 24 ], [ 27, 7, 18, 24 ], [ 27, 8, 18, 24 ],
[ 27, 8, 24, 24 ], [ 27, 9, 16, 24 ], [ 27, 10, 14, 24 ],
[ 27, 10, 19, 24 ], [ 27, 10, 20, 24 ], [ 27, 11, 18, 24 ],
[ 27, 11, 24, 24 ], [ 27, 12, 15, 24 ], [ 27, 12, 20, 24 ],
[ 27, 13, 15, 24 ], [ 27, 13, 17, 24 ], [ 27, 13, 20, 24 ],
[ 27, 14, 18, 24 ], [ 27, 14, 24, 24 ] ]
k = 5: F-action on Pi is () [27,1,5]
Dynkin type is A_1(q) + A_1(q) + T(phi2^4)
Order of center |Z^F|: phi2^4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/384 q ( q^3-12*q^2+44*q-48 )
q congruent 1 modulo 4: 1/384 phi1 ( q^3-15*q^2+71*q-105 )
q congruent 2 modulo 4: 1/384 q ( q^3-12*q^2+44*q-48 )
q congruent 3 modulo 4: 1/384 phi1 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 2, 16 ],
[ 3, 2, 2, 8 ], [ 3, 3, 2, 8 ], [ 3, 4, 2, 8 ], [ 3, 5, 2, 4 ],
[ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ],
[ 7, 1, 4, 64 ], [ 7, 2, 4, 32 ], [ 7, 3, 4, 32 ], [ 7, 4, 4, 32 ],
[ 7, 5, 4, 16 ], [ 8, 1, 2, 16 ], [ 9, 1, 2, 96 ], [ 9, 2, 2, 48 ],
[ 9, 3, 2, 48 ], [ 9, 4, 2, 48 ], [ 9, 5, 2, 24 ], [ 12, 1, 3, 48 ],
[ 12, 2, 3, 24 ], [ 12, 3, 2, 24 ], [ 12, 4, 3, 12 ], [ 13, 1, 4, 96 ],
[ 13, 2, 4, 48 ], [ 14, 1, 2, 64 ], [ 14, 2, 2, 32 ], [ 15, 1, 3, 96 ],
[ 16, 1, 5, 192 ], [ 16, 2, 5, 96 ], [ 16, 3, 5, 96 ], [ 16, 4, 5, 96 ],
[ 16, 5, 3, 96 ], [ 16, 6, 3, 96 ], [ 16, 7, 3, 96 ], [ 16, 8, 4, 96 ],
[ 16, 9, 5, 48 ], [ 16, 10, 3, 48 ], [ 16, 11, 5, 48 ], [ 16, 12, 3, 48 ],
[ 16, 13, 5, 48 ], [ 16, 14, 4, 48 ], [ 16, 15, 5, 48 ], [ 16, 16, 5, 48 ],
[ 16, 17, 4, 48 ], [ 21, 1, 4, 192 ], [ 21, 2, 10, 96 ], [ 21, 3, 10, 96 ],
[ 21, 4, 10, 96 ], [ 21, 5, 10, 48 ], [ 21, 6, 10, 48 ], [ 21, 7, 10, 48 ],
[ 22, 1, 6, 192 ], [ 22, 2, 6, 96 ], [ 22, 3, 4, 96 ], [ 22, 4, 6, 48 ],
[ 27, 2, 10, 192 ], [ 27, 3, 13, 192 ], [ 27, 4, 10, 192 ],
[ 27, 5, 11, 192 ], [ 27, 6, 10, 96 ], [ 27, 7, 10, 96 ], [ 27, 8, 13, 96 ],
[ 27, 9, 12, 96 ], [ 27, 10, 10, 96 ], [ 27, 11, 13, 96 ],
[ 27, 12, 10, 96 ], [ 27, 13, 10, 96 ], [ 27, 14, 13, 96 ] ]
k = 6: F-action on Pi is () [27,1,6]
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 0 modulo 4: 1/32 q ( q^3-8*q^2+20*q-16 )
q congruent 1 modulo 4: 1/32 phi1^2 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/32 q ( q^3-8*q^2+20*q-16 )
q congruent 3 modulo 4: 1/32 phi1^2 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 6 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ],
[ 7, 4, 1, 8 ], [ 7, 5, 1, 4 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 24 ],
[ 9, 1, 2, 8 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 12 ],
[ 9, 3, 2, 4 ], [ 9, 4, 1, 12 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 6 ],
[ 9, 5, 2, 2 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ], [ 12, 2, 1, 4 ],
[ 12, 2, 2, 2 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ],
[ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 2, 1, 4 ], [ 13, 2, 2, 4 ],
[ 14, 1, 1, 16 ], [ 14, 2, 1, 8 ], [ 15, 1, 1, 16 ], [ 15, 1, 4, 8 ],
[ 16, 1, 1, 32 ], [ 16, 1, 3, 16 ], [ 16, 2, 1, 16 ], [ 16, 2, 3, 8 ],
[ 16, 3, 1, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 1, 16 ], [ 16, 4, 3, 8 ],
[ 16, 5, 1, 16 ], [ 16, 5, 2, 8 ], [ 16, 5, 4, 8 ], [ 16, 6, 1, 16 ],
[ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 1, 16 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 8, 1, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 3, 4 ],
[ 16, 10, 1, 8 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 1, 8 ],
[ 16, 11, 3, 8 ], [ 16, 12, 1, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ],
[ 16, 13, 1, 8 ], [ 16, 13, 3, 4 ], [ 16, 14, 1, 8 ], [ 16, 15, 1, 8 ],
[ 16, 15, 3, 4 ], [ 16, 16, 1, 8 ], [ 16, 16, 3, 4 ], [ 16, 17, 1, 8 ],
[ 21, 1, 5, 16 ], [ 21, 2, 2, 8 ], [ 21, 3, 3, 8 ], [ 21, 4, 2, 8 ],
[ 21, 5, 2, 4 ], [ 21, 6, 3, 8 ], [ 21, 7, 2, 8 ], [ 22, 1, 1, 16 ],
[ 22, 1, 2, 16 ], [ 22, 1, 4, 16 ], [ 22, 2, 1, 8 ], [ 22, 2, 2, 8 ],
[ 22, 2, 4, 8 ], [ 22, 3, 1, 8 ], [ 22, 3, 3, 8 ], [ 22, 4, 1, 4 ],
[ 22, 4, 2, 8 ], [ 22, 4, 4, 4 ], [ 27, 2, 2, 16 ], [ 27, 3, 2, 16 ],
[ 27, 3, 6, 16 ], [ 27, 4, 3, 16 ], [ 27, 5, 2, 16 ], [ 27, 6, 2, 8 ],
[ 27, 7, 2, 8 ], [ 27, 8, 2, 8 ], [ 27, 8, 6, 16 ], [ 27, 9, 2, 8 ],
[ 27, 10, 5, 8 ], [ 27, 11, 2, 8 ], [ 27, 11, 6, 16 ], [ 27, 12, 3, 16 ],
[ 27, 13, 3, 8 ], [ 27, 14, 3, 8 ], [ 27, 14, 8, 16 ] ]
k = 7: F-action on Pi is (1,2) [27,1,7]
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 0 modulo 4: 1/32 q^2 ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/32 phi1 phi2 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/32 q^2 ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/32 phi1 phi2 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 6, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 2, 8 ], [ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ],
[ 5, 1, 1, 4 ], [ 7, 1, 3, 16 ], [ 7, 2, 3, 8 ], [ 7, 3, 3, 8 ],
[ 7, 4, 3, 8 ], [ 7, 5, 3, 4 ], [ 9, 1, 3, 16 ], [ 9, 2, 3, 8 ],
[ 9, 3, 3, 8 ], [ 9, 4, 3, 8 ], [ 9, 5, 3, 4 ], [ 12, 1, 1, 8 ],
[ 12, 1, 5, 4 ], [ 12, 2, 1, 4 ], [ 12, 2, 5, 2 ], [ 12, 3, 1, 4 ],
[ 12, 4, 1, 2 ], [ 12, 4, 5, 2 ], [ 16, 1, 4, 8 ], [ 16, 1, 6, 32 ],
[ 16, 2, 4, 4 ], [ 16, 2, 6, 16 ], [ 16, 3, 4, 4 ], [ 16, 3, 6, 16 ],
[ 16, 4, 4, 4 ], [ 16, 4, 6, 16 ], [ 16, 5, 5, 16 ], [ 16, 6, 5, 16 ],
[ 16, 7, 5, 16 ], [ 16, 8, 5, 16 ], [ 16, 9, 4, 2 ], [ 16, 9, 6, 8 ],
[ 16, 10, 5, 8 ], [ 16, 11, 4, 4 ], [ 16, 11, 6, 8 ], [ 16, 11, 9, 4 ],
[ 16, 12, 5, 8 ], [ 16, 13, 4, 4 ], [ 16, 13, 6, 8 ], [ 16, 14, 5, 8 ],
[ 16, 15, 4, 4 ], [ 16, 15, 6, 8 ], [ 16, 16, 4, 4 ], [ 16, 16, 6, 8 ],
[ 16, 17, 5, 8 ], [ 21, 1, 6, 16 ], [ 21, 2, 7, 8 ], [ 21, 3, 9, 8 ],
[ 21, 4, 7, 8 ], [ 21, 5, 7, 4 ], [ 21, 6, 8, 8 ], [ 21, 7, 7, 8 ],
[ 22, 1, 8, 16 ], [ 22, 2, 8, 8 ], [ 22, 4, 8, 8 ], [ 27, 2, 12, 16 ],
[ 27, 3, 15, 16 ], [ 27, 3, 21, 16 ], [ 27, 4, 14, 16 ], [ 27, 5, 13, 16 ],
[ 27, 6, 12, 8 ], [ 27, 7, 12, 8 ], [ 27, 8, 15, 8 ], [ 27, 8, 21, 16 ],
[ 27, 9, 14, 8 ], [ 27, 10, 17, 8 ], [ 27, 11, 15, 8 ], [ 27, 11, 21, 16 ],
[ 27, 12, 14, 16 ], [ 27, 13, 14, 8 ], [ 27, 14, 17, 8 ],
[ 27, 14, 21, 16 ] ]
k = 8: F-action on Pi is (1,2) [27,1,8]
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 0 modulo 4: 1/16 q^2 ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/16 phi1^3 ( q-3 )
q congruent 2 modulo 4: 1/16 q^2 ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/16 phi1^3 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ],
[ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ],
[ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ], [ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ],
[ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ],
[ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ], [ 9, 1, 3, 8 ],
[ 9, 1, 4, 8 ], [ 9, 2, 3, 4 ], [ 9, 2, 4, 4 ], [ 9, 3, 3, 4 ],
[ 9, 3, 4, 4 ], [ 9, 4, 3, 4 ], [ 9, 4, 4, 4 ], [ 9, 5, 3, 2 ],
[ 9, 5, 4, 2 ], [ 12, 1, 2, 4 ], [ 12, 1, 4, 4 ], [ 12, 2, 2, 2 ],
[ 12, 2, 4, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 2, 2 ],
[ 12, 4, 4, 1 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ],
[ 13, 1, 4, 4 ], [ 13, 2, 1, 2 ], [ 13, 2, 2, 2 ], [ 13, 2, 3, 2 ],
[ 13, 2, 4, 2 ], [ 14, 1, 3, 8 ], [ 14, 1, 4, 8 ], [ 14, 2, 3, 4 ],
[ 14, 2, 4, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 7, 16 ], [ 16, 2, 2, 4 ],
[ 16, 2, 7, 8 ], [ 16, 3, 2, 4 ], [ 16, 3, 7, 8 ], [ 16, 4, 2, 4 ],
[ 16, 4, 7, 8 ], [ 16, 5, 6, 8 ], [ 16, 5, 8, 8 ], [ 16, 6, 6, 8 ],
[ 16, 6, 8, 8 ], [ 16, 7, 6, 8 ], [ 16, 7, 8, 8 ], [ 16, 8, 2, 4 ],
[ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ], [ 16, 9, 2, 2 ],
[ 16, 9, 7, 4 ], [ 16, 10, 6, 4 ], [ 16, 10, 8, 4 ], [ 16, 11, 2, 2 ],
[ 16, 11, 7, 2 ], [ 16, 11, 8, 8 ], [ 16, 12, 6, 4 ], [ 16, 12, 8, 4 ],
[ 16, 13, 2, 4 ], [ 16, 13, 7, 4 ], [ 16, 14, 2, 2 ], [ 16, 14, 3, 2 ],
[ 16, 15, 2, 4 ], [ 16, 15, 7, 4 ], [ 16, 16, 2, 4 ], [ 16, 16, 7, 4 ],
[ 16, 17, 2, 2 ], [ 16, 17, 3, 2 ], [ 21, 1, 5, 8 ], [ 21, 1, 7, 8 ],
[ 21, 2, 2, 4 ], [ 21, 2, 9, 4 ], [ 21, 3, 3, 4 ], [ 21, 3, 8, 4 ],
[ 21, 4, 2, 4 ], [ 21, 4, 9, 4 ], [ 21, 5, 2, 2 ], [ 21, 5, 9, 2 ],
[ 21, 6, 3, 4 ], [ 21, 6, 9, 4 ], [ 21, 7, 2, 4 ], [ 21, 7, 9, 4 ],
[ 22, 1, 7, 8 ], [ 22, 1, 9, 8 ], [ 22, 2, 7, 4 ], [ 22, 2, 9, 4 ],
[ 22, 3, 5, 4 ], [ 22, 3, 6, 4 ], [ 22, 3, 7, 4 ], [ 22, 3, 8, 4 ],
[ 22, 4, 7, 2 ], [ 22, 4, 9, 2 ], [ 27, 2, 14, 8 ], [ 27, 2, 17, 8 ],
[ 27, 3, 17, 8 ], [ 27, 3, 19, 8 ], [ 27, 4, 13, 8 ], [ 27, 4, 18, 8 ],
[ 27, 5, 15, 8 ], [ 27, 6, 14, 4 ], [ 27, 6, 17, 4 ], [ 27, 7, 14, 4 ],
[ 27, 7, 17, 4 ], [ 27, 8, 17, 4 ], [ 27, 8, 19, 8 ], [ 27, 9, 15, 4 ],
[ 27, 10, 15, 4 ], [ 27, 10, 16, 4 ], [ 27, 11, 17, 4 ], [ 27, 11, 19, 8 ],
[ 27, 12, 13, 8 ], [ 27, 12, 18, 8 ], [ 27, 13, 13, 4 ], [ 27, 13, 18, 4 ],
[ 27, 14, 16, 4 ], [ 27, 14, 22, 8 ] ]
k = 9: F-action on Pi is () [27,1,9]
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 0 modulo 4: 1/16 q^3 ( q-2 )
q congruent 1 modulo 4: 1/16 phi1^2 phi2 ( q-3 )
q congruent 2 modulo 4: 1/16 q^3 ( q-2 )
q congruent 3 modulo 4: 1/16 phi1^2 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 7, 1, 1, 4 ],
[ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ],
[ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ], [ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ],
[ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ],
[ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ], [ 12, 1, 4, 4 ],
[ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ], [ 12, 3, 3, 2 ],
[ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ], [ 16, 1, 2, 8 ],
[ 16, 1, 4, 8 ], [ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 3, 2, 4 ],
[ 16, 3, 4, 4 ], [ 16, 4, 2, 4 ], [ 16, 4, 4, 4 ], [ 16, 8, 2, 4 ],
[ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ], [ 16, 9, 2, 2 ],
[ 16, 9, 4, 2 ], [ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ], [ 16, 11, 7, 2 ],
[ 16, 11, 9, 4 ], [ 16, 13, 2, 4 ], [ 16, 13, 4, 4 ], [ 16, 14, 2, 2 ],
[ 16, 14, 3, 2 ], [ 16, 15, 2, 4 ], [ 16, 15, 4, 4 ], [ 16, 16, 2, 4 ],
[ 16, 16, 4, 4 ], [ 16, 17, 2, 2 ], [ 16, 17, 3, 2 ], [ 21, 1, 6, 8 ],
[ 21, 1, 8, 8 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 4 ], [ 21, 3, 4, 4 ],
[ 21, 3, 9, 4 ], [ 21, 4, 5, 4 ], [ 21, 4, 7, 4 ], [ 21, 5, 5, 2 ],
[ 21, 5, 7, 2 ], [ 21, 6, 4, 4 ], [ 21, 6, 8, 4 ], [ 21, 7, 5, 4 ],
[ 21, 7, 7, 4 ], [ 27, 2, 5, 8 ], [ 27, 2, 7, 8 ], [ 27, 3, 5, 8 ],
[ 27, 3, 9, 8 ], [ 27, 4, 4, 8 ], [ 27, 4, 9, 8 ], [ 27, 5, 5, 8 ],
[ 27, 6, 5, 4 ], [ 27, 6, 7, 4 ], [ 27, 7, 5, 4 ], [ 27, 7, 7, 4 ],
[ 27, 8, 5, 4 ], [ 27, 8, 9, 8 ], [ 27, 9, 5, 4 ], [ 27, 10, 7, 4 ],
[ 27, 10, 8, 4 ], [ 27, 11, 5, 4 ], [ 27, 11, 9, 8 ], [ 27, 12, 4, 8 ],
[ 27, 12, 9, 8 ], [ 27, 13, 4, 4 ], [ 27, 13, 9, 4 ], [ 27, 14, 4, 4 ],
[ 27, 14, 9, 8 ] ]
k = 10: F-action on Pi is () [27,1,10]
Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2^3)
Order of center |Z^F|: phi1 phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/32 q^2 ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/32 phi1^3 ( q-3 )
q congruent 2 modulo 4: 1/32 q^2 ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/32 phi1^3 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 6 ],
[ 6, 1, 2, 8 ], [ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ],
[ 7, 4, 4, 8 ], [ 7, 5, 4, 4 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 8 ],
[ 9, 1, 2, 24 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 12 ], [ 9, 3, 1, 4 ],
[ 9, 3, 2, 12 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 6 ], [ 12, 1, 2, 4 ], [ 12, 1, 3, 8 ], [ 12, 2, 2, 2 ],
[ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 2, 2 ], [ 12, 4, 3, 2 ],
[ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], [ 13, 2, 3, 4 ], [ 13, 2, 4, 4 ],
[ 14, 1, 2, 16 ], [ 14, 2, 2, 8 ], [ 15, 1, 3, 16 ], [ 15, 1, 4, 8 ],
[ 16, 1, 3, 16 ], [ 16, 1, 5, 32 ], [ 16, 2, 3, 8 ], [ 16, 2, 5, 16 ],
[ 16, 3, 3, 8 ], [ 16, 3, 5, 16 ], [ 16, 4, 3, 8 ], [ 16, 4, 5, 16 ],
[ 16, 5, 2, 8 ], [ 16, 5, 3, 16 ], [ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ],
[ 16, 6, 3, 16 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ], [ 16, 7, 3, 16 ],
[ 16, 7, 4, 8 ], [ 16, 8, 4, 16 ], [ 16, 9, 3, 4 ], [ 16, 9, 5, 8 ],
[ 16, 10, 2, 4 ], [ 16, 10, 3, 8 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ],
[ 16, 11, 5, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 3, 8 ], [ 16, 12, 4, 4 ],
[ 16, 13, 3, 4 ], [ 16, 13, 5, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 3, 4 ],
[ 16, 15, 5, 8 ], [ 16, 16, 3, 4 ], [ 16, 16, 5, 8 ], [ 16, 17, 4, 8 ],
[ 21, 1, 7, 16 ], [ 21, 2, 9, 8 ], [ 21, 3, 8, 8 ], [ 21, 4, 9, 8 ],
[ 21, 5, 9, 4 ], [ 21, 6, 9, 8 ], [ 21, 7, 9, 8 ], [ 22, 1, 3, 16 ],
[ 22, 1, 5, 16 ], [ 22, 1, 6, 16 ], [ 22, 2, 3, 8 ], [ 22, 2, 5, 8 ],
[ 22, 2, 6, 8 ], [ 22, 3, 2, 8 ], [ 22, 3, 4, 8 ], [ 22, 4, 3, 4 ],
[ 22, 4, 5, 8 ], [ 22, 4, 6, 4 ], [ 27, 2, 9, 16 ], [ 27, 3, 8, 16 ],
[ 27, 3, 12, 16 ], [ 27, 4, 8, 16 ], [ 27, 5, 9, 16 ], [ 27, 6, 9, 8 ],
[ 27, 7, 9, 8 ], [ 27, 8, 8, 16 ], [ 27, 8, 12, 8 ], [ 27, 9, 7, 8 ],
[ 27, 10, 6, 8 ], [ 27, 11, 8, 16 ], [ 27, 11, 12, 8 ], [ 27, 12, 8, 16 ],
[ 27, 13, 8, 8 ], [ 27, 14, 10, 16 ], [ 27, 14, 12, 8 ] ]
k = 11: F-action on Pi is (1,2) [27,1,11]
Dynkin type is A_1(q^2) + T(phi2^2 phi4)
Order of center |Z^F|: phi2^2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/32 q^3 ( q-2 )
q congruent 1 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
q congruent 2 modulo 4: 1/32 q^3 ( q-2 )
q congruent 3 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 8, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 8 ], [ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ],
[ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ],
[ 5, 1, 2, 4 ], [ 7, 1, 2, 16 ], [ 7, 2, 2, 8 ], [ 7, 3, 2, 8 ],
[ 7, 4, 2, 8 ], [ 7, 5, 2, 4 ], [ 9, 1, 4, 16 ], [ 9, 2, 4, 8 ],
[ 9, 3, 4, 8 ], [ 9, 4, 4, 8 ], [ 9, 5, 4, 4 ], [ 12, 1, 3, 8 ],
[ 12, 1, 5, 4 ], [ 12, 2, 3, 4 ], [ 12, 2, 5, 2 ], [ 12, 3, 2, 4 ],
[ 12, 4, 3, 2 ], [ 12, 4, 5, 2 ], [ 16, 1, 4, 8 ], [ 16, 1, 8, 32 ],
[ 16, 2, 4, 4 ], [ 16, 2, 8, 16 ], [ 16, 3, 4, 4 ], [ 16, 3, 8, 16 ],
[ 16, 4, 4, 4 ], [ 16, 4, 8, 16 ], [ 16, 5, 7, 16 ], [ 16, 6, 7, 16 ],
[ 16, 7, 7, 16 ], [ 16, 8, 8, 16 ], [ 16, 9, 4, 2 ], [ 16, 9, 8, 8 ],
[ 16, 10, 7, 8 ], [ 16, 11, 4, 4 ], [ 16, 11, 9, 4 ], [ 16, 11, 10, 8 ],
[ 16, 12, 7, 8 ], [ 16, 13, 4, 4 ], [ 16, 13, 8, 8 ], [ 16, 14, 6, 8 ],
[ 16, 15, 4, 4 ], [ 16, 15, 8, 8 ], [ 16, 16, 4, 4 ], [ 16, 16, 8, 8 ],
[ 16, 17, 6, 8 ], [ 21, 1, 8, 16 ], [ 21, 2, 5, 8 ], [ 21, 3, 4, 8 ],
[ 21, 4, 5, 8 ], [ 21, 5, 5, 4 ], [ 21, 6, 4, 8 ], [ 21, 7, 5, 8 ],
[ 22, 1, 10, 16 ], [ 22, 2, 10, 8 ], [ 22, 4, 10, 8 ], [ 27, 2, 20, 16 ],
[ 27, 3, 23, 16 ], [ 27, 3, 25, 16 ], [ 27, 4, 19, 16 ], [ 27, 5, 20, 16 ],
[ 27, 6, 20, 8 ], [ 27, 7, 20, 8 ], [ 27, 8, 23, 16 ], [ 27, 8, 25, 8 ],
[ 27, 9, 18, 8 ], [ 27, 10, 18, 8 ], [ 27, 11, 23, 16 ], [ 27, 11, 25, 8 ],
[ 27, 12, 19, 16 ], [ 27, 13, 19, 8 ], [ 27, 14, 23, 16 ],
[ 27, 14, 25, 8 ] ]
k = 12: F-action on Pi is () [27,1,12]
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 0 modulo 4: 1/32 q ( q^3-4*q^2+8 )
q congruent 1 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
q congruent 2 modulo 4: 1/32 q ( q^3-4*q^2+8 )
q congruent 3 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16, 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 4 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 16 ],
[ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 4 ], [ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ], [ 12, 4, 2, 4 ],
[ 15, 1, 1, 8 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ],
[ 16, 1, 3, 32 ], [ 16, 2, 3, 16 ], [ 16, 3, 3, 16 ], [ 16, 4, 3, 16 ],
[ 16, 5, 2, 16 ], [ 16, 5, 4, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 4, 16 ],
[ 16, 7, 2, 16 ], [ 16, 7, 4, 16 ], [ 16, 9, 3, 8 ], [ 16, 10, 2, 8 ],
[ 16, 10, 4, 8 ], [ 16, 11, 3, 16 ], [ 16, 12, 2, 8 ], [ 16, 12, 4, 8 ],
[ 16, 13, 3, 8 ], [ 16, 15, 3, 8 ], [ 16, 16, 3, 8 ], [ 22, 1, 2, 16 ],
[ 22, 1, 5, 16 ], [ 22, 2, 2, 8 ], [ 22, 2, 5, 8 ], [ 22, 4, 2, 8 ],
[ 22, 4, 5, 8 ], [ 27, 3, 7, 16 ], [ 27, 5, 8, 16 ], [ 27, 8, 7, 16 ],
[ 27, 9, 6, 8 ], [ 27, 9, 10, 16 ], [ 27, 11, 7, 16 ], [ 27, 14, 6, 16 ] ]
k = 13: F-action on Pi is (1,2) [27,1,13]
Dynkin type is A_1(q^2) + T(phi1 phi2 phi4)
Order of center |Z^F|: phi1 phi2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q^3 ( q-2 )
q congruent 1 modulo 4: 1/16 phi1^3 phi2
q congruent 2 modulo 4: 1/16 q^3 ( q-2 )
q congruent 3 modulo 4: 1/16 phi1^3 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 12, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 3, 8 ],
[ 9, 1, 4, 8 ], [ 9, 2, 3, 4 ], [ 9, 2, 4, 4 ], [ 9, 3, 3, 4 ],
[ 9, 3, 4, 4 ], [ 9, 4, 3, 4 ], [ 9, 4, 4, 4 ], [ 9, 5, 3, 2 ],
[ 9, 5, 4, 2 ], [ 12, 1, 2, 4 ], [ 12, 1, 5, 4 ], [ 12, 2, 2, 2 ],
[ 12, 2, 5, 2 ], [ 12, 4, 2, 2 ], [ 12, 4, 5, 2 ], [ 16, 1, 4, 8 ],
[ 16, 1, 7, 16 ], [ 16, 2, 4, 4 ], [ 16, 2, 7, 8 ], [ 16, 3, 4, 4 ],
[ 16, 3, 7, 8 ], [ 16, 4, 4, 4 ], [ 16, 4, 7, 8 ], [ 16, 5, 6, 8 ],
[ 16, 5, 8, 8 ], [ 16, 6, 6, 8 ], [ 16, 6, 8, 8 ], [ 16, 7, 6, 8 ],
[ 16, 7, 8, 8 ], [ 16, 9, 4, 2 ], [ 16, 9, 7, 4 ], [ 16, 10, 6, 4 ],
[ 16, 10, 8, 4 ], [ 16, 11, 4, 4 ], [ 16, 11, 8, 8 ], [ 16, 11, 9, 4 ],
[ 16, 12, 6, 4 ], [ 16, 12, 8, 4 ], [ 16, 13, 4, 4 ], [ 16, 13, 7, 4 ],
[ 16, 15, 4, 4 ], [ 16, 15, 7, 4 ], [ 16, 16, 4, 4 ], [ 16, 16, 7, 4 ],
[ 22, 1, 8, 8 ], [ 22, 1, 10, 8 ], [ 22, 2, 8, 4 ], [ 22, 2, 10, 4 ],
[ 22, 4, 8, 4 ], [ 22, 4, 10, 4 ], [ 27, 3, 20, 8 ], [ 27, 3, 22, 8 ],
[ 27, 5, 19, 8 ], [ 27, 8, 20, 8 ], [ 27, 8, 22, 8 ], [ 27, 9, 17, 4 ],
[ 27, 9, 20, 8 ], [ 27, 11, 20, 8 ], [ 27, 11, 22, 8 ], [ 27, 14, 19, 8 ],
[ 27, 14, 20, 8 ] ]
k = 14: F-action on Pi is () [27,1,14]
Dynkin type is A_1(q) + A_1(q) + T(phi4^2)
Order of center |Z^F|: phi4^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/32 q^2 ( q^2-4 )
q congruent 1 modulo 4: 1/32 phi1 phi2 ( q^2-5 )
q congruent 2 modulo 4: 1/32 q^2 ( q^2-4 )
q congruent 3 modulo 4: 1/32 phi1 phi2 ( q^2-5 )
Fusion of maximal tori of C^F in those of G^F:
[ 11, 17, 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 12, 1, 5, 8 ], [ 12, 2, 5, 4 ], [ 12, 4, 5, 4 ],
[ 15, 1, 5, 16 ], [ 16, 1, 4, 16 ], [ 16, 2, 4, 8 ], [ 16, 3, 4, 8 ],
[ 16, 4, 4, 8 ], [ 16, 9, 4, 4 ], [ 16, 11, 4, 8 ], [ 16, 11, 9, 8 ],
[ 16, 13, 4, 8 ], [ 16, 15, 4, 8 ], [ 16, 16, 4, 8 ], [ 27, 3, 10, 16 ],
[ 27, 5, 10, 16 ], [ 27, 8, 10, 16 ], [ 27, 9, 8, 8 ], [ 27, 9, 11, 16 ],
[ 27, 11, 10, 16 ], [ 27, 14, 7, 16 ] ]
k = 15: F-action on Pi is () [27,1,15]
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 0 modulo 4: 1/12 q phi1 phi2 ( q-2 )
q congruent 1 modulo 4: 1/12 q phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 1/12 q phi1 phi2 ( q-2 )
q congruent 3 modulo 4: 1/12 q phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 18, 22, 22, 20 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ],
[ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ],
[ 8, 1, 1, 4 ], [ 14, 1, 1, 4 ], [ 14, 2, 1, 2 ], [ 21, 1, 9, 6 ],
[ 21, 4, 4, 3 ], [ 21, 7, 4, 6 ], [ 27, 2, 4, 6 ], [ 27, 4, 6, 6 ],
[ 27, 5, 4, 6 ], [ 27, 7, 4, 3 ], [ 27, 12, 6, 12 ] ]
k = 16: F-action on Pi is (1,2) [27,1,16]
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 0 modulo 4: 1/12 q phi1 phi2 ( q-2 )
q congruent 1 modulo 4: 1/12 q phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 1/12 q phi1 phi2 ( q-2 )
q congruent 3 modulo 4: 1/12 q phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 19, 23 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 3, 4 ],
[ 7, 2, 3, 2 ], [ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 3, 1 ],
[ 14, 1, 4, 4 ], [ 14, 2, 4, 2 ], [ 21, 1, 10, 6 ], [ 21, 4, 8, 3 ],
[ 21, 7, 8, 6 ], [ 27, 2, 13, 6 ], [ 27, 4, 17, 6 ], [ 27, 5, 14, 6 ],
[ 27, 7, 13, 3 ], [ 27, 12, 17, 12 ] ]
k = 17: F-action on Pi is (1,2) [27,1,17]
Dynkin type is A_1(q^2) + T(phi1 phi2 phi3)
Order of center |Z^F|: phi1 phi2 phi3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/12 q^2 phi1 phi2
q congruent 1 modulo 4: 1/12 q phi1^2 phi2
q congruent 2 modulo 4: 1/12 q^2 phi1 phi2
q congruent 3 modulo 4: 1/12 q phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 20, 25 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 2, 4 ],
[ 7, 2, 2, 2 ], [ 7, 3, 2, 2 ], [ 7, 4, 2, 2 ], [ 7, 5, 2, 1 ],
[ 14, 1, 3, 4 ], [ 14, 2, 3, 2 ], [ 21, 1, 9, 6 ], [ 21, 4, 4, 3 ],
[ 21, 7, 4, 6 ], [ 27, 2, 19, 6 ], [ 27, 4, 16, 6 ], [ 27, 5, 18, 6 ],
[ 27, 7, 19, 3 ], [ 27, 12, 16, 12 ] ]
k = 18: F-action on Pi is () [27,1,18]
Dynkin type is A_1(q) + A_1(q) + T(phi2^2 phi6)
Order of center |Z^F|: phi2^2 phi6
Numbers of classes in class type:
q congruent 0 modulo 4: 1/12 q^2 phi1 phi2
q congruent 1 modulo 4: 1/12 q phi1^2 phi2
q congruent 2 modulo 4: 1/12 q^2 phi1 phi2
q congruent 3 modulo 4: 1/12 q phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 19, 24, 24, 21 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 4, 4 ],
[ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 4, 1 ],
[ 8, 1, 2, 4 ], [ 14, 1, 2, 4 ], [ 14, 2, 2, 2 ], [ 21, 1, 10, 6 ],
[ 21, 4, 8, 3 ], [ 21, 7, 8, 6 ], [ 27, 2, 8, 6 ], [ 27, 4, 7, 6 ],
[ 27, 5, 7, 6 ], [ 27, 7, 8, 3 ], [ 27, 12, 7, 12 ] ]
k = 19: F-action on Pi is () [27,1,19]
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 0 modulo 4: 1/8 q^2 ( q^2-2 )
q congruent 1 modulo 4: 1/8 phi1^2 phi2^2
q congruent 2 modulo 4: 1/8 q^2 ( q^2-2 )
q congruent 3 modulo 4: 1/8 phi1^2 phi2^2
Fusion of maximal tori of C^F in those of G^F:
[ 28, 32, 31, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 27, 5, 6, 4 ],
[ 27, 9, 9, 4 ] ]
k = 20: F-action on Pi is (1,2) [27,1,20]
Dynkin type is A_1(q^2) + T(phi8)
Order of center |Z^F|: phi8
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^4
q congruent 1 modulo 4: 1/8 phi1 phi2 phi4
q congruent 2 modulo 4: 1/8 q^4
q congruent 3 modulo 4: 1/8 phi1 phi2 phi4
Fusion of maximal tori of C^F in those of G^F:
[ 29, 33 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 27, 5, 17, 4 ],
[ 27, 9, 19, 4 ] ]
j = 2: Omega of order 2, action on Pi: <(1,2)>
k = 1: F-action on Pi is () [27,2,1]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^4)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/48 ( q^3-15*q^2+71*q-105 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/48 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 2 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 7 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 8 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 4 ],
[ 4, 1, 1, 6 ], [ 4, 2, 1, 4 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 8 ],
[ 7, 1, 1, 12 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 12 ], [ 7, 4, 1, 24 ],
[ 7, 5, 1, 16 ], [ 9, 2, 1, 24 ], [ 9, 5, 1, 12 ], [ 12, 1, 1, 24 ],
[ 12, 2, 1, 12 ], [ 12, 3, 1, 18 ], [ 12, 4, 1, 12 ], [ 13, 1, 1, 24 ],
[ 13, 2, 1, 24 ], [ 14, 2, 1, 8 ], [ 16, 4, 1, 48 ], [ 16, 8, 1, 12 ],
[ 16, 9, 1, 24 ], [ 16, 11, 1, 12 ], [ 16, 12, 1, 24 ], [ 16, 13, 1, 24 ],
[ 16, 14, 1, 36 ], [ 16, 17, 1, 12 ], [ 21, 1, 1, 48 ], [ 21, 2, 1, 48 ],
[ 21, 3, 1, 24 ], [ 21, 4, 1, 24 ], [ 21, 5, 1, 24 ], [ 21, 6, 1, 36 ],
[ 21, 7, 1, 12 ], [ 22, 3, 1, 24 ], [ 22, 4, 1, 24 ], [ 27, 6, 1, 24 ],
[ 27, 7, 1, 24 ], [ 27, 8, 1, 48 ], [ 27, 10, 1, 24 ], [ 27, 13, 1, 24 ] ]
k = 2: F-action on Pi is () [27,2,2]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 7, 2, 1, 4 ], [ 7, 3, 1, 4 ],
[ 7, 4, 1, 4 ], [ 7, 5, 1, 4 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 4 ],
[ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 3, 1, 2 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ], [ 13, 1, 1, 4 ],
[ 13, 1, 2, 4 ], [ 13, 2, 1, 4 ], [ 13, 2, 2, 4 ], [ 14, 2, 1, 4 ],
[ 16, 4, 3, 8 ], [ 16, 8, 1, 4 ], [ 16, 9, 3, 4 ], [ 16, 11, 1, 4 ],
[ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ], [ 16, 14, 1, 4 ],
[ 16, 17, 1, 4 ], [ 21, 1, 5, 8 ], [ 21, 2, 2, 8 ], [ 21, 3, 3, 4 ],
[ 21, 4, 2, 4 ], [ 21, 5, 2, 4 ], [ 21, 6, 3, 4 ], [ 21, 7, 2, 4 ],
[ 22, 3, 1, 4 ], [ 22, 3, 3, 4 ], [ 22, 4, 1, 4 ], [ 22, 4, 4, 4 ],
[ 27, 6, 2, 4 ], [ 27, 7, 2, 4 ], [ 27, 8, 2, 8 ], [ 27, 10, 5, 4 ],
[ 27, 13, 3, 4 ] ]
k = 3: F-action on Pi is () [27,2,3]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 4 ],
[ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ],
[ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ],
[ 5, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 8 ], [ 7, 2, 1, 4 ],
[ 7, 2, 2, 4 ], [ 7, 3, 1, 4 ], [ 7, 3, 2, 4 ], [ 7, 3, 3, 4 ],
[ 7, 4, 1, 4 ], [ 7, 4, 2, 8 ], [ 7, 4, 3, 4 ], [ 7, 4, 4, 8 ],
[ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ],
[ 9, 2, 2, 8 ], [ 9, 5, 2, 4 ], [ 12, 1, 3, 8 ], [ 12, 1, 4, 8 ],
[ 12, 2, 3, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 1, 2 ], [ 12, 3, 2, 4 ],
[ 12, 3, 3, 8 ], [ 12, 3, 4, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 4 ], [ 13, 1, 2, 8 ], [ 13, 2, 2, 8 ], [ 16, 4, 2, 8 ],
[ 16, 4, 5, 16 ], [ 16, 8, 1, 4 ], [ 16, 8, 7, 8 ], [ 16, 9, 2, 4 ],
[ 16, 9, 5, 8 ], [ 16, 11, 1, 4 ], [ 16, 11, 7, 4 ], [ 16, 12, 3, 8 ],
[ 16, 13, 2, 8 ], [ 16, 13, 5, 8 ], [ 16, 14, 1, 4 ], [ 16, 14, 2, 8 ],
[ 16, 14, 3, 4 ], [ 16, 14, 4, 8 ], [ 16, 17, 1, 4 ], [ 16, 17, 3, 4 ],
[ 21, 1, 3, 16 ], [ 21, 2, 3, 16 ], [ 21, 2, 4, 8 ], [ 21, 2, 6, 8 ],
[ 21, 3, 2, 8 ], [ 21, 3, 5, 8 ], [ 21, 4, 3, 8 ], [ 21, 5, 3, 8 ],
[ 21, 5, 4, 4 ], [ 21, 5, 6, 4 ], [ 21, 6, 2, 8 ], [ 21, 6, 5, 4 ],
[ 21, 6, 6, 4 ], [ 21, 6, 7, 8 ], [ 21, 7, 3, 4 ], [ 22, 3, 3, 8 ],
[ 22, 4, 4, 8 ], [ 27, 6, 3, 8 ], [ 27, 6, 4, 8 ], [ 27, 7, 3, 8 ],
[ 27, 8, 3, 16 ], [ 27, 8, 4, 8 ], [ 27, 10, 3, 8 ], [ 27, 10, 9, 8 ],
[ 27, 13, 2, 8 ], [ 27, 13, 5, 8 ] ]
k = 4: F-action on Pi is () [27,2,4]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi3)).2
Order of center |Z^F|: phi1 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 18, 22, 22, 20 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ],
[ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 4, 2, 1, 1 ],
[ 6, 1, 1, 2 ], [ 7, 2, 1, 2 ], [ 7, 5, 1, 1 ], [ 14, 2, 1, 2 ],
[ 21, 1, 9, 6 ], [ 21, 4, 4, 3 ], [ 21, 7, 4, 6 ], [ 27, 7, 4, 3 ] ]
k = 5: F-action on Pi is () [27,2,5]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2 phi4)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 2, 2 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 7, 1, 2, 4 ], [ 7, 2, 1, 2 ],
[ 7, 2, 2, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ], [ 7, 4, 2, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 1 ], [ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 3, 3, 2 ],
[ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ], [ 16, 4, 4, 4 ], [ 16, 8, 7, 4 ],
[ 16, 9, 4, 2 ], [ 16, 11, 7, 2 ], [ 16, 13, 4, 4 ], [ 16, 14, 2, 2 ],
[ 16, 17, 3, 2 ], [ 21, 1, 8, 8 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 4 ],
[ 21, 3, 4, 4 ], [ 21, 4, 5, 4 ], [ 21, 5, 5, 2 ], [ 21, 5, 7, 2 ],
[ 21, 6, 4, 4 ], [ 21, 7, 5, 4 ], [ 27, 6, 5, 4 ], [ 27, 7, 5, 4 ],
[ 27, 8, 5, 4 ], [ 27, 10, 7, 4 ], [ 27, 13, 4, 4 ] ]
k = 6: F-action on Pi is () [27,2,6]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 4 ],
[ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ],
[ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ],
[ 5, 1, 1, 4 ], [ 7, 1, 3, 8 ], [ 7, 1, 4, 4 ], [ 7, 2, 3, 4 ],
[ 7, 2, 4, 4 ], [ 7, 3, 2, 4 ], [ 7, 3, 3, 4 ], [ 7, 3, 4, 4 ],
[ 7, 4, 1, 8 ], [ 7, 4, 2, 4 ], [ 7, 4, 3, 8 ], [ 7, 4, 4, 4 ],
[ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ],
[ 9, 2, 1, 8 ], [ 9, 5, 1, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 4, 8 ],
[ 12, 2, 1, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 1, 4 ], [ 12, 3, 2, 2 ],
[ 12, 3, 3, 4 ], [ 12, 3, 4, 8 ], [ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 4 ], [ 13, 1, 3, 8 ], [ 13, 2, 3, 8 ], [ 16, 4, 1, 16 ],
[ 16, 4, 2, 8 ], [ 16, 8, 4, 4 ], [ 16, 8, 6, 8 ], [ 16, 9, 1, 8 ],
[ 16, 9, 2, 4 ], [ 16, 11, 5, 4 ], [ 16, 11, 7, 4 ], [ 16, 12, 1, 8 ],
[ 16, 13, 1, 8 ], [ 16, 13, 2, 8 ], [ 16, 14, 1, 8 ], [ 16, 14, 2, 4 ],
[ 16, 14, 3, 8 ], [ 16, 14, 4, 4 ], [ 16, 17, 2, 4 ], [ 16, 17, 4, 4 ],
[ 21, 1, 2, 16 ], [ 21, 2, 4, 8 ], [ 21, 2, 6, 8 ], [ 21, 2, 8, 16 ],
[ 21, 3, 6, 8 ], [ 21, 3, 7, 8 ], [ 21, 4, 6, 8 ], [ 21, 5, 4, 4 ],
[ 21, 5, 6, 4 ], [ 21, 5, 8, 8 ], [ 21, 6, 2, 4 ], [ 21, 6, 5, 8 ],
[ 21, 6, 6, 8 ], [ 21, 6, 7, 4 ], [ 21, 7, 6, 4 ], [ 22, 3, 2, 8 ],
[ 22, 4, 3, 8 ], [ 27, 6, 6, 8 ], [ 27, 6, 8, 8 ], [ 27, 7, 6, 8 ],
[ 27, 8, 4, 8 ], [ 27, 8, 11, 16 ], [ 27, 10, 2, 8 ], [ 27, 10, 4, 8 ],
[ 27, 13, 6, 8 ], [ 27, 13, 7, 8 ] ]
k = 7: F-action on Pi is () [27,2,7]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2 phi4)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12, 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 7, 1, 3, 4 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ], [ 7, 4, 1, 2 ],
[ 7, 4, 3, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 1 ], [ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 3, 4, 2 ],
[ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ], [ 16, 4, 4, 4 ], [ 16, 8, 6, 4 ],
[ 16, 9, 4, 2 ], [ 16, 11, 7, 2 ], [ 16, 13, 4, 4 ], [ 16, 14, 3, 2 ],
[ 16, 17, 2, 2 ], [ 21, 1, 6, 8 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 4 ],
[ 21, 3, 9, 4 ], [ 21, 4, 7, 4 ], [ 21, 5, 5, 2 ], [ 21, 5, 7, 2 ],
[ 21, 6, 8, 4 ], [ 21, 7, 7, 4 ], [ 27, 6, 7, 4 ], [ 27, 7, 7, 4 ],
[ 27, 8, 5, 4 ], [ 27, 10, 8, 4 ], [ 27, 13, 9, 4 ] ]
k = 8: F-action on Pi is () [27,2,8]
Dynkin type is (A_1(q) + A_1(q) + T(phi2^2 phi6)).2
Order of center |Z^F|: phi2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 19, 24, 24, 21 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ],
[ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 4, 2, 2, 1 ],
[ 6, 1, 2, 2 ], [ 7, 2, 4, 2 ], [ 7, 5, 4, 1 ], [ 14, 2, 2, 2 ],
[ 21, 1, 10, 6 ], [ 21, 4, 8, 3 ], [ 21, 7, 8, 6 ], [ 27, 7, 8, 3 ] ]
k = 9: F-action on Pi is () [27,2,9]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^3
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1^3
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 2, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 4, 4 ], [ 7, 3, 4, 4 ],
[ 7, 4, 4, 4 ], [ 7, 5, 4, 4 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 4 ],
[ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 3, 2, 2 ], [ 12, 4, 2, 2 ], [ 12, 4, 3, 2 ], [ 13, 1, 3, 4 ],
[ 13, 1, 4, 4 ], [ 13, 2, 3, 4 ], [ 13, 2, 4, 4 ], [ 14, 2, 2, 4 ],
[ 16, 4, 3, 8 ], [ 16, 8, 4, 4 ], [ 16, 9, 3, 4 ], [ 16, 11, 5, 4 ],
[ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ], [ 16, 14, 4, 4 ],
[ 16, 17, 4, 4 ], [ 21, 1, 7, 8 ], [ 21, 2, 9, 8 ], [ 21, 3, 8, 4 ],
[ 21, 4, 9, 4 ], [ 21, 5, 9, 4 ], [ 21, 6, 9, 4 ], [ 21, 7, 9, 4 ],
[ 22, 3, 2, 4 ], [ 22, 3, 4, 4 ], [ 22, 4, 3, 4 ], [ 22, 4, 6, 4 ],
[ 27, 6, 9, 4 ], [ 27, 7, 9, 4 ], [ 27, 8, 12, 8 ], [ 27, 10, 6, 4 ],
[ 27, 13, 8, 4 ] ]
k = 10: F-action on Pi is () [27,2,10]
Dynkin type is (A_1(q) + A_1(q) + T(phi2^4)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/48 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/48 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 7 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 8 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 4 ],
[ 4, 1, 2, 6 ], [ 4, 2, 2, 4 ], [ 5, 1, 2, 12 ], [ 6, 1, 2, 8 ],
[ 7, 1, 4, 12 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 12 ], [ 7, 4, 4, 24 ],
[ 7, 5, 4, 16 ], [ 9, 2, 2, 24 ], [ 9, 5, 2, 12 ], [ 12, 1, 3, 24 ],
[ 12, 2, 3, 12 ], [ 12, 3, 2, 18 ], [ 12, 4, 3, 12 ], [ 13, 1, 4, 24 ],
[ 13, 2, 4, 24 ], [ 14, 2, 2, 8 ], [ 16, 4, 5, 48 ], [ 16, 8, 4, 12 ],
[ 16, 9, 5, 24 ], [ 16, 11, 5, 12 ], [ 16, 12, 3, 24 ], [ 16, 13, 5, 24 ],
[ 16, 14, 4, 36 ], [ 16, 17, 4, 12 ], [ 21, 1, 4, 48 ], [ 21, 2, 10, 48 ],
[ 21, 3, 10, 24 ], [ 21, 4, 10, 24 ], [ 21, 5, 10, 24 ], [ 21, 6, 10, 36 ],
[ 21, 7, 10, 12 ], [ 22, 3, 4, 24 ], [ 22, 4, 6, 24 ], [ 27, 6, 10, 24 ],
[ 27, 7, 10, 24 ], [ 27, 8, 13, 48 ], [ 27, 10, 10, 24 ],
[ 27, 13, 10, 24 ] ]
k = 11: F-action on Pi is (1,2) [27,2,11]
Dynkin type is (A_1(q^2) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 6 ],
[ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 3 ],
[ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 4, 2, 1, 3 ], [ 4, 2, 2, 1 ],
[ 5, 1, 1, 4 ], [ 7, 1, 3, 8 ], [ 7, 1, 4, 4 ], [ 7, 2, 3, 6 ],
[ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 3, 8 ], [ 7, 3, 4, 2 ],
[ 7, 4, 1, 4 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 12 ], [ 7, 4, 4, 6 ],
[ 7, 5, 1, 3 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 9 ], [ 7, 5, 4, 3 ],
[ 9, 2, 3, 8 ], [ 9, 5, 3, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 4, 8 ],
[ 12, 2, 1, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 1, 8 ], [ 12, 3, 3, 6 ],
[ 12, 3, 4, 4 ], [ 12, 4, 1, 6 ], [ 12, 4, 4, 3 ], [ 13, 1, 3, 8 ],
[ 13, 2, 1, 4 ], [ 13, 2, 3, 4 ], [ 16, 4, 2, 8 ], [ 16, 4, 6, 16 ],
[ 16, 8, 3, 4 ], [ 16, 8, 5, 8 ], [ 16, 9, 2, 4 ], [ 16, 9, 6, 8 ],
[ 16, 11, 2, 2 ], [ 16, 11, 6, 8 ], [ 16, 12, 5, 8 ], [ 16, 13, 2, 8 ],
[ 16, 13, 6, 8 ], [ 16, 14, 2, 6 ], [ 16, 14, 3, 4 ], [ 16, 14, 5, 16 ],
[ 16, 17, 2, 2 ], [ 16, 17, 5, 8 ], [ 21, 1, 2, 16 ], [ 21, 2, 1, 8 ],
[ 21, 2, 6, 16 ], [ 21, 2, 8, 8 ], [ 21, 3, 6, 8 ], [ 21, 3, 7, 8 ],
[ 21, 4, 6, 8 ], [ 21, 5, 1, 4 ], [ 21, 5, 6, 8 ], [ 21, 5, 8, 4 ],
[ 21, 6, 1, 8 ], [ 21, 6, 6, 8 ], [ 21, 6, 7, 12 ], [ 21, 7, 6, 4 ],
[ 22, 3, 6, 8 ], [ 22, 4, 7, 4 ], [ 27, 6, 11, 8 ], [ 27, 6, 13, 8 ],
[ 27, 7, 11, 8 ], [ 27, 8, 14, 16 ], [ 27, 8, 16, 8 ], [ 27, 10, 11, 8 ],
[ 27, 10, 13, 8 ], [ 27, 13, 11, 8 ], [ 27, 13, 12, 8 ] ]
k = 12: F-action on Pi is (1,2) [27,2,12]
Dynkin type is (A_1(q^2) + T(phi1^2 phi4)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 6, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 2, 4 ], [ 3, 2, 2, 4 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ],
[ 3, 5, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 2, 1, 2 ], [ 7, 1, 3, 4 ],
[ 7, 2, 3, 4 ], [ 7, 3, 3, 4 ], [ 7, 4, 3, 4 ], [ 7, 5, 3, 4 ],
[ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 3, 1, 2 ], [ 12, 4, 1, 2 ],
[ 12, 4, 5, 2 ], [ 16, 4, 4, 4 ], [ 16, 8, 5, 4 ], [ 16, 9, 4, 2 ],
[ 16, 11, 6, 4 ], [ 16, 13, 4, 4 ], [ 16, 14, 5, 4 ], [ 16, 17, 5, 4 ],
[ 21, 1, 6, 8 ], [ 21, 2, 7, 8 ], [ 21, 3, 9, 4 ], [ 21, 4, 7, 4 ],
[ 21, 5, 7, 4 ], [ 21, 6, 8, 4 ], [ 21, 7, 7, 4 ], [ 27, 6, 12, 4 ],
[ 27, 7, 12, 4 ], [ 27, 8, 15, 8 ], [ 27, 10, 17, 4 ], [ 27, 13, 14, 4 ] ]
k = 13: F-action on Pi is (1,2) [27,2,13]
Dynkin type is (A_1(q^2) + T(phi1 phi2 phi6)).2
Order of center |Z^F|: phi2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 19, 23 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 2, 1 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ],
[ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 4, 2, 1, 1 ],
[ 6, 1, 2, 2 ], [ 7, 2, 3, 2 ], [ 7, 5, 3, 1 ], [ 14, 2, 4, 2 ],
[ 21, 1, 10, 6 ], [ 21, 4, 8, 3 ], [ 21, 7, 8, 6 ], [ 27, 7, 13, 3 ] ]
k = 14: F-action on Pi is (1,2) [27,2,14]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^3
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1^3
Fusion of maximal tori of C^F in those of G^F:
[ 7, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 2, 2 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 2, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 3, 2 ], [ 7, 2, 4, 2 ],
[ 7, 3, 1, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 2, 2 ], [ 7, 4, 4, 2 ],
[ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ],
[ 9, 2, 3, 4 ], [ 9, 2, 4, 4 ], [ 9, 5, 3, 2 ], [ 9, 5, 4, 2 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 3, 3, 2 ], [ 12, 4, 2, 2 ],
[ 12, 4, 4, 1 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 4 ], [ 13, 2, 1, 2 ],
[ 13, 2, 2, 2 ], [ 13, 2, 3, 2 ], [ 13, 2, 4, 2 ], [ 14, 2, 4, 4 ],
[ 16, 4, 7, 8 ], [ 16, 8, 3, 4 ], [ 16, 9, 7, 4 ], [ 16, 11, 2, 2 ],
[ 16, 12, 6, 4 ], [ 16, 12, 8, 4 ], [ 16, 13, 7, 4 ], [ 16, 14, 2, 2 ],
[ 16, 17, 2, 2 ], [ 21, 1, 7, 8 ], [ 21, 2, 2, 4 ], [ 21, 2, 9, 4 ],
[ 21, 3, 8, 4 ], [ 21, 4, 9, 4 ], [ 21, 5, 2, 2 ], [ 21, 5, 9, 2 ],
[ 21, 6, 9, 4 ], [ 21, 7, 9, 4 ], [ 22, 3, 6, 4 ], [ 22, 3, 8, 4 ],
[ 22, 4, 7, 2 ], [ 22, 4, 9, 2 ], [ 27, 6, 14, 4 ], [ 27, 7, 14, 4 ],
[ 27, 8, 17, 4 ], [ 27, 10, 15, 4 ], [ 27, 13, 13, 4 ] ]
k = 15: F-action on Pi is (1,2) [27,2,15]
Dynkin type is (A_1(q^2) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/48 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/48 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 2, 2, 2, 4 ],
[ 3, 1, 2, 4 ], [ 3, 2, 1, 6 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 3 ], [ 3, 5, 2, 1 ], [ 4, 1, 2, 6 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 3 ], [ 5, 1, 2, 12 ], [ 6, 1, 2, 8 ],
[ 7, 1, 4, 12 ], [ 7, 2, 3, 2 ], [ 7, 2, 4, 6 ], [ 7, 3, 1, 6 ],
[ 7, 3, 4, 6 ], [ 7, 4, 2, 18 ], [ 7, 4, 4, 6 ], [ 7, 5, 1, 3 ],
[ 7, 5, 2, 9 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 3 ], [ 9, 2, 4, 24 ],
[ 9, 5, 4, 12 ], [ 12, 1, 3, 24 ], [ 12, 2, 3, 12 ], [ 12, 3, 2, 12 ],
[ 12, 3, 3, 6 ], [ 12, 4, 3, 6 ], [ 12, 4, 4, 3 ], [ 13, 1, 4, 24 ],
[ 13, 2, 2, 12 ], [ 13, 2, 4, 12 ], [ 14, 2, 4, 8 ], [ 16, 4, 8, 48 ],
[ 16, 8, 3, 12 ], [ 16, 9, 8, 24 ], [ 16, 11, 2, 6 ], [ 16, 12, 7, 24 ],
[ 16, 13, 8, 24 ], [ 16, 14, 2, 6 ], [ 16, 14, 6, 24 ], [ 16, 17, 2, 6 ],
[ 21, 1, 4, 48 ], [ 21, 2, 3, 24 ], [ 21, 2, 10, 24 ], [ 21, 3, 10, 24 ],
[ 21, 4, 10, 24 ], [ 21, 5, 3, 12 ], [ 21, 5, 10, 12 ], [ 21, 6, 2, 12 ],
[ 21, 6, 10, 12 ], [ 21, 7, 10, 12 ], [ 22, 3, 8, 24 ], [ 22, 4, 9, 12 ],
[ 27, 6, 15, 24 ], [ 27, 7, 15, 24 ], [ 27, 8, 18, 24 ], [ 27, 10, 19, 24 ],
[ 27, 13, 15, 24 ] ]
k = 16: F-action on Pi is (1,2) [27,2,16]
Dynkin type is (A_1(q^2) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/48 ( q^3-15*q^2+71*q-105 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/48 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 2, 2, 2, 4 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 6 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 3 ], [ 4, 1, 1, 6 ],
[ 4, 2, 1, 3 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 8 ],
[ 7, 1, 1, 12 ], [ 7, 2, 1, 6 ], [ 7, 2, 2, 2 ], [ 7, 3, 1, 6 ],
[ 7, 3, 4, 6 ], [ 7, 4, 1, 6 ], [ 7, 4, 3, 18 ], [ 7, 5, 1, 3 ],
[ 7, 5, 2, 1 ], [ 7, 5, 3, 9 ], [ 7, 5, 4, 3 ], [ 9, 2, 3, 24 ],
[ 9, 5, 3, 12 ], [ 12, 1, 1, 24 ], [ 12, 2, 1, 12 ], [ 12, 3, 1, 12 ],
[ 12, 3, 4, 6 ], [ 12, 4, 1, 6 ], [ 12, 4, 4, 3 ], [ 13, 1, 1, 24 ],
[ 13, 2, 1, 12 ], [ 13, 2, 3, 12 ], [ 14, 2, 3, 8 ], [ 16, 4, 6, 48 ],
[ 16, 8, 2, 12 ], [ 16, 9, 6, 24 ], [ 16, 11, 2, 6 ], [ 16, 12, 5, 24 ],
[ 16, 13, 6, 24 ], [ 16, 14, 3, 6 ], [ 16, 14, 5, 24 ], [ 16, 17, 3, 6 ],
[ 21, 1, 1, 48 ], [ 21, 2, 1, 24 ], [ 21, 2, 8, 24 ], [ 21, 3, 1, 24 ],
[ 21, 4, 1, 24 ], [ 21, 5, 1, 12 ], [ 21, 5, 8, 12 ], [ 21, 6, 1, 12 ],
[ 21, 6, 6, 12 ], [ 21, 7, 1, 12 ], [ 22, 3, 5, 24 ], [ 22, 4, 7, 12 ],
[ 27, 6, 16, 24 ], [ 27, 7, 16, 24 ], [ 27, 8, 16, 24 ], [ 27, 10, 12, 24 ],
[ 27, 13, 16, 24 ] ]
k = 17: F-action on Pi is (1,2) [27,2,17]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 2 ],
[ 7, 3, 1, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ], [ 7, 4, 3, 2 ],
[ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ],
[ 9, 2, 3, 4 ], [ 9, 2, 4, 4 ], [ 9, 5, 3, 2 ], [ 9, 5, 4, 2 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 2, 2 ],
[ 12, 4, 4, 1 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 4 ], [ 13, 2, 1, 2 ],
[ 13, 2, 2, 2 ], [ 13, 2, 3, 2 ], [ 13, 2, 4, 2 ], [ 14, 2, 3, 4 ],
[ 16, 4, 7, 8 ], [ 16, 8, 2, 4 ], [ 16, 9, 7, 4 ], [ 16, 11, 2, 2 ],
[ 16, 12, 6, 4 ], [ 16, 12, 8, 4 ], [ 16, 13, 7, 4 ], [ 16, 14, 3, 2 ],
[ 16, 17, 3, 2 ], [ 21, 1, 5, 8 ], [ 21, 2, 2, 4 ], [ 21, 2, 9, 4 ],
[ 21, 3, 3, 4 ], [ 21, 4, 2, 4 ], [ 21, 5, 2, 2 ], [ 21, 5, 9, 2 ],
[ 21, 6, 3, 4 ], [ 21, 7, 2, 4 ], [ 22, 3, 5, 4 ], [ 22, 3, 7, 4 ],
[ 22, 4, 7, 2 ], [ 22, 4, 9, 2 ], [ 27, 6, 17, 4 ], [ 27, 7, 17, 4 ],
[ 27, 8, 17, 4 ], [ 27, 10, 16, 4 ], [ 27, 13, 18, 4 ] ]
k = 18: F-action on Pi is (1,2) [27,2,18]
Dynkin type is (A_1(q^2) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 6 ], [ 3, 2, 2, 2 ],
[ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 3 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 3 ],
[ 5, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 8 ], [ 7, 2, 1, 2 ],
[ 7, 2, 2, 6 ], [ 7, 3, 1, 2 ], [ 7, 3, 2, 8 ], [ 7, 3, 4, 2 ],
[ 7, 4, 1, 6 ], [ 7, 4, 2, 12 ], [ 7, 4, 3, 2 ], [ 7, 4, 4, 4 ],
[ 7, 5, 1, 3 ], [ 7, 5, 2, 9 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 3 ],
[ 9, 2, 4, 8 ], [ 9, 5, 4, 4 ], [ 12, 1, 3, 8 ], [ 12, 1, 4, 8 ],
[ 12, 2, 3, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 2, 8 ], [ 12, 3, 3, 4 ],
[ 12, 3, 4, 6 ], [ 12, 4, 3, 6 ], [ 12, 4, 4, 3 ], [ 13, 1, 2, 8 ],
[ 13, 2, 2, 4 ], [ 13, 2, 4, 4 ], [ 16, 4, 2, 8 ], [ 16, 4, 8, 16 ],
[ 16, 8, 2, 4 ], [ 16, 8, 8, 8 ], [ 16, 9, 2, 4 ], [ 16, 9, 8, 8 ],
[ 16, 11, 2, 2 ], [ 16, 11, 10, 8 ], [ 16, 12, 7, 8 ], [ 16, 13, 2, 8 ],
[ 16, 13, 8, 8 ], [ 16, 14, 2, 4 ], [ 16, 14, 3, 6 ], [ 16, 14, 6, 16 ],
[ 16, 17, 3, 2 ], [ 16, 17, 6, 8 ], [ 21, 1, 3, 16 ], [ 21, 2, 3, 8 ],
[ 21, 2, 4, 16 ], [ 21, 2, 10, 8 ], [ 21, 3, 2, 8 ], [ 21, 3, 5, 8 ],
[ 21, 4, 3, 8 ], [ 21, 5, 3, 4 ], [ 21, 5, 4, 8 ], [ 21, 5, 10, 4 ],
[ 21, 6, 2, 8 ], [ 21, 6, 5, 12 ], [ 21, 6, 10, 8 ], [ 21, 7, 3, 4 ],
[ 22, 3, 7, 8 ], [ 22, 4, 9, 4 ], [ 27, 6, 18, 8 ], [ 27, 6, 19, 8 ],
[ 27, 7, 18, 8 ], [ 27, 8, 18, 8 ], [ 27, 8, 24, 16 ], [ 27, 10, 14, 8 ],
[ 27, 10, 20, 8 ], [ 27, 13, 17, 8 ], [ 27, 13, 20, 8 ] ]
k = 19: F-action on Pi is (1,2) [27,2,19]
Dynkin type is (A_1(q^2) + T(phi1 phi2 phi3)).2
Order of center |Z^F|: phi1 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 20, 25 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ],
[ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 4, 2, 2, 1 ],
[ 6, 1, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 5, 2, 1 ], [ 14, 2, 3, 2 ],
[ 21, 1, 9, 6 ], [ 21, 4, 4, 3 ], [ 21, 7, 4, 6 ], [ 27, 7, 19, 3 ] ]
k = 20: F-action on Pi is (1,2) [27,2,20]
Dynkin type is (A_1(q^2) + T(phi2^2 phi4)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 8, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 4 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ],
[ 3, 5, 1, 2 ], [ 4, 1, 2, 2 ], [ 4, 2, 2, 2 ], [ 7, 1, 2, 4 ],
[ 7, 2, 2, 4 ], [ 7, 3, 2, 4 ], [ 7, 4, 2, 4 ], [ 7, 5, 2, 4 ],
[ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 3, 2, 2 ], [ 12, 4, 3, 2 ],
[ 12, 4, 5, 2 ], [ 16, 4, 4, 4 ], [ 16, 8, 8, 4 ], [ 16, 9, 4, 2 ],
[ 16, 11, 10, 4 ], [ 16, 13, 4, 4 ], [ 16, 14, 6, 4 ], [ 16, 17, 6, 4 ],
[ 21, 1, 8, 8 ], [ 21, 2, 5, 8 ], [ 21, 3, 4, 4 ], [ 21, 4, 5, 4 ],
[ 21, 5, 5, 4 ], [ 21, 6, 4, 4 ], [ 21, 7, 5, 4 ], [ 27, 6, 20, 4 ],
[ 27, 7, 20, 4 ], [ 27, 8, 25, 8 ], [ 27, 10, 18, 4 ], [ 27, 13, 19, 4 ] ]
i = 28: Pi = [ 1, 3 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [28,1,1]
Dynkin type is A_2(q) + T(phi1^4)
Order of center |Z^F|: phi1^4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/48 ( q^4-17*q^3+104*q^2-268*q+240 )
q congruent 1 modulo 4: 1/48 ( q^4-17*q^3+101*q^2-247*q+210 )
q congruent 2 modulo 4: 1/48 ( q^4-17*q^3+104*q^2-268*q+240 )
q congruent 3 modulo 4: 1/48 ( q^4-17*q^3+101*q^2-247*q+210 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 18 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 6 ], [ 4, 2, 1, 3 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 10 ],
[ 7, 1, 1, 12 ], [ 7, 2, 1, 6 ], [ 7, 3, 1, 6 ], [ 7, 4, 1, 6 ],
[ 7, 5, 1, 3 ], [ 8, 1, 1, 12 ], [ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ],
[ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ], [ 12, 1, 1, 24 ], [ 12, 2, 1, 12 ],
[ 12, 3, 1, 12 ], [ 12, 4, 1, 6 ], [ 13, 1, 1, 24 ], [ 13, 2, 1, 12 ],
[ 14, 1, 1, 12 ], [ 14, 2, 1, 6 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ],
[ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 19, 1, 1, 16 ], [ 19, 2, 1, 8 ],
[ 19, 3, 1, 8 ], [ 19, 4, 1, 8 ], [ 19, 5, 1, 4 ], [ 20, 1, 1, 24 ],
[ 20, 2, 1, 12 ], [ 21, 1, 1, 48 ], [ 21, 2, 1, 24 ], [ 21, 3, 1, 24 ],
[ 21, 4, 1, 24 ], [ 21, 5, 1, 12 ], [ 21, 6, 1, 12 ], [ 21, 7, 1, 12 ],
[ 23, 1, 1, 48 ], [ 23, 2, 1, 24 ], [ 23, 3, 1, 24 ], [ 23, 4, 1, 24 ],
[ 23, 5, 1, 24 ], [ 23, 6, 1, 12 ], [ 24, 1, 1, 24 ], [ 24, 2, 1, 12 ],
[ 28, 2, 1, 24 ], [ 28, 3, 1, 24 ], [ 28, 4, 1, 24 ], [ 28, 5, 1, 12 ],
[ 28, 6, 1, 12 ] ]
k = 2: F-action on Pi is () [28,1,2]
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 0 modulo 4: 1/8 q ( q^3-7*q^2+16*q-12 )
q congruent 1 modulo 4: 1/8 q phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 1/8 q ( q^3-7*q^2+16*q-12 )
q congruent 3 modulo 4: 1/8 q phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 22 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 6 ], [ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ],
[ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 4 ],
[ 10, 2, 1, 2 ], [ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 12, 1, 2, 4 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 4 ],
[ 13, 2, 1, 2 ], [ 13, 2, 2, 2 ], [ 14, 1, 1, 4 ], [ 14, 2, 1, 2 ],
[ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 4 ],
[ 18, 2, 1, 2 ], [ 18, 2, 2, 2 ], [ 19, 1, 1, 8 ], [ 19, 2, 1, 4 ],
[ 19, 3, 1, 4 ], [ 19, 4, 1, 4 ], [ 19, 5, 1, 2 ], [ 20, 1, 1, 4 ],
[ 20, 1, 2, 4 ], [ 20, 2, 1, 2 ], [ 20, 2, 2, 2 ], [ 21, 1, 5, 8 ],
[ 21, 2, 2, 4 ], [ 21, 3, 3, 4 ], [ 21, 4, 2, 4 ], [ 21, 5, 2, 2 ],
[ 21, 6, 3, 4 ], [ 21, 7, 2, 4 ], [ 23, 1, 2, 8 ], [ 23, 1, 4, 8 ],
[ 23, 2, 2, 4 ], [ 23, 2, 4, 4 ], [ 23, 3, 2, 4 ], [ 23, 3, 4, 4 ],
[ 23, 4, 2, 4 ], [ 23, 4, 4, 4 ], [ 23, 5, 2, 4 ], [ 23, 5, 4, 4 ],
[ 23, 6, 2, 2 ], [ 23, 6, 4, 2 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 4 ],
[ 24, 2, 1, 2 ], [ 24, 2, 2, 2 ], [ 28, 2, 2, 4 ], [ 28, 3, 2, 4 ],
[ 28, 4, 2, 4 ], [ 28, 4, 4, 4 ], [ 28, 5, 2, 2 ], [ 28, 6, 2, 4 ] ]
k = 3: F-action on Pi is () [28,1,3]
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 0 modulo 4: 1/16 q ( q^3-5*q^2+4*q+4 )
q congruent 1 modulo 4: 1/16 phi1 ( q^3-4*q^2-3*q+18 )
q congruent 2 modulo 4: 1/16 q ( q^3-5*q^2+4*q+4 )
q congruent 3 modulo 4: 1/16 phi1 ( q^3-4*q^2-3*q+18 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 20 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 1, 2 ],
[ 7, 1, 1, 4 ], [ 7, 1, 2, 8 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 4 ],
[ 7, 3, 1, 2 ], [ 7, 3, 2, 4 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 4 ],
[ 7, 5, 1, 1 ], [ 7, 5, 2, 2 ], [ 8, 1, 1, 4 ], [ 12, 1, 3, 8 ],
[ 12, 1, 4, 8 ], [ 12, 2, 3, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 2, 4 ],
[ 12, 3, 3, 4 ], [ 12, 3, 4, 4 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 2 ],
[ 13, 1, 2, 8 ], [ 13, 2, 2, 4 ], [ 14, 1, 1, 4 ], [ 14, 1, 3, 8 ],
[ 14, 2, 1, 2 ], [ 14, 2, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ],
[ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ], [ 21, 1, 3, 16 ], [ 21, 2, 3, 8 ],
[ 21, 2, 4, 8 ], [ 21, 3, 2, 8 ], [ 21, 3, 5, 8 ], [ 21, 4, 3, 8 ],
[ 21, 5, 3, 4 ], [ 21, 5, 4, 4 ], [ 21, 6, 2, 4 ], [ 21, 6, 5, 4 ],
[ 21, 7, 3, 4 ], [ 23, 1, 3, 16 ], [ 23, 2, 3, 8 ], [ 23, 3, 3, 8 ],
[ 23, 4, 3, 8 ], [ 23, 5, 3, 8 ], [ 23, 6, 3, 4 ], [ 24, 1, 2, 8 ],
[ 24, 2, 2, 4 ], [ 28, 2, 3, 8 ], [ 28, 2, 4, 8 ], [ 28, 3, 3, 8 ],
[ 28, 4, 3, 8 ], [ 28, 5, 3, 4 ], [ 28, 5, 4, 8 ], [ 28, 6, 3, 4 ] ]
k = 4: F-action on Pi is () [28,1,4]
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 0 modulo 4: 1/6 q phi1 phi2 ( q-2 )
q congruent 1 modulo 4: 1/6 q phi1 phi2 ( q-2 )
q congruent 2 modulo 4: 1/6 q phi1 phi2 ( q-2 )
q congruent 3 modulo 4: 1/6 q phi1 phi2 ( q-2 )
Fusion of maximal tori of C^F in those of G^F:
[ 18, 22, 26 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 6, 1, 1, 4 ], [ 10, 1, 1, 2 ],
[ 10, 2, 1, 1 ], [ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 19, 1, 1, 4 ],
[ 19, 2, 1, 2 ], [ 19, 3, 1, 2 ], [ 19, 4, 1, 2 ], [ 19, 5, 1, 1 ],
[ 21, 1, 9, 6 ], [ 21, 4, 4, 3 ], [ 21, 7, 4, 6 ], [ 28, 3, 4, 3 ],
[ 28, 6, 4, 6 ] ]
k = 5: F-action on Pi is () [28,1,5]
Dynkin type is A_2(q) + T(phi1 phi2 phi4)
Order of center |Z^F|: phi1 phi2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 phi2 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 phi2^2 ( q-2 )
q congruent 2 modulo 4: 1/8 q^2 phi2 ( q-2 )
q congruent 3 modulo 4: 1/8 phi1 phi2^2 ( q-2 )
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12, 25 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 2, 4 ],
[ 7, 2, 2, 2 ], [ 7, 3, 2, 2 ], [ 7, 4, 2, 2 ], [ 7, 5, 2, 1 ],
[ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 14, 1, 3, 4 ],
[ 14, 2, 3, 2 ], [ 21, 1, 8, 8 ], [ 21, 2, 5, 4 ], [ 21, 3, 4, 4 ],
[ 21, 4, 5, 4 ], [ 21, 5, 5, 2 ], [ 21, 6, 4, 4 ], [ 21, 7, 5, 4 ],
[ 28, 2, 5, 4 ], [ 28, 3, 5, 4 ], [ 28, 5, 5, 4 ], [ 28, 6, 5, 4 ] ]
k = 6: F-action on Pi is (1,3) [28,1,6]
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 0 modulo 4: 1/16 q^2 ( q^2-5*q+6 )
q congruent 1 modulo 4: 1/16 phi1 ( q^3-4*q^2-q+12 )
q congruent 2 modulo 4: 1/16 q^2 ( q^2-5*q+6 )
q congruent 3 modulo 4: 1/16 phi1 ( q^3-4*q^2-q+12 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 19 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 4 ], [ 6, 1, 2, 2 ],
[ 7, 1, 3, 8 ], [ 7, 1, 4, 4 ], [ 7, 2, 3, 4 ], [ 7, 2, 4, 2 ],
[ 7, 3, 3, 4 ], [ 7, 3, 4, 2 ], [ 7, 4, 3, 4 ], [ 7, 4, 4, 2 ],
[ 7, 5, 3, 2 ], [ 7, 5, 4, 1 ], [ 8, 1, 2, 4 ], [ 12, 1, 1, 8 ],
[ 12, 1, 4, 8 ], [ 12, 2, 1, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 1, 4 ],
[ 12, 3, 3, 4 ], [ 12, 3, 4, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 4, 2 ],
[ 13, 1, 3, 8 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 4 ], [ 14, 1, 4, 8 ],
[ 14, 2, 2, 2 ], [ 14, 2, 4, 4 ], [ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ],
[ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 21, 1, 2, 16 ], [ 21, 2, 6, 8 ],
[ 21, 2, 8, 8 ], [ 21, 3, 6, 8 ], [ 21, 3, 7, 8 ], [ 21, 4, 6, 8 ],
[ 21, 5, 6, 4 ], [ 21, 5, 8, 4 ], [ 21, 6, 6, 4 ], [ 21, 6, 7, 4 ],
[ 21, 7, 6, 4 ], [ 23, 1, 5, 16 ], [ 23, 2, 5, 8 ], [ 23, 3, 5, 8 ],
[ 23, 4, 5, 8 ], [ 23, 5, 5, 8 ], [ 23, 6, 5, 4 ], [ 24, 1, 3, 8 ],
[ 24, 2, 3, 4 ], [ 28, 2, 6, 8 ], [ 28, 2, 8, 8 ], [ 28, 3, 6, 8 ],
[ 28, 4, 5, 8 ], [ 28, 5, 6, 8 ], [ 28, 5, 8, 4 ], [ 28, 6, 6, 4 ] ]
k = 7: F-action on Pi is (1,3) [28,1,7]
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 0 modulo 4: 1/8 q^3 phi1
q congruent 1 modulo 4: 1/8 q phi1^2 phi2
q congruent 2 modulo 4: 1/8 q^3 phi1
q congruent 3 modulo 4: 1/8 q phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 8, 12, 23 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 3, 4 ],
[ 7, 2, 3, 2 ], [ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 3, 1 ],
[ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 14, 1, 4, 4 ],
[ 14, 2, 4, 2 ], [ 21, 1, 6, 8 ], [ 21, 2, 7, 4 ], [ 21, 3, 9, 4 ],
[ 21, 4, 7, 4 ], [ 21, 5, 7, 2 ], [ 21, 6, 8, 4 ], [ 21, 7, 7, 4 ],
[ 28, 2, 7, 4 ], [ 28, 3, 7, 4 ], [ 28, 5, 7, 4 ], [ 28, 6, 7, 4 ] ]
k = 8: F-action on Pi is (1,3) [28,1,8]
Dynkin type is ^2A_2(q) + T(phi2^2 phi6)
Order of center |Z^F|: phi2^2 phi6
Numbers of classes in class type:
q congruent 0 modulo 4: 1/6 q^2 phi1 phi2
q congruent 1 modulo 4: 1/6 q^2 phi1 phi2
q congruent 2 modulo 4: 1/6 q^2 phi1 phi2
q congruent 3 modulo 4: 1/6 q^2 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 21, 24, 27 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 6, 1, 2, 4 ], [ 10, 1, 2, 2 ],
[ 10, 2, 2, 1 ], [ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 19, 1, 2, 4 ],
[ 19, 2, 2, 2 ], [ 19, 3, 2, 2 ], [ 19, 4, 2, 2 ], [ 19, 5, 2, 1 ],
[ 21, 1, 10, 6 ], [ 21, 4, 8, 3 ], [ 21, 7, 8, 6 ], [ 28, 3, 8, 3 ],
[ 28, 6, 8, 6 ] ]
k = 9: F-action on Pi is (1,3) [28,1,9]
Dynkin type is ^2A_2(q) + T(phi1 phi2^3)
Order of center |Z^F|: phi1 phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/8 q^2 phi1 ( q-2 )
q congruent 1 modulo 4: 1/8 phi1 ( q^3-2*q^2-q-2 )
q congruent 2 modulo 4: 1/8 q^2 phi1 ( q-2 )
q congruent 3 modulo 4: 1/8 phi1 ( q^3-2*q^2-q-2 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 24 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 2, 6 ], [ 7, 1, 4, 4 ], [ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 4, 1 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 4 ],
[ 10, 2, 2, 2 ], [ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 12, 1, 2, 4 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 4 ],
[ 13, 2, 3, 2 ], [ 13, 2, 4, 2 ], [ 14, 1, 2, 4 ], [ 14, 2, 2, 2 ],
[ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 4 ],
[ 18, 2, 3, 2 ], [ 18, 2, 4, 2 ], [ 19, 1, 2, 8 ], [ 19, 2, 2, 4 ],
[ 19, 3, 2, 4 ], [ 19, 4, 2, 4 ], [ 19, 5, 2, 2 ], [ 20, 1, 3, 4 ],
[ 20, 1, 4, 4 ], [ 20, 2, 3, 2 ], [ 20, 2, 4, 2 ], [ 21, 1, 7, 8 ],
[ 21, 2, 9, 4 ], [ 21, 3, 8, 4 ], [ 21, 4, 9, 4 ], [ 21, 5, 9, 2 ],
[ 21, 6, 9, 4 ], [ 21, 7, 9, 4 ], [ 23, 1, 6, 8 ], [ 23, 1, 8, 8 ],
[ 23, 2, 6, 4 ], [ 23, 2, 8, 4 ], [ 23, 3, 6, 4 ], [ 23, 3, 8, 4 ],
[ 23, 4, 6, 4 ], [ 23, 4, 8, 4 ], [ 23, 5, 6, 4 ], [ 23, 5, 8, 4 ],
[ 23, 6, 6, 2 ], [ 23, 6, 8, 2 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 4 ],
[ 24, 2, 3, 2 ], [ 24, 2, 4, 2 ], [ 28, 2, 9, 4 ], [ 28, 3, 9, 4 ],
[ 28, 4, 6, 4 ], [ 28, 4, 8, 4 ], [ 28, 5, 9, 2 ], [ 28, 6, 9, 4 ] ]
k = 10: F-action on Pi is (1,3) [28,1,10]
Dynkin type is ^2A_2(q) + T(phi2^4)
Order of center |Z^F|: phi2^4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/48 q ( q^3-9*q^2+26*q-24 )
q congruent 1 modulo 4: 1/48 q phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/48 q ( q^3-9*q^2+26*q-24 )
q congruent 3 modulo 4: 1/48 q phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 21 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 6 ], [ 4, 2, 2, 3 ], [ 5, 1, 2, 12 ], [ 6, 1, 2, 10 ],
[ 7, 1, 4, 12 ], [ 7, 2, 4, 6 ], [ 7, 3, 4, 6 ], [ 7, 4, 4, 6 ],
[ 7, 5, 4, 3 ], [ 8, 1, 2, 12 ], [ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ],
[ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ], [ 12, 1, 3, 24 ], [ 12, 2, 3, 12 ],
[ 12, 3, 2, 12 ], [ 12, 4, 3, 6 ], [ 13, 1, 4, 24 ], [ 13, 2, 4, 12 ],
[ 14, 1, 2, 12 ], [ 14, 2, 2, 6 ], [ 17, 1, 2, 24 ], [ 17, 2, 2, 12 ],
[ 18, 1, 4, 24 ], [ 18, 2, 4, 12 ], [ 19, 1, 2, 16 ], [ 19, 2, 2, 8 ],
[ 19, 3, 2, 8 ], [ 19, 4, 2, 8 ], [ 19, 5, 2, 4 ], [ 20, 1, 4, 24 ],
[ 20, 2, 4, 12 ], [ 21, 1, 4, 48 ], [ 21, 2, 10, 24 ], [ 21, 3, 10, 24 ],
[ 21, 4, 10, 24 ], [ 21, 5, 10, 12 ], [ 21, 6, 10, 12 ], [ 21, 7, 10, 12 ],
[ 23, 1, 7, 48 ], [ 23, 2, 7, 24 ], [ 23, 3, 7, 24 ], [ 23, 4, 7, 24 ],
[ 23, 5, 7, 24 ], [ 23, 6, 7, 12 ], [ 24, 1, 4, 24 ], [ 24, 2, 4, 12 ],
[ 28, 2, 10, 24 ], [ 28, 3, 10, 24 ], [ 28, 4, 7, 24 ], [ 28, 5, 10, 12 ],
[ 28, 6, 10, 12 ] ]
j = 2: Omega of order 2, action on Pi: <()>
k = 1: F-action on Pi is () [28,2,1]
Dynkin type is (A_2(q) + T(phi1^4)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 18 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 3 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ],
[ 7, 2, 1, 6 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ], [ 7, 5, 1, 3 ],
[ 8, 1, 1, 4 ], [ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 6 ],
[ 14, 1, 1, 4 ], [ 14, 2, 1, 6 ], [ 21, 3, 1, 8 ], [ 21, 5, 1, 4 ],
[ 21, 6, 1, 4 ], [ 21, 7, 1, 12 ], [ 23, 2, 1, 8 ], [ 23, 6, 1, 4 ],
[ 28, 5, 1, 4 ], [ 28, 6, 1, 12 ] ]
k = 2: F-action on Pi is () [28,2,2]
Dynkin type is (A_2(q) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 22 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ],
[ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ],
[ 8, 1, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 14, 1, 1, 4 ],
[ 14, 2, 1, 2 ], [ 21, 3, 3, 4 ], [ 21, 5, 2, 2 ], [ 21, 6, 3, 4 ],
[ 21, 7, 2, 4 ], [ 23, 2, 2, 4 ], [ 23, 2, 4, 4 ], [ 23, 6, 2, 2 ],
[ 23, 6, 4, 2 ], [ 28, 5, 2, 2 ], [ 28, 6, 2, 4 ] ]
k = 3: F-action on Pi is () [28,2,3]
Dynkin type is (A_2(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 20 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ],
[ 3, 5, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 2 ],
[ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 4 ],
[ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 2 ],
[ 8, 1, 1, 4 ], [ 12, 2, 3, 4 ], [ 12, 3, 4, 4 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 2 ], [ 14, 1, 1, 4 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 4 ],
[ 21, 3, 5, 8 ], [ 21, 5, 3, 4 ], [ 21, 6, 5, 4 ], [ 21, 7, 3, 4 ],
[ 23, 2, 3, 8 ], [ 23, 6, 3, 4 ], [ 28, 5, 3, 4 ], [ 28, 6, 3, 4 ] ]
k = 4: F-action on Pi is () [28,2,4]
Dynkin type is (A_2(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 20 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ],
[ 3, 5, 1, 1 ], [ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 2 ],
[ 6, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 4 ],
[ 7, 3, 2, 2 ], [ 7, 4, 2, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 2 ],
[ 12, 2, 4, 2 ], [ 12, 3, 2, 2 ], [ 12, 3, 3, 2 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 2 ], [ 14, 1, 3, 4 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 4 ],
[ 21, 3, 2, 4 ], [ 21, 5, 4, 2 ], [ 21, 6, 2, 2 ], [ 21, 7, 3, 4 ],
[ 28, 5, 4, 4 ], [ 28, 6, 3, 4 ] ]
k = 5: F-action on Pi is () [28,2,5]
Dynkin type is (A_2(q) + T(phi1 phi2 phi4)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12, 25 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 2, 4 ],
[ 7, 2, 2, 2 ], [ 7, 3, 2, 2 ], [ 7, 4, 2, 2 ], [ 7, 5, 2, 1 ],
[ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 14, 1, 3, 4 ], [ 14, 2, 3, 2 ],
[ 21, 3, 4, 4 ], [ 21, 5, 5, 2 ], [ 21, 6, 4, 4 ], [ 21, 7, 5, 4 ],
[ 28, 5, 5, 4 ], [ 28, 6, 5, 4 ] ]
k = 6: F-action on Pi is (1,3) [28,2,6]
Dynkin type is (^2A_2(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 19 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ],
[ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 1 ],
[ 6, 1, 2, 2 ], [ 7, 1, 3, 4 ], [ 7, 2, 3, 4 ], [ 7, 2, 4, 2 ],
[ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 3, 2 ], [ 7, 5, 4, 1 ],
[ 12, 2, 4, 2 ], [ 12, 3, 1, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 1, 2 ],
[ 12, 4, 4, 2 ], [ 14, 1, 4, 4 ], [ 14, 2, 2, 2 ], [ 14, 2, 4, 4 ],
[ 21, 3, 7, 4 ], [ 21, 5, 6, 2 ], [ 21, 6, 6, 2 ], [ 21, 7, 6, 4 ],
[ 28, 5, 6, 4 ], [ 28, 6, 6, 4 ] ]
k = 7: F-action on Pi is (1,3) [28,2,7]
Dynkin type is (^2A_2(q) + T(phi1 phi2 phi4)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 8, 12, 23 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 3, 4 ],
[ 7, 2, 3, 2 ], [ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 3, 1 ],
[ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 14, 1, 4, 4 ], [ 14, 2, 4, 2 ],
[ 21, 3, 9, 4 ], [ 21, 5, 7, 2 ], [ 21, 6, 8, 4 ], [ 21, 7, 7, 4 ],
[ 28, 5, 7, 4 ], [ 28, 6, 7, 4 ] ]
k = 8: F-action on Pi is (1,3) [28,2,8]
Dynkin type is (^2A_2(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 7, 19 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ],
[ 3, 5, 2, 1 ], [ 4, 1, 2, 2 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 1 ],
[ 6, 1, 2, 2 ], [ 7, 1, 4, 4 ], [ 7, 2, 3, 4 ], [ 7, 2, 4, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 3, 2 ], [ 7, 5, 4, 1 ],
[ 8, 1, 2, 4 ], [ 12, 2, 1, 4 ], [ 12, 3, 3, 4 ], [ 12, 4, 1, 2 ],
[ 12, 4, 4, 2 ], [ 14, 1, 2, 4 ], [ 14, 2, 2, 2 ], [ 14, 2, 4, 4 ],
[ 21, 3, 6, 8 ], [ 21, 5, 8, 4 ], [ 21, 6, 7, 4 ], [ 21, 7, 6, 4 ],
[ 23, 2, 5, 8 ], [ 23, 6, 5, 4 ], [ 28, 5, 8, 4 ], [ 28, 6, 6, 4 ] ]
k = 9: F-action on Pi is (1,3) [28,2,9]
Dynkin type is (^2A_2(q) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 9, 13, 24 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 4, 4 ],
[ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 4, 1 ],
[ 8, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 14, 1, 2, 4 ],
[ 14, 2, 2, 2 ], [ 21, 3, 8, 4 ], [ 21, 5, 9, 2 ], [ 21, 6, 9, 4 ],
[ 21, 7, 9, 4 ], [ 23, 2, 6, 4 ], [ 23, 2, 8, 4 ], [ 23, 6, 6, 2 ],
[ 23, 6, 8, 2 ], [ 28, 5, 9, 2 ], [ 28, 6, 9, 4 ] ]
k = 10: F-action on Pi is (1,3) [28,2,10]
Dynkin type is (^2A_2(q) + T(phi2^4)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 4, 9, 21 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 3 ], [ 6, 1, 2, 2 ], [ 7, 1, 4, 4 ],
[ 7, 2, 4, 6 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 4, 3 ],
[ 8, 1, 2, 4 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 6 ],
[ 14, 1, 2, 4 ], [ 14, 2, 2, 6 ], [ 21, 3, 10, 8 ], [ 21, 5, 10, 4 ],
[ 21, 6, 10, 4 ], [ 21, 7, 10, 12 ], [ 23, 2, 7, 8 ], [ 23, 6, 7, 4 ],
[ 28, 5, 10, 4 ], [ 28, 6, 10, 12 ] ]
i = 29: Pi = [ 1, 4 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [29,1,1]
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 0 modulo 4: 1/32 ( q^4-18*q^3+116*q^2-312*q+288 )
q congruent 1 modulo 4: 1/32 ( q^4-18*q^3+112*q^2-278*q+215 )
q congruent 2 modulo 4: 1/32 ( q^4-18*q^3+116*q^2-312*q+288 )
q congruent 3 modulo 4: 1/32 ( q^4-18*q^3+112*q^2-278*q+231 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 16 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ], [ 7, 4, 1, 8 ],
[ 7, 5, 1, 4 ], [ 8, 1, 1, 20 ], [ 9, 1, 1, 32 ], [ 9, 2, 1, 16 ],
[ 9, 3, 1, 16 ], [ 9, 4, 1, 16 ], [ 9, 5, 1, 8 ], [ 10, 1, 1, 8 ],
[ 10, 2, 1, 4 ], [ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 13, 1, 1, 16 ],
[ 13, 2, 1, 8 ], [ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 40 ],
[ 16, 1, 1, 32 ], [ 16, 2, 1, 16 ], [ 16, 3, 1, 16 ], [ 16, 4, 1, 16 ],
[ 16, 5, 1, 16 ], [ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ], [ 16, 8, 1, 16 ],
[ 16, 9, 1, 8 ], [ 16, 10, 1, 8 ], [ 16, 11, 1, 8 ], [ 16, 12, 1, 8 ],
[ 16, 13, 1, 8 ], [ 16, 14, 1, 8 ], [ 16, 15, 1, 8 ], [ 16, 16, 1, 8 ],
[ 16, 17, 1, 8 ], [ 17, 1, 1, 16 ], [ 17, 2, 1, 8 ], [ 18, 1, 1, 24 ],
[ 18, 2, 1, 12 ], [ 19, 1, 1, 32 ], [ 19, 2, 1, 16 ], [ 19, 3, 1, 16 ],
[ 19, 4, 1, 16 ], [ 19, 5, 1, 8 ], [ 20, 1, 1, 24 ], [ 20, 2, 1, 12 ],
[ 22, 1, 1, 32 ], [ 22, 2, 1, 16 ], [ 22, 3, 1, 16 ], [ 22, 4, 1, 8 ],
[ 23, 1, 1, 16 ], [ 23, 2, 1, 8 ], [ 23, 3, 1, 8 ], [ 23, 4, 1, 8 ],
[ 23, 5, 1, 8 ], [ 23, 6, 1, 4 ], [ 24, 1, 1, 32 ], [ 24, 2, 1, 16 ],
[ 25, 1, 1, 48 ], [ 25, 2, 1, 24 ], [ 25, 3, 1, 24 ], [ 26, 1, 1, 48 ],
[ 26, 2, 1, 24 ], [ 26, 3, 1, 24 ], [ 29, 2, 1, 16 ], [ 29, 3, 1, 16 ],
[ 29, 4, 1, 16 ], [ 29, 5, 1, 16 ], [ 29, 6, 1, 16 ], [ 29, 7, 1, 16 ],
[ 29, 8, 1, 16 ], [ 29, 9, 1, 8 ], [ 29, 10, 1, 8 ], [ 29, 11, 1, 8 ],
[ 29, 12, 1, 8 ], [ 29, 13, 1, 8 ] ]
k = 2: F-action on Pi is () [29,1,2]
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 0 modulo 4: 1/32 q ( q^3-8*q^2+20*q-16 )
q congruent 1 modulo 4: 1/32 phi1 ( q^3-7*q^2+9*q+13 )
q congruent 2 modulo 4: 1/32 q ( q^3-8*q^2+20*q-16 )
q congruent 3 modulo 4: 1/32 phi2 ( q^3-9*q^2+25*q-21 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 12 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 12 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 12 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 2 ],
[ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 1, 24 ], [ 15, 1, 4, 8 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ],
[ 16, 11, 3, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ],
[ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ], [ 22, 1, 2, 16 ], [ 22, 2, 2, 8 ],
[ 22, 4, 2, 8 ], [ 23, 1, 2, 16 ], [ 23, 2, 2, 8 ], [ 23, 3, 2, 8 ],
[ 23, 4, 2, 8 ], [ 23, 5, 2, 8 ], [ 23, 6, 2, 4 ], [ 25, 1, 1, 48 ],
[ 25, 2, 1, 24 ], [ 25, 3, 1, 24 ], [ 26, 1, 2, 16 ], [ 26, 2, 2, 8 ],
[ 26, 3, 5, 8 ], [ 29, 2, 2, 16 ], [ 29, 3, 2, 16 ], [ 29, 4, 2, 16 ],
[ 29, 5, 2, 16 ], [ 29, 6, 2, 16 ], [ 29, 7, 2, 16 ], [ 29, 8, 2, 16 ],
[ 29, 9, 2, 8 ], [ 29, 10, 2, 8 ], [ 29, 11, 2, 8 ], [ 29, 12, 2, 8 ],
[ 29, 13, 2, 8 ] ]
k = 3: F-action on Pi is () [29,1,3]
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 0 modulo 4: 1/32 q^2 ( q^2-6*q+8 )
q congruent 1 modulo 4: 1/32 phi1 ( q^3-5*q^2-q+21 )
q congruent 2 modulo 4: 1/32 q^2 ( q^2-6*q+8 )
q congruent 3 modulo 4: 1/32 phi1 ( q^3-5*q^2-q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 4 ],
[ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 4, 8 ],
[ 7, 5, 4, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ],
[ 12, 1, 3, 8 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ],
[ 13, 1, 3, 16 ], [ 13, 2, 3, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 16 ],
[ 16, 1, 5, 32 ], [ 16, 2, 5, 16 ], [ 16, 3, 5, 16 ], [ 16, 4, 5, 16 ],
[ 16, 5, 3, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ], [ 16, 8, 4, 16 ],
[ 16, 9, 5, 8 ], [ 16, 10, 3, 8 ], [ 16, 11, 5, 8 ], [ 16, 12, 3, 8 ],
[ 16, 13, 5, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 5, 8 ], [ 16, 16, 5, 8 ],
[ 16, 17, 4, 8 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 20, 1, 2, 8 ],
[ 20, 2, 2, 4 ], [ 22, 1, 3, 32 ], [ 22, 2, 3, 16 ], [ 22, 3, 2, 16 ],
[ 22, 4, 3, 8 ], [ 23, 1, 3, 16 ], [ 23, 2, 3, 8 ], [ 23, 3, 3, 8 ],
[ 23, 4, 3, 8 ], [ 23, 5, 3, 8 ], [ 23, 6, 3, 4 ], [ 25, 1, 2, 16 ],
[ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ], [ 26, 1, 2, 16 ], [ 26, 2, 2, 8 ],
[ 26, 3, 5, 8 ], [ 29, 2, 3, 16 ], [ 29, 3, 3, 16 ], [ 29, 4, 3, 16 ],
[ 29, 5, 3, 16 ], [ 29, 6, 3, 16 ], [ 29, 7, 3, 16 ], [ 29, 8, 3, 16 ],
[ 29, 9, 3, 8 ], [ 29, 10, 3, 8 ], [ 29, 11, 3, 8 ], [ 29, 12, 3, 8 ],
[ 29, 13, 3, 8 ] ]
k = 4: F-action on Pi is () [29,1,4]
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 0 modulo 4: 1/32 q ( q^3-8*q^2+20*q-16 )
q congruent 1 modulo 4: 1/32 phi1 ( q^3-7*q^2+9*q+13 )
q congruent 2 modulo 4: 1/32 q ( q^3-8*q^2+20*q-16 )
q congruent 3 modulo 4: 1/32 phi2 ( q^3-9*q^2+25*q-21 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 12 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 12 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 12 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 2 ],
[ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 1, 24 ], [ 15, 1, 4, 8 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ],
[ 16, 11, 3, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ],
[ 20, 1, 1, 24 ], [ 20, 2, 1, 12 ], [ 22, 1, 2, 16 ], [ 22, 2, 2, 8 ],
[ 22, 4, 2, 8 ], [ 23, 1, 4, 16 ], [ 23, 2, 4, 8 ], [ 23, 3, 4, 8 ],
[ 23, 4, 4, 8 ], [ 23, 5, 4, 8 ], [ 23, 6, 4, 4 ], [ 25, 1, 2, 16 ],
[ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ], [ 26, 1, 1, 48 ], [ 26, 2, 1, 24 ],
[ 26, 3, 1, 24 ], [ 29, 2, 4, 16 ], [ 29, 3, 4, 16 ], [ 29, 4, 4, 16 ],
[ 29, 5, 4, 16 ], [ 29, 6, 4, 16 ], [ 29, 7, 4, 16 ], [ 29, 8, 4, 16 ],
[ 29, 9, 4, 8 ], [ 29, 10, 4, 8 ], [ 29, 11, 4, 8 ], [ 29, 12, 4, 8 ],
[ 29, 13, 4, 8 ] ]
k = 5: F-action on Pi is () [29,1,5]
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 0 modulo 4: 1/16 q ( q^3-10*q^2+32*q-32 )
q congruent 1 modulo 4: 1/16 phi1^2 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/16 q ( q^3-10*q^2+32*q-32 )
q congruent 3 modulo 4: 1/16 phi1^2 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 6 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ],
[ 7, 4, 1, 8 ], [ 7, 5, 1, 4 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 24 ],
[ 9, 1, 2, 8 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 12 ],
[ 9, 3, 2, 4 ], [ 9, 4, 1, 12 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 6 ],
[ 9, 5, 2, 2 ], [ 12, 1, 1, 8 ], [ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ],
[ 12, 4, 1, 2 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 2, 1, 4 ],
[ 13, 2, 2, 4 ], [ 14, 1, 1, 16 ], [ 14, 2, 1, 8 ], [ 15, 1, 1, 16 ],
[ 15, 1, 4, 12 ], [ 16, 1, 1, 32 ], [ 16, 2, 1, 16 ], [ 16, 3, 1, 16 ],
[ 16, 4, 1, 16 ], [ 16, 5, 1, 16 ], [ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ],
[ 16, 8, 1, 16 ], [ 16, 9, 1, 8 ], [ 16, 10, 1, 8 ], [ 16, 11, 1, 8 ],
[ 16, 12, 1, 8 ], [ 16, 13, 1, 8 ], [ 16, 14, 1, 8 ], [ 16, 15, 1, 8 ],
[ 16, 16, 1, 8 ], [ 16, 17, 1, 8 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ],
[ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ], [ 22, 1, 1, 16 ], [ 22, 1, 4, 16 ],
[ 22, 2, 1, 8 ], [ 22, 2, 4, 8 ], [ 22, 3, 1, 8 ], [ 22, 3, 3, 8 ],
[ 22, 4, 1, 4 ], [ 22, 4, 4, 4 ], [ 24, 1, 2, 16 ], [ 24, 2, 2, 8 ],
[ 25, 1, 2, 16 ], [ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ], [ 26, 1, 2, 16 ],
[ 26, 2, 2, 8 ], [ 26, 3, 5, 8 ], [ 29, 2, 5, 8 ], [ 29, 3, 5, 8 ],
[ 29, 4, 5, 8 ], [ 29, 5, 5, 8 ], [ 29, 9, 5, 4 ] ]
k = 6: F-action on Pi is () [29,1,6]
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 0 modulo 4: 1/16 q^2 ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/16 phi1 phi4 ( q-3 )
q congruent 2 modulo 4: 1/16 q^2 ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/16 phi1 phi4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 4 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 16 ],
[ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ],
[ 15, 1, 1, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 12 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ],
[ 16, 11, 3, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ],
[ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 22, 1, 2, 8 ], [ 22, 1, 5, 8 ],
[ 22, 2, 2, 4 ], [ 22, 2, 5, 4 ], [ 22, 4, 2, 4 ], [ 22, 4, 5, 4 ],
[ 25, 1, 2, 16 ], [ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ], [ 26, 1, 3, 16 ],
[ 26, 2, 5, 8 ], [ 26, 3, 3, 8 ], [ 29, 2, 6, 8 ], [ 29, 3, 6, 8 ],
[ 29, 4, 6, 8 ], [ 29, 5, 6, 8 ], [ 29, 9, 6, 4 ] ]
k = 7: F-action on Pi is () [29,1,7]
Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2^3)
Order of center |Z^F|: phi1 phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q ( q^3-6*q^2+12*q-8 )
q congruent 1 modulo 4: 1/16 phi1^3 ( q-3 )
q congruent 2 modulo 4: 1/16 q ( q^3-6*q^2+12*q-8 )
q congruent 3 modulo 4: 1/16 phi1^3 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 6 ],
[ 6, 1, 2, 8 ], [ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ],
[ 7, 4, 4, 8 ], [ 7, 5, 4, 4 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 8 ],
[ 9, 1, 2, 24 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 12 ], [ 9, 3, 1, 4 ],
[ 9, 3, 2, 12 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 6 ], [ 12, 1, 3, 8 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ],
[ 12, 4, 3, 2 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], [ 13, 2, 3, 4 ],
[ 13, 2, 4, 4 ], [ 14, 1, 2, 16 ], [ 14, 2, 2, 8 ], [ 15, 1, 3, 16 ],
[ 15, 1, 4, 12 ], [ 16, 1, 5, 32 ], [ 16, 2, 5, 16 ], [ 16, 3, 5, 16 ],
[ 16, 4, 5, 16 ], [ 16, 5, 3, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ],
[ 16, 8, 4, 16 ], [ 16, 9, 5, 8 ], [ 16, 10, 3, 8 ], [ 16, 11, 5, 8 ],
[ 16, 12, 3, 8 ], [ 16, 13, 5, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 5, 8 ],
[ 16, 16, 5, 8 ], [ 16, 17, 4, 8 ], [ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ],
[ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 22, 1, 3, 16 ], [ 22, 1, 6, 16 ],
[ 22, 2, 3, 8 ], [ 22, 2, 6, 8 ], [ 22, 3, 2, 8 ], [ 22, 3, 4, 8 ],
[ 22, 4, 3, 4 ], [ 22, 4, 6, 4 ], [ 24, 1, 3, 16 ], [ 24, 2, 3, 8 ],
[ 25, 1, 3, 16 ], [ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ], [ 26, 1, 3, 16 ],
[ 26, 2, 5, 8 ], [ 26, 3, 3, 8 ], [ 29, 2, 7, 8 ], [ 29, 3, 7, 8 ],
[ 29, 4, 7, 8 ], [ 29, 5, 7, 8 ], [ 29, 9, 7, 4 ] ]
k = 8: F-action on Pi is () [29,1,8]
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 0 modulo 4: 1/16 q^2 ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/16 phi1 phi4 ( q-3 )
q congruent 2 modulo 4: 1/16 q^2 ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/16 phi1 phi4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 4 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 16 ],
[ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ],
[ 15, 1, 1, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 12 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ],
[ 16, 11, 3, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ],
[ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ], [ 22, 1, 2, 8 ], [ 22, 1, 5, 8 ],
[ 22, 2, 2, 4 ], [ 22, 2, 5, 4 ], [ 22, 4, 2, 4 ], [ 22, 4, 5, 4 ],
[ 25, 1, 3, 16 ], [ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ], [ 26, 1, 2, 16 ],
[ 26, 2, 2, 8 ], [ 26, 3, 5, 8 ], [ 29, 2, 8, 8 ], [ 29, 3, 8, 8 ],
[ 29, 4, 8, 8 ], [ 29, 5, 8, 8 ], [ 29, 9, 8, 4 ] ]
k = 9: F-action on Pi is () [29,1,9]
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 0 modulo 4: 1/32 q ( q^3-6*q^2+12*q-8 )
q congruent 1 modulo 4: 1/32 phi1 phi2 ( q^2-6*q+9 )
q congruent 2 modulo 4: 1/32 q ( q^3-6*q^2+12*q-8 )
q congruent 3 modulo 4: 1/32 phi1 phi2 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 4 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ], [ 7, 4, 1, 8 ],
[ 7, 5, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ],
[ 12, 1, 1, 8 ], [ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ],
[ 13, 1, 2, 16 ], [ 13, 2, 2, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 16 ],
[ 16, 1, 1, 32 ], [ 16, 2, 1, 16 ], [ 16, 3, 1, 16 ], [ 16, 4, 1, 16 ],
[ 16, 5, 1, 16 ], [ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ], [ 16, 8, 1, 16 ],
[ 16, 9, 1, 8 ], [ 16, 10, 1, 8 ], [ 16, 11, 1, 8 ], [ 16, 12, 1, 8 ],
[ 16, 13, 1, 8 ], [ 16, 14, 1, 8 ], [ 16, 15, 1, 8 ], [ 16, 16, 1, 8 ],
[ 16, 17, 1, 8 ], [ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ], [ 20, 1, 3, 8 ],
[ 20, 2, 3, 4 ], [ 22, 1, 4, 32 ], [ 22, 2, 4, 16 ], [ 22, 3, 3, 16 ],
[ 22, 4, 4, 8 ], [ 23, 1, 5, 16 ], [ 23, 2, 5, 8 ], [ 23, 3, 5, 8 ],
[ 23, 4, 5, 8 ], [ 23, 5, 5, 8 ], [ 23, 6, 5, 4 ], [ 25, 1, 3, 16 ],
[ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ], [ 26, 1, 3, 16 ], [ 26, 2, 5, 8 ],
[ 26, 3, 3, 8 ], [ 29, 2, 9, 16 ], [ 29, 3, 9, 16 ], [ 29, 4, 9, 16 ],
[ 29, 5, 9, 16 ], [ 29, 6, 5, 16 ], [ 29, 7, 5, 16 ], [ 29, 8, 5, 16 ],
[ 29, 9, 9, 8 ], [ 29, 10, 5, 8 ], [ 29, 11, 5, 8 ], [ 29, 12, 5, 8 ],
[ 29, 13, 5, 8 ] ]
k = 10: F-action on Pi is () [29,1,10]
Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2^3)
Order of center |Z^F|: phi1 phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/32 q^2 ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/32 phi1^2 ( q^2-2*q-5 )
q congruent 2 modulo 4: 1/32 q^2 ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/32 phi2 ( q^3-5*q^2+5*q+3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 24 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 12 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 12 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 6 ],
[ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 8 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ],
[ 16, 11, 3, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ],
[ 20, 1, 4, 24 ], [ 20, 2, 4, 12 ], [ 22, 1, 5, 16 ], [ 22, 2, 5, 8 ],
[ 22, 4, 5, 8 ], [ 23, 1, 6, 16 ], [ 23, 2, 6, 8 ], [ 23, 3, 6, 8 ],
[ 23, 4, 6, 8 ], [ 23, 5, 6, 8 ], [ 23, 6, 6, 4 ], [ 25, 1, 3, 16 ],
[ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ], [ 26, 1, 4, 48 ], [ 26, 2, 10, 24 ],
[ 26, 3, 7, 24 ], [ 29, 2, 10, 16 ], [ 29, 3, 10, 16 ], [ 29, 4, 10, 16 ],
[ 29, 5, 10, 16 ], [ 29, 6, 6, 16 ], [ 29, 7, 6, 16 ], [ 29, 8, 6, 16 ],
[ 29, 9, 10, 8 ], [ 29, 10, 6, 8 ], [ 29, 11, 6, 8 ], [ 29, 12, 6, 8 ],
[ 29, 13, 6, 8 ] ]
k = 11: F-action on Pi is () [29,1,11]
Dynkin type is A_1(q) + A_1(q) + T(phi2^4)
Order of center |Z^F|: phi2^4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/32 q ( q^3-10*q^2+32*q-32 )
q congruent 1 modulo 4: 1/32 phi1 ( q^3-9*q^2+19*q+5 )
q congruent 2 modulo 4: 1/32 q ( q^3-10*q^2+32*q-32 )
q congruent 3 modulo 4: 1/32 ( q^4-10*q^3+28*q^2-14*q-21 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 16 ],
[ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 4, 8 ],
[ 7, 5, 4, 4 ], [ 8, 1, 2, 20 ], [ 9, 1, 2, 32 ], [ 9, 2, 2, 16 ],
[ 9, 3, 2, 16 ], [ 9, 4, 2, 16 ], [ 9, 5, 2, 8 ], [ 10, 1, 2, 8 ],
[ 10, 2, 2, 4 ], [ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ], [ 12, 1, 3, 8 ],
[ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ], [ 13, 1, 4, 16 ],
[ 13, 2, 4, 8 ], [ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 3, 40 ],
[ 16, 1, 5, 32 ], [ 16, 2, 5, 16 ], [ 16, 3, 5, 16 ], [ 16, 4, 5, 16 ],
[ 16, 5, 3, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ], [ 16, 8, 4, 16 ],
[ 16, 9, 5, 8 ], [ 16, 10, 3, 8 ], [ 16, 11, 5, 8 ], [ 16, 12, 3, 8 ],
[ 16, 13, 5, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 5, 8 ], [ 16, 16, 5, 8 ],
[ 16, 17, 4, 8 ], [ 17, 1, 2, 16 ], [ 17, 2, 2, 8 ], [ 18, 1, 4, 24 ],
[ 18, 2, 4, 12 ], [ 19, 1, 2, 32 ], [ 19, 2, 2, 16 ], [ 19, 3, 2, 16 ],
[ 19, 4, 2, 16 ], [ 19, 5, 2, 8 ], [ 20, 1, 4, 24 ], [ 20, 2, 4, 12 ],
[ 22, 1, 6, 32 ], [ 22, 2, 6, 16 ], [ 22, 3, 4, 16 ], [ 22, 4, 6, 8 ],
[ 23, 1, 7, 16 ], [ 23, 2, 7, 8 ], [ 23, 3, 7, 8 ], [ 23, 4, 7, 8 ],
[ 23, 5, 7, 8 ], [ 23, 6, 7, 4 ], [ 24, 1, 4, 32 ], [ 24, 2, 4, 16 ],
[ 25, 1, 4, 48 ], [ 25, 2, 8, 24 ], [ 25, 3, 7, 24 ], [ 26, 1, 4, 48 ],
[ 26, 2, 10, 24 ], [ 26, 3, 7, 24 ], [ 29, 2, 11, 16 ], [ 29, 3, 11, 16 ],
[ 29, 4, 11, 16 ], [ 29, 5, 11, 16 ], [ 29, 6, 7, 16 ], [ 29, 7, 7, 16 ],
[ 29, 8, 7, 16 ], [ 29, 9, 11, 8 ], [ 29, 10, 7, 8 ], [ 29, 11, 7, 8 ],
[ 29, 12, 7, 8 ], [ 29, 13, 7, 8 ] ]
k = 12: F-action on Pi is () [29,1,12]
Dynkin type is A_1(q) + A_1(q) + T(phi1 phi2^3)
Order of center |Z^F|: phi1 phi2^3
Numbers of classes in class type:
q congruent 0 modulo 4: 1/32 q^2 ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/32 phi1^2 ( q^2-2*q-5 )
q congruent 2 modulo 4: 1/32 q^2 ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/32 phi2 ( q^3-5*q^2+5*q+3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 24 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 12 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 12 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 6 ],
[ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 8 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ],
[ 16, 11, 3, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 18, 1, 4, 24 ], [ 18, 2, 4, 12 ],
[ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 22, 1, 5, 16 ], [ 22, 2, 5, 8 ],
[ 22, 4, 5, 8 ], [ 23, 1, 8, 16 ], [ 23, 2, 8, 8 ], [ 23, 3, 8, 8 ],
[ 23, 4, 8, 8 ], [ 23, 5, 8, 8 ], [ 23, 6, 8, 4 ], [ 25, 1, 4, 48 ],
[ 25, 2, 8, 24 ], [ 25, 3, 7, 24 ], [ 26, 1, 3, 16 ], [ 26, 2, 5, 8 ],
[ 26, 3, 3, 8 ], [ 29, 2, 12, 16 ], [ 29, 3, 12, 16 ], [ 29, 4, 12, 16 ],
[ 29, 5, 12, 16 ], [ 29, 6, 8, 16 ], [ 29, 7, 8, 16 ], [ 29, 8, 8, 16 ],
[ 29, 9, 12, 8 ], [ 29, 10, 8, 8 ], [ 29, 11, 8, 8 ], [ 29, 12, 8, 8 ],
[ 29, 13, 8, 8 ] ]
k = 13: F-action on Pi is (1,4) [29,1,13]
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 0 modulo 4: 1/16 q ( q^3-6*q^2+12*q-8 )
q congruent 1 modulo 4: 1/16 phi1 ( q^3-5*q^2+q+19 )
q congruent 2 modulo 4: 1/16 q ( q^3-6*q^2+12*q-8 )
q congruent 3 modulo 4: 1/16 ( q^4-6*q^3+6*q^2+18*q-27 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 6, 8 ], [ 9, 1, 8, 8 ], [ 9, 2, 6, 4 ], [ 9, 2, 8, 4 ],
[ 9, 3, 6, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 6, 4 ], [ 9, 4, 8, 4 ],
[ 9, 5, 6, 2 ], [ 9, 5, 8, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ],
[ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 12, 1, 1, 8 ], [ 12, 2, 1, 4 ],
[ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 15, 1, 2, 4 ], [ 16, 1, 13, 16 ],
[ 16, 2, 13, 8 ], [ 16, 3, 13, 8 ], [ 16, 4, 13, 8 ], [ 16, 5, 11, 8 ],
[ 16, 5, 15, 8 ], [ 16, 6, 11, 8 ], [ 16, 6, 15, 8 ], [ 16, 7, 11, 8 ],
[ 16, 7, 15, 8 ], [ 16, 9, 13, 4 ], [ 16, 10, 11, 4 ], [ 16, 10, 15, 4 ],
[ 16, 12, 11, 4 ], [ 16, 12, 15, 4 ], [ 16, 13, 13, 4 ], [ 16, 14, 9, 8 ],
[ 16, 15, 13, 4 ], [ 16, 16, 13, 4 ], [ 17, 1, 1, 8 ], [ 17, 2, 1, 4 ],
[ 18, 1, 1, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 3, 2 ],
[ 20, 1, 1, 4 ], [ 20, 1, 3, 4 ], [ 20, 2, 1, 2 ], [ 20, 2, 3, 2 ],
[ 23, 1, 1, 8 ], [ 23, 1, 5, 8 ], [ 23, 2, 1, 4 ], [ 23, 2, 5, 4 ],
[ 23, 3, 1, 4 ], [ 23, 3, 5, 4 ], [ 23, 4, 1, 4 ], [ 23, 4, 5, 4 ],
[ 23, 5, 1, 4 ], [ 23, 5, 5, 4 ], [ 23, 6, 1, 2 ], [ 23, 6, 5, 2 ],
[ 25, 1, 5, 8 ], [ 25, 2, 3, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 4, 4 ],
[ 26, 1, 5, 8 ], [ 26, 2, 3, 4 ], [ 26, 3, 2, 4 ], [ 26, 3, 4, 4 ],
[ 29, 2, 13, 8 ], [ 29, 3, 13, 8 ], [ 29, 4, 13, 8 ], [ 29, 5, 13, 8 ],
[ 29, 6, 9, 8 ], [ 29, 6, 13, 8 ], [ 29, 7, 9, 8 ], [ 29, 7, 13, 8 ],
[ 29, 8, 9, 8 ], [ 29, 8, 13, 8 ], [ 29, 9, 13, 4 ], [ 29, 10, 9, 4 ],
[ 29, 10, 13, 4 ], [ 29, 11, 9, 4 ], [ 29, 11, 13, 4 ], [ 29, 12, 9, 4 ],
[ 29, 12, 13, 4 ], [ 29, 13, 9, 4 ], [ 29, 13, 13, 4 ] ]
k = 14: F-action on Pi is (1,4) [29,1,14]
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 0 modulo 4: 1/16 q ( q^3-4*q^2+8 )
q congruent 1 modulo 4: 1/16 phi1 ( q^3-3*q^2-9*q+27 )
q congruent 2 modulo 4: 1/16 q ( q^3-4*q^2+8 )
q congruent 3 modulo 4: 1/16 phi1 ( q^3-3*q^2-9*q+27 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 4, 8 ],
[ 3, 2, 4, 4 ], [ 3, 3, 4, 4 ], [ 3, 4, 4, 4 ], [ 3, 5, 4, 2 ],
[ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 6, 8 ], [ 9, 1, 7, 8 ], [ 9, 2, 6, 4 ], [ 9, 2, 7, 4 ],
[ 9, 3, 6, 4 ], [ 9, 3, 7, 4 ], [ 9, 4, 6, 4 ], [ 9, 4, 7, 4 ],
[ 9, 5, 6, 2 ], [ 9, 5, 7, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ],
[ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 2, 4 ], [ 16, 1, 14, 16 ], [ 16, 2, 14, 8 ],
[ 16, 3, 14, 8 ], [ 16, 4, 14, 8 ], [ 16, 5, 12, 8 ], [ 16, 5, 13, 8 ],
[ 16, 6, 12, 8 ], [ 16, 6, 13, 8 ], [ 16, 7, 12, 8 ], [ 16, 7, 13, 8 ],
[ 16, 9, 14, 4 ], [ 16, 10, 12, 4 ], [ 16, 10, 13, 4 ], [ 16, 12, 12, 4 ],
[ 16, 12, 13, 4 ], [ 16, 13, 14, 4 ], [ 16, 15, 14, 4 ], [ 16, 16, 14, 4 ],
[ 16, 17, 9, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 1, 2 ],
[ 18, 2, 3, 2 ], [ 19, 1, 3, 16 ], [ 19, 2, 3, 8 ], [ 19, 3, 3, 8 ],
[ 19, 4, 3, 8 ], [ 19, 5, 3, 4 ], [ 20, 1, 2, 4 ], [ 20, 1, 4, 4 ],
[ 20, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 23, 1, 2, 8 ], [ 23, 1, 6, 8 ],
[ 23, 2, 2, 4 ], [ 23, 2, 6, 4 ], [ 23, 3, 2, 4 ], [ 23, 3, 6, 4 ],
[ 23, 4, 2, 4 ], [ 23, 4, 6, 4 ], [ 23, 5, 2, 4 ], [ 23, 5, 6, 4 ],
[ 23, 6, 2, 2 ], [ 23, 6, 6, 2 ], [ 25, 1, 5, 8 ], [ 25, 2, 3, 4 ],
[ 25, 3, 2, 4 ], [ 25, 3, 4, 4 ], [ 26, 1, 7, 8 ], [ 26, 2, 8, 4 ],
[ 26, 3, 6, 4 ], [ 26, 3, 8, 4 ], [ 29, 2, 14, 8 ], [ 29, 3, 14, 8 ],
[ 29, 4, 14, 8 ], [ 29, 5, 14, 8 ], [ 29, 6, 10, 8 ], [ 29, 6, 14, 8 ],
[ 29, 7, 10, 8 ], [ 29, 7, 14, 8 ], [ 29, 8, 10, 8 ], [ 29, 8, 14, 8 ],
[ 29, 9, 14, 4 ], [ 29, 10, 10, 4 ], [ 29, 10, 14, 4 ], [ 29, 11, 10, 4 ],
[ 29, 11, 14, 4 ], [ 29, 12, 10, 4 ], [ 29, 12, 14, 4 ], [ 29, 13, 10, 4 ],
[ 29, 13, 14, 4 ] ]
k = 15: F-action on Pi is (1,4) [29,1,15]
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 0 modulo 4: 1/16 q^3 ( q-2 )
q congruent 1 modulo 4: 1/16 phi1^2 ( q^2-7 )
q congruent 2 modulo 4: 1/16 q^3 ( q-2 )
q congruent 3 modulo 4: 1/16 ( q^4-2*q^3-6*q^2+14*q+1 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 2, 4 ],
[ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 5, 8 ], [ 9, 1, 7, 8 ], [ 9, 2, 5, 4 ], [ 9, 2, 7, 4 ],
[ 9, 3, 5, 4 ], [ 9, 3, 7, 4 ], [ 9, 4, 5, 4 ], [ 9, 4, 7, 4 ],
[ 9, 5, 5, 2 ], [ 9, 5, 7, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ],
[ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 12, 1, 3, 8 ], [ 12, 2, 3, 4 ],
[ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ], [ 15, 1, 2, 4 ], [ 16, 1, 12, 16 ],
[ 16, 2, 12, 8 ], [ 16, 3, 12, 8 ], [ 16, 4, 12, 8 ], [ 16, 5, 10, 8 ],
[ 16, 5, 14, 8 ], [ 16, 6, 10, 8 ], [ 16, 6, 14, 8 ], [ 16, 7, 10, 8 ],
[ 16, 7, 14, 8 ], [ 16, 9, 12, 4 ], [ 16, 10, 10, 4 ], [ 16, 10, 14, 4 ],
[ 16, 12, 10, 4 ], [ 16, 12, 14, 4 ], [ 16, 13, 12, 4 ], [ 16, 14, 8, 8 ],
[ 16, 15, 12, 4 ], [ 16, 16, 12, 4 ], [ 17, 1, 2, 8 ], [ 17, 2, 2, 4 ],
[ 18, 1, 2, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 4, 2 ],
[ 20, 1, 2, 4 ], [ 20, 1, 4, 4 ], [ 20, 2, 2, 2 ], [ 20, 2, 4, 2 ],
[ 23, 1, 3, 8 ], [ 23, 1, 7, 8 ], [ 23, 2, 3, 4 ], [ 23, 2, 7, 4 ],
[ 23, 3, 3, 4 ], [ 23, 3, 7, 4 ], [ 23, 4, 3, 4 ], [ 23, 4, 7, 4 ],
[ 23, 5, 3, 4 ], [ 23, 5, 7, 4 ], [ 23, 6, 3, 2 ], [ 23, 6, 7, 2 ],
[ 25, 1, 7, 8 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 8, 4 ],
[ 26, 1, 7, 8 ], [ 26, 2, 8, 4 ], [ 26, 3, 6, 4 ], [ 26, 3, 8, 4 ],
[ 29, 2, 15, 8 ], [ 29, 3, 15, 8 ], [ 29, 4, 15, 8 ], [ 29, 5, 15, 8 ],
[ 29, 6, 11, 8 ], [ 29, 6, 15, 8 ], [ 29, 7, 11, 8 ], [ 29, 7, 15, 8 ],
[ 29, 8, 11, 8 ], [ 29, 8, 15, 8 ], [ 29, 9, 15, 4 ], [ 29, 10, 11, 4 ],
[ 29, 10, 15, 4 ], [ 29, 11, 11, 4 ], [ 29, 11, 15, 4 ], [ 29, 12, 11, 4 ],
[ 29, 12, 15, 4 ], [ 29, 13, 11, 4 ], [ 29, 13, 15, 4 ] ]
k = 16: F-action on Pi is (1,4) [29,1,16]
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 0 modulo 4: 1/16 q ( q^3-4*q^2+8 )
q congruent 1 modulo 4: 1/16 phi1 ( q^3-3*q^2-9*q+27 )
q congruent 2 modulo 4: 1/16 q ( q^3-4*q^2+8 )
q congruent 3 modulo 4: 1/16 phi1 ( q^3-3*q^2-9*q+27 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 3, 8 ],
[ 3, 2, 3, 4 ], [ 3, 3, 3, 4 ], [ 3, 4, 3, 4 ], [ 3, 5, 3, 2 ],
[ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 5, 8 ], [ 9, 1, 8, 8 ], [ 9, 2, 5, 4 ], [ 9, 2, 8, 4 ],
[ 9, 3, 5, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 5, 4 ], [ 9, 4, 8, 4 ],
[ 9, 5, 5, 2 ], [ 9, 5, 8, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ],
[ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 2, 4 ], [ 16, 1, 9, 16 ], [ 16, 2, 9, 8 ],
[ 16, 3, 9, 8 ], [ 16, 4, 9, 8 ], [ 16, 5, 9, 8 ], [ 16, 5, 16, 8 ],
[ 16, 6, 9, 8 ], [ 16, 6, 16, 8 ], [ 16, 7, 9, 8 ], [ 16, 7, 16, 8 ],
[ 16, 9, 9, 4 ], [ 16, 10, 9, 4 ], [ 16, 10, 16, 4 ], [ 16, 12, 9, 4 ],
[ 16, 12, 16, 4 ], [ 16, 13, 9, 4 ], [ 16, 15, 9, 4 ], [ 16, 16, 9, 4 ],
[ 16, 17, 7, 8 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 2, 2 ],
[ 18, 2, 4, 2 ], [ 19, 1, 4, 16 ], [ 19, 2, 4, 8 ], [ 19, 3, 4, 8 ],
[ 19, 4, 4, 8 ], [ 19, 5, 4, 4 ], [ 20, 1, 1, 4 ], [ 20, 1, 3, 4 ],
[ 20, 2, 1, 2 ], [ 20, 2, 3, 2 ], [ 23, 1, 4, 8 ], [ 23, 1, 8, 8 ],
[ 23, 2, 4, 4 ], [ 23, 2, 8, 4 ], [ 23, 3, 4, 4 ], [ 23, 3, 8, 4 ],
[ 23, 4, 4, 4 ], [ 23, 4, 8, 4 ], [ 23, 5, 4, 4 ], [ 23, 5, 8, 4 ],
[ 23, 6, 4, 2 ], [ 23, 6, 8, 2 ], [ 25, 1, 7, 8 ], [ 25, 2, 6, 4 ],
[ 25, 3, 6, 4 ], [ 25, 3, 8, 4 ], [ 26, 1, 5, 8 ], [ 26, 2, 3, 4 ],
[ 26, 3, 2, 4 ], [ 26, 3, 4, 4 ], [ 29, 2, 16, 8 ], [ 29, 3, 16, 8 ],
[ 29, 4, 16, 8 ], [ 29, 5, 16, 8 ], [ 29, 6, 12, 8 ], [ 29, 6, 16, 8 ],
[ 29, 7, 12, 8 ], [ 29, 7, 16, 8 ], [ 29, 8, 12, 8 ], [ 29, 8, 16, 8 ],
[ 29, 9, 16, 4 ], [ 29, 10, 12, 4 ], [ 29, 10, 16, 4 ], [ 29, 11, 12, 4 ],
[ 29, 11, 16, 4 ], [ 29, 12, 12, 4 ], [ 29, 12, 16, 4 ], [ 29, 13, 12, 4 ],
[ 29, 13, 16, 4 ] ]
k = 17: F-action on Pi is (1,4) [29,1,17]
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 0 modulo 4: 1/16 q^2 ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/16 phi1^2 phi2 ( q-3 )
q congruent 2 modulo 4: 1/16 q^2 ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/16 phi1^2 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 28, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 9, 1, 6, 8 ], [ 9, 1, 8, 8 ],
[ 9, 2, 6, 4 ], [ 9, 2, 8, 4 ], [ 9, 3, 6, 4 ], [ 9, 3, 8, 4 ],
[ 9, 4, 6, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 6, 2 ], [ 9, 5, 8, 2 ],
[ 12, 1, 1, 8 ], [ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ],
[ 15, 1, 5, 4 ], [ 16, 1, 13, 16 ], [ 16, 2, 13, 8 ], [ 16, 3, 13, 8 ],
[ 16, 4, 13, 8 ], [ 16, 5, 11, 8 ], [ 16, 5, 15, 8 ], [ 16, 6, 11, 8 ],
[ 16, 6, 15, 8 ], [ 16, 7, 11, 8 ], [ 16, 7, 15, 8 ], [ 16, 9, 13, 4 ],
[ 16, 10, 11, 4 ], [ 16, 10, 15, 4 ], [ 16, 12, 11, 4 ], [ 16, 12, 15, 4 ],
[ 16, 13, 13, 4 ], [ 16, 14, 9, 8 ], [ 16, 15, 13, 4 ], [ 16, 16, 13, 4 ],
[ 25, 1, 6, 8 ], [ 25, 2, 4, 4 ], [ 26, 1, 6, 8 ], [ 26, 2, 4, 4 ],
[ 29, 2, 17, 8 ], [ 29, 3, 17, 8 ], [ 29, 4, 17, 8 ], [ 29, 5, 17, 8 ],
[ 29, 9, 17, 4 ] ]
k = 18: F-action on Pi is (1,4) [29,1,18]
Dynkin type is A_1(q^2) + T(phi1 phi2 phi4)
Order of center |Z^F|: phi1 phi2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q^3 ( q-2 )
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q^2-2*q-1 )
q congruent 2 modulo 4: 1/16 q^3 ( q-2 )
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q^2-2*q-1 )
Fusion of maximal tori of C^F in those of G^F:
[ 31, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 4, 8 ],
[ 3, 2, 4, 4 ], [ 3, 3, 4, 4 ], [ 3, 4, 4, 4 ], [ 3, 5, 4, 2 ],
[ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 6, 8 ], [ 9, 1, 7, 8 ],
[ 9, 2, 6, 4 ], [ 9, 2, 7, 4 ], [ 9, 3, 6, 4 ], [ 9, 3, 7, 4 ],
[ 9, 4, 6, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 6, 2 ], [ 9, 5, 7, 2 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 15, 1, 5, 4 ],
[ 16, 1, 14, 16 ], [ 16, 2, 14, 8 ], [ 16, 3, 14, 8 ], [ 16, 4, 14, 8 ],
[ 16, 5, 12, 8 ], [ 16, 5, 13, 8 ], [ 16, 6, 12, 8 ], [ 16, 6, 13, 8 ],
[ 16, 7, 12, 8 ], [ 16, 7, 13, 8 ], [ 16, 9, 14, 4 ], [ 16, 10, 12, 4 ],
[ 16, 10, 13, 4 ], [ 16, 12, 12, 4 ], [ 16, 12, 13, 4 ], [ 16, 13, 14, 4 ],
[ 16, 15, 14, 4 ], [ 16, 16, 14, 4 ], [ 16, 17, 9, 8 ], [ 25, 1, 6, 8 ],
[ 25, 2, 4, 4 ], [ 26, 1, 8, 8 ], [ 26, 2, 9, 4 ], [ 29, 2, 18, 8 ],
[ 29, 3, 18, 8 ], [ 29, 4, 18, 8 ], [ 29, 5, 18, 8 ], [ 29, 9, 18, 4 ] ]
k = 19: F-action on Pi is (1,4) [29,1,19]
Dynkin type is A_1(q^2) + T(phi2^2 phi4)
Order of center |Z^F|: phi2^2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q^4
q congruent 1 modulo 4: 1/16 phi1^2 phi2^2
q congruent 2 modulo 4: 1/16 q^4
q congruent 3 modulo 4: 1/16 phi1^2 phi2^2
Fusion of maximal tori of C^F in those of G^F:
[ 30, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 2, 4 ],
[ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 9, 1, 5, 8 ], [ 9, 1, 7, 8 ],
[ 9, 2, 5, 4 ], [ 9, 2, 7, 4 ], [ 9, 3, 5, 4 ], [ 9, 3, 7, 4 ],
[ 9, 4, 5, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 5, 2 ], [ 9, 5, 7, 2 ],
[ 12, 1, 3, 8 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ],
[ 15, 1, 5, 4 ], [ 16, 1, 12, 16 ], [ 16, 2, 12, 8 ], [ 16, 3, 12, 8 ],
[ 16, 4, 12, 8 ], [ 16, 5, 10, 8 ], [ 16, 5, 14, 8 ], [ 16, 6, 10, 8 ],
[ 16, 6, 14, 8 ], [ 16, 7, 10, 8 ], [ 16, 7, 14, 8 ], [ 16, 9, 12, 4 ],
[ 16, 10, 10, 4 ], [ 16, 10, 14, 4 ], [ 16, 12, 10, 4 ], [ 16, 12, 14, 4 ],
[ 16, 13, 12, 4 ], [ 16, 14, 8, 8 ], [ 16, 15, 12, 4 ], [ 16, 16, 12, 4 ],
[ 25, 1, 8, 8 ], [ 25, 2, 7, 4 ], [ 26, 1, 8, 8 ], [ 26, 2, 9, 4 ],
[ 29, 2, 19, 8 ], [ 29, 3, 19, 8 ], [ 29, 4, 19, 8 ], [ 29, 5, 19, 8 ],
[ 29, 9, 19, 4 ] ]
k = 20: F-action on Pi is (1,4) [29,1,20]
Dynkin type is A_1(q^2) + T(phi1 phi2 phi4)
Order of center |Z^F|: phi1 phi2 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q^3 ( q-2 )
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q^2-2*q-1 )
q congruent 2 modulo 4: 1/16 q^3 ( q-2 )
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q^2-2*q-1 )
Fusion of maximal tori of C^F in those of G^F:
[ 32, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 3, 8 ],
[ 3, 2, 3, 4 ], [ 3, 3, 3, 4 ], [ 3, 4, 3, 4 ], [ 3, 5, 3, 2 ],
[ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 5, 8 ], [ 9, 1, 8, 8 ],
[ 9, 2, 5, 4 ], [ 9, 2, 8, 4 ], [ 9, 3, 5, 4 ], [ 9, 3, 8, 4 ],
[ 9, 4, 5, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 5, 2 ], [ 9, 5, 8, 2 ],
[ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 15, 1, 5, 4 ],
[ 16, 1, 9, 16 ], [ 16, 2, 9, 8 ], [ 16, 3, 9, 8 ], [ 16, 4, 9, 8 ],
[ 16, 5, 9, 8 ], [ 16, 5, 16, 8 ], [ 16, 6, 9, 8 ], [ 16, 6, 16, 8 ],
[ 16, 7, 9, 8 ], [ 16, 7, 16, 8 ], [ 16, 9, 9, 4 ], [ 16, 10, 9, 4 ],
[ 16, 10, 16, 4 ], [ 16, 12, 9, 4 ], [ 16, 12, 16, 4 ], [ 16, 13, 9, 4 ],
[ 16, 15, 9, 4 ], [ 16, 16, 9, 4 ], [ 16, 17, 7, 8 ], [ 25, 1, 8, 8 ],
[ 25, 2, 7, 4 ], [ 26, 1, 6, 8 ], [ 26, 2, 4, 4 ], [ 29, 2, 20, 8 ],
[ 29, 3, 20, 8 ], [ 29, 4, 20, 8 ], [ 29, 5, 20, 8 ], [ 29, 9, 20, 4 ] ]
j = 4: Omega of order 2, action on Pi: <()>
k = 1: F-action on Pi is () [29,4,1]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^4)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 1, 4 ],
[ 3, 5, 1, 2 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 7, 3, 1, 8 ],
[ 7, 5, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ],
[ 9, 3, 1, 8 ], [ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 12, 2, 1, 4 ],
[ 12, 4, 1, 2 ], [ 13, 2, 1, 8 ], [ 15, 1, 1, 8 ], [ 16, 2, 1, 16 ],
[ 16, 9, 1, 8 ], [ 16, 10, 1, 8 ], [ 16, 11, 1, 8 ], [ 22, 2, 1, 16 ],
[ 22, 4, 1, 8 ], [ 23, 2, 1, 8 ], [ 23, 6, 1, 4 ], [ 29, 9, 1, 8 ],
[ 29, 12, 1, 8 ] ]
k = 2: F-action on Pi is () [29,4,2]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ],
[ 15, 1, 1, 8 ], [ 16, 2, 3, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ],
[ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 22, 2, 2, 8 ], [ 22, 4, 2, 8 ],
[ 23, 2, 2, 8 ], [ 23, 6, 2, 4 ], [ 29, 9, 2, 8 ], [ 29, 12, 2, 8 ] ]
k = 3: F-action on Pi is () [29,4,3]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 2, 4 ],
[ 3, 5, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 7, 3, 4, 8 ],
[ 7, 5, 4, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ],
[ 9, 3, 1, 8 ], [ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 12, 2, 3, 4 ],
[ 12, 4, 3, 2 ], [ 13, 2, 3, 8 ], [ 15, 1, 1, 8 ], [ 16, 2, 5, 16 ],
[ 16, 9, 5, 8 ], [ 16, 10, 3, 8 ], [ 16, 11, 5, 8 ], [ 22, 2, 3, 16 ],
[ 22, 4, 3, 8 ], [ 23, 2, 3, 8 ], [ 23, 6, 3, 4 ], [ 29, 9, 3, 8 ],
[ 29, 12, 3, 8 ] ]
k = 4: F-action on Pi is () [29,4,4]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ],
[ 15, 1, 1, 8 ], [ 16, 2, 3, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ],
[ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 22, 2, 2, 8 ], [ 22, 4, 2, 8 ],
[ 23, 2, 4, 8 ], [ 23, 6, 4, 4 ], [ 29, 9, 4, 8 ], [ 29, 12, 4, 8 ] ]
k = 5: F-action on Pi is () [29,4,5]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2, 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 1, 4 ],
[ 3, 5, 1, 2 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 7, 3, 1, 8 ], [ 7, 5, 1, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 12, 2, 1, 4 ], [ 12, 4, 1, 2 ], [ 13, 2, 1, 4 ], [ 13, 2, 2, 4 ],
[ 15, 1, 4, 4 ], [ 16, 2, 1, 16 ], [ 16, 9, 1, 8 ], [ 16, 10, 1, 8 ],
[ 16, 11, 1, 8 ], [ 22, 2, 1, 8 ], [ 22, 2, 4, 8 ], [ 22, 4, 1, 4 ],
[ 22, 4, 4, 4 ], [ 29, 9, 5, 4 ] ]
k = 6: F-action on Pi is () [29,4,6]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 4, 4 ], [ 16, 2, 3, 8 ], [ 16, 9, 3, 4 ],
[ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 22, 2, 2, 4 ],
[ 22, 2, 5, 4 ], [ 22, 4, 2, 4 ], [ 22, 4, 5, 4 ], [ 29, 9, 6, 4 ] ]
k = 7: F-action on Pi is () [29,4,7]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 2, 4 ],
[ 3, 5, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 7, 3, 4, 8 ], [ 7, 5, 4, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 12, 2, 3, 4 ], [ 12, 4, 3, 2 ], [ 13, 2, 3, 4 ], [ 13, 2, 4, 4 ],
[ 15, 1, 4, 4 ], [ 16, 2, 5, 16 ], [ 16, 9, 5, 8 ], [ 16, 10, 3, 8 ],
[ 16, 11, 5, 8 ], [ 22, 2, 3, 8 ], [ 22, 2, 6, 8 ], [ 22, 4, 3, 4 ],
[ 22, 4, 6, 4 ], [ 29, 9, 7, 4 ] ]
k = 8: F-action on Pi is () [29,4,8]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 4, 4 ], [ 16, 2, 3, 8 ], [ 16, 9, 3, 4 ],
[ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 22, 2, 2, 4 ],
[ 22, 2, 5, 4 ], [ 22, 4, 2, 4 ], [ 22, 4, 5, 4 ], [ 29, 9, 8, 4 ] ]
k = 9: F-action on Pi is () [29,4,9]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 1, 4 ],
[ 3, 5, 1, 2 ], [ 4, 2, 1, 2 ], [ 5, 1, 2, 4 ], [ 7, 3, 1, 8 ],
[ 7, 5, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 12, 2, 1, 4 ],
[ 12, 4, 1, 2 ], [ 13, 2, 2, 8 ], [ 15, 1, 3, 8 ], [ 16, 2, 1, 16 ],
[ 16, 9, 1, 8 ], [ 16, 10, 1, 8 ], [ 16, 11, 1, 8 ], [ 22, 2, 4, 16 ],
[ 22, 4, 4, 8 ], [ 23, 2, 5, 8 ], [ 23, 6, 5, 4 ], [ 29, 9, 9, 8 ],
[ 29, 12, 5, 8 ] ]
k = 10: F-action on Pi is () [29,4,10]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ],
[ 15, 1, 3, 8 ], [ 16, 2, 3, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ],
[ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 22, 2, 5, 8 ], [ 22, 4, 5, 8 ],
[ 23, 2, 6, 8 ], [ 23, 6, 6, 4 ], [ 29, 9, 10, 8 ], [ 29, 12, 6, 8 ] ]
k = 11: F-action on Pi is () [29,4,11]
Dynkin type is (A_1(q) + A_1(q) + T(phi2^4)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 2, 4 ],
[ 3, 5, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 7, 3, 4, 8 ],
[ 7, 5, 4, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 12, 2, 3, 4 ],
[ 12, 4, 3, 2 ], [ 13, 2, 4, 8 ], [ 15, 1, 3, 8 ], [ 16, 2, 5, 16 ],
[ 16, 9, 5, 8 ], [ 16, 10, 3, 8 ], [ 16, 11, 5, 8 ], [ 22, 2, 6, 16 ],
[ 22, 4, 6, 8 ], [ 23, 2, 7, 8 ], [ 23, 6, 7, 4 ], [ 29, 9, 11, 8 ],
[ 29, 12, 7, 8 ] ]
k = 12: F-action on Pi is () [29,4,12]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ],
[ 15, 1, 3, 8 ], [ 16, 2, 3, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 2, 4 ],
[ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 22, 2, 5, 8 ], [ 22, 4, 5, 8 ],
[ 23, 2, 8, 8 ], [ 23, 6, 8, 4 ], [ 29, 9, 12, 8 ], [ 29, 12, 8, 8 ] ]
k = 13: F-action on Pi is (1,4) [29,4,13]
Dynkin type is (A_1(q^2) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 2, 1, 4 ], [ 12, 4, 1, 2 ],
[ 15, 1, 2, 4 ], [ 16, 2, 13, 8 ], [ 16, 9, 13, 4 ], [ 16, 10, 11, 4 ],
[ 16, 10, 15, 4 ], [ 23, 2, 1, 4 ], [ 23, 2, 5, 4 ], [ 23, 6, 1, 2 ],
[ 23, 6, 5, 2 ], [ 29, 9, 13, 4 ], [ 29, 12, 9, 4 ], [ 29, 12, 13, 4 ] ]
k = 14: F-action on Pi is (1,4) [29,4,14]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 4, 4 ],
[ 3, 5, 4, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 2, 4 ], [ 16, 2, 14, 8 ], [ 16, 9, 14, 4 ],
[ 16, 10, 12, 4 ], [ 16, 10, 13, 4 ], [ 23, 2, 2, 4 ], [ 23, 2, 6, 4 ],
[ 23, 6, 2, 2 ], [ 23, 6, 6, 2 ], [ 29, 9, 14, 4 ], [ 29, 12, 10, 4 ],
[ 29, 12, 14, 4 ] ]
k = 15: F-action on Pi is (1,4) [29,4,15]
Dynkin type is (A_1(q^2) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 2, 3, 4 ], [ 12, 4, 3, 2 ],
[ 15, 1, 2, 4 ], [ 16, 2, 12, 8 ], [ 16, 9, 12, 4 ], [ 16, 10, 10, 4 ],
[ 16, 10, 14, 4 ], [ 23, 2, 3, 4 ], [ 23, 2, 7, 4 ], [ 23, 6, 3, 2 ],
[ 23, 6, 7, 2 ], [ 29, 9, 15, 4 ], [ 29, 12, 11, 4 ], [ 29, 12, 15, 4 ] ]
k = 16: F-action on Pi is (1,4) [29,4,16]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 3, 4 ],
[ 3, 5, 3, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 2, 4 ], [ 16, 2, 9, 8 ], [ 16, 9, 9, 4 ],
[ 16, 10, 9, 4 ], [ 16, 10, 16, 4 ], [ 23, 2, 4, 4 ], [ 23, 2, 8, 4 ],
[ 23, 6, 4, 2 ], [ 23, 6, 8, 2 ], [ 29, 9, 16, 4 ], [ 29, 12, 12, 4 ],
[ 29, 12, 16, 4 ] ]
k = 17: F-action on Pi is (1,4) [29,4,17]
Dynkin type is (A_1(q^2) + T(phi1^2 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 28, 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 1, 2 ],
[ 12, 2, 1, 4 ], [ 12, 4, 1, 2 ], [ 15, 1, 5, 4 ], [ 16, 2, 13, 8 ],
[ 16, 9, 13, 4 ], [ 16, 10, 11, 4 ], [ 16, 10, 15, 4 ], [ 29, 9, 17, 4 ] ]
k = 18: F-action on Pi is (1,4) [29,4,18]
Dynkin type is (A_1(q^2) + T(phi1 phi2 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 31, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 4, 4 ],
[ 3, 5, 4, 2 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 15, 1, 5, 4 ],
[ 16, 2, 14, 8 ], [ 16, 9, 14, 4 ], [ 16, 10, 12, 4 ], [ 16, 10, 13, 4 ],
[ 29, 9, 18, 4 ] ]
k = 19: F-action on Pi is (1,4) [29,4,19]
Dynkin type is (A_1(q^2) + T(phi2^2 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 30, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 2, 2 ],
[ 12, 2, 3, 4 ], [ 12, 4, 3, 2 ], [ 15, 1, 5, 4 ], [ 16, 2, 12, 8 ],
[ 16, 9, 12, 4 ], [ 16, 10, 10, 4 ], [ 16, 10, 14, 4 ], [ 29, 9, 19, 4 ] ]
k = 20: F-action on Pi is (1,4) [29,4,20]
Dynkin type is (A_1(q^2) + T(phi1 phi2 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 32, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 3, 4 ],
[ 3, 5, 3, 2 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 15, 1, 5, 4 ],
[ 16, 2, 9, 8 ], [ 16, 9, 9, 4 ], [ 16, 10, 9, 4 ], [ 16, 10, 16, 4 ],
[ 29, 9, 20, 4 ] ]
j = 6: Omega of order 2, action on Pi: <(1,4)>
k = 1: F-action on Pi is () [29,6,1]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^4)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 1, 4 ],
[ 3, 5, 1, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ], [ 11, 2, 1, 2 ],
[ 16, 5, 1, 8 ], [ 16, 10, 1, 4 ], [ 16, 12, 1, 4 ], [ 16, 15, 1, 8 ],
[ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 19, 3, 1, 8 ], [ 19, 5, 1, 4 ],
[ 20, 2, 1, 2 ], [ 23, 3, 1, 4 ], [ 23, 6, 1, 2 ], [ 26, 3, 1, 4 ],
[ 29, 11, 1, 4 ], [ 29, 12, 1, 4 ], [ 29, 13, 1, 4 ] ]
k = 2: F-action on Pi is () [29,6,2]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 9, 4, 2, 4 ], [ 9, 5, 2, 2 ], [ 10, 1, 1, 4 ],
[ 10, 2, 1, 2 ], [ 16, 5, 2, 8 ], [ 16, 10, 2, 4 ], [ 16, 12, 2, 4 ],
[ 16, 15, 3, 4 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 20, 2, 2, 2 ],
[ 23, 3, 2, 4 ], [ 23, 6, 2, 2 ], [ 26, 3, 5, 4 ], [ 29, 11, 2, 4 ],
[ 29, 12, 2, 4 ], [ 29, 13, 2, 4 ] ]
k = 3: F-action on Pi is () [29,6,3]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 2, 4 ],
[ 3, 5, 2, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 16, 5, 3, 8 ], [ 16, 10, 3, 4 ], [ 16, 12, 3, 4 ],
[ 16, 15, 5, 8 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 20, 2, 2, 2 ],
[ 23, 3, 3, 4 ], [ 23, 6, 3, 2 ], [ 26, 3, 5, 4 ], [ 29, 11, 3, 4 ],
[ 29, 12, 3, 4 ], [ 29, 13, 3, 4 ] ]
k = 4: F-action on Pi is () [29,6,4]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 9, 4, 1, 4 ], [ 9, 5, 1, 2 ], [ 11, 2, 1, 2 ],
[ 16, 5, 4, 8 ], [ 16, 10, 4, 4 ], [ 16, 12, 4, 4 ], [ 16, 15, 3, 4 ],
[ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 20, 2, 1, 2 ], [ 23, 3, 4, 4 ],
[ 23, 6, 4, 2 ], [ 26, 3, 1, 4 ], [ 29, 11, 4, 4 ], [ 29, 12, 4, 4 ],
[ 29, 13, 4, 4 ] ]
k = 5: F-action on Pi is () [29,6,5]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 1, 4 ],
[ 3, 5, 1, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 16, 5, 1, 8 ], [ 16, 10, 1, 4 ], [ 16, 12, 1, 4 ],
[ 16, 15, 1, 8 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 20, 2, 3, 2 ],
[ 23, 3, 5, 4 ], [ 23, 6, 5, 2 ], [ 26, 3, 3, 4 ], [ 29, 11, 5, 4 ],
[ 29, 12, 5, 4 ], [ 29, 13, 5, 4 ] ]
k = 6: F-action on Pi is () [29,6,6]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 9, 4, 2, 4 ], [ 9, 5, 2, 2 ], [ 11, 2, 2, 2 ],
[ 16, 5, 2, 8 ], [ 16, 10, 2, 4 ], [ 16, 12, 2, 4 ], [ 16, 15, 3, 4 ],
[ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 20, 2, 4, 2 ], [ 23, 3, 6, 4 ],
[ 23, 6, 6, 2 ], [ 26, 3, 7, 4 ], [ 29, 11, 6, 4 ], [ 29, 12, 6, 4 ],
[ 29, 13, 6, 4 ] ]
k = 7: F-action on Pi is () [29,6,7]
Dynkin type is (A_1(q) + A_1(q) + T(phi2^4)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 2, 4 ],
[ 3, 5, 2, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ], [ 11, 2, 2, 2 ],
[ 16, 5, 3, 8 ], [ 16, 10, 3, 4 ], [ 16, 12, 3, 4 ], [ 16, 15, 5, 8 ],
[ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 19, 3, 2, 8 ], [ 19, 5, 2, 4 ],
[ 20, 2, 4, 2 ], [ 23, 3, 7, 4 ], [ 23, 6, 7, 2 ], [ 26, 3, 7, 4 ],
[ 29, 11, 7, 4 ], [ 29, 12, 7, 4 ], [ 29, 13, 7, 4 ] ]
k = 8: F-action on Pi is () [29,6,8]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 2, 2 ], [ 9, 4, 1, 4 ], [ 9, 5, 1, 2 ], [ 10, 1, 2, 4 ],
[ 10, 2, 2, 2 ], [ 16, 5, 4, 8 ], [ 16, 10, 4, 4 ], [ 16, 12, 4, 4 ],
[ 16, 15, 3, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 20, 2, 3, 2 ],
[ 23, 3, 8, 4 ], [ 23, 6, 8, 2 ], [ 26, 3, 3, 4 ], [ 29, 11, 8, 4 ],
[ 29, 12, 8, 4 ], [ 29, 13, 8, 4 ] ]
k = 9: F-action on Pi is (1,4) [29,6,9]
Dynkin type is (A_1(q^2) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 9, 4, 8, 4 ], [ 9, 5, 8, 2 ], [ 10, 1, 1, 4 ],
[ 10, 2, 1, 2 ], [ 16, 5, 11, 8 ], [ 16, 10, 11, 4 ], [ 16, 12, 11, 4 ],
[ 16, 15, 13, 4 ], [ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 20, 2, 3, 2 ],
[ 23, 3, 5, 4 ], [ 23, 6, 5, 2 ], [ 26, 3, 2, 4 ], [ 29, 11, 9, 4 ],
[ 29, 12, 9, 4 ], [ 29, 13, 9, 4 ] ]
k = 10: F-action on Pi is (1,4) [29,6,10]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 4, 4 ],
[ 3, 5, 4, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 9, 4, 7, 4 ],
[ 9, 5, 7, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ], [ 11, 2, 2, 2 ],
[ 16, 5, 12, 8 ], [ 16, 10, 12, 4 ], [ 16, 12, 12, 4 ], [ 16, 15, 14, 4 ],
[ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 19, 3, 3, 8 ], [ 19, 5, 3, 4 ],
[ 20, 2, 4, 2 ], [ 23, 3, 6, 4 ], [ 23, 6, 6, 2 ], [ 26, 3, 6, 4 ],
[ 29, 11, 10, 4 ], [ 29, 12, 10, 4 ], [ 29, 13, 10, 4 ] ]
k = 11: F-action on Pi is (1,4) [29,6,11]
Dynkin type is (A_1(q^2) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 9, 4, 7, 4 ], [ 9, 5, 7, 2 ], [ 11, 2, 2, 2 ],
[ 16, 5, 10, 8 ], [ 16, 10, 10, 4 ], [ 16, 12, 10, 4 ], [ 16, 15, 12, 4 ],
[ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 23, 3, 7, 4 ],
[ 23, 6, 7, 2 ], [ 26, 3, 6, 4 ], [ 29, 11, 11, 4 ], [ 29, 12, 11, 4 ],
[ 29, 13, 11, 4 ] ]
k = 12: F-action on Pi is (1,4) [29,6,12]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 3, 4 ],
[ 3, 5, 3, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 9, 4, 8, 4 ],
[ 9, 5, 8, 2 ], [ 16, 5, 9, 8 ], [ 16, 10, 9, 4 ], [ 16, 12, 9, 4 ],
[ 16, 15, 9, 4 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ], [ 20, 2, 3, 2 ],
[ 23, 3, 8, 4 ], [ 23, 6, 8, 2 ], [ 26, 3, 2, 4 ], [ 29, 11, 12, 4 ],
[ 29, 12, 12, 4 ], [ 29, 13, 12, 4 ] ]
k = 13: F-action on Pi is (1,4) [29,6,13]
Dynkin type is (A_1(q^2) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 9, 4, 8, 4 ], [ 9, 5, 8, 2 ], [ 11, 2, 1, 2 ],
[ 16, 5, 11, 8 ], [ 16, 10, 11, 4 ], [ 16, 12, 11, 4 ], [ 16, 15, 13, 4 ],
[ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 20, 2, 1, 2 ], [ 23, 3, 1, 4 ],
[ 23, 6, 1, 2 ], [ 26, 3, 4, 4 ], [ 29, 11, 13, 4 ], [ 29, 12, 13, 4 ],
[ 29, 13, 13, 4 ] ]
k = 14: F-action on Pi is (1,4) [29,6,14]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 4, 4 ],
[ 3, 5, 4, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 4, 7, 4 ],
[ 9, 5, 7, 2 ], [ 16, 5, 12, 8 ], [ 16, 10, 12, 4 ], [ 16, 12, 12, 4 ],
[ 16, 15, 14, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ], [ 20, 2, 2, 2 ],
[ 23, 3, 2, 4 ], [ 23, 6, 2, 2 ], [ 26, 3, 8, 4 ], [ 29, 11, 14, 4 ],
[ 29, 12, 14, 4 ], [ 29, 13, 14, 4 ] ]
k = 15: F-action on Pi is (1,4) [29,6,15]
Dynkin type is (A_1(q^2) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 2, 2 ], [ 9, 4, 7, 4 ], [ 9, 5, 7, 2 ], [ 10, 1, 2, 4 ],
[ 10, 2, 2, 2 ], [ 16, 5, 10, 8 ], [ 16, 10, 10, 4 ], [ 16, 12, 10, 4 ],
[ 16, 15, 12, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 20, 2, 2, 2 ],
[ 23, 3, 3, 4 ], [ 23, 6, 3, 2 ], [ 26, 3, 8, 4 ], [ 29, 11, 15, 4 ],
[ 29, 12, 15, 4 ], [ 29, 13, 15, 4 ] ]
k = 16: F-action on Pi is (1,4) [29,6,16]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 3, 4 ],
[ 3, 5, 3, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 9, 4, 8, 4 ],
[ 9, 5, 8, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ], [ 11, 2, 1, 2 ],
[ 16, 5, 9, 8 ], [ 16, 10, 9, 4 ], [ 16, 12, 9, 4 ], [ 16, 15, 9, 4 ],
[ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 19, 3, 4, 8 ], [ 19, 5, 4, 4 ],
[ 20, 2, 1, 2 ], [ 23, 3, 4, 4 ], [ 23, 6, 4, 2 ], [ 26, 3, 4, 4 ],
[ 29, 11, 16, 4 ], [ 29, 12, 16, 4 ], [ 29, 13, 16, 4 ] ]
j = 7: Omega of order 2, action on Pi: <(1,4)>
k = 1: F-action on Pi is () [29,7,1]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^4)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 1, 4 ],
[ 3, 5, 1, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 9, 3, 1, 4 ],
[ 9, 5, 1, 2 ], [ 10, 2, 1, 2 ], [ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ],
[ 16, 6, 1, 8 ], [ 16, 10, 1, 4 ], [ 16, 12, 1, 4 ], [ 16, 16, 1, 8 ],
[ 18, 2, 1, 2 ], [ 19, 4, 1, 8 ], [ 19, 5, 1, 4 ], [ 20, 1, 1, 4 ],
[ 20, 2, 1, 2 ], [ 23, 4, 1, 4 ], [ 23, 6, 1, 2 ], [ 25, 3, 1, 4 ],
[ 29, 10, 1, 4 ], [ 29, 12, 1, 4 ], [ 29, 13, 1, 4 ] ]
k = 2: F-action on Pi is () [29,7,2]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 9, 3, 1, 4 ], [ 9, 5, 1, 2 ], [ 10, 2, 1, 2 ],
[ 16, 6, 2, 8 ], [ 16, 10, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 16, 3, 4 ],
[ 18, 2, 1, 2 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 23, 4, 2, 4 ],
[ 23, 6, 2, 2 ], [ 25, 3, 1, 4 ], [ 29, 10, 2, 4 ], [ 29, 12, 2, 4 ],
[ 29, 13, 2, 4 ] ]
k = 3: F-action on Pi is () [29,7,3]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 2, 4 ],
[ 3, 5, 2, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 9, 3, 2, 4 ],
[ 9, 5, 2, 2 ], [ 16, 6, 3, 8 ], [ 16, 10, 3, 4 ], [ 16, 12, 3, 4 ],
[ 16, 16, 5, 8 ], [ 18, 2, 2, 2 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ],
[ 23, 4, 3, 4 ], [ 23, 6, 3, 2 ], [ 25, 3, 5, 4 ], [ 29, 10, 3, 4 ],
[ 29, 12, 3, 4 ], [ 29, 13, 3, 4 ] ]
k = 4: F-action on Pi is () [29,7,4]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 9, 3, 2, 4 ], [ 9, 5, 2, 2 ], [ 11, 1, 1, 4 ],
[ 11, 2, 1, 2 ], [ 16, 6, 4, 8 ], [ 16, 10, 4, 4 ], [ 16, 12, 2, 4 ],
[ 16, 16, 3, 4 ], [ 18, 2, 2, 2 ], [ 20, 1, 1, 4 ], [ 20, 2, 1, 2 ],
[ 23, 4, 4, 4 ], [ 23, 6, 4, 2 ], [ 25, 3, 5, 4 ], [ 29, 10, 4, 4 ],
[ 29, 12, 4, 4 ], [ 29, 13, 4, 4 ] ]
k = 5: F-action on Pi is () [29,7,5]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 1, 4 ],
[ 3, 5, 1, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 3, 1, 4 ],
[ 9, 5, 1, 2 ], [ 16, 6, 1, 8 ], [ 16, 10, 1, 4 ], [ 16, 12, 1, 4 ],
[ 16, 16, 1, 8 ], [ 18, 2, 3, 2 ], [ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ],
[ 23, 4, 5, 4 ], [ 23, 6, 5, 2 ], [ 25, 3, 3, 4 ], [ 29, 10, 5, 4 ],
[ 29, 12, 5, 4 ], [ 29, 13, 5, 4 ] ]
k = 6: F-action on Pi is () [29,7,6]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 2, 2 ], [ 9, 3, 1, 4 ], [ 9, 5, 1, 2 ], [ 11, 1, 2, 4 ],
[ 11, 2, 2, 2 ], [ 16, 6, 2, 8 ], [ 16, 10, 2, 4 ], [ 16, 12, 4, 4 ],
[ 16, 16, 3, 4 ], [ 18, 2, 3, 2 ], [ 20, 1, 4, 4 ], [ 20, 2, 4, 2 ],
[ 23, 4, 6, 4 ], [ 23, 6, 6, 2 ], [ 25, 3, 3, 4 ], [ 29, 10, 6, 4 ],
[ 29, 12, 6, 4 ], [ 29, 13, 6, 4 ] ]
k = 7: F-action on Pi is () [29,7,7]
Dynkin type is (A_1(q) + A_1(q) + T(phi2^4)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 2, 4 ],
[ 3, 5, 2, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 9, 3, 2, 4 ],
[ 9, 5, 2, 2 ], [ 10, 2, 2, 2 ], [ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ],
[ 16, 6, 3, 8 ], [ 16, 10, 3, 4 ], [ 16, 12, 3, 4 ], [ 16, 16, 5, 8 ],
[ 18, 2, 4, 2 ], [ 19, 4, 2, 8 ], [ 19, 5, 2, 4 ], [ 20, 1, 4, 4 ],
[ 20, 2, 4, 2 ], [ 23, 4, 7, 4 ], [ 23, 6, 7, 2 ], [ 25, 3, 7, 4 ],
[ 29, 10, 7, 4 ], [ 29, 12, 7, 4 ], [ 29, 13, 7, 4 ] ]
k = 8: F-action on Pi is () [29,7,8]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 9, 3, 2, 4 ], [ 9, 5, 2, 2 ], [ 10, 2, 2, 2 ],
[ 16, 6, 4, 8 ], [ 16, 10, 4, 4 ], [ 16, 12, 2, 4 ], [ 16, 16, 3, 4 ],
[ 18, 2, 4, 2 ], [ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ], [ 23, 4, 8, 4 ],
[ 23, 6, 8, 2 ], [ 25, 3, 7, 4 ], [ 29, 10, 8, 4 ], [ 29, 12, 8, 4 ],
[ 29, 13, 8, 4 ] ]
k = 9: F-action on Pi is (1,4) [29,7,9]
Dynkin type is (A_1(q^2) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 9, 3, 6, 4 ], [ 9, 5, 6, 2 ], [ 11, 1, 1, 4 ],
[ 11, 2, 1, 2 ], [ 16, 6, 11, 8 ], [ 16, 10, 11, 4 ], [ 16, 12, 15, 4 ],
[ 16, 16, 13, 4 ], [ 18, 2, 3, 2 ], [ 20, 1, 1, 4 ], [ 20, 2, 1, 2 ],
[ 23, 4, 5, 4 ], [ 23, 6, 5, 2 ], [ 25, 3, 2, 4 ], [ 29, 10, 9, 4 ],
[ 29, 12, 9, 4 ], [ 29, 13, 13, 4 ] ]
k = 10: F-action on Pi is (1,4) [29,7,10]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 4, 4 ],
[ 3, 5, 4, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 9, 3, 6, 4 ],
[ 9, 5, 6, 2 ], [ 16, 6, 12, 8 ], [ 16, 10, 12, 4 ], [ 16, 12, 13, 4 ],
[ 16, 16, 14, 4 ], [ 18, 2, 3, 2 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ],
[ 23, 4, 6, 4 ], [ 23, 6, 6, 2 ], [ 25, 3, 2, 4 ], [ 29, 10, 10, 4 ],
[ 29, 12, 10, 4 ], [ 29, 13, 14, 4 ] ]
k = 11: F-action on Pi is (1,4) [29,7,11]
Dynkin type is (A_1(q^2) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 9, 3, 5, 4 ], [ 9, 5, 5, 2 ], [ 10, 2, 2, 2 ],
[ 16, 6, 10, 8 ], [ 16, 10, 10, 4 ], [ 16, 12, 14, 4 ], [ 16, 16, 12, 4 ],
[ 18, 2, 4, 2 ], [ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 23, 4, 7, 4 ],
[ 23, 6, 7, 2 ], [ 25, 3, 6, 4 ], [ 29, 10, 11, 4 ], [ 29, 12, 11, 4 ],
[ 29, 13, 15, 4 ] ]
k = 12: F-action on Pi is (1,4) [29,7,12]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 3, 4 ],
[ 3, 5, 3, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 9, 3, 5, 4 ],
[ 9, 5, 5, 2 ], [ 10, 2, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ],
[ 16, 6, 9, 8 ], [ 16, 10, 9, 4 ], [ 16, 12, 16, 4 ], [ 16, 16, 9, 4 ],
[ 18, 2, 4, 2 ], [ 19, 4, 4, 8 ], [ 19, 5, 4, 4 ], [ 20, 1, 1, 4 ],
[ 20, 2, 1, 2 ], [ 23, 4, 8, 4 ], [ 23, 6, 8, 2 ], [ 25, 3, 6, 4 ],
[ 29, 10, 12, 4 ], [ 29, 12, 12, 4 ], [ 29, 13, 16, 4 ] ]
k = 13: F-action on Pi is (1,4) [29,7,13]
Dynkin type is (A_1(q^2) + T(phi1^3 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 9, 3, 6, 4 ], [ 9, 5, 6, 2 ], [ 10, 2, 1, 2 ],
[ 16, 6, 11, 8 ], [ 16, 10, 11, 4 ], [ 16, 12, 15, 4 ], [ 16, 16, 13, 4 ],
[ 18, 2, 1, 2 ], [ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ], [ 23, 4, 1, 4 ],
[ 23, 6, 1, 2 ], [ 25, 3, 4, 4 ], [ 29, 10, 13, 4 ], [ 29, 12, 13, 4 ],
[ 29, 13, 9, 4 ] ]
k = 14: F-action on Pi is (1,4) [29,7,14]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 4, 4 ],
[ 3, 5, 4, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 2, 2 ], [ 9, 3, 6, 4 ],
[ 9, 5, 6, 2 ], [ 10, 2, 1, 2 ], [ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ],
[ 16, 6, 12, 8 ], [ 16, 10, 12, 4 ], [ 16, 12, 13, 4 ], [ 16, 16, 14, 4 ],
[ 18, 2, 1, 2 ], [ 19, 4, 3, 8 ], [ 19, 5, 3, 4 ], [ 20, 1, 4, 4 ],
[ 20, 2, 4, 2 ], [ 23, 4, 2, 4 ], [ 23, 6, 2, 2 ], [ 25, 3, 4, 4 ],
[ 29, 10, 14, 4 ], [ 29, 12, 14, 4 ], [ 29, 13, 10, 4 ] ]
k = 15: F-action on Pi is (1,4) [29,7,15]
Dynkin type is (A_1(q^2) + T(phi1 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 2, 2 ], [ 9, 3, 5, 4 ], [ 9, 5, 5, 2 ], [ 11, 1, 2, 4 ],
[ 11, 2, 2, 2 ], [ 16, 6, 10, 8 ], [ 16, 10, 10, 4 ], [ 16, 12, 14, 4 ],
[ 16, 16, 12, 4 ], [ 18, 2, 2, 2 ], [ 20, 1, 4, 4 ], [ 20, 2, 4, 2 ],
[ 23, 4, 3, 4 ], [ 23, 6, 3, 2 ], [ 25, 3, 8, 4 ], [ 29, 10, 15, 4 ],
[ 29, 12, 15, 4 ], [ 29, 13, 11, 4 ] ]
k = 16: F-action on Pi is (1,4) [29,7,16]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 3, 4 ],
[ 3, 5, 3, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 3, 5, 4 ],
[ 9, 5, 5, 2 ], [ 16, 6, 9, 8 ], [ 16, 10, 9, 4 ], [ 16, 12, 16, 4 ],
[ 16, 16, 9, 4 ], [ 18, 2, 2, 2 ], [ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ],
[ 23, 4, 4, 4 ], [ 23, 6, 4, 2 ], [ 25, 3, 8, 4 ], [ 29, 10, 16, 4 ],
[ 29, 12, 16, 4 ], [ 29, 13, 12, 4 ] ]
j = 12: Omega of order 4, action on Pi: <(), ()>
k = 1: F-action on Pi is () [29,12,1]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^4)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5, 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 1, 2 ],
[ 8, 1, 1, 2 ], [ 16, 10, 1, 4 ], [ 23, 6, 1, 2 ] ]
k = 2: F-action on Pi is () [29,12,2]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 16, 10, 2, 4 ], [ 23, 6, 2, 2 ] ]
k = 3: F-action on Pi is () [29,12,3]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7, 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 2, 2 ],
[ 8, 1, 1, 2 ], [ 16, 10, 3, 4 ], [ 23, 6, 3, 2 ] ]
k = 4: F-action on Pi is () [29,12,4]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^3 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10, 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 16, 10, 4, 4 ], [ 23, 6, 4, 2 ] ]
k = 5: F-action on Pi is () [29,12,5]
Dynkin type is (A_1(q) + A_1(q) + T(phi1^2 phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7, 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 1, 2 ],
[ 8, 1, 2, 2 ], [ 16, 10, 1, 4 ], [ 23, 6, 5, 2 ] ]
k = 6: F-action on Pi is () [29,12,6]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 16, 10, 2, 4 ], [ 23, 6, 6, 2 ] ]
k = 7: F-action on Pi is () [29,12,7]
Dynkin type is (A_1(q) + A_1(q) + T(phi2^4)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9, 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 2, 2 ],
[ 8, 1, 2, 2 ], [ 16, 10, 3, 4 ], [ 23, 6, 7, 2 ] ]
k = 8: F-action on Pi is () [29,12,8]
Dynkin type is (A_1(q) + A_1(q) + T(phi1 phi2^3)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13, 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 16, 10, 4, 4 ], [ 23, 6, 8, 2 ] ]
k = 9: F-action on Pi is (1,4) [29,12,9]
Dynkin type is (A_1(q^2) + T(phi1^3 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 16, 10, 11, 4 ], [ 23, 6, 5, 2 ] ]
k = 10: F-action on Pi is (1,4) [29,12,10]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 4, 2 ],
[ 8, 1, 1, 2 ], [ 16, 10, 12, 4 ], [ 23, 6, 6, 2 ] ]
k = 11: F-action on Pi is (1,4) [29,12,11]
Dynkin type is (A_1(q^2) + T(phi1 phi2^3)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 16, 10, 10, 4 ], [ 23, 6, 7, 2 ] ]
k = 12: F-action on Pi is (1,4) [29,12,12]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 3, 2 ],
[ 8, 1, 1, 2 ], [ 16, 10, 9, 4 ], [ 23, 6, 8, 2 ] ]
k = 13: F-action on Pi is (1,4) [29,12,13]
Dynkin type is (A_1(q^2) + T(phi1^3 phi2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 10, 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 16, 10, 11, 4 ], [ 23, 6, 1, 2 ] ]
k = 14: F-action on Pi is (1,4) [29,12,14]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 4, 2 ],
[ 8, 1, 2, 2 ], [ 16, 10, 12, 4 ], [ 23, 6, 2, 2 ] ]
k = 15: F-action on Pi is (1,4) [29,12,15]
Dynkin type is (A_1(q^2) + T(phi1 phi2^3)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 13, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 2, 2 ],
[ 16, 10, 10, 4 ], [ 23, 6, 3, 2 ] ]
k = 16: F-action on Pi is (1,4) [29,12,16]
Dynkin type is (A_1(q^2) + T(phi1^2 phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 3, 2 ],
[ 8, 1, 2, 2 ], [ 16, 10, 9, 4 ], [ 23, 6, 4, 2 ] ]
i = 30: Pi = [ 1 ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [30,1,1]
Dynkin type is A_1(q) + T(phi1^5)
Order of center |Z^F|: phi1^5
Numbers of classes in class type:
q congruent 0 modulo
4: 1/384 ( q^5-26*q^4+260*q^3-1240*q^2+2784*q-2304 )
q congruent 1 modulo
4: 1/384 ( q^5-26*q^4+254*q^3-1168*q^2+2601*q-2430 )
q congruent 2 modulo
4: 1/384 ( q^5-26*q^4+260*q^3-1240*q^2+2784*q-2304 )
q congruent 3 modulo
4: 1/384 ( q^5-26*q^4+254*q^3-1168*q^2+2553*q-2142 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 1, 16 ],
[ 3, 2, 1, 8 ], [ 3, 3, 1, 8 ], [ 3, 4, 1, 8 ], [ 3, 5, 1, 4 ],
[ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 5, 1, 1, 26 ], [ 6, 1, 1, 48 ],
[ 7, 1, 1, 64 ], [ 7, 2, 1, 32 ], [ 7, 3, 1, 32 ], [ 7, 4, 1, 32 ],
[ 7, 5, 1, 16 ], [ 8, 1, 1, 64 ], [ 9, 1, 1, 120 ], [ 9, 2, 1, 60 ],
[ 9, 3, 1, 60 ], [ 9, 4, 1, 60 ], [ 9, 5, 1, 30 ], [ 10, 1, 1, 16 ],
[ 10, 2, 1, 8 ], [ 11, 1, 1, 16 ], [ 11, 2, 1, 8 ], [ 12, 1, 1, 48 ],
[ 12, 2, 1, 24 ], [ 12, 3, 1, 24 ], [ 12, 4, 1, 12 ], [ 13, 1, 1, 112 ],
[ 13, 2, 1, 56 ], [ 14, 1, 1, 160 ], [ 14, 2, 1, 80 ], [ 15, 1, 1, 192 ],
[ 16, 1, 1, 192 ], [ 16, 2, 1, 96 ], [ 16, 3, 1, 96 ], [ 16, 4, 1, 96 ],
[ 16, 5, 1, 96 ], [ 16, 6, 1, 96 ], [ 16, 7, 1, 96 ], [ 16, 8, 1, 96 ],
[ 16, 9, 1, 48 ], [ 16, 10, 1, 48 ], [ 16, 11, 1, 48 ], [ 16, 12, 1, 48 ],
[ 16, 13, 1, 48 ], [ 16, 14, 1, 48 ], [ 16, 15, 1, 48 ], [ 16, 16, 1, 48 ],
[ 16, 17, 1, 48 ], [ 17, 1, 1, 64 ], [ 17, 2, 1, 32 ], [ 18, 1, 1, 112 ],
[ 18, 2, 1, 56 ], [ 19, 1, 1, 128 ], [ 19, 2, 1, 64 ], [ 19, 3, 1, 64 ],
[ 19, 4, 1, 64 ], [ 19, 5, 1, 32 ], [ 20, 1, 1, 112 ], [ 20, 2, 1, 56 ],
[ 21, 1, 1, 192 ], [ 21, 2, 1, 96 ], [ 21, 3, 1, 96 ], [ 21, 4, 1, 96 ],
[ 21, 5, 1, 48 ], [ 21, 6, 1, 48 ], [ 21, 7, 1, 48 ], [ 22, 1, 1, 288 ],
[ 22, 2, 1, 144 ], [ 22, 3, 1, 144 ], [ 22, 4, 1, 72 ], [ 23, 1, 1, 192 ],
[ 23, 2, 1, 96 ], [ 23, 3, 1, 96 ], [ 23, 4, 1, 96 ], [ 23, 5, 1, 96 ],
[ 23, 6, 1, 48 ], [ 24, 1, 1, 256 ], [ 24, 2, 1, 128 ], [ 25, 1, 1, 288 ],
[ 25, 2, 1, 144 ], [ 25, 3, 1, 144 ], [ 26, 1, 1, 288 ], [ 26, 2, 1, 144 ],
[ 26, 3, 1, 144 ], [ 27, 1, 1, 384 ], [ 27, 2, 1, 192 ], [ 27, 3, 1, 192 ],
[ 27, 4, 1, 192 ], [ 27, 5, 1, 192 ], [ 27, 6, 1, 96 ], [ 27, 7, 1, 96 ],
[ 27, 8, 1, 96 ], [ 27, 9, 1, 96 ], [ 27, 10, 1, 96 ], [ 27, 11, 1, 96 ],
[ 27, 12, 1, 96 ], [ 27, 13, 1, 96 ], [ 27, 14, 1, 96 ], [ 28, 1, 1, 384 ],
[ 28, 2, 1, 192 ], [ 28, 3, 1, 192 ], [ 28, 4, 1, 192 ], [ 28, 5, 1, 96 ],
[ 28, 6, 1, 96 ], [ 29, 1, 1, 384 ], [ 29, 2, 1, 192 ], [ 29, 3, 1, 192 ],
[ 29, 4, 1, 192 ], [ 29, 5, 1, 192 ], [ 29, 6, 1, 192 ], [ 29, 7, 1, 192 ],
[ 29, 8, 1, 192 ], [ 29, 9, 1, 96 ], [ 29, 10, 1, 96 ], [ 29, 11, 1, 96 ],
[ 29, 12, 1, 96 ], [ 29, 13, 1, 96 ], [ 30, 2, 1, 192 ], [ 30, 3, 1, 192 ],
[ 30, 4, 1, 192 ], [ 30, 5, 1, 192 ], [ 30, 6, 1, 192 ], [ 30, 7, 1, 192 ],
[ 30, 8, 1, 96 ], [ 30, 9, 1, 96 ], [ 30, 10, 1, 96 ], [ 30, 11, 1, 96 ],
[ 30, 12, 1, 96 ], [ 30, 13, 1, 96 ] ]
k = 2: F-action on Pi is () [30,1,2]
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 0 modulo 4: 1/32 q ( q^4-12*q^3+52*q^2-96*q+64 )
q congruent 1 modulo 4: 1/32 phi1^3 ( q^2-9*q+20 )
q congruent 2 modulo 4: 1/32 q ( q^4-12*q^3+52*q^2-96*q+64 )
q congruent 3 modulo 4: 1/32 ( q^5-12*q^4+50*q^3-88*q^2+69*q-36 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 8 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 16 ], [ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ],
[ 7, 4, 1, 8 ], [ 7, 5, 1, 4 ], [ 8, 1, 1, 20 ], [ 9, 1, 1, 32 ],
[ 9, 1, 2, 8 ], [ 9, 2, 1, 16 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 16 ],
[ 9, 3, 2, 4 ], [ 9, 4, 1, 16 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 8 ],
[ 9, 5, 2, 2 ], [ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ], [ 11, 1, 1, 8 ],
[ 11, 2, 1, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ], [ 12, 2, 1, 4 ],
[ 12, 2, 2, 2 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ],
[ 13, 1, 1, 16 ], [ 13, 1, 2, 8 ], [ 13, 2, 1, 8 ], [ 13, 2, 2, 4 ],
[ 14, 1, 1, 32 ], [ 14, 2, 1, 16 ], [ 15, 1, 1, 40 ], [ 15, 1, 4, 12 ],
[ 16, 1, 1, 32 ], [ 16, 1, 3, 16 ], [ 16, 2, 1, 16 ], [ 16, 2, 3, 8 ],
[ 16, 3, 1, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 1, 16 ], [ 16, 4, 3, 8 ],
[ 16, 5, 1, 16 ], [ 16, 5, 2, 8 ], [ 16, 5, 4, 8 ], [ 16, 6, 1, 16 ],
[ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 1, 16 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 8, 1, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 3, 4 ],
[ 16, 10, 1, 8 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 1, 8 ],
[ 16, 11, 3, 8 ], [ 16, 12, 1, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ],
[ 16, 13, 1, 8 ], [ 16, 13, 3, 4 ], [ 16, 14, 1, 8 ], [ 16, 15, 1, 8 ],
[ 16, 15, 3, 4 ], [ 16, 16, 1, 8 ], [ 16, 16, 3, 4 ], [ 16, 17, 1, 8 ],
[ 17, 1, 1, 16 ], [ 17, 2, 1, 8 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 8 ],
[ 18, 2, 1, 12 ], [ 18, 2, 2, 4 ], [ 19, 1, 1, 32 ], [ 19, 2, 1, 16 ],
[ 19, 3, 1, 16 ], [ 19, 4, 1, 16 ], [ 19, 5, 1, 8 ], [ 20, 1, 1, 24 ],
[ 20, 1, 2, 8 ], [ 20, 2, 1, 12 ], [ 20, 2, 2, 4 ], [ 21, 1, 5, 16 ],
[ 21, 2, 2, 8 ], [ 21, 3, 3, 8 ], [ 21, 4, 2, 8 ], [ 21, 5, 2, 4 ],
[ 21, 6, 3, 8 ], [ 21, 7, 2, 8 ], [ 22, 1, 1, 32 ], [ 22, 1, 2, 24 ],
[ 22, 1, 4, 16 ], [ 22, 2, 1, 16 ], [ 22, 2, 2, 12 ], [ 22, 2, 4, 8 ],
[ 22, 3, 1, 16 ], [ 22, 3, 3, 8 ], [ 22, 4, 1, 8 ], [ 22, 4, 2, 12 ],
[ 22, 4, 4, 4 ], [ 23, 1, 1, 16 ], [ 23, 1, 2, 16 ], [ 23, 1, 4, 16 ],
[ 23, 2, 1, 8 ], [ 23, 2, 2, 8 ], [ 23, 2, 4, 8 ], [ 23, 3, 1, 8 ],
[ 23, 3, 2, 8 ], [ 23, 3, 4, 8 ], [ 23, 4, 1, 8 ], [ 23, 4, 2, 8 ],
[ 23, 4, 4, 8 ], [ 23, 5, 1, 8 ], [ 23, 5, 2, 8 ], [ 23, 5, 4, 8 ],
[ 23, 6, 1, 4 ], [ 23, 6, 2, 4 ], [ 23, 6, 4, 4 ], [ 24, 1, 1, 32 ],
[ 24, 1, 2, 16 ], [ 24, 2, 1, 16 ], [ 24, 2, 2, 8 ], [ 25, 1, 1, 48 ],
[ 25, 1, 2, 16 ], [ 25, 2, 1, 24 ], [ 25, 2, 2, 8 ], [ 25, 3, 1, 24 ],
[ 25, 3, 5, 8 ], [ 26, 1, 1, 48 ], [ 26, 1, 2, 16 ], [ 26, 2, 1, 24 ],
[ 26, 2, 2, 8 ], [ 26, 3, 1, 24 ], [ 26, 3, 5, 8 ], [ 27, 1, 6, 32 ],
[ 27, 2, 2, 16 ], [ 27, 3, 2, 16 ], [ 27, 3, 6, 16 ], [ 27, 4, 3, 16 ],
[ 27, 5, 2, 16 ], [ 27, 6, 2, 8 ], [ 27, 7, 2, 8 ], [ 27, 8, 2, 8 ],
[ 27, 8, 6, 16 ], [ 27, 9, 2, 8 ], [ 27, 10, 5, 8 ], [ 27, 11, 2, 8 ],
[ 27, 11, 6, 16 ], [ 27, 12, 3, 16 ], [ 27, 13, 3, 8 ], [ 27, 14, 3, 8 ],
[ 27, 14, 8, 16 ], [ 28, 1, 2, 32 ], [ 28, 2, 2, 16 ], [ 28, 3, 2, 16 ],
[ 28, 4, 2, 16 ], [ 28, 4, 4, 16 ], [ 28, 5, 2, 8 ], [ 28, 6, 2, 16 ],
[ 29, 1, 1, 32 ], [ 29, 1, 2, 32 ], [ 29, 1, 4, 32 ], [ 29, 1, 5, 16 ],
[ 29, 2, 1, 16 ], [ 29, 2, 2, 16 ], [ 29, 2, 4, 16 ], [ 29, 2, 5, 8 ],
[ 29, 3, 1, 16 ], [ 29, 3, 2, 16 ], [ 29, 3, 4, 16 ], [ 29, 3, 5, 8 ],
[ 29, 4, 1, 16 ], [ 29, 4, 2, 16 ], [ 29, 4, 4, 16 ], [ 29, 4, 5, 8 ],
[ 29, 5, 1, 16 ], [ 29, 5, 2, 16 ], [ 29, 5, 4, 16 ], [ 29, 5, 5, 8 ],
[ 29, 6, 1, 16 ], [ 29, 6, 2, 16 ], [ 29, 6, 4, 16 ], [ 29, 7, 1, 16 ],
[ 29, 7, 2, 16 ], [ 29, 7, 4, 16 ], [ 29, 8, 1, 16 ], [ 29, 8, 2, 16 ],
[ 29, 8, 4, 16 ], [ 29, 9, 1, 8 ], [ 29, 9, 2, 8 ], [ 29, 9, 4, 8 ],
[ 29, 9, 5, 4 ], [ 29, 10, 1, 8 ], [ 29, 10, 2, 8 ], [ 29, 10, 4, 8 ],
[ 29, 11, 1, 8 ], [ 29, 11, 2, 8 ], [ 29, 11, 4, 8 ], [ 29, 12, 1, 8 ],
[ 29, 12, 2, 8 ], [ 29, 12, 4, 8 ], [ 29, 13, 1, 8 ], [ 29, 13, 2, 8 ],
[ 29, 13, 4, 8 ], [ 30, 2, 2, 16 ], [ 30, 3, 2, 16 ], [ 30, 4, 3, 16 ],
[ 30, 4, 8, 16 ], [ 30, 5, 2, 16 ], [ 30, 5, 4, 16 ], [ 30, 6, 2, 16 ],
[ 30, 6, 4, 16 ], [ 30, 7, 2, 16 ], [ 30, 7, 4, 16 ], [ 30, 7, 6, 16 ],
[ 30, 7, 15, 16 ], [ 30, 8, 3, 8 ], [ 30, 9, 3, 8 ], [ 30, 10, 3, 8 ],
[ 30, 11, 2, 8 ], [ 30, 11, 4, 8 ], [ 30, 11, 6, 8 ], [ 30, 11, 15, 8 ],
[ 30, 12, 3, 8 ], [ 30, 12, 8, 8 ], [ 30, 13, 2, 16 ] ]
k = 3: F-action on Pi is () [30,1,3]
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 0 modulo 4: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 )
q congruent 1 modulo 4: 1/64 phi1 ( q^4-9*q^3+13*q^2+61*q-130 )
q congruent 2 modulo 4: 1/64 q ( q^4-10*q^3+28*q^2-8*q-32 )
q congruent 3 modulo 4: 1/64 ( q^5-10*q^4+22*q^3+48*q^2-207*q+162 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 3, 2, 1, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 1, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 1, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 6 ],
[ 5, 1, 2, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ],
[ 7, 1, 3, 16 ], [ 7, 1, 4, 16 ], [ 7, 2, 1, 8 ], [ 7, 2, 2, 8 ],
[ 7, 2, 3, 8 ], [ 7, 2, 4, 8 ], [ 7, 3, 1, 8 ], [ 7, 3, 2, 8 ],
[ 7, 3, 3, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 1, 8 ], [ 7, 4, 2, 8 ],
[ 7, 4, 3, 8 ], [ 7, 4, 4, 8 ], [ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ],
[ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 24 ],
[ 9, 1, 2, 16 ], [ 9, 1, 3, 16 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 8 ],
[ 9, 2, 3, 8 ], [ 9, 3, 1, 12 ], [ 9, 3, 2, 8 ], [ 9, 3, 3, 8 ],
[ 9, 4, 1, 12 ], [ 9, 4, 2, 8 ], [ 9, 4, 3, 8 ], [ 9, 5, 1, 6 ],
[ 9, 5, 2, 4 ], [ 9, 5, 3, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 3, 8 ],
[ 12, 1, 4, 16 ], [ 12, 2, 1, 4 ], [ 12, 2, 3, 4 ], [ 12, 2, 4, 8 ],
[ 12, 3, 1, 4 ], [ 12, 3, 2, 4 ], [ 12, 3, 3, 8 ], [ 12, 3, 4, 8 ],
[ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ], [ 13, 1, 1, 8 ],
[ 13, 1, 2, 16 ], [ 13, 1, 3, 24 ], [ 13, 2, 1, 4 ], [ 13, 2, 2, 8 ],
[ 13, 2, 3, 12 ], [ 14, 1, 1, 16 ], [ 14, 1, 3, 32 ], [ 14, 2, 1, 8 ],
[ 14, 2, 3, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 4, 24 ], [ 16, 1, 1, 32 ],
[ 16, 1, 2, 32 ], [ 16, 1, 5, 32 ], [ 16, 2, 1, 16 ], [ 16, 2, 2, 16 ],
[ 16, 2, 5, 16 ], [ 16, 3, 1, 16 ], [ 16, 3, 2, 16 ], [ 16, 3, 5, 16 ],
[ 16, 4, 1, 16 ], [ 16, 4, 2, 16 ], [ 16, 4, 5, 16 ], [ 16, 5, 1, 16 ],
[ 16, 5, 3, 16 ], [ 16, 6, 1, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 1, 16 ],
[ 16, 7, 3, 16 ], [ 16, 8, 1, 16 ], [ 16, 8, 2, 16 ], [ 16, 8, 3, 16 ],
[ 16, 8, 4, 16 ], [ 16, 8, 6, 16 ], [ 16, 8, 7, 16 ], [ 16, 9, 1, 8 ],
[ 16, 9, 2, 8 ], [ 16, 9, 5, 8 ], [ 16, 10, 1, 8 ], [ 16, 10, 3, 8 ],
[ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ], [ 16, 11, 5, 8 ], [ 16, 11, 7, 8 ],
[ 16, 12, 1, 8 ], [ 16, 12, 3, 8 ], [ 16, 13, 1, 8 ], [ 16, 13, 2, 16 ],
[ 16, 13, 5, 8 ], [ 16, 14, 1, 8 ], [ 16, 14, 2, 8 ], [ 16, 14, 3, 8 ],
[ 16, 14, 4, 8 ], [ 16, 15, 1, 8 ], [ 16, 15, 2, 16 ], [ 16, 15, 5, 8 ],
[ 16, 16, 1, 8 ], [ 16, 16, 2, 16 ], [ 16, 16, 5, 8 ], [ 16, 17, 1, 8 ],
[ 16, 17, 2, 8 ], [ 16, 17, 3, 8 ], [ 16, 17, 4, 8 ], [ 18, 1, 2, 16 ],
[ 18, 2, 2, 8 ], [ 20, 1, 2, 16 ], [ 20, 2, 2, 8 ], [ 21, 1, 2, 32 ],
[ 21, 1, 3, 32 ], [ 21, 2, 3, 16 ], [ 21, 2, 4, 16 ], [ 21, 2, 6, 16 ],
[ 21, 2, 8, 16 ], [ 21, 3, 2, 16 ], [ 21, 3, 5, 16 ], [ 21, 3, 6, 16 ],
[ 21, 3, 7, 16 ], [ 21, 4, 3, 16 ], [ 21, 4, 6, 16 ], [ 21, 5, 3, 8 ],
[ 21, 5, 4, 8 ], [ 21, 5, 6, 8 ], [ 21, 5, 8, 8 ], [ 21, 6, 2, 8 ],
[ 21, 6, 5, 8 ], [ 21, 6, 6, 8 ], [ 21, 6, 7, 8 ], [ 21, 7, 3, 8 ],
[ 21, 7, 6, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 3, 48 ], [ 22, 1, 4, 32 ],
[ 22, 1, 7, 32 ], [ 22, 2, 1, 8 ], [ 22, 2, 3, 24 ], [ 22, 2, 4, 16 ],
[ 22, 2, 7, 16 ], [ 22, 3, 1, 8 ], [ 22, 3, 2, 24 ], [ 22, 3, 3, 16 ],
[ 22, 3, 5, 16 ], [ 22, 3, 6, 16 ], [ 22, 4, 1, 4 ], [ 22, 4, 3, 12 ],
[ 22, 4, 4, 8 ], [ 22, 4, 7, 8 ], [ 23, 1, 3, 32 ], [ 23, 2, 3, 16 ],
[ 23, 3, 3, 16 ], [ 23, 4, 3, 16 ], [ 23, 5, 3, 16 ], [ 23, 6, 3, 8 ],
[ 24, 1, 2, 32 ], [ 24, 2, 2, 16 ], [ 25, 1, 2, 32 ], [ 25, 2, 2, 16 ],
[ 25, 3, 5, 16 ], [ 26, 1, 2, 32 ], [ 26, 2, 2, 16 ], [ 26, 3, 5, 16 ],
[ 27, 1, 3, 64 ], [ 27, 2, 3, 32 ], [ 27, 2, 6, 32 ], [ 27, 3, 3, 32 ],
[ 27, 3, 4, 32 ], [ 27, 3, 11, 32 ], [ 27, 4, 2, 32 ], [ 27, 4, 5, 32 ],
[ 27, 5, 3, 32 ], [ 27, 6, 3, 16 ], [ 27, 6, 4, 16 ], [ 27, 6, 6, 16 ],
[ 27, 6, 8, 16 ], [ 27, 7, 3, 16 ], [ 27, 7, 6, 16 ], [ 27, 8, 3, 16 ],
[ 27, 8, 4, 16 ], [ 27, 8, 11, 16 ], [ 27, 9, 3, 16 ], [ 27, 9, 4, 16 ],
[ 27, 10, 2, 16 ], [ 27, 10, 3, 16 ], [ 27, 10, 4, 16 ], [ 27, 10, 9, 16 ],
[ 27, 11, 3, 16 ], [ 27, 11, 4, 16 ], [ 27, 11, 11, 16 ], [ 27, 12, 2, 16 ],
[ 27, 12, 5, 16 ], [ 27, 13, 2, 16 ], [ 27, 13, 5, 16 ], [ 27, 13, 6, 16 ],
[ 27, 13, 7, 16 ], [ 27, 14, 2, 16 ], [ 27, 14, 5, 16 ], [ 27, 14, 11, 16 ],
[ 28, 1, 3, 64 ], [ 28, 2, 3, 32 ], [ 28, 2, 4, 32 ], [ 28, 3, 3, 32 ],
[ 28, 4, 3, 32 ], [ 28, 5, 3, 16 ], [ 28, 5, 4, 32 ], [ 28, 6, 3, 16 ],
[ 29, 1, 3, 64 ], [ 29, 1, 5, 32 ], [ 29, 2, 3, 32 ], [ 29, 2, 5, 16 ],
[ 29, 3, 3, 32 ], [ 29, 3, 5, 16 ], [ 29, 4, 3, 32 ], [ 29, 4, 5, 16 ],
[ 29, 5, 3, 32 ], [ 29, 5, 5, 16 ], [ 29, 6, 3, 32 ], [ 29, 7, 3, 32 ],
[ 29, 8, 3, 32 ], [ 29, 9, 3, 16 ], [ 29, 9, 5, 8 ], [ 29, 10, 3, 16 ],
[ 29, 11, 3, 16 ], [ 29, 12, 3, 16 ], [ 29, 13, 3, 16 ], [ 30, 2, 3, 32 ],
[ 30, 3, 3, 32 ], [ 30, 4, 2, 32 ], [ 30, 4, 5, 32 ], [ 30, 4, 12, 32 ],
[ 30, 5, 3, 32 ], [ 30, 6, 3, 32 ], [ 30, 7, 3, 32 ], [ 30, 7, 9, 32 ],
[ 30, 8, 2, 16 ], [ 30, 8, 5, 16 ], [ 30, 9, 2, 32 ], [ 30, 9, 5, 16 ],
[ 30, 10, 2, 32 ], [ 30, 10, 5, 16 ], [ 30, 11, 3, 16 ], [ 30, 11, 9, 16 ],
[ 30, 12, 2, 32 ], [ 30, 12, 5, 16 ], [ 30, 12, 12, 16 ], [ 30, 13, 3, 16 ],
[ 30, 13, 6, 16 ] ]
k = 4: F-action on Pi is () [30,1,4]
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 0 modulo 4: 1/12 q phi1 phi2 ( q^2-5*q+6 )
q congruent 1 modulo 4: 1/12 q phi1 phi2 ( q^2-5*q+6 )
q congruent 2 modulo 4: 1/12 q phi1 phi2 ( q^2-5*q+6 )
q congruent 3 modulo 4: 1/12 q phi1 phi2 ( q^2-5*q+6 )
Fusion of maximal tori of C^F in those of G^F:
[ 18, 22 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 1, 6 ],
[ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ],
[ 7, 5, 1, 1 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ],
[ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 13, 1, 1, 4 ], [ 13, 2, 1, 2 ],
[ 14, 1, 1, 4 ], [ 14, 2, 1, 2 ], [ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ],
[ 18, 1, 1, 4 ], [ 18, 2, 1, 2 ], [ 19, 1, 1, 8 ], [ 19, 2, 1, 4 ],
[ 19, 3, 1, 4 ], [ 19, 4, 1, 4 ], [ 19, 5, 1, 2 ], [ 20, 1, 1, 4 ],
[ 20, 2, 1, 2 ], [ 21, 1, 9, 6 ], [ 21, 4, 4, 3 ], [ 21, 7, 4, 6 ],
[ 24, 1, 1, 4 ], [ 24, 2, 1, 2 ], [ 27, 1, 15, 12 ], [ 27, 2, 4, 6 ],
[ 27, 4, 6, 6 ], [ 27, 5, 4, 6 ], [ 27, 7, 4, 3 ], [ 27, 12, 6, 12 ],
[ 28, 1, 4, 12 ], [ 28, 3, 4, 6 ], [ 28, 6, 4, 12 ], [ 30, 2, 4, 6 ],
[ 30, 3, 4, 6 ], [ 30, 13, 4, 12 ] ]
k = 5: F-action on Pi is () [30,1,5]
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 0 modulo 4: 1/16 q^2 ( q^3-4*q^2+8 )
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q^3-4*q^2-q+12 )
q congruent 2 modulo 4: 1/16 q^2 ( q^3-4*q^2+8 )
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q^3-4*q^2-q+12 )
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ],
[ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 1 ], [ 9, 1, 3, 8 ], [ 9, 2, 3, 4 ], [ 9, 3, 3, 4 ],
[ 9, 4, 3, 4 ], [ 9, 5, 3, 2 ], [ 12, 1, 4, 4 ], [ 12, 1, 5, 4 ],
[ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ],
[ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ],
[ 13, 2, 1, 2 ], [ 13, 2, 3, 2 ], [ 14, 1, 3, 8 ], [ 14, 2, 3, 4 ],
[ 16, 1, 2, 8 ], [ 16, 1, 4, 8 ], [ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ],
[ 16, 3, 2, 4 ], [ 16, 3, 4, 4 ], [ 16, 4, 2, 4 ], [ 16, 4, 4, 4 ],
[ 16, 8, 2, 4 ], [ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ],
[ 16, 9, 2, 2 ], [ 16, 9, 4, 2 ], [ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ],
[ 16, 11, 7, 2 ], [ 16, 11, 9, 4 ], [ 16, 13, 2, 4 ], [ 16, 13, 4, 4 ],
[ 16, 14, 2, 2 ], [ 16, 14, 3, 2 ], [ 16, 15, 2, 4 ], [ 16, 15, 4, 4 ],
[ 16, 16, 2, 4 ], [ 16, 16, 4, 4 ], [ 16, 17, 2, 2 ], [ 16, 17, 3, 2 ],
[ 21, 1, 6, 8 ], [ 21, 1, 8, 8 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 4 ],
[ 21, 3, 4, 4 ], [ 21, 3, 9, 4 ], [ 21, 4, 5, 4 ], [ 21, 4, 7, 4 ],
[ 21, 5, 5, 2 ], [ 21, 5, 7, 2 ], [ 21, 6, 4, 4 ], [ 21, 6, 8, 4 ],
[ 21, 7, 5, 4 ], [ 21, 7, 7, 4 ], [ 22, 1, 7, 8 ], [ 22, 1, 8, 8 ],
[ 22, 2, 7, 4 ], [ 22, 2, 8, 4 ], [ 22, 3, 5, 4 ], [ 22, 3, 6, 4 ],
[ 22, 4, 7, 2 ], [ 22, 4, 8, 4 ], [ 27, 1, 9, 16 ], [ 27, 2, 5, 8 ],
[ 27, 2, 7, 8 ], [ 27, 3, 5, 8 ], [ 27, 3, 9, 8 ], [ 27, 4, 4, 8 ],
[ 27, 4, 9, 8 ], [ 27, 5, 5, 8 ], [ 27, 6, 5, 4 ], [ 27, 6, 7, 4 ],
[ 27, 7, 5, 4 ], [ 27, 7, 7, 4 ], [ 27, 8, 5, 4 ], [ 27, 8, 9, 8 ],
[ 27, 9, 5, 4 ], [ 27, 10, 7, 4 ], [ 27, 10, 8, 4 ], [ 27, 11, 5, 4 ],
[ 27, 11, 9, 8 ], [ 27, 12, 4, 8 ], [ 27, 12, 9, 8 ], [ 27, 13, 4, 4 ],
[ 27, 13, 9, 4 ], [ 27, 14, 4, 4 ], [ 27, 14, 9, 8 ], [ 28, 1, 5, 16 ],
[ 28, 2, 5, 8 ], [ 28, 3, 5, 8 ], [ 28, 5, 5, 8 ], [ 28, 6, 5, 8 ],
[ 30, 2, 5, 8 ], [ 30, 3, 5, 8 ], [ 30, 4, 4, 8 ], [ 30, 4, 9, 8 ],
[ 30, 8, 4, 4 ], [ 30, 9, 4, 8 ], [ 30, 10, 4, 8 ], [ 30, 12, 4, 8 ],
[ 30, 12, 9, 8 ], [ 30, 13, 5, 8 ], [ 30, 13, 7, 8 ] ]
k = 6: F-action on Pi is () [30,1,6]
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 0 modulo 4: 1/16 q^2 ( q^3-2*q^2-2*q+4 )
q congruent 1 modulo 4: 1/16 q phi1 phi2 ( q^2-2*q-1 )
q congruent 2 modulo 4: 1/16 q^2 ( q^3-2*q^2-2*q+4 )
q congruent 3 modulo 4: 1/16 q phi1 phi2 ( q^2-2*q-1 )
Fusion of maximal tori of C^F in those of G^F:
[ 28, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ],
[ 9, 3, 6, 4 ], [ 9, 4, 6, 4 ], [ 9, 5, 6, 2 ], [ 10, 1, 1, 4 ],
[ 10, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 18, 1, 1, 4 ],
[ 18, 1, 3, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 3, 2 ], [ 25, 1, 5, 8 ],
[ 25, 1, 6, 8 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 2, 4 ],
[ 25, 3, 4, 4 ], [ 27, 1, 19, 8 ], [ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ],
[ 30, 2, 6, 8 ], [ 30, 3, 6, 8 ], [ 30, 5, 5, 8 ], [ 30, 5, 8, 8 ],
[ 30, 8, 6, 8 ], [ 30, 9, 6, 4 ], [ 30, 10, 6, 8 ] ]
k = 7: F-action on Pi is () [30,1,7]
Dynkin type is A_1(q) + T(phi1 phi2^2 phi6)
Order of center |Z^F|: phi1 phi2^2 phi6
Numbers of classes in class type:
q congruent 0 modulo 4: 1/12 q phi1 phi2^2 ( q-2 )
q congruent 1 modulo 4: 1/12 q phi1 phi2^2 ( q-2 )
q congruent 2 modulo 4: 1/12 q phi1 phi2^2 ( q-2 )
q congruent 3 modulo 4: 1/12 q phi1 phi2^2 ( q-2 )
Fusion of maximal tori of C^F in those of G^F:
[ 19, 24 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 6, 1, 2, 2 ],
[ 7, 1, 4, 4 ], [ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ],
[ 7, 5, 4, 1 ], [ 8, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 2, 3, 2 ],
[ 14, 1, 2, 4 ], [ 14, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 2, 3, 2 ],
[ 20, 1, 3, 4 ], [ 20, 2, 3, 2 ], [ 21, 1, 10, 6 ], [ 21, 4, 8, 3 ],
[ 21, 7, 8, 6 ], [ 24, 1, 3, 4 ], [ 24, 2, 3, 2 ], [ 27, 1, 18, 12 ],
[ 27, 2, 8, 6 ], [ 27, 4, 7, 6 ], [ 27, 5, 7, 6 ], [ 27, 7, 8, 3 ],
[ 27, 12, 7, 12 ], [ 30, 2, 7, 6 ], [ 30, 3, 7, 6 ], [ 30, 13, 8, 12 ] ]
k = 8: F-action on Pi is () [30,1,8]
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 0 modulo 4: 1/16 q^2 ( q^3-2*q^2-2*q+4 )
q congruent 1 modulo 4: 1/16 q phi1 phi2 ( q^2-2*q-1 )
q congruent 2 modulo 4: 1/16 q^2 ( q^3-2*q^2-2*q+4 )
q congruent 3 modulo 4: 1/16 q phi1 phi2 ( q^2-2*q-1 )
Fusion of maximal tori of C^F in those of G^F:
[ 28, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ],
[ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 8, 2 ], [ 11, 1, 1, 4 ],
[ 11, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 20, 1, 1, 4 ],
[ 20, 1, 3, 4 ], [ 20, 2, 1, 2 ], [ 20, 2, 3, 2 ], [ 26, 1, 5, 8 ],
[ 26, 1, 6, 8 ], [ 26, 2, 3, 4 ], [ 26, 2, 4, 4 ], [ 26, 3, 2, 4 ],
[ 26, 3, 4, 4 ], [ 27, 1, 19, 8 ], [ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ],
[ 30, 2, 8, 8 ], [ 30, 3, 8, 8 ], [ 30, 6, 5, 8 ], [ 30, 6, 8, 8 ],
[ 30, 8, 7, 8 ], [ 30, 9, 7, 8 ], [ 30, 10, 7, 4 ] ]
k = 9: F-action on Pi is () [30,1,9]
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 0 modulo 4: 1/64 q ( q^4-6*q^3+8*q^2+8*q-16 )
q congruent 1 modulo 4: 1/64 phi1 ( q^4-5*q^3+q^2+5*q+30 )
q congruent 2 modulo 4: 1/64 q ( q^4-6*q^3+8*q^2+8*q-16 )
q congruent 3 modulo 4: 1/64 ( q^5-6*q^4+6*q^3+4*q^2+41*q-78 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 5, 1, 2, 4 ], [ 8, 1, 1, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 24 ],
[ 9, 1, 2, 16 ], [ 9, 1, 6, 16 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 8 ],
[ 9, 2, 6, 8 ], [ 9, 3, 1, 12 ], [ 9, 3, 2, 8 ], [ 9, 3, 6, 8 ],
[ 9, 4, 1, 12 ], [ 9, 4, 2, 8 ], [ 9, 4, 6, 8 ], [ 9, 5, 1, 6 ],
[ 9, 5, 2, 4 ], [ 9, 5, 6, 4 ], [ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ],
[ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ], [ 12, 4, 2, 4 ], [ 15, 1, 1, 24 ],
[ 15, 1, 2, 16 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 16 ], [ 16, 1, 3, 32 ],
[ 16, 2, 3, 16 ], [ 16, 3, 3, 16 ], [ 16, 4, 3, 16 ], [ 16, 5, 2, 16 ],
[ 16, 5, 4, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 4, 16 ], [ 16, 7, 2, 16 ],
[ 16, 7, 4, 16 ], [ 16, 9, 3, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ],
[ 16, 11, 3, 16 ], [ 16, 12, 2, 8 ], [ 16, 12, 4, 8 ], [ 16, 13, 3, 8 ],
[ 16, 15, 3, 8 ], [ 16, 16, 3, 8 ], [ 18, 1, 1, 24 ], [ 18, 1, 3, 8 ],
[ 18, 2, 1, 12 ], [ 18, 2, 3, 4 ], [ 20, 1, 2, 16 ], [ 20, 2, 2, 8 ],
[ 22, 1, 2, 32 ], [ 22, 1, 5, 16 ], [ 22, 2, 2, 16 ], [ 22, 2, 5, 8 ],
[ 22, 4, 2, 16 ], [ 22, 4, 5, 8 ], [ 23, 1, 2, 32 ], [ 23, 2, 2, 16 ],
[ 23, 3, 2, 16 ], [ 23, 4, 2, 16 ], [ 23, 5, 2, 16 ], [ 23, 6, 2, 8 ],
[ 25, 1, 1, 48 ], [ 25, 1, 3, 16 ], [ 25, 1, 5, 32 ], [ 25, 2, 1, 24 ],
[ 25, 2, 3, 16 ], [ 25, 2, 5, 8 ], [ 25, 3, 1, 24 ], [ 25, 3, 2, 16 ],
[ 25, 3, 3, 8 ], [ 25, 3, 4, 16 ], [ 26, 1, 2, 32 ], [ 26, 2, 2, 16 ],
[ 26, 3, 5, 16 ], [ 27, 1, 12, 32 ], [ 27, 3, 7, 16 ], [ 27, 5, 8, 16 ],
[ 27, 8, 7, 16 ], [ 27, 9, 6, 8 ], [ 27, 9, 10, 16 ], [ 27, 11, 7, 16 ],
[ 27, 14, 6, 16 ], [ 29, 1, 2, 64 ], [ 29, 1, 8, 32 ], [ 29, 2, 2, 32 ],
[ 29, 2, 8, 16 ], [ 29, 3, 2, 32 ], [ 29, 3, 8, 16 ], [ 29, 4, 2, 32 ],
[ 29, 4, 8, 16 ], [ 29, 5, 2, 32 ], [ 29, 5, 8, 16 ], [ 29, 6, 2, 32 ],
[ 29, 7, 2, 32 ], [ 29, 8, 2, 32 ], [ 29, 9, 2, 16 ], [ 29, 9, 8, 8 ],
[ 29, 10, 2, 16 ], [ 29, 11, 2, 16 ], [ 29, 12, 2, 16 ], [ 29, 13, 2, 16 ],
[ 30, 2, 9, 32 ], [ 30, 3, 9, 32 ], [ 30, 4, 6, 32 ], [ 30, 5, 6, 32 ],
[ 30, 5, 9, 32 ], [ 30, 5, 14, 32 ], [ 30, 6, 9, 32 ], [ 30, 7, 5, 32 ],
[ 30, 7, 13, 32 ], [ 30, 8, 8, 32 ], [ 30, 8, 12, 16 ], [ 30, 9, 8, 16 ],
[ 30, 9, 12, 16 ], [ 30, 10, 8, 32 ], [ 30, 10, 12, 16 ], [ 30, 11, 5, 16 ],
[ 30, 11, 13, 16 ], [ 30, 12, 6, 16 ] ]
k = 10: F-action on Pi is () [30,1,10]
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 0 modulo 4: 1/32 q^3 ( q^2-4*q+4 )
q congruent 1 modulo 4: 1/32 phi1^2 ( q^3-2*q^2-3*q-4 )
q congruent 2 modulo 4: 1/32 q^3 ( q^2-4*q+4 )
q congruent 3 modulo 4: 1/32 phi2 ( q^4-5*q^3+7*q^2-7*q+12 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 6 ],
[ 6, 1, 2, 8 ], [ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ],
[ 7, 4, 4, 8 ], [ 7, 5, 4, 4 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 8 ],
[ 9, 1, 1, 16 ], [ 9, 1, 2, 24 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 12 ],
[ 9, 3, 1, 8 ], [ 9, 3, 2, 12 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 12 ],
[ 9, 5, 1, 4 ], [ 9, 5, 2, 6 ], [ 12, 1, 2, 4 ], [ 12, 1, 3, 8 ],
[ 12, 2, 2, 2 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 2, 2 ],
[ 12, 4, 3, 2 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 8 ], [ 13, 2, 3, 8 ],
[ 13, 2, 4, 4 ], [ 14, 1, 2, 16 ], [ 14, 2, 2, 8 ], [ 15, 1, 1, 8 ],
[ 15, 1, 3, 16 ], [ 15, 1, 4, 20 ], [ 16, 1, 3, 16 ], [ 16, 1, 5, 32 ],
[ 16, 2, 3, 8 ], [ 16, 2, 5, 16 ], [ 16, 3, 3, 8 ], [ 16, 3, 5, 16 ],
[ 16, 4, 3, 8 ], [ 16, 4, 5, 16 ], [ 16, 5, 2, 8 ], [ 16, 5, 3, 16 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 3, 16 ], [ 16, 6, 4, 8 ],
[ 16, 7, 2, 8 ], [ 16, 7, 3, 16 ], [ 16, 7, 4, 8 ], [ 16, 8, 4, 16 ],
[ 16, 9, 3, 4 ], [ 16, 9, 5, 8 ], [ 16, 10, 2, 4 ], [ 16, 10, 3, 8 ],
[ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 16, 11, 5, 8 ], [ 16, 12, 2, 4 ],
[ 16, 12, 3, 8 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ], [ 16, 13, 5, 8 ],
[ 16, 14, 4, 8 ], [ 16, 15, 3, 4 ], [ 16, 15, 5, 8 ], [ 16, 16, 3, 4 ],
[ 16, 16, 5, 8 ], [ 16, 17, 4, 8 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 8 ],
[ 18, 2, 2, 4 ], [ 18, 2, 3, 4 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 8 ],
[ 20, 2, 2, 4 ], [ 20, 2, 3, 4 ], [ 21, 1, 7, 16 ], [ 21, 2, 9, 8 ],
[ 21, 3, 8, 8 ], [ 21, 4, 9, 8 ], [ 21, 5, 9, 4 ], [ 21, 6, 9, 8 ],
[ 21, 7, 9, 8 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 32 ], [ 22, 1, 5, 16 ],
[ 22, 1, 6, 16 ], [ 22, 2, 2, 4 ], [ 22, 2, 3, 16 ], [ 22, 2, 5, 8 ],
[ 22, 2, 6, 8 ], [ 22, 3, 2, 16 ], [ 22, 3, 4, 8 ], [ 22, 4, 2, 4 ],
[ 22, 4, 3, 8 ], [ 22, 4, 5, 8 ], [ 22, 4, 6, 4 ], [ 23, 1, 3, 16 ],
[ 23, 2, 3, 8 ], [ 23, 3, 3, 8 ], [ 23, 4, 3, 8 ], [ 23, 5, 3, 8 ],
[ 23, 6, 3, 4 ], [ 24, 1, 3, 16 ], [ 24, 2, 3, 8 ], [ 25, 1, 2, 16 ],
[ 25, 1, 3, 16 ], [ 25, 2, 2, 8 ], [ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ],
[ 25, 3, 5, 8 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 16 ], [ 26, 2, 2, 8 ],
[ 26, 2, 5, 8 ], [ 26, 3, 3, 8 ], [ 26, 3, 5, 8 ], [ 27, 1, 10, 32 ],
[ 27, 2, 9, 16 ], [ 27, 3, 8, 16 ], [ 27, 3, 12, 16 ], [ 27, 4, 8, 16 ],
[ 27, 5, 9, 16 ], [ 27, 6, 9, 8 ], [ 27, 7, 9, 8 ], [ 27, 8, 8, 16 ],
[ 27, 8, 12, 8 ], [ 27, 9, 7, 8 ], [ 27, 10, 6, 8 ], [ 27, 11, 8, 16 ],
[ 27, 11, 12, 8 ], [ 27, 12, 8, 16 ], [ 27, 13, 8, 8 ], [ 27, 14, 10, 16 ],
[ 27, 14, 12, 8 ], [ 29, 1, 3, 32 ], [ 29, 1, 6, 16 ], [ 29, 1, 7, 16 ],
[ 29, 1, 8, 16 ], [ 29, 2, 3, 16 ], [ 29, 2, 6, 8 ], [ 29, 2, 7, 8 ],
[ 29, 2, 8, 8 ], [ 29, 3, 3, 16 ], [ 29, 3, 6, 8 ], [ 29, 3, 7, 8 ],
[ 29, 3, 8, 8 ], [ 29, 4, 3, 16 ], [ 29, 4, 6, 8 ], [ 29, 4, 7, 8 ],
[ 29, 4, 8, 8 ], [ 29, 5, 3, 16 ], [ 29, 5, 6, 8 ], [ 29, 5, 7, 8 ],
[ 29, 5, 8, 8 ], [ 29, 6, 3, 16 ], [ 29, 7, 3, 16 ], [ 29, 8, 3, 16 ],
[ 29, 9, 3, 8 ], [ 29, 9, 6, 4 ], [ 29, 9, 7, 4 ], [ 29, 9, 8, 4 ],
[ 29, 10, 3, 8 ], [ 29, 11, 3, 8 ], [ 29, 12, 3, 8 ], [ 29, 13, 3, 8 ],
[ 30, 2, 10, 16 ], [ 30, 3, 10, 16 ], [ 30, 4, 10, 16 ], [ 30, 4, 13, 16 ],
[ 30, 5, 10, 16 ], [ 30, 5, 13, 16 ], [ 30, 6, 10, 16 ], [ 30, 6, 12, 16 ],
[ 30, 7, 7, 16 ], [ 30, 7, 10, 16 ], [ 30, 7, 12, 16 ], [ 30, 7, 14, 16 ],
[ 30, 8, 14, 8 ], [ 30, 9, 14, 8 ], [ 30, 10, 14, 8 ], [ 30, 11, 7, 8 ],
[ 30, 11, 10, 8 ], [ 30, 11, 12, 8 ], [ 30, 11, 14, 8 ], [ 30, 12, 10, 8 ],
[ 30, 12, 13, 8 ], [ 30, 13, 9, 16 ] ]
k = 11: F-action on Pi is () [30,1,11]
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 0 modulo 4: 1/64 q ( q^4-6*q^3+8*q^2+8*q-16 )
q congruent 1 modulo 4: 1/64 phi1 ( q^4-5*q^3+q^2+5*q+30 )
q congruent 2 modulo 4: 1/64 q ( q^4-6*q^3+8*q^2+8*q-16 )
q congruent 3 modulo 4: 1/64 ( q^5-6*q^4+6*q^3+4*q^2+41*q-78 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 5, 1, 2, 4 ], [ 8, 1, 1, 12 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 24 ],
[ 9, 1, 2, 16 ], [ 9, 1, 8, 16 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 8 ],
[ 9, 2, 8, 8 ], [ 9, 3, 1, 12 ], [ 9, 3, 2, 8 ], [ 9, 3, 8, 8 ],
[ 9, 4, 1, 12 ], [ 9, 4, 2, 8 ], [ 9, 4, 8, 8 ], [ 9, 5, 1, 6 ],
[ 9, 5, 2, 4 ], [ 9, 5, 8, 4 ], [ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ],
[ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ], [ 12, 4, 2, 4 ], [ 15, 1, 1, 24 ],
[ 15, 1, 2, 16 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 16 ], [ 16, 1, 3, 32 ],
[ 16, 2, 3, 16 ], [ 16, 3, 3, 16 ], [ 16, 4, 3, 16 ], [ 16, 5, 2, 16 ],
[ 16, 5, 4, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 4, 16 ], [ 16, 7, 2, 16 ],
[ 16, 7, 4, 16 ], [ 16, 9, 3, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ],
[ 16, 11, 3, 16 ], [ 16, 12, 2, 8 ], [ 16, 12, 4, 8 ], [ 16, 13, 3, 8 ],
[ 16, 15, 3, 8 ], [ 16, 16, 3, 8 ], [ 18, 1, 2, 16 ], [ 18, 2, 2, 8 ],
[ 20, 1, 1, 24 ], [ 20, 1, 3, 8 ], [ 20, 2, 1, 12 ], [ 20, 2, 3, 4 ],
[ 22, 1, 2, 32 ], [ 22, 1, 5, 16 ], [ 22, 2, 2, 16 ], [ 22, 2, 5, 8 ],
[ 22, 4, 2, 16 ], [ 22, 4, 5, 8 ], [ 23, 1, 4, 32 ], [ 23, 2, 4, 16 ],
[ 23, 3, 4, 16 ], [ 23, 4, 4, 16 ], [ 23, 5, 4, 16 ], [ 23, 6, 4, 8 ],
[ 25, 1, 2, 32 ], [ 25, 2, 2, 16 ], [ 25, 3, 5, 16 ], [ 26, 1, 1, 48 ],
[ 26, 1, 3, 16 ], [ 26, 1, 5, 32 ], [ 26, 2, 1, 24 ], [ 26, 2, 3, 16 ],
[ 26, 2, 5, 8 ], [ 26, 3, 1, 24 ], [ 26, 3, 2, 16 ], [ 26, 3, 3, 8 ],
[ 26, 3, 4, 16 ], [ 27, 1, 12, 32 ], [ 27, 3, 7, 16 ], [ 27, 5, 8, 16 ],
[ 27, 8, 7, 16 ], [ 27, 9, 6, 8 ], [ 27, 9, 10, 16 ], [ 27, 11, 7, 16 ],
[ 27, 14, 6, 16 ], [ 29, 1, 4, 64 ], [ 29, 1, 6, 32 ], [ 29, 2, 4, 32 ],
[ 29, 2, 6, 16 ], [ 29, 3, 4, 32 ], [ 29, 3, 6, 16 ], [ 29, 4, 4, 32 ],
[ 29, 4, 6, 16 ], [ 29, 5, 4, 32 ], [ 29, 5, 6, 16 ], [ 29, 6, 4, 32 ],
[ 29, 7, 4, 32 ], [ 29, 8, 4, 32 ], [ 29, 9, 4, 16 ], [ 29, 9, 6, 8 ],
[ 29, 10, 4, 16 ], [ 29, 11, 4, 16 ], [ 29, 12, 4, 16 ], [ 29, 13, 4, 16 ],
[ 30, 2, 11, 32 ], [ 30, 3, 11, 32 ], [ 30, 4, 11, 32 ], [ 30, 5, 11, 32 ],
[ 30, 6, 6, 32 ], [ 30, 6, 11, 32 ], [ 30, 6, 14, 32 ], [ 30, 7, 8, 32 ],
[ 30, 7, 16, 32 ], [ 30, 8, 9, 32 ], [ 30, 8, 15, 16 ], [ 30, 9, 9, 32 ],
[ 30, 9, 15, 16 ], [ 30, 10, 9, 16 ], [ 30, 10, 15, 16 ], [ 30, 11, 8, 16 ],
[ 30, 11, 16, 16 ], [ 30, 12, 11, 16 ] ]
k = 12: F-action on Pi is () [30,1,12]
Dynkin type is A_1(q) + T(phi1 phi4^2)
Order of center |Z^F|: phi1 phi4^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/32 q^2 ( q^3-2*q^2-4*q+8 )
q congruent 1 modulo 4: 1/32 phi1^2 phi2 ( q^2-q-6 )
q congruent 2 modulo 4: 1/32 q^2 ( q^3-2*q^2-4*q+8 )
q congruent 3 modulo 4: 1/32 phi1^2 phi2 ( q^2-q-6 )
Fusion of maximal tori of C^F in those of G^F:
[ 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 9, 1, 3, 8 ], [ 9, 1, 6, 8 ],
[ 9, 1, 8, 8 ], [ 9, 2, 3, 4 ], [ 9, 2, 6, 4 ], [ 9, 2, 8, 4 ],
[ 9, 3, 3, 4 ], [ 9, 3, 6, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 3, 4 ],
[ 9, 4, 6, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 3, 2 ], [ 9, 5, 6, 2 ],
[ 9, 5, 8, 2 ], [ 12, 1, 5, 8 ], [ 12, 2, 5, 4 ], [ 12, 4, 5, 4 ],
[ 15, 1, 5, 16 ], [ 16, 1, 4, 16 ], [ 16, 2, 4, 8 ], [ 16, 3, 4, 8 ],
[ 16, 4, 4, 8 ], [ 16, 9, 4, 4 ], [ 16, 11, 4, 8 ], [ 16, 11, 9, 8 ],
[ 16, 13, 4, 8 ], [ 16, 15, 4, 8 ], [ 16, 16, 4, 8 ], [ 22, 1, 8, 16 ],
[ 22, 2, 8, 8 ], [ 22, 4, 8, 8 ], [ 25, 1, 6, 16 ], [ 25, 2, 4, 8 ],
[ 26, 1, 6, 16 ], [ 26, 2, 4, 8 ], [ 27, 1, 14, 32 ], [ 27, 3, 10, 16 ],
[ 27, 5, 10, 16 ], [ 27, 8, 10, 16 ], [ 27, 9, 8, 8 ], [ 27, 9, 11, 16 ],
[ 27, 11, 10, 16 ], [ 27, 14, 7, 16 ], [ 30, 2, 12, 16 ], [ 30, 3, 12, 16 ],
[ 30, 4, 7, 16 ], [ 30, 5, 7, 16 ], [ 30, 6, 7, 16 ], [ 30, 8, 10, 16 ],
[ 30, 8, 11, 16 ], [ 30, 8, 13, 8 ], [ 30, 9, 10, 16 ], [ 30, 9, 11, 8 ],
[ 30, 9, 13, 16 ], [ 30, 10, 10, 8 ], [ 30, 10, 11, 16 ],
[ 30, 10, 13, 16 ], [ 30, 12, 7, 16 ] ]
k = 13: F-action on Pi is () [30,1,13]
Dynkin type is A_1(q) + T(phi1 phi2^4)
Order of center |Z^F|: phi1 phi2^4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/384 q ( q^4-10*q^3+36*q^2-56*q+32 )
q congruent 1 modulo 4: 1/384 phi1 ( q^4-9*q^3+21*q^2-11*q+30 )
q congruent 2 modulo 4: 1/384 q ( q^4-10*q^3+36*q^2-56*q+32 )
q congruent 3 modulo 4: 1/384 phi2 ( q^4-11*q^3+41*q^2-73*q+66 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 2, 16 ],
[ 3, 2, 2, 8 ], [ 3, 3, 2, 8 ], [ 3, 4, 2, 8 ], [ 3, 5, 2, 4 ],
[ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 24 ],
[ 6, 1, 2, 32 ], [ 7, 1, 4, 64 ], [ 7, 2, 4, 32 ], [ 7, 3, 4, 32 ],
[ 7, 4, 4, 32 ], [ 7, 5, 4, 16 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 24 ],
[ 9, 1, 2, 96 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 48 ], [ 9, 3, 1, 12 ],
[ 9, 3, 2, 48 ], [ 9, 4, 1, 12 ], [ 9, 4, 2, 48 ], [ 9, 5, 1, 6 ],
[ 9, 5, 2, 24 ], [ 12, 1, 3, 48 ], [ 12, 2, 3, 24 ], [ 12, 3, 2, 24 ],
[ 12, 4, 3, 12 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 96 ], [ 13, 2, 3, 8 ],
[ 13, 2, 4, 48 ], [ 14, 1, 2, 64 ], [ 14, 2, 2, 32 ], [ 15, 1, 3, 96 ],
[ 15, 1, 4, 48 ], [ 16, 1, 5, 192 ], [ 16, 2, 5, 96 ], [ 16, 3, 5, 96 ],
[ 16, 4, 5, 96 ], [ 16, 5, 3, 96 ], [ 16, 6, 3, 96 ], [ 16, 7, 3, 96 ],
[ 16, 8, 4, 96 ], [ 16, 9, 5, 48 ], [ 16, 10, 3, 48 ], [ 16, 11, 5, 48 ],
[ 16, 12, 3, 48 ], [ 16, 13, 5, 48 ], [ 16, 14, 4, 48 ], [ 16, 15, 5, 48 ],
[ 16, 16, 5, 48 ], [ 16, 17, 4, 48 ], [ 18, 1, 3, 16 ], [ 18, 2, 3, 8 ],
[ 20, 1, 3, 16 ], [ 20, 2, 3, 8 ], [ 21, 1, 4, 192 ], [ 21, 2, 10, 96 ],
[ 21, 3, 10, 96 ], [ 21, 4, 10, 96 ], [ 21, 5, 10, 48 ], [ 21, 6, 10, 48 ],
[ 21, 7, 10, 48 ], [ 22, 1, 3, 96 ], [ 22, 1, 6, 192 ], [ 22, 2, 3, 48 ],
[ 22, 2, 6, 96 ], [ 22, 3, 2, 48 ], [ 22, 3, 4, 96 ], [ 22, 4, 3, 24 ],
[ 22, 4, 6, 48 ], [ 24, 1, 3, 64 ], [ 24, 2, 3, 32 ], [ 25, 1, 3, 96 ],
[ 25, 2, 5, 48 ], [ 25, 3, 3, 48 ], [ 26, 1, 3, 96 ], [ 26, 2, 5, 48 ],
[ 26, 3, 3, 48 ], [ 27, 1, 5, 384 ], [ 27, 2, 10, 192 ], [ 27, 3, 13, 192 ],
[ 27, 4, 10, 192 ], [ 27, 5, 11, 192 ], [ 27, 6, 10, 96 ],
[ 27, 7, 10, 96 ], [ 27, 8, 13, 96 ], [ 27, 9, 12, 96 ], [ 27, 10, 10, 96 ],
[ 27, 11, 13, 96 ], [ 27, 12, 10, 96 ], [ 27, 13, 10, 96 ],
[ 27, 14, 13, 96 ], [ 29, 1, 7, 192 ], [ 29, 2, 7, 96 ], [ 29, 3, 7, 96 ],
[ 29, 4, 7, 96 ], [ 29, 5, 7, 96 ], [ 29, 9, 7, 48 ], [ 30, 2, 13, 192 ],
[ 30, 3, 13, 192 ], [ 30, 4, 14, 192 ], [ 30, 5, 12, 192 ],
[ 30, 6, 13, 192 ], [ 30, 7, 11, 192 ], [ 30, 8, 16, 96 ],
[ 30, 9, 16, 96 ], [ 30, 10, 16, 96 ], [ 30, 11, 11, 96 ],
[ 30, 12, 14, 96 ], [ 30, 13, 10, 96 ] ]
k = 14: F-action on Pi is () [30,1,14]
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 0 modulo 4: 1/384 q ( q^4-16*q^3+92*q^2-224*q+192 )
q congruent 1 modulo 4: 1/384 phi1^2 ( q^3-14*q^2+57*q-60 )
q congruent 2 modulo 4: 1/384 q ( q^4-16*q^3+92*q^2-224*q+192 )
q congruent 3 modulo
4: 1/384 ( q^5-16*q^4+86*q^3-188*q^2+225*q-252 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 1, 16 ],
[ 3, 2, 1, 8 ], [ 3, 3, 1, 8 ], [ 3, 4, 1, 8 ], [ 3, 5, 1, 4 ],
[ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 5, 1, 1, 24 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 32 ], [ 7, 1, 1, 64 ], [ 7, 2, 1, 32 ], [ 7, 3, 1, 32 ],
[ 7, 4, 1, 32 ], [ 7, 5, 1, 16 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 96 ],
[ 9, 1, 2, 24 ], [ 9, 2, 1, 48 ], [ 9, 2, 2, 12 ], [ 9, 3, 1, 48 ],
[ 9, 3, 2, 12 ], [ 9, 4, 1, 48 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 24 ],
[ 9, 5, 2, 6 ], [ 12, 1, 1, 48 ], [ 12, 2, 1, 24 ], [ 12, 3, 1, 24 ],
[ 12, 4, 1, 12 ], [ 13, 1, 1, 96 ], [ 13, 1, 2, 16 ], [ 13, 2, 1, 48 ],
[ 13, 2, 2, 8 ], [ 14, 1, 1, 64 ], [ 14, 2, 1, 32 ], [ 15, 1, 1, 96 ],
[ 15, 1, 4, 48 ], [ 16, 1, 1, 192 ], [ 16, 2, 1, 96 ], [ 16, 3, 1, 96 ],
[ 16, 4, 1, 96 ], [ 16, 5, 1, 96 ], [ 16, 6, 1, 96 ], [ 16, 7, 1, 96 ],
[ 16, 8, 1, 96 ], [ 16, 9, 1, 48 ], [ 16, 10, 1, 48 ], [ 16, 11, 1, 48 ],
[ 16, 12, 1, 48 ], [ 16, 13, 1, 48 ], [ 16, 14, 1, 48 ], [ 16, 15, 1, 48 ],
[ 16, 16, 1, 48 ], [ 16, 17, 1, 48 ], [ 18, 1, 2, 16 ], [ 18, 2, 2, 8 ],
[ 20, 1, 2, 16 ], [ 20, 2, 2, 8 ], [ 21, 1, 1, 192 ], [ 21, 2, 1, 96 ],
[ 21, 3, 1, 96 ], [ 21, 4, 1, 96 ], [ 21, 5, 1, 48 ], [ 21, 6, 1, 48 ],
[ 21, 7, 1, 48 ], [ 22, 1, 1, 192 ], [ 22, 1, 4, 96 ], [ 22, 2, 1, 96 ],
[ 22, 2, 4, 48 ], [ 22, 3, 1, 96 ], [ 22, 3, 3, 48 ], [ 22, 4, 1, 48 ],
[ 22, 4, 4, 24 ], [ 24, 1, 2, 64 ], [ 24, 2, 2, 32 ], [ 25, 1, 2, 96 ],
[ 25, 2, 2, 48 ], [ 25, 3, 5, 48 ], [ 26, 1, 2, 96 ], [ 26, 2, 2, 48 ],
[ 26, 3, 5, 48 ], [ 27, 1, 1, 384 ], [ 27, 2, 1, 192 ], [ 27, 3, 1, 192 ],
[ 27, 4, 1, 192 ], [ 27, 5, 1, 192 ], [ 27, 6, 1, 96 ], [ 27, 7, 1, 96 ],
[ 27, 8, 1, 96 ], [ 27, 9, 1, 96 ], [ 27, 10, 1, 96 ], [ 27, 11, 1, 96 ],
[ 27, 12, 1, 96 ], [ 27, 13, 1, 96 ], [ 27, 14, 1, 96 ], [ 29, 1, 5, 192 ],
[ 29, 2, 5, 96 ], [ 29, 3, 5, 96 ], [ 29, 4, 5, 96 ], [ 29, 5, 5, 96 ],
[ 29, 9, 5, 48 ], [ 30, 2, 14, 192 ], [ 30, 3, 14, 192 ],
[ 30, 4, 15, 192 ], [ 30, 5, 15, 192 ], [ 30, 6, 15, 192 ],
[ 30, 7, 17, 192 ], [ 30, 8, 17, 96 ], [ 30, 9, 17, 96 ],
[ 30, 10, 17, 96 ], [ 30, 11, 17, 96 ], [ 30, 12, 15, 96 ],
[ 30, 13, 11, 96 ] ]
k = 15: F-action on Pi is () [30,1,15]
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 0 modulo 4: 1/32 q^2 ( q^3-6*q^2+12*q-8 )
q congruent 1 modulo 4: 1/32 phi1 ( q^4-5*q^3+5*q^2-3*q+18 )
q congruent 2 modulo 4: 1/32 q^2 ( q^3-6*q^2+12*q-8 )
q congruent 3 modulo 4: 1/32 phi1 ( q^4-5*q^3+5*q^2-3*q+18 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 6 ], [ 5, 1, 2, 4 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ],
[ 7, 4, 1, 8 ], [ 7, 5, 1, 4 ], [ 8, 1, 1, 8 ], [ 8, 1, 2, 4 ],
[ 9, 1, 1, 24 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 8 ],
[ 9, 3, 1, 12 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 12 ], [ 9, 4, 2, 8 ],
[ 9, 5, 1, 6 ], [ 9, 5, 2, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ],
[ 12, 2, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ],
[ 12, 4, 2, 2 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 16 ], [ 13, 2, 1, 4 ],
[ 13, 2, 2, 8 ], [ 14, 1, 1, 16 ], [ 14, 2, 1, 8 ], [ 15, 1, 1, 16 ],
[ 15, 1, 3, 8 ], [ 15, 1, 4, 20 ], [ 16, 1, 1, 32 ], [ 16, 1, 3, 16 ],
[ 16, 2, 1, 16 ], [ 16, 2, 3, 8 ], [ 16, 3, 1, 16 ], [ 16, 3, 3, 8 ],
[ 16, 4, 1, 16 ], [ 16, 4, 3, 8 ], [ 16, 5, 1, 16 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 1, 16 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ],
[ 16, 7, 1, 16 ], [ 16, 7, 2, 8 ], [ 16, 7, 4, 8 ], [ 16, 8, 1, 16 ],
[ 16, 9, 1, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 1, 8 ], [ 16, 10, 2, 4 ],
[ 16, 10, 4, 4 ], [ 16, 11, 1, 8 ], [ 16, 11, 3, 8 ], [ 16, 12, 1, 8 ],
[ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 1, 8 ], [ 16, 13, 3, 4 ],
[ 16, 14, 1, 8 ], [ 16, 15, 1, 8 ], [ 16, 15, 3, 4 ], [ 16, 16, 1, 8 ],
[ 16, 16, 3, 4 ], [ 16, 17, 1, 8 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 8 ],
[ 18, 2, 2, 4 ], [ 18, 2, 3, 4 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 8 ],
[ 20, 2, 2, 4 ], [ 20, 2, 3, 4 ], [ 21, 1, 5, 16 ], [ 21, 2, 2, 8 ],
[ 21, 3, 3, 8 ], [ 21, 4, 2, 8 ], [ 21, 5, 2, 4 ], [ 21, 6, 3, 8 ],
[ 21, 7, 2, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 16 ], [ 22, 1, 4, 32 ],
[ 22, 1, 5, 8 ], [ 22, 2, 1, 8 ], [ 22, 2, 2, 8 ], [ 22, 2, 4, 16 ],
[ 22, 2, 5, 4 ], [ 22, 3, 1, 8 ], [ 22, 3, 3, 16 ], [ 22, 4, 1, 4 ],
[ 22, 4, 2, 8 ], [ 22, 4, 4, 8 ], [ 22, 4, 5, 4 ], [ 23, 1, 5, 16 ],
[ 23, 2, 5, 8 ], [ 23, 3, 5, 8 ], [ 23, 4, 5, 8 ], [ 23, 5, 5, 8 ],
[ 23, 6, 5, 4 ], [ 24, 1, 2, 16 ], [ 24, 2, 2, 8 ], [ 25, 1, 2, 16 ],
[ 25, 1, 3, 16 ], [ 25, 2, 2, 8 ], [ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ],
[ 25, 3, 5, 8 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 16 ], [ 26, 2, 2, 8 ],
[ 26, 2, 5, 8 ], [ 26, 3, 3, 8 ], [ 26, 3, 5, 8 ], [ 27, 1, 6, 32 ],
[ 27, 2, 2, 16 ], [ 27, 3, 2, 16 ], [ 27, 3, 6, 16 ], [ 27, 4, 3, 16 ],
[ 27, 5, 2, 16 ], [ 27, 6, 2, 8 ], [ 27, 7, 2, 8 ], [ 27, 8, 2, 8 ],
[ 27, 8, 6, 16 ], [ 27, 9, 2, 8 ], [ 27, 10, 5, 8 ], [ 27, 11, 2, 8 ],
[ 27, 11, 6, 16 ], [ 27, 12, 3, 16 ], [ 27, 13, 3, 8 ], [ 27, 14, 3, 8 ],
[ 27, 14, 8, 16 ], [ 29, 1, 5, 16 ], [ 29, 1, 6, 16 ], [ 29, 1, 8, 16 ],
[ 29, 1, 9, 32 ], [ 29, 2, 5, 8 ], [ 29, 2, 6, 8 ], [ 29, 2, 8, 8 ],
[ 29, 2, 9, 16 ], [ 29, 3, 5, 8 ], [ 29, 3, 6, 8 ], [ 29, 3, 8, 8 ],
[ 29, 3, 9, 16 ], [ 29, 4, 5, 8 ], [ 29, 4, 6, 8 ], [ 29, 4, 8, 8 ],
[ 29, 4, 9, 16 ], [ 29, 5, 5, 8 ], [ 29, 5, 6, 8 ], [ 29, 5, 8, 8 ],
[ 29, 5, 9, 16 ], [ 29, 6, 5, 16 ], [ 29, 7, 5, 16 ], [ 29, 8, 5, 16 ],
[ 29, 9, 5, 4 ], [ 29, 9, 6, 4 ], [ 29, 9, 8, 4 ], [ 29, 9, 9, 8 ],
[ 29, 10, 5, 8 ], [ 29, 11, 5, 8 ], [ 29, 12, 5, 8 ], [ 29, 13, 5, 8 ],
[ 30, 2, 15, 16 ], [ 30, 3, 15, 16 ], [ 30, 4, 17, 16 ], [ 30, 4, 22, 16 ],
[ 30, 5, 16, 16 ], [ 30, 5, 18, 16 ], [ 30, 6, 16, 16 ], [ 30, 6, 18, 16 ],
[ 30, 7, 18, 16 ], [ 30, 7, 20, 16 ], [ 30, 7, 22, 16 ], [ 30, 7, 31, 16 ],
[ 30, 8, 19, 8 ], [ 30, 9, 19, 8 ], [ 30, 10, 19, 8 ], [ 30, 11, 18, 8 ],
[ 30, 11, 20, 8 ], [ 30, 11, 22, 8 ], [ 30, 11, 31, 8 ], [ 30, 12, 17, 8 ],
[ 30, 12, 22, 8 ], [ 30, 13, 12, 16 ] ]
k = 16: F-action on Pi is () [30,1,16]
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 0 modulo 4: 1/64 q^2 ( q^3-8*q^2+20*q-16 )
q congruent 1 modulo 4: 1/64 phi1 ( q^4-7*q^3+7*q^2+35*q-68 )
q congruent 2 modulo 4: 1/64 q^2 ( q^3-8*q^2+20*q-16 )
q congruent 3 modulo 4: 1/64 ( q^5-8*q^4+14*q^3+28*q^2-87*q+36 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 3, 2, 1, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 1, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 1, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ],
[ 7, 1, 3, 16 ], [ 7, 1, 4, 16 ], [ 7, 2, 1, 8 ], [ 7, 2, 2, 8 ],
[ 7, 2, 3, 8 ], [ 7, 2, 4, 8 ], [ 7, 3, 1, 8 ], [ 7, 3, 2, 8 ],
[ 7, 3, 3, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 1, 8 ], [ 7, 4, 2, 8 ],
[ 7, 4, 3, 8 ], [ 7, 4, 4, 8 ], [ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ],
[ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 16 ],
[ 9, 1, 2, 24 ], [ 9, 1, 4, 16 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 12 ],
[ 9, 2, 4, 8 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 12 ], [ 9, 3, 4, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 12 ], [ 9, 4, 4, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 6 ], [ 9, 5, 4, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 3, 8 ],
[ 12, 1, 4, 16 ], [ 12, 2, 1, 4 ], [ 12, 2, 3, 4 ], [ 12, 2, 4, 8 ],
[ 12, 3, 1, 4 ], [ 12, 3, 2, 4 ], [ 12, 3, 3, 8 ], [ 12, 3, 4, 8 ],
[ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ], [ 13, 1, 2, 24 ],
[ 13, 1, 3, 16 ], [ 13, 1, 4, 8 ], [ 13, 2, 2, 12 ], [ 13, 2, 3, 8 ],
[ 13, 2, 4, 4 ], [ 14, 1, 2, 16 ], [ 14, 1, 4, 32 ], [ 14, 2, 2, 8 ],
[ 14, 2, 4, 16 ], [ 15, 1, 3, 16 ], [ 15, 1, 4, 24 ], [ 16, 1, 1, 32 ],
[ 16, 1, 2, 32 ], [ 16, 1, 5, 32 ], [ 16, 2, 1, 16 ], [ 16, 2, 2, 16 ],
[ 16, 2, 5, 16 ], [ 16, 3, 1, 16 ], [ 16, 3, 2, 16 ], [ 16, 3, 5, 16 ],
[ 16, 4, 1, 16 ], [ 16, 4, 2, 16 ], [ 16, 4, 5, 16 ], [ 16, 5, 1, 16 ],
[ 16, 5, 3, 16 ], [ 16, 6, 1, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 1, 16 ],
[ 16, 7, 3, 16 ], [ 16, 8, 1, 16 ], [ 16, 8, 2, 16 ], [ 16, 8, 3, 16 ],
[ 16, 8, 4, 16 ], [ 16, 8, 6, 16 ], [ 16, 8, 7, 16 ], [ 16, 9, 1, 8 ],
[ 16, 9, 2, 8 ], [ 16, 9, 5, 8 ], [ 16, 10, 1, 8 ], [ 16, 10, 3, 8 ],
[ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ], [ 16, 11, 5, 8 ], [ 16, 11, 7, 8 ],
[ 16, 12, 1, 8 ], [ 16, 12, 3, 8 ], [ 16, 13, 1, 8 ], [ 16, 13, 2, 16 ],
[ 16, 13, 5, 8 ], [ 16, 14, 1, 8 ], [ 16, 14, 2, 8 ], [ 16, 14, 3, 8 ],
[ 16, 14, 4, 8 ], [ 16, 15, 1, 8 ], [ 16, 15, 2, 16 ], [ 16, 15, 5, 8 ],
[ 16, 16, 1, 8 ], [ 16, 16, 2, 16 ], [ 16, 16, 5, 8 ], [ 16, 17, 1, 8 ],
[ 16, 17, 2, 8 ], [ 16, 17, 3, 8 ], [ 16, 17, 4, 8 ], [ 18, 1, 3, 16 ],
[ 18, 2, 3, 8 ], [ 20, 1, 3, 16 ], [ 20, 2, 3, 8 ], [ 21, 1, 2, 32 ],
[ 21, 1, 3, 32 ], [ 21, 2, 3, 16 ], [ 21, 2, 4, 16 ], [ 21, 2, 6, 16 ],
[ 21, 2, 8, 16 ], [ 21, 3, 2, 16 ], [ 21, 3, 5, 16 ], [ 21, 3, 6, 16 ],
[ 21, 3, 7, 16 ], [ 21, 4, 3, 16 ], [ 21, 4, 6, 16 ], [ 21, 5, 3, 8 ],
[ 21, 5, 4, 8 ], [ 21, 5, 6, 8 ], [ 21, 5, 8, 8 ], [ 21, 6, 2, 8 ],
[ 21, 6, 5, 8 ], [ 21, 6, 6, 8 ], [ 21, 6, 7, 8 ], [ 21, 7, 3, 8 ],
[ 21, 7, 6, 8 ], [ 22, 1, 3, 32 ], [ 22, 1, 4, 48 ], [ 22, 1, 6, 16 ],
[ 22, 1, 9, 32 ], [ 22, 2, 3, 16 ], [ 22, 2, 4, 24 ], [ 22, 2, 6, 8 ],
[ 22, 2, 9, 16 ], [ 22, 3, 2, 16 ], [ 22, 3, 3, 24 ], [ 22, 3, 4, 8 ],
[ 22, 3, 7, 16 ], [ 22, 3, 8, 16 ], [ 22, 4, 3, 8 ], [ 22, 4, 4, 12 ],
[ 22, 4, 6, 4 ], [ 22, 4, 9, 8 ], [ 23, 1, 5, 32 ], [ 23, 2, 5, 16 ],
[ 23, 3, 5, 16 ], [ 23, 4, 5, 16 ], [ 23, 5, 5, 16 ], [ 23, 6, 5, 8 ],
[ 24, 1, 3, 32 ], [ 24, 2, 3, 16 ], [ 25, 1, 3, 32 ], [ 25, 2, 5, 16 ],
[ 25, 3, 3, 16 ], [ 26, 1, 3, 32 ], [ 26, 2, 5, 16 ], [ 26, 3, 3, 16 ],
[ 27, 1, 3, 64 ], [ 27, 2, 3, 32 ], [ 27, 2, 6, 32 ], [ 27, 3, 3, 32 ],
[ 27, 3, 4, 32 ], [ 27, 3, 11, 32 ], [ 27, 4, 2, 32 ], [ 27, 4, 5, 32 ],
[ 27, 5, 3, 32 ], [ 27, 6, 3, 16 ], [ 27, 6, 4, 16 ], [ 27, 6, 6, 16 ],
[ 27, 6, 8, 16 ], [ 27, 7, 3, 16 ], [ 27, 7, 6, 16 ], [ 27, 8, 3, 16 ],
[ 27, 8, 4, 16 ], [ 27, 8, 11, 16 ], [ 27, 9, 3, 16 ], [ 27, 9, 4, 16 ],
[ 27, 10, 2, 16 ], [ 27, 10, 3, 16 ], [ 27, 10, 4, 16 ], [ 27, 10, 9, 16 ],
[ 27, 11, 3, 16 ], [ 27, 11, 4, 16 ], [ 27, 11, 11, 16 ], [ 27, 12, 2, 16 ],
[ 27, 12, 5, 16 ], [ 27, 13, 2, 16 ], [ 27, 13, 5, 16 ], [ 27, 13, 6, 16 ],
[ 27, 13, 7, 16 ], [ 27, 14, 2, 16 ], [ 27, 14, 5, 16 ], [ 27, 14, 11, 16 ],
[ 28, 1, 6, 64 ], [ 28, 2, 6, 32 ], [ 28, 2, 8, 32 ], [ 28, 3, 6, 32 ],
[ 28, 4, 5, 32 ], [ 28, 5, 6, 32 ], [ 28, 5, 8, 16 ], [ 28, 6, 6, 16 ],
[ 29, 1, 7, 32 ], [ 29, 1, 9, 64 ], [ 29, 2, 7, 16 ], [ 29, 2, 9, 32 ],
[ 29, 3, 7, 16 ], [ 29, 3, 9, 32 ], [ 29, 4, 7, 16 ], [ 29, 4, 9, 32 ],
[ 29, 5, 7, 16 ], [ 29, 5, 9, 32 ], [ 29, 6, 5, 32 ], [ 29, 7, 5, 32 ],
[ 29, 8, 5, 32 ], [ 29, 9, 7, 8 ], [ 29, 9, 9, 16 ], [ 29, 10, 5, 16 ],
[ 29, 11, 5, 16 ], [ 29, 12, 5, 16 ], [ 29, 13, 5, 16 ], [ 30, 2, 16, 32 ],
[ 30, 3, 16, 32 ], [ 30, 4, 16, 32 ], [ 30, 4, 19, 32 ], [ 30, 4, 26, 32 ],
[ 30, 5, 17, 32 ], [ 30, 6, 17, 32 ], [ 30, 7, 19, 32 ], [ 30, 7, 25, 32 ],
[ 30, 8, 18, 16 ], [ 30, 8, 21, 16 ], [ 30, 9, 18, 32 ], [ 30, 9, 21, 16 ],
[ 30, 10, 18, 32 ], [ 30, 10, 21, 16 ], [ 30, 11, 19, 16 ],
[ 30, 11, 25, 16 ], [ 30, 12, 16, 32 ], [ 30, 12, 19, 16 ],
[ 30, 12, 26, 16 ], [ 30, 13, 13, 16 ], [ 30, 13, 16, 16 ] ]
k = 17: F-action on Pi is () [30,1,17]
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 0 modulo 4: 1/12 q^2 phi1^2 phi2
q congruent 1 modulo 4: 1/12 q^2 phi1^2 phi2
q congruent 2 modulo 4: 1/12 q^2 phi1^2 phi2
q congruent 3 modulo 4: 1/12 q^2 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 22, 20 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 1, 2 ],
[ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ],
[ 7, 5, 1, 1 ], [ 8, 1, 1, 4 ], [ 13, 1, 2, 4 ], [ 13, 2, 2, 2 ],
[ 14, 1, 1, 4 ], [ 14, 2, 1, 2 ], [ 18, 1, 2, 4 ], [ 18, 2, 2, 2 ],
[ 20, 1, 2, 4 ], [ 20, 2, 2, 2 ], [ 21, 1, 9, 6 ], [ 21, 4, 4, 3 ],
[ 21, 7, 4, 6 ], [ 24, 1, 2, 4 ], [ 24, 2, 2, 2 ], [ 27, 1, 15, 12 ],
[ 27, 2, 4, 6 ], [ 27, 4, 6, 6 ], [ 27, 5, 4, 6 ], [ 27, 7, 4, 3 ],
[ 27, 12, 6, 12 ], [ 30, 2, 17, 6 ], [ 30, 3, 17, 6 ], [ 30, 13, 14, 12 ] ]
k = 18: F-action on Pi is () [30,1,18]
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 0 modulo 4: 1/16 q^4 ( q-2 )
q congruent 1 modulo 4: 1/16 phi1^2 phi2^2 ( q-2 )
q congruent 2 modulo 4: 1/16 q^4 ( q-2 )
q congruent 3 modulo 4: 1/16 phi1^2 phi2^2 ( q-2 )
Fusion of maximal tori of C^F in those of G^F:
[ 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ],
[ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 1 ], [ 9, 1, 4, 8 ], [ 9, 2, 4, 4 ], [ 9, 3, 4, 4 ],
[ 9, 4, 4, 4 ], [ 9, 5, 4, 2 ], [ 12, 1, 4, 4 ], [ 12, 1, 5, 4 ],
[ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ],
[ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ],
[ 13, 2, 2, 2 ], [ 13, 2, 4, 2 ], [ 14, 1, 4, 8 ], [ 14, 2, 4, 4 ],
[ 16, 1, 2, 8 ], [ 16, 1, 4, 8 ], [ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ],
[ 16, 3, 2, 4 ], [ 16, 3, 4, 4 ], [ 16, 4, 2, 4 ], [ 16, 4, 4, 4 ],
[ 16, 8, 2, 4 ], [ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ],
[ 16, 9, 2, 2 ], [ 16, 9, 4, 2 ], [ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ],
[ 16, 11, 7, 2 ], [ 16, 11, 9, 4 ], [ 16, 13, 2, 4 ], [ 16, 13, 4, 4 ],
[ 16, 14, 2, 2 ], [ 16, 14, 3, 2 ], [ 16, 15, 2, 4 ], [ 16, 15, 4, 4 ],
[ 16, 16, 2, 4 ], [ 16, 16, 4, 4 ], [ 16, 17, 2, 2 ], [ 16, 17, 3, 2 ],
[ 21, 1, 6, 8 ], [ 21, 1, 8, 8 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 4 ],
[ 21, 3, 4, 4 ], [ 21, 3, 9, 4 ], [ 21, 4, 5, 4 ], [ 21, 4, 7, 4 ],
[ 21, 5, 5, 2 ], [ 21, 5, 7, 2 ], [ 21, 6, 4, 4 ], [ 21, 6, 8, 4 ],
[ 21, 7, 5, 4 ], [ 21, 7, 7, 4 ], [ 22, 1, 9, 8 ], [ 22, 1, 10, 8 ],
[ 22, 2, 9, 4 ], [ 22, 2, 10, 4 ], [ 22, 3, 7, 4 ], [ 22, 3, 8, 4 ],
[ 22, 4, 9, 2 ], [ 22, 4, 10, 4 ], [ 27, 1, 9, 16 ], [ 27, 2, 5, 8 ],
[ 27, 2, 7, 8 ], [ 27, 3, 5, 8 ], [ 27, 3, 9, 8 ], [ 27, 4, 4, 8 ],
[ 27, 4, 9, 8 ], [ 27, 5, 5, 8 ], [ 27, 6, 5, 4 ], [ 27, 6, 7, 4 ],
[ 27, 7, 5, 4 ], [ 27, 7, 7, 4 ], [ 27, 8, 5, 4 ], [ 27, 8, 9, 8 ],
[ 27, 9, 5, 4 ], [ 27, 10, 7, 4 ], [ 27, 10, 8, 4 ], [ 27, 11, 5, 4 ],
[ 27, 11, 9, 8 ], [ 27, 12, 4, 8 ], [ 27, 12, 9, 8 ], [ 27, 13, 4, 4 ],
[ 27, 13, 9, 4 ], [ 27, 14, 4, 4 ], [ 27, 14, 9, 8 ], [ 28, 1, 7, 16 ],
[ 28, 2, 7, 8 ], [ 28, 3, 7, 8 ], [ 28, 5, 7, 8 ], [ 28, 6, 7, 8 ],
[ 30, 2, 18, 8 ], [ 30, 3, 18, 8 ], [ 30, 4, 18, 8 ], [ 30, 4, 23, 8 ],
[ 30, 8, 20, 4 ], [ 30, 9, 20, 8 ], [ 30, 10, 20, 8 ], [ 30, 12, 18, 8 ],
[ 30, 12, 23, 8 ], [ 30, 13, 15, 8 ], [ 30, 13, 17, 8 ] ]
k = 19: F-action on Pi is () [30,1,19]
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 0 modulo 4: 1/16 q^3 ( q^2-2 )
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q^3-q-2 )
q congruent 2 modulo 4: 1/16 q^3 ( q^2-2 )
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q^3-q-2 )
Fusion of maximal tori of C^F in those of G^F:
[ 32, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ],
[ 9, 3, 5, 4 ], [ 9, 4, 5, 4 ], [ 9, 5, 5, 2 ], [ 10, 1, 2, 4 ],
[ 10, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 18, 1, 2, 4 ],
[ 18, 1, 4, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 25, 1, 7, 8 ],
[ 25, 1, 8, 8 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 3, 6, 4 ],
[ 25, 3, 8, 4 ], [ 27, 1, 19, 8 ], [ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ],
[ 30, 2, 19, 8 ], [ 30, 3, 19, 8 ], [ 30, 5, 19, 8 ], [ 30, 5, 22, 8 ],
[ 30, 8, 22, 8 ], [ 30, 9, 22, 4 ], [ 30, 10, 22, 8 ] ]
k = 20: F-action on Pi is () [30,1,20]
Dynkin type is A_1(q) + T(phi2^3 phi6)
Order of center |Z^F|: phi2^3 phi6
Numbers of classes in class type:
q congruent 0 modulo 4: 1/12 q^2 phi1^2 phi2
q congruent 1 modulo 4: 1/12 q^2 phi1^2 phi2
q congruent 2 modulo 4: 1/12 q^2 phi1^2 phi2
q congruent 3 modulo 4: 1/12 q^2 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 24, 21 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ], [ 6, 1, 2, 6 ],
[ 7, 1, 4, 4 ], [ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ],
[ 7, 5, 4, 1 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ],
[ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 13, 1, 4, 4 ], [ 13, 2, 4, 2 ],
[ 14, 1, 2, 4 ], [ 14, 2, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ],
[ 18, 1, 4, 4 ], [ 18, 2, 4, 2 ], [ 19, 1, 2, 8 ], [ 19, 2, 2, 4 ],
[ 19, 3, 2, 4 ], [ 19, 4, 2, 4 ], [ 19, 5, 2, 2 ], [ 20, 1, 4, 4 ],
[ 20, 2, 4, 2 ], [ 21, 1, 10, 6 ], [ 21, 4, 8, 3 ], [ 21, 7, 8, 6 ],
[ 24, 1, 4, 4 ], [ 24, 2, 4, 2 ], [ 27, 1, 18, 12 ], [ 27, 2, 8, 6 ],
[ 27, 4, 7, 6 ], [ 27, 5, 7, 6 ], [ 27, 7, 8, 3 ], [ 27, 12, 7, 12 ],
[ 28, 1, 8, 12 ], [ 28, 3, 8, 6 ], [ 28, 6, 8, 12 ], [ 30, 2, 20, 6 ],
[ 30, 3, 20, 6 ], [ 30, 13, 18, 12 ] ]
k = 21: F-action on Pi is () [30,1,21]
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 0 modulo 4: 1/16 q^3 ( q^2-2 )
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q^3-q-2 )
q congruent 2 modulo 4: 1/16 q^3 ( q^2-2 )
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q^3-q-2 )
Fusion of maximal tori of C^F in those of G^F:
[ 31, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ],
[ 9, 3, 7, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 7, 2 ], [ 11, 1, 2, 4 ],
[ 11, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 20, 1, 2, 4 ],
[ 20, 1, 4, 4 ], [ 20, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 26, 1, 7, 8 ],
[ 26, 1, 8, 8 ], [ 26, 2, 8, 4 ], [ 26, 2, 9, 4 ], [ 26, 3, 6, 4 ],
[ 26, 3, 8, 4 ], [ 27, 1, 19, 8 ], [ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ],
[ 30, 2, 21, 8 ], [ 30, 3, 21, 8 ], [ 30, 6, 19, 8 ], [ 30, 6, 22, 8 ],
[ 30, 8, 23, 8 ], [ 30, 9, 23, 8 ], [ 30, 10, 23, 4 ] ]
k = 22: F-action on Pi is () [30,1,22]
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 0 modulo 4: 1/64 q^2 ( q^3-4*q^2+8 )
q congruent 1 modulo 4: 1/64 phi1 ( q^4-3*q^3-5*q^2-5*q+60 )
q congruent 2 modulo 4: 1/64 q^2 ( q^3-4*q^2+8 )
q congruent 3 modulo 4: 1/64 ( q^5-4*q^4-2*q^3+49*q-12 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 6 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 16 ],
[ 9, 1, 2, 24 ], [ 9, 1, 5, 16 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 12 ],
[ 9, 2, 5, 8 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 12 ], [ 9, 3, 5, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 12 ], [ 9, 4, 5, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 6 ], [ 9, 5, 5, 4 ], [ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ],
[ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ], [ 12, 4, 2, 4 ], [ 15, 1, 1, 8 ],
[ 15, 1, 2, 16 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 16 ], [ 16, 1, 3, 32 ],
[ 16, 2, 3, 16 ], [ 16, 3, 3, 16 ], [ 16, 4, 3, 16 ], [ 16, 5, 2, 16 ],
[ 16, 5, 4, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 4, 16 ], [ 16, 7, 2, 16 ],
[ 16, 7, 4, 16 ], [ 16, 9, 3, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ],
[ 16, 11, 3, 16 ], [ 16, 12, 2, 8 ], [ 16, 12, 4, 8 ], [ 16, 13, 3, 8 ],
[ 16, 15, 3, 8 ], [ 16, 16, 3, 8 ], [ 18, 1, 2, 8 ], [ 18, 1, 4, 24 ],
[ 18, 2, 2, 4 ], [ 18, 2, 4, 12 ], [ 20, 1, 3, 16 ], [ 20, 2, 3, 8 ],
[ 22, 1, 2, 16 ], [ 22, 1, 5, 32 ], [ 22, 2, 2, 8 ], [ 22, 2, 5, 16 ],
[ 22, 4, 2, 8 ], [ 22, 4, 5, 16 ], [ 23, 1, 8, 32 ], [ 23, 2, 8, 16 ],
[ 23, 3, 8, 16 ], [ 23, 4, 8, 16 ], [ 23, 5, 8, 16 ], [ 23, 6, 8, 8 ],
[ 25, 1, 2, 16 ], [ 25, 1, 4, 48 ], [ 25, 1, 7, 32 ], [ 25, 2, 2, 8 ],
[ 25, 2, 6, 16 ], [ 25, 2, 8, 24 ], [ 25, 3, 5, 8 ], [ 25, 3, 6, 16 ],
[ 25, 3, 7, 24 ], [ 25, 3, 8, 16 ], [ 26, 1, 3, 32 ], [ 26, 2, 5, 16 ],
[ 26, 3, 3, 16 ], [ 27, 1, 12, 32 ], [ 27, 3, 7, 16 ], [ 27, 5, 8, 16 ],
[ 27, 8, 7, 16 ], [ 27, 9, 6, 8 ], [ 27, 9, 10, 16 ], [ 27, 11, 7, 16 ],
[ 27, 14, 6, 16 ], [ 29, 1, 6, 32 ], [ 29, 1, 12, 64 ], [ 29, 2, 6, 16 ],
[ 29, 2, 12, 32 ], [ 29, 3, 6, 16 ], [ 29, 3, 12, 32 ], [ 29, 4, 6, 16 ],
[ 29, 4, 12, 32 ], [ 29, 5, 6, 16 ], [ 29, 5, 12, 32 ], [ 29, 6, 8, 32 ],
[ 29, 7, 8, 32 ], [ 29, 8, 8, 32 ], [ 29, 9, 6, 8 ], [ 29, 9, 12, 16 ],
[ 29, 10, 8, 16 ], [ 29, 11, 8, 16 ], [ 29, 12, 8, 16 ], [ 29, 13, 8, 16 ],
[ 30, 2, 22, 32 ], [ 30, 3, 22, 32 ], [ 30, 4, 20, 32 ], [ 30, 5, 20, 32 ],
[ 30, 5, 23, 32 ], [ 30, 5, 28, 32 ], [ 30, 6, 23, 32 ], [ 30, 7, 21, 32 ],
[ 30, 7, 29, 32 ], [ 30, 8, 24, 32 ], [ 30, 8, 28, 16 ], [ 30, 9, 24, 16 ],
[ 30, 9, 28, 16 ], [ 30, 10, 24, 32 ], [ 30, 10, 28, 16 ],
[ 30, 11, 21, 16 ], [ 30, 11, 29, 16 ], [ 30, 12, 20, 16 ] ]
k = 23: F-action on Pi is () [30,1,23]
Dynkin type is A_1(q) + T(phi1 phi2^4)
Order of center |Z^F|: phi1 phi2^4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/32 q^2 ( q^3-6*q^2+12*q-8 )
q congruent 1 modulo 4: 1/32 phi1 ( q^4-5*q^3+5*q^2-3*q+18 )
q congruent 2 modulo 4: 1/32 q^2 ( q^3-6*q^2+12*q-8 )
q congruent 3 modulo 4: 1/32 phi1 ( q^4-5*q^3+5*q^2-3*q+18 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 8 ],
[ 6, 1, 2, 16 ], [ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ],
[ 7, 4, 4, 8 ], [ 7, 5, 4, 4 ], [ 8, 1, 2, 20 ], [ 9, 1, 1, 8 ],
[ 9, 1, 2, 32 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 16 ], [ 9, 3, 1, 4 ],
[ 9, 3, 2, 16 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 16 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 8 ], [ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ], [ 11, 1, 2, 8 ],
[ 11, 2, 2, 4 ], [ 12, 1, 2, 4 ], [ 12, 1, 3, 8 ], [ 12, 2, 2, 2 ],
[ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 2, 2 ], [ 12, 4, 3, 2 ],
[ 13, 1, 3, 8 ], [ 13, 1, 4, 16 ], [ 13, 2, 3, 4 ], [ 13, 2, 4, 8 ],
[ 14, 1, 2, 32 ], [ 14, 2, 2, 16 ], [ 15, 1, 3, 40 ], [ 15, 1, 4, 12 ],
[ 16, 1, 3, 16 ], [ 16, 1, 5, 32 ], [ 16, 2, 3, 8 ], [ 16, 2, 5, 16 ],
[ 16, 3, 3, 8 ], [ 16, 3, 5, 16 ], [ 16, 4, 3, 8 ], [ 16, 4, 5, 16 ],
[ 16, 5, 2, 8 ], [ 16, 5, 3, 16 ], [ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ],
[ 16, 6, 3, 16 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ], [ 16, 7, 3, 16 ],
[ 16, 7, 4, 8 ], [ 16, 8, 4, 16 ], [ 16, 9, 3, 4 ], [ 16, 9, 5, 8 ],
[ 16, 10, 2, 4 ], [ 16, 10, 3, 8 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ],
[ 16, 11, 5, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 3, 8 ], [ 16, 12, 4, 4 ],
[ 16, 13, 3, 4 ], [ 16, 13, 5, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 3, 4 ],
[ 16, 15, 5, 8 ], [ 16, 16, 3, 4 ], [ 16, 16, 5, 8 ], [ 16, 17, 4, 8 ],
[ 17, 1, 2, 16 ], [ 17, 2, 2, 8 ], [ 18, 1, 3, 8 ], [ 18, 1, 4, 24 ],
[ 18, 2, 3, 4 ], [ 18, 2, 4, 12 ], [ 19, 1, 2, 32 ], [ 19, 2, 2, 16 ],
[ 19, 3, 2, 16 ], [ 19, 4, 2, 16 ], [ 19, 5, 2, 8 ], [ 20, 1, 3, 8 ],
[ 20, 1, 4, 24 ], [ 20, 2, 3, 4 ], [ 20, 2, 4, 12 ], [ 21, 1, 7, 16 ],
[ 21, 2, 9, 8 ], [ 21, 3, 8, 8 ], [ 21, 4, 9, 8 ], [ 21, 5, 9, 4 ],
[ 21, 6, 9, 8 ], [ 21, 7, 9, 8 ], [ 22, 1, 3, 16 ], [ 22, 1, 5, 24 ],
[ 22, 1, 6, 32 ], [ 22, 2, 3, 8 ], [ 22, 2, 5, 12 ], [ 22, 2, 6, 16 ],
[ 22, 3, 2, 8 ], [ 22, 3, 4, 16 ], [ 22, 4, 3, 4 ], [ 22, 4, 5, 12 ],
[ 22, 4, 6, 8 ], [ 23, 1, 6, 16 ], [ 23, 1, 7, 16 ], [ 23, 1, 8, 16 ],
[ 23, 2, 6, 8 ], [ 23, 2, 7, 8 ], [ 23, 2, 8, 8 ], [ 23, 3, 6, 8 ],
[ 23, 3, 7, 8 ], [ 23, 3, 8, 8 ], [ 23, 4, 6, 8 ], [ 23, 4, 7, 8 ],
[ 23, 4, 8, 8 ], [ 23, 5, 6, 8 ], [ 23, 5, 7, 8 ], [ 23, 5, 8, 8 ],
[ 23, 6, 6, 4 ], [ 23, 6, 7, 4 ], [ 23, 6, 8, 4 ], [ 24, 1, 3, 16 ],
[ 24, 1, 4, 32 ], [ 24, 2, 3, 8 ], [ 24, 2, 4, 16 ], [ 25, 1, 3, 16 ],
[ 25, 1, 4, 48 ], [ 25, 2, 5, 8 ], [ 25, 2, 8, 24 ], [ 25, 3, 3, 8 ],
[ 25, 3, 7, 24 ], [ 26, 1, 3, 16 ], [ 26, 1, 4, 48 ], [ 26, 2, 5, 8 ],
[ 26, 2, 10, 24 ], [ 26, 3, 3, 8 ], [ 26, 3, 7, 24 ], [ 27, 1, 10, 32 ],
[ 27, 2, 9, 16 ], [ 27, 3, 8, 16 ], [ 27, 3, 12, 16 ], [ 27, 4, 8, 16 ],
[ 27, 5, 9, 16 ], [ 27, 6, 9, 8 ], [ 27, 7, 9, 8 ], [ 27, 8, 8, 16 ],
[ 27, 8, 12, 8 ], [ 27, 9, 7, 8 ], [ 27, 10, 6, 8 ], [ 27, 11, 8, 16 ],
[ 27, 11, 12, 8 ], [ 27, 12, 8, 16 ], [ 27, 13, 8, 8 ], [ 27, 14, 10, 16 ],
[ 27, 14, 12, 8 ], [ 28, 1, 9, 32 ], [ 28, 2, 9, 16 ], [ 28, 3, 9, 16 ],
[ 28, 4, 6, 16 ], [ 28, 4, 8, 16 ], [ 28, 5, 9, 8 ], [ 28, 6, 9, 16 ],
[ 29, 1, 7, 16 ], [ 29, 1, 10, 32 ], [ 29, 1, 11, 32 ], [ 29, 1, 12, 32 ],
[ 29, 2, 7, 8 ], [ 29, 2, 10, 16 ], [ 29, 2, 11, 16 ], [ 29, 2, 12, 16 ],
[ 29, 3, 7, 8 ], [ 29, 3, 10, 16 ], [ 29, 3, 11, 16 ], [ 29, 3, 12, 16 ],
[ 29, 4, 7, 8 ], [ 29, 4, 10, 16 ], [ 29, 4, 11, 16 ], [ 29, 4, 12, 16 ],
[ 29, 5, 7, 8 ], [ 29, 5, 10, 16 ], [ 29, 5, 11, 16 ], [ 29, 5, 12, 16 ],
[ 29, 6, 6, 16 ], [ 29, 6, 7, 16 ], [ 29, 6, 8, 16 ], [ 29, 7, 6, 16 ],
[ 29, 7, 7, 16 ], [ 29, 7, 8, 16 ], [ 29, 8, 6, 16 ], [ 29, 8, 7, 16 ],
[ 29, 8, 8, 16 ], [ 29, 9, 7, 4 ], [ 29, 9, 10, 8 ], [ 29, 9, 11, 8 ],
[ 29, 9, 12, 8 ], [ 29, 10, 6, 8 ], [ 29, 10, 7, 8 ], [ 29, 10, 8, 8 ],
[ 29, 11, 6, 8 ], [ 29, 11, 7, 8 ], [ 29, 11, 8, 8 ], [ 29, 12, 6, 8 ],
[ 29, 12, 7, 8 ], [ 29, 12, 8, 8 ], [ 29, 13, 6, 8 ], [ 29, 13, 7, 8 ],
[ 29, 13, 8, 8 ], [ 30, 2, 23, 16 ], [ 30, 3, 23, 16 ], [ 30, 4, 24, 16 ],
[ 30, 4, 27, 16 ], [ 30, 5, 24, 16 ], [ 30, 5, 27, 16 ], [ 30, 6, 24, 16 ],
[ 30, 6, 26, 16 ], [ 30, 7, 23, 16 ], [ 30, 7, 26, 16 ], [ 30, 7, 28, 16 ],
[ 30, 7, 30, 16 ], [ 30, 8, 30, 8 ], [ 30, 9, 30, 8 ], [ 30, 10, 30, 8 ],
[ 30, 11, 23, 8 ], [ 30, 11, 26, 8 ], [ 30, 11, 28, 8 ], [ 30, 11, 30, 8 ],
[ 30, 12, 24, 8 ], [ 30, 12, 27, 8 ], [ 30, 13, 19, 16 ] ]
k = 24: F-action on Pi is () [30,1,24]
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 0 modulo 4: 1/64 q^2 ( q^3-4*q^2+8 )
q congruent 1 modulo 4: 1/64 phi1 ( q^4-3*q^3-5*q^2-5*q+60 )
q congruent 2 modulo 4: 1/64 q^2 ( q^3-4*q^2+8 )
q congruent 3 modulo 4: 1/64 ( q^5-4*q^4-2*q^3+49*q-12 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 6 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 12 ], [ 9, 1, 1, 16 ],
[ 9, 1, 2, 24 ], [ 9, 1, 7, 16 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 12 ],
[ 9, 2, 7, 8 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 12 ], [ 9, 3, 7, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 12 ], [ 9, 4, 7, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 6 ], [ 9, 5, 7, 4 ], [ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ],
[ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ], [ 12, 4, 2, 4 ], [ 15, 1, 1, 8 ],
[ 15, 1, 2, 16 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 16 ], [ 16, 1, 3, 32 ],
[ 16, 2, 3, 16 ], [ 16, 3, 3, 16 ], [ 16, 4, 3, 16 ], [ 16, 5, 2, 16 ],
[ 16, 5, 4, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 4, 16 ], [ 16, 7, 2, 16 ],
[ 16, 7, 4, 16 ], [ 16, 9, 3, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ],
[ 16, 11, 3, 16 ], [ 16, 12, 2, 8 ], [ 16, 12, 4, 8 ], [ 16, 13, 3, 8 ],
[ 16, 15, 3, 8 ], [ 16, 16, 3, 8 ], [ 18, 1, 3, 16 ], [ 18, 2, 3, 8 ],
[ 20, 1, 2, 8 ], [ 20, 1, 4, 24 ], [ 20, 2, 2, 4 ], [ 20, 2, 4, 12 ],
[ 22, 1, 2, 16 ], [ 22, 1, 5, 32 ], [ 22, 2, 2, 8 ], [ 22, 2, 5, 16 ],
[ 22, 4, 2, 8 ], [ 22, 4, 5, 16 ], [ 23, 1, 6, 32 ], [ 23, 2, 6, 16 ],
[ 23, 3, 6, 16 ], [ 23, 4, 6, 16 ], [ 23, 5, 6, 16 ], [ 23, 6, 6, 8 ],
[ 25, 1, 3, 32 ], [ 25, 2, 5, 16 ], [ 25, 3, 3, 16 ], [ 26, 1, 2, 16 ],
[ 26, 1, 4, 48 ], [ 26, 1, 7, 32 ], [ 26, 2, 2, 8 ], [ 26, 2, 8, 16 ],
[ 26, 2, 10, 24 ], [ 26, 3, 5, 8 ], [ 26, 3, 6, 16 ], [ 26, 3, 7, 24 ],
[ 26, 3, 8, 16 ], [ 27, 1, 12, 32 ], [ 27, 3, 7, 16 ], [ 27, 5, 8, 16 ],
[ 27, 8, 7, 16 ], [ 27, 9, 6, 8 ], [ 27, 9, 10, 16 ], [ 27, 11, 7, 16 ],
[ 27, 14, 6, 16 ], [ 29, 1, 8, 32 ], [ 29, 1, 10, 64 ], [ 29, 2, 8, 16 ],
[ 29, 2, 10, 32 ], [ 29, 3, 8, 16 ], [ 29, 3, 10, 32 ], [ 29, 4, 8, 16 ],
[ 29, 4, 10, 32 ], [ 29, 5, 8, 16 ], [ 29, 5, 10, 32 ], [ 29, 6, 6, 32 ],
[ 29, 7, 6, 32 ], [ 29, 8, 6, 32 ], [ 29, 9, 8, 8 ], [ 29, 9, 10, 16 ],
[ 29, 10, 6, 16 ], [ 29, 11, 6, 16 ], [ 29, 12, 6, 16 ], [ 29, 13, 6, 16 ],
[ 30, 2, 24, 32 ], [ 30, 3, 24, 32 ], [ 30, 4, 25, 32 ], [ 30, 5, 25, 32 ],
[ 30, 6, 20, 32 ], [ 30, 6, 25, 32 ], [ 30, 6, 28, 32 ], [ 30, 7, 24, 32 ],
[ 30, 7, 32, 32 ], [ 30, 8, 25, 32 ], [ 30, 8, 31, 16 ], [ 30, 9, 25, 32 ],
[ 30, 9, 31, 16 ], [ 30, 10, 25, 16 ], [ 30, 10, 31, 16 ],
[ 30, 11, 24, 16 ], [ 30, 11, 32, 16 ], [ 30, 12, 25, 16 ] ]
k = 25: F-action on Pi is () [30,1,25]
Dynkin type is A_1(q) + T(phi2 phi4^2)
Order of center |Z^F|: phi2 phi4^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/32 q^3 ( q^2-4 )
q congruent 1 modulo 4: 1/32 phi1 phi2^2 ( q^2-q-4 )
q congruent 2 modulo 4: 1/32 q^3 ( q^2-4 )
q congruent 3 modulo 4: 1/32 phi1 phi2^2 ( q^2-q-4 )
Fusion of maximal tori of C^F in those of G^F:
[ 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 4, 8 ], [ 9, 1, 5, 8 ],
[ 9, 1, 7, 8 ], [ 9, 2, 4, 4 ], [ 9, 2, 5, 4 ], [ 9, 2, 7, 4 ],
[ 9, 3, 4, 4 ], [ 9, 3, 5, 4 ], [ 9, 3, 7, 4 ], [ 9, 4, 4, 4 ],
[ 9, 4, 5, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 4, 2 ], [ 9, 5, 5, 2 ],
[ 9, 5, 7, 2 ], [ 12, 1, 5, 8 ], [ 12, 2, 5, 4 ], [ 12, 4, 5, 4 ],
[ 15, 1, 5, 16 ], [ 16, 1, 4, 16 ], [ 16, 2, 4, 8 ], [ 16, 3, 4, 8 ],
[ 16, 4, 4, 8 ], [ 16, 9, 4, 4 ], [ 16, 11, 4, 8 ], [ 16, 11, 9, 8 ],
[ 16, 13, 4, 8 ], [ 16, 15, 4, 8 ], [ 16, 16, 4, 8 ], [ 22, 1, 10, 16 ],
[ 22, 2, 10, 8 ], [ 22, 4, 10, 8 ], [ 25, 1, 8, 16 ], [ 25, 2, 7, 8 ],
[ 26, 1, 8, 16 ], [ 26, 2, 9, 8 ], [ 27, 1, 14, 32 ], [ 27, 3, 10, 16 ],
[ 27, 5, 10, 16 ], [ 27, 8, 10, 16 ], [ 27, 9, 8, 8 ], [ 27, 9, 11, 16 ],
[ 27, 11, 10, 16 ], [ 27, 14, 7, 16 ], [ 30, 2, 25, 16 ], [ 30, 3, 25, 16 ],
[ 30, 4, 21, 16 ], [ 30, 5, 21, 16 ], [ 30, 6, 21, 16 ], [ 30, 8, 26, 16 ],
[ 30, 8, 27, 16 ], [ 30, 8, 29, 8 ], [ 30, 9, 26, 16 ], [ 30, 9, 27, 8 ],
[ 30, 9, 29, 16 ], [ 30, 10, 26, 8 ], [ 30, 10, 27, 16 ],
[ 30, 10, 29, 16 ], [ 30, 12, 21, 16 ] ]
k = 26: F-action on Pi is () [30,1,26]
Dynkin type is A_1(q) + T(phi2^5)
Order of center |Z^F|: phi2^5
Numbers of classes in class type:
q congruent 0 modulo 4: 1/384 q ( q^4-16*q^3+92*q^2-224*q+192 )
q congruent 1 modulo 4: 1/384 phi1^2 ( q^3-14*q^2+57*q-60 )
q congruent 2 modulo 4: 1/384 q ( q^4-16*q^3+92*q^2-224*q+192 )
q congruent 3 modulo
4: 1/384 ( q^5-16*q^4+86*q^3-188*q^2+225*q-252 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 2, 16 ],
[ 3, 2, 2, 8 ], [ 3, 3, 2, 8 ], [ 3, 4, 2, 8 ], [ 3, 5, 2, 4 ],
[ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 5, 1, 2, 26 ], [ 6, 1, 2, 48 ],
[ 7, 1, 4, 64 ], [ 7, 2, 4, 32 ], [ 7, 3, 4, 32 ], [ 7, 4, 4, 32 ],
[ 7, 5, 4, 16 ], [ 8, 1, 2, 64 ], [ 9, 1, 2, 120 ], [ 9, 2, 2, 60 ],
[ 9, 3, 2, 60 ], [ 9, 4, 2, 60 ], [ 9, 5, 2, 30 ], [ 10, 1, 2, 16 ],
[ 10, 2, 2, 8 ], [ 11, 1, 2, 16 ], [ 11, 2, 2, 8 ], [ 12, 1, 3, 48 ],
[ 12, 2, 3, 24 ], [ 12, 3, 2, 24 ], [ 12, 4, 3, 12 ], [ 13, 1, 4, 112 ],
[ 13, 2, 4, 56 ], [ 14, 1, 2, 160 ], [ 14, 2, 2, 80 ], [ 15, 1, 3, 192 ],
[ 16, 1, 5, 192 ], [ 16, 2, 5, 96 ], [ 16, 3, 5, 96 ], [ 16, 4, 5, 96 ],
[ 16, 5, 3, 96 ], [ 16, 6, 3, 96 ], [ 16, 7, 3, 96 ], [ 16, 8, 4, 96 ],
[ 16, 9, 5, 48 ], [ 16, 10, 3, 48 ], [ 16, 11, 5, 48 ], [ 16, 12, 3, 48 ],
[ 16, 13, 5, 48 ], [ 16, 14, 4, 48 ], [ 16, 15, 5, 48 ], [ 16, 16, 5, 48 ],
[ 16, 17, 4, 48 ], [ 17, 1, 2, 64 ], [ 17, 2, 2, 32 ], [ 18, 1, 4, 112 ],
[ 18, 2, 4, 56 ], [ 19, 1, 2, 128 ], [ 19, 2, 2, 64 ], [ 19, 3, 2, 64 ],
[ 19, 4, 2, 64 ], [ 19, 5, 2, 32 ], [ 20, 1, 4, 112 ], [ 20, 2, 4, 56 ],
[ 21, 1, 4, 192 ], [ 21, 2, 10, 96 ], [ 21, 3, 10, 96 ], [ 21, 4, 10, 96 ],
[ 21, 5, 10, 48 ], [ 21, 6, 10, 48 ], [ 21, 7, 10, 48 ], [ 22, 1, 6, 288 ],
[ 22, 2, 6, 144 ], [ 22, 3, 4, 144 ], [ 22, 4, 6, 72 ], [ 23, 1, 7, 192 ],
[ 23, 2, 7, 96 ], [ 23, 3, 7, 96 ], [ 23, 4, 7, 96 ], [ 23, 5, 7, 96 ],
[ 23, 6, 7, 48 ], [ 24, 1, 4, 256 ], [ 24, 2, 4, 128 ], [ 25, 1, 4, 288 ],
[ 25, 2, 8, 144 ], [ 25, 3, 7, 144 ], [ 26, 1, 4, 288 ], [ 26, 2, 10, 144 ],
[ 26, 3, 7, 144 ], [ 27, 1, 5, 384 ], [ 27, 2, 10, 192 ],
[ 27, 3, 13, 192 ], [ 27, 4, 10, 192 ], [ 27, 5, 11, 192 ],
[ 27, 6, 10, 96 ], [ 27, 7, 10, 96 ], [ 27, 8, 13, 96 ], [ 27, 9, 12, 96 ],
[ 27, 10, 10, 96 ], [ 27, 11, 13, 96 ], [ 27, 12, 10, 96 ],
[ 27, 13, 10, 96 ], [ 27, 14, 13, 96 ], [ 28, 1, 10, 384 ],
[ 28, 2, 10, 192 ], [ 28, 3, 10, 192 ], [ 28, 4, 7, 192 ],
[ 28, 5, 10, 96 ], [ 28, 6, 10, 96 ], [ 29, 1, 11, 384 ],
[ 29, 2, 11, 192 ], [ 29, 3, 11, 192 ], [ 29, 4, 11, 192 ],
[ 29, 5, 11, 192 ], [ 29, 6, 7, 192 ], [ 29, 7, 7, 192 ], [ 29, 8, 7, 192 ],
[ 29, 9, 11, 96 ], [ 29, 10, 7, 96 ], [ 29, 11, 7, 96 ], [ 29, 12, 7, 96 ],
[ 29, 13, 7, 96 ], [ 30, 2, 26, 192 ], [ 30, 3, 26, 192 ],
[ 30, 4, 28, 192 ], [ 30, 5, 26, 192 ], [ 30, 6, 27, 192 ],
[ 30, 7, 27, 192 ], [ 30, 8, 32, 96 ], [ 30, 9, 32, 96 ],
[ 30, 10, 32, 96 ], [ 30, 11, 27, 96 ], [ 30, 12, 28, 96 ],
[ 30, 13, 20, 96 ] ]
j = 4: Omega of order 2, action on Pi: <()>
k = 1: F-action on Pi is () [30,4,1]
Dynkin type is (A_1(q) + T(phi1^5)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 ( q^3-15*q^2+67*q-85 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 7 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 8 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 4 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 4 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 8 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 16 ], [ 7, 3, 1, 16 ], [ 7, 4, 1, 16 ],
[ 7, 5, 1, 16 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 24 ], [ 9, 2, 1, 20 ],
[ 9, 3, 1, 12 ], [ 9, 4, 1, 12 ], [ 9, 5, 1, 10 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 8 ], [ 12, 3, 1, 12 ], [ 12, 4, 1, 12 ], [ 13, 1, 1, 8 ],
[ 13, 2, 1, 16 ], [ 14, 1, 1, 16 ], [ 14, 2, 1, 24 ], [ 15, 1, 1, 16 ],
[ 16, 1, 1, 32 ], [ 16, 2, 1, 32 ], [ 16, 3, 1, 16 ], [ 16, 4, 1, 16 ],
[ 16, 5, 1, 16 ], [ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ], [ 16, 8, 1, 32 ],
[ 16, 9, 1, 16 ], [ 16, 10, 1, 16 ], [ 16, 11, 1, 32 ], [ 16, 12, 1, 8 ],
[ 16, 13, 1, 8 ], [ 16, 14, 1, 24 ], [ 16, 15, 1, 8 ], [ 16, 16, 1, 8 ],
[ 16, 17, 1, 24 ], [ 21, 2, 1, 16 ], [ 21, 3, 1, 16 ], [ 21, 5, 1, 16 ],
[ 21, 6, 1, 24 ], [ 21, 7, 1, 24 ], [ 22, 1, 1, 16 ], [ 22, 2, 1, 32 ],
[ 22, 3, 1, 24 ], [ 22, 4, 1, 32 ], [ 23, 2, 1, 16 ], [ 23, 6, 1, 8 ],
[ 27, 3, 1, 32 ], [ 27, 6, 1, 16 ], [ 27, 8, 1, 16 ], [ 27, 9, 1, 32 ],
[ 27, 10, 1, 16 ], [ 27, 11, 1, 16 ], [ 27, 12, 1, 48 ], [ 27, 13, 1, 16 ],
[ 27, 14, 1, 16 ], [ 28, 2, 1, 32 ], [ 28, 5, 1, 16 ], [ 28, 6, 1, 48 ],
[ 29, 4, 1, 32 ], [ 29, 9, 1, 16 ], [ 29, 12, 1, 16 ], [ 30, 8, 1, 32 ],
[ 30, 11, 1, 16 ], [ 30, 12, 1, 16 ], [ 30, 13, 1, 48 ] ]
k = 2: F-action on Pi is () [30,4,2]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ],
[ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 1, 4 ], [ 7, 2, 2, 4 ], [ 7, 2, 3, 4 ],
[ 7, 2, 4, 4 ], [ 7, 3, 1, 4 ], [ 7, 3, 2, 4 ], [ 7, 3, 3, 4 ],
[ 7, 3, 4, 4 ], [ 7, 4, 1, 4 ], [ 7, 4, 2, 4 ], [ 7, 4, 3, 4 ],
[ 7, 4, 4, 4 ], [ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ],
[ 7, 5, 4, 4 ], [ 9, 1, 3, 8 ], [ 9, 2, 1, 4 ], [ 9, 2, 3, 8 ],
[ 9, 3, 3, 4 ], [ 9, 4, 3, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 3, 4 ],
[ 12, 1, 4, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 1, 2 ], [ 12, 3, 2, 2 ],
[ 12, 3, 3, 4 ], [ 12, 3, 4, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 13, 2, 1, 4 ],
[ 13, 2, 3, 4 ], [ 14, 1, 3, 8 ], [ 14, 2, 1, 4 ], [ 14, 2, 3, 8 ],
[ 16, 1, 2, 8 ], [ 16, 2, 2, 8 ], [ 16, 3, 2, 4 ], [ 16, 4, 2, 4 ],
[ 16, 8, 1, 4 ], [ 16, 8, 2, 8 ], [ 16, 8, 3, 8 ], [ 16, 8, 4, 4 ],
[ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ], [ 16, 9, 2, 4 ], [ 16, 11, 1, 4 ],
[ 16, 11, 2, 8 ], [ 16, 11, 5, 4 ], [ 16, 11, 7, 4 ], [ 16, 13, 2, 4 ],
[ 16, 14, 1, 4 ], [ 16, 14, 2, 4 ], [ 16, 14, 3, 4 ], [ 16, 14, 4, 4 ],
[ 16, 15, 2, 4 ], [ 16, 16, 2, 4 ], [ 16, 17, 1, 4 ], [ 16, 17, 2, 4 ],
[ 16, 17, 3, 4 ], [ 16, 17, 4, 4 ], [ 21, 2, 4, 4 ], [ 21, 2, 6, 4 ],
[ 21, 3, 2, 4 ], [ 21, 3, 7, 4 ], [ 21, 5, 4, 4 ], [ 21, 5, 6, 4 ],
[ 21, 6, 2, 4 ], [ 21, 6, 5, 4 ], [ 21, 6, 6, 4 ], [ 21, 6, 7, 4 ],
[ 21, 7, 3, 4 ], [ 21, 7, 6, 4 ], [ 22, 1, 7, 8 ], [ 22, 2, 7, 8 ],
[ 22, 3, 1, 4 ], [ 22, 3, 2, 4 ], [ 22, 3, 5, 8 ], [ 22, 3, 6, 8 ],
[ 22, 4, 1, 4 ], [ 22, 4, 3, 4 ], [ 22, 4, 7, 8 ], [ 27, 3, 4, 8 ],
[ 27, 6, 4, 4 ], [ 27, 6, 6, 4 ], [ 27, 8, 4, 4 ], [ 27, 9, 4, 8 ],
[ 27, 10, 3, 4 ], [ 27, 10, 4, 4 ], [ 27, 11, 4, 4 ], [ 27, 12, 2, 8 ],
[ 27, 12, 5, 8 ], [ 27, 13, 2, 4 ], [ 27, 13, 7, 4 ], [ 27, 14, 2, 4 ],
[ 28, 2, 4, 8 ], [ 28, 5, 4, 8 ], [ 28, 6, 3, 8 ], [ 30, 8, 2, 8 ],
[ 30, 12, 2, 8 ], [ 30, 13, 3, 8 ], [ 30, 13, 6, 8 ] ]
k = 3: F-action on Pi is () [30,4,3]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^3-9*q^2+19*q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 8 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ], [ 7, 4, 1, 8 ],
[ 7, 5, 1, 4 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 24 ], [ 9, 2, 1, 12 ],
[ 9, 3, 1, 12 ], [ 9, 4, 1, 12 ], [ 9, 5, 1, 6 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ],
[ 12, 4, 2, 2 ], [ 13, 1, 1, 8 ], [ 13, 2, 1, 4 ], [ 14, 1, 1, 16 ],
[ 14, 2, 1, 8 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 32 ], [ 16, 2, 1, 16 ],
[ 16, 2, 3, 8 ], [ 16, 3, 1, 16 ], [ 16, 4, 1, 16 ], [ 16, 5, 1, 16 ],
[ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ], [ 16, 8, 1, 16 ], [ 16, 9, 1, 8 ],
[ 16, 9, 3, 4 ], [ 16, 10, 1, 8 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ],
[ 16, 11, 1, 8 ], [ 16, 11, 3, 8 ], [ 16, 12, 1, 8 ], [ 16, 13, 1, 8 ],
[ 16, 14, 1, 8 ], [ 16, 15, 1, 8 ], [ 16, 16, 1, 8 ], [ 16, 17, 1, 8 ],
[ 21, 3, 3, 8 ], [ 21, 5, 2, 4 ], [ 21, 6, 3, 8 ], [ 21, 7, 2, 8 ],
[ 22, 1, 1, 16 ], [ 22, 2, 1, 8 ], [ 22, 2, 2, 12 ], [ 22, 3, 1, 8 ],
[ 22, 4, 1, 4 ], [ 22, 4, 2, 12 ], [ 23, 2, 2, 8 ], [ 23, 2, 4, 8 ],
[ 23, 6, 2, 4 ], [ 23, 6, 4, 4 ], [ 27, 3, 6, 16 ], [ 27, 6, 2, 8 ],
[ 27, 8, 6, 16 ], [ 27, 9, 2, 8 ], [ 27, 10, 5, 8 ], [ 27, 11, 6, 16 ],
[ 27, 12, 3, 16 ], [ 27, 13, 3, 8 ], [ 27, 14, 8, 16 ], [ 28, 2, 2, 16 ],
[ 28, 5, 2, 8 ], [ 28, 6, 2, 16 ], [ 29, 4, 2, 16 ], [ 29, 4, 4, 16 ],
[ 29, 9, 2, 8 ], [ 29, 9, 4, 8 ], [ 29, 12, 2, 8 ], [ 29, 12, 4, 8 ],
[ 30, 8, 3, 8 ], [ 30, 11, 2, 8 ], [ 30, 11, 4, 8 ], [ 30, 12, 3, 8 ],
[ 30, 13, 2, 16 ] ]
k = 4: F-action on Pi is () [30,4,4]
Dynkin type is (A_1(q) + T(phi1^2 phi2 phi4)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ],
[ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 1 ], [ 9, 1, 3, 8 ], [ 9, 2, 3, 4 ], [ 9, 3, 3, 4 ],
[ 9, 4, 3, 4 ], [ 9, 5, 3, 2 ], [ 12, 1, 4, 4 ], [ 12, 2, 4, 2 ],
[ 12, 2, 5, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ],
[ 12, 4, 5, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 13, 2, 1, 2 ],
[ 13, 2, 3, 2 ], [ 14, 1, 3, 8 ], [ 14, 2, 3, 4 ], [ 16, 1, 2, 8 ],
[ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 3, 2, 4 ], [ 16, 4, 2, 4 ],
[ 16, 8, 2, 4 ], [ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ],
[ 16, 9, 2, 2 ], [ 16, 9, 4, 2 ], [ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ],
[ 16, 11, 7, 2 ], [ 16, 11, 9, 4 ], [ 16, 13, 2, 4 ], [ 16, 14, 2, 2 ],
[ 16, 14, 3, 2 ], [ 16, 15, 2, 4 ], [ 16, 16, 2, 4 ], [ 16, 17, 2, 2 ],
[ 16, 17, 3, 2 ], [ 21, 3, 4, 4 ], [ 21, 3, 9, 4 ], [ 21, 5, 5, 2 ],
[ 21, 5, 7, 2 ], [ 21, 6, 4, 4 ], [ 21, 6, 8, 4 ], [ 21, 7, 5, 4 ],
[ 21, 7, 7, 4 ], [ 22, 1, 7, 8 ], [ 22, 2, 7, 4 ], [ 22, 2, 8, 4 ],
[ 22, 3, 5, 4 ], [ 22, 3, 6, 4 ], [ 22, 4, 7, 2 ], [ 22, 4, 8, 4 ],
[ 27, 3, 9, 8 ], [ 27, 6, 5, 4 ], [ 27, 6, 7, 4 ], [ 27, 8, 9, 8 ],
[ 27, 9, 5, 4 ], [ 27, 10, 7, 4 ], [ 27, 10, 8, 4 ], [ 27, 11, 9, 8 ],
[ 27, 12, 4, 8 ], [ 27, 12, 9, 8 ], [ 27, 13, 4, 4 ], [ 27, 13, 9, 4 ],
[ 27, 14, 9, 8 ], [ 28, 2, 5, 8 ], [ 28, 5, 5, 8 ], [ 28, 6, 5, 8 ],
[ 30, 8, 4, 4 ], [ 30, 12, 4, 8 ], [ 30, 13, 5, 8 ], [ 30, 13, 7, 8 ] ]
k = 5: F-action on Pi is () [30,4,5]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 ( q^3-15*q^2+67*q-85 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 2, 2, 2, 4 ],
[ 3, 1, 1, 8 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 4 ], [ 3, 3, 1, 4 ],
[ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 6 ], [ 6, 1, 1, 8 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 2, 2, 8 ], [ 7, 3, 1, 8 ],
[ 7, 3, 4, 8 ], [ 7, 4, 1, 8 ], [ 7, 4, 3, 8 ], [ 7, 5, 1, 4 ],
[ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ], [ 8, 1, 1, 8 ],
[ 9, 1, 1, 24 ], [ 9, 2, 1, 12 ], [ 9, 2, 3, 8 ], [ 9, 3, 1, 12 ],
[ 9, 4, 1, 12 ], [ 9, 5, 1, 6 ], [ 9, 5, 3, 4 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 2, 3, 4 ], [ 12, 3, 1, 4 ], [ 12, 3, 4, 8 ],
[ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ], [ 13, 1, 1, 8 ],
[ 13, 2, 1, 4 ], [ 13, 2, 3, 12 ], [ 14, 1, 1, 16 ], [ 14, 2, 1, 8 ],
[ 14, 2, 3, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 32 ], [ 16, 2, 1, 16 ],
[ 16, 2, 5, 16 ], [ 16, 3, 1, 16 ], [ 16, 4, 1, 16 ], [ 16, 5, 1, 16 ],
[ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ], [ 16, 8, 1, 16 ], [ 16, 8, 2, 16 ],
[ 16, 9, 1, 8 ], [ 16, 9, 5, 8 ], [ 16, 10, 1, 8 ], [ 16, 10, 3, 8 ],
[ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ], [ 16, 11, 5, 8 ], [ 16, 12, 1, 8 ],
[ 16, 13, 1, 8 ], [ 16, 14, 1, 8 ], [ 16, 14, 3, 8 ], [ 16, 15, 1, 8 ],
[ 16, 16, 1, 8 ], [ 16, 17, 1, 8 ], [ 16, 17, 3, 8 ], [ 21, 2, 8, 16 ],
[ 21, 3, 5, 16 ], [ 21, 5, 3, 8 ], [ 21, 5, 8, 8 ], [ 21, 6, 5, 8 ],
[ 21, 6, 6, 8 ], [ 21, 7, 3, 8 ], [ 22, 1, 1, 16 ], [ 22, 2, 1, 8 ],
[ 22, 2, 3, 24 ], [ 22, 3, 1, 8 ], [ 22, 3, 5, 16 ], [ 22, 4, 1, 4 ],
[ 22, 4, 3, 12 ], [ 22, 4, 7, 8 ], [ 23, 2, 3, 16 ], [ 23, 6, 3, 8 ],
[ 27, 3, 11, 32 ], [ 27, 6, 3, 16 ], [ 27, 8, 11, 16 ], [ 27, 9, 3, 16 ],
[ 27, 10, 9, 16 ], [ 27, 11, 11, 16 ], [ 27, 12, 5, 16 ], [ 27, 13, 5, 16 ],
[ 27, 14, 11, 16 ], [ 28, 2, 3, 32 ], [ 28, 5, 3, 16 ], [ 28, 6, 3, 16 ],
[ 29, 4, 3, 32 ], [ 29, 9, 3, 16 ], [ 29, 12, 3, 16 ], [ 30, 8, 5, 16 ],
[ 30, 11, 3, 16 ], [ 30, 12, 5, 16 ], [ 30, 13, 3, 16 ] ]
k = 6: F-action on Pi is () [30,4,6]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^3-3*q^2-5*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 2, 6, 8 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 6, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 4 ],
[ 12, 4, 2, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ],
[ 16, 11, 3, 16 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 22, 1, 2, 8 ], [ 22, 2, 2, 12 ],
[ 22, 2, 5, 4 ], [ 22, 4, 2, 12 ], [ 22, 4, 5, 4 ], [ 23, 2, 2, 8 ],
[ 23, 6, 2, 4 ], [ 27, 3, 7, 8 ], [ 27, 8, 7, 8 ], [ 27, 9, 6, 8 ],
[ 27, 11, 7, 8 ], [ 27, 14, 6, 8 ], [ 29, 4, 2, 16 ], [ 29, 4, 8, 8 ],
[ 29, 9, 2, 8 ], [ 29, 9, 8, 4 ], [ 29, 12, 2, 8 ], [ 30, 8, 12, 16 ],
[ 30, 11, 5, 8 ], [ 30, 11, 13, 8 ], [ 30, 12, 6, 8 ] ]
k = 7: F-action on Pi is () [30,4,7]
Dynkin type is (A_1(q) + T(phi1 phi4^2)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 9, 1, 3, 8 ], [ 9, 2, 3, 4 ],
[ 9, 2, 6, 4 ], [ 9, 2, 8, 4 ], [ 9, 3, 3, 4 ], [ 9, 4, 3, 4 ],
[ 9, 5, 3, 2 ], [ 9, 5, 6, 2 ], [ 9, 5, 8, 2 ], [ 12, 1, 5, 4 ],
[ 12, 2, 5, 4 ], [ 12, 4, 5, 4 ], [ 16, 1, 4, 8 ], [ 16, 2, 4, 8 ],
[ 16, 3, 4, 4 ], [ 16, 4, 4, 4 ], [ 16, 9, 4, 4 ], [ 16, 11, 4, 8 ],
[ 16, 11, 9, 8 ], [ 16, 13, 4, 4 ], [ 16, 15, 4, 4 ], [ 16, 16, 4, 4 ],
[ 22, 1, 8, 8 ], [ 22, 2, 8, 8 ], [ 22, 4, 8, 8 ], [ 27, 3, 10, 8 ],
[ 27, 8, 10, 8 ], [ 27, 9, 8, 8 ], [ 27, 11, 10, 8 ], [ 27, 14, 7, 8 ],
[ 30, 8, 13, 8 ], [ 30, 12, 7, 8 ] ]
k = 8: F-action on Pi is () [30,4,8]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-4*q-1 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 1, 4 ],
[ 3, 5, 1, 2 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ],
[ 7, 3, 1, 8 ], [ 7, 5, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ],
[ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 1, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ], [ 13, 2, 1, 8 ], [ 13, 2, 2, 4 ],
[ 15, 1, 1, 8 ], [ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ], [ 16, 2, 1, 16 ],
[ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 1, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 1, 8 ],
[ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 1, 8 ], [ 16, 11, 3, 8 ],
[ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ], [ 16, 15, 3, 4 ],
[ 16, 16, 3, 4 ], [ 21, 2, 2, 8 ], [ 21, 5, 2, 4 ], [ 22, 1, 2, 8 ],
[ 22, 2, 1, 16 ], [ 22, 2, 2, 4 ], [ 22, 2, 4, 8 ], [ 22, 4, 1, 8 ],
[ 22, 4, 2, 4 ], [ 22, 4, 4, 4 ], [ 23, 2, 1, 8 ], [ 23, 6, 1, 4 ],
[ 27, 3, 2, 16 ], [ 27, 8, 2, 8 ], [ 27, 9, 2, 8 ], [ 27, 11, 2, 8 ],
[ 27, 14, 3, 8 ], [ 29, 4, 1, 16 ], [ 29, 4, 5, 8 ], [ 29, 9, 1, 8 ],
[ 29, 9, 5, 4 ], [ 29, 12, 1, 8 ], [ 30, 8, 3, 8 ], [ 30, 11, 6, 8 ],
[ 30, 11, 15, 8 ], [ 30, 12, 8, 8 ] ]
k = 9: F-action on Pi is () [30,4,9]
Dynkin type is (A_1(q) + T(phi1^2 phi2 phi4)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 6, 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 5, 1, 1 ],
[ 3, 5, 2, 1 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ],
[ 7, 3, 1, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ], [ 7, 3, 4, 2 ],
[ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ],
[ 9, 1, 3, 8 ], [ 9, 2, 3, 4 ], [ 9, 3, 3, 4 ], [ 9, 4, 3, 4 ],
[ 9, 5, 3, 2 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ],
[ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ], [ 13, 2, 1, 2 ], [ 13, 2, 3, 2 ],
[ 16, 1, 4, 8 ], [ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 3, 4, 4 ],
[ 16, 4, 4, 4 ], [ 16, 9, 2, 2 ], [ 16, 9, 4, 2 ], [ 16, 11, 2, 2 ],
[ 16, 11, 4, 4 ], [ 16, 11, 7, 2 ], [ 16, 11, 9, 4 ], [ 16, 13, 4, 4 ],
[ 16, 15, 4, 4 ], [ 16, 16, 4, 4 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 4 ],
[ 21, 5, 5, 2 ], [ 21, 5, 7, 2 ], [ 22, 1, 8, 8 ], [ 22, 2, 7, 4 ],
[ 22, 2, 8, 4 ], [ 22, 4, 7, 2 ], [ 22, 4, 8, 4 ], [ 27, 3, 5, 8 ],
[ 27, 8, 5, 4 ], [ 27, 9, 5, 4 ], [ 27, 11, 5, 4 ], [ 27, 14, 4, 4 ],
[ 30, 8, 4, 4 ], [ 30, 12, 9, 8 ] ]
k = 10: F-action on Pi is () [30,4,10]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-4*q-1 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 2, 4 ],
[ 3, 5, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ],
[ 7, 3, 4, 8 ], [ 7, 5, 4, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ],
[ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 2, 3, 4 ],
[ 12, 4, 2, 2 ], [ 12, 4, 3, 2 ], [ 13, 2, 3, 8 ], [ 13, 2, 4, 4 ],
[ 15, 1, 1, 8 ], [ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ], [ 16, 2, 3, 8 ],
[ 16, 2, 5, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ], [ 16, 9, 5, 8 ], [ 16, 10, 2, 4 ],
[ 16, 10, 3, 8 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 16, 11, 5, 8 ],
[ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ], [ 16, 15, 3, 4 ],
[ 16, 16, 3, 4 ], [ 21, 2, 9, 8 ], [ 21, 5, 9, 4 ], [ 22, 1, 2, 8 ],
[ 22, 2, 2, 4 ], [ 22, 2, 3, 16 ], [ 22, 2, 6, 8 ], [ 22, 4, 2, 4 ],
[ 22, 4, 3, 8 ], [ 22, 4, 6, 4 ], [ 23, 2, 3, 8 ], [ 23, 6, 3, 4 ],
[ 27, 3, 12, 16 ], [ 27, 8, 12, 8 ], [ 27, 9, 7, 8 ], [ 27, 11, 12, 8 ],
[ 27, 14, 12, 8 ], [ 29, 4, 3, 16 ], [ 29, 4, 7, 8 ], [ 29, 9, 3, 8 ],
[ 29, 9, 7, 4 ], [ 29, 12, 3, 8 ], [ 30, 8, 14, 8 ], [ 30, 11, 7, 8 ],
[ 30, 11, 14, 8 ], [ 30, 12, 10, 8 ] ]
k = 11: F-action on Pi is () [30,4,11]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^3-3*q^2-5*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 2, 8, 8 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 8, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 4 ],
[ 12, 4, 2, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ],
[ 16, 11, 3, 16 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 22, 1, 2, 8 ], [ 22, 2, 2, 12 ],
[ 22, 2, 5, 4 ], [ 22, 4, 2, 12 ], [ 22, 4, 5, 4 ], [ 23, 2, 4, 8 ],
[ 23, 6, 4, 4 ], [ 27, 3, 7, 8 ], [ 27, 8, 7, 8 ], [ 27, 9, 6, 8 ],
[ 27, 11, 7, 8 ], [ 27, 14, 6, 8 ], [ 29, 4, 4, 16 ], [ 29, 4, 6, 8 ],
[ 29, 9, 4, 8 ], [ 29, 9, 6, 4 ], [ 29, 12, 4, 8 ], [ 30, 8, 15, 16 ],
[ 30, 11, 8, 8 ], [ 30, 11, 16, 8 ], [ 30, 12, 11, 8 ] ]
k = 12: F-action on Pi is () [30,4,12]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 2, 2, 2, 4 ],
[ 3, 1, 2, 8 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 2, 4 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ],
[ 7, 1, 4, 16 ], [ 7, 2, 3, 8 ], [ 7, 2, 4, 8 ], [ 7, 3, 1, 8 ],
[ 7, 3, 4, 8 ], [ 7, 4, 2, 8 ], [ 7, 4, 4, 8 ], [ 7, 5, 1, 4 ],
[ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ], [ 9, 1, 1, 8 ],
[ 9, 1, 2, 16 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 2, 3, 8 ],
[ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ],
[ 9, 5, 1, 2 ], [ 9, 5, 2, 4 ], [ 9, 5, 3, 4 ], [ 12, 1, 3, 8 ],
[ 12, 2, 1, 4 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 3, 3, 8 ],
[ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ], [ 13, 1, 3, 8 ],
[ 13, 2, 1, 4 ], [ 13, 2, 2, 8 ], [ 13, 2, 3, 4 ], [ 15, 1, 4, 8 ],
[ 16, 1, 5, 32 ], [ 16, 2, 1, 16 ], [ 16, 2, 5, 16 ], [ 16, 3, 5, 16 ],
[ 16, 4, 5, 16 ], [ 16, 5, 3, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ],
[ 16, 8, 3, 16 ], [ 16, 8, 4, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 5, 8 ],
[ 16, 10, 1, 8 ], [ 16, 10, 3, 8 ], [ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ],
[ 16, 11, 5, 8 ], [ 16, 12, 3, 8 ], [ 16, 13, 5, 8 ], [ 16, 14, 2, 8 ],
[ 16, 14, 4, 8 ], [ 16, 15, 5, 8 ], [ 16, 16, 5, 8 ], [ 16, 17, 2, 8 ],
[ 16, 17, 4, 8 ], [ 21, 2, 3, 16 ], [ 21, 3, 6, 16 ], [ 21, 5, 3, 8 ],
[ 21, 5, 8, 8 ], [ 21, 6, 2, 8 ], [ 21, 6, 7, 8 ], [ 21, 7, 6, 8 ],
[ 22, 1, 3, 16 ], [ 22, 2, 1, 8 ], [ 22, 2, 3, 8 ], [ 22, 2, 4, 16 ],
[ 22, 3, 2, 8 ], [ 22, 3, 6, 16 ], [ 22, 4, 1, 4 ], [ 22, 4, 3, 4 ],
[ 22, 4, 4, 8 ], [ 22, 4, 7, 8 ], [ 27, 3, 3, 32 ], [ 27, 6, 8, 16 ],
[ 27, 8, 3, 16 ], [ 27, 9, 3, 16 ], [ 27, 10, 2, 16 ], [ 27, 11, 3, 16 ],
[ 27, 12, 2, 16 ], [ 27, 13, 6, 16 ], [ 27, 14, 5, 16 ], [ 29, 4, 5, 16 ],
[ 29, 9, 5, 8 ], [ 30, 8, 5, 16 ], [ 30, 11, 9, 16 ], [ 30, 12, 12, 16 ],
[ 30, 13, 6, 16 ] ]
k = 13: F-action on Pi is () [30,4,13]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ],
[ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 4, 8 ],
[ 7, 5, 4, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 4 ], [ 12, 1, 3, 8 ],
[ 12, 2, 2, 2 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 2, 2 ],
[ 12, 4, 3, 2 ], [ 13, 1, 3, 8 ], [ 13, 2, 3, 4 ], [ 15, 1, 4, 8 ],
[ 16, 1, 5, 32 ], [ 16, 2, 3, 8 ], [ 16, 2, 5, 16 ], [ 16, 3, 5, 16 ],
[ 16, 4, 5, 16 ], [ 16, 5, 3, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ],
[ 16, 8, 4, 16 ], [ 16, 9, 3, 4 ], [ 16, 9, 5, 8 ], [ 16, 10, 2, 4 ],
[ 16, 10, 3, 8 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 16, 11, 5, 8 ],
[ 16, 12, 3, 8 ], [ 16, 13, 5, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 5, 8 ],
[ 16, 16, 5, 8 ], [ 16, 17, 4, 8 ], [ 21, 3, 8, 8 ], [ 21, 5, 9, 4 ],
[ 21, 6, 9, 8 ], [ 21, 7, 9, 8 ], [ 22, 1, 3, 16 ], [ 22, 2, 2, 4 ],
[ 22, 2, 3, 8 ], [ 22, 2, 5, 8 ], [ 22, 3, 2, 8 ], [ 22, 4, 2, 4 ],
[ 22, 4, 3, 4 ], [ 22, 4, 5, 8 ], [ 27, 3, 8, 16 ], [ 27, 6, 9, 8 ],
[ 27, 8, 8, 16 ], [ 27, 9, 7, 8 ], [ 27, 10, 6, 8 ], [ 27, 11, 8, 16 ],
[ 27, 12, 8, 16 ], [ 27, 13, 8, 8 ], [ 27, 14, 10, 16 ], [ 29, 4, 6, 8 ],
[ 29, 4, 8, 8 ], [ 29, 9, 6, 4 ], [ 29, 9, 8, 4 ], [ 30, 8, 14, 8 ],
[ 30, 11, 10, 8 ], [ 30, 11, 12, 8 ], [ 30, 12, 13, 8 ], [ 30, 13, 9, 16 ] ]
k = 14: F-action on Pi is () [30,4,14]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 7 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 8 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 4 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ],
[ 7, 1, 4, 16 ], [ 7, 2, 4, 16 ], [ 7, 3, 4, 16 ], [ 7, 4, 4, 16 ],
[ 7, 5, 4, 16 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 12 ],
[ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 8 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 4 ], [ 12, 1, 3, 8 ],
[ 12, 2, 3, 8 ], [ 12, 3, 2, 12 ], [ 12, 4, 3, 12 ], [ 13, 1, 3, 8 ],
[ 13, 2, 3, 8 ], [ 13, 2, 4, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 5, 32 ],
[ 16, 2, 5, 32 ], [ 16, 3, 5, 16 ], [ 16, 4, 5, 16 ], [ 16, 5, 3, 16 ],
[ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ], [ 16, 8, 4, 32 ], [ 16, 9, 5, 16 ],
[ 16, 10, 3, 16 ], [ 16, 11, 5, 32 ], [ 16, 12, 3, 8 ], [ 16, 13, 5, 8 ],
[ 16, 14, 4, 24 ], [ 16, 15, 5, 8 ], [ 16, 16, 5, 8 ], [ 16, 17, 4, 24 ],
[ 21, 2, 10, 16 ], [ 21, 3, 10, 16 ], [ 21, 5, 10, 16 ], [ 21, 6, 10, 24 ],
[ 21, 7, 10, 24 ], [ 22, 1, 3, 16 ], [ 22, 2, 3, 16 ], [ 22, 2, 6, 16 ],
[ 22, 3, 2, 24 ], [ 22, 4, 3, 24 ], [ 22, 4, 6, 8 ], [ 27, 3, 13, 32 ],
[ 27, 6, 10, 16 ], [ 27, 8, 13, 16 ], [ 27, 9, 12, 32 ], [ 27, 10, 10, 16 ],
[ 27, 11, 13, 16 ], [ 27, 12, 10, 48 ], [ 27, 13, 10, 16 ],
[ 27, 14, 13, 16 ], [ 29, 4, 7, 16 ], [ 29, 9, 7, 8 ], [ 30, 8, 16, 32 ],
[ 30, 11, 11, 16 ], [ 30, 12, 14, 16 ], [ 30, 13, 10, 48 ] ]
k = 15: F-action on Pi is () [30,4,15]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^3-9*q^2+19*q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 7 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 8 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 4 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 4 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 16 ], [ 7, 3, 1, 16 ], [ 7, 4, 1, 16 ],
[ 7, 5, 1, 16 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ],
[ 9, 2, 2, 12 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 6 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 8 ], [ 12, 3, 1, 12 ], [ 12, 4, 1, 12 ], [ 13, 1, 2, 8 ],
[ 13, 2, 1, 8 ], [ 13, 2, 2, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 1, 32 ],
[ 16, 2, 1, 32 ], [ 16, 3, 1, 16 ], [ 16, 4, 1, 16 ], [ 16, 5, 1, 16 ],
[ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ], [ 16, 8, 1, 32 ], [ 16, 9, 1, 16 ],
[ 16, 10, 1, 16 ], [ 16, 11, 1, 32 ], [ 16, 12, 1, 8 ], [ 16, 13, 1, 8 ],
[ 16, 14, 1, 24 ], [ 16, 15, 1, 8 ], [ 16, 16, 1, 8 ], [ 16, 17, 1, 24 ],
[ 21, 2, 1, 16 ], [ 21, 3, 1, 16 ], [ 21, 5, 1, 16 ], [ 21, 6, 1, 24 ],
[ 21, 7, 1, 24 ], [ 22, 1, 4, 16 ], [ 22, 2, 1, 16 ], [ 22, 2, 4, 16 ],
[ 22, 3, 3, 24 ], [ 22, 4, 1, 8 ], [ 22, 4, 4, 24 ], [ 27, 3, 1, 32 ],
[ 27, 6, 1, 16 ], [ 27, 8, 1, 16 ], [ 27, 9, 1, 32 ], [ 27, 10, 1, 16 ],
[ 27, 11, 1, 16 ], [ 27, 12, 1, 48 ], [ 27, 13, 1, 16 ], [ 27, 14, 1, 16 ],
[ 29, 4, 5, 16 ], [ 29, 9, 5, 8 ], [ 30, 8, 17, 32 ], [ 30, 11, 17, 16 ],
[ 30, 12, 15, 16 ], [ 30, 13, 11, 48 ] ]
k = 16: F-action on Pi is () [30,4,16]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 1, 4 ], [ 7, 2, 2, 4 ], [ 7, 2, 3, 4 ],
[ 7, 2, 4, 4 ], [ 7, 3, 1, 4 ], [ 7, 3, 2, 4 ], [ 7, 3, 3, 4 ],
[ 7, 3, 4, 4 ], [ 7, 4, 1, 4 ], [ 7, 4, 2, 4 ], [ 7, 4, 3, 4 ],
[ 7, 4, 4, 4 ], [ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ],
[ 7, 5, 4, 4 ], [ 9, 1, 4, 8 ], [ 9, 2, 2, 4 ], [ 9, 2, 4, 8 ],
[ 9, 3, 4, 4 ], [ 9, 4, 4, 4 ], [ 9, 5, 2, 2 ], [ 9, 5, 4, 4 ],
[ 12, 1, 4, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 1, 2 ], [ 12, 3, 2, 2 ],
[ 12, 3, 3, 4 ], [ 12, 3, 4, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 13, 2, 2, 4 ],
[ 13, 2, 4, 4 ], [ 14, 1, 4, 8 ], [ 14, 2, 2, 4 ], [ 14, 2, 4, 8 ],
[ 16, 1, 2, 8 ], [ 16, 2, 2, 8 ], [ 16, 3, 2, 4 ], [ 16, 4, 2, 4 ],
[ 16, 8, 1, 4 ], [ 16, 8, 2, 8 ], [ 16, 8, 3, 8 ], [ 16, 8, 4, 4 ],
[ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ], [ 16, 9, 2, 4 ], [ 16, 11, 1, 4 ],
[ 16, 11, 2, 8 ], [ 16, 11, 5, 4 ], [ 16, 11, 7, 4 ], [ 16, 13, 2, 4 ],
[ 16, 14, 1, 4 ], [ 16, 14, 2, 4 ], [ 16, 14, 3, 4 ], [ 16, 14, 4, 4 ],
[ 16, 15, 2, 4 ], [ 16, 16, 2, 4 ], [ 16, 17, 1, 4 ], [ 16, 17, 2, 4 ],
[ 16, 17, 3, 4 ], [ 16, 17, 4, 4 ], [ 21, 2, 4, 4 ], [ 21, 2, 6, 4 ],
[ 21, 3, 2, 4 ], [ 21, 3, 7, 4 ], [ 21, 5, 4, 4 ], [ 21, 5, 6, 4 ],
[ 21, 6, 2, 4 ], [ 21, 6, 5, 4 ], [ 21, 6, 6, 4 ], [ 21, 6, 7, 4 ],
[ 21, 7, 3, 4 ], [ 21, 7, 6, 4 ], [ 22, 1, 9, 8 ], [ 22, 2, 9, 8 ],
[ 22, 3, 3, 4 ], [ 22, 3, 4, 4 ], [ 22, 3, 7, 8 ], [ 22, 3, 8, 8 ],
[ 22, 4, 4, 4 ], [ 22, 4, 6, 4 ], [ 22, 4, 9, 8 ], [ 27, 3, 4, 8 ],
[ 27, 6, 4, 4 ], [ 27, 6, 6, 4 ], [ 27, 8, 4, 4 ], [ 27, 9, 4, 8 ],
[ 27, 10, 3, 4 ], [ 27, 10, 4, 4 ], [ 27, 11, 4, 4 ], [ 27, 12, 2, 8 ],
[ 27, 12, 5, 8 ], [ 27, 13, 2, 4 ], [ 27, 13, 7, 4 ], [ 27, 14, 2, 4 ],
[ 28, 2, 6, 8 ], [ 28, 5, 6, 8 ], [ 28, 6, 6, 8 ], [ 30, 8, 18, 8 ],
[ 30, 12, 16, 8 ], [ 30, 13, 13, 8 ], [ 30, 13, 16, 8 ] ]
k = 17: F-action on Pi is () [30,4,17]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-2*q-7 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ], [ 7, 4, 1, 8 ],
[ 7, 5, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 2 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ],
[ 12, 4, 2, 2 ], [ 13, 1, 2, 8 ], [ 13, 2, 2, 4 ], [ 15, 1, 4, 8 ],
[ 16, 1, 1, 32 ], [ 16, 2, 1, 16 ], [ 16, 2, 3, 8 ], [ 16, 3, 1, 16 ],
[ 16, 4, 1, 16 ], [ 16, 5, 1, 16 ], [ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ],
[ 16, 8, 1, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 1, 8 ],
[ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 1, 8 ], [ 16, 11, 3, 8 ],
[ 16, 12, 1, 8 ], [ 16, 13, 1, 8 ], [ 16, 14, 1, 8 ], [ 16, 15, 1, 8 ],
[ 16, 16, 1, 8 ], [ 16, 17, 1, 8 ], [ 21, 3, 3, 8 ], [ 21, 5, 2, 4 ],
[ 21, 6, 3, 8 ], [ 21, 7, 2, 8 ], [ 22, 1, 4, 16 ], [ 22, 2, 2, 8 ],
[ 22, 2, 4, 8 ], [ 22, 2, 5, 4 ], [ 22, 3, 3, 8 ], [ 22, 4, 2, 8 ],
[ 22, 4, 4, 4 ], [ 22, 4, 5, 4 ], [ 27, 3, 6, 16 ], [ 27, 6, 2, 8 ],
[ 27, 8, 6, 16 ], [ 27, 9, 2, 8 ], [ 27, 10, 5, 8 ], [ 27, 11, 6, 16 ],
[ 27, 12, 3, 16 ], [ 27, 13, 3, 8 ], [ 27, 14, 8, 16 ], [ 29, 4, 6, 8 ],
[ 29, 4, 8, 8 ], [ 29, 9, 6, 4 ], [ 29, 9, 8, 4 ], [ 30, 8, 19, 8 ],
[ 30, 11, 18, 8 ], [ 30, 11, 20, 8 ], [ 30, 12, 17, 8 ], [ 30, 13, 12, 16 ]
]
k = 18: F-action on Pi is () [30,4,18]
Dynkin type is (A_1(q) + T(phi1 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ],
[ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 1 ], [ 9, 1, 4, 8 ], [ 9, 2, 4, 4 ], [ 9, 3, 4, 4 ],
[ 9, 4, 4, 4 ], [ 9, 5, 4, 2 ], [ 12, 1, 4, 4 ], [ 12, 2, 4, 2 ],
[ 12, 2, 5, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ],
[ 12, 4, 5, 2 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 13, 2, 2, 2 ],
[ 13, 2, 4, 2 ], [ 14, 1, 4, 8 ], [ 14, 2, 4, 4 ], [ 16, 1, 2, 8 ],
[ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 3, 2, 4 ], [ 16, 4, 2, 4 ],
[ 16, 8, 2, 4 ], [ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ],
[ 16, 9, 2, 2 ], [ 16, 9, 4, 2 ], [ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ],
[ 16, 11, 7, 2 ], [ 16, 11, 9, 4 ], [ 16, 13, 2, 4 ], [ 16, 14, 2, 2 ],
[ 16, 14, 3, 2 ], [ 16, 15, 2, 4 ], [ 16, 16, 2, 4 ], [ 16, 17, 2, 2 ],
[ 16, 17, 3, 2 ], [ 21, 3, 4, 4 ], [ 21, 3, 9, 4 ], [ 21, 5, 5, 2 ],
[ 21, 5, 7, 2 ], [ 21, 6, 4, 4 ], [ 21, 6, 8, 4 ], [ 21, 7, 5, 4 ],
[ 21, 7, 7, 4 ], [ 22, 1, 9, 8 ], [ 22, 2, 9, 4 ], [ 22, 2, 10, 4 ],
[ 22, 3, 7, 4 ], [ 22, 3, 8, 4 ], [ 22, 4, 9, 2 ], [ 22, 4, 10, 4 ],
[ 27, 3, 9, 8 ], [ 27, 6, 5, 4 ], [ 27, 6, 7, 4 ], [ 27, 8, 9, 8 ],
[ 27, 9, 5, 4 ], [ 27, 10, 7, 4 ], [ 27, 10, 8, 4 ], [ 27, 11, 9, 8 ],
[ 27, 12, 4, 8 ], [ 27, 12, 9, 8 ], [ 27, 13, 4, 4 ], [ 27, 13, 9, 4 ],
[ 27, 14, 9, 8 ], [ 28, 2, 7, 8 ], [ 28, 5, 7, 8 ], [ 28, 6, 7, 8 ],
[ 30, 8, 20, 4 ], [ 30, 12, 18, 8 ], [ 30, 13, 15, 8 ], [ 30, 13, 17, 8 ] ]
k = 19: F-action on Pi is () [30,4,19]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^3-9*q^2+19*q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 2, 2, 2, 4 ],
[ 3, 1, 1, 8 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 4 ], [ 3, 3, 1, 4 ],
[ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ],
[ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 2, 2, 8 ], [ 7, 3, 1, 8 ],
[ 7, 3, 4, 8 ], [ 7, 4, 1, 8 ], [ 7, 4, 3, 8 ], [ 7, 5, 1, 4 ],
[ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ], [ 9, 1, 1, 16 ],
[ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 2, 4, 8 ],
[ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ],
[ 9, 5, 1, 4 ], [ 9, 5, 2, 2 ], [ 9, 5, 4, 4 ], [ 12, 1, 1, 8 ],
[ 12, 2, 1, 4 ], [ 12, 2, 3, 4 ], [ 12, 3, 1, 4 ], [ 12, 3, 4, 8 ],
[ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ], [ 13, 1, 2, 8 ],
[ 13, 2, 2, 4 ], [ 13, 2, 3, 8 ], [ 13, 2, 4, 4 ], [ 15, 1, 4, 8 ],
[ 16, 1, 1, 32 ], [ 16, 2, 1, 16 ], [ 16, 2, 5, 16 ], [ 16, 3, 1, 16 ],
[ 16, 4, 1, 16 ], [ 16, 5, 1, 16 ], [ 16, 6, 1, 16 ], [ 16, 7, 1, 16 ],
[ 16, 8, 1, 16 ], [ 16, 8, 2, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 5, 8 ],
[ 16, 10, 1, 8 ], [ 16, 10, 3, 8 ], [ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ],
[ 16, 11, 5, 8 ], [ 16, 12, 1, 8 ], [ 16, 13, 1, 8 ], [ 16, 14, 1, 8 ],
[ 16, 14, 3, 8 ], [ 16, 15, 1, 8 ], [ 16, 16, 1, 8 ], [ 16, 17, 1, 8 ],
[ 16, 17, 3, 8 ], [ 21, 2, 8, 16 ], [ 21, 3, 5, 16 ], [ 21, 5, 3, 8 ],
[ 21, 5, 8, 8 ], [ 21, 6, 5, 8 ], [ 21, 6, 6, 8 ], [ 21, 7, 3, 8 ],
[ 22, 1, 4, 16 ], [ 22, 2, 3, 16 ], [ 22, 2, 4, 8 ], [ 22, 2, 6, 8 ],
[ 22, 3, 3, 8 ], [ 22, 3, 7, 16 ], [ 22, 4, 3, 8 ], [ 22, 4, 4, 4 ],
[ 22, 4, 6, 4 ], [ 22, 4, 9, 8 ], [ 27, 3, 11, 32 ], [ 27, 6, 3, 16 ],
[ 27, 8, 11, 16 ], [ 27, 9, 3, 16 ], [ 27, 10, 9, 16 ], [ 27, 11, 11, 16 ],
[ 27, 12, 5, 16 ], [ 27, 13, 5, 16 ], [ 27, 14, 11, 16 ], [ 29, 4, 7, 16 ],
[ 29, 9, 7, 8 ], [ 30, 8, 21, 16 ], [ 30, 11, 19, 16 ], [ 30, 12, 19, 16 ],
[ 30, 13, 13, 16 ] ]
k = 20: F-action on Pi is () [30,4,20]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 2, 5, 8 ], [ 9, 3, 1, 4 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 9, 5, 5, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 4 ],
[ 12, 4, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ],
[ 16, 11, 3, 16 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 22, 1, 5, 8 ], [ 22, 2, 2, 4 ],
[ 22, 2, 5, 12 ], [ 22, 4, 2, 4 ], [ 22, 4, 5, 12 ], [ 23, 2, 8, 8 ],
[ 23, 6, 8, 4 ], [ 27, 3, 7, 8 ], [ 27, 8, 7, 8 ], [ 27, 9, 6, 8 ],
[ 27, 11, 7, 8 ], [ 27, 14, 6, 8 ], [ 29, 4, 6, 8 ], [ 29, 4, 12, 16 ],
[ 29, 9, 6, 4 ], [ 29, 9, 12, 8 ], [ 29, 12, 8, 8 ], [ 30, 8, 28, 16 ],
[ 30, 11, 21, 8 ], [ 30, 11, 29, 8 ], [ 30, 12, 20, 8 ] ]
k = 21: F-action on Pi is () [30,4,21]
Dynkin type is (A_1(q) + T(phi2 phi4^2)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2^2
Fusion of maximal tori of C^F in those of G^F:
[ 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 4, 8 ], [ 9, 2, 4, 4 ],
[ 9, 2, 5, 4 ], [ 9, 2, 7, 4 ], [ 9, 3, 4, 4 ], [ 9, 4, 4, 4 ],
[ 9, 5, 4, 2 ], [ 9, 5, 5, 2 ], [ 9, 5, 7, 2 ], [ 12, 1, 5, 4 ],
[ 12, 2, 5, 4 ], [ 12, 4, 5, 4 ], [ 16, 1, 4, 8 ], [ 16, 2, 4, 8 ],
[ 16, 3, 4, 4 ], [ 16, 4, 4, 4 ], [ 16, 9, 4, 4 ], [ 16, 11, 4, 8 ],
[ 16, 11, 9, 8 ], [ 16, 13, 4, 4 ], [ 16, 15, 4, 4 ], [ 16, 16, 4, 4 ],
[ 22, 1, 10, 8 ], [ 22, 2, 10, 8 ], [ 22, 4, 10, 8 ], [ 27, 3, 10, 8 ],
[ 27, 8, 10, 8 ], [ 27, 9, 8, 8 ], [ 27, 11, 10, 8 ], [ 27, 14, 7, 8 ],
[ 30, 8, 29, 8 ], [ 30, 12, 21, 8 ] ]
k = 22: F-action on Pi is () [30,4,22]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^3
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 1, 4 ],
[ 3, 5, 1, 2 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ],
[ 7, 3, 1, 8 ], [ 7, 5, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ],
[ 9, 1, 2, 16 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 1, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ], [ 13, 2, 1, 4 ], [ 13, 2, 2, 8 ],
[ 15, 1, 3, 8 ], [ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ], [ 16, 2, 1, 16 ],
[ 16, 2, 3, 8 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 1, 8 ], [ 16, 9, 3, 4 ], [ 16, 10, 1, 8 ],
[ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 1, 8 ], [ 16, 11, 3, 8 ],
[ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ], [ 16, 15, 3, 4 ],
[ 16, 16, 3, 4 ], [ 21, 2, 2, 8 ], [ 21, 5, 2, 4 ], [ 22, 1, 5, 8 ],
[ 22, 2, 1, 8 ], [ 22, 2, 4, 16 ], [ 22, 2, 5, 4 ], [ 22, 4, 1, 4 ],
[ 22, 4, 4, 8 ], [ 22, 4, 5, 4 ], [ 23, 2, 5, 8 ], [ 23, 6, 5, 4 ],
[ 27, 3, 2, 16 ], [ 27, 8, 2, 8 ], [ 27, 9, 2, 8 ], [ 27, 11, 2, 8 ],
[ 27, 14, 3, 8 ], [ 29, 4, 5, 8 ], [ 29, 4, 9, 16 ], [ 29, 9, 5, 4 ],
[ 29, 9, 9, 8 ], [ 29, 12, 5, 8 ], [ 30, 8, 19, 8 ], [ 30, 11, 22, 8 ],
[ 30, 11, 31, 8 ], [ 30, 12, 22, 8 ] ]
k = 23: F-action on Pi is () [30,4,23]
Dynkin type is (A_1(q) + T(phi1 phi2^2 phi4)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 12, 8 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 5, 1, 1 ],
[ 3, 5, 2, 1 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 2, 2 ],
[ 7, 3, 1, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ], [ 7, 3, 4, 2 ],
[ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ],
[ 9, 1, 4, 8 ], [ 9, 2, 4, 4 ], [ 9, 3, 4, 4 ], [ 9, 4, 4, 4 ],
[ 9, 5, 4, 2 ], [ 12, 1, 5, 4 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ],
[ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ], [ 13, 2, 2, 2 ], [ 13, 2, 4, 2 ],
[ 16, 1, 4, 8 ], [ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 3, 4, 4 ],
[ 16, 4, 4, 4 ], [ 16, 9, 2, 2 ], [ 16, 9, 4, 2 ], [ 16, 11, 2, 2 ],
[ 16, 11, 4, 4 ], [ 16, 11, 7, 2 ], [ 16, 11, 9, 4 ], [ 16, 13, 4, 4 ],
[ 16, 15, 4, 4 ], [ 16, 16, 4, 4 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 4 ],
[ 21, 5, 5, 2 ], [ 21, 5, 7, 2 ], [ 22, 1, 10, 8 ], [ 22, 2, 9, 4 ],
[ 22, 2, 10, 4 ], [ 22, 4, 9, 2 ], [ 22, 4, 10, 4 ], [ 27, 3, 5, 8 ],
[ 27, 8, 5, 4 ], [ 27, 9, 5, 4 ], [ 27, 11, 5, 4 ], [ 27, 14, 4, 4 ],
[ 30, 8, 20, 4 ], [ 30, 12, 23, 8 ] ]
k = 24: F-action on Pi is () [30,4,24]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^3
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 2, 4 ],
[ 3, 5, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ],
[ 7, 3, 4, 8 ], [ 7, 5, 4, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ],
[ 9, 1, 2, 16 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 2, 3, 4 ],
[ 12, 4, 2, 2 ], [ 12, 4, 3, 2 ], [ 13, 2, 3, 4 ], [ 13, 2, 4, 8 ],
[ 15, 1, 3, 8 ], [ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ], [ 16, 2, 3, 8 ],
[ 16, 2, 5, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 4 ], [ 16, 9, 5, 8 ], [ 16, 10, 2, 4 ],
[ 16, 10, 3, 8 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ], [ 16, 11, 5, 8 ],
[ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ], [ 16, 15, 3, 4 ],
[ 16, 16, 3, 4 ], [ 21, 2, 9, 8 ], [ 21, 5, 9, 4 ], [ 22, 1, 5, 8 ],
[ 22, 2, 3, 8 ], [ 22, 2, 5, 4 ], [ 22, 2, 6, 16 ], [ 22, 4, 3, 4 ],
[ 22, 4, 5, 4 ], [ 22, 4, 6, 8 ], [ 23, 2, 7, 8 ], [ 23, 6, 7, 4 ],
[ 27, 3, 12, 16 ], [ 27, 8, 12, 8 ], [ 27, 9, 7, 8 ], [ 27, 11, 12, 8 ],
[ 27, 14, 12, 8 ], [ 29, 4, 7, 8 ], [ 29, 4, 11, 16 ], [ 29, 9, 7, 4 ],
[ 29, 9, 11, 8 ], [ 29, 12, 7, 8 ], [ 30, 8, 30, 8 ], [ 30, 11, 23, 8 ],
[ 30, 11, 30, 8 ], [ 30, 12, 24, 8 ] ]
k = 25: F-action on Pi is () [30,4,25]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 2, 7, 8 ], [ 9, 3, 1, 4 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 9, 5, 7, 4 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 4 ],
[ 12, 4, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 4 ], [ 16, 1, 3, 16 ],
[ 16, 2, 3, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 3, 8 ], [ 16, 5, 2, 8 ],
[ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 9, 3, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ],
[ 16, 11, 3, 16 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 13, 3, 4 ],
[ 16, 15, 3, 4 ], [ 16, 16, 3, 4 ], [ 22, 1, 5, 8 ], [ 22, 2, 2, 4 ],
[ 22, 2, 5, 12 ], [ 22, 4, 2, 4 ], [ 22, 4, 5, 12 ], [ 23, 2, 6, 8 ],
[ 23, 6, 6, 4 ], [ 27, 3, 7, 8 ], [ 27, 8, 7, 8 ], [ 27, 9, 6, 8 ],
[ 27, 11, 7, 8 ], [ 27, 14, 6, 8 ], [ 29, 4, 8, 8 ], [ 29, 4, 10, 16 ],
[ 29, 9, 8, 4 ], [ 29, 9, 10, 8 ], [ 29, 12, 6, 8 ], [ 30, 8, 31, 16 ],
[ 30, 11, 24, 8 ], [ 30, 11, 32, 8 ], [ 30, 12, 25, 8 ] ]
k = 26: F-action on Pi is () [30,4,26]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^3-9*q^2+19*q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 2, 2, 2, 4 ],
[ 3, 1, 2, 8 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 2, 4 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 6 ], [ 6, 1, 2, 8 ],
[ 7, 1, 4, 16 ], [ 7, 2, 3, 8 ], [ 7, 2, 4, 8 ], [ 7, 3, 1, 8 ],
[ 7, 3, 4, 8 ], [ 7, 4, 2, 8 ], [ 7, 4, 4, 8 ], [ 7, 5, 1, 4 ],
[ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ], [ 8, 1, 2, 8 ],
[ 9, 1, 2, 24 ], [ 9, 2, 2, 12 ], [ 9, 2, 4, 8 ], [ 9, 3, 2, 12 ],
[ 9, 4, 2, 12 ], [ 9, 5, 2, 6 ], [ 9, 5, 4, 4 ], [ 12, 1, 3, 8 ],
[ 12, 2, 1, 4 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 3, 3, 8 ],
[ 12, 4, 1, 2 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ], [ 13, 1, 4, 8 ],
[ 13, 2, 2, 12 ], [ 13, 2, 4, 4 ], [ 14, 1, 2, 16 ], [ 14, 2, 2, 8 ],
[ 14, 2, 4, 16 ], [ 15, 1, 3, 16 ], [ 16, 1, 5, 32 ], [ 16, 2, 1, 16 ],
[ 16, 2, 5, 16 ], [ 16, 3, 5, 16 ], [ 16, 4, 5, 16 ], [ 16, 5, 3, 16 ],
[ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ], [ 16, 8, 3, 16 ], [ 16, 8, 4, 16 ],
[ 16, 9, 1, 8 ], [ 16, 9, 5, 8 ], [ 16, 10, 1, 8 ], [ 16, 10, 3, 8 ],
[ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ], [ 16, 11, 5, 8 ], [ 16, 12, 3, 8 ],
[ 16, 13, 5, 8 ], [ 16, 14, 2, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 5, 8 ],
[ 16, 16, 5, 8 ], [ 16, 17, 2, 8 ], [ 16, 17, 4, 8 ], [ 21, 2, 3, 16 ],
[ 21, 3, 6, 16 ], [ 21, 5, 3, 8 ], [ 21, 5, 8, 8 ], [ 21, 6, 2, 8 ],
[ 21, 6, 7, 8 ], [ 21, 7, 6, 8 ], [ 22, 1, 6, 16 ], [ 22, 2, 4, 24 ],
[ 22, 2, 6, 8 ], [ 22, 3, 4, 8 ], [ 22, 3, 8, 16 ], [ 22, 4, 4, 12 ],
[ 22, 4, 6, 4 ], [ 22, 4, 9, 8 ], [ 23, 2, 5, 16 ], [ 23, 6, 5, 8 ],
[ 27, 3, 3, 32 ], [ 27, 6, 8, 16 ], [ 27, 8, 3, 16 ], [ 27, 9, 3, 16 ],
[ 27, 10, 2, 16 ], [ 27, 11, 3, 16 ], [ 27, 12, 2, 16 ], [ 27, 13, 6, 16 ],
[ 27, 14, 5, 16 ], [ 28, 2, 8, 32 ], [ 28, 5, 8, 16 ], [ 28, 6, 6, 16 ],
[ 29, 4, 9, 32 ], [ 29, 9, 9, 16 ], [ 29, 12, 5, 16 ], [ 30, 8, 21, 16 ],
[ 30, 11, 25, 16 ], [ 30, 12, 26, 16 ], [ 30, 13, 16, 16 ] ]
k = 27: F-action on Pi is () [30,4,27]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-2*q-7 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 6 ], [ 6, 1, 2, 8 ],
[ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 4, 8 ],
[ 7, 5, 4, 4 ], [ 8, 1, 2, 8 ], [ 9, 1, 2, 24 ], [ 9, 2, 2, 12 ],
[ 9, 3, 2, 12 ], [ 9, 4, 2, 12 ], [ 9, 5, 2, 6 ], [ 12, 1, 3, 8 ],
[ 12, 2, 2, 2 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 2, 2 ],
[ 12, 4, 3, 2 ], [ 13, 1, 4, 8 ], [ 13, 2, 4, 4 ], [ 14, 1, 2, 16 ],
[ 14, 2, 2, 8 ], [ 15, 1, 3, 16 ], [ 16, 1, 5, 32 ], [ 16, 2, 3, 8 ],
[ 16, 2, 5, 16 ], [ 16, 3, 5, 16 ], [ 16, 4, 5, 16 ], [ 16, 5, 3, 16 ],
[ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ], [ 16, 8, 4, 16 ], [ 16, 9, 3, 4 ],
[ 16, 9, 5, 8 ], [ 16, 10, 2, 4 ], [ 16, 10, 3, 8 ], [ 16, 10, 4, 4 ],
[ 16, 11, 3, 8 ], [ 16, 11, 5, 8 ], [ 16, 12, 3, 8 ], [ 16, 13, 5, 8 ],
[ 16, 14, 4, 8 ], [ 16, 15, 5, 8 ], [ 16, 16, 5, 8 ], [ 16, 17, 4, 8 ],
[ 21, 3, 8, 8 ], [ 21, 5, 9, 4 ], [ 21, 6, 9, 8 ], [ 21, 7, 9, 8 ],
[ 22, 1, 6, 16 ], [ 22, 2, 5, 12 ], [ 22, 2, 6, 8 ], [ 22, 3, 4, 8 ],
[ 22, 4, 5, 12 ], [ 22, 4, 6, 4 ], [ 23, 2, 6, 8 ], [ 23, 2, 8, 8 ],
[ 23, 6, 6, 4 ], [ 23, 6, 8, 4 ], [ 27, 3, 8, 16 ], [ 27, 6, 9, 8 ],
[ 27, 8, 8, 16 ], [ 27, 9, 7, 8 ], [ 27, 10, 6, 8 ], [ 27, 11, 8, 16 ],
[ 27, 12, 8, 16 ], [ 27, 13, 8, 8 ], [ 27, 14, 10, 16 ], [ 28, 2, 9, 16 ],
[ 28, 5, 9, 8 ], [ 28, 6, 9, 16 ], [ 29, 4, 10, 16 ], [ 29, 4, 12, 16 ],
[ 29, 9, 10, 8 ], [ 29, 9, 12, 8 ], [ 29, 12, 6, 8 ], [ 29, 12, 8, 8 ],
[ 30, 8, 30, 8 ], [ 30, 11, 26, 8 ], [ 30, 11, 28, 8 ], [ 30, 12, 27, 8 ],
[ 30, 13, 19, 16 ] ]
k = 28: F-action on Pi is () [30,4,28]
Dynkin type is (A_1(q) + T(phi2^5)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^3-9*q^2+19*q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 7 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 8 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 4 ], [ 5, 1, 2, 6 ], [ 6, 1, 2, 8 ],
[ 7, 1, 4, 16 ], [ 7, 2, 4, 16 ], [ 7, 3, 4, 16 ], [ 7, 4, 4, 16 ],
[ 7, 5, 4, 16 ], [ 8, 1, 2, 8 ], [ 9, 1, 2, 24 ], [ 9, 2, 2, 20 ],
[ 9, 3, 2, 12 ], [ 9, 4, 2, 12 ], [ 9, 5, 2, 10 ], [ 12, 1, 3, 8 ],
[ 12, 2, 3, 8 ], [ 12, 3, 2, 12 ], [ 12, 4, 3, 12 ], [ 13, 1, 4, 8 ],
[ 13, 2, 4, 16 ], [ 14, 1, 2, 16 ], [ 14, 2, 2, 24 ], [ 15, 1, 3, 16 ],
[ 16, 1, 5, 32 ], [ 16, 2, 5, 32 ], [ 16, 3, 5, 16 ], [ 16, 4, 5, 16 ],
[ 16, 5, 3, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 3, 16 ], [ 16, 8, 4, 32 ],
[ 16, 9, 5, 16 ], [ 16, 10, 3, 16 ], [ 16, 11, 5, 32 ], [ 16, 12, 3, 8 ],
[ 16, 13, 5, 8 ], [ 16, 14, 4, 24 ], [ 16, 15, 5, 8 ], [ 16, 16, 5, 8 ],
[ 16, 17, 4, 24 ], [ 21, 2, 10, 16 ], [ 21, 3, 10, 16 ], [ 21, 5, 10, 16 ],
[ 21, 6, 10, 24 ], [ 21, 7, 10, 24 ], [ 22, 1, 6, 16 ], [ 22, 2, 6, 32 ],
[ 22, 3, 4, 24 ], [ 22, 4, 6, 32 ], [ 23, 2, 7, 16 ], [ 23, 6, 7, 8 ],
[ 27, 3, 13, 32 ], [ 27, 6, 10, 16 ], [ 27, 8, 13, 16 ], [ 27, 9, 12, 32 ],
[ 27, 10, 10, 16 ], [ 27, 11, 13, 16 ], [ 27, 12, 10, 48 ],
[ 27, 13, 10, 16 ], [ 27, 14, 13, 16 ], [ 28, 2, 10, 32 ],
[ 28, 5, 10, 16 ], [ 28, 6, 10, 48 ], [ 29, 4, 11, 32 ], [ 29, 9, 11, 16 ],
[ 29, 12, 7, 16 ], [ 30, 8, 32, 32 ], [ 30, 11, 27, 16 ],
[ 30, 12, 28, 16 ], [ 30, 13, 20, 48 ] ]
j = 5: Omega of order 2, action on Pi: <()>
k = 1: F-action on Pi is () [30,5,1]
Dynkin type is (A_1(q) + T(phi1^5)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 16 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 8 ], [ 10, 2, 1, 4 ], [ 15, 1, 1, 8 ],
[ 18, 2, 1, 12 ], [ 23, 4, 1, 16 ], [ 23, 6, 1, 8 ], [ 25, 2, 1, 24 ],
[ 25, 3, 1, 16 ], [ 29, 3, 1, 32 ], [ 29, 9, 1, 16 ], [ 29, 11, 1, 16 ],
[ 30, 9, 1, 32 ], [ 30, 11, 1, 16 ] ]
k = 2: F-action on Pi is () [30,5,2]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 15, 1, 1, 8 ], [ 18, 2, 2, 4 ],
[ 23, 4, 4, 8 ], [ 23, 6, 4, 4 ], [ 25, 2, 2, 8 ], [ 29, 3, 4, 16 ],
[ 29, 3, 5, 8 ], [ 29, 9, 4, 8 ], [ 29, 9, 5, 4 ], [ 29, 11, 4, 8 ],
[ 30, 9, 3, 8 ], [ 30, 11, 4, 8 ], [ 30, 11, 15, 8 ] ]
k = 3: F-action on Pi is () [30,5,3]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 3, 3, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 9, 5, 3, 4 ], [ 15, 1, 4, 4 ], [ 18, 2, 2, 4 ], [ 23, 4, 3, 8 ],
[ 23, 6, 3, 4 ], [ 25, 2, 2, 8 ], [ 29, 3, 3, 16 ], [ 29, 3, 5, 8 ],
[ 29, 9, 3, 8 ], [ 29, 9, 5, 4 ], [ 29, 11, 3, 8 ], [ 30, 9, 5, 16 ],
[ 30, 11, 3, 8 ], [ 30, 11, 9, 8 ] ]
k = 4: F-action on Pi is () [30,5,4]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 10, 2, 1, 4 ],
[ 15, 1, 4, 4 ], [ 18, 2, 1, 12 ], [ 23, 4, 1, 8 ], [ 23, 4, 2, 8 ],
[ 23, 6, 1, 4 ], [ 23, 6, 2, 4 ], [ 25, 2, 1, 24 ], [ 29, 3, 1, 16 ],
[ 29, 3, 2, 16 ], [ 29, 9, 1, 8 ], [ 29, 9, 2, 8 ], [ 29, 11, 1, 8 ],
[ 29, 11, 2, 8 ], [ 30, 9, 3, 8 ], [ 30, 11, 2, 8 ], [ 30, 11, 6, 8 ] ]
k = 5: F-action on Pi is () [30,5,5]
Dynkin type is (A_1(q) + T(phi1^2 phi2 phi4)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 28, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 25, 2, 4, 4 ], [ 30, 9, 6, 4 ] ]
k = 6: F-action on Pi is () [30,5,6]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 9, 3, 1, 4 ], [ 9, 3, 6, 4 ], [ 9, 5, 1, 2 ],
[ 9, 5, 6, 2 ], [ 10, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 18, 2, 1, 2 ],
[ 18, 2, 3, 2 ], [ 25, 2, 3, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ],
[ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 30, 9, 8, 8 ] ]
k = 7: F-action on Pi is () [30,5,7]
Dynkin type is (A_1(q) + T(phi1 phi4^2)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 9, 3, 3, 4 ],
[ 9, 3, 8, 4 ], [ 9, 5, 3, 2 ], [ 9, 5, 8, 2 ], [ 15, 1, 5, 4 ],
[ 25, 2, 4, 4 ], [ 30, 9, 11, 8 ] ]
k = 8: F-action on Pi is () [30,5,8]
Dynkin type is (A_1(q) + T(phi1^2 phi2 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 28, 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 10, 2, 1, 2 ],
[ 15, 1, 5, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 3, 2 ], [ 25, 2, 3, 4 ],
[ 30, 9, 6, 4 ] ]
k = 9: F-action on Pi is () [30,5,9]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 3, 6, 8 ], [ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 6, 4 ],
[ 15, 1, 1, 8 ], [ 18, 2, 3, 4 ], [ 25, 2, 5, 8 ], [ 25, 3, 2, 16 ],
[ 29, 3, 8, 16 ], [ 29, 9, 8, 8 ], [ 30, 9, 12, 16 ], [ 30, 11, 13, 16 ] ]
k = 10: F-action on Pi is () [30,5,10]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 15, 1, 4, 4 ],
[ 18, 2, 3, 4 ], [ 25, 2, 5, 8 ], [ 29, 3, 7, 8 ], [ 29, 3, 8, 8 ],
[ 29, 9, 7, 4 ], [ 29, 9, 8, 4 ], [ 30, 9, 14, 8 ], [ 30, 11, 12, 8 ],
[ 30, 11, 14, 8 ] ]
k = 11: F-action on Pi is () [30,5,11]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 3, 8, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 9, 5, 8, 4 ], [ 15, 1, 4, 4 ], [ 18, 2, 2, 4 ], [ 23, 4, 4, 8 ],
[ 23, 6, 4, 4 ], [ 25, 2, 2, 8 ], [ 29, 3, 4, 16 ], [ 29, 3, 6, 8 ],
[ 29, 9, 4, 8 ], [ 29, 9, 6, 4 ], [ 29, 11, 4, 8 ], [ 30, 9, 15, 16 ],
[ 30, 11, 8, 8 ], [ 30, 11, 16, 8 ] ]
k = 12: F-action on Pi is () [30,5,12]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ],
[ 15, 1, 3, 8 ], [ 18, 2, 3, 4 ], [ 25, 2, 5, 8 ], [ 25, 3, 3, 16 ],
[ 29, 3, 7, 16 ], [ 29, 9, 7, 8 ], [ 30, 9, 16, 32 ], [ 30, 11, 11, 16 ] ]
k = 13: F-action on Pi is () [30,5,13]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 15, 1, 3, 8 ], [ 18, 2, 2, 4 ],
[ 23, 4, 3, 8 ], [ 23, 6, 3, 4 ], [ 25, 2, 2, 8 ], [ 29, 3, 3, 16 ],
[ 29, 3, 6, 8 ], [ 29, 9, 3, 8 ], [ 29, 9, 6, 4 ], [ 29, 11, 3, 8 ],
[ 30, 9, 14, 8 ], [ 30, 11, 7, 8 ], [ 30, 11, 10, 8 ] ]
k = 14: F-action on Pi is () [30,5,14]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 3, 6, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 9, 5, 6, 4 ],
[ 10, 2, 1, 4 ], [ 15, 1, 3, 8 ], [ 18, 2, 1, 12 ], [ 23, 4, 2, 16 ],
[ 23, 6, 2, 8 ], [ 25, 2, 1, 24 ], [ 25, 3, 4, 16 ], [ 29, 3, 2, 32 ],
[ 29, 9, 2, 16 ], [ 29, 11, 2, 16 ], [ 30, 9, 12, 16 ], [ 30, 11, 5, 16 ] ]
k = 15: F-action on Pi is () [30,5,15]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ],
[ 15, 1, 1, 8 ], [ 18, 2, 2, 4 ], [ 25, 2, 2, 8 ], [ 25, 3, 5, 16 ],
[ 29, 3, 5, 16 ], [ 29, 9, 5, 8 ], [ 30, 9, 17, 32 ], [ 30, 11, 17, 16 ] ]
k = 16: F-action on Pi is () [30,5,16]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 15, 1, 1, 8 ], [ 18, 2, 3, 4 ],
[ 23, 4, 5, 8 ], [ 23, 6, 5, 4 ], [ 25, 2, 5, 8 ], [ 29, 3, 8, 8 ],
[ 29, 3, 9, 16 ], [ 29, 9, 8, 4 ], [ 29, 9, 9, 8 ], [ 29, 11, 5, 8 ],
[ 30, 9, 19, 8 ], [ 30, 11, 20, 8 ], [ 30, 11, 31, 8 ] ]
k = 17: F-action on Pi is () [30,5,17]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 3, 4, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 9, 5, 4, 4 ], [ 15, 1, 4, 4 ], [ 18, 2, 3, 4 ], [ 23, 4, 5, 8 ],
[ 23, 6, 5, 4 ], [ 25, 2, 5, 8 ], [ 29, 3, 7, 8 ], [ 29, 3, 9, 16 ],
[ 29, 9, 7, 4 ], [ 29, 9, 9, 8 ], [ 29, 11, 5, 8 ], [ 30, 9, 21, 16 ],
[ 30, 11, 19, 8 ], [ 30, 11, 25, 8 ] ]
k = 18: F-action on Pi is () [30,5,18]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 15, 1, 4, 4 ],
[ 18, 2, 2, 4 ], [ 25, 2, 2, 8 ], [ 29, 3, 5, 8 ], [ 29, 3, 6, 8 ],
[ 29, 9, 5, 4 ], [ 29, 9, 6, 4 ], [ 30, 9, 19, 8 ], [ 30, 11, 18, 8 ],
[ 30, 11, 22, 8 ] ]
k = 19: F-action on Pi is () [30,5,19]
Dynkin type is (A_1(q) + T(phi1 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 32, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 25, 2, 7, 4 ], [ 30, 9, 22, 4 ] ]
k = 20: F-action on Pi is () [30,5,20]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 9, 3, 2, 4 ], [ 9, 3, 5, 4 ], [ 9, 5, 2, 2 ],
[ 9, 5, 5, 2 ], [ 10, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 2, 2, 2 ],
[ 18, 2, 4, 2 ], [ 25, 2, 6, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ],
[ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 30, 9, 24, 8 ] ]
k = 21: F-action on Pi is () [30,5,21]
Dynkin type is (A_1(q) + T(phi2 phi4^2)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 9, 3, 4, 4 ],
[ 9, 3, 7, 4 ], [ 9, 5, 4, 2 ], [ 9, 5, 7, 2 ], [ 15, 1, 5, 4 ],
[ 25, 2, 7, 4 ], [ 30, 9, 27, 8 ] ]
k = 22: F-action on Pi is () [30,5,22]
Dynkin type is (A_1(q) + T(phi1 phi2^2 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 32, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 10, 2, 2, 2 ],
[ 15, 1, 5, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 25, 2, 6, 4 ],
[ 30, 9, 22, 4 ] ]
k = 23: F-action on Pi is () [30,5,23]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 3, 5, 8 ], [ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 5, 4 ],
[ 10, 2, 2, 4 ], [ 15, 1, 1, 8 ], [ 18, 2, 4, 12 ], [ 23, 4, 8, 16 ],
[ 23, 6, 8, 8 ], [ 25, 2, 8, 24 ], [ 25, 3, 6, 16 ], [ 29, 3, 12, 32 ],
[ 29, 9, 12, 16 ], [ 29, 11, 8, 16 ], [ 30, 9, 28, 16 ], [ 30, 11, 29, 16 ]
]
k = 24: F-action on Pi is () [30,5,24]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 10, 2, 2, 4 ],
[ 15, 1, 4, 4 ], [ 18, 2, 4, 12 ], [ 23, 4, 7, 8 ], [ 23, 4, 8, 8 ],
[ 23, 6, 7, 4 ], [ 23, 6, 8, 4 ], [ 25, 2, 8, 24 ], [ 29, 3, 11, 16 ],
[ 29, 3, 12, 16 ], [ 29, 9, 11, 8 ], [ 29, 9, 12, 8 ], [ 29, 11, 7, 8 ],
[ 29, 11, 8, 8 ], [ 30, 9, 30, 8 ], [ 30, 11, 28, 8 ], [ 30, 11, 30, 8 ] ]
k = 25: F-action on Pi is () [30,5,25]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 3, 7, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 9, 5, 7, 4 ], [ 15, 1, 4, 4 ], [ 18, 2, 3, 4 ], [ 23, 4, 6, 8 ],
[ 23, 6, 6, 4 ], [ 25, 2, 5, 8 ], [ 29, 3, 8, 8 ], [ 29, 3, 10, 16 ],
[ 29, 9, 8, 4 ], [ 29, 9, 10, 8 ], [ 29, 11, 6, 8 ], [ 30, 9, 31, 16 ],
[ 30, 11, 24, 8 ], [ 30, 11, 32, 8 ] ]
k = 26: F-action on Pi is () [30,5,26]
Dynkin type is (A_1(q) + T(phi2^5)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 16 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 8 ], [ 10, 2, 2, 4 ], [ 15, 1, 3, 8 ],
[ 18, 2, 4, 12 ], [ 23, 4, 7, 16 ], [ 23, 6, 7, 8 ], [ 25, 2, 8, 24 ],
[ 25, 3, 7, 16 ], [ 29, 3, 11, 32 ], [ 29, 9, 11, 16 ], [ 29, 11, 7, 16 ],
[ 30, 9, 32, 32 ], [ 30, 11, 27, 16 ] ]
k = 27: F-action on Pi is () [30,5,27]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 15, 1, 3, 8 ], [ 18, 2, 3, 4 ],
[ 23, 4, 6, 8 ], [ 23, 6, 6, 4 ], [ 25, 2, 5, 8 ], [ 29, 3, 7, 8 ],
[ 29, 3, 10, 16 ], [ 29, 9, 7, 4 ], [ 29, 9, 10, 8 ], [ 29, 11, 6, 8 ],
[ 30, 9, 30, 8 ], [ 30, 11, 23, 8 ], [ 30, 11, 26, 8 ] ]
k = 28: F-action on Pi is () [30,5,28]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 3, 5, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 9, 5, 5, 4 ],
[ 15, 1, 3, 8 ], [ 18, 2, 2, 4 ], [ 25, 2, 2, 8 ], [ 25, 3, 8, 16 ],
[ 29, 3, 6, 16 ], [ 29, 9, 6, 8 ], [ 30, 9, 28, 16 ], [ 30, 11, 21, 16 ] ]
j = 6: Omega of order 2, action on Pi: <()>
k = 1: F-action on Pi is () [30,6,1]
Dynkin type is (A_1(q) + T(phi1^5)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 16 ], [ 9, 5, 1, 8 ], [ 11, 2, 1, 4 ], [ 15, 1, 1, 8 ],
[ 20, 2, 1, 12 ], [ 23, 3, 1, 16 ], [ 23, 6, 1, 8 ], [ 26, 2, 1, 24 ],
[ 26, 3, 1, 16 ], [ 29, 2, 1, 32 ], [ 29, 9, 1, 16 ], [ 29, 10, 1, 16 ],
[ 30, 10, 1, 32 ], [ 30, 11, 1, 16 ] ]
k = 2: F-action on Pi is () [30,6,2]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 11, 2, 1, 4 ],
[ 15, 1, 4, 4 ], [ 20, 2, 1, 12 ], [ 23, 3, 1, 8 ], [ 23, 3, 4, 8 ],
[ 23, 6, 1, 4 ], [ 23, 6, 4, 4 ], [ 26, 2, 1, 24 ], [ 29, 2, 1, 16 ],
[ 29, 2, 4, 16 ], [ 29, 9, 1, 8 ], [ 29, 9, 4, 8 ], [ 29, 10, 1, 8 ],
[ 29, 10, 4, 8 ], [ 30, 10, 3, 8 ], [ 30, 11, 4, 8 ], [ 30, 11, 6, 8 ] ]
k = 3: F-action on Pi is () [30,6,3]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 4, 3, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 9, 5, 3, 4 ], [ 15, 1, 4, 4 ], [ 20, 2, 2, 4 ], [ 23, 3, 3, 8 ],
[ 23, 6, 3, 4 ], [ 26, 2, 2, 8 ], [ 29, 2, 3, 16 ], [ 29, 2, 5, 8 ],
[ 29, 9, 3, 8 ], [ 29, 9, 5, 4 ], [ 29, 10, 3, 8 ], [ 30, 10, 5, 16 ],
[ 30, 11, 3, 8 ], [ 30, 11, 9, 8 ] ]
k = 4: F-action on Pi is () [30,6,4]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 15, 1, 1, 8 ], [ 20, 2, 2, 4 ],
[ 23, 3, 2, 8 ], [ 23, 6, 2, 4 ], [ 26, 2, 2, 8 ], [ 29, 2, 2, 16 ],
[ 29, 2, 5, 8 ], [ 29, 9, 2, 8 ], [ 29, 9, 5, 4 ], [ 29, 10, 2, 8 ],
[ 30, 10, 3, 8 ], [ 30, 11, 2, 8 ], [ 30, 11, 15, 8 ] ]
k = 5: F-action on Pi is () [30,6,5]
Dynkin type is (A_1(q) + T(phi1^2 phi2 phi4)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 28, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 26, 2, 4, 4 ], [ 30, 10, 7, 4 ] ]
k = 6: F-action on Pi is () [30,6,6]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 9, 4, 1, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 1, 2 ],
[ 9, 5, 8, 2 ], [ 11, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 20, 2, 1, 2 ],
[ 20, 2, 3, 2 ], [ 26, 2, 3, 4 ], [ 26, 3, 1, 4 ], [ 26, 3, 2, 4 ],
[ 26, 3, 3, 4 ], [ 26, 3, 4, 4 ], [ 30, 10, 9, 8 ] ]
k = 7: F-action on Pi is () [30,6,7]
Dynkin type is (A_1(q) + T(phi1 phi4^2)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 11, 17 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 9, 4, 3, 4 ],
[ 9, 4, 6, 4 ], [ 9, 5, 3, 2 ], [ 9, 5, 6, 2 ], [ 15, 1, 5, 4 ],
[ 26, 2, 4, 4 ], [ 30, 10, 10, 8 ] ]
k = 8: F-action on Pi is () [30,6,8]
Dynkin type is (A_1(q) + T(phi1^2 phi2 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 28, 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 11, 2, 1, 2 ],
[ 15, 1, 5, 4 ], [ 20, 2, 1, 2 ], [ 20, 2, 3, 2 ], [ 26, 2, 3, 4 ],
[ 30, 10, 7, 4 ] ]
k = 9: F-action on Pi is () [30,6,9]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 4, 6, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 9, 5, 6, 4 ], [ 15, 1, 4, 4 ], [ 20, 2, 2, 4 ], [ 23, 3, 2, 8 ],
[ 23, 6, 2, 4 ], [ 26, 2, 2, 8 ], [ 29, 2, 2, 16 ], [ 29, 2, 8, 8 ],
[ 29, 9, 2, 8 ], [ 29, 9, 8, 4 ], [ 29, 10, 2, 8 ], [ 30, 10, 12, 16 ],
[ 30, 11, 5, 8 ], [ 30, 11, 13, 8 ] ]
k = 10: F-action on Pi is () [30,6,10]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 15, 1, 4, 4 ],
[ 20, 2, 3, 4 ], [ 26, 2, 5, 8 ], [ 29, 2, 6, 8 ], [ 29, 2, 7, 8 ],
[ 29, 9, 6, 4 ], [ 29, 9, 7, 4 ], [ 30, 10, 14, 8 ], [ 30, 11, 10, 8 ],
[ 30, 11, 14, 8 ] ]
k = 11: F-action on Pi is () [30,6,11]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 8, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 8, 4 ],
[ 15, 1, 1, 8 ], [ 20, 2, 3, 4 ], [ 26, 2, 5, 8 ], [ 26, 3, 2, 16 ],
[ 29, 2, 6, 16 ], [ 29, 9, 6, 8 ], [ 30, 10, 15, 16 ], [ 30, 11, 16, 16 ] ]
k = 12: F-action on Pi is () [30,6,12]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 15, 1, 3, 8 ], [ 20, 2, 2, 4 ],
[ 23, 3, 3, 8 ], [ 23, 6, 3, 4 ], [ 26, 2, 2, 8 ], [ 29, 2, 3, 16 ],
[ 29, 2, 8, 8 ], [ 29, 9, 3, 8 ], [ 29, 9, 8, 4 ], [ 29, 10, 3, 8 ],
[ 30, 10, 14, 8 ], [ 30, 11, 7, 8 ], [ 30, 11, 12, 8 ] ]
k = 13: F-action on Pi is () [30,6,13]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ],
[ 15, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 26, 2, 5, 8 ], [ 26, 3, 3, 16 ],
[ 29, 2, 7, 16 ], [ 29, 9, 7, 8 ], [ 30, 10, 16, 32 ], [ 30, 11, 11, 16 ] ]
k = 14: F-action on Pi is () [30,6,14]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 4, 8, 8 ], [ 9, 5, 2, 4 ], [ 9, 5, 8, 4 ],
[ 11, 2, 1, 4 ], [ 15, 1, 3, 8 ], [ 20, 2, 1, 12 ], [ 23, 3, 4, 16 ],
[ 23, 6, 4, 8 ], [ 26, 2, 1, 24 ], [ 26, 3, 4, 16 ], [ 29, 2, 4, 32 ],
[ 29, 9, 4, 16 ], [ 29, 10, 4, 16 ], [ 30, 10, 15, 16 ], [ 30, 11, 8, 16 ] ]
k = 15: F-action on Pi is () [30,6,15]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ],
[ 15, 1, 1, 8 ], [ 20, 2, 2, 4 ], [ 26, 2, 2, 8 ], [ 26, 3, 5, 16 ],
[ 29, 2, 5, 16 ], [ 29, 9, 5, 8 ], [ 30, 10, 17, 32 ], [ 30, 11, 17, 16 ] ]
k = 16: F-action on Pi is () [30,6,16]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 15, 1, 4, 4 ],
[ 20, 2, 2, 4 ], [ 26, 2, 2, 8 ], [ 29, 2, 5, 8 ], [ 29, 2, 8, 8 ],
[ 29, 9, 5, 4 ], [ 29, 9, 8, 4 ], [ 30, 10, 19, 8 ], [ 30, 11, 20, 8 ],
[ 30, 11, 22, 8 ] ]
k = 17: F-action on Pi is () [30,6,17]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 4, 4, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 9, 5, 4, 4 ], [ 15, 1, 4, 4 ], [ 20, 2, 3, 4 ], [ 23, 3, 5, 8 ],
[ 23, 6, 5, 4 ], [ 26, 2, 5, 8 ], [ 29, 2, 7, 8 ], [ 29, 2, 9, 16 ],
[ 29, 9, 7, 4 ], [ 29, 9, 9, 8 ], [ 29, 10, 5, 8 ], [ 30, 10, 21, 16 ],
[ 30, 11, 19, 8 ], [ 30, 11, 25, 8 ] ]
k = 18: F-action on Pi is () [30,6,18]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 15, 1, 1, 8 ], [ 20, 2, 3, 4 ],
[ 23, 3, 5, 8 ], [ 23, 6, 5, 4 ], [ 26, 2, 5, 8 ], [ 29, 2, 6, 8 ],
[ 29, 2, 9, 16 ], [ 29, 9, 6, 4 ], [ 29, 9, 9, 8 ], [ 29, 10, 5, 8 ],
[ 30, 10, 19, 8 ], [ 30, 11, 18, 8 ], [ 30, 11, 31, 8 ] ]
k = 19: F-action on Pi is () [30,6,19]
Dynkin type is (A_1(q) + T(phi1 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 31, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 26, 2, 9, 4 ], [ 30, 10, 23, 4 ] ]
k = 20: F-action on Pi is () [30,6,20]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 9, 4, 2, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 2, 2 ],
[ 9, 5, 7, 2 ], [ 11, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 20, 2, 2, 2 ],
[ 20, 2, 4, 2 ], [ 26, 2, 8, 4 ], [ 26, 3, 5, 4 ], [ 26, 3, 6, 4 ],
[ 26, 3, 7, 4 ], [ 26, 3, 8, 4 ], [ 30, 10, 25, 8 ] ]
k = 21: F-action on Pi is () [30,6,21]
Dynkin type is (A_1(q) + T(phi2 phi4^2)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 17, 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 9, 4, 4, 4 ],
[ 9, 4, 5, 4 ], [ 9, 5, 4, 2 ], [ 9, 5, 5, 2 ], [ 15, 1, 5, 4 ],
[ 26, 2, 9, 4 ], [ 30, 10, 26, 8 ] ]
k = 22: F-action on Pi is () [30,6,22]
Dynkin type is (A_1(q) + T(phi1 phi2^2 phi4)).2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 31, 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 11, 2, 2, 2 ],
[ 15, 1, 5, 4 ], [ 20, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 26, 2, 8, 4 ],
[ 30, 10, 23, 4 ] ]
k = 23: F-action on Pi is () [30,6,23]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 4, 5, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ],
[ 9, 5, 5, 4 ], [ 15, 1, 4, 4 ], [ 20, 2, 3, 4 ], [ 23, 3, 8, 8 ],
[ 23, 6, 8, 4 ], [ 26, 2, 5, 8 ], [ 29, 2, 6, 8 ], [ 29, 2, 12, 16 ],
[ 29, 9, 6, 4 ], [ 29, 9, 12, 8 ], [ 29, 10, 8, 8 ], [ 30, 10, 28, 16 ],
[ 30, 11, 21, 8 ], [ 30, 11, 29, 8 ] ]
k = 24: F-action on Pi is () [30,6,24]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 11, 2, 2, 4 ],
[ 15, 1, 4, 4 ], [ 20, 2, 4, 12 ], [ 23, 3, 6, 8 ], [ 23, 3, 7, 8 ],
[ 23, 6, 6, 4 ], [ 23, 6, 7, 4 ], [ 26, 2, 10, 24 ], [ 29, 2, 10, 16 ],
[ 29, 2, 11, 16 ], [ 29, 9, 10, 8 ], [ 29, 9, 11, 8 ], [ 29, 10, 6, 8 ],
[ 29, 10, 7, 8 ], [ 30, 10, 30, 8 ], [ 30, 11, 26, 8 ], [ 30, 11, 30, 8 ] ]
k = 25: F-action on Pi is () [30,6,25]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 7, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 7, 4 ],
[ 11, 2, 2, 4 ], [ 15, 1, 1, 8 ], [ 20, 2, 4, 12 ], [ 23, 3, 6, 16 ],
[ 23, 6, 6, 8 ], [ 26, 2, 10, 24 ], [ 26, 3, 6, 16 ], [ 29, 2, 10, 32 ],
[ 29, 9, 10, 16 ], [ 29, 10, 6, 16 ], [ 30, 10, 31, 16 ],
[ 30, 11, 32, 16 ] ]
k = 26: F-action on Pi is () [30,6,26]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 15, 1, 3, 8 ], [ 20, 2, 3, 4 ],
[ 23, 3, 8, 8 ], [ 23, 6, 8, 4 ], [ 26, 2, 5, 8 ], [ 29, 2, 7, 8 ],
[ 29, 2, 12, 16 ], [ 29, 9, 7, 4 ], [ 29, 9, 12, 8 ], [ 29, 10, 8, 8 ],
[ 30, 10, 30, 8 ], [ 30, 11, 23, 8 ], [ 30, 11, 28, 8 ] ]
k = 27: F-action on Pi is () [30,6,27]
Dynkin type is (A_1(q) + T(phi2^5)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 16 ], [ 9, 5, 2, 8 ], [ 11, 2, 2, 4 ], [ 15, 1, 3, 8 ],
[ 20, 2, 4, 12 ], [ 23, 3, 7, 16 ], [ 23, 6, 7, 8 ], [ 26, 2, 10, 24 ],
[ 26, 3, 7, 16 ], [ 29, 2, 11, 32 ], [ 29, 9, 11, 16 ], [ 29, 10, 7, 16 ],
[ 30, 10, 32, 32 ], [ 30, 11, 27, 16 ] ]
k = 28: F-action on Pi is () [30,6,28]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 4, 7, 8 ], [ 9, 5, 2, 4 ], [ 9, 5, 7, 4 ],
[ 15, 1, 3, 8 ], [ 20, 2, 2, 4 ], [ 26, 2, 2, 8 ], [ 26, 3, 8, 16 ],
[ 29, 2, 8, 16 ], [ 29, 9, 8, 8 ], [ 30, 10, 31, 16 ], [ 30, 11, 24, 16 ] ]
j = 11: Omega of order 4, action on Pi: <(), ()>
k = 1: F-action on Pi is () [30,11,1]
Dynkin type is (A_1(q) + T(phi1^5)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 1, 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 6 ], [ 23, 6, 1, 4 ], [ 29, 9, 1, 8 ] ]
k = 2: F-action on Pi is () [30,11,2]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 23, 6, 2, 4 ], [ 29, 9, 2, 8 ] ]
k = 3: F-action on Pi is () [30,11,3]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 9, 5, 3, 4 ], [ 23, 6, 3, 4 ], [ 29, 9, 3, 8 ] ]
k = 4: F-action on Pi is () [30,11,4]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 23, 6, 4, 4 ], [ 29, 9, 4, 8 ] ]
k = 5: F-action on Pi is () [30,11,5]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 6, 4 ], [ 23, 6, 2, 4 ], [ 29, 9, 2, 8 ] ]
k = 6: F-action on Pi is () [30,11,6]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 23, 6, 1, 4 ], [ 29, 9, 1, 8 ] ]
k = 7: F-action on Pi is () [30,11,7]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 23, 6, 3, 4 ], [ 29, 9, 3, 8 ] ]
k = 8: F-action on Pi is () [30,11,8]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 8, 4 ], [ 23, 6, 4, 4 ], [ 29, 9, 4, 8 ] ]
k = 9: F-action on Pi is () [30,11,9]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 2, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 3, 4 ], [ 29, 9, 5, 4 ] ]
k = 10: F-action on Pi is () [30,11,10]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 29, 9, 6, 4 ] ]
k = 11: F-action on Pi is () [30,11,11]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 3, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 1, 4 ], [ 9, 5, 2, 2 ], [ 29, 9, 7, 4 ] ]
k = 12: F-action on Pi is () [30,11,12]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 29, 9, 8, 4 ] ]
k = 13: F-action on Pi is () [30,11,13]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 9, 5, 6, 4 ], [ 29, 9, 8, 4 ] ]
k = 14: F-action on Pi is () [30,11,14]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 7, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 29, 9, 7, 4 ] ]
k = 15: F-action on Pi is () [30,11,15]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 5, 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 29, 9, 5, 4 ] ]
k = 16: F-action on Pi is () [30,11,16]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 9, 5, 8, 4 ], [ 29, 9, 6, 4 ] ]
k = 17: F-action on Pi is () [30,11,17]
Dynkin type is (A_1(q) + T(phi1^4 phi2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5, 2 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 9, 5, 2, 4 ], [ 29, 9, 5, 4 ] ]
k = 18: F-action on Pi is () [30,11,18]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 29, 9, 6, 4 ] ]
k = 19: F-action on Pi is () [30,11,19]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 9, 5, 4, 4 ], [ 29, 9, 7, 4 ] ]
k = 20: F-action on Pi is () [30,11,20]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 29, 9, 8, 4 ] ]
k = 21: F-action on Pi is () [30,11,21]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 5, 4 ], [ 29, 9, 6, 4 ] ]
k = 22: F-action on Pi is () [30,11,22]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 29, 9, 5, 4 ] ]
k = 23: F-action on Pi is () [30,11,23]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 29, 9, 7, 4 ] ]
k = 24: F-action on Pi is () [30,11,24]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 7, 4 ], [ 29, 9, 8, 4 ] ]
k = 25: F-action on Pi is () [30,11,25]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 7, 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 4, 4 ], [ 23, 6, 5, 4 ], [ 29, 9, 9, 8 ] ]
k = 26: F-action on Pi is () [30,11,26]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 23, 6, 6, 4 ], [ 29, 9, 10, 8 ] ]
k = 27: F-action on Pi is () [30,11,27]
Dynkin type is (A_1(q) + T(phi2^5)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 9, 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 6 ], [ 23, 6, 7, 4 ], [ 29, 9, 11, 8 ] ]
k = 28: F-action on Pi is () [30,11,28]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2.2
Order of center |Z^F|: phi2 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 phi1
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 2 ],
[ 9, 1, 2, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 2, 4 ],
[ 9, 5, 2, 2 ], [ 23, 6, 8, 4 ], [ 29, 9, 12, 8 ] ]
k = 29: F-action on Pi is () [30,11,29]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 16, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 9, 5, 5, 4 ], [ 23, 6, 8, 4 ], [ 29, 9, 12, 8 ] ]
k = 30: F-action on Pi is () [30,11,30]
Dynkin type is (A_1(q) + T(phi1 phi2^4)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13, 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 23, 6, 7, 4 ], [ 29, 9, 11, 8 ] ]
k = 31: F-action on Pi is () [30,11,31]
Dynkin type is (A_1(q) + T(phi1^3 phi2^2)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
2, q congruent 1 modulo 4
1, q congruent 2 modulo 4
4, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 0
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/4 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10, 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 23, 6, 5, 4 ], [ 29, 9, 9, 8 ] ]
k = 32: F-action on Pi is () [30,11,32]
Dynkin type is (A_1(q) + T(phi1^2 phi2^3)).2.2
Order of center |Z^F|: phi1 times
1, q congruent 0 modulo 4
4, q congruent 1 modulo 4
1, q congruent 2 modulo 4
2, q congruent 3 modulo 4
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/4 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 0
Fusion of maximal tori of C^F in those of G^F:
[ 15, 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 9, 1, 1, 8 ], [ 9, 2, 1, 4 ], [ 9, 3, 1, 4 ], [ 9, 4, 1, 4 ],
[ 9, 5, 1, 2 ], [ 9, 5, 7, 4 ], [ 23, 6, 6, 4 ], [ 29, 9, 10, 8 ] ]
i = 31: Pi = [ ]
j = 1: Omega trivial
k = 1: F-action on Pi is () [31,1,1]
Dynkin type is A_0(q) + T(phi1^6)
Order of center |Z^F|: phi1^6
Numbers of classes in class type:
q congruent 0 modulo
4: 1/23040 ( q^6-36*q^5+520*q^4-3840*q^3+15184*q^2-30144*q+23040 )
q congruent 1 modulo
4: 1/23040 ( q^6-36*q^5+505*q^4-3600*q^3+14659*q^2-36684*q+48195 )
q congruent 2 modulo
4: 1/23040 ( q^6-36*q^5+520*q^4-3840*q^3+15184*q^2-30144*q+23040 )
q congruent 3 modulo
4: 1/23040 ( q^6-36*q^5+505*q^4-3600*q^3+14659*q^2-35244*q+38115 )
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, 30 ], [ 2, 2, 1, 15 ], [ 3, 1, 1, 40 ],
[ 3, 2, 1, 20 ], [ 3, 3, 1, 20 ], [ 3, 4, 1, 20 ], [ 3, 5, 1, 10 ],
[ 4, 1, 1, 12 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 60 ], [ 6, 1, 1, 160 ],
[ 7, 1, 1, 240 ], [ 7, 2, 1, 120 ], [ 7, 3, 1, 120 ], [ 7, 4, 1, 120 ],
[ 7, 5, 1, 60 ], [ 8, 1, 1, 240 ], [ 9, 1, 1, 720 ], [ 9, 2, 1, 360 ],
[ 9, 3, 1, 360 ], [ 9, 4, 1, 360 ], [ 9, 5, 1, 180 ], [ 10, 1, 1, 32 ],
[ 10, 2, 1, 16 ], [ 11, 1, 1, 32 ], [ 11, 2, 1, 16 ], [ 12, 1, 1, 120 ],
[ 12, 2, 1, 60 ], [ 12, 3, 1, 60 ], [ 12, 4, 1, 30 ], [ 13, 1, 1, 480 ],
[ 13, 2, 1, 240 ], [ 14, 1, 1, 960 ], [ 14, 2, 1, 480 ], [ 15, 1, 1, 1440 ],
[ 16, 1, 1, 1440 ], [ 16, 2, 1, 720 ], [ 16, 3, 1, 720 ], [ 16, 4, 1, 720 ],
[ 16, 5, 1, 720 ], [ 16, 6, 1, 720 ], [ 16, 7, 1, 720 ], [ 16, 8, 1, 720 ],
[ 16, 9, 1, 360 ], [ 16, 10, 1, 360 ], [ 16, 11, 1, 360 ],
[ 16, 12, 1, 360 ], [ 16, 13, 1, 360 ], [ 16, 14, 1, 360 ],
[ 16, 15, 1, 360 ], [ 16, 16, 1, 360 ], [ 16, 17, 1, 360 ],
[ 17, 1, 1, 192 ], [ 17, 2, 1, 96 ], [ 18, 1, 1, 480 ], [ 18, 2, 1, 240 ],
[ 19, 1, 1, 640 ], [ 19, 2, 1, 320 ], [ 19, 3, 1, 320 ], [ 19, 4, 1, 320 ],
[ 19, 5, 1, 160 ], [ 20, 1, 1, 480 ], [ 20, 2, 1, 240 ], [ 21, 1, 1, 960 ],
[ 21, 2, 1, 480 ], [ 21, 3, 1, 480 ], [ 21, 4, 1, 480 ], [ 21, 5, 1, 240 ],
[ 21, 6, 1, 240 ], [ 21, 7, 1, 240 ], [ 22, 1, 1, 2880 ],
[ 22, 2, 1, 1440 ], [ 22, 3, 1, 1440 ], [ 22, 4, 1, 720 ],
[ 23, 1, 1, 960 ], [ 23, 2, 1, 480 ], [ 23, 3, 1, 480 ], [ 23, 4, 1, 480 ],
[ 23, 5, 1, 480 ], [ 23, 6, 1, 240 ], [ 24, 1, 1, 1920 ], [ 24, 2, 1, 960 ],
[ 25, 1, 1, 2880 ], [ 25, 2, 1, 1440 ], [ 25, 3, 1, 1440 ],
[ 26, 1, 1, 2880 ], [ 26, 2, 1, 1440 ], [ 26, 3, 1, 1440 ],
[ 27, 1, 1, 5760 ], [ 27, 2, 1, 2880 ], [ 27, 3, 1, 2880 ],
[ 27, 4, 1, 2880 ], [ 27, 5, 1, 2880 ], [ 27, 6, 1, 1440 ],
[ 27, 7, 1, 1440 ], [ 27, 8, 1, 1440 ], [ 27, 9, 1, 1440 ],
[ 27, 10, 1, 1440 ], [ 27, 11, 1, 1440 ], [ 27, 12, 1, 1440 ],
[ 27, 13, 1, 1440 ], [ 27, 14, 1, 1440 ], [ 28, 1, 1, 3840 ],
[ 28, 2, 1, 1920 ], [ 28, 3, 1, 1920 ], [ 28, 4, 1, 1920 ],
[ 28, 5, 1, 960 ], [ 28, 6, 1, 960 ], [ 29, 1, 1, 5760 ],
[ 29, 2, 1, 2880 ], [ 29, 3, 1, 2880 ], [ 29, 4, 1, 2880 ],
[ 29, 5, 1, 2880 ], [ 29, 6, 1, 2880 ], [ 29, 7, 1, 2880 ],
[ 29, 8, 1, 2880 ], [ 29, 9, 1, 1440 ], [ 29, 10, 1, 1440 ],
[ 29, 11, 1, 1440 ], [ 29, 12, 1, 1440 ], [ 29, 13, 1, 1440 ],
[ 30, 1, 1, 11520 ], [ 30, 2, 1, 5760 ], [ 30, 3, 1, 5760 ],
[ 30, 4, 1, 5760 ], [ 30, 5, 1, 5760 ], [ 30, 6, 1, 5760 ],
[ 30, 7, 1, 5760 ], [ 30, 8, 1, 2880 ], [ 30, 9, 1, 2880 ],
[ 30, 10, 1, 2880 ], [ 30, 11, 1, 2880 ], [ 30, 12, 1, 2880 ],
[ 30, 13, 1, 2880 ], [ 31, 2, 1, 11520 ], [ 31, 3, 1, 11520 ],
[ 31, 4, 1, 11520 ], [ 31, 5, 1, 11520 ], [ 31, 6, 1, 11520 ],
[ 31, 7, 1, 11520 ], [ 31, 8, 1, 11520 ], [ 31, 9, 1, 5760 ],
[ 31, 10, 1, 5760 ], [ 31, 11, 1, 5760 ], [ 31, 12, 1, 5760 ],
[ 31, 13, 1, 5760 ], [ 31, 14, 1, 5760 ], [ 31, 15, 1, 5760 ],
[ 31, 16, 1, 5760 ], [ 31, 17, 1, 5760 ], [ 31, 18, 1, 5760 ],
[ 31, 19, 1, 5760 ], [ 31, 20, 1, 5760 ], [ 31, 21, 1, 5760 ],
[ 31, 22, 1, 5760 ], [ 31, 23, 1, 5760 ], [ 31, 24, 1, 5760 ],
[ 31, 25, 1, 5760 ], [ 31, 26, 1, 5760 ], [ 31, 27, 1, 5760 ],
[ 31, 28, 1, 5760 ], [ 31, 29, 1, 5760 ], [ 31, 30, 1, 5760 ],
[ 31, 31, 1, 5760 ], [ 31, 32, 1, 5760 ], [ 31, 33, 1, 5760 ] ]
k = 2: F-action on Pi is () [31,1,2]
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 0 modulo
4: 1/1536 q ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 )
q congruent 1 modulo
4: 1/1536 phi1 ( q^5-15*q^4+54*q^3+126*q^2-967*q+1185 )
q congruent 2 modulo
4: 1/1536 q ( q^5-16*q^4+84*q^3-128*q^2-160*q+384 )
q congruent 3 modulo
4: 1/1536 phi1 ( q^5-15*q^4+54*q^3+126*q^2-967*q+1281 )
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, 14 ], [ 2, 1, 2, 16 ], [ 2, 2, 1, 7 ],
[ 2, 2, 2, 8 ], [ 3, 1, 1, 16 ], [ 3, 1, 2, 24 ], [ 3, 2, 1, 8 ],
[ 3, 2, 2, 12 ], [ 3, 3, 1, 8 ], [ 3, 3, 2, 12 ], [ 3, 4, 1, 8 ],
[ 3, 4, 2, 12 ], [ 3, 5, 1, 4 ], [ 3, 5, 2, 6 ], [ 4, 1, 1, 8 ],
[ 4, 1, 2, 4 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 24 ],
[ 5, 1, 2, 4 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 64 ], [ 7, 1, 2, 32 ],
[ 7, 1, 3, 96 ], [ 7, 1, 4, 48 ], [ 7, 2, 1, 32 ], [ 7, 2, 2, 16 ],
[ 7, 2, 3, 48 ], [ 7, 2, 4, 24 ], [ 7, 3, 1, 32 ], [ 7, 3, 2, 16 ],
[ 7, 3, 3, 48 ], [ 7, 3, 4, 24 ], [ 7, 4, 1, 32 ], [ 7, 4, 2, 16 ],
[ 7, 4, 3, 48 ], [ 7, 4, 4, 24 ], [ 7, 5, 1, 16 ], [ 7, 5, 2, 8 ],
[ 7, 5, 3, 24 ], [ 7, 5, 4, 12 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 96 ],
[ 9, 1, 2, 48 ], [ 9, 1, 3, 192 ], [ 9, 2, 1, 48 ], [ 9, 2, 2, 24 ],
[ 9, 2, 3, 96 ], [ 9, 3, 1, 48 ], [ 9, 3, 2, 24 ], [ 9, 3, 3, 96 ],
[ 9, 4, 1, 48 ], [ 9, 4, 2, 24 ], [ 9, 4, 3, 96 ], [ 9, 5, 1, 24 ],
[ 9, 5, 2, 12 ], [ 9, 5, 3, 48 ], [ 12, 1, 1, 48 ], [ 12, 1, 3, 8 ],
[ 12, 1, 4, 32 ], [ 12, 2, 1, 24 ], [ 12, 2, 3, 4 ], [ 12, 2, 4, 16 ],
[ 12, 3, 1, 24 ], [ 12, 3, 2, 4 ], [ 12, 3, 3, 16 ], [ 12, 3, 4, 16 ],
[ 12, 4, 1, 12 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 8 ], [ 13, 1, 1, 96 ],
[ 13, 1, 2, 32 ], [ 13, 1, 3, 96 ], [ 13, 2, 1, 48 ], [ 13, 2, 2, 16 ],
[ 13, 2, 3, 48 ], [ 14, 1, 1, 64 ], [ 14, 1, 3, 128 ], [ 14, 2, 1, 32 ],
[ 14, 2, 3, 64 ], [ 15, 1, 1, 96 ], [ 15, 1, 4, 96 ], [ 16, 1, 1, 192 ],
[ 16, 1, 2, 192 ], [ 16, 1, 5, 96 ], [ 16, 1, 6, 384 ], [ 16, 2, 1, 96 ],
[ 16, 2, 2, 96 ], [ 16, 2, 5, 48 ], [ 16, 2, 6, 192 ], [ 16, 3, 1, 96 ],
[ 16, 3, 2, 96 ], [ 16, 3, 5, 48 ], [ 16, 3, 6, 192 ], [ 16, 4, 1, 96 ],
[ 16, 4, 2, 96 ], [ 16, 4, 5, 48 ], [ 16, 4, 6, 192 ], [ 16, 5, 1, 96 ],
[ 16, 5, 3, 48 ], [ 16, 5, 5, 192 ], [ 16, 6, 1, 96 ], [ 16, 6, 3, 48 ],
[ 16, 6, 5, 192 ], [ 16, 7, 1, 96 ], [ 16, 7, 3, 48 ], [ 16, 7, 5, 192 ],
[ 16, 8, 1, 96 ], [ 16, 8, 2, 96 ], [ 16, 8, 3, 96 ], [ 16, 8, 4, 48 ],
[ 16, 8, 5, 192 ], [ 16, 8, 6, 96 ], [ 16, 8, 7, 96 ], [ 16, 9, 1, 48 ],
[ 16, 9, 2, 48 ], [ 16, 9, 5, 24 ], [ 16, 9, 6, 96 ], [ 16, 10, 1, 48 ],
[ 16, 10, 3, 24 ], [ 16, 10, 5, 96 ], [ 16, 11, 1, 48 ], [ 16, 11, 2, 48 ],
[ 16, 11, 5, 24 ], [ 16, 11, 6, 96 ], [ 16, 11, 7, 48 ], [ 16, 12, 1, 48 ],
[ 16, 12, 3, 24 ], [ 16, 12, 5, 96 ], [ 16, 13, 1, 48 ], [ 16, 13, 2, 96 ],
[ 16, 13, 5, 24 ], [ 16, 13, 6, 96 ], [ 16, 14, 1, 48 ], [ 16, 14, 2, 48 ],
[ 16, 14, 3, 48 ], [ 16, 14, 4, 24 ], [ 16, 14, 5, 96 ], [ 16, 15, 1, 48 ],
[ 16, 15, 2, 96 ], [ 16, 15, 5, 24 ], [ 16, 15, 6, 96 ], [ 16, 16, 1, 48 ],
[ 16, 16, 2, 96 ], [ 16, 16, 5, 24 ], [ 16, 16, 6, 96 ], [ 16, 17, 1, 48 ],
[ 16, 17, 2, 48 ], [ 16, 17, 3, 48 ], [ 16, 17, 4, 24 ], [ 16, 17, 5, 96 ],
[ 18, 1, 2, 32 ], [ 18, 2, 2, 16 ], [ 20, 1, 2, 32 ], [ 20, 2, 2, 16 ],
[ 21, 1, 1, 192 ], [ 21, 1, 2, 192 ], [ 21, 1, 3, 64 ], [ 21, 2, 1, 96 ],
[ 21, 2, 3, 32 ], [ 21, 2, 4, 32 ], [ 21, 2, 6, 96 ], [ 21, 2, 8, 96 ],
[ 21, 3, 1, 96 ], [ 21, 3, 2, 32 ], [ 21, 3, 5, 32 ], [ 21, 3, 6, 96 ],
[ 21, 3, 7, 96 ], [ 21, 4, 1, 96 ], [ 21, 4, 3, 32 ], [ 21, 4, 6, 96 ],
[ 21, 5, 1, 48 ], [ 21, 5, 3, 16 ], [ 21, 5, 4, 16 ], [ 21, 5, 6, 48 ],
[ 21, 5, 8, 48 ], [ 21, 6, 1, 48 ], [ 21, 6, 2, 16 ], [ 21, 6, 5, 16 ],
[ 21, 6, 6, 48 ], [ 21, 6, 7, 48 ], [ 21, 7, 1, 48 ], [ 21, 7, 3, 16 ],
[ 21, 7, 6, 48 ], [ 22, 1, 1, 192 ], [ 22, 1, 3, 192 ], [ 22, 1, 4, 192 ],
[ 22, 1, 7, 384 ], [ 22, 2, 1, 96 ], [ 22, 2, 3, 96 ], [ 22, 2, 4, 96 ],
[ 22, 2, 7, 192 ], [ 22, 3, 1, 96 ], [ 22, 3, 2, 96 ], [ 22, 3, 3, 96 ],
[ 22, 3, 5, 192 ], [ 22, 3, 6, 192 ], [ 22, 4, 1, 48 ], [ 22, 4, 3, 48 ],
[ 22, 4, 4, 48 ], [ 22, 4, 7, 96 ], [ 23, 1, 3, 64 ], [ 23, 2, 3, 32 ],
[ 23, 3, 3, 32 ], [ 23, 4, 3, 32 ], [ 23, 5, 3, 32 ], [ 23, 6, 3, 16 ],
[ 24, 1, 2, 128 ], [ 24, 2, 2, 64 ], [ 25, 1, 2, 192 ], [ 25, 2, 2, 96 ],
[ 25, 3, 5, 96 ], [ 26, 1, 2, 192 ], [ 26, 2, 2, 96 ], [ 26, 3, 5, 96 ],
[ 27, 1, 1, 384 ], [ 27, 1, 2, 768 ], [ 27, 1, 3, 384 ], [ 27, 2, 1, 192 ],
[ 27, 2, 3, 192 ], [ 27, 2, 6, 192 ], [ 27, 2, 11, 384 ],
[ 27, 2, 16, 384 ], [ 27, 3, 1, 192 ], [ 27, 3, 3, 192 ], [ 27, 3, 4, 192 ],
[ 27, 3, 11, 192 ], [ 27, 3, 14, 384 ], [ 27, 3, 16, 384 ],
[ 27, 4, 1, 192 ], [ 27, 4, 2, 192 ], [ 27, 4, 5, 192 ], [ 27, 4, 11, 384 ],
[ 27, 4, 12, 384 ], [ 27, 5, 1, 192 ], [ 27, 5, 3, 192 ],
[ 27, 5, 12, 384 ], [ 27, 6, 1, 96 ], [ 27, 6, 3, 96 ], [ 27, 6, 4, 96 ],
[ 27, 6, 6, 96 ], [ 27, 6, 8, 96 ], [ 27, 6, 11, 192 ], [ 27, 6, 13, 192 ],
[ 27, 6, 16, 192 ], [ 27, 7, 1, 96 ], [ 27, 7, 3, 96 ], [ 27, 7, 6, 96 ],
[ 27, 7, 11, 192 ], [ 27, 7, 16, 192 ], [ 27, 8, 1, 96 ], [ 27, 8, 3, 96 ],
[ 27, 8, 4, 96 ], [ 27, 8, 11, 96 ], [ 27, 8, 14, 192 ], [ 27, 8, 16, 192 ],
[ 27, 9, 1, 96 ], [ 27, 9, 3, 96 ], [ 27, 9, 4, 96 ], [ 27, 9, 13, 192 ],
[ 27, 10, 1, 96 ], [ 27, 10, 2, 96 ], [ 27, 10, 3, 96 ], [ 27, 10, 4, 96 ],
[ 27, 10, 9, 96 ], [ 27, 10, 11, 192 ], [ 27, 10, 12, 192 ],
[ 27, 10, 13, 192 ], [ 27, 11, 1, 96 ], [ 27, 11, 3, 96 ],
[ 27, 11, 4, 96 ], [ 27, 11, 11, 96 ], [ 27, 11, 14, 192 ],
[ 27, 11, 16, 192 ], [ 27, 12, 1, 96 ], [ 27, 12, 2, 96 ],
[ 27, 12, 5, 96 ], [ 27, 12, 11, 192 ], [ 27, 12, 12, 192 ],
[ 27, 13, 1, 96 ], [ 27, 13, 2, 96 ], [ 27, 13, 5, 96 ], [ 27, 13, 6, 96 ],
[ 27, 13, 7, 96 ], [ 27, 13, 11, 192 ], [ 27, 13, 12, 192 ],
[ 27, 13, 16, 192 ], [ 27, 14, 1, 96 ], [ 27, 14, 2, 96 ],
[ 27, 14, 5, 96 ], [ 27, 14, 11, 96 ], [ 27, 14, 14, 192 ],
[ 27, 14, 15, 192 ], [ 28, 1, 3, 256 ], [ 28, 2, 3, 128 ],
[ 28, 2, 4, 128 ], [ 28, 3, 3, 128 ], [ 28, 4, 3, 128 ], [ 28, 5, 3, 64 ],
[ 28, 5, 4, 128 ], [ 28, 6, 3, 64 ], [ 29, 1, 3, 384 ], [ 29, 1, 5, 384 ],
[ 29, 2, 3, 192 ], [ 29, 2, 5, 192 ], [ 29, 3, 3, 192 ], [ 29, 3, 5, 192 ],
[ 29, 4, 3, 192 ], [ 29, 4, 5, 192 ], [ 29, 5, 3, 192 ], [ 29, 5, 5, 192 ],
[ 29, 6, 3, 192 ], [ 29, 7, 3, 192 ], [ 29, 8, 3, 192 ], [ 29, 9, 3, 96 ],
[ 29, 9, 5, 96 ], [ 29, 10, 3, 96 ], [ 29, 11, 3, 96 ], [ 29, 12, 3, 96 ],
[ 29, 13, 3, 96 ], [ 30, 1, 3, 768 ], [ 30, 1, 14, 768 ], [ 30, 2, 3, 384 ],
[ 30, 2, 14, 384 ], [ 30, 3, 3, 384 ], [ 30, 3, 14, 384 ],
[ 30, 4, 2, 384 ], [ 30, 4, 5, 384 ], [ 30, 4, 12, 384 ],
[ 30, 4, 15, 384 ], [ 30, 5, 3, 384 ], [ 30, 5, 15, 384 ],
[ 30, 6, 3, 384 ], [ 30, 6, 15, 384 ], [ 30, 7, 3, 384 ], [ 30, 7, 9, 384 ],
[ 30, 7, 17, 384 ], [ 30, 8, 2, 192 ], [ 30, 8, 5, 192 ],
[ 30, 8, 17, 192 ], [ 30, 9, 2, 384 ], [ 30, 9, 5, 192 ],
[ 30, 9, 17, 192 ], [ 30, 10, 2, 384 ], [ 30, 10, 5, 192 ],
[ 30, 10, 17, 192 ], [ 30, 11, 3, 192 ], [ 30, 11, 9, 192 ],
[ 30, 11, 17, 192 ], [ 30, 12, 2, 384 ], [ 30, 12, 5, 192 ],
[ 30, 12, 12, 192 ], [ 30, 12, 15, 192 ], [ 30, 13, 3, 192 ],
[ 30, 13, 6, 192 ], [ 30, 13, 11, 192 ], [ 31, 2, 18, 768 ],
[ 31, 2, 23, 768 ], [ 31, 2, 50, 768 ], [ 31, 3, 18, 768 ],
[ 31, 3, 23, 768 ], [ 31, 3, 50, 768 ], [ 31, 4, 2, 768 ],
[ 31, 5, 3, 768 ], [ 31, 5, 9, 768 ], [ 31, 6, 3, 768 ], [ 31, 6, 43, 768 ],
[ 31, 7, 3, 768 ], [ 31, 8, 3, 768 ], [ 31, 9, 18, 384 ],
[ 31, 9, 23, 384 ], [ 31, 9, 51, 384 ], [ 31, 10, 3, 384 ],
[ 31, 10, 4, 384 ], [ 31, 10, 11, 384 ], [ 31, 10, 25, 384 ],
[ 31, 11, 18, 384 ], [ 31, 11, 23, 384 ], [ 31, 11, 51, 768 ],
[ 31, 12, 3, 384 ], [ 31, 12, 43, 384 ], [ 31, 13, 3, 384 ],
[ 31, 13, 9, 384 ], [ 31, 13, 29, 768 ], [ 31, 13, 45, 384 ],
[ 31, 14, 20, 384 ], [ 31, 14, 27, 384 ], [ 31, 14, 39, 384 ],
[ 31, 15, 3, 384 ], [ 31, 15, 6, 384 ], [ 31, 15, 21, 384 ],
[ 31, 15, 26, 384 ], [ 31, 15, 41, 384 ], [ 31, 16, 18, 384 ],
[ 31, 16, 23, 384 ], [ 31, 16, 50, 384 ], [ 31, 17, 16, 384 ],
[ 31, 17, 28, 384 ], [ 31, 18, 3, 384 ], [ 31, 18, 9, 384 ],
[ 31, 18, 25, 768 ], [ 31, 19, 3, 384 ], [ 31, 19, 9, 384 ],
[ 31, 19, 25, 768 ], [ 31, 20, 3, 384 ], [ 31, 20, 9, 384 ],
[ 31, 20, 25, 768 ], [ 31, 21, 2, 384 ], [ 31, 21, 5, 384 ],
[ 31, 21, 6, 384 ], [ 31, 21, 7, 384 ], [ 31, 21, 21, 384 ],
[ 31, 22, 3, 384 ], [ 31, 23, 18, 384 ], [ 31, 23, 23, 384 ],
[ 31, 23, 50, 768 ], [ 31, 24, 3, 384 ], [ 31, 24, 9, 384 ],
[ 31, 25, 3, 384 ], [ 31, 25, 9, 384 ], [ 31, 26, 3, 384 ],
[ 31, 26, 4, 768 ], [ 31, 26, 49, 384 ], [ 31, 27, 3, 384 ],
[ 31, 27, 43, 384 ], [ 31, 28, 3, 384 ], [ 31, 28, 43, 384 ],
[ 31, 29, 3, 384 ], [ 31, 29, 7, 384 ], [ 31, 29, 29, 768 ],
[ 31, 29, 45, 384 ], [ 31, 30, 3, 384 ], [ 31, 31, 25, 384 ],
[ 31, 32, 3, 384 ], [ 31, 32, 4, 768 ], [ 31, 32, 49, 384 ],
[ 31, 33, 3, 384 ], [ 31, 33, 4, 768 ], [ 31, 33, 49, 384 ] ]
k = 3: F-action on Pi is () [31,1,3]
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 0 modulo
4: 1/1536 q ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 )
q congruent 1 modulo
4: 1/1536 phi1 ( q^5-11*q^4+22*q^3+118*q^2-471*q+405 )
q congruent 2 modulo
4: 1/1536 q ( q^5-12*q^4+48*q^3-64*q^2-16*q+64 )
q congruent 3 modulo
4: 1/1536 ( q^6-12*q^5+33*q^4+96*q^3-589*q^2+780*q-117 )
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, 14 ], [ 2, 1, 2, 16 ], [ 2, 2, 1, 7 ],
[ 2, 2, 2, 8 ], [ 3, 1, 1, 24 ], [ 3, 1, 2, 16 ], [ 3, 2, 1, 12 ],
[ 3, 2, 2, 8 ], [ 3, 3, 1, 12 ], [ 3, 3, 2, 8 ], [ 3, 4, 1, 12 ],
[ 3, 4, 2, 8 ], [ 3, 5, 1, 6 ], [ 3, 5, 2, 4 ], [ 4, 1, 1, 4 ],
[ 4, 1, 2, 8 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 4 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 1, 48 ], [ 7, 1, 2, 96 ],
[ 7, 1, 3, 32 ], [ 7, 1, 4, 64 ], [ 7, 2, 1, 24 ], [ 7, 2, 2, 48 ],
[ 7, 2, 3, 16 ], [ 7, 2, 4, 32 ], [ 7, 3, 1, 24 ], [ 7, 3, 2, 48 ],
[ 7, 3, 3, 16 ], [ 7, 3, 4, 32 ], [ 7, 4, 1, 24 ], [ 7, 4, 2, 48 ],
[ 7, 4, 3, 16 ], [ 7, 4, 4, 32 ], [ 7, 5, 1, 12 ], [ 7, 5, 2, 24 ],
[ 7, 5, 3, 8 ], [ 7, 5, 4, 16 ], [ 8, 1, 2, 16 ], [ 9, 1, 1, 48 ],
[ 9, 1, 2, 96 ], [ 9, 1, 4, 192 ], [ 9, 2, 1, 24 ], [ 9, 2, 2, 48 ],
[ 9, 2, 4, 96 ], [ 9, 3, 1, 24 ], [ 9, 3, 2, 48 ], [ 9, 3, 4, 96 ],
[ 9, 4, 1, 24 ], [ 9, 4, 2, 48 ], [ 9, 4, 4, 96 ], [ 9, 5, 1, 12 ],
[ 9, 5, 2, 24 ], [ 9, 5, 4, 48 ], [ 12, 1, 1, 8 ], [ 12, 1, 3, 48 ],
[ 12, 1, 4, 32 ], [ 12, 2, 1, 4 ], [ 12, 2, 3, 24 ], [ 12, 2, 4, 16 ],
[ 12, 3, 1, 4 ], [ 12, 3, 2, 24 ], [ 12, 3, 3, 16 ], [ 12, 3, 4, 16 ],
[ 12, 4, 1, 2 ], [ 12, 4, 3, 12 ], [ 12, 4, 4, 8 ], [ 13, 1, 2, 96 ],
[ 13, 1, 3, 32 ], [ 13, 1, 4, 96 ], [ 13, 2, 2, 48 ], [ 13, 2, 3, 16 ],
[ 13, 2, 4, 48 ], [ 14, 1, 2, 64 ], [ 14, 1, 4, 128 ], [ 14, 2, 2, 32 ],
[ 14, 2, 4, 64 ], [ 15, 1, 3, 96 ], [ 15, 1, 4, 96 ], [ 16, 1, 1, 96 ],
[ 16, 1, 2, 192 ], [ 16, 1, 5, 192 ], [ 16, 1, 8, 384 ], [ 16, 2, 1, 48 ],
[ 16, 2, 2, 96 ], [ 16, 2, 5, 96 ], [ 16, 2, 8, 192 ], [ 16, 3, 1, 48 ],
[ 16, 3, 2, 96 ], [ 16, 3, 5, 96 ], [ 16, 3, 8, 192 ], [ 16, 4, 1, 48 ],
[ 16, 4, 2, 96 ], [ 16, 4, 5, 96 ], [ 16, 4, 8, 192 ], [ 16, 5, 1, 48 ],
[ 16, 5, 3, 96 ], [ 16, 5, 7, 192 ], [ 16, 6, 1, 48 ], [ 16, 6, 3, 96 ],
[ 16, 6, 7, 192 ], [ 16, 7, 1, 48 ], [ 16, 7, 3, 96 ], [ 16, 7, 7, 192 ],
[ 16, 8, 1, 48 ], [ 16, 8, 2, 96 ], [ 16, 8, 3, 96 ], [ 16, 8, 4, 96 ],
[ 16, 8, 6, 96 ], [ 16, 8, 7, 96 ], [ 16, 8, 8, 192 ], [ 16, 9, 1, 24 ],
[ 16, 9, 2, 48 ], [ 16, 9, 5, 48 ], [ 16, 9, 8, 96 ], [ 16, 10, 1, 24 ],
[ 16, 10, 3, 48 ], [ 16, 10, 7, 96 ], [ 16, 11, 1, 24 ], [ 16, 11, 2, 48 ],
[ 16, 11, 5, 48 ], [ 16, 11, 7, 48 ], [ 16, 11, 10, 96 ], [ 16, 12, 1, 24 ],
[ 16, 12, 3, 48 ], [ 16, 12, 7, 96 ], [ 16, 13, 1, 24 ], [ 16, 13, 2, 96 ],
[ 16, 13, 5, 48 ], [ 16, 13, 8, 96 ], [ 16, 14, 1, 24 ], [ 16, 14, 2, 48 ],
[ 16, 14, 3, 48 ], [ 16, 14, 4, 48 ], [ 16, 14, 6, 96 ], [ 16, 15, 1, 24 ],
[ 16, 15, 2, 96 ], [ 16, 15, 5, 48 ], [ 16, 15, 8, 96 ], [ 16, 16, 1, 24 ],
[ 16, 16, 2, 96 ], [ 16, 16, 5, 48 ], [ 16, 16, 8, 96 ], [ 16, 17, 1, 24 ],
[ 16, 17, 2, 48 ], [ 16, 17, 3, 48 ], [ 16, 17, 4, 48 ], [ 16, 17, 6, 96 ],
[ 18, 1, 3, 32 ], [ 18, 2, 3, 16 ], [ 20, 1, 3, 32 ], [ 20, 2, 3, 16 ],
[ 21, 1, 2, 64 ], [ 21, 1, 3, 192 ], [ 21, 1, 4, 192 ], [ 21, 2, 3, 96 ],
[ 21, 2, 4, 96 ], [ 21, 2, 6, 32 ], [ 21, 2, 8, 32 ], [ 21, 2, 10, 96 ],
[ 21, 3, 2, 96 ], [ 21, 3, 5, 96 ], [ 21, 3, 6, 32 ], [ 21, 3, 7, 32 ],
[ 21, 3, 10, 96 ], [ 21, 4, 3, 96 ], [ 21, 4, 6, 32 ], [ 21, 4, 10, 96 ],
[ 21, 5, 3, 48 ], [ 21, 5, 4, 48 ], [ 21, 5, 6, 16 ], [ 21, 5, 8, 16 ],
[ 21, 5, 10, 48 ], [ 21, 6, 2, 48 ], [ 21, 6, 5, 48 ], [ 21, 6, 6, 16 ],
[ 21, 6, 7, 16 ], [ 21, 6, 10, 48 ], [ 21, 7, 3, 48 ], [ 21, 7, 6, 16 ],
[ 21, 7, 10, 48 ], [ 22, 1, 3, 192 ], [ 22, 1, 4, 192 ], [ 22, 1, 6, 192 ],
[ 22, 1, 9, 384 ], [ 22, 2, 3, 96 ], [ 22, 2, 4, 96 ], [ 22, 2, 6, 96 ],
[ 22, 2, 9, 192 ], [ 22, 3, 2, 96 ], [ 22, 3, 3, 96 ], [ 22, 3, 4, 96 ],
[ 22, 3, 7, 192 ], [ 22, 3, 8, 192 ], [ 22, 4, 3, 48 ], [ 22, 4, 4, 48 ],
[ 22, 4, 6, 48 ], [ 22, 4, 9, 96 ], [ 23, 1, 5, 64 ], [ 23, 2, 5, 32 ],
[ 23, 3, 5, 32 ], [ 23, 4, 5, 32 ], [ 23, 5, 5, 32 ], [ 23, 6, 5, 16 ],
[ 24, 1, 3, 128 ], [ 24, 2, 3, 64 ], [ 25, 1, 3, 192 ], [ 25, 2, 5, 96 ],
[ 25, 3, 3, 96 ], [ 26, 1, 3, 192 ], [ 26, 2, 5, 96 ], [ 26, 3, 3, 96 ],
[ 27, 1, 3, 384 ], [ 27, 1, 4, 768 ], [ 27, 1, 5, 384 ], [ 27, 2, 3, 192 ],
[ 27, 2, 6, 192 ], [ 27, 2, 10, 192 ], [ 27, 2, 15, 384 ],
[ 27, 2, 18, 384 ], [ 27, 3, 3, 192 ], [ 27, 3, 4, 192 ],
[ 27, 3, 11, 192 ], [ 27, 3, 13, 192 ], [ 27, 3, 18, 384 ],
[ 27, 3, 24, 384 ], [ 27, 4, 2, 192 ], [ 27, 4, 5, 192 ],
[ 27, 4, 10, 192 ], [ 27, 4, 15, 384 ], [ 27, 4, 20, 384 ],
[ 27, 5, 3, 192 ], [ 27, 5, 11, 192 ], [ 27, 5, 16, 384 ], [ 27, 6, 3, 96 ],
[ 27, 6, 4, 96 ], [ 27, 6, 6, 96 ], [ 27, 6, 8, 96 ], [ 27, 6, 10, 96 ],
[ 27, 6, 15, 192 ], [ 27, 6, 18, 192 ], [ 27, 6, 19, 192 ],
[ 27, 7, 3, 96 ], [ 27, 7, 6, 96 ], [ 27, 7, 10, 96 ], [ 27, 7, 15, 192 ],
[ 27, 7, 18, 192 ], [ 27, 8, 3, 96 ], [ 27, 8, 4, 96 ], [ 27, 8, 11, 96 ],
[ 27, 8, 13, 96 ], [ 27, 8, 18, 192 ], [ 27, 8, 24, 192 ], [ 27, 9, 3, 96 ],
[ 27, 9, 4, 96 ], [ 27, 9, 12, 96 ], [ 27, 9, 16, 192 ], [ 27, 10, 2, 96 ],
[ 27, 10, 3, 96 ], [ 27, 10, 4, 96 ], [ 27, 10, 9, 96 ], [ 27, 10, 10, 96 ],
[ 27, 10, 14, 192 ], [ 27, 10, 19, 192 ], [ 27, 10, 20, 192 ],
[ 27, 11, 3, 96 ], [ 27, 11, 4, 96 ], [ 27, 11, 11, 96 ],
[ 27, 11, 13, 96 ], [ 27, 11, 18, 192 ], [ 27, 11, 24, 192 ],
[ 27, 12, 2, 96 ], [ 27, 12, 5, 96 ], [ 27, 12, 10, 96 ],
[ 27, 12, 15, 192 ], [ 27, 12, 20, 192 ], [ 27, 13, 2, 96 ],
[ 27, 13, 5, 96 ], [ 27, 13, 6, 96 ], [ 27, 13, 7, 96 ], [ 27, 13, 10, 96 ],
[ 27, 13, 15, 192 ], [ 27, 13, 17, 192 ], [ 27, 13, 20, 192 ],
[ 27, 14, 2, 96 ], [ 27, 14, 5, 96 ], [ 27, 14, 11, 96 ],
[ 27, 14, 13, 96 ], [ 27, 14, 18, 192 ], [ 27, 14, 24, 192 ],
[ 28, 1, 6, 256 ], [ 28, 2, 6, 128 ], [ 28, 2, 8, 128 ], [ 28, 3, 6, 128 ],
[ 28, 4, 5, 128 ], [ 28, 5, 6, 128 ], [ 28, 5, 8, 64 ], [ 28, 6, 6, 64 ],
[ 29, 1, 7, 384 ], [ 29, 1, 9, 384 ], [ 29, 2, 7, 192 ], [ 29, 2, 9, 192 ],
[ 29, 3, 7, 192 ], [ 29, 3, 9, 192 ], [ 29, 4, 7, 192 ], [ 29, 4, 9, 192 ],
[ 29, 5, 7, 192 ], [ 29, 5, 9, 192 ], [ 29, 6, 5, 192 ], [ 29, 7, 5, 192 ],
[ 29, 8, 5, 192 ], [ 29, 9, 7, 96 ], [ 29, 9, 9, 96 ], [ 29, 10, 5, 96 ],
[ 29, 11, 5, 96 ], [ 29, 12, 5, 96 ], [ 29, 13, 5, 96 ], [ 30, 1, 13, 768 ],
[ 30, 1, 16, 768 ], [ 30, 2, 13, 384 ], [ 30, 2, 16, 384 ],
[ 30, 3, 13, 384 ], [ 30, 3, 16, 384 ], [ 30, 4, 14, 384 ],
[ 30, 4, 16, 384 ], [ 30, 4, 19, 384 ], [ 30, 4, 26, 384 ],
[ 30, 5, 12, 384 ], [ 30, 5, 17, 384 ], [ 30, 6, 13, 384 ],
[ 30, 6, 17, 384 ], [ 30, 7, 11, 384 ], [ 30, 7, 19, 384 ],
[ 30, 7, 25, 384 ], [ 30, 8, 16, 192 ], [ 30, 8, 18, 192 ],
[ 30, 8, 21, 192 ], [ 30, 9, 16, 192 ], [ 30, 9, 18, 384 ],
[ 30, 9, 21, 192 ], [ 30, 10, 16, 192 ], [ 30, 10, 18, 384 ],
[ 30, 10, 21, 192 ], [ 30, 11, 11, 192 ], [ 30, 11, 19, 192 ],
[ 30, 11, 25, 192 ], [ 30, 12, 14, 192 ], [ 30, 12, 16, 384 ],
[ 30, 12, 19, 192 ], [ 30, 12, 26, 192 ], [ 30, 13, 10, 192 ],
[ 30, 13, 13, 192 ], [ 30, 13, 16, 192 ], [ 31, 2, 12, 768 ],
[ 31, 2, 31, 768 ], [ 31, 2, 52, 768 ], [ 31, 3, 12, 768 ],
[ 31, 3, 30, 768 ], [ 31, 3, 51, 768 ], [ 31, 4, 3, 768 ],
[ 31, 5, 11, 768 ], [ 31, 5, 49, 768 ], [ 31, 6, 12, 768 ],
[ 31, 6, 45, 768 ], [ 31, 7, 12, 768 ], [ 31, 8, 12, 768 ],
[ 31, 9, 12, 384 ], [ 31, 9, 31, 384 ], [ 31, 9, 49, 384 ],
[ 31, 10, 13, 384 ], [ 31, 10, 27, 384 ], [ 31, 10, 31, 384 ],
[ 31, 10, 54, 384 ], [ 31, 11, 12, 384 ], [ 31, 11, 30, 384 ],
[ 31, 11, 52, 768 ], [ 31, 12, 13, 384 ], [ 31, 12, 45, 384 ],
[ 31, 13, 11, 384 ], [ 31, 13, 31, 768 ], [ 31, 13, 47, 384 ],
[ 31, 13, 53, 384 ], [ 31, 14, 34, 384 ], [ 31, 14, 37, 384 ],
[ 31, 14, 40, 384 ], [ 31, 15, 10, 384 ], [ 31, 15, 25, 384 ],
[ 31, 15, 28, 384 ], [ 31, 15, 43, 384 ], [ 31, 15, 46, 384 ],
[ 31, 16, 12, 384 ], [ 31, 16, 30, 384 ], [ 31, 16, 51, 384 ],
[ 31, 17, 6, 384 ], [ 31, 17, 33, 384 ], [ 31, 18, 11, 384 ],
[ 31, 18, 27, 768 ], [ 31, 18, 61, 384 ], [ 31, 19, 11, 384 ],
[ 31, 19, 27, 768 ], [ 31, 19, 61, 384 ], [ 31, 20, 11, 384 ],
[ 31, 20, 27, 768 ], [ 31, 20, 61, 384 ], [ 31, 21, 10, 384 ],
[ 31, 21, 22, 384 ], [ 31, 21, 25, 384 ], [ 31, 21, 46, 384 ],
[ 31, 21, 47, 384 ], [ 31, 22, 12, 384 ], [ 31, 23, 12, 384 ],
[ 31, 23, 30, 384 ], [ 31, 23, 49, 768 ], [ 31, 24, 11, 384 ],
[ 31, 24, 53, 384 ], [ 31, 25, 11, 384 ], [ 31, 25, 53, 384 ],
[ 31, 26, 16, 384 ], [ 31, 26, 51, 384 ], [ 31, 26, 52, 768 ],
[ 31, 27, 12, 384 ], [ 31, 27, 45, 384 ], [ 31, 28, 12, 384 ],
[ 31, 28, 45, 384 ], [ 31, 29, 9, 384 ], [ 31, 29, 33, 768 ],
[ 31, 29, 47, 384 ], [ 31, 29, 51, 384 ], [ 31, 30, 9, 384 ],
[ 31, 31, 5, 384 ], [ 31, 32, 16, 384 ], [ 31, 32, 51, 384 ],
[ 31, 32, 52, 768 ], [ 31, 33, 16, 384 ], [ 31, 33, 51, 384 ],
[ 31, 33, 52, 768 ] ]
k = 4: F-action on Pi is () [31,1,4]
Dynkin type is A_0(q) + T(phi2^6)
Order of center |Z^F|: phi2^6
Numbers of classes in class type:
q congruent 0 modulo
4: 1/23040 q ( q^5-24*q^4+220*q^3-960*q^2+1984*q-1536 )
q congruent 1 modulo
4: 1/23040 phi1 ( q^5-23*q^4+182*q^3-658*q^2+1881*q-4455 )
q congruent 2 modulo
4: 1/23040 q ( q^5-24*q^4+220*q^3-960*q^2+1984*q-1536 )
q congruent 3 modulo
4: 1/23040 ( q^6-24*q^5+205*q^4-840*q^3+2539*q^2-7776*q+11655 )
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, 30 ], [ 2, 2, 1, 15 ], [ 3, 1, 2, 40 ],
[ 3, 2, 2, 20 ], [ 3, 3, 2, 20 ], [ 3, 4, 2, 20 ], [ 3, 5, 2, 10 ],
[ 4, 1, 2, 12 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 60 ], [ 6, 1, 2, 160 ],
[ 7, 1, 4, 240 ], [ 7, 2, 4, 120 ], [ 7, 3, 4, 120 ], [ 7, 4, 4, 120 ],
[ 7, 5, 4, 60 ], [ 8, 1, 2, 240 ], [ 9, 1, 2, 720 ], [ 9, 2, 2, 360 ],
[ 9, 3, 2, 360 ], [ 9, 4, 2, 360 ], [ 9, 5, 2, 180 ], [ 10, 1, 2, 32 ],
[ 10, 2, 2, 16 ], [ 11, 1, 2, 32 ], [ 11, 2, 2, 16 ], [ 12, 1, 3, 120 ],
[ 12, 2, 3, 60 ], [ 12, 3, 2, 60 ], [ 12, 4, 3, 30 ], [ 13, 1, 4, 480 ],
[ 13, 2, 4, 240 ], [ 14, 1, 2, 960 ], [ 14, 2, 2, 480 ], [ 15, 1, 3, 1440 ],
[ 16, 1, 5, 1440 ], [ 16, 2, 5, 720 ], [ 16, 3, 5, 720 ], [ 16, 4, 5, 720 ],
[ 16, 5, 3, 720 ], [ 16, 6, 3, 720 ], [ 16, 7, 3, 720 ], [ 16, 8, 4, 720 ],
[ 16, 9, 5, 360 ], [ 16, 10, 3, 360 ], [ 16, 11, 5, 360 ],
[ 16, 12, 3, 360 ], [ 16, 13, 5, 360 ], [ 16, 14, 4, 360 ],
[ 16, 15, 5, 360 ], [ 16, 16, 5, 360 ], [ 16, 17, 4, 360 ],
[ 17, 1, 2, 192 ], [ 17, 2, 2, 96 ], [ 18, 1, 4, 480 ], [ 18, 2, 4, 240 ],
[ 19, 1, 2, 640 ], [ 19, 2, 2, 320 ], [ 19, 3, 2, 320 ], [ 19, 4, 2, 320 ],
[ 19, 5, 2, 160 ], [ 20, 1, 4, 480 ], [ 20, 2, 4, 240 ], [ 21, 1, 4, 960 ],
[ 21, 2, 10, 480 ], [ 21, 3, 10, 480 ], [ 21, 4, 10, 480 ],
[ 21, 5, 10, 240 ], [ 21, 6, 10, 240 ], [ 21, 7, 10, 240 ],
[ 22, 1, 6, 2880 ], [ 22, 2, 6, 1440 ], [ 22, 3, 4, 1440 ],
[ 22, 4, 6, 720 ], [ 23, 1, 7, 960 ], [ 23, 2, 7, 480 ], [ 23, 3, 7, 480 ],
[ 23, 4, 7, 480 ], [ 23, 5, 7, 480 ], [ 23, 6, 7, 240 ], [ 24, 1, 4, 1920 ],
[ 24, 2, 4, 960 ], [ 25, 1, 4, 2880 ], [ 25, 2, 8, 1440 ],
[ 25, 3, 7, 1440 ], [ 26, 1, 4, 2880 ], [ 26, 2, 10, 1440 ],
[ 26, 3, 7, 1440 ], [ 27, 1, 5, 5760 ], [ 27, 2, 10, 2880 ],
[ 27, 3, 13, 2880 ], [ 27, 4, 10, 2880 ], [ 27, 5, 11, 2880 ],
[ 27, 6, 10, 1440 ], [ 27, 7, 10, 1440 ], [ 27, 8, 13, 1440 ],
[ 27, 9, 12, 1440 ], [ 27, 10, 10, 1440 ], [ 27, 11, 13, 1440 ],
[ 27, 12, 10, 1440 ], [ 27, 13, 10, 1440 ], [ 27, 14, 13, 1440 ],
[ 28, 1, 10, 3840 ], [ 28, 2, 10, 1920 ], [ 28, 3, 10, 1920 ],
[ 28, 4, 7, 1920 ], [ 28, 5, 10, 960 ], [ 28, 6, 10, 960 ],
[ 29, 1, 11, 5760 ], [ 29, 2, 11, 2880 ], [ 29, 3, 11, 2880 ],
[ 29, 4, 11, 2880 ], [ 29, 5, 11, 2880 ], [ 29, 6, 7, 2880 ],
[ 29, 7, 7, 2880 ], [ 29, 8, 7, 2880 ], [ 29, 9, 11, 1440 ],
[ 29, 10, 7, 1440 ], [ 29, 11, 7, 1440 ], [ 29, 12, 7, 1440 ],
[ 29, 13, 7, 1440 ], [ 30, 1, 26, 11520 ], [ 30, 2, 26, 5760 ],
[ 30, 3, 26, 5760 ], [ 30, 4, 28, 5760 ], [ 30, 5, 26, 5760 ],
[ 30, 6, 27, 5760 ], [ 30, 7, 27, 5760 ], [ 30, 8, 32, 2880 ],
[ 30, 9, 32, 2880 ], [ 30, 10, 32, 2880 ], [ 30, 11, 27, 2880 ],
[ 30, 12, 28, 2880 ], [ 30, 13, 20, 2880 ], [ 31, 2, 22, 11520 ],
[ 31, 3, 22, 11520 ], [ 31, 4, 4, 11520 ], [ 31, 5, 51, 11520 ],
[ 31, 6, 54, 11520 ], [ 31, 7, 40, 11520 ], [ 31, 8, 40, 11520 ],
[ 31, 9, 22, 5760 ], [ 31, 10, 56, 5760 ], [ 31, 11, 22, 5760 ],
[ 31, 12, 55, 5760 ], [ 31, 13, 55, 5760 ], [ 31, 14, 38, 5760 ],
[ 31, 15, 50, 5760 ], [ 31, 16, 22, 5760 ], [ 31, 17, 20, 5760 ],
[ 31, 18, 63, 5760 ], [ 31, 19, 63, 5760 ], [ 31, 20, 63, 5760 ],
[ 31, 21, 50, 5760 ], [ 31, 22, 40, 5760 ], [ 31, 23, 22, 5760 ],
[ 31, 24, 55, 5760 ], [ 31, 25, 55, 5760 ], [ 31, 26, 64, 5760 ],
[ 31, 27, 54, 5760 ], [ 31, 28, 54, 5760 ], [ 31, 29, 53, 5760 ],
[ 31, 30, 32, 5760 ], [ 31, 31, 29, 5760 ], [ 31, 32, 64, 5760 ],
[ 31, 33, 64, 5760 ] ]
k = 5: F-action on Pi is () [31,1,5]
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 0 modulo
4: 1/768 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 )
q congruent 1 modulo
4: 1/768 phi1 ( q^5-17*q^4+100*q^3-256*q^2+403*q-615 )
q congruent 2 modulo
4: 1/768 q ( q^5-18*q^4+124*q^3-408*q^2+640*q-384 )
q congruent 3 modulo
4: 1/768 ( q^6-18*q^5+117*q^4-356*q^3+659*q^2-1018*q+903 )
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, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 1, 16 ],
[ 3, 2, 1, 8 ], [ 3, 3, 1, 8 ], [ 3, 4, 1, 8 ], [ 3, 5, 1, 4 ],
[ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 5, 1, 1, 26 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 48 ], [ 7, 1, 1, 64 ], [ 7, 2, 1, 32 ], [ 7, 3, 1, 32 ],
[ 7, 4, 1, 32 ], [ 7, 5, 1, 16 ], [ 8, 1, 1, 64 ], [ 9, 1, 1, 120 ],
[ 9, 1, 2, 24 ], [ 9, 2, 1, 60 ], [ 9, 2, 2, 12 ], [ 9, 3, 1, 60 ],
[ 9, 3, 2, 12 ], [ 9, 4, 1, 60 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 30 ],
[ 9, 5, 2, 6 ], [ 10, 1, 1, 16 ], [ 10, 2, 1, 8 ], [ 11, 1, 1, 16 ],
[ 11, 2, 1, 8 ], [ 12, 1, 1, 48 ], [ 12, 1, 2, 4 ], [ 12, 2, 1, 24 ],
[ 12, 2, 2, 2 ], [ 12, 3, 1, 24 ], [ 12, 4, 1, 12 ], [ 12, 4, 2, 2 ],
[ 13, 1, 1, 112 ], [ 13, 1, 2, 16 ], [ 13, 2, 1, 56 ], [ 13, 2, 2, 8 ],
[ 14, 1, 1, 160 ], [ 14, 2, 1, 80 ], [ 15, 1, 1, 192 ], [ 15, 1, 4, 48 ],
[ 16, 1, 1, 192 ], [ 16, 1, 3, 48 ], [ 16, 2, 1, 96 ], [ 16, 2, 3, 24 ],
[ 16, 3, 1, 96 ], [ 16, 3, 3, 24 ], [ 16, 4, 1, 96 ], [ 16, 4, 3, 24 ],
[ 16, 5, 1, 96 ], [ 16, 5, 2, 24 ], [ 16, 5, 4, 24 ], [ 16, 6, 1, 96 ],
[ 16, 6, 2, 24 ], [ 16, 6, 4, 24 ], [ 16, 7, 1, 96 ], [ 16, 7, 2, 24 ],
[ 16, 7, 4, 24 ], [ 16, 8, 1, 96 ], [ 16, 9, 1, 48 ], [ 16, 9, 3, 12 ],
[ 16, 10, 1, 48 ], [ 16, 10, 2, 12 ], [ 16, 10, 4, 12 ], [ 16, 11, 1, 48 ],
[ 16, 11, 3, 24 ], [ 16, 12, 1, 48 ], [ 16, 12, 2, 12 ], [ 16, 12, 4, 12 ],
[ 16, 13, 1, 48 ], [ 16, 13, 3, 12 ], [ 16, 14, 1, 48 ], [ 16, 15, 1, 48 ],
[ 16, 15, 3, 12 ], [ 16, 16, 1, 48 ], [ 16, 16, 3, 12 ], [ 16, 17, 1, 48 ],
[ 17, 1, 1, 64 ], [ 17, 2, 1, 32 ], [ 18, 1, 1, 112 ], [ 18, 1, 2, 16 ],
[ 18, 2, 1, 56 ], [ 18, 2, 2, 8 ], [ 19, 1, 1, 128 ], [ 19, 2, 1, 64 ],
[ 19, 3, 1, 64 ], [ 19, 4, 1, 64 ], [ 19, 5, 1, 32 ], [ 20, 1, 1, 112 ],
[ 20, 1, 2, 16 ], [ 20, 2, 1, 56 ], [ 20, 2, 2, 8 ], [ 21, 1, 1, 192 ],
[ 21, 1, 5, 32 ], [ 21, 2, 1, 96 ], [ 21, 2, 2, 16 ], [ 21, 3, 1, 96 ],
[ 21, 3, 3, 16 ], [ 21, 4, 1, 96 ], [ 21, 4, 2, 16 ], [ 21, 5, 1, 48 ],
[ 21, 5, 2, 8 ], [ 21, 6, 1, 48 ], [ 21, 6, 3, 16 ], [ 21, 7, 1, 48 ],
[ 21, 7, 2, 16 ], [ 22, 1, 1, 288 ], [ 22, 1, 2, 96 ], [ 22, 1, 4, 96 ],
[ 22, 2, 1, 144 ], [ 22, 2, 2, 48 ], [ 22, 2, 4, 48 ], [ 22, 3, 1, 144 ],
[ 22, 3, 3, 48 ], [ 22, 4, 1, 72 ], [ 22, 4, 2, 48 ], [ 22, 4, 4, 24 ],
[ 23, 1, 1, 192 ], [ 23, 1, 2, 32 ], [ 23, 1, 4, 32 ], [ 23, 2, 1, 96 ],
[ 23, 2, 2, 16 ], [ 23, 2, 4, 16 ], [ 23, 3, 1, 96 ], [ 23, 3, 2, 16 ],
[ 23, 3, 4, 16 ], [ 23, 4, 1, 96 ], [ 23, 4, 2, 16 ], [ 23, 4, 4, 16 ],
[ 23, 5, 1, 96 ], [ 23, 5, 2, 16 ], [ 23, 5, 4, 16 ], [ 23, 6, 1, 48 ],
[ 23, 6, 2, 8 ], [ 23, 6, 4, 8 ], [ 24, 1, 1, 256 ], [ 24, 1, 2, 64 ],
[ 24, 2, 1, 128 ], [ 24, 2, 2, 32 ], [ 25, 1, 1, 288 ], [ 25, 1, 2, 96 ],
[ 25, 2, 1, 144 ], [ 25, 2, 2, 48 ], [ 25, 3, 1, 144 ], [ 25, 3, 5, 48 ],
[ 26, 1, 1, 288 ], [ 26, 1, 2, 96 ], [ 26, 2, 1, 144 ], [ 26, 2, 2, 48 ],
[ 26, 3, 1, 144 ], [ 26, 3, 5, 48 ], [ 27, 1, 1, 384 ], [ 27, 1, 6, 192 ],
[ 27, 2, 1, 192 ], [ 27, 2, 2, 96 ], [ 27, 3, 1, 192 ], [ 27, 3, 2, 96 ],
[ 27, 3, 6, 96 ], [ 27, 4, 1, 192 ], [ 27, 4, 3, 96 ], [ 27, 5, 1, 192 ],
[ 27, 5, 2, 96 ], [ 27, 6, 1, 96 ], [ 27, 6, 2, 48 ], [ 27, 7, 1, 96 ],
[ 27, 7, 2, 48 ], [ 27, 8, 1, 96 ], [ 27, 8, 2, 48 ], [ 27, 8, 6, 96 ],
[ 27, 9, 1, 96 ], [ 27, 9, 2, 48 ], [ 27, 10, 1, 96 ], [ 27, 10, 5, 48 ],
[ 27, 11, 1, 96 ], [ 27, 11, 2, 48 ], [ 27, 11, 6, 96 ], [ 27, 12, 1, 96 ],
[ 27, 12, 3, 96 ], [ 27, 13, 1, 96 ], [ 27, 13, 3, 48 ], [ 27, 14, 1, 96 ],
[ 27, 14, 3, 48 ], [ 27, 14, 8, 96 ], [ 28, 1, 1, 384 ], [ 28, 1, 2, 128 ],
[ 28, 2, 1, 192 ], [ 28, 2, 2, 64 ], [ 28, 3, 1, 192 ], [ 28, 3, 2, 64 ],
[ 28, 4, 1, 192 ], [ 28, 4, 2, 64 ], [ 28, 4, 4, 64 ], [ 28, 5, 1, 96 ],
[ 28, 5, 2, 32 ], [ 28, 6, 1, 96 ], [ 28, 6, 2, 64 ], [ 29, 1, 1, 384 ],
[ 29, 1, 2, 192 ], [ 29, 1, 4, 192 ], [ 29, 1, 5, 192 ], [ 29, 2, 1, 192 ],
[ 29, 2, 2, 96 ], [ 29, 2, 4, 96 ], [ 29, 2, 5, 96 ], [ 29, 3, 1, 192 ],
[ 29, 3, 2, 96 ], [ 29, 3, 4, 96 ], [ 29, 3, 5, 96 ], [ 29, 4, 1, 192 ],
[ 29, 4, 2, 96 ], [ 29, 4, 4, 96 ], [ 29, 4, 5, 96 ], [ 29, 5, 1, 192 ],
[ 29, 5, 2, 96 ], [ 29, 5, 4, 96 ], [ 29, 5, 5, 96 ], [ 29, 6, 1, 192 ],
[ 29, 6, 2, 96 ], [ 29, 6, 4, 96 ], [ 29, 7, 1, 192 ], [ 29, 7, 2, 96 ],
[ 29, 7, 4, 96 ], [ 29, 8, 1, 192 ], [ 29, 8, 2, 96 ], [ 29, 8, 4, 96 ],
[ 29, 9, 1, 96 ], [ 29, 9, 2, 48 ], [ 29, 9, 4, 48 ], [ 29, 9, 5, 48 ],
[ 29, 10, 1, 96 ], [ 29, 10, 2, 48 ], [ 29, 10, 4, 48 ], [ 29, 11, 1, 96 ],
[ 29, 11, 2, 48 ], [ 29, 11, 4, 48 ], [ 29, 12, 1, 96 ], [ 29, 12, 2, 48 ],
[ 29, 12, 4, 48 ], [ 29, 13, 1, 96 ], [ 29, 13, 2, 48 ], [ 29, 13, 4, 48 ],
[ 30, 1, 1, 384 ], [ 30, 1, 2, 384 ], [ 30, 1, 14, 384 ], [ 30, 2, 1, 192 ],
[ 30, 2, 2, 192 ], [ 30, 2, 14, 192 ], [ 30, 3, 1, 192 ], [ 30, 3, 2, 192 ],
[ 30, 3, 14, 192 ], [ 30, 4, 1, 192 ], [ 30, 4, 3, 192 ], [ 30, 4, 8, 192 ],
[ 30, 4, 15, 192 ], [ 30, 5, 1, 192 ], [ 30, 5, 2, 192 ], [ 30, 5, 4, 192 ],
[ 30, 5, 15, 192 ], [ 30, 6, 1, 192 ], [ 30, 6, 2, 192 ], [ 30, 6, 4, 192 ],
[ 30, 6, 15, 192 ], [ 30, 7, 1, 192 ], [ 30, 7, 2, 192 ], [ 30, 7, 4, 192 ],
[ 30, 7, 6, 192 ], [ 30, 7, 15, 192 ], [ 30, 7, 17, 192 ], [ 30, 8, 1, 96 ],
[ 30, 8, 3, 96 ], [ 30, 8, 17, 96 ], [ 30, 9, 1, 96 ], [ 30, 9, 3, 96 ],
[ 30, 9, 17, 96 ], [ 30, 10, 1, 96 ], [ 30, 10, 3, 96 ], [ 30, 10, 17, 96 ],
[ 30, 11, 1, 96 ], [ 30, 11, 2, 96 ], [ 30, 11, 4, 96 ], [ 30, 11, 6, 96 ],
[ 30, 11, 15, 96 ], [ 30, 11, 17, 96 ], [ 30, 12, 1, 96 ],
[ 30, 12, 3, 96 ], [ 30, 12, 8, 96 ], [ 30, 12, 15, 96 ], [ 30, 13, 1, 96 ],
[ 30, 13, 2, 192 ], [ 30, 13, 11, 96 ], [ 31, 2, 35, 384 ],
[ 31, 2, 43, 384 ], [ 31, 3, 34, 384 ], [ 31, 3, 48, 384 ],
[ 31, 4, 5, 384 ], [ 31, 5, 2, 384 ], [ 31, 5, 4, 384 ], [ 31, 5, 5, 384 ],
[ 31, 6, 2, 384 ], [ 31, 6, 4, 384 ], [ 31, 6, 15, 384 ],
[ 31, 6, 29, 384 ], [ 31, 7, 2, 384 ], [ 31, 7, 4, 384 ], [ 31, 8, 2, 384 ],
[ 31, 8, 4, 384 ], [ 31, 9, 35, 192 ], [ 31, 9, 43, 192 ],
[ 31, 10, 2, 192 ], [ 31, 10, 6, 192 ], [ 31, 11, 34, 192 ],
[ 31, 11, 44, 192 ], [ 31, 12, 2, 192 ], [ 31, 12, 4, 192 ],
[ 31, 12, 15, 192 ], [ 31, 12, 29, 192 ], [ 31, 13, 2, 192 ],
[ 31, 13, 4, 192 ], [ 31, 13, 5, 192 ], [ 31, 13, 13, 192 ],
[ 31, 14, 41, 192 ], [ 31, 14, 45, 384 ], [ 31, 15, 2, 192 ],
[ 31, 15, 11, 384 ], [ 31, 16, 34, 192 ], [ 31, 16, 48, 192 ],
[ 31, 17, 22, 192 ], [ 31, 18, 2, 192 ], [ 31, 18, 4, 192 ],
[ 31, 18, 5, 192 ], [ 31, 19, 2, 192 ], [ 31, 19, 4, 192 ],
[ 31, 19, 5, 192 ], [ 31, 20, 2, 192 ], [ 31, 20, 4, 192 ],
[ 31, 20, 5, 192 ], [ 31, 21, 3, 384 ], [ 31, 21, 11, 192 ],
[ 31, 22, 2, 192 ], [ 31, 22, 4, 192 ], [ 31, 23, 34, 192 ],
[ 31, 23, 37, 192 ], [ 31, 24, 2, 192 ], [ 31, 24, 4, 192 ],
[ 31, 24, 5, 192 ], [ 31, 24, 13, 192 ], [ 31, 25, 2, 192 ],
[ 31, 25, 4, 192 ], [ 31, 25, 5, 192 ], [ 31, 25, 13, 192 ],
[ 31, 26, 2, 192 ], [ 31, 26, 17, 192 ], [ 31, 26, 33, 192 ],
[ 31, 27, 2, 192 ], [ 31, 27, 4, 192 ], [ 31, 27, 15, 192 ],
[ 31, 27, 29, 192 ], [ 31, 28, 2, 192 ], [ 31, 28, 4, 192 ],
[ 31, 28, 15, 192 ], [ 31, 28, 29, 192 ], [ 31, 29, 2, 192 ],
[ 31, 29, 4, 192 ], [ 31, 29, 10, 192 ], [ 31, 29, 13, 192 ],
[ 31, 30, 2, 192 ], [ 31, 30, 4, 192 ], [ 31, 31, 9, 192 ],
[ 31, 31, 17, 192 ], [ 31, 32, 2, 192 ], [ 31, 32, 17, 192 ],
[ 31, 32, 33, 192 ], [ 31, 33, 2, 192 ], [ 31, 33, 17, 192 ],
[ 31, 33, 33, 192 ] ]
k = 6: F-action on Pi is () [31,1,6]
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 0 modulo 4: 1/192 q^2 ( q^4-8*q^3+14*q^2+20*q-48 )
q congruent 1 modulo 4: 1/192 phi1 phi2 ( q^4-8*q^3+8*q^2+56*q-105 )
q congruent 2 modulo 4: 1/192 q^2 ( q^4-8*q^3+14*q^2+20*q-48 )
q congruent 3 modulo 4: 1/192 phi1 phi2 ( q^4-8*q^3+8*q^2+56*q-105 )
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, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 12 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 6 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 6 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 6 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 3 ], [ 4, 1, 1, 6 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 3 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 12 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 36 ],
[ 7, 1, 4, 12 ], [ 7, 2, 1, 6 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 18 ],
[ 7, 2, 4, 6 ], [ 7, 3, 1, 6 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 18 ],
[ 7, 3, 4, 6 ], [ 7, 4, 1, 6 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 18 ],
[ 7, 4, 4, 6 ], [ 7, 5, 1, 3 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 9 ],
[ 7, 5, 4, 3 ], [ 9, 1, 3, 48 ], [ 9, 2, 3, 24 ], [ 9, 3, 3, 24 ],
[ 9, 4, 3, 24 ], [ 9, 5, 3, 12 ], [ 12, 1, 1, 24 ], [ 12, 1, 4, 12 ],
[ 12, 1, 5, 4 ], [ 12, 2, 1, 12 ], [ 12, 2, 4, 6 ], [ 12, 2, 5, 2 ],
[ 12, 3, 1, 12 ], [ 12, 3, 3, 6 ], [ 12, 3, 4, 6 ], [ 12, 4, 1, 6 ],
[ 12, 4, 4, 3 ], [ 12, 4, 5, 2 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 24 ],
[ 13, 2, 1, 12 ], [ 13, 2, 3, 12 ], [ 14, 1, 3, 16 ], [ 14, 2, 3, 8 ],
[ 16, 1, 2, 24 ], [ 16, 1, 4, 24 ], [ 16, 1, 6, 96 ], [ 16, 2, 2, 12 ],
[ 16, 2, 4, 12 ], [ 16, 2, 6, 48 ], [ 16, 3, 2, 12 ], [ 16, 3, 4, 12 ],
[ 16, 3, 6, 48 ], [ 16, 4, 2, 12 ], [ 16, 4, 4, 12 ], [ 16, 4, 6, 48 ],
[ 16, 5, 5, 48 ], [ 16, 6, 5, 48 ], [ 16, 7, 5, 48 ], [ 16, 8, 2, 12 ],
[ 16, 8, 3, 12 ], [ 16, 8, 5, 48 ], [ 16, 8, 6, 12 ], [ 16, 8, 7, 12 ],
[ 16, 9, 2, 6 ], [ 16, 9, 4, 6 ], [ 16, 9, 6, 24 ], [ 16, 10, 5, 24 ],
[ 16, 11, 2, 6 ], [ 16, 11, 4, 12 ], [ 16, 11, 6, 24 ], [ 16, 11, 7, 6 ],
[ 16, 11, 9, 12 ], [ 16, 12, 5, 24 ], [ 16, 13, 2, 12 ], [ 16, 13, 4, 12 ],
[ 16, 13, 6, 24 ], [ 16, 14, 2, 6 ], [ 16, 14, 3, 6 ], [ 16, 14, 5, 24 ],
[ 16, 15, 2, 12 ], [ 16, 15, 4, 12 ], [ 16, 15, 6, 24 ], [ 16, 16, 2, 12 ],
[ 16, 16, 4, 12 ], [ 16, 16, 6, 24 ], [ 16, 17, 2, 6 ], [ 16, 17, 3, 6 ],
[ 16, 17, 5, 24 ], [ 21, 1, 1, 48 ], [ 21, 1, 2, 48 ], [ 21, 1, 6, 24 ],
[ 21, 1, 8, 8 ], [ 21, 2, 1, 24 ], [ 21, 2, 5, 4 ], [ 21, 2, 6, 24 ],
[ 21, 2, 7, 12 ], [ 21, 2, 8, 24 ], [ 21, 3, 1, 24 ], [ 21, 3, 4, 4 ],
[ 21, 3, 6, 24 ], [ 21, 3, 7, 24 ], [ 21, 3, 9, 12 ], [ 21, 4, 1, 24 ],
[ 21, 4, 5, 4 ], [ 21, 4, 6, 24 ], [ 21, 4, 7, 12 ], [ 21, 5, 1, 12 ],
[ 21, 5, 5, 2 ], [ 21, 5, 6, 12 ], [ 21, 5, 7, 6 ], [ 21, 5, 8, 12 ],
[ 21, 6, 1, 12 ], [ 21, 6, 4, 4 ], [ 21, 6, 6, 12 ], [ 21, 6, 7, 12 ],
[ 21, 6, 8, 12 ], [ 21, 7, 1, 12 ], [ 21, 7, 5, 4 ], [ 21, 7, 6, 12 ],
[ 21, 7, 7, 12 ], [ 22, 1, 7, 48 ], [ 22, 1, 8, 48 ], [ 22, 2, 7, 24 ],
[ 22, 2, 8, 24 ], [ 22, 3, 5, 24 ], [ 22, 3, 6, 24 ], [ 22, 4, 7, 12 ],
[ 22, 4, 8, 24 ], [ 27, 1, 2, 96 ], [ 27, 1, 7, 96 ], [ 27, 1, 9, 48 ],
[ 27, 2, 5, 24 ], [ 27, 2, 7, 24 ], [ 27, 2, 11, 48 ], [ 27, 2, 12, 48 ],
[ 27, 2, 16, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 24 ], [ 27, 3, 14, 48 ],
[ 27, 3, 15, 48 ], [ 27, 3, 16, 48 ], [ 27, 3, 21, 48 ], [ 27, 4, 4, 24 ],
[ 27, 4, 9, 24 ], [ 27, 4, 11, 48 ], [ 27, 4, 12, 48 ], [ 27, 4, 14, 48 ],
[ 27, 5, 5, 24 ], [ 27, 5, 12, 48 ], [ 27, 5, 13, 48 ], [ 27, 6, 5, 12 ],
[ 27, 6, 7, 12 ], [ 27, 6, 11, 24 ], [ 27, 6, 12, 24 ], [ 27, 6, 13, 24 ],
[ 27, 6, 16, 24 ], [ 27, 7, 5, 12 ], [ 27, 7, 7, 12 ], [ 27, 7, 11, 24 ],
[ 27, 7, 12, 24 ], [ 27, 7, 16, 24 ], [ 27, 8, 5, 12 ], [ 27, 8, 9, 24 ],
[ 27, 8, 14, 24 ], [ 27, 8, 15, 24 ], [ 27, 8, 16, 24 ], [ 27, 8, 21, 48 ],
[ 27, 9, 5, 12 ], [ 27, 9, 13, 24 ], [ 27, 9, 14, 24 ], [ 27, 10, 7, 12 ],
[ 27, 10, 8, 12 ], [ 27, 10, 11, 24 ], [ 27, 10, 12, 24 ],
[ 27, 10, 13, 24 ], [ 27, 10, 17, 24 ], [ 27, 11, 5, 12 ],
[ 27, 11, 9, 24 ], [ 27, 11, 14, 24 ], [ 27, 11, 15, 24 ],
[ 27, 11, 16, 24 ], [ 27, 11, 21, 48 ], [ 27, 12, 4, 24 ],
[ 27, 12, 9, 24 ], [ 27, 12, 11, 24 ], [ 27, 12, 12, 24 ],
[ 27, 12, 14, 48 ], [ 27, 13, 4, 12 ], [ 27, 13, 9, 12 ],
[ 27, 13, 11, 24 ], [ 27, 13, 12, 24 ], [ 27, 13, 14, 24 ],
[ 27, 13, 16, 24 ], [ 27, 14, 4, 12 ], [ 27, 14, 9, 24 ],
[ 27, 14, 14, 24 ], [ 27, 14, 15, 24 ], [ 27, 14, 17, 24 ],
[ 27, 14, 21, 48 ], [ 28, 1, 5, 32 ], [ 28, 2, 5, 16 ], [ 28, 3, 5, 16 ],
[ 28, 5, 5, 16 ], [ 28, 6, 5, 16 ], [ 30, 1, 5, 96 ], [ 30, 2, 5, 48 ],
[ 30, 3, 5, 48 ], [ 30, 4, 4, 48 ], [ 30, 4, 9, 48 ], [ 30, 8, 4, 24 ],
[ 30, 9, 4, 48 ], [ 30, 10, 4, 48 ], [ 30, 12, 4, 48 ], [ 30, 12, 9, 48 ],
[ 30, 13, 5, 48 ], [ 30, 13, 7, 48 ], [ 31, 2, 19, 96 ], [ 31, 2, 24, 96 ],
[ 31, 2, 27, 96 ], [ 31, 3, 19, 96 ], [ 31, 3, 25, 96 ], [ 31, 3, 27, 96 ],
[ 31, 4, 6, 96 ], [ 31, 5, 25, 96 ], [ 31, 9, 19, 48 ], [ 31, 9, 26, 48 ],
[ 31, 9, 27, 48 ], [ 31, 10, 5, 48 ], [ 31, 10, 9, 48 ], [ 31, 10, 26, 48 ],
[ 31, 11, 19, 96 ], [ 31, 11, 24, 48 ], [ 31, 11, 25, 96 ],
[ 31, 13, 33, 96 ], [ 31, 13, 37, 96 ], [ 31, 14, 21, 48 ],
[ 31, 14, 23, 48 ], [ 31, 14, 28, 96 ], [ 31, 14, 31, 96 ],
[ 31, 15, 5, 48 ], [ 31, 15, 7, 48 ], [ 31, 15, 22, 48 ],
[ 31, 15, 31, 96 ], [ 31, 15, 36, 96 ], [ 31, 16, 19, 48 ],
[ 31, 16, 25, 48 ], [ 31, 16, 27, 48 ], [ 31, 17, 17, 48 ],
[ 31, 18, 29, 96 ], [ 31, 19, 29, 96 ], [ 31, 20, 29, 96 ],
[ 31, 21, 4, 96 ], [ 31, 21, 8, 96 ], [ 31, 21, 26, 48 ],
[ 31, 21, 27, 48 ], [ 31, 21, 31, 48 ], [ 31, 23, 20, 96 ],
[ 31, 23, 25, 48 ], [ 31, 23, 26, 96 ], [ 31, 26, 5, 96 ],
[ 31, 29, 30, 96 ], [ 31, 29, 37, 96 ], [ 31, 32, 5, 96 ],
[ 31, 33, 5, 96 ] ]
k = 7: F-action on Pi is () [31,1,7]
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 0 modulo 4: 1/128 q^2 ( q^4-6*q^3+8*q^2+8*q-16 )
q congruent 1 modulo 4: 1/128 phi1^2 ( q^4-4*q^3-8*q^2+32*q+11 )
q congruent 2 modulo 4: 1/128 q^2 ( q^4-6*q^3+8*q^2+8*q-16 )
q congruent 3 modulo
4: 1/128 ( q^6-6*q^5+q^4+44*q^3-61*q^2+10*q-21 )
Fusion of maximal tori of C^F in those of G^F:
[ 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 3, 2, 1, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 1, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 1, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 6 ],
[ 5, 1, 2, 6 ], [ 6, 1, 1, 8 ], [ 6, 1, 2, 8 ], [ 7, 1, 1, 16 ],
[ 7, 1, 2, 16 ], [ 7, 1, 3, 16 ], [ 7, 1, 4, 16 ], [ 7, 2, 1, 8 ],
[ 7, 2, 2, 8 ], [ 7, 2, 3, 8 ], [ 7, 2, 4, 8 ], [ 7, 3, 1, 8 ],
[ 7, 3, 2, 8 ], [ 7, 3, 3, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 1, 8 ],
[ 7, 4, 2, 8 ], [ 7, 4, 3, 8 ], [ 7, 4, 4, 8 ], [ 7, 5, 1, 4 ],
[ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ], [ 8, 1, 1, 8 ],
[ 8, 1, 2, 8 ], [ 9, 1, 1, 24 ], [ 9, 1, 2, 24 ], [ 9, 1, 3, 16 ],
[ 9, 1, 4, 16 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 12 ], [ 9, 2, 3, 8 ],
[ 9, 2, 4, 8 ], [ 9, 3, 1, 12 ], [ 9, 3, 2, 12 ], [ 9, 3, 3, 8 ],
[ 9, 3, 4, 8 ], [ 9, 4, 1, 12 ], [ 9, 4, 2, 12 ], [ 9, 4, 3, 8 ],
[ 9, 4, 4, 8 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 6 ], [ 9, 5, 3, 4 ],
[ 9, 5, 4, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ], [ 12, 1, 3, 8 ],
[ 12, 1, 4, 16 ], [ 12, 2, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 2, 3, 4 ],
[ 12, 2, 4, 8 ], [ 12, 3, 1, 4 ], [ 12, 3, 2, 4 ], [ 12, 3, 3, 8 ],
[ 12, 3, 4, 8 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 24 ], [ 13, 1, 3, 24 ],
[ 13, 1, 4, 8 ], [ 13, 2, 1, 4 ], [ 13, 2, 2, 12 ], [ 13, 2, 3, 12 ],
[ 13, 2, 4, 4 ], [ 14, 1, 1, 16 ], [ 14, 1, 2, 16 ], [ 14, 1, 3, 32 ],
[ 14, 1, 4, 32 ], [ 14, 2, 1, 8 ], [ 14, 2, 2, 8 ], [ 14, 2, 3, 16 ],
[ 14, 2, 4, 16 ], [ 15, 1, 1, 16 ], [ 15, 1, 3, 16 ], [ 15, 1, 4, 32 ],
[ 16, 1, 1, 32 ], [ 16, 1, 2, 32 ], [ 16, 1, 3, 16 ], [ 16, 1, 5, 32 ],
[ 16, 1, 7, 32 ], [ 16, 2, 1, 16 ], [ 16, 2, 2, 16 ], [ 16, 2, 3, 8 ],
[ 16, 2, 5, 16 ], [ 16, 2, 7, 16 ], [ 16, 3, 1, 16 ], [ 16, 3, 2, 16 ],
[ 16, 3, 3, 8 ], [ 16, 3, 5, 16 ], [ 16, 3, 7, 16 ], [ 16, 4, 1, 16 ],
[ 16, 4, 2, 16 ], [ 16, 4, 3, 8 ], [ 16, 4, 5, 16 ], [ 16, 4, 7, 16 ],
[ 16, 5, 1, 16 ], [ 16, 5, 2, 8 ], [ 16, 5, 3, 16 ], [ 16, 5, 4, 8 ],
[ 16, 5, 6, 16 ], [ 16, 5, 8, 16 ], [ 16, 6, 1, 16 ], [ 16, 6, 2, 8 ],
[ 16, 6, 3, 16 ], [ 16, 6, 4, 8 ], [ 16, 6, 6, 16 ], [ 16, 6, 8, 16 ],
[ 16, 7, 1, 16 ], [ 16, 7, 2, 8 ], [ 16, 7, 3, 16 ], [ 16, 7, 4, 8 ],
[ 16, 7, 6, 16 ], [ 16, 7, 8, 16 ], [ 16, 8, 1, 16 ], [ 16, 8, 2, 16 ],
[ 16, 8, 3, 16 ], [ 16, 8, 4, 16 ], [ 16, 8, 6, 16 ], [ 16, 8, 7, 16 ],
[ 16, 9, 1, 8 ], [ 16, 9, 2, 8 ], [ 16, 9, 3, 4 ], [ 16, 9, 5, 8 ],
[ 16, 9, 7, 8 ], [ 16, 10, 1, 8 ], [ 16, 10, 2, 4 ], [ 16, 10, 3, 8 ],
[ 16, 10, 4, 4 ], [ 16, 10, 6, 8 ], [ 16, 10, 8, 8 ], [ 16, 11, 1, 8 ],
[ 16, 11, 2, 8 ], [ 16, 11, 3, 8 ], [ 16, 11, 5, 8 ], [ 16, 11, 7, 8 ],
[ 16, 11, 8, 16 ], [ 16, 12, 1, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 3, 8 ],
[ 16, 12, 4, 4 ], [ 16, 12, 6, 8 ], [ 16, 12, 8, 8 ], [ 16, 13, 1, 8 ],
[ 16, 13, 2, 16 ], [ 16, 13, 3, 4 ], [ 16, 13, 5, 8 ], [ 16, 13, 7, 8 ],
[ 16, 14, 1, 8 ], [ 16, 14, 2, 8 ], [ 16, 14, 3, 8 ], [ 16, 14, 4, 8 ],
[ 16, 15, 1, 8 ], [ 16, 15, 2, 16 ], [ 16, 15, 3, 4 ], [ 16, 15, 5, 8 ],
[ 16, 15, 7, 8 ], [ 16, 16, 1, 8 ], [ 16, 16, 2, 16 ], [ 16, 16, 3, 4 ],
[ 16, 16, 5, 8 ], [ 16, 16, 7, 8 ], [ 16, 17, 1, 8 ], [ 16, 17, 2, 8 ],
[ 16, 17, 3, 8 ], [ 16, 17, 4, 8 ], [ 18, 1, 2, 16 ], [ 18, 1, 3, 16 ],
[ 18, 2, 2, 8 ], [ 18, 2, 3, 8 ], [ 20, 1, 2, 16 ], [ 20, 1, 3, 16 ],
[ 20, 2, 2, 8 ], [ 20, 2, 3, 8 ], [ 21, 1, 2, 32 ], [ 21, 1, 3, 32 ],
[ 21, 1, 5, 16 ], [ 21, 1, 7, 16 ], [ 21, 2, 2, 8 ], [ 21, 2, 3, 16 ],
[ 21, 2, 4, 16 ], [ 21, 2, 6, 16 ], [ 21, 2, 8, 16 ], [ 21, 2, 9, 8 ],
[ 21, 3, 2, 16 ], [ 21, 3, 3, 8 ], [ 21, 3, 5, 16 ], [ 21, 3, 6, 16 ],
[ 21, 3, 7, 16 ], [ 21, 3, 8, 8 ], [ 21, 4, 2, 8 ], [ 21, 4, 3, 16 ],
[ 21, 4, 6, 16 ], [ 21, 4, 9, 8 ], [ 21, 5, 2, 4 ], [ 21, 5, 3, 8 ],
[ 21, 5, 4, 8 ], [ 21, 5, 6, 8 ], [ 21, 5, 8, 8 ], [ 21, 5, 9, 4 ],
[ 21, 6, 2, 8 ], [ 21, 6, 3, 8 ], [ 21, 6, 5, 8 ], [ 21, 6, 6, 8 ],
[ 21, 6, 7, 8 ], [ 21, 6, 9, 8 ], [ 21, 7, 2, 8 ], [ 21, 7, 3, 8 ],
[ 21, 7, 6, 8 ], [ 21, 7, 9, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 16 ],
[ 22, 1, 3, 48 ], [ 22, 1, 4, 48 ], [ 22, 1, 5, 16 ], [ 22, 1, 6, 16 ],
[ 22, 1, 7, 32 ], [ 22, 1, 9, 32 ], [ 22, 2, 1, 8 ], [ 22, 2, 2, 8 ],
[ 22, 2, 3, 24 ], [ 22, 2, 4, 24 ], [ 22, 2, 5, 8 ], [ 22, 2, 6, 8 ],
[ 22, 2, 7, 16 ], [ 22, 2, 9, 16 ], [ 22, 3, 1, 8 ], [ 22, 3, 2, 24 ],
[ 22, 3, 3, 24 ], [ 22, 3, 4, 8 ], [ 22, 3, 5, 16 ], [ 22, 3, 6, 16 ],
[ 22, 3, 7, 16 ], [ 22, 3, 8, 16 ], [ 22, 4, 1, 4 ], [ 22, 4, 2, 8 ],
[ 22, 4, 3, 12 ], [ 22, 4, 4, 12 ], [ 22, 4, 5, 8 ], [ 22, 4, 6, 4 ],
[ 22, 4, 7, 8 ], [ 22, 4, 9, 8 ], [ 23, 1, 3, 32 ], [ 23, 1, 5, 32 ],
[ 23, 2, 3, 16 ], [ 23, 2, 5, 16 ], [ 23, 3, 3, 16 ], [ 23, 3, 5, 16 ],
[ 23, 4, 3, 16 ], [ 23, 4, 5, 16 ], [ 23, 5, 3, 16 ], [ 23, 5, 5, 16 ],
[ 23, 6, 3, 8 ], [ 23, 6, 5, 8 ], [ 24, 1, 2, 32 ], [ 24, 1, 3, 32 ],
[ 24, 2, 2, 16 ], [ 24, 2, 3, 16 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 32 ],
[ 25, 2, 2, 16 ], [ 25, 2, 5, 16 ], [ 25, 3, 3, 16 ], [ 25, 3, 5, 16 ],
[ 26, 1, 2, 32 ], [ 26, 1, 3, 32 ], [ 26, 2, 2, 16 ], [ 26, 2, 5, 16 ],
[ 26, 3, 3, 16 ], [ 26, 3, 5, 16 ], [ 27, 1, 3, 64 ], [ 27, 1, 6, 32 ],
[ 27, 1, 8, 64 ], [ 27, 1, 10, 32 ], [ 27, 2, 2, 16 ], [ 27, 2, 3, 32 ],
[ 27, 2, 6, 32 ], [ 27, 2, 9, 16 ], [ 27, 2, 14, 32 ], [ 27, 2, 17, 32 ],
[ 27, 3, 2, 16 ], [ 27, 3, 3, 32 ], [ 27, 3, 4, 32 ], [ 27, 3, 6, 16 ],
[ 27, 3, 8, 16 ], [ 27, 3, 11, 32 ], [ 27, 3, 12, 16 ], [ 27, 3, 17, 32 ],
[ 27, 3, 19, 32 ], [ 27, 4, 2, 32 ], [ 27, 4, 3, 16 ], [ 27, 4, 5, 32 ],
[ 27, 4, 8, 16 ], [ 27, 4, 13, 32 ], [ 27, 4, 18, 32 ], [ 27, 5, 2, 16 ],
[ 27, 5, 3, 32 ], [ 27, 5, 9, 16 ], [ 27, 5, 15, 32 ], [ 27, 6, 2, 8 ],
[ 27, 6, 3, 16 ], [ 27, 6, 4, 16 ], [ 27, 6, 6, 16 ], [ 27, 6, 8, 16 ],
[ 27, 6, 9, 8 ], [ 27, 6, 14, 16 ], [ 27, 6, 17, 16 ], [ 27, 7, 2, 8 ],
[ 27, 7, 3, 16 ], [ 27, 7, 6, 16 ], [ 27, 7, 9, 8 ], [ 27, 7, 14, 16 ],
[ 27, 7, 17, 16 ], [ 27, 8, 2, 8 ], [ 27, 8, 3, 16 ], [ 27, 8, 4, 16 ],
[ 27, 8, 6, 16 ], [ 27, 8, 8, 16 ], [ 27, 8, 11, 16 ], [ 27, 8, 12, 8 ],
[ 27, 8, 17, 16 ], [ 27, 8, 19, 32 ], [ 27, 9, 2, 8 ], [ 27, 9, 3, 16 ],
[ 27, 9, 4, 16 ], [ 27, 9, 7, 8 ], [ 27, 9, 15, 16 ], [ 27, 10, 2, 16 ],
[ 27, 10, 3, 16 ], [ 27, 10, 4, 16 ], [ 27, 10, 5, 8 ], [ 27, 10, 6, 8 ],
[ 27, 10, 9, 16 ], [ 27, 10, 15, 16 ], [ 27, 10, 16, 16 ], [ 27, 11, 2, 8 ],
[ 27, 11, 3, 16 ], [ 27, 11, 4, 16 ], [ 27, 11, 6, 16 ], [ 27, 11, 8, 16 ],
[ 27, 11, 11, 16 ], [ 27, 11, 12, 8 ], [ 27, 11, 17, 16 ],
[ 27, 11, 19, 32 ], [ 27, 12, 2, 16 ], [ 27, 12, 3, 16 ], [ 27, 12, 5, 16 ],
[ 27, 12, 8, 16 ], [ 27, 12, 13, 32 ], [ 27, 12, 18, 32 ],
[ 27, 13, 2, 16 ], [ 27, 13, 3, 8 ], [ 27, 13, 5, 16 ], [ 27, 13, 6, 16 ],
[ 27, 13, 7, 16 ], [ 27, 13, 8, 8 ], [ 27, 13, 13, 16 ], [ 27, 13, 18, 16 ],
[ 27, 14, 2, 16 ], [ 27, 14, 3, 8 ], [ 27, 14, 5, 16 ], [ 27, 14, 8, 16 ],
[ 27, 14, 10, 16 ], [ 27, 14, 11, 16 ], [ 27, 14, 12, 8 ],
[ 27, 14, 16, 16 ], [ 27, 14, 22, 32 ], [ 28, 1, 3, 64 ], [ 28, 1, 6, 64 ],
[ 28, 2, 3, 32 ], [ 28, 2, 4, 32 ], [ 28, 2, 6, 32 ], [ 28, 2, 8, 32 ],
[ 28, 3, 3, 32 ], [ 28, 3, 6, 32 ], [ 28, 4, 3, 32 ], [ 28, 4, 5, 32 ],
[ 28, 5, 3, 16 ], [ 28, 5, 4, 32 ], [ 28, 5, 6, 32 ], [ 28, 5, 8, 16 ],
[ 28, 6, 3, 16 ], [ 28, 6, 6, 16 ], [ 29, 1, 3, 64 ], [ 29, 1, 5, 32 ],
[ 29, 1, 6, 32 ], [ 29, 1, 7, 32 ], [ 29, 1, 8, 32 ], [ 29, 1, 9, 64 ],
[ 29, 2, 3, 32 ], [ 29, 2, 5, 16 ], [ 29, 2, 6, 16 ], [ 29, 2, 7, 16 ],
[ 29, 2, 8, 16 ], [ 29, 2, 9, 32 ], [ 29, 3, 3, 32 ], [ 29, 3, 5, 16 ],
[ 29, 3, 6, 16 ], [ 29, 3, 7, 16 ], [ 29, 3, 8, 16 ], [ 29, 3, 9, 32 ],
[ 29, 4, 3, 32 ], [ 29, 4, 5, 16 ], [ 29, 4, 6, 16 ], [ 29, 4, 7, 16 ],
[ 29, 4, 8, 16 ], [ 29, 4, 9, 32 ], [ 29, 5, 3, 32 ], [ 29, 5, 5, 16 ],
[ 29, 5, 6, 16 ], [ 29, 5, 7, 16 ], [ 29, 5, 8, 16 ], [ 29, 5, 9, 32 ],
[ 29, 6, 3, 32 ], [ 29, 6, 5, 32 ], [ 29, 7, 3, 32 ], [ 29, 7, 5, 32 ],
[ 29, 8, 3, 32 ], [ 29, 8, 5, 32 ], [ 29, 9, 3, 16 ], [ 29, 9, 5, 8 ],
[ 29, 9, 6, 8 ], [ 29, 9, 7, 8 ], [ 29, 9, 8, 8 ], [ 29, 9, 9, 16 ],
[ 29, 10, 3, 16 ], [ 29, 10, 5, 16 ], [ 29, 11, 3, 16 ], [ 29, 11, 5, 16 ],
[ 29, 12, 3, 16 ], [ 29, 12, 5, 16 ], [ 29, 13, 3, 16 ], [ 29, 13, 5, 16 ],
[ 30, 1, 3, 64 ], [ 30, 1, 10, 64 ], [ 30, 1, 15, 64 ], [ 30, 1, 16, 64 ],
[ 30, 2, 3, 32 ], [ 30, 2, 10, 32 ], [ 30, 2, 15, 32 ], [ 30, 2, 16, 32 ],
[ 30, 3, 3, 32 ], [ 30, 3, 10, 32 ], [ 30, 3, 15, 32 ], [ 30, 3, 16, 32 ],
[ 30, 4, 2, 32 ], [ 30, 4, 5, 32 ], [ 30, 4, 10, 32 ], [ 30, 4, 12, 32 ],
[ 30, 4, 13, 32 ], [ 30, 4, 16, 32 ], [ 30, 4, 17, 32 ], [ 30, 4, 19, 32 ],
[ 30, 4, 22, 32 ], [ 30, 4, 26, 32 ], [ 30, 5, 3, 32 ], [ 30, 5, 10, 32 ],
[ 30, 5, 13, 32 ], [ 30, 5, 16, 32 ], [ 30, 5, 17, 32 ], [ 30, 5, 18, 32 ],
[ 30, 6, 3, 32 ], [ 30, 6, 10, 32 ], [ 30, 6, 12, 32 ], [ 30, 6, 16, 32 ],
[ 30, 6, 17, 32 ], [ 30, 6, 18, 32 ], [ 30, 7, 3, 32 ], [ 30, 7, 7, 32 ],
[ 30, 7, 9, 32 ], [ 30, 7, 10, 32 ], [ 30, 7, 12, 32 ], [ 30, 7, 14, 32 ],
[ 30, 7, 18, 32 ], [ 30, 7, 19, 32 ], [ 30, 7, 20, 32 ], [ 30, 7, 22, 32 ],
[ 30, 7, 25, 32 ], [ 30, 7, 31, 32 ], [ 30, 8, 2, 16 ], [ 30, 8, 5, 16 ],
[ 30, 8, 14, 16 ], [ 30, 8, 18, 16 ], [ 30, 8, 19, 16 ], [ 30, 8, 21, 16 ],
[ 30, 9, 2, 32 ], [ 30, 9, 5, 16 ], [ 30, 9, 14, 16 ], [ 30, 9, 18, 32 ],
[ 30, 9, 19, 16 ], [ 30, 9, 21, 16 ], [ 30, 10, 2, 32 ], [ 30, 10, 5, 16 ],
[ 30, 10, 14, 16 ], [ 30, 10, 18, 32 ], [ 30, 10, 19, 16 ],
[ 30, 10, 21, 16 ], [ 30, 11, 3, 16 ], [ 30, 11, 7, 16 ], [ 30, 11, 9, 16 ],
[ 30, 11, 10, 16 ], [ 30, 11, 12, 16 ], [ 30, 11, 14, 16 ],
[ 30, 11, 18, 16 ], [ 30, 11, 19, 16 ], [ 30, 11, 20, 16 ],
[ 30, 11, 22, 16 ], [ 30, 11, 25, 16 ], [ 30, 11, 31, 16 ],
[ 30, 12, 2, 32 ], [ 30, 12, 5, 16 ], [ 30, 12, 10, 16 ],
[ 30, 12, 12, 16 ], [ 30, 12, 13, 16 ], [ 30, 12, 16, 32 ],
[ 30, 12, 17, 16 ], [ 30, 12, 19, 16 ], [ 30, 12, 22, 16 ],
[ 30, 12, 26, 16 ], [ 30, 13, 3, 16 ], [ 30, 13, 6, 16 ], [ 30, 13, 9, 32 ],
[ 30, 13, 12, 32 ], [ 30, 13, 13, 16 ], [ 30, 13, 16, 16 ],
[ 31, 2, 44, 64 ], [ 31, 2, 46, 64 ], [ 31, 2, 48, 64 ], [ 31, 2, 53, 64 ],
[ 31, 3, 36, 64 ], [ 31, 3, 44, 64 ], [ 31, 3, 45, 64 ], [ 31, 3, 53, 64 ],
[ 31, 4, 7, 64 ], [ 31, 5, 7, 64 ], [ 31, 5, 10, 64 ], [ 31, 5, 12, 64 ],
[ 31, 5, 17, 64 ], [ 31, 6, 6, 64 ], [ 31, 6, 13, 64 ], [ 31, 6, 17, 64 ],
[ 31, 6, 31, 64 ], [ 31, 6, 44, 64 ], [ 31, 6, 46, 64 ], [ 31, 7, 6, 64 ],
[ 31, 7, 13, 64 ], [ 31, 8, 6, 64 ], [ 31, 8, 13, 64 ], [ 31, 9, 44, 32 ],
[ 31, 9, 46, 32 ], [ 31, 9, 48, 32 ], [ 31, 9, 53, 32 ], [ 31, 10, 8, 32 ],
[ 31, 10, 12, 32 ], [ 31, 10, 15, 32 ], [ 31, 10, 16, 32 ],
[ 31, 10, 28, 32 ], [ 31, 11, 42, 32 ], [ 31, 11, 47, 32 ],
[ 31, 11, 48, 32 ], [ 31, 11, 53, 64 ], [ 31, 12, 6, 32 ],
[ 31, 12, 12, 32 ], [ 31, 12, 17, 32 ], [ 31, 12, 31, 32 ],
[ 31, 12, 44, 32 ], [ 31, 12, 46, 32 ], [ 31, 13, 7, 32 ],
[ 31, 13, 10, 32 ], [ 31, 13, 12, 32 ], [ 31, 13, 15, 32 ],
[ 31, 13, 21, 32 ], [ 31, 13, 30, 64 ], [ 31, 13, 32, 64 ],
[ 31, 13, 46, 32 ], [ 31, 13, 48, 32 ], [ 31, 13, 49, 32 ],
[ 31, 14, 42, 32 ], [ 31, 14, 43, 32 ], [ 31, 14, 46, 64 ],
[ 31, 14, 47, 64 ], [ 31, 15, 9, 32 ], [ 31, 15, 13, 64 ],
[ 31, 15, 16, 64 ], [ 31, 15, 24, 32 ], [ 31, 15, 27, 32 ],
[ 31, 15, 42, 32 ], [ 31, 16, 36, 32 ], [ 31, 16, 44, 32 ],
[ 31, 16, 45, 32 ], [ 31, 16, 53, 32 ], [ 31, 17, 32, 32 ],
[ 31, 17, 36, 32 ], [ 31, 18, 7, 32 ], [ 31, 18, 10, 32 ],
[ 31, 18, 12, 32 ], [ 31, 18, 17, 32 ], [ 31, 18, 26, 64 ],
[ 31, 18, 28, 64 ], [ 31, 19, 7, 32 ], [ 31, 19, 10, 32 ],
[ 31, 19, 12, 32 ], [ 31, 19, 17, 32 ], [ 31, 19, 26, 64 ],
[ 31, 19, 28, 64 ], [ 31, 20, 7, 32 ], [ 31, 20, 10, 32 ],
[ 31, 20, 12, 32 ], [ 31, 20, 17, 32 ], [ 31, 20, 26, 64 ],
[ 31, 20, 28, 64 ], [ 31, 21, 9, 64 ], [ 31, 21, 12, 32 ],
[ 31, 21, 15, 32 ], [ 31, 21, 16, 32 ], [ 31, 21, 17, 32 ],
[ 31, 21, 23, 64 ], [ 31, 22, 6, 32 ], [ 31, 22, 13, 32 ],
[ 31, 23, 36, 32 ], [ 31, 23, 47, 32 ], [ 31, 23, 48, 32 ],
[ 31, 23, 53, 64 ], [ 31, 24, 7, 32 ], [ 31, 24, 10, 32 ],
[ 31, 24, 12, 32 ], [ 31, 24, 15, 32 ], [ 31, 24, 21, 32 ],
[ 31, 24, 45, 32 ], [ 31, 25, 7, 32 ], [ 31, 25, 10, 32 ],
[ 31, 25, 12, 32 ], [ 31, 25, 15, 32 ], [ 31, 25, 21, 32 ],
[ 31, 25, 49, 32 ], [ 31, 26, 7, 32 ], [ 31, 26, 19, 32 ],
[ 31, 26, 20, 64 ], [ 31, 26, 35, 32 ], [ 31, 26, 36, 64 ],
[ 31, 26, 50, 32 ], [ 31, 27, 6, 32 ], [ 31, 27, 13, 32 ],
[ 31, 27, 17, 32 ], [ 31, 27, 31, 32 ], [ 31, 27, 44, 32 ],
[ 31, 27, 46, 32 ], [ 31, 28, 6, 32 ], [ 31, 28, 13, 32 ],
[ 31, 28, 17, 32 ], [ 31, 28, 31, 32 ], [ 31, 28, 44, 32 ],
[ 31, 28, 46, 32 ], [ 31, 29, 6, 32 ], [ 31, 29, 8, 32 ],
[ 31, 29, 12, 32 ], [ 31, 29, 15, 32 ], [ 31, 29, 21, 32 ],
[ 31, 29, 31, 64 ], [ 31, 29, 35, 64 ], [ 31, 29, 46, 32 ],
[ 31, 29, 48, 32 ], [ 31, 29, 54, 32 ], [ 31, 30, 6, 32 ],
[ 31, 30, 8, 32 ], [ 31, 30, 10, 32 ], [ 31, 30, 12, 32 ],
[ 31, 32, 7, 32 ], [ 31, 32, 19, 32 ], [ 31, 32, 20, 64 ],
[ 31, 32, 35, 32 ], [ 31, 32, 36, 64 ], [ 31, 32, 50, 32 ],
[ 31, 33, 7, 32 ], [ 31, 33, 19, 32 ], [ 31, 33, 20, 64 ],
[ 31, 33, 35, 32 ], [ 31, 33, 36, 64 ], [ 31, 33, 50, 32 ] ]
k = 8: F-action on Pi is () [31,1,8]
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 0 modulo 4: 1/192 q^3 ( q^3-4*q^2+2*q+4 )
q congruent 1 modulo 4: 1/192 phi1^2 phi2 ( q^3-3*q^2-7*q+21 )
q congruent 2 modulo 4: 1/192 q^3 ( q^3-4*q^2+2*q+4 )
q congruent 3 modulo 4: 1/192 phi1^2 phi2 ( q^3-3*q^2-7*q+21 )
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, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 12 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 6 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 6 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 6 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 3 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 6 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 3 ], [ 5, 1, 2, 12 ],
[ 6, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 36 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 12 ], [ 7, 2, 1, 6 ], [ 7, 2, 2, 18 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 6 ], [ 7, 3, 1, 6 ], [ 7, 3, 2, 18 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 6 ], [ 7, 4, 1, 6 ], [ 7, 4, 2, 18 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 6 ], [ 7, 5, 1, 3 ], [ 7, 5, 2, 9 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 3 ], [ 9, 1, 4, 48 ], [ 9, 2, 4, 24 ], [ 9, 3, 4, 24 ],
[ 9, 4, 4, 24 ], [ 9, 5, 4, 12 ], [ 12, 1, 3, 24 ], [ 12, 1, 4, 12 ],
[ 12, 1, 5, 4 ], [ 12, 2, 3, 12 ], [ 12, 2, 4, 6 ], [ 12, 2, 5, 2 ],
[ 12, 3, 2, 12 ], [ 12, 3, 3, 6 ], [ 12, 3, 4, 6 ], [ 12, 4, 3, 6 ],
[ 12, 4, 4, 3 ], [ 12, 4, 5, 2 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 24 ],
[ 13, 2, 2, 12 ], [ 13, 2, 4, 12 ], [ 14, 1, 4, 16 ], [ 14, 2, 4, 8 ],
[ 16, 1, 2, 24 ], [ 16, 1, 4, 24 ], [ 16, 1, 8, 96 ], [ 16, 2, 2, 12 ],
[ 16, 2, 4, 12 ], [ 16, 2, 8, 48 ], [ 16, 3, 2, 12 ], [ 16, 3, 4, 12 ],
[ 16, 3, 8, 48 ], [ 16, 4, 2, 12 ], [ 16, 4, 4, 12 ], [ 16, 4, 8, 48 ],
[ 16, 5, 7, 48 ], [ 16, 6, 7, 48 ], [ 16, 7, 7, 48 ], [ 16, 8, 2, 12 ],
[ 16, 8, 3, 12 ], [ 16, 8, 6, 12 ], [ 16, 8, 7, 12 ], [ 16, 8, 8, 48 ],
[ 16, 9, 2, 6 ], [ 16, 9, 4, 6 ], [ 16, 9, 8, 24 ], [ 16, 10, 7, 24 ],
[ 16, 11, 2, 6 ], [ 16, 11, 4, 12 ], [ 16, 11, 7, 6 ], [ 16, 11, 9, 12 ],
[ 16, 11, 10, 24 ], [ 16, 12, 7, 24 ], [ 16, 13, 2, 12 ], [ 16, 13, 4, 12 ],
[ 16, 13, 8, 24 ], [ 16, 14, 2, 6 ], [ 16, 14, 3, 6 ], [ 16, 14, 6, 24 ],
[ 16, 15, 2, 12 ], [ 16, 15, 4, 12 ], [ 16, 15, 8, 24 ], [ 16, 16, 2, 12 ],
[ 16, 16, 4, 12 ], [ 16, 16, 8, 24 ], [ 16, 17, 2, 6 ], [ 16, 17, 3, 6 ],
[ 16, 17, 6, 24 ], [ 21, 1, 3, 48 ], [ 21, 1, 4, 48 ], [ 21, 1, 6, 8 ],
[ 21, 1, 8, 24 ], [ 21, 2, 3, 24 ], [ 21, 2, 4, 24 ], [ 21, 2, 5, 12 ],
[ 21, 2, 7, 4 ], [ 21, 2, 10, 24 ], [ 21, 3, 2, 24 ], [ 21, 3, 4, 12 ],
[ 21, 3, 5, 24 ], [ 21, 3, 9, 4 ], [ 21, 3, 10, 24 ], [ 21, 4, 3, 24 ],
[ 21, 4, 5, 12 ], [ 21, 4, 7, 4 ], [ 21, 4, 10, 24 ], [ 21, 5, 3, 12 ],
[ 21, 5, 4, 12 ], [ 21, 5, 5, 6 ], [ 21, 5, 7, 2 ], [ 21, 5, 10, 12 ],
[ 21, 6, 2, 12 ], [ 21, 6, 4, 12 ], [ 21, 6, 5, 12 ], [ 21, 6, 8, 4 ],
[ 21, 6, 10, 12 ], [ 21, 7, 3, 12 ], [ 21, 7, 5, 12 ], [ 21, 7, 7, 4 ],
[ 21, 7, 10, 12 ], [ 22, 1, 9, 48 ], [ 22, 1, 10, 48 ], [ 22, 2, 9, 24 ],
[ 22, 2, 10, 24 ], [ 22, 3, 7, 24 ], [ 22, 3, 8, 24 ], [ 22, 4, 9, 12 ],
[ 22, 4, 10, 24 ], [ 27, 1, 4, 96 ], [ 27, 1, 9, 48 ], [ 27, 1, 11, 96 ],
[ 27, 2, 5, 24 ], [ 27, 2, 7, 24 ], [ 27, 2, 15, 48 ], [ 27, 2, 18, 48 ],
[ 27, 2, 20, 48 ], [ 27, 3, 5, 24 ], [ 27, 3, 9, 24 ], [ 27, 3, 18, 48 ],
[ 27, 3, 23, 48 ], [ 27, 3, 24, 48 ], [ 27, 3, 25, 48 ], [ 27, 4, 4, 24 ],
[ 27, 4, 9, 24 ], [ 27, 4, 15, 48 ], [ 27, 4, 19, 48 ], [ 27, 4, 20, 48 ],
[ 27, 5, 5, 24 ], [ 27, 5, 16, 48 ], [ 27, 5, 20, 48 ], [ 27, 6, 5, 12 ],
[ 27, 6, 7, 12 ], [ 27, 6, 15, 24 ], [ 27, 6, 18, 24 ], [ 27, 6, 19, 24 ],
[ 27, 6, 20, 24 ], [ 27, 7, 5, 12 ], [ 27, 7, 7, 12 ], [ 27, 7, 15, 24 ],
[ 27, 7, 18, 24 ], [ 27, 7, 20, 24 ], [ 27, 8, 5, 12 ], [ 27, 8, 9, 24 ],
[ 27, 8, 18, 24 ], [ 27, 8, 23, 48 ], [ 27, 8, 24, 24 ], [ 27, 8, 25, 24 ],
[ 27, 9, 5, 12 ], [ 27, 9, 16, 24 ], [ 27, 9, 18, 24 ], [ 27, 10, 7, 12 ],
[ 27, 10, 8, 12 ], [ 27, 10, 14, 24 ], [ 27, 10, 18, 24 ],
[ 27, 10, 19, 24 ], [ 27, 10, 20, 24 ], [ 27, 11, 5, 12 ],
[ 27, 11, 9, 24 ], [ 27, 11, 18, 24 ], [ 27, 11, 23, 48 ],
[ 27, 11, 24, 24 ], [ 27, 11, 25, 24 ], [ 27, 12, 4, 24 ],
[ 27, 12, 9, 24 ], [ 27, 12, 15, 24 ], [ 27, 12, 19, 48 ],
[ 27, 12, 20, 24 ], [ 27, 13, 4, 12 ], [ 27, 13, 9, 12 ],
[ 27, 13, 15, 24 ], [ 27, 13, 17, 24 ], [ 27, 13, 19, 24 ],
[ 27, 13, 20, 24 ], [ 27, 14, 4, 12 ], [ 27, 14, 9, 24 ],
[ 27, 14, 18, 24 ], [ 27, 14, 23, 48 ], [ 27, 14, 24, 24 ],
[ 27, 14, 25, 24 ], [ 28, 1, 7, 32 ], [ 28, 2, 7, 16 ], [ 28, 3, 7, 16 ],
[ 28, 5, 7, 16 ], [ 28, 6, 7, 16 ], [ 30, 1, 18, 96 ], [ 30, 2, 18, 48 ],
[ 30, 3, 18, 48 ], [ 30, 4, 18, 48 ], [ 30, 4, 23, 48 ], [ 30, 8, 20, 24 ],
[ 30, 9, 20, 48 ], [ 30, 10, 20, 48 ], [ 30, 12, 18, 48 ],
[ 30, 12, 23, 48 ], [ 30, 13, 15, 48 ], [ 30, 13, 17, 48 ],
[ 31, 2, 20, 96 ], [ 31, 2, 25, 96 ], [ 31, 2, 26, 96 ], [ 31, 3, 20, 96 ],
[ 31, 3, 24, 96 ], [ 31, 3, 26, 96 ], [ 31, 4, 8, 96 ], [ 31, 5, 27, 96 ],
[ 31, 9, 20, 48 ], [ 31, 9, 24, 48 ], [ 31, 9, 25, 48 ], [ 31, 10, 30, 48 ],
[ 31, 10, 32, 48 ], [ 31, 10, 34, 48 ], [ 31, 11, 20, 96 ],
[ 31, 11, 26, 48 ], [ 31, 11, 27, 96 ], [ 31, 13, 35, 96 ],
[ 31, 13, 39, 96 ], [ 31, 14, 22, 48 ], [ 31, 14, 24, 48 ],
[ 31, 14, 29, 96 ], [ 31, 14, 30, 96 ], [ 31, 15, 30, 48 ],
[ 31, 15, 35, 96 ], [ 31, 15, 38, 96 ], [ 31, 15, 45, 48 ],
[ 31, 15, 47, 48 ], [ 31, 16, 20, 48 ], [ 31, 16, 24, 48 ],
[ 31, 16, 26, 48 ], [ 31, 17, 18, 48 ], [ 31, 18, 31, 96 ],
[ 31, 19, 31, 96 ], [ 31, 20, 31, 96 ], [ 31, 21, 24, 96 ],
[ 31, 21, 30, 48 ], [ 31, 21, 32, 48 ], [ 31, 21, 35, 48 ],
[ 31, 21, 48, 96 ], [ 31, 23, 19, 96 ], [ 31, 23, 24, 96 ],
[ 31, 23, 27, 48 ], [ 31, 26, 53, 96 ], [ 31, 29, 34, 96 ],
[ 31, 29, 41, 96 ], [ 31, 32, 53, 96 ], [ 31, 33, 53, 96 ] ]
k = 9: F-action on Pi is () [31,1,9]
Dynkin type is A_0(q) + T(phi1 phi2^5)
Order of center |Z^F|: phi1 phi2^5
Numbers of classes in class type:
q congruent 0 modulo 4: 1/768 q^2 ( q^4-10*q^3+36*q^2-56*q+32 )
q congruent 1 modulo
4: 1/768 phi1 ( q^5-9*q^4+20*q^3-16*q^2+131*q-255 )
q congruent 2 modulo 4: 1/768 q^2 ( q^4-10*q^3+36*q^2-56*q+32 )
q congruent 3 modulo
4: 1/768 ( q^6-10*q^5+29*q^4-36*q^3+147*q^2-386*q+159 )
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, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 2, 16 ],
[ 3, 2, 2, 8 ], [ 3, 3, 2, 8 ], [ 3, 4, 2, 8 ], [ 3, 5, 2, 4 ],
[ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 26 ],
[ 6, 1, 2, 48 ], [ 7, 1, 4, 64 ], [ 7, 2, 4, 32 ], [ 7, 3, 4, 32 ],
[ 7, 4, 4, 32 ], [ 7, 5, 4, 16 ], [ 8, 1, 2, 64 ], [ 9, 1, 1, 24 ],
[ 9, 1, 2, 120 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 60 ], [ 9, 3, 1, 12 ],
[ 9, 3, 2, 60 ], [ 9, 4, 1, 12 ], [ 9, 4, 2, 60 ], [ 9, 5, 1, 6 ],
[ 9, 5, 2, 30 ], [ 10, 1, 2, 16 ], [ 10, 2, 2, 8 ], [ 11, 1, 2, 16 ],
[ 11, 2, 2, 8 ], [ 12, 1, 2, 4 ], [ 12, 1, 3, 48 ], [ 12, 2, 2, 2 ],
[ 12, 2, 3, 24 ], [ 12, 3, 2, 24 ], [ 12, 4, 2, 2 ], [ 12, 4, 3, 12 ],
[ 13, 1, 3, 16 ], [ 13, 1, 4, 112 ], [ 13, 2, 3, 8 ], [ 13, 2, 4, 56 ],
[ 14, 1, 2, 160 ], [ 14, 2, 2, 80 ], [ 15, 1, 3, 192 ], [ 15, 1, 4, 48 ],
[ 16, 1, 3, 48 ], [ 16, 1, 5, 192 ], [ 16, 2, 3, 24 ], [ 16, 2, 5, 96 ],
[ 16, 3, 3, 24 ], [ 16, 3, 5, 96 ], [ 16, 4, 3, 24 ], [ 16, 4, 5, 96 ],
[ 16, 5, 2, 24 ], [ 16, 5, 3, 96 ], [ 16, 5, 4, 24 ], [ 16, 6, 2, 24 ],
[ 16, 6, 3, 96 ], [ 16, 6, 4, 24 ], [ 16, 7, 2, 24 ], [ 16, 7, 3, 96 ],
[ 16, 7, 4, 24 ], [ 16, 8, 4, 96 ], [ 16, 9, 3, 12 ], [ 16, 9, 5, 48 ],
[ 16, 10, 2, 12 ], [ 16, 10, 3, 48 ], [ 16, 10, 4, 12 ], [ 16, 11, 3, 24 ],
[ 16, 11, 5, 48 ], [ 16, 12, 2, 12 ], [ 16, 12, 3, 48 ], [ 16, 12, 4, 12 ],
[ 16, 13, 3, 12 ], [ 16, 13, 5, 48 ], [ 16, 14, 4, 48 ], [ 16, 15, 3, 12 ],
[ 16, 15, 5, 48 ], [ 16, 16, 3, 12 ], [ 16, 16, 5, 48 ], [ 16, 17, 4, 48 ],
[ 17, 1, 2, 64 ], [ 17, 2, 2, 32 ], [ 18, 1, 3, 16 ], [ 18, 1, 4, 112 ],
[ 18, 2, 3, 8 ], [ 18, 2, 4, 56 ], [ 19, 1, 2, 128 ], [ 19, 2, 2, 64 ],
[ 19, 3, 2, 64 ], [ 19, 4, 2, 64 ], [ 19, 5, 2, 32 ], [ 20, 1, 3, 16 ],
[ 20, 1, 4, 112 ], [ 20, 2, 3, 8 ], [ 20, 2, 4, 56 ], [ 21, 1, 4, 192 ],
[ 21, 1, 7, 32 ], [ 21, 2, 9, 16 ], [ 21, 2, 10, 96 ], [ 21, 3, 8, 16 ],
[ 21, 3, 10, 96 ], [ 21, 4, 9, 16 ], [ 21, 4, 10, 96 ], [ 21, 5, 9, 8 ],
[ 21, 5, 10, 48 ], [ 21, 6, 9, 16 ], [ 21, 6, 10, 48 ], [ 21, 7, 9, 16 ],
[ 21, 7, 10, 48 ], [ 22, 1, 3, 96 ], [ 22, 1, 5, 96 ], [ 22, 1, 6, 288 ],
[ 22, 2, 3, 48 ], [ 22, 2, 5, 48 ], [ 22, 2, 6, 144 ], [ 22, 3, 2, 48 ],
[ 22, 3, 4, 144 ], [ 22, 4, 3, 24 ], [ 22, 4, 5, 48 ], [ 22, 4, 6, 72 ],
[ 23, 1, 6, 32 ], [ 23, 1, 7, 192 ], [ 23, 1, 8, 32 ], [ 23, 2, 6, 16 ],
[ 23, 2, 7, 96 ], [ 23, 2, 8, 16 ], [ 23, 3, 6, 16 ], [ 23, 3, 7, 96 ],
[ 23, 3, 8, 16 ], [ 23, 4, 6, 16 ], [ 23, 4, 7, 96 ], [ 23, 4, 8, 16 ],
[ 23, 5, 6, 16 ], [ 23, 5, 7, 96 ], [ 23, 5, 8, 16 ], [ 23, 6, 6, 8 ],
[ 23, 6, 7, 48 ], [ 23, 6, 8, 8 ], [ 24, 1, 3, 64 ], [ 24, 1, 4, 256 ],
[ 24, 2, 3, 32 ], [ 24, 2, 4, 128 ], [ 25, 1, 3, 96 ], [ 25, 1, 4, 288 ],
[ 25, 2, 5, 48 ], [ 25, 2, 8, 144 ], [ 25, 3, 3, 48 ], [ 25, 3, 7, 144 ],
[ 26, 1, 3, 96 ], [ 26, 1, 4, 288 ], [ 26, 2, 5, 48 ], [ 26, 2, 10, 144 ],
[ 26, 3, 3, 48 ], [ 26, 3, 7, 144 ], [ 27, 1, 5, 384 ], [ 27, 1, 10, 192 ],
[ 27, 2, 9, 96 ], [ 27, 2, 10, 192 ], [ 27, 3, 8, 96 ], [ 27, 3, 12, 96 ],
[ 27, 3, 13, 192 ], [ 27, 4, 8, 96 ], [ 27, 4, 10, 192 ], [ 27, 5, 9, 96 ],
[ 27, 5, 11, 192 ], [ 27, 6, 9, 48 ], [ 27, 6, 10, 96 ], [ 27, 7, 9, 48 ],
[ 27, 7, 10, 96 ], [ 27, 8, 8, 96 ], [ 27, 8, 12, 48 ], [ 27, 8, 13, 96 ],
[ 27, 9, 7, 48 ], [ 27, 9, 12, 96 ], [ 27, 10, 6, 48 ], [ 27, 10, 10, 96 ],
[ 27, 11, 8, 96 ], [ 27, 11, 12, 48 ], [ 27, 11, 13, 96 ],
[ 27, 12, 8, 96 ], [ 27, 12, 10, 96 ], [ 27, 13, 8, 48 ],
[ 27, 13, 10, 96 ], [ 27, 14, 10, 96 ], [ 27, 14, 12, 48 ],
[ 27, 14, 13, 96 ], [ 28, 1, 9, 128 ], [ 28, 1, 10, 384 ], [ 28, 2, 9, 64 ],
[ 28, 2, 10, 192 ], [ 28, 3, 9, 64 ], [ 28, 3, 10, 192 ], [ 28, 4, 6, 64 ],
[ 28, 4, 7, 192 ], [ 28, 4, 8, 64 ], [ 28, 5, 9, 32 ], [ 28, 5, 10, 96 ],
[ 28, 6, 9, 64 ], [ 28, 6, 10, 96 ], [ 29, 1, 7, 192 ], [ 29, 1, 10, 192 ],
[ 29, 1, 11, 384 ], [ 29, 1, 12, 192 ], [ 29, 2, 7, 96 ], [ 29, 2, 10, 96 ],
[ 29, 2, 11, 192 ], [ 29, 2, 12, 96 ], [ 29, 3, 7, 96 ], [ 29, 3, 10, 96 ],
[ 29, 3, 11, 192 ], [ 29, 3, 12, 96 ], [ 29, 4, 7, 96 ], [ 29, 4, 10, 96 ],
[ 29, 4, 11, 192 ], [ 29, 4, 12, 96 ], [ 29, 5, 7, 96 ], [ 29, 5, 10, 96 ],
[ 29, 5, 11, 192 ], [ 29, 5, 12, 96 ], [ 29, 6, 6, 96 ], [ 29, 6, 7, 192 ],
[ 29, 6, 8, 96 ], [ 29, 7, 6, 96 ], [ 29, 7, 7, 192 ], [ 29, 7, 8, 96 ],
[ 29, 8, 6, 96 ], [ 29, 8, 7, 192 ], [ 29, 8, 8, 96 ], [ 29, 9, 7, 48 ],
[ 29, 9, 10, 48 ], [ 29, 9, 11, 96 ], [ 29, 9, 12, 48 ], [ 29, 10, 6, 48 ],
[ 29, 10, 7, 96 ], [ 29, 10, 8, 48 ], [ 29, 11, 6, 48 ], [ 29, 11, 7, 96 ],
[ 29, 11, 8, 48 ], [ 29, 12, 6, 48 ], [ 29, 12, 7, 96 ], [ 29, 12, 8, 48 ],
[ 29, 13, 6, 48 ], [ 29, 13, 7, 96 ], [ 29, 13, 8, 48 ], [ 30, 1, 13, 384 ],
[ 30, 1, 23, 384 ], [ 30, 1, 26, 384 ], [ 30, 2, 13, 192 ],
[ 30, 2, 23, 192 ], [ 30, 2, 26, 192 ], [ 30, 3, 13, 192 ],
[ 30, 3, 23, 192 ], [ 30, 3, 26, 192 ], [ 30, 4, 14, 192 ],
[ 30, 4, 24, 192 ], [ 30, 4, 27, 192 ], [ 30, 4, 28, 192 ],
[ 30, 5, 12, 192 ], [ 30, 5, 24, 192 ], [ 30, 5, 26, 192 ],
[ 30, 5, 27, 192 ], [ 30, 6, 13, 192 ], [ 30, 6, 24, 192 ],
[ 30, 6, 26, 192 ], [ 30, 6, 27, 192 ], [ 30, 7, 11, 192 ],
[ 30, 7, 23, 192 ], [ 30, 7, 26, 192 ], [ 30, 7, 27, 192 ],
[ 30, 7, 28, 192 ], [ 30, 7, 30, 192 ], [ 30, 8, 16, 96 ],
[ 30, 8, 30, 96 ], [ 30, 8, 32, 96 ], [ 30, 9, 16, 96 ], [ 30, 9, 30, 96 ],
[ 30, 9, 32, 96 ], [ 30, 10, 16, 96 ], [ 30, 10, 30, 96 ],
[ 30, 10, 32, 96 ], [ 30, 11, 11, 96 ], [ 30, 11, 23, 96 ],
[ 30, 11, 26, 96 ], [ 30, 11, 27, 96 ], [ 30, 11, 28, 96 ],
[ 30, 11, 30, 96 ], [ 30, 12, 14, 96 ], [ 30, 12, 24, 96 ],
[ 30, 12, 27, 96 ], [ 30, 12, 28, 96 ], [ 30, 13, 10, 96 ],
[ 30, 13, 19, 192 ], [ 30, 13, 20, 96 ], [ 31, 2, 30, 384 ],
[ 31, 2, 45, 384 ], [ 31, 3, 35, 384 ], [ 31, 3, 37, 384 ],
[ 31, 4, 9, 384 ], [ 31, 5, 19, 384 ], [ 31, 5, 50, 384 ],
[ 31, 5, 52, 384 ], [ 31, 6, 26, 384 ], [ 31, 6, 40, 384 ],
[ 31, 6, 48, 384 ], [ 31, 6, 55, 384 ], [ 31, 7, 22, 384 ],
[ 31, 7, 39, 384 ], [ 31, 8, 22, 384 ], [ 31, 8, 37, 384 ],
[ 31, 9, 30, 192 ], [ 31, 9, 45, 192 ], [ 31, 10, 24, 192 ],
[ 31, 10, 55, 192 ], [ 31, 11, 35, 192 ], [ 31, 11, 46, 192 ],
[ 31, 12, 27, 192 ], [ 31, 12, 41, 192 ], [ 31, 12, 48, 192 ],
[ 31, 12, 54, 192 ], [ 31, 13, 23, 192 ], [ 31, 13, 51, 192 ],
[ 31, 13, 54, 192 ], [ 31, 13, 56, 192 ], [ 31, 14, 44, 192 ],
[ 31, 14, 48, 384 ], [ 31, 15, 20, 384 ], [ 31, 15, 49, 192 ],
[ 31, 16, 35, 192 ], [ 31, 16, 37, 192 ], [ 31, 17, 21, 192 ],
[ 31, 18, 19, 192 ], [ 31, 18, 62, 192 ], [ 31, 18, 64, 192 ],
[ 31, 19, 19, 192 ], [ 31, 19, 62, 192 ], [ 31, 19, 64, 192 ],
[ 31, 20, 19, 192 ], [ 31, 20, 62, 192 ], [ 31, 20, 64, 192 ],
[ 31, 21, 20, 192 ], [ 31, 21, 49, 384 ], [ 31, 22, 22, 192 ],
[ 31, 22, 39, 192 ], [ 31, 23, 35, 192 ], [ 31, 23, 44, 192 ],
[ 31, 24, 23, 192 ], [ 31, 24, 47, 192 ], [ 31, 24, 54, 192 ],
[ 31, 24, 56, 192 ], [ 31, 25, 23, 192 ], [ 31, 25, 51, 192 ],
[ 31, 25, 54, 192 ], [ 31, 25, 56, 192 ], [ 31, 26, 32, 192 ],
[ 31, 26, 48, 192 ], [ 31, 26, 55, 192 ], [ 31, 27, 26, 192 ],
[ 31, 27, 40, 192 ], [ 31, 27, 48, 192 ], [ 31, 27, 55, 192 ],
[ 31, 28, 26, 192 ], [ 31, 28, 40, 192 ], [ 31, 28, 48, 192 ],
[ 31, 28, 55, 192 ], [ 31, 29, 23, 192 ], [ 31, 29, 50, 192 ],
[ 31, 29, 52, 192 ], [ 31, 29, 56, 192 ], [ 31, 30, 18, 192 ],
[ 31, 30, 30, 192 ], [ 31, 31, 13, 192 ], [ 31, 31, 21, 192 ],
[ 31, 32, 32, 192 ], [ 31, 32, 48, 192 ], [ 31, 32, 55, 192 ],
[ 31, 33, 32, 192 ], [ 31, 33, 48, 192 ], [ 31, 33, 55, 192 ] ]
k = 10: F-action on Pi is () [31,1,10]
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 0 modulo 4: 1/128 q ( q^5-8*q^4+20*q^3-8*q^2-32*q+32 )
q congruent 1 modulo
4: 1/128 phi1 ( q^5-7*q^4+10*q^3+2*q^2+85*q-219 )
q congruent 2 modulo 4: 1/128 q ( q^5-8*q^4+20*q^3-8*q^2-32*q+32 )
q congruent 3 modulo
4: 1/128 ( q^6-8*q^5+17*q^4-8*q^3+83*q^2-336*q+315 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 8 ], [ 5, 1, 2, 4 ],
[ 6, 1, 1, 16 ], [ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ],
[ 7, 4, 1, 8 ], [ 7, 5, 1, 4 ], [ 8, 1, 1, 20 ], [ 8, 1, 2, 4 ],
[ 9, 1, 1, 32 ], [ 9, 1, 2, 16 ], [ 9, 1, 6, 16 ], [ 9, 1, 8, 16 ],
[ 9, 2, 1, 16 ], [ 9, 2, 2, 8 ], [ 9, 2, 6, 8 ], [ 9, 2, 8, 8 ],
[ 9, 3, 1, 16 ], [ 9, 3, 2, 8 ], [ 9, 3, 6, 8 ], [ 9, 3, 8, 8 ],
[ 9, 4, 1, 16 ], [ 9, 4, 2, 8 ], [ 9, 4, 6, 8 ], [ 9, 4, 8, 8 ],
[ 9, 5, 1, 8 ], [ 9, 5, 2, 4 ], [ 9, 5, 6, 4 ], [ 9, 5, 8, 4 ],
[ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ], [ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ],
[ 12, 1, 1, 8 ], [ 12, 1, 2, 8 ], [ 12, 2, 1, 4 ], [ 12, 2, 2, 4 ],
[ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 4 ], [ 13, 1, 1, 16 ],
[ 13, 1, 2, 16 ], [ 13, 2, 1, 8 ], [ 13, 2, 2, 8 ], [ 14, 1, 1, 32 ],
[ 14, 2, 1, 16 ], [ 15, 1, 1, 40 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 8 ],
[ 15, 1, 4, 24 ], [ 16, 1, 1, 32 ], [ 16, 1, 3, 32 ], [ 16, 1, 13, 32 ],
[ 16, 2, 1, 16 ], [ 16, 2, 3, 16 ], [ 16, 2, 13, 16 ], [ 16, 3, 1, 16 ],
[ 16, 3, 3, 16 ], [ 16, 3, 13, 16 ], [ 16, 4, 1, 16 ], [ 16, 4, 3, 16 ],
[ 16, 4, 13, 16 ], [ 16, 5, 1, 16 ], [ 16, 5, 2, 16 ], [ 16, 5, 4, 16 ],
[ 16, 5, 11, 16 ], [ 16, 5, 15, 16 ], [ 16, 6, 1, 16 ], [ 16, 6, 2, 16 ],
[ 16, 6, 4, 16 ], [ 16, 6, 11, 16 ], [ 16, 6, 15, 16 ], [ 16, 7, 1, 16 ],
[ 16, 7, 2, 16 ], [ 16, 7, 4, 16 ], [ 16, 7, 11, 16 ], [ 16, 7, 15, 16 ],
[ 16, 8, 1, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 3, 8 ], [ 16, 9, 13, 8 ],
[ 16, 10, 1, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ], [ 16, 10, 11, 8 ],
[ 16, 10, 15, 8 ], [ 16, 11, 1, 8 ], [ 16, 11, 3, 16 ], [ 16, 12, 1, 8 ],
[ 16, 12, 2, 8 ], [ 16, 12, 4, 8 ], [ 16, 12, 11, 8 ], [ 16, 12, 15, 8 ],
[ 16, 13, 1, 8 ], [ 16, 13, 3, 8 ], [ 16, 13, 13, 8 ], [ 16, 14, 1, 8 ],
[ 16, 14, 9, 16 ], [ 16, 15, 1, 8 ], [ 16, 15, 3, 8 ], [ 16, 15, 13, 8 ],
[ 16, 16, 1, 8 ], [ 16, 16, 3, 8 ], [ 16, 16, 13, 8 ], [ 16, 17, 1, 8 ],
[ 17, 1, 1, 16 ], [ 17, 2, 1, 8 ], [ 18, 1, 1, 24 ], [ 18, 1, 2, 16 ],
[ 18, 1, 3, 8 ], [ 18, 2, 1, 12 ], [ 18, 2, 2, 8 ], [ 18, 2, 3, 4 ],
[ 19, 1, 1, 32 ], [ 19, 2, 1, 16 ], [ 19, 3, 1, 16 ], [ 19, 4, 1, 16 ],
[ 19, 5, 1, 8 ], [ 20, 1, 1, 24 ], [ 20, 1, 2, 16 ], [ 20, 1, 3, 8 ],
[ 20, 2, 1, 12 ], [ 20, 2, 2, 8 ], [ 20, 2, 3, 4 ], [ 21, 1, 5, 32 ],
[ 21, 2, 2, 16 ], [ 21, 3, 3, 16 ], [ 21, 4, 2, 16 ], [ 21, 5, 2, 8 ],
[ 21, 6, 3, 16 ], [ 21, 7, 2, 16 ], [ 22, 1, 1, 32 ], [ 22, 1, 2, 48 ],
[ 22, 1, 4, 32 ], [ 22, 1, 5, 16 ], [ 22, 2, 1, 16 ], [ 22, 2, 2, 24 ],
[ 22, 2, 4, 16 ], [ 22, 2, 5, 8 ], [ 22, 3, 1, 16 ], [ 22, 3, 3, 16 ],
[ 22, 4, 1, 8 ], [ 22, 4, 2, 24 ], [ 22, 4, 4, 8 ], [ 22, 4, 5, 8 ],
[ 23, 1, 1, 16 ], [ 23, 1, 2, 32 ], [ 23, 1, 4, 32 ], [ 23, 1, 5, 16 ],
[ 23, 2, 1, 8 ], [ 23, 2, 2, 16 ], [ 23, 2, 4, 16 ], [ 23, 2, 5, 8 ],
[ 23, 3, 1, 8 ], [ 23, 3, 2, 16 ], [ 23, 3, 4, 16 ], [ 23, 3, 5, 8 ],
[ 23, 4, 1, 8 ], [ 23, 4, 2, 16 ], [ 23, 4, 4, 16 ], [ 23, 4, 5, 8 ],
[ 23, 5, 1, 8 ], [ 23, 5, 2, 16 ], [ 23, 5, 4, 16 ], [ 23, 5, 5, 8 ],
[ 23, 6, 1, 4 ], [ 23, 6, 2, 8 ], [ 23, 6, 4, 8 ], [ 23, 6, 5, 4 ],
[ 24, 1, 1, 32 ], [ 24, 1, 2, 32 ], [ 24, 2, 1, 16 ], [ 24, 2, 2, 16 ],
[ 25, 1, 1, 48 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 16 ], [ 25, 1, 5, 32 ],
[ 25, 2, 1, 24 ], [ 25, 2, 2, 16 ], [ 25, 2, 3, 16 ], [ 25, 2, 5, 8 ],
[ 25, 3, 1, 24 ], [ 25, 3, 2, 16 ], [ 25, 3, 3, 8 ], [ 25, 3, 4, 16 ],
[ 25, 3, 5, 16 ], [ 26, 1, 1, 48 ], [ 26, 1, 2, 32 ], [ 26, 1, 3, 16 ],
[ 26, 1, 5, 32 ], [ 26, 2, 1, 24 ], [ 26, 2, 2, 16 ], [ 26, 2, 3, 16 ],
[ 26, 2, 5, 8 ], [ 26, 3, 1, 24 ], [ 26, 3, 2, 16 ], [ 26, 3, 3, 8 ],
[ 26, 3, 4, 16 ], [ 26, 3, 5, 16 ], [ 27, 1, 6, 64 ], [ 27, 1, 12, 32 ],
[ 27, 2, 2, 32 ], [ 27, 3, 2, 32 ], [ 27, 3, 6, 32 ], [ 27, 3, 7, 16 ],
[ 27, 4, 3, 32 ], [ 27, 5, 2, 32 ], [ 27, 5, 8, 16 ], [ 27, 6, 2, 16 ],
[ 27, 7, 2, 16 ], [ 27, 8, 2, 16 ], [ 27, 8, 6, 32 ], [ 27, 8, 7, 16 ],
[ 27, 9, 2, 16 ], [ 27, 9, 6, 8 ], [ 27, 9, 10, 16 ], [ 27, 10, 5, 16 ],
[ 27, 11, 2, 16 ], [ 27, 11, 6, 32 ], [ 27, 11, 7, 16 ], [ 27, 12, 3, 32 ],
[ 27, 13, 3, 16 ], [ 27, 14, 3, 16 ], [ 27, 14, 6, 16 ], [ 27, 14, 8, 32 ],
[ 28, 1, 2, 64 ], [ 28, 2, 2, 32 ], [ 28, 3, 2, 32 ], [ 28, 4, 2, 32 ],
[ 28, 4, 4, 32 ], [ 28, 5, 2, 16 ], [ 28, 6, 2, 32 ], [ 29, 1, 1, 32 ],
[ 29, 1, 2, 64 ], [ 29, 1, 4, 64 ], [ 29, 1, 5, 32 ], [ 29, 1, 6, 32 ],
[ 29, 1, 8, 32 ], [ 29, 1, 9, 32 ], [ 29, 1, 13, 64 ], [ 29, 2, 1, 16 ],
[ 29, 2, 2, 32 ], [ 29, 2, 4, 32 ], [ 29, 2, 5, 16 ], [ 29, 2, 6, 16 ],
[ 29, 2, 8, 16 ], [ 29, 2, 9, 16 ], [ 29, 2, 13, 32 ], [ 29, 3, 1, 16 ],
[ 29, 3, 2, 32 ], [ 29, 3, 4, 32 ], [ 29, 3, 5, 16 ], [ 29, 3, 6, 16 ],
[ 29, 3, 8, 16 ], [ 29, 3, 9, 16 ], [ 29, 3, 13, 32 ], [ 29, 4, 1, 16 ],
[ 29, 4, 2, 32 ], [ 29, 4, 4, 32 ], [ 29, 4, 5, 16 ], [ 29, 4, 6, 16 ],
[ 29, 4, 8, 16 ], [ 29, 4, 9, 16 ], [ 29, 4, 13, 32 ], [ 29, 5, 1, 16 ],
[ 29, 5, 2, 32 ], [ 29, 5, 4, 32 ], [ 29, 5, 5, 16 ], [ 29, 5, 6, 16 ],
[ 29, 5, 8, 16 ], [ 29, 5, 9, 16 ], [ 29, 5, 13, 32 ], [ 29, 6, 1, 16 ],
[ 29, 6, 2, 32 ], [ 29, 6, 4, 32 ], [ 29, 6, 5, 16 ], [ 29, 6, 9, 32 ],
[ 29, 6, 13, 32 ], [ 29, 7, 1, 16 ], [ 29, 7, 2, 32 ], [ 29, 7, 4, 32 ],
[ 29, 7, 5, 16 ], [ 29, 7, 9, 32 ], [ 29, 7, 13, 32 ], [ 29, 8, 1, 16 ],
[ 29, 8, 2, 32 ], [ 29, 8, 4, 32 ], [ 29, 8, 5, 16 ], [ 29, 8, 9, 32 ],
[ 29, 8, 13, 32 ], [ 29, 9, 1, 8 ], [ 29, 9, 2, 16 ], [ 29, 9, 4, 16 ],
[ 29, 9, 5, 8 ], [ 29, 9, 6, 8 ], [ 29, 9, 8, 8 ], [ 29, 9, 9, 8 ],
[ 29, 9, 13, 16 ], [ 29, 10, 1, 8 ], [ 29, 10, 2, 16 ], [ 29, 10, 4, 16 ],
[ 29, 10, 5, 8 ], [ 29, 10, 9, 16 ], [ 29, 10, 13, 16 ], [ 29, 11, 1, 8 ],
[ 29, 11, 2, 16 ], [ 29, 11, 4, 16 ], [ 29, 11, 5, 8 ], [ 29, 11, 9, 16 ],
[ 29, 11, 13, 16 ], [ 29, 12, 1, 8 ], [ 29, 12, 2, 16 ], [ 29, 12, 4, 16 ],
[ 29, 12, 5, 8 ], [ 29, 12, 9, 16 ], [ 29, 12, 13, 16 ], [ 29, 13, 1, 8 ],
[ 29, 13, 2, 16 ], [ 29, 13, 4, 16 ], [ 29, 13, 5, 8 ], [ 29, 13, 9, 16 ],
[ 29, 13, 13, 16 ], [ 30, 1, 2, 64 ], [ 30, 1, 9, 64 ], [ 30, 1, 11, 64 ],
[ 30, 1, 15, 64 ], [ 30, 2, 2, 32 ], [ 30, 2, 9, 32 ], [ 30, 2, 11, 32 ],
[ 30, 2, 15, 32 ], [ 30, 3, 2, 32 ], [ 30, 3, 9, 32 ], [ 30, 3, 11, 32 ],
[ 30, 3, 15, 32 ], [ 30, 4, 3, 32 ], [ 30, 4, 6, 32 ], [ 30, 4, 8, 32 ],
[ 30, 4, 11, 32 ], [ 30, 4, 17, 32 ], [ 30, 4, 22, 32 ], [ 30, 5, 2, 32 ],
[ 30, 5, 4, 32 ], [ 30, 5, 6, 32 ], [ 30, 5, 9, 32 ], [ 30, 5, 11, 32 ],
[ 30, 5, 14, 32 ], [ 30, 5, 16, 32 ], [ 30, 5, 18, 32 ], [ 30, 6, 2, 32 ],
[ 30, 6, 4, 32 ], [ 30, 6, 6, 32 ], [ 30, 6, 9, 32 ], [ 30, 6, 11, 32 ],
[ 30, 6, 14, 32 ], [ 30, 6, 16, 32 ], [ 30, 6, 18, 32 ], [ 30, 7, 2, 32 ],
[ 30, 7, 4, 32 ], [ 30, 7, 5, 32 ], [ 30, 7, 6, 32 ], [ 30, 7, 8, 32 ],
[ 30, 7, 13, 32 ], [ 30, 7, 15, 32 ], [ 30, 7, 16, 32 ], [ 30, 7, 18, 32 ],
[ 30, 7, 20, 32 ], [ 30, 7, 22, 32 ], [ 30, 7, 31, 32 ], [ 30, 8, 3, 16 ],
[ 30, 8, 8, 32 ], [ 30, 8, 9, 32 ], [ 30, 8, 12, 16 ], [ 30, 8, 15, 16 ],
[ 30, 8, 19, 16 ], [ 30, 9, 3, 16 ], [ 30, 9, 8, 16 ], [ 30, 9, 9, 32 ],
[ 30, 9, 12, 16 ], [ 30, 9, 15, 16 ], [ 30, 9, 19, 16 ], [ 30, 10, 3, 16 ],
[ 30, 10, 8, 32 ], [ 30, 10, 9, 16 ], [ 30, 10, 12, 16 ],
[ 30, 10, 15, 16 ], [ 30, 10, 19, 16 ], [ 30, 11, 2, 16 ],
[ 30, 11, 4, 16 ], [ 30, 11, 5, 16 ], [ 30, 11, 6, 16 ], [ 30, 11, 8, 16 ],
[ 30, 11, 13, 16 ], [ 30, 11, 15, 16 ], [ 30, 11, 16, 16 ],
[ 30, 11, 18, 16 ], [ 30, 11, 20, 16 ], [ 30, 11, 22, 16 ],
[ 30, 11, 31, 16 ], [ 30, 12, 3, 16 ], [ 30, 12, 6, 16 ], [ 30, 12, 8, 16 ],
[ 30, 12, 11, 16 ], [ 30, 12, 17, 16 ], [ 30, 12, 22, 16 ],
[ 30, 13, 2, 32 ], [ 30, 13, 12, 32 ], [ 31, 2, 36, 64 ], [ 31, 2, 51, 64 ],
[ 31, 3, 38, 64 ], [ 31, 3, 49, 64 ], [ 31, 4, 10, 64 ], [ 31, 5, 6, 64 ],
[ 31, 5, 8, 64 ], [ 31, 5, 13, 64 ], [ 31, 5, 21, 64 ], [ 31, 6, 5, 64 ],
[ 31, 6, 7, 64 ], [ 31, 6, 9, 64 ], [ 31, 6, 14, 64 ], [ 31, 6, 16, 64 ],
[ 31, 6, 18, 64 ], [ 31, 6, 30, 64 ], [ 31, 6, 32, 64 ], [ 31, 7, 5, 64 ],
[ 31, 7, 7, 64 ], [ 31, 7, 9, 64 ], [ 31, 7, 14, 64 ], [ 31, 8, 5, 64 ],
[ 31, 8, 7, 64 ], [ 31, 8, 9, 64 ], [ 31, 8, 14, 64 ], [ 31, 9, 36, 32 ],
[ 31, 9, 50, 32 ], [ 31, 10, 7, 32 ], [ 31, 10, 14, 32 ],
[ 31, 10, 44, 64 ], [ 31, 11, 36, 32 ], [ 31, 11, 50, 32 ],
[ 31, 12, 5, 32 ], [ 31, 12, 7, 32 ], [ 31, 12, 10, 32 ],
[ 31, 12, 14, 32 ], [ 31, 12, 16, 32 ], [ 31, 12, 18, 32 ],
[ 31, 12, 30, 32 ], [ 31, 12, 32, 32 ], [ 31, 13, 6, 32 ],
[ 31, 13, 8, 32 ], [ 31, 13, 14, 32 ], [ 31, 13, 16, 32 ],
[ 31, 13, 17, 32 ], [ 31, 13, 25, 32 ], [ 31, 14, 49, 64 ],
[ 31, 15, 12, 64 ], [ 31, 16, 38, 32 ], [ 31, 16, 49, 32 ],
[ 31, 17, 23, 32 ], [ 31, 17, 37, 64 ], [ 31, 18, 6, 32 ],
[ 31, 18, 8, 32 ], [ 31, 18, 13, 32 ], [ 31, 18, 21, 32 ],
[ 31, 18, 41, 32 ], [ 31, 18, 57, 64 ], [ 31, 19, 6, 32 ],
[ 31, 19, 8, 32 ], [ 31, 19, 13, 32 ], [ 31, 19, 21, 32 ],
[ 31, 19, 41, 32 ], [ 31, 19, 57, 64 ], [ 31, 20, 6, 32 ],
[ 31, 20, 8, 32 ], [ 31, 20, 13, 32 ], [ 31, 20, 21, 32 ],
[ 31, 20, 41, 64 ], [ 31, 20, 57, 32 ], [ 31, 21, 13, 64 ],
[ 31, 22, 5, 32 ], [ 31, 22, 7, 32 ], [ 31, 22, 9, 32 ], [ 31, 22, 14, 32 ],
[ 31, 23, 38, 32 ], [ 31, 23, 52, 32 ], [ 31, 24, 6, 32 ],
[ 31, 24, 8, 32 ], [ 31, 24, 14, 32 ], [ 31, 24, 16, 32 ],
[ 31, 24, 17, 32 ], [ 31, 24, 25, 32 ], [ 31, 24, 37, 32 ],
[ 31, 24, 49, 32 ], [ 31, 25, 6, 32 ], [ 31, 25, 8, 32 ],
[ 31, 25, 14, 32 ], [ 31, 25, 16, 32 ], [ 31, 25, 17, 32 ],
[ 31, 25, 25, 32 ], [ 31, 25, 33, 32 ], [ 31, 25, 45, 32 ],
[ 31, 26, 6, 32 ], [ 31, 26, 8, 32 ], [ 31, 26, 11, 32 ],
[ 31, 26, 15, 64 ], [ 31, 26, 18, 32 ], [ 31, 26, 34, 32 ],
[ 31, 27, 5, 32 ], [ 31, 27, 7, 32 ], [ 31, 27, 9, 32 ], [ 31, 27, 14, 32 ],
[ 31, 27, 16, 32 ], [ 31, 27, 18, 32 ], [ 31, 27, 30, 32 ],
[ 31, 27, 32, 32 ], [ 31, 28, 5, 32 ], [ 31, 28, 7, 32 ], [ 31, 28, 9, 32 ],
[ 31, 28, 14, 32 ], [ 31, 28, 16, 32 ], [ 31, 28, 18, 32 ],
[ 31, 28, 30, 32 ], [ 31, 28, 32, 32 ], [ 31, 29, 5, 32 ],
[ 31, 29, 11, 32 ], [ 31, 29, 14, 32 ], [ 31, 29, 16, 32 ],
[ 31, 29, 17, 32 ], [ 31, 29, 25, 32 ], [ 31, 30, 5, 32 ],
[ 31, 30, 7, 32 ], [ 31, 30, 11, 32 ], [ 31, 30, 13, 32 ],
[ 31, 31, 2, 32 ], [ 31, 31, 3, 32 ], [ 31, 31, 4, 32 ], [ 31, 31, 6, 32 ],
[ 31, 31, 7, 32 ], [ 31, 31, 8, 32 ], [ 31, 32, 6, 32 ], [ 31, 32, 8, 32 ],
[ 31, 32, 11, 32 ], [ 31, 32, 15, 64 ], [ 31, 32, 18, 32 ],
[ 31, 32, 34, 32 ], [ 31, 33, 6, 32 ], [ 31, 33, 8, 32 ],
[ 31, 33, 11, 32 ], [ 31, 33, 15, 64 ], [ 31, 33, 18, 32 ],
[ 31, 33, 34, 32 ] ]
k = 11: F-action on Pi is () [31,1,11]
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 0 modulo 4: 1/128 q^2 ( q^4-4*q^3+16*q-16 )
q congruent 1 modulo 4: 1/128 phi1 phi2^3 ( q^2-6*q+9 )
q congruent 2 modulo 4: 1/128 q^2 ( q^4-4*q^3+16*q-16 )
q congruent 3 modulo 4: 1/128 phi1 phi2^3 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 2, 8 ], [ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ],
[ 5, 1, 1, 4 ], [ 7, 1, 3, 16 ], [ 7, 2, 3, 8 ], [ 7, 3, 3, 8 ],
[ 7, 4, 3, 8 ], [ 7, 5, 3, 4 ], [ 9, 1, 3, 16 ], [ 9, 1, 6, 16 ],
[ 9, 1, 8, 16 ], [ 9, 2, 3, 8 ], [ 9, 2, 6, 8 ], [ 9, 2, 8, 8 ],
[ 9, 3, 3, 8 ], [ 9, 3, 6, 8 ], [ 9, 3, 8, 8 ], [ 9, 4, 3, 8 ],
[ 9, 4, 6, 8 ], [ 9, 4, 8, 8 ], [ 9, 5, 3, 4 ], [ 9, 5, 6, 4 ],
[ 9, 5, 8, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 5, 8 ], [ 12, 2, 1, 4 ],
[ 12, 2, 5, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 5, 4 ],
[ 15, 1, 5, 16 ], [ 16, 1, 4, 16 ], [ 16, 1, 6, 32 ], [ 16, 1, 13, 32 ],
[ 16, 2, 4, 8 ], [ 16, 2, 6, 16 ], [ 16, 2, 13, 16 ], [ 16, 3, 4, 8 ],
[ 16, 3, 6, 16 ], [ 16, 3, 13, 16 ], [ 16, 4, 4, 8 ], [ 16, 4, 6, 16 ],
[ 16, 4, 13, 16 ], [ 16, 5, 5, 16 ], [ 16, 5, 11, 16 ], [ 16, 5, 15, 16 ],
[ 16, 6, 5, 16 ], [ 16, 6, 11, 16 ], [ 16, 6, 15, 16 ], [ 16, 7, 5, 16 ],
[ 16, 7, 11, 16 ], [ 16, 7, 15, 16 ], [ 16, 8, 5, 16 ], [ 16, 9, 4, 4 ],
[ 16, 9, 6, 8 ], [ 16, 9, 13, 8 ], [ 16, 10, 5, 8 ], [ 16, 10, 11, 8 ],
[ 16, 10, 15, 8 ], [ 16, 11, 4, 8 ], [ 16, 11, 6, 8 ], [ 16, 11, 9, 8 ],
[ 16, 12, 5, 8 ], [ 16, 12, 11, 8 ], [ 16, 12, 15, 8 ], [ 16, 13, 4, 8 ],
[ 16, 13, 6, 8 ], [ 16, 13, 13, 8 ], [ 16, 14, 5, 8 ], [ 16, 14, 9, 16 ],
[ 16, 15, 4, 8 ], [ 16, 15, 6, 8 ], [ 16, 15, 13, 8 ], [ 16, 16, 4, 8 ],
[ 16, 16, 6, 8 ], [ 16, 16, 13, 8 ], [ 16, 17, 5, 8 ], [ 21, 1, 6, 32 ],
[ 21, 2, 7, 16 ], [ 21, 3, 9, 16 ], [ 21, 4, 7, 16 ], [ 21, 5, 7, 8 ],
[ 21, 6, 8, 16 ], [ 21, 7, 7, 16 ], [ 22, 1, 8, 32 ], [ 22, 2, 8, 16 ],
[ 22, 4, 8, 16 ], [ 25, 1, 6, 32 ], [ 25, 2, 4, 16 ], [ 26, 1, 6, 32 ],
[ 26, 2, 4, 16 ], [ 27, 1, 7, 64 ], [ 27, 1, 14, 32 ], [ 27, 2, 12, 32 ],
[ 27, 3, 10, 16 ], [ 27, 3, 15, 32 ], [ 27, 3, 21, 32 ], [ 27, 4, 14, 32 ],
[ 27, 5, 10, 16 ], [ 27, 5, 13, 32 ], [ 27, 6, 12, 16 ], [ 27, 7, 12, 16 ],
[ 27, 8, 10, 16 ], [ 27, 8, 15, 16 ], [ 27, 8, 21, 32 ], [ 27, 9, 8, 8 ],
[ 27, 9, 11, 16 ], [ 27, 9, 14, 16 ], [ 27, 10, 17, 16 ],
[ 27, 11, 10, 16 ], [ 27, 11, 15, 16 ], [ 27, 11, 21, 32 ],
[ 27, 12, 14, 32 ], [ 27, 13, 14, 16 ], [ 27, 14, 7, 16 ],
[ 27, 14, 17, 16 ], [ 27, 14, 21, 32 ], [ 29, 1, 17, 64 ],
[ 29, 2, 17, 32 ], [ 29, 3, 17, 32 ], [ 29, 4, 17, 32 ], [ 29, 5, 17, 32 ],
[ 29, 9, 17, 16 ], [ 30, 1, 12, 64 ], [ 30, 2, 12, 32 ], [ 30, 3, 12, 32 ],
[ 30, 4, 7, 32 ], [ 30, 5, 7, 32 ], [ 30, 6, 7, 32 ], [ 30, 8, 10, 32 ],
[ 30, 8, 11, 32 ], [ 30, 8, 13, 16 ], [ 30, 9, 10, 32 ], [ 30, 9, 11, 16 ],
[ 30, 9, 13, 32 ], [ 30, 10, 10, 16 ], [ 30, 10, 11, 32 ],
[ 30, 10, 13, 32 ], [ 30, 12, 7, 32 ], [ 31, 2, 15, 64 ], [ 31, 2, 33, 64 ],
[ 31, 3, 15, 64 ], [ 31, 3, 31, 64 ], [ 31, 4, 11, 64 ], [ 31, 5, 29, 64 ],
[ 31, 6, 10, 64 ], [ 31, 7, 10, 64 ], [ 31, 8, 10, 64 ], [ 31, 9, 15, 32 ],
[ 31, 9, 32, 32 ], [ 31, 10, 10, 32 ], [ 31, 10, 33, 32 ],
[ 31, 10, 45, 64 ], [ 31, 11, 13, 32 ], [ 31, 11, 31, 64 ],
[ 31, 12, 9, 32 ], [ 31, 13, 41, 64 ], [ 31, 14, 36, 64 ],
[ 31, 15, 32, 64 ], [ 31, 16, 15, 32 ], [ 31, 16, 31, 32 ],
[ 31, 17, 9, 32 ], [ 31, 17, 13, 64 ], [ 31, 18, 33, 64 ],
[ 31, 18, 45, 32 ], [ 31, 18, 53, 64 ], [ 31, 19, 33, 64 ],
[ 31, 19, 45, 32 ], [ 31, 19, 53, 64 ], [ 31, 20, 33, 64 ],
[ 31, 20, 45, 64 ], [ 31, 20, 53, 32 ], [ 31, 21, 28, 64 ],
[ 31, 22, 10, 32 ], [ 31, 23, 13, 32 ], [ 31, 23, 32, 64 ],
[ 31, 24, 33, 32 ], [ 31, 25, 37, 32 ], [ 31, 26, 9, 64 ],
[ 31, 26, 12, 32 ], [ 31, 26, 14, 64 ], [ 31, 27, 10, 32 ],
[ 31, 28, 10, 32 ], [ 31, 29, 38, 64 ], [ 31, 32, 9, 64 ],
[ 31, 32, 12, 32 ], [ 31, 32, 14, 64 ], [ 31, 33, 9, 64 ],
[ 31, 33, 12, 32 ], [ 31, 33, 14, 64 ] ]
k = 12: F-action on Pi is () [31,1,12]
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 0 modulo 4: 1/32 q^3 ( q^3-2*q^2-2*q+4 )
q congruent 1 modulo 4: 1/32 phi1^2 phi2 ( q^3-q^2-5*q+1 )
q congruent 2 modulo 4: 1/32 q^3 ( q^3-2*q^2-2*q+4 )
q congruent 3 modulo 4: 1/32 phi1^2 phi2 ( q^3-q^2-5*q+1 )
Fusion of maximal tori of C^F in those of G^F:
[ 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ],
[ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ],
[ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ], [ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ],
[ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ],
[ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ], [ 9, 1, 3, 8 ],
[ 9, 1, 4, 8 ], [ 9, 2, 3, 4 ], [ 9, 2, 4, 4 ], [ 9, 3, 3, 4 ],
[ 9, 3, 4, 4 ], [ 9, 4, 3, 4 ], [ 9, 4, 4, 4 ], [ 9, 5, 3, 2 ],
[ 9, 5, 4, 2 ], [ 12, 1, 2, 4 ], [ 12, 1, 4, 4 ], [ 12, 1, 5, 4 ],
[ 12, 2, 2, 2 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ], [ 12, 3, 3, 2 ],
[ 12, 3, 4, 2 ], [ 12, 4, 2, 2 ], [ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ],
[ 13, 1, 1, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 4 ],
[ 13, 2, 1, 2 ], [ 13, 2, 2, 2 ], [ 13, 2, 3, 2 ], [ 13, 2, 4, 2 ],
[ 14, 1, 3, 8 ], [ 14, 1, 4, 8 ], [ 14, 2, 3, 4 ], [ 14, 2, 4, 4 ],
[ 16, 1, 2, 8 ], [ 16, 1, 4, 8 ], [ 16, 1, 7, 16 ], [ 16, 1, 11, 16 ],
[ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 2, 7, 8 ], [ 16, 2, 11, 8 ],
[ 16, 3, 2, 4 ], [ 16, 3, 4, 4 ], [ 16, 3, 7, 8 ], [ 16, 3, 11, 8 ],
[ 16, 4, 2, 4 ], [ 16, 4, 4, 4 ], [ 16, 4, 7, 8 ], [ 16, 4, 11, 8 ],
[ 16, 5, 6, 8 ], [ 16, 5, 8, 8 ], [ 16, 6, 6, 8 ], [ 16, 6, 8, 8 ],
[ 16, 7, 6, 8 ], [ 16, 7, 8, 8 ], [ 16, 8, 2, 4 ], [ 16, 8, 3, 4 ],
[ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ], [ 16, 9, 2, 2 ], [ 16, 9, 4, 2 ],
[ 16, 9, 7, 4 ], [ 16, 9, 11, 4 ], [ 16, 10, 6, 4 ], [ 16, 10, 8, 4 ],
[ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ], [ 16, 11, 7, 2 ], [ 16, 11, 8, 8 ],
[ 16, 11, 9, 4 ], [ 16, 12, 6, 4 ], [ 16, 12, 8, 4 ], [ 16, 13, 2, 4 ],
[ 16, 13, 4, 4 ], [ 16, 13, 7, 4 ], [ 16, 13, 11, 8 ], [ 16, 14, 2, 2 ],
[ 16, 14, 3, 2 ], [ 16, 14, 7, 8 ], [ 16, 14, 10, 8 ], [ 16, 15, 2, 4 ],
[ 16, 15, 4, 4 ], [ 16, 15, 7, 4 ], [ 16, 15, 11, 8 ], [ 16, 16, 2, 4 ],
[ 16, 16, 4, 4 ], [ 16, 16, 7, 4 ], [ 16, 16, 11, 8 ], [ 16, 17, 2, 2 ],
[ 16, 17, 3, 2 ], [ 21, 1, 5, 8 ], [ 21, 1, 6, 8 ], [ 21, 1, 7, 8 ],
[ 21, 1, 8, 8 ], [ 21, 2, 2, 4 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 4 ],
[ 21, 2, 9, 4 ], [ 21, 3, 3, 4 ], [ 21, 3, 4, 4 ], [ 21, 3, 8, 4 ],
[ 21, 3, 9, 4 ], [ 21, 4, 2, 4 ], [ 21, 4, 5, 4 ], [ 21, 4, 7, 4 ],
[ 21, 4, 9, 4 ], [ 21, 5, 2, 2 ], [ 21, 5, 5, 2 ], [ 21, 5, 7, 2 ],
[ 21, 5, 9, 2 ], [ 21, 6, 3, 4 ], [ 21, 6, 4, 4 ], [ 21, 6, 8, 4 ],
[ 21, 6, 9, 4 ], [ 21, 7, 2, 4 ], [ 21, 7, 5, 4 ], [ 21, 7, 7, 4 ],
[ 21, 7, 9, 4 ], [ 22, 1, 7, 8 ], [ 22, 1, 8, 8 ], [ 22, 1, 9, 8 ],
[ 22, 1, 10, 8 ], [ 22, 2, 7, 4 ], [ 22, 2, 8, 4 ], [ 22, 2, 9, 4 ],
[ 22, 2, 10, 4 ], [ 22, 3, 5, 4 ], [ 22, 3, 6, 4 ], [ 22, 3, 7, 4 ],
[ 22, 3, 8, 4 ], [ 22, 4, 7, 2 ], [ 22, 4, 8, 4 ], [ 22, 4, 9, 2 ],
[ 22, 4, 10, 4 ], [ 27, 1, 8, 16 ], [ 27, 1, 9, 16 ], [ 27, 1, 13, 16 ],
[ 27, 2, 5, 8 ], [ 27, 2, 7, 8 ], [ 27, 2, 14, 8 ], [ 27, 2, 17, 8 ],
[ 27, 3, 5, 8 ], [ 27, 3, 9, 8 ], [ 27, 3, 17, 8 ], [ 27, 3, 19, 8 ],
[ 27, 3, 20, 8 ], [ 27, 3, 22, 8 ], [ 27, 4, 4, 8 ], [ 27, 4, 9, 8 ],
[ 27, 4, 13, 8 ], [ 27, 4, 18, 8 ], [ 27, 5, 5, 8 ], [ 27, 5, 15, 8 ],
[ 27, 5, 19, 8 ], [ 27, 6, 5, 4 ], [ 27, 6, 7, 4 ], [ 27, 6, 14, 4 ],
[ 27, 6, 17, 4 ], [ 27, 7, 5, 4 ], [ 27, 7, 7, 4 ], [ 27, 7, 14, 4 ],
[ 27, 7, 17, 4 ], [ 27, 8, 5, 4 ], [ 27, 8, 9, 8 ], [ 27, 8, 17, 4 ],
[ 27, 8, 19, 8 ], [ 27, 8, 20, 8 ], [ 27, 8, 22, 8 ], [ 27, 9, 5, 4 ],
[ 27, 9, 15, 4 ], [ 27, 9, 17, 4 ], [ 27, 9, 20, 8 ], [ 27, 10, 7, 4 ],
[ 27, 10, 8, 4 ], [ 27, 10, 15, 4 ], [ 27, 10, 16, 4 ], [ 27, 11, 5, 4 ],
[ 27, 11, 9, 8 ], [ 27, 11, 17, 4 ], [ 27, 11, 19, 8 ], [ 27, 11, 20, 8 ],
[ 27, 11, 22, 8 ], [ 27, 12, 4, 8 ], [ 27, 12, 9, 8 ], [ 27, 12, 13, 8 ],
[ 27, 12, 18, 8 ], [ 27, 13, 4, 4 ], [ 27, 13, 9, 4 ], [ 27, 13, 13, 4 ],
[ 27, 13, 18, 4 ], [ 27, 14, 4, 4 ], [ 27, 14, 9, 8 ], [ 27, 14, 16, 4 ],
[ 27, 14, 19, 8 ], [ 27, 14, 20, 8 ], [ 27, 14, 22, 8 ], [ 28, 1, 5, 16 ],
[ 28, 1, 7, 16 ], [ 28, 2, 5, 8 ], [ 28, 2, 7, 8 ], [ 28, 3, 5, 8 ],
[ 28, 3, 7, 8 ], [ 28, 5, 5, 8 ], [ 28, 5, 7, 8 ], [ 28, 6, 5, 8 ],
[ 28, 6, 7, 8 ], [ 30, 1, 5, 16 ], [ 30, 1, 18, 16 ], [ 30, 2, 5, 8 ],
[ 30, 2, 18, 8 ], [ 30, 3, 5, 8 ], [ 30, 3, 18, 8 ], [ 30, 4, 4, 8 ],
[ 30, 4, 9, 8 ], [ 30, 4, 18, 8 ], [ 30, 4, 23, 8 ], [ 30, 8, 4, 4 ],
[ 30, 8, 20, 4 ], [ 30, 9, 4, 8 ], [ 30, 9, 20, 8 ], [ 30, 10, 4, 8 ],
[ 30, 10, 20, 8 ], [ 30, 12, 4, 8 ], [ 30, 12, 9, 8 ], [ 30, 12, 18, 8 ],
[ 30, 12, 23, 8 ], [ 30, 13, 5, 8 ], [ 30, 13, 7, 8 ], [ 30, 13, 15, 8 ],
[ 30, 13, 17, 8 ], [ 31, 2, 21, 16 ], [ 31, 2, 28, 16 ], [ 31, 2, 29, 16 ],
[ 31, 3, 21, 16 ], [ 31, 3, 28, 16 ], [ 31, 3, 29, 16 ], [ 31, 4, 12, 16 ],
[ 31, 5, 26, 16 ], [ 31, 5, 28, 16 ], [ 31, 9, 21, 8 ], [ 31, 9, 28, 8 ],
[ 31, 9, 29, 8 ], [ 31, 10, 17, 8 ], [ 31, 10, 21, 8 ], [ 31, 10, 29, 8 ],
[ 31, 10, 47, 16 ], [ 31, 11, 21, 16 ], [ 31, 11, 28, 16 ],
[ 31, 11, 29, 8 ], [ 31, 13, 34, 16 ], [ 31, 13, 36, 16 ],
[ 31, 13, 38, 16 ], [ 31, 13, 40, 16 ], [ 31, 14, 25, 16 ],
[ 31, 14, 26, 16 ], [ 31, 14, 32, 16 ], [ 31, 14, 33, 16 ],
[ 31, 15, 15, 16 ], [ 31, 15, 17, 16 ], [ 31, 15, 34, 16 ],
[ 31, 15, 37, 16 ], [ 31, 16, 21, 8 ], [ 31, 16, 28, 8 ], [ 31, 16, 29, 8 ],
[ 31, 17, 19, 8 ], [ 31, 17, 29, 16 ], [ 31, 18, 30, 16 ],
[ 31, 18, 32, 16 ], [ 31, 19, 30, 16 ], [ 31, 19, 32, 16 ],
[ 31, 20, 30, 16 ], [ 31, 20, 32, 16 ], [ 31, 21, 14, 16 ],
[ 31, 21, 18, 16 ], [ 31, 21, 29, 16 ], [ 31, 21, 33, 16 ],
[ 31, 23, 21, 16 ], [ 31, 23, 28, 8 ], [ 31, 23, 29, 16 ],
[ 31, 26, 21, 16 ], [ 31, 26, 37, 16 ], [ 31, 29, 32, 16 ],
[ 31, 29, 36, 16 ], [ 31, 29, 39, 16 ], [ 31, 29, 43, 16 ],
[ 31, 32, 21, 16 ], [ 31, 32, 37, 16 ], [ 31, 33, 21, 16 ],
[ 31, 33, 37, 16 ] ]
k = 13: F-action on Pi is () [31,1,13]
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 0 modulo 4: 1/128 q^3 ( q^3-4*q^2+8 )
q congruent 1 modulo 4: 1/128 phi1^2 ( q^4-2*q^3-8*q^2-14*q+87 )
q congruent 2 modulo 4: 1/128 q^3 ( q^3-4*q^2+8 )
q congruent 3 modulo 4: 1/128 ( q^6-4*q^5-3*q^4+107*q^2-156*q-9 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 8 ],
[ 6, 1, 2, 16 ], [ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ],
[ 7, 4, 4, 8 ], [ 7, 5, 4, 4 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 20 ],
[ 9, 1, 1, 16 ], [ 9, 1, 2, 32 ], [ 9, 1, 5, 16 ], [ 9, 1, 7, 16 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 16 ], [ 9, 2, 5, 8 ], [ 9, 2, 7, 8 ],
[ 9, 3, 1, 8 ], [ 9, 3, 2, 16 ], [ 9, 3, 5, 8 ], [ 9, 3, 7, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 16 ], [ 9, 4, 5, 8 ], [ 9, 4, 7, 8 ],
[ 9, 5, 1, 4 ], [ 9, 5, 2, 8 ], [ 9, 5, 5, 4 ], [ 9, 5, 7, 4 ],
[ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ], [ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ],
[ 12, 1, 2, 8 ], [ 12, 1, 3, 8 ], [ 12, 2, 2, 4 ], [ 12, 2, 3, 4 ],
[ 12, 3, 2, 4 ], [ 12, 4, 2, 4 ], [ 12, 4, 3, 2 ], [ 13, 1, 3, 16 ],
[ 13, 1, 4, 16 ], [ 13, 2, 3, 8 ], [ 13, 2, 4, 8 ], [ 14, 1, 2, 32 ],
[ 14, 2, 2, 16 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 40 ],
[ 15, 1, 4, 24 ], [ 16, 1, 3, 32 ], [ 16, 1, 5, 32 ], [ 16, 1, 12, 32 ],
[ 16, 2, 3, 16 ], [ 16, 2, 5, 16 ], [ 16, 2, 12, 16 ], [ 16, 3, 3, 16 ],
[ 16, 3, 5, 16 ], [ 16, 3, 12, 16 ], [ 16, 4, 3, 16 ], [ 16, 4, 5, 16 ],
[ 16, 4, 12, 16 ], [ 16, 5, 2, 16 ], [ 16, 5, 3, 16 ], [ 16, 5, 4, 16 ],
[ 16, 5, 10, 16 ], [ 16, 5, 14, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 3, 16 ],
[ 16, 6, 4, 16 ], [ 16, 6, 10, 16 ], [ 16, 6, 14, 16 ], [ 16, 7, 2, 16 ],
[ 16, 7, 3, 16 ], [ 16, 7, 4, 16 ], [ 16, 7, 10, 16 ], [ 16, 7, 14, 16 ],
[ 16, 8, 4, 16 ], [ 16, 9, 3, 8 ], [ 16, 9, 5, 8 ], [ 16, 9, 12, 8 ],
[ 16, 10, 2, 8 ], [ 16, 10, 3, 8 ], [ 16, 10, 4, 8 ], [ 16, 10, 10, 8 ],
[ 16, 10, 14, 8 ], [ 16, 11, 3, 16 ], [ 16, 11, 5, 8 ], [ 16, 12, 2, 8 ],
[ 16, 12, 3, 8 ], [ 16, 12, 4, 8 ], [ 16, 12, 10, 8 ], [ 16, 12, 14, 8 ],
[ 16, 13, 3, 8 ], [ 16, 13, 5, 8 ], [ 16, 13, 12, 8 ], [ 16, 14, 4, 8 ],
[ 16, 14, 8, 16 ], [ 16, 15, 3, 8 ], [ 16, 15, 5, 8 ], [ 16, 15, 12, 8 ],
[ 16, 16, 3, 8 ], [ 16, 16, 5, 8 ], [ 16, 16, 12, 8 ], [ 16, 17, 4, 8 ],
[ 17, 1, 2, 16 ], [ 17, 2, 2, 8 ], [ 18, 1, 2, 8 ], [ 18, 1, 3, 16 ],
[ 18, 1, 4, 24 ], [ 18, 2, 2, 4 ], [ 18, 2, 3, 8 ], [ 18, 2, 4, 12 ],
[ 19, 1, 2, 32 ], [ 19, 2, 2, 16 ], [ 19, 3, 2, 16 ], [ 19, 4, 2, 16 ],
[ 19, 5, 2, 8 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 24 ],
[ 20, 2, 2, 4 ], [ 20, 2, 3, 8 ], [ 20, 2, 4, 12 ], [ 21, 1, 7, 32 ],
[ 21, 2, 9, 16 ], [ 21, 3, 8, 16 ], [ 21, 4, 9, 16 ], [ 21, 5, 9, 8 ],
[ 21, 6, 9, 16 ], [ 21, 7, 9, 16 ], [ 22, 1, 2, 16 ], [ 22, 1, 3, 32 ],
[ 22, 1, 5, 48 ], [ 22, 1, 6, 32 ], [ 22, 2, 2, 8 ], [ 22, 2, 3, 16 ],
[ 22, 2, 5, 24 ], [ 22, 2, 6, 16 ], [ 22, 3, 2, 16 ], [ 22, 3, 4, 16 ],
[ 22, 4, 2, 8 ], [ 22, 4, 3, 8 ], [ 22, 4, 5, 24 ], [ 22, 4, 6, 8 ],
[ 23, 1, 3, 16 ], [ 23, 1, 6, 32 ], [ 23, 1, 7, 16 ], [ 23, 1, 8, 32 ],
[ 23, 2, 3, 8 ], [ 23, 2, 6, 16 ], [ 23, 2, 7, 8 ], [ 23, 2, 8, 16 ],
[ 23, 3, 3, 8 ], [ 23, 3, 6, 16 ], [ 23, 3, 7, 8 ], [ 23, 3, 8, 16 ],
[ 23, 4, 3, 8 ], [ 23, 4, 6, 16 ], [ 23, 4, 7, 8 ], [ 23, 4, 8, 16 ],
[ 23, 5, 3, 8 ], [ 23, 5, 6, 16 ], [ 23, 5, 7, 8 ], [ 23, 5, 8, 16 ],
[ 23, 6, 3, 4 ], [ 23, 6, 6, 8 ], [ 23, 6, 7, 4 ], [ 23, 6, 8, 8 ],
[ 24, 1, 3, 32 ], [ 24, 1, 4, 32 ], [ 24, 2, 3, 16 ], [ 24, 2, 4, 16 ],
[ 25, 1, 2, 16 ], [ 25, 1, 3, 32 ], [ 25, 1, 4, 48 ], [ 25, 1, 7, 32 ],
[ 25, 2, 2, 8 ], [ 25, 2, 5, 16 ], [ 25, 2, 6, 16 ], [ 25, 2, 8, 24 ],
[ 25, 3, 3, 16 ], [ 25, 3, 5, 8 ], [ 25, 3, 6, 16 ], [ 25, 3, 7, 24 ],
[ 25, 3, 8, 16 ], [ 26, 1, 2, 16 ], [ 26, 1, 3, 32 ], [ 26, 1, 4, 48 ],
[ 26, 1, 7, 32 ], [ 26, 2, 2, 8 ], [ 26, 2, 5, 16 ], [ 26, 2, 8, 16 ],
[ 26, 2, 10, 24 ], [ 26, 3, 3, 16 ], [ 26, 3, 5, 8 ], [ 26, 3, 6, 16 ],
[ 26, 3, 7, 24 ], [ 26, 3, 8, 16 ], [ 27, 1, 10, 64 ], [ 27, 1, 12, 32 ],
[ 27, 2, 9, 32 ], [ 27, 3, 7, 16 ], [ 27, 3, 8, 32 ], [ 27, 3, 12, 32 ],
[ 27, 4, 8, 32 ], [ 27, 5, 8, 16 ], [ 27, 5, 9, 32 ], [ 27, 6, 9, 16 ],
[ 27, 7, 9, 16 ], [ 27, 8, 7, 16 ], [ 27, 8, 8, 32 ], [ 27, 8, 12, 16 ],
[ 27, 9, 6, 8 ], [ 27, 9, 7, 16 ], [ 27, 9, 10, 16 ], [ 27, 10, 6, 16 ],
[ 27, 11, 7, 16 ], [ 27, 11, 8, 32 ], [ 27, 11, 12, 16 ], [ 27, 12, 8, 32 ],
[ 27, 13, 8, 16 ], [ 27, 14, 6, 16 ], [ 27, 14, 10, 32 ],
[ 27, 14, 12, 16 ], [ 28, 1, 9, 64 ], [ 28, 2, 9, 32 ], [ 28, 3, 9, 32 ],
[ 28, 4, 6, 32 ], [ 28, 4, 8, 32 ], [ 28, 5, 9, 16 ], [ 28, 6, 9, 32 ],
[ 29, 1, 3, 32 ], [ 29, 1, 6, 32 ], [ 29, 1, 7, 32 ], [ 29, 1, 8, 32 ],
[ 29, 1, 10, 64 ], [ 29, 1, 11, 32 ], [ 29, 1, 12, 64 ], [ 29, 1, 15, 64 ],
[ 29, 2, 3, 16 ], [ 29, 2, 6, 16 ], [ 29, 2, 7, 16 ], [ 29, 2, 8, 16 ],
[ 29, 2, 10, 32 ], [ 29, 2, 11, 16 ], [ 29, 2, 12, 32 ], [ 29, 2, 15, 32 ],
[ 29, 3, 3, 16 ], [ 29, 3, 6, 16 ], [ 29, 3, 7, 16 ], [ 29, 3, 8, 16 ],
[ 29, 3, 10, 32 ], [ 29, 3, 11, 16 ], [ 29, 3, 12, 32 ], [ 29, 3, 15, 32 ],
[ 29, 4, 3, 16 ], [ 29, 4, 6, 16 ], [ 29, 4, 7, 16 ], [ 29, 4, 8, 16 ],
[ 29, 4, 10, 32 ], [ 29, 4, 11, 16 ], [ 29, 4, 12, 32 ], [ 29, 4, 15, 32 ],
[ 29, 5, 3, 16 ], [ 29, 5, 6, 16 ], [ 29, 5, 7, 16 ], [ 29, 5, 8, 16 ],
[ 29, 5, 10, 32 ], [ 29, 5, 11, 16 ], [ 29, 5, 12, 32 ], [ 29, 5, 15, 32 ],
[ 29, 6, 3, 16 ], [ 29, 6, 6, 32 ], [ 29, 6, 7, 16 ], [ 29, 6, 8, 32 ],
[ 29, 6, 11, 32 ], [ 29, 6, 15, 32 ], [ 29, 7, 3, 16 ], [ 29, 7, 6, 32 ],
[ 29, 7, 7, 16 ], [ 29, 7, 8, 32 ], [ 29, 7, 11, 32 ], [ 29, 7, 15, 32 ],
[ 29, 8, 3, 16 ], [ 29, 8, 6, 32 ], [ 29, 8, 7, 16 ], [ 29, 8, 8, 32 ],
[ 29, 8, 11, 32 ], [ 29, 8, 15, 32 ], [ 29, 9, 3, 8 ], [ 29, 9, 6, 8 ],
[ 29, 9, 7, 8 ], [ 29, 9, 8, 8 ], [ 29, 9, 10, 16 ], [ 29, 9, 11, 8 ],
[ 29, 9, 12, 16 ], [ 29, 9, 15, 16 ], [ 29, 10, 3, 8 ], [ 29, 10, 6, 16 ],
[ 29, 10, 7, 8 ], [ 29, 10, 8, 16 ], [ 29, 10, 11, 16 ], [ 29, 10, 15, 16 ],
[ 29, 11, 3, 8 ], [ 29, 11, 6, 16 ], [ 29, 11, 7, 8 ], [ 29, 11, 8, 16 ],
[ 29, 11, 11, 16 ], [ 29, 11, 15, 16 ], [ 29, 12, 3, 8 ], [ 29, 12, 6, 16 ],
[ 29, 12, 7, 8 ], [ 29, 12, 8, 16 ], [ 29, 12, 11, 16 ], [ 29, 12, 15, 16 ],
[ 29, 13, 3, 8 ], [ 29, 13, 6, 16 ], [ 29, 13, 7, 8 ], [ 29, 13, 8, 16 ],
[ 29, 13, 11, 16 ], [ 29, 13, 15, 16 ], [ 30, 1, 10, 64 ],
[ 30, 1, 22, 64 ], [ 30, 1, 23, 64 ], [ 30, 1, 24, 64 ], [ 30, 2, 10, 32 ],
[ 30, 2, 22, 32 ], [ 30, 2, 23, 32 ], [ 30, 2, 24, 32 ], [ 30, 3, 10, 32 ],
[ 30, 3, 22, 32 ], [ 30, 3, 23, 32 ], [ 30, 3, 24, 32 ], [ 30, 4, 10, 32 ],
[ 30, 4, 13, 32 ], [ 30, 4, 20, 32 ], [ 30, 4, 24, 32 ], [ 30, 4, 25, 32 ],
[ 30, 4, 27, 32 ], [ 30, 5, 10, 32 ], [ 30, 5, 13, 32 ], [ 30, 5, 20, 32 ],
[ 30, 5, 23, 32 ], [ 30, 5, 24, 32 ], [ 30, 5, 25, 32 ], [ 30, 5, 27, 32 ],
[ 30, 5, 28, 32 ], [ 30, 6, 10, 32 ], [ 30, 6, 12, 32 ], [ 30, 6, 20, 32 ],
[ 30, 6, 23, 32 ], [ 30, 6, 24, 32 ], [ 30, 6, 25, 32 ], [ 30, 6, 26, 32 ],
[ 30, 6, 28, 32 ], [ 30, 7, 7, 32 ], [ 30, 7, 10, 32 ], [ 30, 7, 12, 32 ],
[ 30, 7, 14, 32 ], [ 30, 7, 21, 32 ], [ 30, 7, 23, 32 ], [ 30, 7, 24, 32 ],
[ 30, 7, 26, 32 ], [ 30, 7, 28, 32 ], [ 30, 7, 29, 32 ], [ 30, 7, 30, 32 ],
[ 30, 7, 32, 32 ], [ 30, 8, 14, 16 ], [ 30, 8, 24, 32 ], [ 30, 8, 25, 32 ],
[ 30, 8, 28, 16 ], [ 30, 8, 30, 16 ], [ 30, 8, 31, 16 ], [ 30, 9, 14, 16 ],
[ 30, 9, 24, 16 ], [ 30, 9, 25, 32 ], [ 30, 9, 28, 16 ], [ 30, 9, 30, 16 ],
[ 30, 9, 31, 16 ], [ 30, 10, 14, 16 ], [ 30, 10, 24, 32 ],
[ 30, 10, 25, 16 ], [ 30, 10, 28, 16 ], [ 30, 10, 30, 16 ],
[ 30, 10, 31, 16 ], [ 30, 11, 7, 16 ], [ 30, 11, 10, 16 ],
[ 30, 11, 12, 16 ], [ 30, 11, 14, 16 ], [ 30, 11, 21, 16 ],
[ 30, 11, 23, 16 ], [ 30, 11, 24, 16 ], [ 30, 11, 26, 16 ],
[ 30, 11, 28, 16 ], [ 30, 11, 29, 16 ], [ 30, 11, 30, 16 ],
[ 30, 11, 32, 16 ], [ 30, 12, 10, 16 ], [ 30, 12, 13, 16 ],
[ 30, 12, 20, 16 ], [ 30, 12, 24, 16 ], [ 30, 12, 25, 16 ],
[ 30, 12, 27, 16 ], [ 30, 13, 9, 32 ], [ 30, 13, 19, 32 ],
[ 31, 2, 42, 64 ], [ 31, 2, 49, 64 ], [ 31, 3, 43, 64 ], [ 31, 3, 52, 64 ],
[ 31, 4, 13, 64 ], [ 31, 5, 15, 64 ], [ 31, 5, 18, 64 ], [ 31, 5, 20, 64 ],
[ 31, 5, 23, 64 ], [ 31, 6, 20, 64 ], [ 31, 6, 27, 64 ], [ 31, 6, 34, 64 ],
[ 31, 6, 41, 64 ], [ 31, 6, 47, 64 ], [ 31, 6, 49, 64 ], [ 31, 6, 51, 64 ],
[ 31, 6, 56, 64 ], [ 31, 7, 16, 64 ], [ 31, 7, 23, 64 ], [ 31, 7, 32, 64 ],
[ 31, 7, 38, 64 ], [ 31, 8, 16, 64 ], [ 31, 8, 23, 64 ], [ 31, 8, 33, 64 ],
[ 31, 8, 38, 64 ], [ 31, 9, 42, 32 ], [ 31, 9, 52, 32 ], [ 31, 10, 19, 32 ],
[ 31, 10, 23, 32 ], [ 31, 10, 50, 64 ], [ 31, 11, 41, 32 ],
[ 31, 11, 49, 32 ], [ 31, 12, 20, 32 ], [ 31, 12, 26, 32 ],
[ 31, 12, 34, 32 ], [ 31, 12, 40, 32 ], [ 31, 12, 47, 32 ],
[ 31, 12, 49, 32 ], [ 31, 12, 52, 32 ], [ 31, 12, 56, 32 ],
[ 31, 13, 19, 32 ], [ 31, 13, 22, 32 ], [ 31, 13, 24, 32 ],
[ 31, 13, 27, 32 ], [ 31, 13, 50, 32 ], [ 31, 13, 52, 32 ],
[ 31, 14, 50, 64 ], [ 31, 15, 19, 64 ], [ 31, 16, 43, 32 ],
[ 31, 16, 52, 32 ], [ 31, 17, 31, 32 ], [ 31, 17, 38, 64 ],
[ 31, 18, 15, 32 ], [ 31, 18, 18, 32 ], [ 31, 18, 20, 32 ],
[ 31, 18, 23, 32 ], [ 31, 18, 43, 32 ], [ 31, 18, 59, 64 ],
[ 31, 19, 15, 32 ], [ 31, 19, 18, 32 ], [ 31, 19, 20, 32 ],
[ 31, 19, 23, 32 ], [ 31, 19, 43, 32 ], [ 31, 19, 59, 64 ],
[ 31, 20, 15, 32 ], [ 31, 20, 18, 32 ], [ 31, 20, 20, 32 ],
[ 31, 20, 23, 32 ], [ 31, 20, 43, 64 ], [ 31, 20, 59, 32 ],
[ 31, 21, 19, 64 ], [ 31, 22, 16, 32 ], [ 31, 22, 23, 32 ],
[ 31, 22, 32, 32 ], [ 31, 22, 38, 32 ], [ 31, 23, 43, 32 ],
[ 31, 23, 51, 32 ], [ 31, 24, 19, 32 ], [ 31, 24, 22, 32 ],
[ 31, 24, 24, 32 ], [ 31, 24, 27, 32 ], [ 31, 24, 39, 32 ],
[ 31, 24, 46, 32 ], [ 31, 24, 48, 32 ], [ 31, 24, 51, 32 ],
[ 31, 25, 19, 32 ], [ 31, 25, 22, 32 ], [ 31, 25, 24, 32 ],
[ 31, 25, 27, 32 ], [ 31, 25, 35, 32 ], [ 31, 25, 47, 32 ],
[ 31, 25, 50, 32 ], [ 31, 25, 52, 32 ], [ 31, 26, 23, 32 ],
[ 31, 26, 39, 32 ], [ 31, 26, 54, 32 ], [ 31, 26, 56, 32 ],
[ 31, 26, 59, 32 ], [ 31, 26, 63, 64 ], [ 31, 27, 20, 32 ],
[ 31, 27, 27, 32 ], [ 31, 27, 34, 32 ], [ 31, 27, 41, 32 ],
[ 31, 27, 47, 32 ], [ 31, 27, 49, 32 ], [ 31, 27, 51, 32 ],
[ 31, 27, 56, 32 ], [ 31, 28, 20, 32 ], [ 31, 28, 27, 32 ],
[ 31, 28, 34, 32 ], [ 31, 28, 41, 32 ], [ 31, 28, 47, 32 ],
[ 31, 28, 49, 32 ], [ 31, 28, 51, 32 ], [ 31, 28, 56, 32 ],
[ 31, 29, 19, 32 ], [ 31, 29, 22, 32 ], [ 31, 29, 24, 32 ],
[ 31, 29, 27, 32 ], [ 31, 29, 49, 32 ], [ 31, 29, 55, 32 ],
[ 31, 30, 15, 32 ], [ 31, 30, 17, 32 ], [ 31, 30, 20, 32 ],
[ 31, 30, 29, 32 ], [ 31, 31, 26, 32 ], [ 31, 31, 27, 32 ],
[ 31, 31, 28, 32 ], [ 31, 31, 30, 32 ], [ 31, 31, 31, 32 ],
[ 31, 31, 32, 32 ], [ 31, 32, 23, 32 ], [ 31, 32, 39, 32 ],
[ 31, 32, 54, 32 ], [ 31, 32, 56, 32 ], [ 31, 32, 59, 32 ],
[ 31, 32, 63, 64 ], [ 31, 33, 23, 32 ], [ 31, 33, 39, 32 ],
[ 31, 33, 54, 32 ], [ 31, 33, 56, 32 ], [ 31, 33, 59, 32 ],
[ 31, 33, 63, 64 ] ]
k = 14: F-action on Pi is () [31,1,14]
Dynkin type is A_0(q) + T(phi2^2 phi4^2)
Order of center |Z^F|: phi2^2 phi4^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/128 q^4 ( q^2-4 )
q congruent 1 modulo 4: 1/128 phi1^2 phi2 ( q^3+q^2-5*q-13 )
q congruent 2 modulo 4: 1/128 q^4 ( q^2-4 )
q congruent 3 modulo 4: 1/128 phi1^2 phi2 ( q^3+q^2-5*q-13 )
Fusion of maximal tori of C^F in those of G^F:
[ 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 8 ], [ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ],
[ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ],
[ 5, 1, 2, 4 ], [ 7, 1, 2, 16 ], [ 7, 2, 2, 8 ], [ 7, 3, 2, 8 ],
[ 7, 4, 2, 8 ], [ 7, 5, 2, 4 ], [ 9, 1, 4, 16 ], [ 9, 1, 5, 16 ],
[ 9, 1, 7, 16 ], [ 9, 2, 4, 8 ], [ 9, 2, 5, 8 ], [ 9, 2, 7, 8 ],
[ 9, 3, 4, 8 ], [ 9, 3, 5, 8 ], [ 9, 3, 7, 8 ], [ 9, 4, 4, 8 ],
[ 9, 4, 5, 8 ], [ 9, 4, 7, 8 ], [ 9, 5, 4, 4 ], [ 9, 5, 5, 4 ],
[ 9, 5, 7, 4 ], [ 12, 1, 3, 8 ], [ 12, 1, 5, 8 ], [ 12, 2, 3, 4 ],
[ 12, 2, 5, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ], [ 12, 4, 5, 4 ],
[ 15, 1, 5, 16 ], [ 16, 1, 4, 16 ], [ 16, 1, 8, 32 ], [ 16, 1, 12, 32 ],
[ 16, 2, 4, 8 ], [ 16, 2, 8, 16 ], [ 16, 2, 12, 16 ], [ 16, 3, 4, 8 ],
[ 16, 3, 8, 16 ], [ 16, 3, 12, 16 ], [ 16, 4, 4, 8 ], [ 16, 4, 8, 16 ],
[ 16, 4, 12, 16 ], [ 16, 5, 7, 16 ], [ 16, 5, 10, 16 ], [ 16, 5, 14, 16 ],
[ 16, 6, 7, 16 ], [ 16, 6, 10, 16 ], [ 16, 6, 14, 16 ], [ 16, 7, 7, 16 ],
[ 16, 7, 10, 16 ], [ 16, 7, 14, 16 ], [ 16, 8, 8, 16 ], [ 16, 9, 4, 4 ],
[ 16, 9, 8, 8 ], [ 16, 9, 12, 8 ], [ 16, 10, 7, 8 ], [ 16, 10, 10, 8 ],
[ 16, 10, 14, 8 ], [ 16, 11, 4, 8 ], [ 16, 11, 9, 8 ], [ 16, 11, 10, 8 ],
[ 16, 12, 7, 8 ], [ 16, 12, 10, 8 ], [ 16, 12, 14, 8 ], [ 16, 13, 4, 8 ],
[ 16, 13, 8, 8 ], [ 16, 13, 12, 8 ], [ 16, 14, 6, 8 ], [ 16, 14, 8, 16 ],
[ 16, 15, 4, 8 ], [ 16, 15, 8, 8 ], [ 16, 15, 12, 8 ], [ 16, 16, 4, 8 ],
[ 16, 16, 8, 8 ], [ 16, 16, 12, 8 ], [ 16, 17, 6, 8 ], [ 21, 1, 8, 32 ],
[ 21, 2, 5, 16 ], [ 21, 3, 4, 16 ], [ 21, 4, 5, 16 ], [ 21, 5, 5, 8 ],
[ 21, 6, 4, 16 ], [ 21, 7, 5, 16 ], [ 22, 1, 10, 32 ], [ 22, 2, 10, 16 ],
[ 22, 4, 10, 16 ], [ 25, 1, 8, 32 ], [ 25, 2, 7, 16 ], [ 26, 1, 8, 32 ],
[ 26, 2, 9, 16 ], [ 27, 1, 11, 64 ], [ 27, 1, 14, 32 ], [ 27, 2, 20, 32 ],
[ 27, 3, 10, 16 ], [ 27, 3, 23, 32 ], [ 27, 3, 25, 32 ], [ 27, 4, 19, 32 ],
[ 27, 5, 10, 16 ], [ 27, 5, 20, 32 ], [ 27, 6, 20, 16 ], [ 27, 7, 20, 16 ],
[ 27, 8, 10, 16 ], [ 27, 8, 23, 32 ], [ 27, 8, 25, 16 ], [ 27, 9, 8, 8 ],
[ 27, 9, 11, 16 ], [ 27, 9, 18, 16 ], [ 27, 10, 18, 16 ],
[ 27, 11, 10, 16 ], [ 27, 11, 23, 32 ], [ 27, 11, 25, 16 ],
[ 27, 12, 19, 32 ], [ 27, 13, 19, 16 ], [ 27, 14, 7, 16 ],
[ 27, 14, 23, 32 ], [ 27, 14, 25, 16 ], [ 29, 1, 19, 64 ],
[ 29, 2, 19, 32 ], [ 29, 3, 19, 32 ], [ 29, 4, 19, 32 ], [ 29, 5, 19, 32 ],
[ 29, 9, 19, 16 ], [ 30, 1, 25, 64 ], [ 30, 2, 25, 32 ], [ 30, 3, 25, 32 ],
[ 30, 4, 21, 32 ], [ 30, 5, 21, 32 ], [ 30, 6, 21, 32 ], [ 30, 8, 26, 32 ],
[ 30, 8, 27, 32 ], [ 30, 8, 29, 16 ], [ 30, 9, 26, 32 ], [ 30, 9, 27, 16 ],
[ 30, 9, 29, 32 ], [ 30, 10, 26, 16 ], [ 30, 10, 27, 32 ],
[ 30, 10, 29, 32 ], [ 30, 12, 21, 32 ], [ 31, 2, 13, 64 ],
[ 31, 2, 32, 64 ], [ 31, 3, 13, 64 ], [ 31, 3, 32, 64 ], [ 31, 4, 14, 64 ],
[ 31, 5, 31, 64 ], [ 31, 6, 52, 64 ], [ 31, 7, 34, 64 ], [ 31, 8, 31, 64 ],
[ 31, 9, 13, 32 ], [ 31, 9, 33, 32 ], [ 31, 10, 36, 32 ],
[ 31, 10, 37, 32 ], [ 31, 10, 49, 64 ], [ 31, 11, 15, 32 ],
[ 31, 11, 32, 64 ], [ 31, 12, 51, 32 ], [ 31, 13, 43, 64 ],
[ 31, 14, 35, 64 ], [ 31, 15, 40, 64 ], [ 31, 16, 13, 32 ],
[ 31, 16, 32, 32 ], [ 31, 17, 7, 32 ], [ 31, 17, 11, 64 ],
[ 31, 18, 35, 64 ], [ 31, 18, 47, 32 ], [ 31, 18, 55, 64 ],
[ 31, 19, 35, 64 ], [ 31, 19, 47, 32 ], [ 31, 19, 55, 64 ],
[ 31, 20, 35, 64 ], [ 31, 20, 47, 64 ], [ 31, 20, 55, 32 ],
[ 31, 21, 34, 64 ], [ 31, 22, 34, 32 ], [ 31, 23, 15, 32 ],
[ 31, 23, 31, 64 ], [ 31, 24, 35, 32 ], [ 31, 25, 39, 32 ],
[ 31, 26, 57, 64 ], [ 31, 26, 60, 32 ], [ 31, 26, 62, 64 ],
[ 31, 27, 52, 32 ], [ 31, 28, 52, 32 ], [ 31, 29, 42, 64 ],
[ 31, 32, 57, 64 ], [ 31, 32, 60, 32 ], [ 31, 32, 62, 64 ],
[ 31, 33, 57, 64 ], [ 31, 33, 60, 32 ], [ 31, 33, 62, 64 ] ]
k = 15: F-action on Pi is () [31,1,15]
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 0 modulo 4: 1/384 q ( q^5-6*q^4+40*q^2-16*q-64 )
q congruent 1 modulo
4: 1/384 phi1 ( q^5-5*q^4-8*q^3+12*q^2+263*q-519 )
q congruent 2 modulo 4: 1/384 q ( q^5-6*q^4+40*q^2-16*q-64 )
q congruent 3 modulo
4: 1/384 phi1 ( q^5-5*q^4-8*q^3+12*q^2+263*q-519 )
Fusion of maximal tori of C^F in those of G^F:
[ 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 4, 16 ],
[ 3, 2, 4, 8 ], [ 3, 3, 4, 8 ], [ 3, 4, 4, 8 ], [ 3, 5, 4, 4 ],
[ 5, 1, 1, 6 ], [ 5, 1, 2, 6 ], [ 8, 1, 1, 12 ], [ 8, 1, 2, 12 ],
[ 9, 1, 1, 24 ], [ 9, 1, 2, 24 ], [ 9, 1, 6, 48 ], [ 9, 1, 7, 48 ],
[ 9, 2, 1, 12 ], [ 9, 2, 2, 12 ], [ 9, 2, 6, 24 ], [ 9, 2, 7, 24 ],
[ 9, 3, 1, 12 ], [ 9, 3, 2, 12 ], [ 9, 3, 6, 24 ], [ 9, 3, 7, 24 ],
[ 9, 4, 1, 12 ], [ 9, 4, 2, 12 ], [ 9, 4, 6, 24 ], [ 9, 4, 7, 24 ],
[ 9, 5, 1, 6 ], [ 9, 5, 2, 6 ], [ 9, 5, 6, 12 ], [ 9, 5, 7, 12 ],
[ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ], [ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ],
[ 12, 1, 2, 12 ], [ 12, 2, 2, 6 ], [ 12, 4, 2, 6 ], [ 15, 1, 1, 24 ],
[ 15, 1, 2, 48 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 24 ], [ 16, 1, 3, 48 ],
[ 16, 1, 14, 96 ], [ 16, 2, 3, 24 ], [ 16, 2, 14, 48 ], [ 16, 3, 3, 24 ],
[ 16, 3, 14, 48 ], [ 16, 4, 3, 24 ], [ 16, 4, 14, 48 ], [ 16, 5, 2, 24 ],
[ 16, 5, 4, 24 ], [ 16, 5, 12, 48 ], [ 16, 5, 13, 48 ], [ 16, 6, 2, 24 ],
[ 16, 6, 4, 24 ], [ 16, 6, 12, 48 ], [ 16, 6, 13, 48 ], [ 16, 7, 2, 24 ],
[ 16, 7, 4, 24 ], [ 16, 7, 12, 48 ], [ 16, 7, 13, 48 ], [ 16, 9, 3, 12 ],
[ 16, 9, 14, 24 ], [ 16, 10, 2, 12 ], [ 16, 10, 4, 12 ], [ 16, 10, 12, 24 ],
[ 16, 10, 13, 24 ], [ 16, 11, 3, 24 ], [ 16, 12, 2, 12 ], [ 16, 12, 4, 12 ],
[ 16, 12, 12, 24 ], [ 16, 12, 13, 24 ], [ 16, 13, 3, 12 ],
[ 16, 13, 14, 24 ], [ 16, 15, 3, 12 ], [ 16, 15, 14, 24 ],
[ 16, 16, 3, 12 ], [ 16, 16, 14, 24 ], [ 16, 17, 9, 48 ], [ 18, 1, 1, 24 ],
[ 18, 1, 3, 24 ], [ 18, 2, 1, 12 ], [ 18, 2, 3, 12 ], [ 19, 1, 3, 64 ],
[ 19, 2, 3, 32 ], [ 19, 3, 3, 32 ], [ 19, 4, 3, 32 ], [ 19, 5, 3, 16 ],
[ 20, 1, 2, 24 ], [ 20, 1, 4, 24 ], [ 20, 2, 2, 12 ], [ 20, 2, 4, 12 ],
[ 22, 1, 2, 48 ], [ 22, 1, 5, 48 ], [ 22, 2, 2, 24 ], [ 22, 2, 5, 24 ],
[ 22, 4, 2, 24 ], [ 22, 4, 5, 24 ], [ 23, 1, 2, 48 ], [ 23, 1, 6, 48 ],
[ 23, 2, 2, 24 ], [ 23, 2, 6, 24 ], [ 23, 3, 2, 24 ], [ 23, 3, 6, 24 ],
[ 23, 4, 2, 24 ], [ 23, 4, 6, 24 ], [ 23, 5, 2, 24 ], [ 23, 5, 6, 24 ],
[ 23, 6, 2, 12 ], [ 23, 6, 6, 12 ], [ 25, 1, 1, 48 ], [ 25, 1, 3, 48 ],
[ 25, 1, 5, 96 ], [ 25, 2, 1, 24 ], [ 25, 2, 3, 48 ], [ 25, 2, 5, 24 ],
[ 25, 3, 1, 24 ], [ 25, 3, 2, 48 ], [ 25, 3, 3, 24 ], [ 25, 3, 4, 48 ],
[ 26, 1, 2, 48 ], [ 26, 1, 4, 48 ], [ 26, 1, 7, 96 ], [ 26, 2, 2, 24 ],
[ 26, 2, 8, 48 ], [ 26, 2, 10, 24 ], [ 26, 3, 5, 24 ], [ 26, 3, 6, 48 ],
[ 26, 3, 7, 24 ], [ 26, 3, 8, 48 ], [ 27, 1, 12, 96 ], [ 27, 3, 7, 48 ],
[ 27, 5, 8, 48 ], [ 27, 8, 7, 48 ], [ 27, 9, 6, 24 ], [ 27, 9, 10, 48 ],
[ 27, 11, 7, 48 ], [ 27, 14, 6, 48 ], [ 29, 1, 2, 96 ], [ 29, 1, 8, 96 ],
[ 29, 1, 10, 96 ], [ 29, 1, 14, 192 ], [ 29, 2, 2, 48 ], [ 29, 2, 8, 48 ],
[ 29, 2, 10, 48 ], [ 29, 2, 14, 96 ], [ 29, 3, 2, 48 ], [ 29, 3, 8, 48 ],
[ 29, 3, 10, 48 ], [ 29, 3, 14, 96 ], [ 29, 4, 2, 48 ], [ 29, 4, 8, 48 ],
[ 29, 4, 10, 48 ], [ 29, 4, 14, 96 ], [ 29, 5, 2, 48 ], [ 29, 5, 8, 48 ],
[ 29, 5, 10, 48 ], [ 29, 5, 14, 96 ], [ 29, 6, 2, 48 ], [ 29, 6, 6, 48 ],
[ 29, 6, 10, 96 ], [ 29, 6, 14, 96 ], [ 29, 7, 2, 48 ], [ 29, 7, 6, 48 ],
[ 29, 7, 10, 96 ], [ 29, 7, 14, 96 ], [ 29, 8, 2, 48 ], [ 29, 8, 6, 48 ],
[ 29, 8, 10, 96 ], [ 29, 8, 14, 96 ], [ 29, 9, 2, 24 ], [ 29, 9, 8, 24 ],
[ 29, 9, 10, 24 ], [ 29, 9, 14, 48 ], [ 29, 10, 2, 24 ], [ 29, 10, 6, 24 ],
[ 29, 10, 10, 48 ], [ 29, 10, 14, 48 ], [ 29, 11, 2, 24 ],
[ 29, 11, 6, 24 ], [ 29, 11, 10, 48 ], [ 29, 11, 14, 48 ],
[ 29, 12, 2, 24 ], [ 29, 12, 6, 24 ], [ 29, 12, 10, 48 ],
[ 29, 12, 14, 48 ], [ 29, 13, 2, 24 ], [ 29, 13, 6, 24 ],
[ 29, 13, 10, 48 ], [ 29, 13, 14, 48 ], [ 30, 1, 9, 192 ],
[ 30, 1, 24, 192 ], [ 30, 2, 9, 96 ], [ 30, 2, 24, 96 ], [ 30, 3, 9, 96 ],
[ 30, 3, 24, 96 ], [ 30, 4, 6, 96 ], [ 30, 4, 25, 96 ], [ 30, 5, 6, 96 ],
[ 30, 5, 9, 96 ], [ 30, 5, 14, 96 ], [ 30, 5, 25, 96 ], [ 30, 6, 9, 96 ],
[ 30, 6, 20, 96 ], [ 30, 6, 25, 96 ], [ 30, 6, 28, 96 ], [ 30, 7, 5, 96 ],
[ 30, 7, 13, 96 ], [ 30, 7, 24, 96 ], [ 30, 7, 32, 96 ], [ 30, 8, 8, 96 ],
[ 30, 8, 12, 48 ], [ 30, 8, 25, 96 ], [ 30, 8, 31, 48 ], [ 30, 9, 8, 48 ],
[ 30, 9, 12, 48 ], [ 30, 9, 25, 96 ], [ 30, 9, 31, 48 ], [ 30, 10, 8, 96 ],
[ 30, 10, 12, 48 ], [ 30, 10, 25, 48 ], [ 30, 10, 31, 48 ],
[ 30, 11, 5, 48 ], [ 30, 11, 13, 48 ], [ 30, 11, 24, 48 ],
[ 30, 11, 32, 48 ], [ 30, 12, 6, 48 ], [ 30, 12, 25, 48 ],
[ 31, 2, 41, 192 ], [ 31, 3, 46, 192 ], [ 31, 4, 15, 192 ],
[ 31, 5, 16, 192 ], [ 31, 5, 22, 192 ], [ 31, 6, 21, 192 ],
[ 31, 6, 33, 192 ], [ 31, 6, 37, 192 ], [ 31, 6, 42, 192 ],
[ 31, 7, 17, 192 ], [ 31, 7, 31, 192 ], [ 31, 7, 37, 192 ],
[ 31, 8, 17, 192 ], [ 31, 8, 34, 192 ], [ 31, 8, 39, 192 ],
[ 31, 9, 41, 96 ], [ 31, 10, 20, 96 ], [ 31, 10, 39, 192 ],
[ 31, 11, 45, 96 ], [ 31, 12, 21, 96 ], [ 31, 12, 24, 96 ],
[ 31, 12, 28, 96 ], [ 31, 12, 33, 96 ], [ 31, 13, 20, 96 ],
[ 31, 13, 26, 96 ], [ 31, 16, 46, 96 ], [ 31, 17, 30, 96 ],
[ 31, 17, 39, 192 ], [ 31, 18, 16, 96 ], [ 31, 18, 22, 96 ],
[ 31, 18, 42, 96 ], [ 31, 18, 60, 192 ], [ 31, 19, 16, 96 ],
[ 31, 19, 22, 96 ], [ 31, 19, 42, 96 ], [ 31, 19, 60, 192 ],
[ 31, 20, 16, 96 ], [ 31, 20, 22, 96 ], [ 31, 20, 42, 192 ],
[ 31, 20, 60, 96 ], [ 31, 22, 17, 96 ], [ 31, 22, 31, 96 ],
[ 31, 22, 37, 96 ], [ 31, 23, 45, 96 ], [ 31, 24, 20, 96 ],
[ 31, 24, 26, 96 ], [ 31, 24, 40, 96 ], [ 31, 24, 52, 96 ],
[ 31, 25, 20, 96 ], [ 31, 25, 26, 96 ], [ 31, 25, 34, 96 ],
[ 31, 25, 46, 96 ], [ 31, 26, 24, 96 ], [ 31, 26, 31, 192 ],
[ 31, 26, 38, 96 ], [ 31, 26, 43, 96 ], [ 31, 27, 21, 96 ],
[ 31, 27, 33, 96 ], [ 31, 27, 37, 96 ], [ 31, 27, 42, 96 ],
[ 31, 28, 21, 96 ], [ 31, 28, 33, 96 ], [ 31, 28, 37, 96 ],
[ 31, 28, 42, 96 ], [ 31, 29, 20, 96 ], [ 31, 29, 26, 96 ],
[ 31, 30, 16, 96 ], [ 31, 30, 19, 96 ], [ 31, 31, 18, 96 ],
[ 31, 31, 19, 96 ], [ 31, 31, 20, 96 ], [ 31, 31, 22, 96 ],
[ 31, 31, 23, 96 ], [ 31, 31, 24, 96 ], [ 31, 32, 24, 96 ],
[ 31, 32, 31, 192 ], [ 31, 32, 38, 96 ], [ 31, 32, 43, 96 ],
[ 31, 33, 24, 96 ], [ 31, 33, 31, 192 ], [ 31, 33, 38, 96 ],
[ 31, 33, 43, 96 ] ]
k = 16: F-action on Pi is () [31,1,16]
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 0 modulo 4: 1/384 q ( q^5-6*q^4+40*q^2-16*q-64 )
q congruent 1 modulo
4: 1/384 phi1 ( q^5-5*q^4-8*q^3+12*q^2+263*q-519 )
q congruent 2 modulo 4: 1/384 q ( q^5-6*q^4+40*q^2-16*q-64 )
q congruent 3 modulo
4: 1/384 phi1 ( q^5-5*q^4-8*q^3+12*q^2+263*q-519 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 3, 16 ],
[ 3, 2, 3, 8 ], [ 3, 3, 3, 8 ], [ 3, 4, 3, 8 ], [ 3, 5, 3, 4 ],
[ 5, 1, 1, 6 ], [ 5, 1, 2, 6 ], [ 8, 1, 1, 12 ], [ 8, 1, 2, 12 ],
[ 9, 1, 1, 24 ], [ 9, 1, 2, 24 ], [ 9, 1, 5, 48 ], [ 9, 1, 8, 48 ],
[ 9, 2, 1, 12 ], [ 9, 2, 2, 12 ], [ 9, 2, 5, 24 ], [ 9, 2, 8, 24 ],
[ 9, 3, 1, 12 ], [ 9, 3, 2, 12 ], [ 9, 3, 5, 24 ], [ 9, 3, 8, 24 ],
[ 9, 4, 1, 12 ], [ 9, 4, 2, 12 ], [ 9, 4, 5, 24 ], [ 9, 4, 8, 24 ],
[ 9, 5, 1, 6 ], [ 9, 5, 2, 6 ], [ 9, 5, 5, 12 ], [ 9, 5, 8, 12 ],
[ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ], [ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ],
[ 12, 1, 2, 12 ], [ 12, 2, 2, 6 ], [ 12, 4, 2, 6 ], [ 15, 1, 1, 24 ],
[ 15, 1, 2, 48 ], [ 15, 1, 3, 24 ], [ 15, 1, 4, 24 ], [ 16, 1, 3, 48 ],
[ 16, 1, 9, 96 ], [ 16, 2, 3, 24 ], [ 16, 2, 9, 48 ], [ 16, 3, 3, 24 ],
[ 16, 3, 9, 48 ], [ 16, 4, 3, 24 ], [ 16, 4, 9, 48 ], [ 16, 5, 2, 24 ],
[ 16, 5, 4, 24 ], [ 16, 5, 9, 48 ], [ 16, 5, 16, 48 ], [ 16, 6, 2, 24 ],
[ 16, 6, 4, 24 ], [ 16, 6, 9, 48 ], [ 16, 6, 16, 48 ], [ 16, 7, 2, 24 ],
[ 16, 7, 4, 24 ], [ 16, 7, 9, 48 ], [ 16, 7, 16, 48 ], [ 16, 9, 3, 12 ],
[ 16, 9, 9, 24 ], [ 16, 10, 2, 12 ], [ 16, 10, 4, 12 ], [ 16, 10, 9, 24 ],
[ 16, 10, 16, 24 ], [ 16, 11, 3, 24 ], [ 16, 12, 2, 12 ], [ 16, 12, 4, 12 ],
[ 16, 12, 9, 24 ], [ 16, 12, 16, 24 ], [ 16, 13, 3, 12 ], [ 16, 13, 9, 24 ],
[ 16, 15, 3, 12 ], [ 16, 15, 9, 24 ], [ 16, 16, 3, 12 ], [ 16, 16, 9, 24 ],
[ 16, 17, 7, 48 ], [ 18, 1, 2, 24 ], [ 18, 1, 4, 24 ], [ 18, 2, 2, 12 ],
[ 18, 2, 4, 12 ], [ 19, 1, 4, 64 ], [ 19, 2, 4, 32 ], [ 19, 3, 4, 32 ],
[ 19, 4, 4, 32 ], [ 19, 5, 4, 16 ], [ 20, 1, 1, 24 ], [ 20, 1, 3, 24 ],
[ 20, 2, 1, 12 ], [ 20, 2, 3, 12 ], [ 22, 1, 2, 48 ], [ 22, 1, 5, 48 ],
[ 22, 2, 2, 24 ], [ 22, 2, 5, 24 ], [ 22, 4, 2, 24 ], [ 22, 4, 5, 24 ],
[ 23, 1, 4, 48 ], [ 23, 1, 8, 48 ], [ 23, 2, 4, 24 ], [ 23, 2, 8, 24 ],
[ 23, 3, 4, 24 ], [ 23, 3, 8, 24 ], [ 23, 4, 4, 24 ], [ 23, 4, 8, 24 ],
[ 23, 5, 4, 24 ], [ 23, 5, 8, 24 ], [ 23, 6, 4, 12 ], [ 23, 6, 8, 12 ],
[ 25, 1, 2, 48 ], [ 25, 1, 4, 48 ], [ 25, 1, 7, 96 ], [ 25, 2, 2, 24 ],
[ 25, 2, 6, 48 ], [ 25, 2, 8, 24 ], [ 25, 3, 5, 24 ], [ 25, 3, 6, 48 ],
[ 25, 3, 7, 24 ], [ 25, 3, 8, 48 ], [ 26, 1, 1, 48 ], [ 26, 1, 3, 48 ],
[ 26, 1, 5, 96 ], [ 26, 2, 1, 24 ], [ 26, 2, 3, 48 ], [ 26, 2, 5, 24 ],
[ 26, 3, 1, 24 ], [ 26, 3, 2, 48 ], [ 26, 3, 3, 24 ], [ 26, 3, 4, 48 ],
[ 27, 1, 12, 96 ], [ 27, 3, 7, 48 ], [ 27, 5, 8, 48 ], [ 27, 8, 7, 48 ],
[ 27, 9, 6, 24 ], [ 27, 9, 10, 48 ], [ 27, 11, 7, 48 ], [ 27, 14, 6, 48 ],
[ 29, 1, 4, 96 ], [ 29, 1, 6, 96 ], [ 29, 1, 12, 96 ], [ 29, 1, 16, 192 ],
[ 29, 2, 4, 48 ], [ 29, 2, 6, 48 ], [ 29, 2, 12, 48 ], [ 29, 2, 16, 96 ],
[ 29, 3, 4, 48 ], [ 29, 3, 6, 48 ], [ 29, 3, 12, 48 ], [ 29, 3, 16, 96 ],
[ 29, 4, 4, 48 ], [ 29, 4, 6, 48 ], [ 29, 4, 12, 48 ], [ 29, 4, 16, 96 ],
[ 29, 5, 4, 48 ], [ 29, 5, 6, 48 ], [ 29, 5, 12, 48 ], [ 29, 5, 16, 96 ],
[ 29, 6, 4, 48 ], [ 29, 6, 8, 48 ], [ 29, 6, 12, 96 ], [ 29, 6, 16, 96 ],
[ 29, 7, 4, 48 ], [ 29, 7, 8, 48 ], [ 29, 7, 12, 96 ], [ 29, 7, 16, 96 ],
[ 29, 8, 4, 48 ], [ 29, 8, 8, 48 ], [ 29, 8, 12, 96 ], [ 29, 8, 16, 96 ],
[ 29, 9, 4, 24 ], [ 29, 9, 6, 24 ], [ 29, 9, 12, 24 ], [ 29, 9, 16, 48 ],
[ 29, 10, 4, 24 ], [ 29, 10, 8, 24 ], [ 29, 10, 12, 48 ],
[ 29, 10, 16, 48 ], [ 29, 11, 4, 24 ], [ 29, 11, 8, 24 ],
[ 29, 11, 12, 48 ], [ 29, 11, 16, 48 ], [ 29, 12, 4, 24 ],
[ 29, 12, 8, 24 ], [ 29, 12, 12, 48 ], [ 29, 12, 16, 48 ],
[ 29, 13, 4, 24 ], [ 29, 13, 8, 24 ], [ 29, 13, 12, 48 ],
[ 29, 13, 16, 48 ], [ 30, 1, 11, 192 ], [ 30, 1, 22, 192 ],
[ 30, 2, 11, 96 ], [ 30, 2, 22, 96 ], [ 30, 3, 11, 96 ], [ 30, 3, 22, 96 ],
[ 30, 4, 11, 96 ], [ 30, 4, 20, 96 ], [ 30, 5, 11, 96 ], [ 30, 5, 20, 96 ],
[ 30, 5, 23, 96 ], [ 30, 5, 28, 96 ], [ 30, 6, 6, 96 ], [ 30, 6, 11, 96 ],
[ 30, 6, 14, 96 ], [ 30, 6, 23, 96 ], [ 30, 7, 8, 96 ], [ 30, 7, 16, 96 ],
[ 30, 7, 21, 96 ], [ 30, 7, 29, 96 ], [ 30, 8, 9, 96 ], [ 30, 8, 15, 48 ],
[ 30, 8, 24, 96 ], [ 30, 8, 28, 48 ], [ 30, 9, 9, 96 ], [ 30, 9, 15, 48 ],
[ 30, 9, 24, 48 ], [ 30, 9, 28, 48 ], [ 30, 10, 9, 48 ], [ 30, 10, 15, 48 ],
[ 30, 10, 24, 96 ], [ 30, 10, 28, 48 ], [ 30, 11, 8, 48 ],
[ 30, 11, 16, 48 ], [ 30, 11, 21, 48 ], [ 30, 11, 29, 48 ],
[ 30, 12, 11, 48 ], [ 30, 12, 20, 48 ], [ 31, 2, 47, 192 ],
[ 31, 3, 47, 192 ], [ 31, 4, 16, 192 ], [ 31, 5, 14, 192 ],
[ 31, 5, 24, 192 ], [ 31, 6, 19, 192 ], [ 31, 6, 23, 192 ],
[ 31, 6, 28, 192 ], [ 31, 6, 35, 192 ], [ 31, 7, 15, 192 ],
[ 31, 7, 19, 192 ], [ 31, 7, 24, 192 ], [ 31, 8, 15, 192 ],
[ 31, 8, 19, 192 ], [ 31, 8, 24, 192 ], [ 31, 9, 47, 96 ],
[ 31, 10, 18, 96 ], [ 31, 10, 53, 192 ], [ 31, 11, 43, 96 ],
[ 31, 12, 19, 96 ], [ 31, 12, 35, 96 ], [ 31, 12, 38, 96 ],
[ 31, 12, 42, 96 ], [ 31, 13, 18, 96 ], [ 31, 13, 28, 96 ],
[ 31, 16, 47, 96 ], [ 31, 17, 35, 96 ], [ 31, 17, 40, 192 ],
[ 31, 18, 14, 96 ], [ 31, 18, 24, 96 ], [ 31, 18, 44, 96 ],
[ 31, 18, 58, 192 ], [ 31, 19, 14, 96 ], [ 31, 19, 24, 96 ],
[ 31, 19, 44, 96 ], [ 31, 19, 58, 192 ], [ 31, 20, 14, 96 ],
[ 31, 20, 24, 96 ], [ 31, 20, 44, 192 ], [ 31, 20, 58, 96 ],
[ 31, 22, 15, 96 ], [ 31, 22, 19, 96 ], [ 31, 22, 24, 96 ],
[ 31, 23, 46, 96 ], [ 31, 24, 18, 96 ], [ 31, 24, 28, 96 ],
[ 31, 24, 38, 96 ], [ 31, 24, 50, 96 ], [ 31, 25, 18, 96 ],
[ 31, 25, 28, 96 ], [ 31, 25, 36, 96 ], [ 31, 25, 48, 96 ],
[ 31, 26, 22, 96 ], [ 31, 26, 27, 96 ], [ 31, 26, 40, 96 ],
[ 31, 26, 47, 192 ], [ 31, 27, 19, 96 ], [ 31, 27, 23, 96 ],
[ 31, 27, 28, 96 ], [ 31, 27, 35, 96 ], [ 31, 28, 19, 96 ],
[ 31, 28, 23, 96 ], [ 31, 28, 28, 96 ], [ 31, 28, 35, 96 ],
[ 31, 29, 18, 96 ], [ 31, 29, 28, 96 ], [ 31, 30, 14, 96 ],
[ 31, 30, 31, 96 ], [ 31, 31, 10, 96 ], [ 31, 31, 11, 96 ],
[ 31, 31, 12, 96 ], [ 31, 31, 14, 96 ], [ 31, 31, 15, 96 ],
[ 31, 31, 16, 96 ], [ 31, 32, 22, 96 ], [ 31, 32, 27, 96 ],
[ 31, 32, 40, 96 ], [ 31, 32, 47, 192 ], [ 31, 33, 22, 96 ],
[ 31, 33, 27, 96 ], [ 31, 33, 40, 96 ], [ 31, 33, 47, 192 ] ]
k = 17: F-action on Pi is () [31,1,17]
Dynkin type is A_0(q) + T(phi1 phi2 phi4^2)
Order of center |Z^F|: phi1 phi2 phi4^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/64 q^3 ( q^3-2*q^2-4*q+8 )
q congruent 1 modulo 4: 1/64 phi1 phi2 ( q^4-2*q^3-6*q^2+2*q+21 )
q congruent 2 modulo 4: 1/64 q^3 ( q^3-2*q^2-4*q+8 )
q congruent 3 modulo 4: 1/64 phi1 phi2 ( q^4-2*q^3-6*q^2+2*q+21 )
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, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 3, 8 ], [ 3, 1, 4, 8 ], [ 3, 2, 3, 4 ],
[ 3, 2, 4, 4 ], [ 3, 3, 3, 4 ], [ 3, 3, 4, 4 ], [ 3, 4, 3, 4 ],
[ 3, 4, 4, 4 ], [ 3, 5, 3, 2 ], [ 3, 5, 4, 2 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 3, 8 ], [ 9, 1, 4, 8 ], [ 9, 1, 5, 8 ],
[ 9, 1, 6, 8 ], [ 9, 1, 7, 8 ], [ 9, 1, 8, 8 ], [ 9, 2, 3, 4 ],
[ 9, 2, 4, 4 ], [ 9, 2, 5, 4 ], [ 9, 2, 6, 4 ], [ 9, 2, 7, 4 ],
[ 9, 2, 8, 4 ], [ 9, 3, 3, 4 ], [ 9, 3, 4, 4 ], [ 9, 3, 5, 4 ],
[ 9, 3, 6, 4 ], [ 9, 3, 7, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 3, 4 ],
[ 9, 4, 4, 4 ], [ 9, 4, 5, 4 ], [ 9, 4, 6, 4 ], [ 9, 4, 7, 4 ],
[ 9, 4, 8, 4 ], [ 9, 5, 3, 2 ], [ 9, 5, 4, 2 ], [ 9, 5, 5, 2 ],
[ 9, 5, 6, 2 ], [ 9, 5, 7, 2 ], [ 9, 5, 8, 2 ], [ 12, 1, 2, 4 ],
[ 12, 1, 5, 8 ], [ 12, 2, 2, 2 ], [ 12, 2, 5, 4 ], [ 12, 4, 2, 2 ],
[ 12, 4, 5, 4 ], [ 15, 1, 5, 16 ], [ 16, 1, 4, 16 ], [ 16, 1, 7, 16 ],
[ 16, 1, 9, 16 ], [ 16, 1, 10, 32 ], [ 16, 1, 14, 16 ], [ 16, 2, 4, 8 ],
[ 16, 2, 7, 8 ], [ 16, 2, 9, 8 ], [ 16, 2, 10, 16 ], [ 16, 2, 14, 8 ],
[ 16, 3, 4, 8 ], [ 16, 3, 7, 8 ], [ 16, 3, 9, 8 ], [ 16, 3, 10, 16 ],
[ 16, 3, 14, 8 ], [ 16, 4, 4, 8 ], [ 16, 4, 7, 8 ], [ 16, 4, 9, 8 ],
[ 16, 4, 10, 16 ], [ 16, 4, 14, 8 ], [ 16, 5, 6, 8 ], [ 16, 5, 8, 8 ],
[ 16, 5, 9, 8 ], [ 16, 5, 12, 8 ], [ 16, 5, 13, 8 ], [ 16, 5, 16, 8 ],
[ 16, 6, 6, 8 ], [ 16, 6, 8, 8 ], [ 16, 6, 9, 8 ], [ 16, 6, 12, 8 ],
[ 16, 6, 13, 8 ], [ 16, 6, 16, 8 ], [ 16, 7, 6, 8 ], [ 16, 7, 8, 8 ],
[ 16, 7, 9, 8 ], [ 16, 7, 12, 8 ], [ 16, 7, 13, 8 ], [ 16, 7, 16, 8 ],
[ 16, 9, 4, 4 ], [ 16, 9, 7, 4 ], [ 16, 9, 9, 4 ], [ 16, 9, 10, 8 ],
[ 16, 9, 14, 4 ], [ 16, 10, 6, 4 ], [ 16, 10, 8, 4 ], [ 16, 10, 9, 4 ],
[ 16, 10, 12, 4 ], [ 16, 10, 13, 4 ], [ 16, 10, 16, 4 ], [ 16, 11, 4, 8 ],
[ 16, 11, 8, 8 ], [ 16, 11, 9, 8 ], [ 16, 12, 6, 4 ], [ 16, 12, 8, 4 ],
[ 16, 12, 9, 4 ], [ 16, 12, 12, 4 ], [ 16, 12, 13, 4 ], [ 16, 12, 16, 4 ],
[ 16, 13, 4, 8 ], [ 16, 13, 7, 4 ], [ 16, 13, 9, 4 ], [ 16, 13, 10, 16 ],
[ 16, 13, 14, 4 ], [ 16, 15, 4, 8 ], [ 16, 15, 7, 4 ], [ 16, 15, 9, 4 ],
[ 16, 15, 10, 16 ], [ 16, 15, 14, 4 ], [ 16, 16, 4, 8 ], [ 16, 16, 7, 4 ],
[ 16, 16, 9, 4 ], [ 16, 16, 10, 16 ], [ 16, 16, 14, 4 ], [ 16, 17, 7, 8 ],
[ 16, 17, 8, 16 ], [ 16, 17, 9, 8 ], [ 16, 17, 10, 16 ], [ 22, 1, 8, 16 ],
[ 22, 1, 10, 16 ], [ 22, 2, 8, 8 ], [ 22, 2, 10, 8 ], [ 22, 4, 8, 8 ],
[ 22, 4, 10, 8 ], [ 25, 1, 6, 16 ], [ 25, 1, 8, 16 ], [ 25, 2, 4, 8 ],
[ 25, 2, 7, 8 ], [ 26, 1, 6, 16 ], [ 26, 1, 8, 16 ], [ 26, 2, 4, 8 ],
[ 26, 2, 9, 8 ], [ 27, 1, 13, 32 ], [ 27, 1, 14, 32 ], [ 27, 3, 10, 16 ],
[ 27, 3, 20, 16 ], [ 27, 3, 22, 16 ], [ 27, 5, 10, 16 ], [ 27, 5, 19, 16 ],
[ 27, 8, 10, 16 ], [ 27, 8, 20, 16 ], [ 27, 8, 22, 16 ], [ 27, 9, 8, 8 ],
[ 27, 9, 11, 16 ], [ 27, 9, 17, 8 ], [ 27, 9, 20, 16 ], [ 27, 11, 10, 16 ],
[ 27, 11, 20, 16 ], [ 27, 11, 22, 16 ], [ 27, 14, 7, 16 ],
[ 27, 14, 19, 16 ], [ 27, 14, 20, 16 ], [ 29, 1, 18, 32 ],
[ 29, 1, 20, 32 ], [ 29, 2, 18, 16 ], [ 29, 2, 20, 16 ], [ 29, 3, 18, 16 ],
[ 29, 3, 20, 16 ], [ 29, 4, 18, 16 ], [ 29, 4, 20, 16 ], [ 29, 5, 18, 16 ],
[ 29, 5, 20, 16 ], [ 29, 9, 18, 8 ], [ 29, 9, 20, 8 ], [ 30, 1, 12, 32 ],
[ 30, 1, 25, 32 ], [ 30, 2, 12, 16 ], [ 30, 2, 25, 16 ], [ 30, 3, 12, 16 ],
[ 30, 3, 25, 16 ], [ 30, 4, 7, 16 ], [ 30, 4, 21, 16 ], [ 30, 5, 7, 16 ],
[ 30, 5, 21, 16 ], [ 30, 6, 7, 16 ], [ 30, 6, 21, 16 ], [ 30, 8, 10, 16 ],
[ 30, 8, 11, 16 ], [ 30, 8, 13, 8 ], [ 30, 8, 26, 16 ], [ 30, 8, 27, 16 ],
[ 30, 8, 29, 8 ], [ 30, 9, 10, 16 ], [ 30, 9, 11, 8 ], [ 30, 9, 13, 16 ],
[ 30, 9, 26, 16 ], [ 30, 9, 27, 8 ], [ 30, 9, 29, 16 ], [ 30, 10, 10, 8 ],
[ 30, 10, 11, 16 ], [ 30, 10, 13, 16 ], [ 30, 10, 26, 8 ],
[ 30, 10, 27, 16 ], [ 30, 10, 29, 16 ], [ 30, 12, 7, 16 ],
[ 30, 12, 21, 16 ], [ 31, 2, 17, 32 ], [ 31, 2, 34, 32 ], [ 31, 3, 17, 32 ],
[ 31, 3, 33, 32 ], [ 31, 4, 17, 32 ], [ 31, 5, 30, 32 ], [ 31, 5, 32, 32 ],
[ 31, 6, 24, 32 ], [ 31, 6, 38, 32 ], [ 31, 7, 20, 32 ], [ 31, 7, 33, 32 ],
[ 31, 8, 20, 32 ], [ 31, 8, 32, 32 ], [ 31, 9, 17, 16 ], [ 31, 9, 34, 16 ],
[ 31, 10, 22, 16 ], [ 31, 10, 35, 16 ], [ 31, 10, 40, 32 ],
[ 31, 10, 42, 32 ], [ 31, 10, 52, 32 ], [ 31, 11, 17, 16 ],
[ 31, 11, 33, 32 ], [ 31, 12, 23, 16 ], [ 31, 12, 37, 16 ],
[ 31, 13, 42, 32 ], [ 31, 13, 44, 32 ], [ 31, 16, 17, 16 ],
[ 31, 16, 33, 16 ], [ 31, 17, 12, 16 ], [ 31, 17, 14, 32 ],
[ 31, 17, 15, 32 ], [ 31, 17, 34, 32 ], [ 31, 18, 34, 32 ],
[ 31, 18, 36, 32 ], [ 31, 18, 46, 16 ], [ 31, 18, 48, 16 ],
[ 31, 18, 54, 32 ], [ 31, 18, 56, 32 ], [ 31, 19, 34, 32 ],
[ 31, 19, 36, 32 ], [ 31, 19, 46, 16 ], [ 31, 19, 48, 16 ],
[ 31, 19, 54, 32 ], [ 31, 19, 56, 32 ], [ 31, 20, 34, 32 ],
[ 31, 20, 36, 32 ], [ 31, 20, 46, 32 ], [ 31, 20, 48, 32 ],
[ 31, 20, 54, 16 ], [ 31, 20, 56, 16 ], [ 31, 22, 20, 16 ],
[ 31, 22, 33, 16 ], [ 31, 23, 17, 16 ], [ 31, 23, 33, 32 ],
[ 31, 24, 34, 16 ], [ 31, 24, 36, 16 ], [ 31, 25, 38, 16 ],
[ 31, 25, 40, 16 ], [ 31, 26, 25, 32 ], [ 31, 26, 28, 16 ],
[ 31, 26, 30, 32 ], [ 31, 26, 41, 32 ], [ 31, 26, 44, 16 ],
[ 31, 26, 46, 32 ], [ 31, 27, 24, 16 ], [ 31, 27, 38, 16 ],
[ 31, 28, 24, 16 ], [ 31, 28, 38, 16 ], [ 31, 29, 40, 32 ],
[ 31, 29, 44, 32 ], [ 31, 32, 25, 32 ], [ 31, 32, 28, 16 ],
[ 31, 32, 30, 32 ], [ 31, 32, 41, 32 ], [ 31, 32, 44, 16 ],
[ 31, 32, 46, 32 ], [ 31, 33, 25, 32 ], [ 31, 33, 28, 16 ],
[ 31, 33, 30, 32 ], [ 31, 33, 41, 32 ], [ 31, 33, 44, 16 ],
[ 31, 33, 46, 32 ] ]
k = 18: F-action on Pi is () [31,1,18]
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 0 modulo 4: 1/144 q phi1 phi2 ( q^3-9*q^2+26*q-24 )
q congruent 1 modulo 4: 1/144 q phi1^2 phi2 ( q^2-8*q+15 )
q congruent 2 modulo 4: 1/144 q phi1 phi2 ( q^3-9*q^2+26*q-24 )
q congruent 3 modulo 4: 1/144 q phi1^2 phi2 ( q^2-8*q+15 )
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 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 6 ], [ 4, 2, 1, 3 ], [ 5, 1, 1, 12 ], [ 6, 1, 1, 10 ],
[ 7, 1, 1, 12 ], [ 7, 2, 1, 6 ], [ 7, 3, 1, 6 ], [ 7, 4, 1, 6 ],
[ 7, 5, 1, 3 ], [ 8, 1, 1, 12 ], [ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ],
[ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ], [ 12, 1, 1, 24 ], [ 12, 2, 1, 12 ],
[ 12, 3, 1, 12 ], [ 12, 4, 1, 6 ], [ 13, 1, 1, 24 ], [ 13, 2, 1, 12 ],
[ 14, 1, 1, 12 ], [ 14, 2, 1, 6 ], [ 17, 1, 1, 24 ], [ 17, 2, 1, 12 ],
[ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 19, 1, 1, 16 ], [ 19, 2, 1, 8 ],
[ 19, 3, 1, 8 ], [ 19, 4, 1, 8 ], [ 19, 5, 1, 4 ], [ 20, 1, 1, 24 ],
[ 20, 2, 1, 12 ], [ 21, 1, 1, 48 ], [ 21, 1, 9, 6 ], [ 21, 2, 1, 24 ],
[ 21, 3, 1, 24 ], [ 21, 4, 1, 24 ], [ 21, 4, 4, 3 ], [ 21, 5, 1, 12 ],
[ 21, 6, 1, 12 ], [ 21, 7, 1, 12 ], [ 21, 7, 4, 6 ], [ 23, 1, 1, 48 ],
[ 23, 2, 1, 24 ], [ 23, 3, 1, 24 ], [ 23, 4, 1, 24 ], [ 23, 5, 1, 24 ],
[ 23, 6, 1, 12 ], [ 24, 1, 1, 24 ], [ 24, 2, 1, 12 ], [ 27, 1, 15, 36 ],
[ 27, 2, 4, 18 ], [ 27, 4, 6, 18 ], [ 27, 5, 4, 18 ], [ 27, 7, 4, 9 ],
[ 27, 12, 6, 36 ], [ 28, 1, 1, 48 ], [ 28, 1, 4, 24 ], [ 28, 2, 1, 24 ],
[ 28, 3, 1, 24 ], [ 28, 3, 4, 12 ], [ 28, 4, 1, 24 ], [ 28, 5, 1, 12 ],
[ 28, 6, 1, 12 ], [ 28, 6, 4, 24 ], [ 30, 1, 4, 72 ], [ 30, 2, 4, 36 ],
[ 30, 3, 4, 36 ], [ 30, 13, 4, 72 ], [ 31, 2, 2, 72 ], [ 31, 3, 2, 72 ],
[ 31, 4, 18, 72 ], [ 31, 5, 37, 72 ], [ 31, 9, 2, 36 ], [ 31, 11, 2, 36 ],
[ 31, 14, 2, 36 ], [ 31, 14, 3, 144 ], [ 31, 15, 4, 36 ], [ 31, 16, 2, 36 ],
[ 31, 21, 36, 36 ], [ 31, 23, 2, 36 ] ]
k = 19: F-action on Pi is () [31,1,19]
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 0 modulo 4: 1/48 q phi1 phi2 ( q^3-3*q^2-2*q+8 )
q congruent 1 modulo 4: 1/48 q phi1 phi2 ( q^3-3*q^2-5*q+15 )
q congruent 2 modulo 4: 1/48 q phi1 phi2 ( q^3-3*q^2-2*q+8 )
q congruent 3 modulo 4: 1/48 q phi1 phi2 ( q^3-3*q^2-5*q+15 )
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 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 4 ], [ 6, 1, 2, 2 ],
[ 7, 1, 3, 8 ], [ 7, 1, 4, 4 ], [ 7, 2, 3, 4 ], [ 7, 2, 4, 2 ],
[ 7, 3, 3, 4 ], [ 7, 3, 4, 2 ], [ 7, 4, 3, 4 ], [ 7, 4, 4, 2 ],
[ 7, 5, 3, 2 ], [ 7, 5, 4, 1 ], [ 8, 1, 2, 4 ], [ 12, 1, 1, 8 ],
[ 12, 1, 4, 8 ], [ 12, 2, 1, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 1, 4 ],
[ 12, 3, 3, 4 ], [ 12, 3, 4, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 4, 2 ],
[ 13, 1, 3, 8 ], [ 13, 2, 3, 4 ], [ 14, 1, 2, 4 ], [ 14, 1, 4, 8 ],
[ 14, 2, 2, 2 ], [ 14, 2, 4, 4 ], [ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ],
[ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 21, 1, 2, 16 ], [ 21, 1, 10, 6 ],
[ 21, 2, 6, 8 ], [ 21, 2, 8, 8 ], [ 21, 3, 6, 8 ], [ 21, 3, 7, 8 ],
[ 21, 4, 6, 8 ], [ 21, 4, 8, 3 ], [ 21, 5, 6, 4 ], [ 21, 5, 8, 4 ],
[ 21, 6, 6, 4 ], [ 21, 6, 7, 4 ], [ 21, 7, 6, 4 ], [ 21, 7, 8, 6 ],
[ 23, 1, 5, 16 ], [ 23, 2, 5, 8 ], [ 23, 3, 5, 8 ], [ 23, 4, 5, 8 ],
[ 23, 5, 5, 8 ], [ 23, 6, 5, 4 ], [ 24, 1, 3, 8 ], [ 24, 2, 3, 4 ],
[ 27, 1, 16, 24 ], [ 27, 1, 18, 12 ], [ 27, 2, 8, 6 ], [ 27, 2, 13, 12 ],
[ 27, 4, 7, 6 ], [ 27, 4, 17, 12 ], [ 27, 5, 7, 6 ], [ 27, 5, 14, 12 ],
[ 27, 7, 8, 3 ], [ 27, 7, 13, 6 ], [ 27, 12, 7, 12 ], [ 27, 12, 17, 24 ],
[ 28, 1, 6, 16 ], [ 28, 2, 6, 8 ], [ 28, 2, 8, 8 ], [ 28, 3, 6, 8 ],
[ 28, 4, 5, 8 ], [ 28, 5, 6, 8 ], [ 28, 5, 8, 4 ], [ 28, 6, 6, 4 ],
[ 30, 1, 7, 24 ], [ 30, 2, 7, 12 ], [ 30, 3, 7, 12 ], [ 30, 13, 8, 24 ],
[ 31, 2, 6, 24 ], [ 31, 2, 10, 24 ], [ 31, 3, 6, 24 ], [ 31, 3, 10, 24 ],
[ 31, 4, 19, 24 ], [ 31, 5, 41, 24 ], [ 31, 9, 6, 12 ], [ 31, 9, 11, 12 ],
[ 31, 11, 6, 12 ], [ 31, 11, 10, 24 ], [ 31, 14, 9, 12 ],
[ 31, 14, 16, 48 ], [ 31, 15, 8, 12 ], [ 31, 15, 23, 12 ],
[ 31, 16, 6, 12 ], [ 31, 16, 10, 12 ], [ 31, 21, 41, 12 ],
[ 31, 21, 42, 12 ], [ 31, 23, 6, 12 ], [ 31, 23, 10, 24 ] ]
k = 20: F-action on Pi is () [31,1,20]
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 0 modulo 4: 1/48 q^2 phi1 phi2^2 ( q-2 )
q congruent 1 modulo 4: 1/48 q phi1^2 phi2 ( q^2-5 )
q congruent 2 modulo 4: 1/48 q^2 phi1 phi2^2 ( q-2 )
q congruent 3 modulo 4: 1/48 q phi1^2 phi2 ( q^2-5 )
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, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ],
[ 4, 2, 1, 1 ], [ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 6, 1, 1, 2 ],
[ 7, 1, 1, 4 ], [ 7, 1, 2, 8 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 4 ],
[ 7, 3, 1, 2 ], [ 7, 3, 2, 4 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 4 ],
[ 7, 5, 1, 1 ], [ 7, 5, 2, 2 ], [ 8, 1, 1, 4 ], [ 12, 1, 3, 8 ],
[ 12, 1, 4, 8 ], [ 12, 2, 3, 4 ], [ 12, 2, 4, 4 ], [ 12, 3, 2, 4 ],
[ 12, 3, 3, 4 ], [ 12, 3, 4, 4 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 2 ],
[ 13, 1, 2, 8 ], [ 13, 2, 2, 4 ], [ 14, 1, 1, 4 ], [ 14, 1, 3, 8 ],
[ 14, 2, 1, 2 ], [ 14, 2, 3, 4 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ],
[ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ], [ 21, 1, 3, 16 ], [ 21, 1, 9, 6 ],
[ 21, 2, 3, 8 ], [ 21, 2, 4, 8 ], [ 21, 3, 2, 8 ], [ 21, 3, 5, 8 ],
[ 21, 4, 3, 8 ], [ 21, 4, 4, 3 ], [ 21, 5, 3, 4 ], [ 21, 5, 4, 4 ],
[ 21, 6, 2, 4 ], [ 21, 6, 5, 4 ], [ 21, 7, 3, 4 ], [ 21, 7, 4, 6 ],
[ 23, 1, 3, 16 ], [ 23, 2, 3, 8 ], [ 23, 3, 3, 8 ], [ 23, 4, 3, 8 ],
[ 23, 5, 3, 8 ], [ 23, 6, 3, 4 ], [ 24, 1, 2, 8 ], [ 24, 2, 2, 4 ],
[ 27, 1, 15, 12 ], [ 27, 1, 17, 24 ], [ 27, 2, 4, 6 ], [ 27, 2, 19, 12 ],
[ 27, 4, 6, 6 ], [ 27, 4, 16, 12 ], [ 27, 5, 4, 6 ], [ 27, 5, 18, 12 ],
[ 27, 7, 4, 3 ], [ 27, 7, 19, 6 ], [ 27, 12, 6, 12 ], [ 27, 12, 16, 24 ],
[ 28, 1, 3, 16 ], [ 28, 2, 3, 8 ], [ 28, 2, 4, 8 ], [ 28, 3, 3, 8 ],
[ 28, 4, 3, 8 ], [ 28, 5, 3, 4 ], [ 28, 5, 4, 8 ], [ 28, 6, 3, 4 ],
[ 30, 1, 17, 24 ], [ 30, 2, 17, 12 ], [ 30, 3, 17, 12 ], [ 30, 13, 14, 24 ],
[ 31, 2, 3, 24 ], [ 31, 2, 9, 24 ], [ 31, 3, 3, 24 ], [ 31, 3, 11, 24 ],
[ 31, 4, 20, 24 ], [ 31, 5, 39, 24 ], [ 31, 9, 3, 12 ], [ 31, 9, 10, 12 ],
[ 31, 11, 3, 12 ], [ 31, 11, 11, 24 ], [ 31, 14, 5, 12 ],
[ 31, 14, 12, 48 ], [ 31, 15, 29, 12 ], [ 31, 15, 44, 12 ],
[ 31, 16, 3, 12 ], [ 31, 16, 11, 12 ], [ 31, 21, 37, 12 ],
[ 31, 21, 40, 12 ], [ 31, 23, 3, 12 ], [ 31, 23, 11, 24 ] ]
k = 21: F-action on Pi is () [31,1,21]
Dynkin type is A_0(q) + T(phi2^4 phi6)
Order of center |Z^F|: phi2^4 phi6
Numbers of classes in class type:
q congruent 0 modulo 4: 1/144 q^2 phi1^2 phi2 ( q-2 )
q congruent 1 modulo 4: 1/144 q phi1^2 phi2^2 ( q-3 )
q congruent 2 modulo 4: 1/144 q^2 phi1^2 phi2 ( q-2 )
q congruent 3 modulo 4: 1/144 q phi1^2 phi2^2 ( q-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, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 6 ], [ 4, 2, 2, 3 ], [ 5, 1, 2, 12 ], [ 6, 1, 2, 10 ],
[ 7, 1, 4, 12 ], [ 7, 2, 4, 6 ], [ 7, 3, 4, 6 ], [ 7, 4, 4, 6 ],
[ 7, 5, 4, 3 ], [ 8, 1, 2, 12 ], [ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ],
[ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ], [ 12, 1, 3, 24 ], [ 12, 2, 3, 12 ],
[ 12, 3, 2, 12 ], [ 12, 4, 3, 6 ], [ 13, 1, 4, 24 ], [ 13, 2, 4, 12 ],
[ 14, 1, 2, 12 ], [ 14, 2, 2, 6 ], [ 17, 1, 2, 24 ], [ 17, 2, 2, 12 ],
[ 18, 1, 4, 24 ], [ 18, 2, 4, 12 ], [ 19, 1, 2, 16 ], [ 19, 2, 2, 8 ],
[ 19, 3, 2, 8 ], [ 19, 4, 2, 8 ], [ 19, 5, 2, 4 ], [ 20, 1, 4, 24 ],
[ 20, 2, 4, 12 ], [ 21, 1, 4, 48 ], [ 21, 1, 10, 6 ], [ 21, 2, 10, 24 ],
[ 21, 3, 10, 24 ], [ 21, 4, 8, 3 ], [ 21, 4, 10, 24 ], [ 21, 5, 10, 12 ],
[ 21, 6, 10, 12 ], [ 21, 7, 8, 6 ], [ 21, 7, 10, 12 ], [ 23, 1, 7, 48 ],
[ 23, 2, 7, 24 ], [ 23, 3, 7, 24 ], [ 23, 4, 7, 24 ], [ 23, 5, 7, 24 ],
[ 23, 6, 7, 12 ], [ 24, 1, 4, 24 ], [ 24, 2, 4, 12 ], [ 27, 1, 18, 36 ],
[ 27, 2, 8, 18 ], [ 27, 4, 7, 18 ], [ 27, 5, 7, 18 ], [ 27, 7, 8, 9 ],
[ 27, 12, 7, 36 ], [ 28, 1, 8, 24 ], [ 28, 1, 10, 48 ], [ 28, 2, 10, 24 ],
[ 28, 3, 8, 12 ], [ 28, 3, 10, 24 ], [ 28, 4, 7, 24 ], [ 28, 5, 10, 12 ],
[ 28, 6, 8, 24 ], [ 28, 6, 10, 12 ], [ 30, 1, 20, 72 ], [ 30, 2, 20, 36 ],
[ 30, 3, 20, 36 ], [ 30, 13, 18, 72 ], [ 31, 2, 7, 72 ], [ 31, 3, 7, 72 ],
[ 31, 4, 21, 72 ], [ 31, 5, 43, 72 ], [ 31, 9, 7, 36 ], [ 31, 11, 7, 36 ],
[ 31, 14, 8, 36 ], [ 31, 14, 15, 144 ], [ 31, 15, 48, 36 ],
[ 31, 16, 7, 36 ], [ 31, 21, 45, 36 ], [ 31, 23, 7, 36 ] ]
k = 22: F-action on Pi is () [31,1,22]
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 0 modulo 4: 1/24 q^2 phi1^2 phi2 ( q-2 )
q congruent 1 modulo 4: 1/24 q phi1^2 phi2 ( q^2-2*q-1 )
q congruent 2 modulo 4: 1/24 q^2 phi1^2 phi2 ( q-2 )
q congruent 3 modulo 4: 1/24 q phi1^2 phi2 ( q^2-2*q-1 )
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, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 6 ], [ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ],
[ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 4 ],
[ 10, 2, 1, 2 ], [ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 12, 1, 2, 4 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 4 ],
[ 13, 2, 1, 2 ], [ 13, 2, 2, 2 ], [ 14, 1, 1, 4 ], [ 14, 2, 1, 2 ],
[ 17, 1, 1, 4 ], [ 17, 2, 1, 2 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 4 ],
[ 18, 2, 1, 2 ], [ 18, 2, 2, 2 ], [ 19, 1, 1, 8 ], [ 19, 2, 1, 4 ],
[ 19, 3, 1, 4 ], [ 19, 4, 1, 4 ], [ 19, 5, 1, 2 ], [ 20, 1, 1, 4 ],
[ 20, 1, 2, 4 ], [ 20, 2, 1, 2 ], [ 20, 2, 2, 2 ], [ 21, 1, 5, 8 ],
[ 21, 1, 9, 6 ], [ 21, 2, 2, 4 ], [ 21, 3, 3, 4 ], [ 21, 4, 2, 4 ],
[ 21, 4, 4, 3 ], [ 21, 5, 2, 2 ], [ 21, 6, 3, 4 ], [ 21, 7, 2, 4 ],
[ 21, 7, 4, 6 ], [ 23, 1, 2, 8 ], [ 23, 1, 4, 8 ], [ 23, 2, 2, 4 ],
[ 23, 2, 4, 4 ], [ 23, 3, 2, 4 ], [ 23, 3, 4, 4 ], [ 23, 4, 2, 4 ],
[ 23, 4, 4, 4 ], [ 23, 5, 2, 4 ], [ 23, 5, 4, 4 ], [ 23, 6, 2, 2 ],
[ 23, 6, 4, 2 ], [ 24, 1, 1, 4 ], [ 24, 1, 2, 4 ], [ 24, 2, 1, 2 ],
[ 24, 2, 2, 2 ], [ 27, 1, 15, 12 ], [ 27, 2, 4, 6 ], [ 27, 4, 6, 6 ],
[ 27, 5, 4, 6 ], [ 27, 7, 4, 3 ], [ 27, 12, 6, 12 ], [ 28, 1, 2, 8 ],
[ 28, 1, 4, 12 ], [ 28, 2, 2, 4 ], [ 28, 3, 2, 4 ], [ 28, 3, 4, 6 ],
[ 28, 4, 2, 4 ], [ 28, 4, 4, 4 ], [ 28, 5, 2, 2 ], [ 28, 6, 2, 4 ],
[ 28, 6, 4, 12 ], [ 30, 1, 4, 12 ], [ 30, 1, 17, 12 ], [ 30, 2, 4, 6 ],
[ 30, 2, 17, 6 ], [ 30, 3, 4, 6 ], [ 30, 3, 17, 6 ], [ 30, 13, 4, 12 ],
[ 30, 13, 14, 12 ], [ 31, 2, 8, 12 ], [ 31, 3, 8, 12 ], [ 31, 4, 22, 12 ],
[ 31, 5, 38, 12 ], [ 31, 5, 40, 12 ], [ 31, 9, 8, 6 ], [ 31, 11, 8, 6 ],
[ 31, 14, 10, 12 ], [ 31, 14, 17, 24 ], [ 31, 15, 14, 12 ],
[ 31, 16, 8, 6 ], [ 31, 21, 38, 12 ], [ 31, 23, 8, 6 ] ]
k = 23: F-action on Pi is () [31,1,23]
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 0 modulo 4: 1/24 q^3 phi1^2 phi2
q congruent 1 modulo 4: 1/24 q phi1^3 phi2^2
q congruent 2 modulo 4: 1/24 q^3 phi1^2 phi2
q congruent 3 modulo 4: 1/24 q phi1^3 phi2^2
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, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 3, 4 ],
[ 7, 2, 3, 2 ], [ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 3, 1 ],
[ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 14, 1, 4, 4 ],
[ 14, 2, 4, 2 ], [ 21, 1, 6, 8 ], [ 21, 1, 10, 6 ], [ 21, 2, 7, 4 ],
[ 21, 3, 9, 4 ], [ 21, 4, 7, 4 ], [ 21, 4, 8, 3 ], [ 21, 5, 7, 2 ],
[ 21, 6, 8, 4 ], [ 21, 7, 7, 4 ], [ 21, 7, 8, 6 ], [ 27, 1, 16, 12 ],
[ 27, 2, 13, 6 ], [ 27, 4, 17, 6 ], [ 27, 5, 14, 6 ], [ 27, 7, 13, 3 ],
[ 27, 12, 17, 12 ], [ 28, 1, 7, 8 ], [ 28, 2, 7, 4 ], [ 28, 3, 7, 4 ],
[ 28, 5, 7, 4 ], [ 28, 6, 7, 4 ], [ 31, 2, 5, 12 ], [ 31, 3, 4, 12 ],
[ 31, 4, 23, 12 ], [ 31, 9, 5, 6 ], [ 31, 11, 4, 12 ], [ 31, 14, 6, 12 ],
[ 31, 14, 14, 24 ], [ 31, 15, 33, 12 ], [ 31, 16, 4, 6 ],
[ 31, 21, 43, 12 ], [ 31, 23, 4, 12 ] ]
k = 24: F-action on Pi is () [31,1,24]
Dynkin type is A_0(q) + T(phi1 phi2^3 phi6)
Order of center |Z^F|: phi1 phi2^3 phi6
Numbers of classes in class type:
q congruent 0 modulo 4: 1/24 q^2 phi1 phi2^2 ( q-2 )
q congruent 1 modulo 4: 1/24 q phi1 phi2^2 ( q^2-2*q-1 )
q congruent 2 modulo 4: 1/24 q^2 phi1 phi2^2 ( q-2 )
q congruent 3 modulo 4: 1/24 q phi1 phi2^2 ( q^2-2*q-1 )
Fusion of maximal tori of C^F in those of G^F:
[ 24 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ],
[ 6, 1, 2, 6 ], [ 7, 1, 4, 4 ], [ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ],
[ 7, 4, 4, 2 ], [ 7, 5, 4, 1 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 4 ],
[ 10, 2, 2, 2 ], [ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 12, 1, 2, 4 ],
[ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 4 ],
[ 13, 2, 3, 2 ], [ 13, 2, 4, 2 ], [ 14, 1, 2, 4 ], [ 14, 2, 2, 2 ],
[ 17, 1, 2, 4 ], [ 17, 2, 2, 2 ], [ 18, 1, 3, 4 ], [ 18, 1, 4, 4 ],
[ 18, 2, 3, 2 ], [ 18, 2, 4, 2 ], [ 19, 1, 2, 8 ], [ 19, 2, 2, 4 ],
[ 19, 3, 2, 4 ], [ 19, 4, 2, 4 ], [ 19, 5, 2, 2 ], [ 20, 1, 3, 4 ],
[ 20, 1, 4, 4 ], [ 20, 2, 3, 2 ], [ 20, 2, 4, 2 ], [ 21, 1, 7, 8 ],
[ 21, 1, 10, 6 ], [ 21, 2, 9, 4 ], [ 21, 3, 8, 4 ], [ 21, 4, 8, 3 ],
[ 21, 4, 9, 4 ], [ 21, 5, 9, 2 ], [ 21, 6, 9, 4 ], [ 21, 7, 8, 6 ],
[ 21, 7, 9, 4 ], [ 23, 1, 6, 8 ], [ 23, 1, 8, 8 ], [ 23, 2, 6, 4 ],
[ 23, 2, 8, 4 ], [ 23, 3, 6, 4 ], [ 23, 3, 8, 4 ], [ 23, 4, 6, 4 ],
[ 23, 4, 8, 4 ], [ 23, 5, 6, 4 ], [ 23, 5, 8, 4 ], [ 23, 6, 6, 2 ],
[ 23, 6, 8, 2 ], [ 24, 1, 3, 4 ], [ 24, 1, 4, 4 ], [ 24, 2, 3, 2 ],
[ 24, 2, 4, 2 ], [ 27, 1, 18, 12 ], [ 27, 2, 8, 6 ], [ 27, 4, 7, 6 ],
[ 27, 5, 7, 6 ], [ 27, 7, 8, 3 ], [ 27, 12, 7, 12 ], [ 28, 1, 8, 12 ],
[ 28, 1, 9, 8 ], [ 28, 2, 9, 4 ], [ 28, 3, 8, 6 ], [ 28, 3, 9, 4 ],
[ 28, 4, 6, 4 ], [ 28, 4, 8, 4 ], [ 28, 5, 9, 2 ], [ 28, 6, 8, 12 ],
[ 28, 6, 9, 4 ], [ 30, 1, 7, 12 ], [ 30, 1, 20, 12 ], [ 30, 2, 7, 6 ],
[ 30, 2, 20, 6 ], [ 30, 3, 7, 6 ], [ 30, 3, 20, 6 ], [ 30, 13, 8, 12 ],
[ 30, 13, 18, 12 ], [ 31, 2, 11, 12 ], [ 31, 3, 9, 12 ], [ 31, 4, 24, 12 ],
[ 31, 5, 42, 12 ], [ 31, 5, 44, 12 ], [ 31, 9, 9, 6 ], [ 31, 11, 9, 6 ],
[ 31, 14, 11, 12 ], [ 31, 14, 18, 24 ], [ 31, 15, 18, 12 ],
[ 31, 16, 9, 6 ], [ 31, 21, 44, 12 ], [ 31, 23, 9, 6 ] ]
k = 25: F-action on Pi is () [31,1,25]
Dynkin type is A_0(q) + T(phi1 phi2 phi3 phi4)
Order of center |Z^F|: phi1 phi2 phi3 phi4
Numbers of classes in class type:
q congruent 0 modulo 4: 1/24 q^3 phi1 phi2^2
q congruent 1 modulo 4: 1/24 q phi1^2 phi2^3
q congruent 2 modulo 4: 1/24 q^3 phi1 phi2^2
q congruent 3 modulo 4: 1/24 q phi1^2 phi2^3
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, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 2, 4 ],
[ 7, 2, 2, 2 ], [ 7, 3, 2, 2 ], [ 7, 4, 2, 2 ], [ 7, 5, 2, 1 ],
[ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 14, 1, 3, 4 ],
[ 14, 2, 3, 2 ], [ 21, 1, 8, 8 ], [ 21, 1, 9, 6 ], [ 21, 2, 5, 4 ],
[ 21, 3, 4, 4 ], [ 21, 4, 4, 3 ], [ 21, 4, 5, 4 ], [ 21, 5, 5, 2 ],
[ 21, 6, 4, 4 ], [ 21, 7, 4, 6 ], [ 21, 7, 5, 4 ], [ 27, 1, 17, 12 ],
[ 27, 2, 19, 6 ], [ 27, 4, 16, 6 ], [ 27, 5, 18, 6 ], [ 27, 7, 19, 3 ],
[ 27, 12, 16, 12 ], [ 28, 1, 5, 8 ], [ 28, 2, 5, 4 ], [ 28, 3, 5, 4 ],
[ 28, 5, 5, 4 ], [ 28, 6, 5, 4 ], [ 31, 2, 4, 12 ], [ 31, 3, 5, 12 ],
[ 31, 4, 25, 12 ], [ 31, 9, 4, 6 ], [ 31, 11, 5, 12 ], [ 31, 14, 7, 12 ],
[ 31, 14, 13, 24 ], [ 31, 15, 39, 12 ], [ 31, 16, 5, 6 ],
[ 31, 21, 39, 12 ], [ 31, 23, 5, 12 ] ]
k = 26: F-action on Pi is () [31,1,26]
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 0 modulo 4: 1/36 q phi1 phi2 ( q^3-q-6 )
q congruent 1 modulo 4: 1/36 q phi1 phi2 ( q^3-q-12 )
q congruent 2 modulo 4: 1/36 q phi1 phi2 ( q^3-q-6 )
q congruent 3 modulo 4: 1/36 q phi1 phi2 ( q^3-q-12 )
Fusion of maximal tori of C^F in those of G^F:
[ 26 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ],
[ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 6, 1, 1, 4 ], [ 10, 1, 1, 2 ],
[ 10, 2, 1, 1 ], [ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 19, 1, 1, 4 ],
[ 19, 2, 1, 2 ], [ 19, 3, 1, 2 ], [ 19, 4, 1, 2 ], [ 19, 5, 1, 1 ],
[ 21, 1, 9, 12 ], [ 21, 4, 4, 6 ], [ 21, 7, 4, 12 ], [ 25, 1, 9, 18 ],
[ 25, 2, 9, 9 ], [ 26, 1, 9, 18 ], [ 26, 2, 6, 9 ], [ 28, 1, 4, 12 ],
[ 28, 3, 4, 6 ], [ 28, 6, 4, 12 ], [ 31, 4, 26, 18 ], [ 31, 7, 26, 18 ],
[ 31, 8, 27, 18 ], [ 31, 14, 4, 36 ], [ 31, 17, 2, 36 ], [ 31, 22, 26, 9 ],
[ 31, 30, 24, 36 ], [ 31, 30, 26, 36 ] ]
k = 27: F-action on Pi is () [31,1,27]
Dynkin type is A_0(q) + T(phi2^2 phi6^2)
Order of center |Z^F|: phi2^2 phi6^2
Numbers of classes in class type:
q congruent 0 modulo 4: 1/36 q phi1 phi2 ( q^3-q-6 )
q congruent 1 modulo 4: 1/36 q phi1 phi2 ( q^3-q-12 )
q congruent 2 modulo 4: 1/36 q phi1 phi2 ( q^3-q-6 )
q congruent 3 modulo 4: 1/36 q phi1 phi2 ( q^3-q-12 )
Fusion of maximal tori of C^F in those of G^F:
[ 27 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 6, 1, 2, 4 ], [ 10, 1, 2, 2 ],
[ 10, 2, 2, 1 ], [ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 19, 1, 2, 4 ],
[ 19, 2, 2, 2 ], [ 19, 3, 2, 2 ], [ 19, 4, 2, 2 ], [ 19, 5, 2, 1 ],
[ 21, 1, 10, 12 ], [ 21, 4, 8, 6 ], [ 21, 7, 8, 12 ], [ 25, 1, 10, 18 ],
[ 25, 2, 10, 9 ], [ 26, 1, 10, 18 ], [ 26, 2, 7, 9 ], [ 28, 1, 8, 12 ],
[ 28, 3, 8, 6 ], [ 28, 6, 8, 12 ], [ 31, 4, 27, 18 ], [ 31, 7, 27, 18 ],
[ 31, 8, 26, 18 ], [ 31, 14, 19, 36 ], [ 31, 17, 5, 36 ], [ 31, 22, 27, 9 ],
[ 31, 30, 22, 36 ], [ 31, 30, 27, 36 ] ]
k = 28: F-action on Pi is () [31,1,28]
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 0 modulo 4: 1/32 q^2 ( q^4-4*q^3+2*q^2+8*q-8 )
q congruent 1 modulo 4: 1/32 phi1 phi2 ( q^4-4*q^3+2*q^2+9 )
q congruent 2 modulo 4: 1/32 q^2 ( q^4-4*q^3+2*q^2+8*q-8 )
q congruent 3 modulo 4: 1/32 phi1 phi2 ( q^4-4*q^3+2*q^2+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 6, 8 ], [ 9, 1, 8, 8 ], [ 9, 2, 6, 4 ], [ 9, 2, 8, 4 ],
[ 9, 3, 6, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 6, 4 ], [ 9, 4, 8, 4 ],
[ 9, 5, 6, 2 ], [ 9, 5, 8, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ],
[ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 12, 1, 1, 8 ], [ 12, 2, 1, 4 ],
[ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ],
[ 16, 1, 13, 16 ], [ 16, 2, 13, 8 ], [ 16, 3, 13, 8 ], [ 16, 4, 13, 8 ],
[ 16, 5, 11, 8 ], [ 16, 5, 15, 8 ], [ 16, 6, 11, 8 ], [ 16, 6, 15, 8 ],
[ 16, 7, 11, 8 ], [ 16, 7, 15, 8 ], [ 16, 9, 13, 4 ], [ 16, 10, 11, 4 ],
[ 16, 10, 15, 4 ], [ 16, 12, 11, 4 ], [ 16, 12, 15, 4 ], [ 16, 13, 13, 4 ],
[ 16, 14, 9, 8 ], [ 16, 15, 13, 4 ], [ 16, 16, 13, 4 ], [ 17, 1, 1, 8 ],
[ 17, 2, 1, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 1, 2 ],
[ 18, 2, 3, 2 ], [ 20, 1, 1, 4 ], [ 20, 1, 3, 4 ], [ 20, 2, 1, 2 ],
[ 20, 2, 3, 2 ], [ 23, 1, 1, 8 ], [ 23, 1, 5, 8 ], [ 23, 2, 1, 4 ],
[ 23, 2, 5, 4 ], [ 23, 3, 1, 4 ], [ 23, 3, 5, 4 ], [ 23, 4, 1, 4 ],
[ 23, 4, 5, 4 ], [ 23, 5, 1, 4 ], [ 23, 5, 5, 4 ], [ 23, 6, 1, 2 ],
[ 23, 6, 5, 2 ], [ 25, 1, 5, 8 ], [ 25, 1, 6, 8 ], [ 25, 2, 3, 4 ],
[ 25, 2, 4, 4 ], [ 25, 3, 2, 4 ], [ 25, 3, 4, 4 ], [ 26, 1, 5, 8 ],
[ 26, 1, 6, 8 ], [ 26, 2, 3, 4 ], [ 26, 2, 4, 4 ], [ 26, 3, 2, 4 ],
[ 26, 3, 4, 4 ], [ 27, 1, 19, 8 ], [ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ],
[ 29, 1, 13, 16 ], [ 29, 1, 17, 16 ], [ 29, 2, 13, 8 ], [ 29, 2, 17, 8 ],
[ 29, 3, 13, 8 ], [ 29, 3, 17, 8 ], [ 29, 4, 13, 8 ], [ 29, 4, 17, 8 ],
[ 29, 5, 13, 8 ], [ 29, 5, 17, 8 ], [ 29, 6, 9, 8 ], [ 29, 6, 13, 8 ],
[ 29, 7, 9, 8 ], [ 29, 7, 13, 8 ], [ 29, 8, 9, 8 ], [ 29, 8, 13, 8 ],
[ 29, 9, 13, 4 ], [ 29, 9, 17, 4 ], [ 29, 10, 9, 4 ], [ 29, 10, 13, 4 ],
[ 29, 11, 9, 4 ], [ 29, 11, 13, 4 ], [ 29, 12, 9, 4 ], [ 29, 12, 13, 4 ],
[ 29, 13, 9, 4 ], [ 29, 13, 13, 4 ], [ 30, 1, 6, 16 ], [ 30, 1, 8, 16 ],
[ 30, 2, 6, 8 ], [ 30, 2, 8, 8 ], [ 30, 3, 6, 8 ], [ 30, 3, 8, 8 ],
[ 30, 5, 5, 8 ], [ 30, 5, 8, 8 ], [ 30, 6, 5, 8 ], [ 30, 6, 8, 8 ],
[ 30, 8, 6, 8 ], [ 30, 8, 7, 8 ], [ 30, 9, 6, 4 ], [ 30, 9, 7, 8 ],
[ 30, 10, 6, 8 ], [ 30, 10, 7, 4 ], [ 31, 2, 37, 16 ], [ 31, 3, 41, 16 ],
[ 31, 4, 28, 16 ], [ 31, 5, 33, 16 ], [ 31, 5, 45, 16 ], [ 31, 6, 8, 16 ],
[ 31, 6, 11, 16 ], [ 31, 7, 8, 16 ], [ 31, 7, 11, 16 ], [ 31, 8, 8, 16 ],
[ 31, 8, 11, 16 ], [ 31, 9, 38, 8 ], [ 31, 10, 43, 16 ], [ 31, 11, 39, 8 ],
[ 31, 12, 8, 8 ], [ 31, 12, 11, 8 ], [ 31, 16, 41, 8 ], [ 31, 17, 24, 16 ],
[ 31, 18, 37, 8 ], [ 31, 18, 49, 16 ], [ 31, 19, 37, 8 ],
[ 31, 19, 49, 16 ], [ 31, 20, 37, 16 ], [ 31, 20, 49, 8 ], [ 31, 22, 8, 8 ],
[ 31, 22, 11, 8 ], [ 31, 23, 41, 8 ], [ 31, 24, 29, 8 ], [ 31, 24, 41, 8 ],
[ 31, 25, 29, 8 ], [ 31, 25, 41, 8 ], [ 31, 26, 10, 8 ], [ 31, 26, 13, 16 ],
[ 31, 27, 8, 8 ], [ 31, 27, 11, 8 ], [ 31, 28, 8, 8 ], [ 31, 28, 11, 8 ],
[ 31, 32, 10, 8 ], [ 31, 32, 13, 16 ], [ 31, 33, 10, 8 ],
[ 31, 33, 13, 16 ] ]
k = 29: F-action on Pi is () [31,1,29]
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 0 modulo 4: 1/16 q^4 ( q^2-2 )
q congruent 1 modulo 4: 1/16 phi1 phi2 phi4 ( q^2-3 )
q congruent 2 modulo 4: 1/16 q^4 ( q^2-2 )
q congruent 3 modulo 4: 1/16 phi1 phi2 phi4 ( q^2-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 29 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 12, 1, 4, 4 ],
[ 12, 2, 4, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 4, 1 ],
[ 16, 1, 11, 8 ], [ 16, 2, 11, 4 ], [ 16, 3, 11, 4 ], [ 16, 4, 11, 4 ],
[ 16, 9, 11, 2 ], [ 16, 13, 11, 4 ], [ 16, 14, 7, 4 ], [ 16, 14, 10, 4 ],
[ 16, 15, 11, 4 ], [ 16, 16, 11, 4 ], [ 27, 1, 20, 8 ], [ 27, 5, 17, 4 ],
[ 27, 9, 19, 4 ], [ 31, 2, 16, 8 ], [ 31, 3, 16, 8 ], [ 31, 4, 29, 8 ],
[ 31, 9, 16, 4 ], [ 31, 10, 46, 8 ], [ 31, 11, 14, 8 ], [ 31, 16, 16, 4 ],
[ 31, 17, 10, 8 ], [ 31, 23, 14, 8 ] ]
k = 30: F-action on Pi is () [31,1,30]
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 0 modulo 4: 1/32 q^4 ( q^2-2 )
q congruent 1 modulo 4: 1/32 phi1^2 phi2 ( q^3+q^2-q-5 )
q congruent 2 modulo 4: 1/32 q^4 ( q^2-2 )
q congruent 3 modulo 4: 1/32 phi1^2 phi2 ( q^3+q^2-q-5 )
Fusion of maximal tori of C^F in those of G^F:
[ 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 1, 2, 4 ],
[ 4, 2, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 5, 8 ], [ 9, 1, 7, 8 ], [ 9, 2, 5, 4 ], [ 9, 2, 7, 4 ],
[ 9, 3, 5, 4 ], [ 9, 3, 7, 4 ], [ 9, 4, 5, 4 ], [ 9, 4, 7, 4 ],
[ 9, 5, 5, 2 ], [ 9, 5, 7, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ],
[ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 12, 1, 3, 8 ], [ 12, 2, 3, 4 ],
[ 12, 3, 2, 4 ], [ 12, 4, 3, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ],
[ 16, 1, 12, 16 ], [ 16, 2, 12, 8 ], [ 16, 3, 12, 8 ], [ 16, 4, 12, 8 ],
[ 16, 5, 10, 8 ], [ 16, 5, 14, 8 ], [ 16, 6, 10, 8 ], [ 16, 6, 14, 8 ],
[ 16, 7, 10, 8 ], [ 16, 7, 14, 8 ], [ 16, 9, 12, 4 ], [ 16, 10, 10, 4 ],
[ 16, 10, 14, 4 ], [ 16, 12, 10, 4 ], [ 16, 12, 14, 4 ], [ 16, 13, 12, 4 ],
[ 16, 14, 8, 8 ], [ 16, 15, 12, 4 ], [ 16, 16, 12, 4 ], [ 17, 1, 2, 8 ],
[ 17, 2, 2, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 2, 2 ],
[ 18, 2, 4, 2 ], [ 20, 1, 2, 4 ], [ 20, 1, 4, 4 ], [ 20, 2, 2, 2 ],
[ 20, 2, 4, 2 ], [ 23, 1, 3, 8 ], [ 23, 1, 7, 8 ], [ 23, 2, 3, 4 ],
[ 23, 2, 7, 4 ], [ 23, 3, 3, 4 ], [ 23, 3, 7, 4 ], [ 23, 4, 3, 4 ],
[ 23, 4, 7, 4 ], [ 23, 5, 3, 4 ], [ 23, 5, 7, 4 ], [ 23, 6, 3, 2 ],
[ 23, 6, 7, 2 ], [ 25, 1, 7, 8 ], [ 25, 1, 8, 8 ], [ 25, 2, 6, 4 ],
[ 25, 2, 7, 4 ], [ 25, 3, 6, 4 ], [ 25, 3, 8, 4 ], [ 26, 1, 7, 8 ],
[ 26, 1, 8, 8 ], [ 26, 2, 8, 4 ], [ 26, 2, 9, 4 ], [ 26, 3, 6, 4 ],
[ 26, 3, 8, 4 ], [ 27, 1, 19, 8 ], [ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ],
[ 29, 1, 15, 16 ], [ 29, 1, 19, 16 ], [ 29, 2, 15, 8 ], [ 29, 2, 19, 8 ],
[ 29, 3, 15, 8 ], [ 29, 3, 19, 8 ], [ 29, 4, 15, 8 ], [ 29, 4, 19, 8 ],
[ 29, 5, 15, 8 ], [ 29, 5, 19, 8 ], [ 29, 6, 11, 8 ], [ 29, 6, 15, 8 ],
[ 29, 7, 11, 8 ], [ 29, 7, 15, 8 ], [ 29, 8, 11, 8 ], [ 29, 8, 15, 8 ],
[ 29, 9, 15, 4 ], [ 29, 9, 19, 4 ], [ 29, 10, 11, 4 ], [ 29, 10, 15, 4 ],
[ 29, 11, 11, 4 ], [ 29, 11, 15, 4 ], [ 29, 12, 11, 4 ], [ 29, 12, 15, 4 ],
[ 29, 13, 11, 4 ], [ 29, 13, 15, 4 ], [ 30, 1, 19, 16 ], [ 30, 1, 21, 16 ],
[ 30, 2, 19, 8 ], [ 30, 2, 21, 8 ], [ 30, 3, 19, 8 ], [ 30, 3, 21, 8 ],
[ 30, 5, 19, 8 ], [ 30, 5, 22, 8 ], [ 30, 6, 19, 8 ], [ 30, 6, 22, 8 ],
[ 30, 8, 22, 8 ], [ 30, 8, 23, 8 ], [ 30, 9, 22, 4 ], [ 30, 9, 23, 8 ],
[ 30, 10, 22, 8 ], [ 30, 10, 23, 4 ], [ 31, 2, 39, 16 ], [ 31, 3, 42, 16 ],
[ 31, 4, 30, 16 ], [ 31, 5, 35, 16 ], [ 31, 5, 47, 16 ], [ 31, 6, 50, 16 ],
[ 31, 6, 53, 16 ], [ 31, 7, 30, 16 ], [ 31, 7, 36, 16 ], [ 31, 8, 29, 16 ],
[ 31, 8, 35, 16 ], [ 31, 9, 37, 8 ], [ 31, 10, 48, 16 ], [ 31, 11, 37, 8 ],
[ 31, 12, 50, 8 ], [ 31, 12, 53, 8 ], [ 31, 16, 42, 8 ], [ 31, 17, 26, 16 ],
[ 31, 18, 39, 8 ], [ 31, 18, 51, 16 ], [ 31, 19, 39, 8 ],
[ 31, 19, 51, 16 ], [ 31, 20, 39, 16 ], [ 31, 20, 51, 8 ],
[ 31, 22, 30, 8 ], [ 31, 22, 36, 8 ], [ 31, 23, 42, 8 ], [ 31, 24, 31, 8 ],
[ 31, 24, 43, 8 ], [ 31, 25, 31, 8 ], [ 31, 25, 43, 8 ], [ 31, 26, 58, 8 ],
[ 31, 26, 61, 16 ], [ 31, 27, 50, 8 ], [ 31, 27, 53, 8 ], [ 31, 28, 50, 8 ],
[ 31, 28, 53, 8 ], [ 31, 32, 58, 8 ], [ 31, 32, 61, 16 ], [ 31, 33, 58, 8 ],
[ 31, 33, 61, 16 ] ]
k = 31: F-action on Pi is () [31,1,31]
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 0 modulo 4: 1/32 q^3 ( q^3-2*q^2-2*q+4 )
q congruent 1 modulo 4: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2-2*q+9 )
q congruent 2 modulo 4: 1/32 q^3 ( q^3-2*q^2-2*q+4 )
q congruent 3 modulo 4: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2-2*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 4, 8 ],
[ 3, 2, 4, 4 ], [ 3, 3, 4, 4 ], [ 3, 4, 4, 4 ], [ 3, 5, 4, 2 ],
[ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 6, 8 ], [ 9, 1, 7, 8 ], [ 9, 2, 6, 4 ], [ 9, 2, 7, 4 ],
[ 9, 3, 6, 4 ], [ 9, 3, 7, 4 ], [ 9, 4, 6, 4 ], [ 9, 4, 7, 4 ],
[ 9, 5, 6, 2 ], [ 9, 5, 7, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ],
[ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 16, 1, 14, 16 ],
[ 16, 2, 14, 8 ], [ 16, 3, 14, 8 ], [ 16, 4, 14, 8 ], [ 16, 5, 12, 8 ],
[ 16, 5, 13, 8 ], [ 16, 6, 12, 8 ], [ 16, 6, 13, 8 ], [ 16, 7, 12, 8 ],
[ 16, 7, 13, 8 ], [ 16, 9, 14, 4 ], [ 16, 10, 12, 4 ], [ 16, 10, 13, 4 ],
[ 16, 12, 12, 4 ], [ 16, 12, 13, 4 ], [ 16, 13, 14, 4 ], [ 16, 15, 14, 4 ],
[ 16, 16, 14, 4 ], [ 16, 17, 9, 8 ], [ 18, 1, 1, 4 ], [ 18, 1, 3, 4 ],
[ 18, 2, 1, 2 ], [ 18, 2, 3, 2 ], [ 19, 1, 3, 16 ], [ 19, 2, 3, 8 ],
[ 19, 3, 3, 8 ], [ 19, 4, 3, 8 ], [ 19, 5, 3, 4 ], [ 20, 1, 2, 4 ],
[ 20, 1, 4, 4 ], [ 20, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 23, 1, 2, 8 ],
[ 23, 1, 6, 8 ], [ 23, 2, 2, 4 ], [ 23, 2, 6, 4 ], [ 23, 3, 2, 4 ],
[ 23, 3, 6, 4 ], [ 23, 4, 2, 4 ], [ 23, 4, 6, 4 ], [ 23, 5, 2, 4 ],
[ 23, 5, 6, 4 ], [ 23, 6, 2, 2 ], [ 23, 6, 6, 2 ], [ 25, 1, 5, 8 ],
[ 25, 1, 6, 8 ], [ 25, 2, 3, 4 ], [ 25, 2, 4, 4 ], [ 25, 3, 2, 4 ],
[ 25, 3, 4, 4 ], [ 26, 1, 7, 8 ], [ 26, 1, 8, 8 ], [ 26, 2, 8, 4 ],
[ 26, 2, 9, 4 ], [ 26, 3, 6, 4 ], [ 26, 3, 8, 4 ], [ 27, 1, 19, 8 ],
[ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ], [ 29, 1, 14, 16 ], [ 29, 1, 18, 16 ],
[ 29, 2, 14, 8 ], [ 29, 2, 18, 8 ], [ 29, 3, 14, 8 ], [ 29, 3, 18, 8 ],
[ 29, 4, 14, 8 ], [ 29, 4, 18, 8 ], [ 29, 5, 14, 8 ], [ 29, 5, 18, 8 ],
[ 29, 6, 10, 8 ], [ 29, 6, 14, 8 ], [ 29, 7, 10, 8 ], [ 29, 7, 14, 8 ],
[ 29, 8, 10, 8 ], [ 29, 8, 14, 8 ], [ 29, 9, 14, 4 ], [ 29, 9, 18, 4 ],
[ 29, 10, 10, 4 ], [ 29, 10, 14, 4 ], [ 29, 11, 10, 4 ], [ 29, 11, 14, 4 ],
[ 29, 12, 10, 4 ], [ 29, 12, 14, 4 ], [ 29, 13, 10, 4 ], [ 29, 13, 14, 4 ],
[ 30, 1, 6, 16 ], [ 30, 1, 21, 16 ], [ 30, 2, 6, 8 ], [ 30, 2, 21, 8 ],
[ 30, 3, 6, 8 ], [ 30, 3, 21, 8 ], [ 30, 5, 5, 8 ], [ 30, 5, 8, 8 ],
[ 30, 6, 19, 8 ], [ 30, 6, 22, 8 ], [ 30, 8, 6, 8 ], [ 30, 8, 23, 8 ],
[ 30, 9, 6, 4 ], [ 30, 9, 23, 8 ], [ 30, 10, 6, 8 ], [ 30, 10, 23, 4 ],
[ 31, 2, 38, 16 ], [ 31, 3, 39, 16 ], [ 31, 4, 31, 16 ], [ 31, 5, 34, 16 ],
[ 31, 5, 48, 16 ], [ 31, 6, 36, 16 ], [ 31, 6, 39, 16 ], [ 31, 7, 29, 16 ],
[ 31, 7, 35, 16 ], [ 31, 8, 30, 16 ], [ 31, 8, 36, 16 ], [ 31, 9, 40, 8 ],
[ 31, 10, 38, 16 ], [ 31, 11, 40, 8 ], [ 31, 12, 22, 8 ], [ 31, 12, 25, 8 ],
[ 31, 16, 39, 8 ], [ 31, 17, 25, 16 ], [ 31, 18, 38, 8 ],
[ 31, 18, 52, 16 ], [ 31, 19, 38, 8 ], [ 31, 19, 52, 16 ],
[ 31, 20, 38, 16 ], [ 31, 20, 52, 8 ], [ 31, 22, 29, 8 ], [ 31, 22, 35, 8 ],
[ 31, 23, 39, 8 ], [ 31, 24, 32, 8 ], [ 31, 24, 44, 8 ], [ 31, 25, 30, 8 ],
[ 31, 25, 42, 8 ], [ 31, 26, 29, 16 ], [ 31, 26, 42, 8 ], [ 31, 27, 36, 8 ],
[ 31, 27, 39, 8 ], [ 31, 28, 36, 8 ], [ 31, 28, 39, 8 ], [ 31, 32, 29, 16 ],
[ 31, 32, 42, 8 ], [ 31, 33, 29, 16 ], [ 31, 33, 42, 8 ] ]
k = 32: F-action on Pi is () [31,1,32]
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 0 modulo 4: 1/32 q^3 ( q^3-2*q^2-2*q+4 )
q congruent 1 modulo 4: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2-2*q+9 )
q congruent 2 modulo 4: 1/32 q^3 ( q^3-2*q^2-2*q+4 )
q congruent 3 modulo 4: 1/32 phi1 phi2 ( q^4-2*q^3-2*q^2-2*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 3, 8 ],
[ 3, 2, 3, 4 ], [ 3, 3, 3, 4 ], [ 3, 4, 3, 4 ], [ 3, 5, 3, 2 ],
[ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 5, 8 ], [ 9, 1, 8, 8 ], [ 9, 2, 5, 4 ], [ 9, 2, 8, 4 ],
[ 9, 3, 5, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 5, 4 ], [ 9, 4, 8, 4 ],
[ 9, 5, 5, 2 ], [ 9, 5, 8, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ],
[ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ], [ 12, 1, 2, 4 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 16, 1, 9, 16 ],
[ 16, 2, 9, 8 ], [ 16, 3, 9, 8 ], [ 16, 4, 9, 8 ], [ 16, 5, 9, 8 ],
[ 16, 5, 16, 8 ], [ 16, 6, 9, 8 ], [ 16, 6, 16, 8 ], [ 16, 7, 9, 8 ],
[ 16, 7, 16, 8 ], [ 16, 9, 9, 4 ], [ 16, 10, 9, 4 ], [ 16, 10, 16, 4 ],
[ 16, 12, 9, 4 ], [ 16, 12, 16, 4 ], [ 16, 13, 9, 4 ], [ 16, 15, 9, 4 ],
[ 16, 16, 9, 4 ], [ 16, 17, 7, 8 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 4 ],
[ 18, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 19, 1, 4, 16 ], [ 19, 2, 4, 8 ],
[ 19, 3, 4, 8 ], [ 19, 4, 4, 8 ], [ 19, 5, 4, 4 ], [ 20, 1, 1, 4 ],
[ 20, 1, 3, 4 ], [ 20, 2, 1, 2 ], [ 20, 2, 3, 2 ], [ 23, 1, 4, 8 ],
[ 23, 1, 8, 8 ], [ 23, 2, 4, 4 ], [ 23, 2, 8, 4 ], [ 23, 3, 4, 4 ],
[ 23, 3, 8, 4 ], [ 23, 4, 4, 4 ], [ 23, 4, 8, 4 ], [ 23, 5, 4, 4 ],
[ 23, 5, 8, 4 ], [ 23, 6, 4, 2 ], [ 23, 6, 8, 2 ], [ 25, 1, 7, 8 ],
[ 25, 1, 8, 8 ], [ 25, 2, 6, 4 ], [ 25, 2, 7, 4 ], [ 25, 3, 6, 4 ],
[ 25, 3, 8, 4 ], [ 26, 1, 5, 8 ], [ 26, 1, 6, 8 ], [ 26, 2, 3, 4 ],
[ 26, 2, 4, 4 ], [ 26, 3, 2, 4 ], [ 26, 3, 4, 4 ], [ 27, 1, 19, 8 ],
[ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ], [ 29, 1, 16, 16 ], [ 29, 1, 20, 16 ],
[ 29, 2, 16, 8 ], [ 29, 2, 20, 8 ], [ 29, 3, 16, 8 ], [ 29, 3, 20, 8 ],
[ 29, 4, 16, 8 ], [ 29, 4, 20, 8 ], [ 29, 5, 16, 8 ], [ 29, 5, 20, 8 ],
[ 29, 6, 12, 8 ], [ 29, 6, 16, 8 ], [ 29, 7, 12, 8 ], [ 29, 7, 16, 8 ],
[ 29, 8, 12, 8 ], [ 29, 8, 16, 8 ], [ 29, 9, 16, 4 ], [ 29, 9, 20, 4 ],
[ 29, 10, 12, 4 ], [ 29, 10, 16, 4 ], [ 29, 11, 12, 4 ], [ 29, 11, 16, 4 ],
[ 29, 12, 12, 4 ], [ 29, 12, 16, 4 ], [ 29, 13, 12, 4 ], [ 29, 13, 16, 4 ],
[ 30, 1, 8, 16 ], [ 30, 1, 19, 16 ], [ 30, 2, 8, 8 ], [ 30, 2, 19, 8 ],
[ 30, 3, 8, 8 ], [ 30, 3, 19, 8 ], [ 30, 5, 19, 8 ], [ 30, 5, 22, 8 ],
[ 30, 6, 5, 8 ], [ 30, 6, 8, 8 ], [ 30, 8, 7, 8 ], [ 30, 8, 22, 8 ],
[ 30, 9, 7, 8 ], [ 30, 9, 22, 4 ], [ 30, 10, 7, 4 ], [ 30, 10, 22, 8 ],
[ 31, 2, 40, 16 ], [ 31, 3, 40, 16 ], [ 31, 4, 32, 16 ], [ 31, 5, 36, 16 ],
[ 31, 5, 46, 16 ], [ 31, 6, 22, 16 ], [ 31, 6, 25, 16 ], [ 31, 7, 18, 16 ],
[ 31, 7, 21, 16 ], [ 31, 8, 18, 16 ], [ 31, 8, 21, 16 ], [ 31, 9, 39, 8 ],
[ 31, 10, 51, 16 ], [ 31, 11, 38, 8 ], [ 31, 12, 36, 8 ], [ 31, 12, 39, 8 ],
[ 31, 16, 40, 8 ], [ 31, 17, 27, 16 ], [ 31, 18, 40, 8 ],
[ 31, 18, 50, 16 ], [ 31, 19, 40, 8 ], [ 31, 19, 50, 16 ],
[ 31, 20, 40, 16 ], [ 31, 20, 50, 8 ], [ 31, 22, 18, 8 ], [ 31, 22, 21, 8 ],
[ 31, 23, 40, 8 ], [ 31, 24, 30, 8 ], [ 31, 24, 42, 8 ], [ 31, 25, 32, 8 ],
[ 31, 25, 44, 8 ], [ 31, 26, 26, 8 ], [ 31, 26, 45, 16 ], [ 31, 27, 22, 8 ],
[ 31, 27, 25, 8 ], [ 31, 28, 22, 8 ], [ 31, 28, 25, 8 ], [ 31, 32, 26, 8 ],
[ 31, 32, 45, 16 ], [ 31, 33, 26, 8 ], [ 31, 33, 45, 16 ] ]
k = 33: F-action on Pi is () [31,1,33]
Dynkin type is A_0(q) + T(phi4 phi8)
Order of center |Z^F|: phi4 phi8
Numbers of classes in class type:
q congruent 0 modulo 4: 1/16 q^6
q congruent 1 modulo 4: 1/16 phi1^2 phi2^2 phi4
q congruent 2 modulo 4: 1/16 q^6
q congruent 3 modulo 4: 1/16 phi1^2 phi2^2 phi4
Fusion of maximal tori of C^F in those of G^F:
[ 33 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 3, 4 ],
[ 3, 1, 4, 4 ], [ 3, 2, 3, 2 ], [ 3, 2, 4, 2 ], [ 3, 3, 3, 2 ],
[ 3, 3, 4, 2 ], [ 3, 4, 3, 2 ], [ 3, 4, 4, 2 ], [ 3, 5, 3, 1 ],
[ 3, 5, 4, 1 ], [ 12, 1, 5, 4 ], [ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ],
[ 16, 1, 10, 8 ], [ 16, 2, 10, 4 ], [ 16, 3, 10, 4 ], [ 16, 4, 10, 4 ],
[ 16, 9, 10, 2 ], [ 16, 13, 10, 4 ], [ 16, 15, 10, 4 ], [ 16, 16, 10, 4 ],
[ 16, 17, 8, 4 ], [ 16, 17, 10, 4 ], [ 27, 1, 20, 8 ], [ 27, 5, 17, 4 ],
[ 27, 9, 19, 4 ], [ 31, 2, 14, 8 ], [ 31, 3, 14, 8 ], [ 31, 4, 33, 8 ],
[ 31, 9, 14, 4 ], [ 31, 10, 41, 8 ], [ 31, 11, 16, 8 ], [ 31, 16, 14, 4 ],
[ 31, 17, 8, 8 ], [ 31, 23, 16, 8 ] ]
k = 34: F-action on Pi is () [31,1,34]
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 0 modulo 4: 1/10 q phi1^2 phi2 phi4
q congruent 1 modulo 4: 1/10 q phi1^2 phi2 phi4
q congruent 2 modulo 4: 1/10 q phi1^2 phi2 phi4
q congruent 3 modulo 4: 1/10 q phi1^2 phi2 phi4
Fusion of maximal tori of C^F in those of G^F:
[ 34 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 10, 1, 1, 2 ],
[ 10, 2, 1, 1 ], [ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 17, 1, 1, 2 ],
[ 17, 2, 1, 1 ], [ 31, 4, 34, 5 ] ]
k = 35: F-action on Pi is () [31,1,35]
Dynkin type is A_0(q) + T(phi2^2 phi10)
Order of center |Z^F|: phi2^2 phi10
Numbers of classes in class type:
q congruent 0 modulo 4: 1/10 q phi1 phi2^2 phi4
q congruent 1 modulo 4: 1/10 q phi1 phi2^2 phi4
q congruent 2 modulo 4: 1/10 q phi1 phi2^2 phi4
q congruent 3 modulo 4: 1/10 q phi1 phi2^2 phi4
Fusion of maximal tori of C^F in those of G^F:
[ 35 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 10, 1, 2, 2 ],
[ 10, 2, 2, 1 ], [ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 17, 1, 2, 2 ],
[ 17, 2, 2, 1 ], [ 31, 4, 35, 5 ] ]
k = 36: F-action on Pi is () [31,1,36]
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 0 modulo 4: 1/12 q phi1^2 phi2 ( q^2+q+2 )
q congruent 1 modulo 4: 1/12 q phi1 phi2 ( q^3+q-4 )
q congruent 2 modulo 4: 1/12 q phi1^2 phi2 ( q^2+q+2 )
q congruent 3 modulo 4: 1/12 q phi1 phi2 ( q^3+q-4 )
Fusion of maximal tori of C^F in those of G^F:
[ 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 4, 4 ], [ 3, 2, 4, 2 ], [ 3, 3, 4, 2 ],
[ 3, 4, 4, 2 ], [ 3, 5, 4, 1 ], [ 10, 1, 1, 2 ], [ 10, 2, 1, 1 ],
[ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 19, 1, 3, 4 ], [ 19, 2, 3, 2 ],
[ 19, 3, 3, 2 ], [ 19, 4, 3, 2 ], [ 19, 5, 3, 1 ], [ 25, 1, 9, 6 ],
[ 25, 2, 9, 3 ], [ 26, 1, 10, 6 ], [ 26, 2, 7, 3 ], [ 31, 4, 36, 6 ],
[ 31, 7, 25, 6 ], [ 31, 8, 28, 6 ], [ 31, 17, 3, 12 ], [ 31, 22, 25, 3 ],
[ 31, 30, 23, 12 ], [ 31, 30, 28, 12 ] ]
k = 37: F-action on Pi is () [31,1,37]
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 0 modulo 4: 1/12 q phi1^2 phi2 ( q^2+q+2 )
q congruent 1 modulo 4: 1/12 q phi1 phi2 ( q^3+q-4 )
q congruent 2 modulo 4: 1/12 q phi1^2 phi2 ( q^2+q+2 )
q congruent 3 modulo 4: 1/12 q phi1 phi2 ( q^3+q-4 )
Fusion of maximal tori of C^F in those of G^F:
[ 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 3, 4 ], [ 3, 2, 3, 2 ], [ 3, 3, 3, 2 ],
[ 3, 4, 3, 2 ], [ 3, 5, 3, 1 ], [ 10, 1, 2, 2 ], [ 10, 2, 2, 1 ],
[ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 19, 1, 4, 4 ], [ 19, 2, 4, 2 ],
[ 19, 3, 4, 2 ], [ 19, 4, 4, 2 ], [ 19, 5, 4, 1 ], [ 25, 1, 10, 6 ],
[ 25, 2, 10, 3 ], [ 26, 1, 9, 6 ], [ 26, 2, 6, 3 ], [ 31, 4, 37, 6 ],
[ 31, 7, 28, 6 ], [ 31, 8, 25, 6 ], [ 31, 17, 4, 12 ], [ 31, 22, 28, 3 ],
[ 31, 30, 21, 12 ], [ 31, 30, 25, 12 ] ]
j = 2: Omega of order 2, action on Pi: <()>
k = 1: F-action on Pi is () [31,2,1]
Dynkin type is (A_0(q) + T(phi1^6)).2
Order of center |Z^F|: phi1^4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/768 phi1 ( q^3-23*q^2+171*q-405 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/768 ( q^4-24*q^3+194*q^2-624*q+693 )
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, 14 ], [ 2, 2, 1, 15 ], [ 3, 1, 1, 16 ],
[ 3, 2, 1, 20 ], [ 3, 3, 1, 8 ], [ 3, 4, 1, 8 ], [ 3, 5, 1, 10 ],
[ 4, 1, 1, 8 ], [ 4, 2, 1, 6 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ],
[ 7, 1, 1, 64 ], [ 7, 2, 1, 48 ], [ 7, 3, 1, 56 ], [ 7, 4, 1, 80 ],
[ 7, 5, 1, 60 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 96 ], [ 9, 2, 1, 144 ],
[ 9, 3, 1, 48 ], [ 9, 4, 1, 48 ], [ 9, 5, 1, 72 ], [ 12, 1, 1, 48 ],
[ 12, 2, 1, 28 ], [ 12, 3, 1, 40 ], [ 12, 4, 1, 30 ], [ 13, 1, 1, 96 ],
[ 13, 2, 1, 96 ], [ 14, 1, 1, 64 ], [ 14, 2, 1, 96 ], [ 15, 1, 1, 96 ],
[ 16, 1, 1, 192 ], [ 16, 2, 1, 144 ], [ 16, 3, 1, 96 ], [ 16, 4, 1, 288 ],
[ 16, 5, 1, 96 ], [ 16, 6, 1, 96 ], [ 16, 7, 1, 96 ], [ 16, 8, 1, 192 ],
[ 16, 9, 1, 168 ], [ 16, 10, 1, 72 ], [ 16, 11, 1, 168 ],
[ 16, 12, 1, 144 ], [ 16, 13, 1, 144 ], [ 16, 14, 1, 240 ],
[ 16, 15, 1, 48 ], [ 16, 16, 1, 48 ], [ 16, 17, 1, 144 ], [ 21, 1, 1, 192 ],
[ 21, 2, 1, 192 ], [ 21, 3, 1, 128 ], [ 21, 4, 1, 96 ], [ 21, 5, 1, 112 ],
[ 21, 6, 1, 160 ], [ 21, 7, 1, 96 ], [ 22, 1, 1, 192 ], [ 22, 2, 1, 192 ],
[ 22, 3, 1, 288 ], [ 22, 4, 1, 288 ], [ 23, 2, 1, 32 ], [ 23, 6, 1, 16 ],
[ 27, 1, 1, 384 ], [ 27, 2, 1, 576 ], [ 27, 3, 1, 384 ], [ 27, 4, 1, 192 ],
[ 27, 5, 1, 192 ], [ 27, 6, 1, 384 ], [ 27, 7, 1, 288 ], [ 27, 8, 1, 576 ],
[ 27, 9, 1, 288 ], [ 27, 10, 1, 384 ], [ 27, 11, 1, 192 ],
[ 27, 12, 1, 384 ], [ 27, 13, 1, 384 ], [ 27, 14, 1, 192 ],
[ 28, 2, 1, 128 ], [ 28, 5, 1, 64 ], [ 28, 6, 1, 192 ], [ 29, 4, 1, 192 ],
[ 29, 9, 1, 96 ], [ 29, 12, 1, 96 ], [ 30, 4, 1, 384 ], [ 30, 8, 1, 384 ],
[ 30, 11, 1, 192 ], [ 30, 12, 1, 192 ], [ 30, 13, 1, 576 ],
[ 31, 9, 1, 384 ], [ 31, 10, 1, 768 ], [ 31, 11, 1, 384 ],
[ 31, 12, 1, 384 ], [ 31, 13, 1, 384 ], [ 31, 14, 1, 1152 ],
[ 31, 15, 1, 384 ], [ 31, 16, 1, 384 ], [ 31, 21, 1, 384 ],
[ 31, 23, 1, 384 ], [ 31, 29, 1, 384 ] ]
k = 2: F-action on Pi is () [31,2,2]
Dynkin type is (A_0(q) + T(phi1^4 phi3)).2
Order of center |Z^F|: phi1^2 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/24 q phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/24 q phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 18 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 3 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ],
[ 7, 2, 1, 6 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ], [ 7, 5, 1, 3 ],
[ 8, 1, 1, 4 ], [ 12, 2, 1, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 6 ],
[ 14, 1, 1, 4 ], [ 14, 2, 1, 6 ], [ 21, 1, 9, 6 ], [ 21, 3, 1, 8 ],
[ 21, 4, 4, 3 ], [ 21, 5, 1, 4 ], [ 21, 6, 1, 4 ], [ 21, 7, 1, 12 ],
[ 21, 7, 4, 6 ], [ 23, 2, 1, 8 ], [ 23, 6, 1, 4 ], [ 27, 1, 15, 12 ],
[ 27, 2, 4, 18 ], [ 27, 4, 6, 6 ], [ 27, 5, 4, 6 ], [ 27, 7, 4, 9 ],
[ 27, 12, 6, 12 ], [ 28, 2, 1, 8 ], [ 28, 5, 1, 4 ], [ 28, 6, 1, 12 ],
[ 31, 9, 2, 12 ], [ 31, 11, 2, 12 ], [ 31, 14, 2, 36 ], [ 31, 15, 4, 12 ],
[ 31, 16, 2, 12 ], [ 31, 21, 36, 12 ], [ 31, 23, 2, 12 ] ]
k = 3: F-action on Pi is () [31,2,3]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi3)).2
Order of center |Z^F|: phi1^2 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/24 q phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/24 q phi1 phi2 ( q-3 )
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, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ],
[ 3, 5, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 2 ],
[ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 4 ],
[ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 2 ],
[ 8, 1, 1, 4 ], [ 12, 2, 3, 4 ], [ 12, 3, 4, 4 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 2 ], [ 14, 1, 1, 4 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 4 ],
[ 21, 1, 9, 6 ], [ 21, 3, 5, 8 ], [ 21, 4, 4, 3 ], [ 21, 5, 3, 4 ],
[ 21, 6, 5, 4 ], [ 21, 7, 3, 4 ], [ 21, 7, 4, 6 ], [ 23, 2, 3, 8 ],
[ 23, 6, 3, 4 ], [ 27, 1, 15, 12 ], [ 27, 2, 4, 6 ], [ 27, 2, 19, 12 ],
[ 27, 4, 6, 6 ], [ 27, 5, 4, 6 ], [ 27, 7, 4, 3 ], [ 27, 7, 19, 6 ],
[ 27, 12, 6, 12 ], [ 28, 2, 3, 8 ], [ 28, 5, 3, 4 ], [ 28, 6, 3, 4 ],
[ 31, 9, 3, 12 ], [ 31, 11, 3, 12 ], [ 31, 14, 5, 12 ], [ 31, 15, 44, 12 ],
[ 31, 16, 3, 12 ], [ 31, 21, 40, 12 ], [ 31, 23, 3, 12 ] ]
k = 4: F-action on Pi is () [31,2,4]
Dynkin type is (A_0(q) + T(phi1 phi2 phi3 phi4)).2
Order of center |Z^F|: phi1 phi2 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/12 q phi1 phi2^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/12 q phi1 phi2^2
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, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 2, 4 ],
[ 7, 2, 2, 2 ], [ 7, 3, 2, 2 ], [ 7, 4, 2, 2 ], [ 7, 5, 2, 1 ],
[ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 14, 1, 3, 4 ], [ 14, 2, 3, 2 ],
[ 21, 1, 9, 6 ], [ 21, 3, 4, 4 ], [ 21, 4, 4, 3 ], [ 21, 5, 5, 2 ],
[ 21, 6, 4, 4 ], [ 21, 7, 4, 6 ], [ 21, 7, 5, 4 ], [ 27, 1, 17, 12 ],
[ 27, 2, 19, 6 ], [ 27, 4, 16, 6 ], [ 27, 5, 18, 6 ], [ 27, 7, 19, 3 ],
[ 27, 12, 16, 12 ], [ 28, 2, 5, 4 ], [ 28, 5, 5, 4 ], [ 28, 6, 5, 4 ],
[ 31, 9, 4, 6 ], [ 31, 11, 5, 12 ], [ 31, 14, 7, 12 ], [ 31, 15, 39, 12 ],
[ 31, 16, 5, 6 ], [ 31, 21, 39, 12 ], [ 31, 23, 5, 12 ] ]
k = 5: F-action on Pi is () [31,2,5]
Dynkin type is (A_0(q) + T(phi1 phi2 phi4 phi6)).2
Order of center |Z^F|: phi1 phi2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/12 q phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/12 q phi1^2 phi2
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, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 3, 4 ],
[ 7, 2, 3, 2 ], [ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 3, 1 ],
[ 12, 2, 5, 2 ], [ 12, 4, 5, 2 ], [ 14, 1, 4, 4 ], [ 14, 2, 4, 2 ],
[ 21, 1, 10, 6 ], [ 21, 3, 9, 4 ], [ 21, 4, 8, 3 ], [ 21, 5, 7, 2 ],
[ 21, 6, 8, 4 ], [ 21, 7, 7, 4 ], [ 21, 7, 8, 6 ], [ 27, 1, 16, 12 ],
[ 27, 2, 13, 6 ], [ 27, 4, 17, 6 ], [ 27, 5, 14, 6 ], [ 27, 7, 13, 3 ],
[ 27, 12, 17, 12 ], [ 28, 2, 7, 4 ], [ 28, 5, 7, 4 ], [ 28, 6, 7, 4 ],
[ 31, 9, 5, 6 ], [ 31, 11, 4, 12 ], [ 31, 14, 6, 12 ], [ 31, 15, 33, 12 ],
[ 31, 16, 4, 6 ], [ 31, 21, 43, 12 ], [ 31, 23, 4, 12 ] ]
k = 6: F-action on Pi is () [31,2,6]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi6)).2
Order of center |Z^F|: phi2^2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/24 q phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/24 q phi1^2 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, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ],
[ 3, 5, 2, 1 ], [ 4, 1, 2, 2 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 1 ],
[ 6, 1, 2, 2 ], [ 7, 1, 4, 4 ], [ 7, 2, 3, 4 ], [ 7, 2, 4, 2 ],
[ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 3, 2 ], [ 7, 5, 4, 1 ],
[ 8, 1, 2, 4 ], [ 12, 2, 1, 4 ], [ 12, 3, 3, 4 ], [ 12, 4, 1, 2 ],
[ 12, 4, 4, 2 ], [ 14, 1, 2, 4 ], [ 14, 2, 2, 2 ], [ 14, 2, 4, 4 ],
[ 21, 1, 10, 6 ], [ 21, 3, 6, 8 ], [ 21, 4, 8, 3 ], [ 21, 5, 8, 4 ],
[ 21, 6, 7, 4 ], [ 21, 7, 6, 4 ], [ 21, 7, 8, 6 ], [ 23, 2, 5, 8 ],
[ 23, 6, 5, 4 ], [ 27, 1, 18, 12 ], [ 27, 2, 8, 6 ], [ 27, 2, 13, 12 ],
[ 27, 4, 7, 6 ], [ 27, 5, 7, 6 ], [ 27, 7, 8, 3 ], [ 27, 7, 13, 6 ],
[ 27, 12, 7, 12 ], [ 28, 2, 8, 8 ], [ 28, 5, 8, 4 ], [ 28, 6, 6, 4 ],
[ 31, 9, 6, 12 ], [ 31, 11, 6, 12 ], [ 31, 14, 9, 12 ], [ 31, 15, 8, 12 ],
[ 31, 16, 6, 12 ], [ 31, 21, 42, 12 ], [ 31, 23, 6, 12 ] ]
k = 7: F-action on Pi is () [31,2,7]
Dynkin type is (A_0(q) + T(phi2^4 phi6)).2
Order of center |Z^F|: phi2^2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/24 q phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/24 q phi1^2 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, 2 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 3 ], [ 6, 1, 2, 2 ], [ 7, 1, 4, 4 ],
[ 7, 2, 4, 6 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 4, 3 ],
[ 8, 1, 2, 4 ], [ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 3, 6 ],
[ 14, 1, 2, 4 ], [ 14, 2, 2, 6 ], [ 21, 1, 10, 6 ], [ 21, 3, 10, 8 ],
[ 21, 4, 8, 3 ], [ 21, 5, 10, 4 ], [ 21, 6, 10, 4 ], [ 21, 7, 8, 6 ],
[ 21, 7, 10, 12 ], [ 23, 2, 7, 8 ], [ 23, 6, 7, 4 ], [ 27, 1, 18, 12 ],
[ 27, 2, 8, 18 ], [ 27, 4, 7, 6 ], [ 27, 5, 7, 6 ], [ 27, 7, 8, 9 ],
[ 27, 12, 7, 12 ], [ 28, 2, 10, 8 ], [ 28, 5, 10, 4 ], [ 28, 6, 10, 12 ],
[ 31, 9, 7, 12 ], [ 31, 11, 7, 12 ], [ 31, 14, 8, 36 ], [ 31, 15, 48, 12 ],
[ 31, 16, 7, 12 ], [ 31, 21, 45, 12 ], [ 31, 23, 7, 12 ] ]
k = 8: F-action on Pi is () [31,2,8]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi3)).2
Order of center |Z^F|: phi1^2 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/12 q phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/12 q phi1^2 phi2
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, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 1, 4 ],
[ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ],
[ 4, 1, 1, 2 ], [ 4, 2, 1, 1 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 4 ],
[ 7, 2, 1, 2 ], [ 7, 3, 1, 2 ], [ 7, 4, 1, 2 ], [ 7, 5, 1, 1 ],
[ 8, 1, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 14, 1, 1, 4 ],
[ 14, 2, 1, 2 ], [ 21, 1, 9, 6 ], [ 21, 3, 3, 4 ], [ 21, 4, 4, 3 ],
[ 21, 5, 2, 2 ], [ 21, 6, 3, 4 ], [ 21, 7, 2, 4 ], [ 21, 7, 4, 6 ],
[ 23, 2, 2, 4 ], [ 23, 2, 4, 4 ], [ 23, 6, 2, 2 ], [ 23, 6, 4, 2 ],
[ 27, 1, 15, 12 ], [ 27, 2, 4, 6 ], [ 27, 4, 6, 6 ], [ 27, 5, 4, 6 ],
[ 27, 7, 4, 3 ], [ 27, 12, 6, 12 ], [ 28, 2, 2, 4 ], [ 28, 5, 2, 2 ],
[ 28, 6, 2, 4 ], [ 31, 9, 8, 6 ], [ 31, 11, 8, 6 ], [ 31, 14, 10, 12 ],
[ 31, 15, 14, 12 ], [ 31, 16, 8, 6 ], [ 31, 21, 38, 12 ], [ 31, 23, 8, 6 ] ]
k = 9: F-action on Pi is () [31,2,9]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi3)).2
Order of center |Z^F|: phi1 phi2 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/12 q phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/12 q phi1^2 phi2
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, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 1, 4 ], [ 3, 2, 1, 2 ], [ 3, 3, 1, 2 ], [ 3, 4, 1, 2 ],
[ 3, 5, 1, 1 ], [ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 2 ],
[ 6, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 7, 2, 1, 2 ], [ 7, 2, 2, 4 ],
[ 7, 3, 2, 2 ], [ 7, 4, 2, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 2 ],
[ 12, 2, 4, 2 ], [ 12, 3, 2, 2 ], [ 12, 3, 3, 2 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 2 ], [ 14, 1, 3, 4 ], [ 14, 2, 1, 2 ], [ 14, 2, 3, 4 ],
[ 21, 1, 9, 6 ], [ 21, 3, 2, 4 ], [ 21, 4, 4, 3 ], [ 21, 5, 4, 2 ],
[ 21, 6, 2, 2 ], [ 21, 7, 3, 4 ], [ 21, 7, 4, 6 ], [ 27, 1, 17, 12 ],
[ 27, 2, 4, 6 ], [ 27, 2, 19, 12 ], [ 27, 4, 16, 6 ], [ 27, 5, 18, 6 ],
[ 27, 7, 4, 3 ], [ 27, 7, 19, 6 ], [ 27, 12, 16, 12 ], [ 28, 2, 4, 4 ],
[ 28, 5, 4, 4 ], [ 28, 6, 3, 4 ], [ 31, 9, 10, 6 ], [ 31, 11, 11, 12 ],
[ 31, 14, 5, 12 ], [ 31, 15, 29, 6 ], [ 31, 16, 11, 6 ], [ 31, 21, 37, 6 ],
[ 31, 23, 11, 12 ] ]
k = 10: F-action on Pi is () [31,2,10]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi6)).2
Order of center |Z^F|: phi1 phi2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/12 q phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/12 q phi1 phi2 ( q-3 )
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, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 2, 2 ],
[ 3, 1, 2, 4 ], [ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ],
[ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 1 ],
[ 6, 1, 2, 2 ], [ 7, 1, 3, 4 ], [ 7, 2, 3, 4 ], [ 7, 2, 4, 2 ],
[ 7, 3, 3, 2 ], [ 7, 4, 3, 2 ], [ 7, 5, 3, 2 ], [ 7, 5, 4, 1 ],
[ 12, 2, 4, 2 ], [ 12, 3, 1, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 1, 2 ],
[ 12, 4, 4, 2 ], [ 14, 1, 4, 4 ], [ 14, 2, 2, 2 ], [ 14, 2, 4, 4 ],
[ 21, 1, 10, 6 ], [ 21, 3, 7, 4 ], [ 21, 4, 8, 3 ], [ 21, 5, 6, 2 ],
[ 21, 6, 6, 2 ], [ 21, 7, 6, 4 ], [ 21, 7, 8, 6 ], [ 27, 1, 16, 12 ],
[ 27, 2, 8, 6 ], [ 27, 2, 13, 12 ], [ 27, 4, 17, 6 ], [ 27, 5, 14, 6 ],
[ 27, 7, 8, 3 ], [ 27, 7, 13, 6 ], [ 27, 12, 17, 12 ], [ 28, 2, 6, 4 ],
[ 28, 5, 6, 4 ], [ 28, 6, 6, 4 ], [ 31, 9, 11, 6 ], [ 31, 11, 10, 12 ],
[ 31, 14, 9, 12 ], [ 31, 15, 23, 6 ], [ 31, 16, 10, 6 ], [ 31, 21, 41, 6 ],
[ 31, 23, 10, 12 ] ]
k = 11: F-action on Pi is () [31,2,11]
Dynkin type is (A_0(q) + T(phi1 phi2^3 phi6)).2
Order of center |Z^F|: phi2^2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/12 q phi1 phi2^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/12 q phi1 phi2^2
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, 2 ], [ 2, 2, 1, 1 ], [ 3, 1, 2, 4 ],
[ 3, 2, 2, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 2 ], [ 4, 2, 2, 1 ], [ 6, 1, 2, 2 ], [ 7, 1, 4, 4 ],
[ 7, 2, 4, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 4, 1 ],
[ 8, 1, 2, 4 ], [ 12, 2, 2, 2 ], [ 12, 4, 2, 2 ], [ 14, 1, 2, 4 ],
[ 14, 2, 2, 2 ], [ 21, 1, 10, 6 ], [ 21, 3, 8, 4 ], [ 21, 4, 8, 3 ],
[ 21, 5, 9, 2 ], [ 21, 6, 9, 4 ], [ 21, 7, 8, 6 ], [ 21, 7, 9, 4 ],
[ 23, 2, 6, 4 ], [ 23, 2, 8, 4 ], [ 23, 6, 6, 2 ], [ 23, 6, 8, 2 ],
[ 27, 1, 18, 12 ], [ 27, 2, 8, 6 ], [ 27, 4, 7, 6 ], [ 27, 5, 7, 6 ],
[ 27, 7, 8, 3 ], [ 27, 12, 7, 12 ], [ 28, 2, 9, 4 ], [ 28, 5, 9, 2 ],
[ 28, 6, 9, 4 ], [ 31, 9, 9, 6 ], [ 31, 11, 9, 6 ], [ 31, 14, 11, 12 ],
[ 31, 15, 18, 12 ], [ 31, 16, 9, 6 ], [ 31, 21, 44, 12 ], [ 31, 23, 9, 6 ] ]
k = 12: F-action on Pi is () [31,2,12]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi2^4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/768 phi1^2 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/768 phi2 ( q^3-17*q^2+91*q-147 )
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, 14 ], [ 2, 2, 1, 7 ], [ 2, 2, 2, 8 ],
[ 3, 1, 2, 16 ], [ 3, 2, 1, 12 ], [ 3, 2, 2, 8 ], [ 3, 3, 2, 8 ],
[ 3, 4, 2, 8 ], [ 3, 5, 1, 6 ], [ 3, 5, 2, 4 ], [ 4, 1, 2, 8 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 4 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ],
[ 7, 1, 4, 64 ], [ 7, 2, 3, 16 ], [ 7, 2, 4, 32 ], [ 7, 3, 1, 24 ],
[ 7, 3, 4, 32 ], [ 7, 4, 2, 48 ], [ 7, 4, 4, 32 ], [ 7, 5, 1, 12 ],
[ 7, 5, 2, 24 ], [ 7, 5, 3, 8 ], [ 7, 5, 4, 16 ], [ 8, 1, 2, 16 ],
[ 9, 1, 2, 96 ], [ 9, 2, 2, 48 ], [ 9, 2, 4, 96 ], [ 9, 3, 2, 48 ],
[ 9, 4, 2, 48 ], [ 9, 5, 2, 24 ], [ 9, 5, 4, 48 ], [ 12, 1, 3, 48 ],
[ 12, 2, 1, 4 ], [ 12, 2, 3, 24 ], [ 12, 3, 2, 24 ], [ 12, 3, 3, 16 ],
[ 12, 4, 1, 2 ], [ 12, 4, 3, 12 ], [ 12, 4, 4, 8 ], [ 13, 1, 4, 96 ],
[ 13, 2, 2, 48 ], [ 13, 2, 4, 48 ], [ 14, 1, 2, 64 ], [ 14, 2, 2, 32 ],
[ 14, 2, 4, 64 ], [ 15, 1, 3, 96 ], [ 16, 1, 5, 192 ], [ 16, 2, 1, 48 ],
[ 16, 2, 5, 96 ], [ 16, 3, 5, 96 ], [ 16, 4, 5, 96 ], [ 16, 4, 8, 192 ],
[ 16, 5, 3, 96 ], [ 16, 6, 3, 96 ], [ 16, 7, 3, 96 ], [ 16, 8, 3, 96 ],
[ 16, 8, 4, 96 ], [ 16, 9, 1, 24 ], [ 16, 9, 5, 48 ], [ 16, 9, 8, 96 ],
[ 16, 10, 1, 24 ], [ 16, 10, 3, 48 ], [ 16, 11, 1, 24 ], [ 16, 11, 2, 48 ],
[ 16, 11, 5, 48 ], [ 16, 12, 3, 48 ], [ 16, 12, 7, 96 ], [ 16, 13, 5, 48 ],
[ 16, 13, 8, 96 ], [ 16, 14, 2, 48 ], [ 16, 14, 4, 48 ], [ 16, 14, 6, 96 ],
[ 16, 15, 5, 48 ], [ 16, 16, 5, 48 ], [ 16, 17, 2, 48 ], [ 16, 17, 4, 48 ],
[ 21, 1, 4, 192 ], [ 21, 2, 3, 96 ], [ 21, 2, 10, 96 ], [ 21, 3, 6, 32 ],
[ 21, 3, 10, 96 ], [ 21, 4, 10, 96 ], [ 21, 5, 3, 48 ], [ 21, 5, 8, 16 ],
[ 21, 5, 10, 48 ], [ 21, 6, 2, 48 ], [ 21, 6, 7, 16 ], [ 21, 6, 10, 48 ],
[ 21, 7, 6, 16 ], [ 21, 7, 10, 48 ], [ 22, 1, 6, 192 ], [ 22, 2, 4, 96 ],
[ 22, 2, 6, 96 ], [ 22, 3, 4, 96 ], [ 22, 3, 8, 192 ], [ 22, 4, 4, 48 ],
[ 22, 4, 6, 48 ], [ 22, 4, 9, 96 ], [ 23, 2, 5, 32 ], [ 23, 6, 5, 16 ],
[ 27, 1, 5, 384 ], [ 27, 2, 10, 192 ], [ 27, 2, 15, 384 ],
[ 27, 3, 3, 192 ], [ 27, 3, 13, 192 ], [ 27, 4, 10, 192 ],
[ 27, 5, 11, 192 ], [ 27, 6, 8, 96 ], [ 27, 6, 10, 96 ], [ 27, 6, 15, 192 ],
[ 27, 7, 10, 96 ], [ 27, 7, 15, 192 ], [ 27, 8, 3, 96 ], [ 27, 8, 13, 96 ],
[ 27, 8, 18, 192 ], [ 27, 9, 3, 96 ], [ 27, 9, 12, 96 ], [ 27, 10, 2, 96 ],
[ 27, 10, 10, 96 ], [ 27, 10, 19, 192 ], [ 27, 11, 3, 96 ],
[ 27, 11, 13, 96 ], [ 27, 12, 2, 96 ], [ 27, 12, 10, 96 ],
[ 27, 13, 6, 96 ], [ 27, 13, 10, 96 ], [ 27, 13, 15, 192 ],
[ 27, 14, 5, 96 ], [ 27, 14, 13, 96 ], [ 28, 2, 8, 128 ], [ 28, 5, 8, 64 ],
[ 28, 6, 6, 64 ], [ 29, 4, 9, 192 ], [ 29, 9, 9, 96 ], [ 29, 12, 5, 96 ],
[ 30, 4, 26, 384 ], [ 30, 8, 21, 192 ], [ 30, 11, 25, 192 ],
[ 30, 12, 26, 192 ], [ 30, 13, 16, 192 ], [ 31, 9, 12, 384 ],
[ 31, 10, 13, 384 ], [ 31, 11, 12, 384 ], [ 31, 12, 13, 384 ],
[ 31, 13, 11, 384 ], [ 31, 14, 40, 384 ], [ 31, 15, 10, 384 ],
[ 31, 16, 12, 384 ], [ 31, 21, 47, 384 ], [ 31, 23, 12, 384 ],
[ 31, 29, 51, 384 ] ]
k = 13: F-action on Pi is () [31,2,13]
Dynkin type is (A_0(q) + T(phi2^2 phi4^2)).2
Order of center |Z^F|: phi4^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 phi2 ( q^2-9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 phi2 ( q^2-9 )
Fusion of maximal tori of C^F in those of G^F:
[ 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 2, 1, 4 ], [ 3, 5, 1, 2 ], [ 4, 2, 2, 2 ],
[ 7, 3, 2, 8 ], [ 7, 5, 2, 4 ], [ 12, 1, 5, 8 ], [ 12, 2, 3, 4 ],
[ 12, 2, 5, 4 ], [ 12, 4, 3, 2 ], [ 12, 4, 5, 4 ], [ 15, 1, 5, 16 ],
[ 16, 1, 4, 16 ], [ 16, 2, 4, 8 ], [ 16, 2, 8, 16 ], [ 16, 2, 12, 16 ],
[ 16, 3, 4, 8 ], [ 16, 4, 4, 8 ], [ 16, 9, 4, 4 ], [ 16, 9, 8, 8 ],
[ 16, 9, 12, 8 ], [ 16, 10, 7, 8 ], [ 16, 10, 10, 8 ], [ 16, 10, 14, 8 ],
[ 16, 11, 4, 8 ], [ 16, 11, 9, 8 ], [ 16, 11, 10, 8 ], [ 16, 13, 4, 8 ],
[ 16, 15, 4, 8 ], [ 16, 16, 4, 8 ], [ 21, 2, 5, 16 ], [ 21, 5, 5, 8 ],
[ 27, 1, 14, 32 ], [ 27, 3, 10, 16 ], [ 27, 3, 25, 32 ], [ 27, 5, 10, 16 ],
[ 27, 8, 10, 16 ], [ 27, 8, 25, 16 ], [ 27, 9, 8, 8 ], [ 27, 9, 11, 16 ],
[ 27, 9, 18, 16 ], [ 27, 11, 10, 16 ], [ 27, 11, 25, 16 ],
[ 27, 14, 7, 16 ], [ 27, 14, 25, 16 ], [ 29, 4, 19, 32 ], [ 29, 9, 19, 16 ],
[ 31, 9, 13, 32 ], [ 31, 10, 36, 32 ], [ 31, 11, 15, 32 ],
[ 31, 12, 51, 32 ], [ 31, 16, 13, 32 ], [ 31, 23, 15, 32 ] ]
k = 14: F-action on Pi is () [31,2,14]
Dynkin type is (A_0(q) + T(phi4 phi8)).2
Order of center |Z^F|: phi8 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2 phi4
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2 phi4
Fusion of maximal tori of C^F in those of G^F:
[ 33 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 3, 2, 3, 2 ],
[ 3, 2, 4, 2 ], [ 3, 5, 3, 1 ], [ 3, 5, 4, 1 ], [ 12, 2, 5, 2 ],
[ 12, 4, 5, 2 ], [ 16, 2, 10, 4 ], [ 16, 9, 10, 2 ], [ 27, 1, 20, 8 ],
[ 27, 5, 17, 4 ], [ 27, 9, 19, 4 ], [ 31, 9, 14, 4 ], [ 31, 11, 16, 8 ],
[ 31, 16, 14, 4 ], [ 31, 23, 16, 8 ] ]
k = 15: F-action on Pi is () [31,2,15]
Dynkin type is (A_0(q) + T(phi1^2 phi4^2)).2
Order of center |Z^F|: phi4^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 phi2 ( q^2-9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 phi2 ( q^2-9 )
Fusion of maximal tori of C^F in those of G^F:
[ 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 2, 2, 4 ], [ 3, 5, 2, 2 ], [ 4, 2, 1, 2 ],
[ 7, 3, 3, 8 ], [ 7, 5, 3, 4 ], [ 12, 1, 5, 8 ], [ 12, 2, 1, 4 ],
[ 12, 2, 5, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 5, 4 ], [ 15, 1, 5, 16 ],
[ 16, 1, 4, 16 ], [ 16, 2, 4, 8 ], [ 16, 2, 6, 16 ], [ 16, 2, 13, 16 ],
[ 16, 3, 4, 8 ], [ 16, 4, 4, 8 ], [ 16, 9, 4, 4 ], [ 16, 9, 6, 8 ],
[ 16, 9, 13, 8 ], [ 16, 10, 5, 8 ], [ 16, 10, 11, 8 ], [ 16, 10, 15, 8 ],
[ 16, 11, 4, 8 ], [ 16, 11, 6, 8 ], [ 16, 11, 9, 8 ], [ 16, 13, 4, 8 ],
[ 16, 15, 4, 8 ], [ 16, 16, 4, 8 ], [ 21, 2, 7, 16 ], [ 21, 5, 7, 8 ],
[ 27, 1, 14, 32 ], [ 27, 3, 10, 16 ], [ 27, 3, 15, 32 ], [ 27, 5, 10, 16 ],
[ 27, 8, 10, 16 ], [ 27, 8, 15, 16 ], [ 27, 9, 8, 8 ], [ 27, 9, 11, 16 ],
[ 27, 9, 14, 16 ], [ 27, 11, 10, 16 ], [ 27, 11, 15, 16 ],
[ 27, 14, 7, 16 ], [ 27, 14, 17, 16 ], [ 29, 4, 17, 32 ], [ 29, 9, 17, 16 ],
[ 31, 9, 15, 32 ], [ 31, 10, 10, 32 ], [ 31, 11, 13, 32 ],
[ 31, 12, 9, 32 ], [ 31, 16, 15, 32 ], [ 31, 23, 13, 32 ] ]
k = 16: F-action on Pi is () [31,2,16]
Dynkin type is (A_0(q) + T(phi1 phi2 phi8)).2
Order of center |Z^F|: phi8 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2 phi4
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2 phi4
Fusion of maximal tori of C^F in those of G^F:
[ 29 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 2, 1 ], [ 4, 2, 1, 1 ],
[ 4, 2, 2, 1 ], [ 12, 2, 4, 2 ], [ 12, 4, 4, 1 ], [ 16, 2, 11, 4 ],
[ 16, 9, 11, 2 ], [ 27, 1, 20, 8 ], [ 27, 5, 17, 4 ], [ 27, 9, 19, 4 ],
[ 31, 9, 16, 4 ], [ 31, 11, 14, 8 ], [ 31, 16, 16, 4 ], [ 31, 23, 14, 8 ] ]
k = 17: F-action on Pi is () [31,2,17]
Dynkin type is (A_0(q) + T(phi1 phi2 phi4^2)).2
Order of center |Z^F|: phi4^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 phi2 ( q^2-9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1 phi2 ( q^2-9 )
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, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 2, 3, 4 ], [ 3, 2, 4, 4 ], [ 3, 5, 3, 2 ],
[ 3, 5, 4, 2 ], [ 12, 1, 5, 8 ], [ 12, 2, 2, 2 ], [ 12, 2, 5, 4 ],
[ 12, 4, 2, 2 ], [ 12, 4, 5, 4 ], [ 15, 1, 5, 16 ], [ 16, 1, 4, 16 ],
[ 16, 2, 4, 8 ], [ 16, 2, 7, 8 ], [ 16, 2, 9, 8 ], [ 16, 2, 14, 8 ],
[ 16, 3, 4, 8 ], [ 16, 4, 4, 8 ], [ 16, 4, 10, 16 ], [ 16, 9, 4, 4 ],
[ 16, 9, 7, 4 ], [ 16, 9, 9, 4 ], [ 16, 9, 10, 8 ], [ 16, 9, 14, 4 ],
[ 16, 10, 6, 4 ], [ 16, 10, 8, 4 ], [ 16, 10, 9, 4 ], [ 16, 10, 12, 4 ],
[ 16, 10, 13, 4 ], [ 16, 10, 16, 4 ], [ 16, 11, 4, 8 ], [ 16, 11, 8, 8 ],
[ 16, 11, 9, 8 ], [ 16, 13, 4, 8 ], [ 16, 13, 10, 16 ], [ 16, 15, 4, 8 ],
[ 16, 16, 4, 8 ], [ 27, 1, 14, 32 ], [ 27, 3, 10, 16 ], [ 27, 3, 20, 16 ],
[ 27, 5, 10, 16 ], [ 27, 8, 10, 16 ], [ 27, 8, 20, 16 ], [ 27, 9, 8, 8 ],
[ 27, 9, 11, 16 ], [ 27, 9, 17, 8 ], [ 27, 11, 10, 16 ], [ 27, 11, 20, 16 ],
[ 27, 14, 7, 16 ], [ 27, 14, 20, 16 ], [ 29, 4, 18, 16 ], [ 29, 4, 20, 16 ],
[ 29, 9, 18, 8 ], [ 29, 9, 20, 8 ], [ 31, 9, 17, 16 ], [ 31, 10, 22, 16 ],
[ 31, 11, 17, 16 ], [ 31, 12, 23, 16 ], [ 31, 12, 37, 16 ],
[ 31, 16, 17, 16 ], [ 31, 23, 17, 16 ] ]
k = 18: F-action on Pi is () [31,2,18]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/768 phi1 ( q^3-23*q^2+171*q-405 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/768 ( q^4-24*q^3+194*q^2-624*q+693 )
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, 14 ], [ 2, 2, 1, 7 ], [ 2, 2, 2, 8 ],
[ 3, 1, 1, 16 ], [ 3, 2, 1, 8 ], [ 3, 2, 2, 12 ], [ 3, 3, 1, 8 ],
[ 3, 4, 1, 8 ], [ 3, 5, 1, 4 ], [ 3, 5, 2, 6 ], [ 4, 1, 1, 8 ],
[ 4, 2, 1, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ],
[ 7, 1, 1, 64 ], [ 7, 2, 1, 32 ], [ 7, 2, 2, 16 ], [ 7, 3, 1, 32 ],
[ 7, 3, 4, 24 ], [ 7, 4, 1, 32 ], [ 7, 4, 3, 48 ], [ 7, 5, 1, 16 ],
[ 7, 5, 2, 8 ], [ 7, 5, 3, 24 ], [ 7, 5, 4, 12 ], [ 8, 1, 1, 16 ],
[ 9, 1, 1, 96 ], [ 9, 2, 1, 48 ], [ 9, 2, 3, 96 ], [ 9, 3, 1, 48 ],
[ 9, 4, 1, 48 ], [ 9, 5, 1, 24 ], [ 9, 5, 3, 48 ], [ 12, 1, 1, 48 ],
[ 12, 2, 1, 24 ], [ 12, 2, 3, 4 ], [ 12, 3, 1, 24 ], [ 12, 3, 4, 16 ],
[ 12, 4, 1, 12 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 8 ], [ 13, 1, 1, 96 ],
[ 13, 2, 1, 48 ], [ 13, 2, 3, 48 ], [ 14, 1, 1, 64 ], [ 14, 2, 1, 32 ],
[ 14, 2, 3, 64 ], [ 15, 1, 1, 96 ], [ 16, 1, 1, 192 ], [ 16, 2, 1, 96 ],
[ 16, 2, 5, 48 ], [ 16, 3, 1, 96 ], [ 16, 4, 1, 96 ], [ 16, 4, 6, 192 ],
[ 16, 5, 1, 96 ], [ 16, 6, 1, 96 ], [ 16, 7, 1, 96 ], [ 16, 8, 1, 96 ],
[ 16, 8, 2, 96 ], [ 16, 9, 1, 48 ], [ 16, 9, 5, 24 ], [ 16, 9, 6, 96 ],
[ 16, 10, 1, 48 ], [ 16, 10, 3, 24 ], [ 16, 11, 1, 48 ], [ 16, 11, 2, 48 ],
[ 16, 11, 5, 24 ], [ 16, 12, 1, 48 ], [ 16, 12, 5, 96 ], [ 16, 13, 1, 48 ],
[ 16, 13, 6, 96 ], [ 16, 14, 1, 48 ], [ 16, 14, 3, 48 ], [ 16, 14, 5, 96 ],
[ 16, 15, 1, 48 ], [ 16, 16, 1, 48 ], [ 16, 17, 1, 48 ], [ 16, 17, 3, 48 ],
[ 21, 1, 1, 192 ], [ 21, 2, 1, 96 ], [ 21, 2, 8, 96 ], [ 21, 3, 1, 96 ],
[ 21, 3, 5, 32 ], [ 21, 4, 1, 96 ], [ 21, 5, 1, 48 ], [ 21, 5, 3, 16 ],
[ 21, 5, 8, 48 ], [ 21, 6, 1, 48 ], [ 21, 6, 5, 16 ], [ 21, 6, 6, 48 ],
[ 21, 7, 1, 48 ], [ 21, 7, 3, 16 ], [ 22, 1, 1, 192 ], [ 22, 2, 1, 96 ],
[ 22, 2, 3, 96 ], [ 22, 3, 1, 96 ], [ 22, 3, 5, 192 ], [ 22, 4, 1, 48 ],
[ 22, 4, 3, 48 ], [ 22, 4, 7, 96 ], [ 23, 2, 3, 32 ], [ 23, 6, 3, 16 ],
[ 27, 1, 1, 384 ], [ 27, 2, 1, 192 ], [ 27, 2, 16, 384 ], [ 27, 3, 1, 192 ],
[ 27, 3, 11, 192 ], [ 27, 4, 1, 192 ], [ 27, 5, 1, 192 ], [ 27, 6, 1, 96 ],
[ 27, 6, 3, 96 ], [ 27, 6, 16, 192 ], [ 27, 7, 1, 96 ], [ 27, 7, 16, 192 ],
[ 27, 8, 1, 96 ], [ 27, 8, 11, 96 ], [ 27, 8, 16, 192 ], [ 27, 9, 1, 96 ],
[ 27, 9, 3, 96 ], [ 27, 10, 1, 96 ], [ 27, 10, 9, 96 ], [ 27, 10, 12, 192 ],
[ 27, 11, 1, 96 ], [ 27, 11, 11, 96 ], [ 27, 12, 1, 96 ], [ 27, 12, 5, 96 ],
[ 27, 13, 1, 96 ], [ 27, 13, 5, 96 ], [ 27, 13, 16, 192 ],
[ 27, 14, 1, 96 ], [ 27, 14, 11, 96 ], [ 28, 2, 3, 128 ], [ 28, 5, 3, 64 ],
[ 28, 6, 3, 64 ], [ 29, 4, 3, 192 ], [ 29, 9, 3, 96 ], [ 29, 12, 3, 96 ],
[ 30, 4, 5, 384 ], [ 30, 8, 5, 192 ], [ 30, 11, 3, 192 ],
[ 30, 12, 5, 192 ], [ 30, 13, 3, 192 ], [ 31, 9, 18, 384 ],
[ 31, 10, 3, 384 ], [ 31, 11, 18, 384 ], [ 31, 12, 43, 384 ],
[ 31, 13, 45, 384 ], [ 31, 14, 27, 384 ], [ 31, 15, 41, 384 ],
[ 31, 16, 18, 384 ], [ 31, 21, 5, 384 ], [ 31, 23, 18, 384 ],
[ 31, 29, 3, 384 ] ]
k = 19: F-action on Pi is () [31,2,19]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2
Order of center |Z^F|: phi1^3 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/96 phi1 phi2 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/96 phi1 phi2 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 12 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 6 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 6 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 6 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 3 ], [ 4, 1, 1, 6 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 3 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 12 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 36 ],
[ 7, 1, 4, 12 ], [ 7, 2, 1, 6 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 18 ],
[ 7, 2, 4, 6 ], [ 7, 3, 1, 6 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 18 ],
[ 7, 3, 4, 6 ], [ 7, 4, 1, 6 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 18 ],
[ 7, 4, 4, 6 ], [ 7, 5, 1, 3 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 9 ],
[ 7, 5, 4, 3 ], [ 9, 1, 3, 48 ], [ 9, 2, 3, 24 ], [ 9, 3, 3, 24 ],
[ 9, 4, 3, 24 ], [ 9, 5, 3, 12 ], [ 12, 1, 1, 24 ], [ 12, 1, 4, 12 ],
[ 12, 2, 1, 12 ], [ 12, 2, 4, 6 ], [ 12, 2, 5, 2 ], [ 12, 3, 1, 12 ],
[ 12, 3, 3, 6 ], [ 12, 3, 4, 6 ], [ 12, 4, 1, 6 ], [ 12, 4, 4, 3 ],
[ 12, 4, 5, 2 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 24 ], [ 13, 2, 1, 12 ],
[ 13, 2, 3, 12 ], [ 14, 1, 3, 16 ], [ 14, 2, 3, 8 ], [ 16, 1, 2, 24 ],
[ 16, 1, 6, 96 ], [ 16, 2, 2, 12 ], [ 16, 2, 4, 12 ], [ 16, 2, 6, 48 ],
[ 16, 3, 2, 12 ], [ 16, 3, 6, 48 ], [ 16, 4, 2, 12 ], [ 16, 4, 6, 48 ],
[ 16, 5, 5, 48 ], [ 16, 6, 5, 48 ], [ 16, 7, 5, 48 ], [ 16, 8, 2, 12 ],
[ 16, 8, 3, 12 ], [ 16, 8, 5, 48 ], [ 16, 8, 6, 12 ], [ 16, 8, 7, 12 ],
[ 16, 9, 2, 6 ], [ 16, 9, 4, 6 ], [ 16, 9, 6, 24 ], [ 16, 10, 5, 24 ],
[ 16, 11, 2, 6 ], [ 16, 11, 4, 12 ], [ 16, 11, 6, 24 ], [ 16, 11, 7, 6 ],
[ 16, 11, 9, 12 ], [ 16, 12, 5, 24 ], [ 16, 13, 2, 12 ], [ 16, 13, 6, 24 ],
[ 16, 14, 2, 6 ], [ 16, 14, 3, 6 ], [ 16, 14, 5, 24 ], [ 16, 15, 2, 12 ],
[ 16, 15, 6, 24 ], [ 16, 16, 2, 12 ], [ 16, 16, 6, 24 ], [ 16, 17, 2, 6 ],
[ 16, 17, 3, 6 ], [ 16, 17, 5, 24 ], [ 21, 1, 1, 48 ], [ 21, 1, 2, 48 ],
[ 21, 2, 1, 24 ], [ 21, 2, 6, 24 ], [ 21, 2, 8, 24 ], [ 21, 3, 1, 24 ],
[ 21, 3, 4, 4 ], [ 21, 3, 6, 24 ], [ 21, 3, 7, 24 ], [ 21, 3, 9, 12 ],
[ 21, 4, 1, 24 ], [ 21, 4, 6, 24 ], [ 21, 5, 1, 12 ], [ 21, 5, 5, 2 ],
[ 21, 5, 6, 12 ], [ 21, 5, 7, 6 ], [ 21, 5, 8, 12 ], [ 21, 6, 1, 12 ],
[ 21, 6, 4, 4 ], [ 21, 6, 6, 12 ], [ 21, 6, 7, 12 ], [ 21, 6, 8, 12 ],
[ 21, 7, 1, 12 ], [ 21, 7, 5, 4 ], [ 21, 7, 6, 12 ], [ 21, 7, 7, 12 ],
[ 22, 1, 7, 48 ], [ 22, 2, 7, 24 ], [ 22, 2, 8, 24 ], [ 22, 3, 5, 24 ],
[ 22, 3, 6, 24 ], [ 22, 4, 7, 12 ], [ 22, 4, 8, 24 ], [ 27, 1, 2, 96 ],
[ 27, 2, 11, 48 ], [ 27, 2, 16, 48 ], [ 27, 3, 9, 24 ], [ 27, 3, 14, 48 ],
[ 27, 3, 16, 48 ], [ 27, 3, 21, 48 ], [ 27, 4, 11, 48 ], [ 27, 4, 12, 48 ],
[ 27, 5, 12, 48 ], [ 27, 6, 5, 12 ], [ 27, 6, 7, 12 ], [ 27, 6, 11, 24 ],
[ 27, 6, 12, 24 ], [ 27, 6, 13, 24 ], [ 27, 6, 16, 24 ], [ 27, 7, 11, 24 ],
[ 27, 7, 16, 24 ], [ 27, 8, 9, 24 ], [ 27, 8, 14, 24 ], [ 27, 8, 16, 24 ],
[ 27, 8, 21, 48 ], [ 27, 9, 5, 12 ], [ 27, 9, 13, 24 ], [ 27, 9, 14, 24 ],
[ 27, 10, 7, 12 ], [ 27, 10, 8, 12 ], [ 27, 10, 11, 24 ],
[ 27, 10, 12, 24 ], [ 27, 10, 13, 24 ], [ 27, 10, 17, 24 ],
[ 27, 11, 9, 24 ], [ 27, 11, 14, 24 ], [ 27, 11, 16, 24 ],
[ 27, 11, 21, 48 ], [ 27, 12, 4, 24 ], [ 27, 12, 9, 24 ],
[ 27, 12, 11, 24 ], [ 27, 12, 12, 24 ], [ 27, 12, 14, 48 ],
[ 27, 13, 4, 12 ], [ 27, 13, 9, 12 ], [ 27, 13, 11, 24 ],
[ 27, 13, 12, 24 ], [ 27, 13, 14, 24 ], [ 27, 13, 16, 24 ],
[ 27, 14, 9, 24 ], [ 27, 14, 14, 24 ], [ 27, 14, 15, 24 ],
[ 27, 14, 21, 48 ], [ 28, 2, 5, 16 ], [ 28, 5, 5, 16 ], [ 28, 6, 5, 16 ],
[ 30, 4, 4, 48 ], [ 30, 8, 4, 24 ], [ 30, 12, 4, 48 ], [ 30, 13, 5, 48 ],
[ 30, 13, 7, 48 ], [ 31, 9, 19, 48 ], [ 31, 10, 5, 48 ], [ 31, 10, 26, 48 ],
[ 31, 11, 19, 96 ], [ 31, 13, 37, 96 ], [ 31, 14, 28, 96 ],
[ 31, 14, 31, 96 ], [ 31, 15, 31, 96 ], [ 31, 15, 36, 96 ],
[ 31, 16, 19, 48 ], [ 31, 21, 4, 96 ], [ 31, 21, 8, 96 ],
[ 31, 23, 20, 96 ], [ 31, 29, 30, 96 ] ]
k = 20: F-action on Pi is () [31,2,20]
Dynkin type is (A_0(q) + T(phi1 phi2^3 phi4)).2
Order of center |Z^F|: phi1 phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/96 phi1^2 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/96 phi1^2 phi2 ( 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, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 12 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 6 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 6 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 6 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 3 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 6 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 3 ], [ 5, 1, 2, 12 ],
[ 6, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 36 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 12 ], [ 7, 2, 1, 6 ], [ 7, 2, 2, 18 ], [ 7, 2, 3, 2 ],
[ 7, 2, 4, 6 ], [ 7, 3, 1, 6 ], [ 7, 3, 2, 18 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 6 ], [ 7, 4, 1, 6 ], [ 7, 4, 2, 18 ], [ 7, 4, 3, 2 ],
[ 7, 4, 4, 6 ], [ 7, 5, 1, 3 ], [ 7, 5, 2, 9 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 3 ], [ 9, 1, 4, 48 ], [ 9, 2, 4, 24 ], [ 9, 3, 4, 24 ],
[ 9, 4, 4, 24 ], [ 9, 5, 4, 12 ], [ 12, 1, 3, 24 ], [ 12, 1, 4, 12 ],
[ 12, 2, 3, 12 ], [ 12, 2, 4, 6 ], [ 12, 2, 5, 2 ], [ 12, 3, 2, 12 ],
[ 12, 3, 3, 6 ], [ 12, 3, 4, 6 ], [ 12, 4, 3, 6 ], [ 12, 4, 4, 3 ],
[ 12, 4, 5, 2 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 24 ], [ 13, 2, 2, 12 ],
[ 13, 2, 4, 12 ], [ 14, 1, 4, 16 ], [ 14, 2, 4, 8 ], [ 16, 1, 2, 24 ],
[ 16, 1, 8, 96 ], [ 16, 2, 2, 12 ], [ 16, 2, 4, 12 ], [ 16, 2, 8, 48 ],
[ 16, 3, 2, 12 ], [ 16, 3, 8, 48 ], [ 16, 4, 2, 12 ], [ 16, 4, 8, 48 ],
[ 16, 5, 7, 48 ], [ 16, 6, 7, 48 ], [ 16, 7, 7, 48 ], [ 16, 8, 2, 12 ],
[ 16, 8, 3, 12 ], [ 16, 8, 6, 12 ], [ 16, 8, 7, 12 ], [ 16, 8, 8, 48 ],
[ 16, 9, 2, 6 ], [ 16, 9, 4, 6 ], [ 16, 9, 8, 24 ], [ 16, 10, 7, 24 ],
[ 16, 11, 2, 6 ], [ 16, 11, 4, 12 ], [ 16, 11, 7, 6 ], [ 16, 11, 9, 12 ],
[ 16, 11, 10, 24 ], [ 16, 12, 7, 24 ], [ 16, 13, 2, 12 ], [ 16, 13, 8, 24 ],
[ 16, 14, 2, 6 ], [ 16, 14, 3, 6 ], [ 16, 14, 6, 24 ], [ 16, 15, 2, 12 ],
[ 16, 15, 8, 24 ], [ 16, 16, 2, 12 ], [ 16, 16, 8, 24 ], [ 16, 17, 2, 6 ],
[ 16, 17, 3, 6 ], [ 16, 17, 6, 24 ], [ 21, 1, 3, 48 ], [ 21, 1, 4, 48 ],
[ 21, 2, 3, 24 ], [ 21, 2, 4, 24 ], [ 21, 2, 10, 24 ], [ 21, 3, 2, 24 ],
[ 21, 3, 4, 12 ], [ 21, 3, 5, 24 ], [ 21, 3, 9, 4 ], [ 21, 3, 10, 24 ],
[ 21, 4, 3, 24 ], [ 21, 4, 10, 24 ], [ 21, 5, 3, 12 ], [ 21, 5, 4, 12 ],
[ 21, 5, 5, 6 ], [ 21, 5, 7, 2 ], [ 21, 5, 10, 12 ], [ 21, 6, 2, 12 ],
[ 21, 6, 4, 12 ], [ 21, 6, 5, 12 ], [ 21, 6, 8, 4 ], [ 21, 6, 10, 12 ],
[ 21, 7, 3, 12 ], [ 21, 7, 5, 12 ], [ 21, 7, 7, 4 ], [ 21, 7, 10, 12 ],
[ 22, 1, 9, 48 ], [ 22, 2, 9, 24 ], [ 22, 2, 10, 24 ], [ 22, 3, 7, 24 ],
[ 22, 3, 8, 24 ], [ 22, 4, 9, 12 ], [ 22, 4, 10, 24 ], [ 27, 1, 4, 96 ],
[ 27, 2, 15, 48 ], [ 27, 2, 18, 48 ], [ 27, 3, 9, 24 ], [ 27, 3, 18, 48 ],
[ 27, 3, 23, 48 ], [ 27, 3, 24, 48 ], [ 27, 4, 15, 48 ], [ 27, 4, 20, 48 ],
[ 27, 5, 16, 48 ], [ 27, 6, 5, 12 ], [ 27, 6, 7, 12 ], [ 27, 6, 15, 24 ],
[ 27, 6, 18, 24 ], [ 27, 6, 19, 24 ], [ 27, 6, 20, 24 ], [ 27, 7, 15, 24 ],
[ 27, 7, 18, 24 ], [ 27, 8, 9, 24 ], [ 27, 8, 18, 24 ], [ 27, 8, 23, 48 ],
[ 27, 8, 24, 24 ], [ 27, 9, 5, 12 ], [ 27, 9, 16, 24 ], [ 27, 9, 18, 24 ],
[ 27, 10, 7, 12 ], [ 27, 10, 8, 12 ], [ 27, 10, 14, 24 ],
[ 27, 10, 18, 24 ], [ 27, 10, 19, 24 ], [ 27, 10, 20, 24 ],
[ 27, 11, 9, 24 ], [ 27, 11, 18, 24 ], [ 27, 11, 23, 48 ],
[ 27, 11, 24, 24 ], [ 27, 12, 4, 24 ], [ 27, 12, 9, 24 ],
[ 27, 12, 15, 24 ], [ 27, 12, 19, 48 ], [ 27, 12, 20, 24 ],
[ 27, 13, 4, 12 ], [ 27, 13, 9, 12 ], [ 27, 13, 15, 24 ],
[ 27, 13, 17, 24 ], [ 27, 13, 19, 24 ], [ 27, 13, 20, 24 ],
[ 27, 14, 9, 24 ], [ 27, 14, 18, 24 ], [ 27, 14, 23, 48 ],
[ 27, 14, 24, 24 ], [ 28, 2, 7, 16 ], [ 28, 5, 7, 16 ], [ 28, 6, 7, 16 ],
[ 30, 4, 18, 48 ], [ 30, 8, 20, 24 ], [ 30, 12, 18, 48 ],
[ 30, 13, 15, 48 ], [ 30, 13, 17, 48 ], [ 31, 9, 20, 48 ],
[ 31, 10, 32, 48 ], [ 31, 10, 34, 48 ], [ 31, 11, 20, 96 ],
[ 31, 13, 39, 96 ], [ 31, 14, 29, 96 ], [ 31, 14, 30, 96 ],
[ 31, 15, 35, 96 ], [ 31, 15, 38, 96 ], [ 31, 16, 20, 48 ],
[ 31, 21, 24, 96 ], [ 31, 21, 48, 96 ], [ 31, 23, 19, 96 ],
[ 31, 29, 34, 96 ] ]
k = 21: F-action on Pi is () [31,2,21]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1^2 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ],
[ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ],
[ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ], [ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ],
[ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ],
[ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ], [ 9, 1, 3, 8 ],
[ 9, 1, 4, 8 ], [ 9, 2, 3, 4 ], [ 9, 2, 4, 4 ], [ 9, 3, 3, 4 ],
[ 9, 3, 4, 4 ], [ 9, 4, 3, 4 ], [ 9, 4, 4, 4 ], [ 9, 5, 3, 2 ],
[ 9, 5, 4, 2 ], [ 12, 1, 2, 4 ], [ 12, 1, 4, 4 ], [ 12, 2, 2, 2 ],
[ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ],
[ 12, 4, 2, 2 ], [ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ], [ 13, 1, 1, 4 ],
[ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 4 ], [ 13, 2, 1, 2 ],
[ 13, 2, 2, 2 ], [ 13, 2, 3, 2 ], [ 13, 2, 4, 2 ], [ 14, 1, 3, 8 ],
[ 14, 1, 4, 8 ], [ 14, 2, 3, 4 ], [ 14, 2, 4, 4 ], [ 16, 1, 2, 8 ],
[ 16, 1, 7, 16 ], [ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 2, 7, 8 ],
[ 16, 3, 2, 4 ], [ 16, 3, 7, 8 ], [ 16, 4, 2, 4 ], [ 16, 4, 7, 8 ],
[ 16, 4, 11, 8 ], [ 16, 5, 6, 8 ], [ 16, 5, 8, 8 ], [ 16, 6, 6, 8 ],
[ 16, 6, 8, 8 ], [ 16, 7, 6, 8 ], [ 16, 7, 8, 8 ], [ 16, 8, 2, 4 ],
[ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ], [ 16, 9, 2, 2 ],
[ 16, 9, 4, 2 ], [ 16, 9, 7, 4 ], [ 16, 9, 11, 4 ], [ 16, 10, 6, 4 ],
[ 16, 10, 8, 4 ], [ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ], [ 16, 11, 7, 2 ],
[ 16, 11, 8, 8 ], [ 16, 11, 9, 4 ], [ 16, 12, 6, 4 ], [ 16, 12, 8, 4 ],
[ 16, 13, 2, 4 ], [ 16, 13, 7, 4 ], [ 16, 13, 11, 8 ], [ 16, 14, 2, 2 ],
[ 16, 14, 3, 2 ], [ 16, 14, 7, 8 ], [ 16, 14, 10, 8 ], [ 16, 15, 2, 4 ],
[ 16, 15, 7, 4 ], [ 16, 16, 2, 4 ], [ 16, 16, 7, 4 ], [ 16, 17, 2, 2 ],
[ 16, 17, 3, 2 ], [ 21, 1, 5, 8 ], [ 21, 1, 7, 8 ], [ 21, 2, 2, 4 ],
[ 21, 2, 9, 4 ], [ 21, 3, 3, 4 ], [ 21, 3, 4, 4 ], [ 21, 3, 8, 4 ],
[ 21, 3, 9, 4 ], [ 21, 4, 2, 4 ], [ 21, 4, 9, 4 ], [ 21, 5, 2, 2 ],
[ 21, 5, 5, 2 ], [ 21, 5, 7, 2 ], [ 21, 5, 9, 2 ], [ 21, 6, 3, 4 ],
[ 21, 6, 4, 4 ], [ 21, 6, 8, 4 ], [ 21, 6, 9, 4 ], [ 21, 7, 2, 4 ],
[ 21, 7, 5, 4 ], [ 21, 7, 7, 4 ], [ 21, 7, 9, 4 ], [ 22, 1, 7, 8 ],
[ 22, 1, 9, 8 ], [ 22, 2, 7, 4 ], [ 22, 2, 8, 4 ], [ 22, 2, 9, 4 ],
[ 22, 2, 10, 4 ], [ 22, 3, 5, 4 ], [ 22, 3, 6, 4 ], [ 22, 3, 7, 4 ],
[ 22, 3, 8, 4 ], [ 22, 4, 7, 2 ], [ 22, 4, 8, 4 ], [ 22, 4, 9, 2 ],
[ 22, 4, 10, 4 ], [ 27, 1, 8, 16 ], [ 27, 2, 14, 8 ], [ 27, 2, 17, 8 ],
[ 27, 3, 9, 8 ], [ 27, 3, 17, 8 ], [ 27, 3, 19, 8 ], [ 27, 3, 22, 8 ],
[ 27, 4, 13, 8 ], [ 27, 4, 18, 8 ], [ 27, 5, 15, 8 ], [ 27, 6, 5, 4 ],
[ 27, 6, 7, 4 ], [ 27, 6, 14, 4 ], [ 27, 6, 17, 4 ], [ 27, 7, 14, 4 ],
[ 27, 7, 17, 4 ], [ 27, 8, 9, 8 ], [ 27, 8, 17, 4 ], [ 27, 8, 19, 8 ],
[ 27, 8, 22, 8 ], [ 27, 9, 5, 4 ], [ 27, 9, 15, 4 ], [ 27, 9, 17, 4 ],
[ 27, 10, 7, 4 ], [ 27, 10, 8, 4 ], [ 27, 10, 15, 4 ], [ 27, 10, 16, 4 ],
[ 27, 11, 9, 8 ], [ 27, 11, 17, 4 ], [ 27, 11, 19, 8 ], [ 27, 11, 22, 8 ],
[ 27, 12, 4, 8 ], [ 27, 12, 9, 8 ], [ 27, 12, 13, 8 ], [ 27, 12, 18, 8 ],
[ 27, 13, 4, 4 ], [ 27, 13, 9, 4 ], [ 27, 13, 13, 4 ], [ 27, 13, 18, 4 ],
[ 27, 14, 9, 8 ], [ 27, 14, 16, 4 ], [ 27, 14, 19, 8 ], [ 27, 14, 22, 8 ],
[ 28, 2, 5, 8 ], [ 28, 2, 7, 8 ], [ 28, 5, 5, 8 ], [ 28, 5, 7, 8 ],
[ 28, 6, 5, 8 ], [ 28, 6, 7, 8 ], [ 30, 4, 4, 8 ], [ 30, 4, 18, 8 ],
[ 30, 8, 4, 4 ], [ 30, 8, 20, 4 ], [ 30, 12, 4, 8 ], [ 30, 12, 18, 8 ],
[ 30, 13, 5, 8 ], [ 30, 13, 7, 8 ], [ 30, 13, 15, 8 ], [ 30, 13, 17, 8 ],
[ 31, 9, 21, 8 ], [ 31, 10, 17, 8 ], [ 31, 10, 29, 8 ], [ 31, 11, 21, 16 ],
[ 31, 13, 38, 16 ], [ 31, 13, 40, 16 ], [ 31, 14, 32, 16 ],
[ 31, 14, 33, 16 ], [ 31, 15, 34, 16 ], [ 31, 15, 37, 16 ],
[ 31, 16, 21, 8 ], [ 31, 21, 14, 16 ], [ 31, 21, 18, 16 ],
[ 31, 23, 21, 16 ], [ 31, 29, 32, 16 ], [ 31, 29, 36, 16 ] ]
k = 22: F-action on Pi is () [31,2,22]
Dynkin type is (A_0(q) + T(phi2^6)).2
Order of center |Z^F|: phi2^4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/768 phi1^2 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/768 phi2 ( q^3-17*q^2+91*q-147 )
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, 14 ], [ 2, 2, 1, 15 ], [ 3, 1, 2, 16 ],
[ 3, 2, 2, 20 ], [ 3, 3, 2, 8 ], [ 3, 4, 2, 8 ], [ 3, 5, 2, 10 ],
[ 4, 1, 2, 8 ], [ 4, 2, 2, 6 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ],
[ 7, 1, 4, 64 ], [ 7, 2, 4, 48 ], [ 7, 3, 4, 56 ], [ 7, 4, 4, 80 ],
[ 7, 5, 4, 60 ], [ 8, 1, 2, 16 ], [ 9, 1, 2, 96 ], [ 9, 2, 2, 144 ],
[ 9, 3, 2, 48 ], [ 9, 4, 2, 48 ], [ 9, 5, 2, 72 ], [ 12, 1, 3, 48 ],
[ 12, 2, 3, 28 ], [ 12, 3, 2, 40 ], [ 12, 4, 3, 30 ], [ 13, 1, 4, 96 ],
[ 13, 2, 4, 96 ], [ 14, 1, 2, 64 ], [ 14, 2, 2, 96 ], [ 15, 1, 3, 96 ],
[ 16, 1, 5, 192 ], [ 16, 2, 5, 144 ], [ 16, 3, 5, 96 ], [ 16, 4, 5, 288 ],
[ 16, 5, 3, 96 ], [ 16, 6, 3, 96 ], [ 16, 7, 3, 96 ], [ 16, 8, 4, 192 ],
[ 16, 9, 5, 168 ], [ 16, 10, 3, 72 ], [ 16, 11, 5, 168 ],
[ 16, 12, 3, 144 ], [ 16, 13, 5, 144 ], [ 16, 14, 4, 240 ],
[ 16, 15, 5, 48 ], [ 16, 16, 5, 48 ], [ 16, 17, 4, 144 ], [ 21, 1, 4, 192 ],
[ 21, 2, 10, 192 ], [ 21, 3, 10, 128 ], [ 21, 4, 10, 96 ],
[ 21, 5, 10, 112 ], [ 21, 6, 10, 160 ], [ 21, 7, 10, 96 ],
[ 22, 1, 6, 192 ], [ 22, 2, 6, 192 ], [ 22, 3, 4, 288 ], [ 22, 4, 6, 288 ],
[ 23, 2, 7, 32 ], [ 23, 6, 7, 16 ], [ 27, 1, 5, 384 ], [ 27, 2, 10, 576 ],
[ 27, 3, 13, 384 ], [ 27, 4, 10, 192 ], [ 27, 5, 11, 192 ],
[ 27, 6, 10, 384 ], [ 27, 7, 10, 288 ], [ 27, 8, 13, 576 ],
[ 27, 9, 12, 288 ], [ 27, 10, 10, 384 ], [ 27, 11, 13, 192 ],
[ 27, 12, 10, 384 ], [ 27, 13, 10, 384 ], [ 27, 14, 13, 192 ],
[ 28, 2, 10, 128 ], [ 28, 5, 10, 64 ], [ 28, 6, 10, 192 ],
[ 29, 4, 11, 192 ], [ 29, 9, 11, 96 ], [ 29, 12, 7, 96 ],
[ 30, 4, 28, 384 ], [ 30, 8, 32, 384 ], [ 30, 11, 27, 192 ],
[ 30, 12, 28, 192 ], [ 30, 13, 20, 576 ], [ 31, 9, 22, 384 ],
[ 31, 10, 56, 768 ], [ 31, 11, 22, 384 ], [ 31, 12, 55, 384 ],
[ 31, 13, 55, 384 ], [ 31, 14, 38, 1152 ], [ 31, 15, 50, 384 ],
[ 31, 16, 22, 384 ], [ 31, 21, 50, 384 ], [ 31, 23, 22, 384 ],
[ 31, 29, 53, 384 ] ]
k = 23: F-action on Pi is () [31,2,23]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/128 phi1^2 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/128 ( q^4-12*q^3+46*q^2-60*q+9 )
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, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 7 ],
[ 2, 2, 2, 8 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 3, 2, 1, 8 ],
[ 3, 2, 2, 12 ], [ 3, 3, 1, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 1, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 4 ], [ 3, 5, 2, 6 ], [ 4, 1, 1, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 4 ], [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ], [ 7, 1, 3, 16 ],
[ 7, 1, 4, 16 ], [ 7, 2, 1, 16 ], [ 7, 2, 2, 8 ], [ 7, 2, 3, 16 ],
[ 7, 2, 4, 8 ], [ 7, 3, 1, 16 ], [ 7, 3, 2, 8 ], [ 7, 3, 3, 24 ],
[ 7, 3, 4, 8 ], [ 7, 4, 1, 16 ], [ 7, 4, 2, 16 ], [ 7, 4, 3, 24 ],
[ 7, 4, 4, 24 ], [ 7, 5, 1, 16 ], [ 7, 5, 2, 8 ], [ 7, 5, 3, 24 ],
[ 7, 5, 4, 12 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ],
[ 9, 2, 2, 24 ], [ 9, 2, 3, 16 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 12 ],
[ 9, 5, 3, 8 ], [ 12, 1, 1, 8 ], [ 12, 1, 3, 8 ], [ 12, 1, 4, 16 ],
[ 12, 2, 1, 8 ], [ 12, 2, 3, 4 ], [ 12, 2, 4, 8 ], [ 12, 3, 1, 12 ],
[ 12, 3, 2, 4 ], [ 12, 3, 3, 16 ], [ 12, 3, 4, 8 ], [ 12, 4, 1, 12 ],
[ 12, 4, 3, 2 ], [ 12, 4, 4, 8 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ],
[ 13, 2, 1, 8 ], [ 13, 2, 2, 16 ], [ 13, 2, 3, 8 ], [ 15, 1, 4, 16 ],
[ 16, 1, 1, 32 ], [ 16, 1, 2, 32 ], [ 16, 1, 5, 32 ], [ 16, 2, 1, 32 ],
[ 16, 2, 2, 16 ], [ 16, 2, 5, 16 ], [ 16, 2, 6, 32 ], [ 16, 3, 1, 16 ],
[ 16, 3, 2, 16 ], [ 16, 3, 5, 16 ], [ 16, 4, 1, 16 ], [ 16, 4, 2, 48 ],
[ 16, 4, 5, 48 ], [ 16, 4, 6, 32 ], [ 16, 5, 1, 16 ], [ 16, 5, 3, 16 ],
[ 16, 6, 1, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 1, 16 ], [ 16, 7, 3, 16 ],
[ 16, 8, 1, 32 ], [ 16, 8, 2, 16 ], [ 16, 8, 3, 32 ], [ 16, 8, 4, 16 ],
[ 16, 8, 5, 32 ], [ 16, 8, 6, 16 ], [ 16, 8, 7, 48 ], [ 16, 9, 1, 16 ],
[ 16, 9, 2, 24 ], [ 16, 9, 5, 24 ], [ 16, 9, 6, 32 ], [ 16, 10, 1, 16 ],
[ 16, 10, 3, 8 ], [ 16, 10, 5, 16 ], [ 16, 11, 1, 32 ], [ 16, 11, 2, 16 ],
[ 16, 11, 5, 8 ], [ 16, 11, 6, 48 ], [ 16, 11, 7, 24 ], [ 16, 12, 1, 8 ],
[ 16, 12, 3, 24 ], [ 16, 12, 5, 16 ], [ 16, 13, 1, 8 ], [ 16, 13, 2, 48 ],
[ 16, 13, 5, 24 ], [ 16, 13, 6, 16 ], [ 16, 14, 1, 24 ], [ 16, 14, 2, 48 ],
[ 16, 14, 3, 24 ], [ 16, 14, 4, 24 ], [ 16, 14, 5, 48 ], [ 16, 15, 1, 8 ],
[ 16, 15, 2, 16 ], [ 16, 15, 5, 8 ], [ 16, 16, 1, 8 ], [ 16, 16, 2, 16 ],
[ 16, 16, 5, 8 ], [ 16, 17, 1, 24 ], [ 16, 17, 2, 16 ], [ 16, 17, 3, 24 ],
[ 16, 17, 4, 8 ], [ 16, 17, 5, 32 ], [ 21, 1, 2, 32 ], [ 21, 1, 3, 32 ],
[ 21, 2, 1, 16 ], [ 21, 2, 3, 32 ], [ 21, 2, 4, 16 ], [ 21, 2, 6, 48 ],
[ 21, 2, 8, 16 ], [ 21, 3, 1, 16 ], [ 21, 3, 2, 16 ], [ 21, 3, 5, 16 ],
[ 21, 3, 6, 32 ], [ 21, 3, 7, 16 ], [ 21, 4, 3, 16 ], [ 21, 4, 6, 16 ],
[ 21, 5, 1, 16 ], [ 21, 5, 3, 16 ], [ 21, 5, 4, 8 ], [ 21, 5, 6, 24 ],
[ 21, 5, 8, 16 ], [ 21, 6, 1, 24 ], [ 21, 6, 2, 16 ], [ 21, 6, 5, 8 ],
[ 21, 6, 6, 24 ], [ 21, 6, 7, 48 ], [ 21, 7, 1, 24 ], [ 21, 7, 3, 8 ],
[ 21, 7, 6, 16 ], [ 22, 1, 3, 32 ], [ 22, 1, 4, 32 ], [ 22, 2, 1, 16 ],
[ 22, 2, 3, 16 ], [ 22, 2, 4, 32 ], [ 22, 3, 2, 16 ], [ 22, 3, 3, 48 ],
[ 22, 3, 6, 32 ], [ 22, 4, 1, 8 ], [ 22, 4, 3, 8 ], [ 22, 4, 4, 48 ],
[ 22, 4, 7, 16 ], [ 27, 1, 3, 64 ], [ 27, 2, 3, 96 ], [ 27, 2, 6, 32 ],
[ 27, 2, 11, 64 ], [ 27, 3, 1, 32 ], [ 27, 3, 3, 64 ], [ 27, 3, 4, 32 ],
[ 27, 3, 11, 32 ], [ 27, 3, 14, 64 ], [ 27, 4, 2, 32 ], [ 27, 4, 5, 32 ],
[ 27, 5, 3, 32 ], [ 27, 6, 1, 16 ], [ 27, 6, 3, 48 ], [ 27, 6, 4, 48 ],
[ 27, 6, 6, 16 ], [ 27, 6, 8, 32 ], [ 27, 6, 11, 32 ], [ 27, 6, 13, 64 ],
[ 27, 6, 16, 32 ], [ 27, 7, 3, 48 ], [ 27, 7, 6, 16 ], [ 27, 7, 11, 32 ],
[ 27, 8, 1, 16 ], [ 27, 8, 3, 96 ], [ 27, 8, 4, 48 ], [ 27, 8, 11, 16 ],
[ 27, 8, 14, 96 ], [ 27, 8, 16, 32 ], [ 27, 9, 1, 32 ], [ 27, 9, 3, 32 ],
[ 27, 9, 4, 16 ], [ 27, 9, 13, 32 ], [ 27, 10, 1, 16 ], [ 27, 10, 2, 32 ],
[ 27, 10, 3, 48 ], [ 27, 10, 4, 16 ], [ 27, 10, 9, 48 ], [ 27, 10, 11, 64 ],
[ 27, 10, 12, 32 ], [ 27, 10, 13, 32 ], [ 27, 11, 1, 16 ],
[ 27, 11, 3, 32 ], [ 27, 11, 4, 16 ], [ 27, 11, 11, 16 ],
[ 27, 11, 14, 32 ], [ 27, 12, 1, 48 ], [ 27, 12, 2, 32 ], [ 27, 12, 5, 16 ],
[ 27, 12, 11, 96 ], [ 27, 12, 12, 32 ], [ 27, 13, 1, 16 ],
[ 27, 13, 2, 48 ], [ 27, 13, 5, 48 ], [ 27, 13, 6, 32 ], [ 27, 13, 7, 16 ],
[ 27, 13, 11, 64 ], [ 27, 13, 12, 32 ], [ 27, 13, 16, 32 ],
[ 27, 14, 1, 16 ], [ 27, 14, 2, 16 ], [ 27, 14, 5, 32 ], [ 27, 14, 11, 16 ],
[ 27, 14, 15, 32 ], [ 29, 4, 5, 32 ], [ 29, 9, 5, 16 ], [ 30, 4, 12, 64 ],
[ 30, 4, 15, 64 ], [ 30, 8, 5, 32 ], [ 30, 8, 17, 64 ], [ 30, 11, 9, 32 ],
[ 30, 11, 17, 32 ], [ 30, 12, 12, 32 ], [ 30, 12, 15, 32 ],
[ 30, 13, 6, 32 ], [ 30, 13, 11, 96 ], [ 31, 9, 23, 64 ], [ 31, 10, 3, 64 ],
[ 31, 10, 4, 64 ], [ 31, 10, 11, 128 ], [ 31, 11, 23, 64 ],
[ 31, 12, 3, 64 ], [ 31, 13, 3, 64 ], [ 31, 13, 9, 64 ],
[ 31, 14, 20, 192 ], [ 31, 14, 39, 64 ], [ 31, 15, 3, 64 ],
[ 31, 15, 6, 64 ], [ 31, 16, 23, 64 ], [ 31, 21, 7, 64 ],
[ 31, 21, 21, 64 ], [ 31, 23, 23, 64 ], [ 31, 29, 7, 64 ],
[ 31, 29, 45, 64 ] ]
k = 24: F-action on Pi is () [31,2,24]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2
Order of center |Z^F|: phi1 phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
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, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 6 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 3 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 3 ], [ 4, 2, 2, 1 ], [ 7, 1, 1, 4 ],
[ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 1, 6 ],
[ 7, 2, 2, 2 ], [ 7, 2, 3, 6 ], [ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 2 ], [ 7, 3, 3, 10 ], [ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ],
[ 7, 4, 2, 2 ], [ 7, 4, 3, 6 ], [ 7, 4, 4, 6 ], [ 7, 5, 1, 3 ],
[ 7, 5, 2, 1 ], [ 7, 5, 3, 9 ], [ 7, 5, 4, 3 ], [ 12, 1, 4, 4 ],
[ 12, 1, 5, 4 ], [ 12, 2, 1, 4 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ],
[ 12, 3, 1, 4 ], [ 12, 3, 3, 6 ], [ 12, 3, 4, 2 ], [ 12, 4, 1, 6 ],
[ 12, 4, 4, 3 ], [ 12, 4, 5, 2 ], [ 16, 1, 2, 8 ], [ 16, 1, 4, 8 ],
[ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 2, 6, 16 ], [ 16, 3, 2, 4 ],
[ 16, 3, 4, 4 ], [ 16, 4, 2, 4 ], [ 16, 4, 4, 12 ], [ 16, 8, 2, 4 ],
[ 16, 8, 3, 4 ], [ 16, 8, 5, 8 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 12 ],
[ 16, 9, 2, 2 ], [ 16, 9, 4, 6 ], [ 16, 9, 6, 8 ], [ 16, 10, 5, 8 ],
[ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ], [ 16, 11, 6, 16 ], [ 16, 11, 7, 6 ],
[ 16, 11, 9, 4 ], [ 16, 13, 2, 4 ], [ 16, 13, 4, 12 ], [ 16, 14, 2, 6 ],
[ 16, 14, 3, 2 ], [ 16, 14, 5, 8 ], [ 16, 15, 2, 4 ], [ 16, 15, 4, 4 ],
[ 16, 16, 2, 4 ], [ 16, 16, 4, 4 ], [ 16, 17, 2, 2 ], [ 16, 17, 3, 6 ],
[ 16, 17, 5, 8 ], [ 21, 1, 6, 8 ], [ 21, 1, 8, 8 ], [ 21, 2, 5, 4 ],
[ 21, 2, 6, 8 ], [ 21, 2, 7, 12 ], [ 21, 3, 1, 8 ], [ 21, 3, 4, 4 ],
[ 21, 3, 6, 8 ], [ 21, 3, 9, 4 ], [ 21, 4, 5, 4 ], [ 21, 4, 7, 4 ],
[ 21, 5, 1, 4 ], [ 21, 5, 5, 2 ], [ 21, 5, 6, 4 ], [ 21, 5, 7, 6 ],
[ 21, 5, 8, 4 ], [ 21, 6, 1, 4 ], [ 21, 6, 4, 4 ], [ 21, 6, 6, 4 ],
[ 21, 6, 7, 12 ], [ 21, 6, 8, 4 ], [ 21, 7, 1, 12 ], [ 21, 7, 5, 4 ],
[ 21, 7, 6, 4 ], [ 21, 7, 7, 4 ], [ 27, 1, 9, 16 ], [ 27, 2, 5, 24 ],
[ 27, 2, 7, 8 ], [ 27, 2, 12, 16 ], [ 27, 3, 5, 8 ], [ 27, 3, 9, 8 ],
[ 27, 3, 14, 16 ], [ 27, 3, 15, 16 ], [ 27, 4, 4, 8 ], [ 27, 4, 9, 8 ],
[ 27, 5, 5, 8 ], [ 27, 6, 5, 12 ], [ 27, 6, 7, 4 ], [ 27, 6, 12, 8 ],
[ 27, 6, 13, 8 ], [ 27, 6, 16, 8 ], [ 27, 7, 5, 12 ], [ 27, 7, 7, 4 ],
[ 27, 7, 12, 8 ], [ 27, 8, 5, 12 ], [ 27, 8, 9, 8 ], [ 27, 8, 14, 8 ],
[ 27, 8, 15, 24 ], [ 27, 9, 5, 4 ], [ 27, 9, 13, 8 ], [ 27, 9, 14, 8 ],
[ 27, 10, 7, 12 ], [ 27, 10, 8, 4 ], [ 27, 10, 11, 8 ], [ 27, 10, 12, 8 ],
[ 27, 10, 17, 8 ], [ 27, 11, 5, 4 ], [ 27, 11, 9, 8 ], [ 27, 11, 14, 8 ],
[ 27, 11, 15, 8 ], [ 27, 12, 4, 8 ], [ 27, 12, 9, 8 ], [ 27, 12, 11, 24 ],
[ 27, 12, 12, 8 ], [ 27, 13, 4, 12 ], [ 27, 13, 9, 4 ], [ 27, 13, 11, 8 ],
[ 27, 13, 14, 8 ], [ 27, 13, 16, 8 ], [ 27, 14, 4, 4 ], [ 27, 14, 9, 8 ],
[ 27, 14, 15, 8 ], [ 27, 14, 17, 8 ], [ 31, 9, 27, 16 ], [ 31, 10, 5, 16 ],
[ 31, 10, 9, 16 ], [ 31, 11, 24, 16 ], [ 31, 14, 21, 16 ],
[ 31, 14, 23, 48 ], [ 31, 15, 5, 16 ], [ 31, 15, 7, 16 ],
[ 31, 16, 27, 16 ], [ 31, 21, 27, 16 ], [ 31, 21, 31, 16 ],
[ 31, 23, 25, 16 ] ]
k = 25: F-action on Pi is () [31,2,25]
Dynkin type is (A_0(q) + T(phi1 phi2^3 phi4)).2
Order of center |Z^F|: phi2^2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1^2 phi2 ( 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 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 8 ], [ 3, 2, 1, 6 ], [ 3, 2, 2, 2 ],
[ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 3 ], [ 3, 5, 2, 1 ],
[ 4, 1, 2, 4 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 3 ], [ 5, 1, 2, 4 ],
[ 7, 1, 2, 16 ], [ 7, 2, 1, 4 ], [ 7, 2, 2, 12 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 10 ], [ 7, 3, 3, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 2, 12 ],
[ 7, 4, 4, 4 ], [ 7, 5, 1, 3 ], [ 7, 5, 2, 9 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 3 ], [ 9, 1, 4, 16 ], [ 9, 2, 4, 8 ], [ 9, 3, 4, 8 ],
[ 9, 4, 4, 8 ], [ 9, 5, 4, 4 ], [ 12, 1, 3, 8 ], [ 12, 1, 5, 4 ],
[ 12, 2, 3, 4 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ], [ 12, 3, 2, 8 ],
[ 12, 3, 3, 4 ], [ 12, 4, 3, 6 ], [ 12, 4, 4, 3 ], [ 12, 4, 5, 2 ],
[ 13, 2, 2, 4 ], [ 13, 2, 4, 4 ], [ 16, 1, 4, 8 ], [ 16, 1, 8, 32 ],
[ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 2, 8, 16 ], [ 16, 3, 4, 4 ],
[ 16, 3, 8, 16 ], [ 16, 4, 4, 12 ], [ 16, 4, 8, 16 ], [ 16, 5, 7, 16 ],
[ 16, 6, 7, 16 ], [ 16, 7, 7, 16 ], [ 16, 8, 7, 8 ], [ 16, 8, 8, 24 ],
[ 16, 9, 2, 2 ], [ 16, 9, 4, 6 ], [ 16, 9, 8, 8 ], [ 16, 10, 7, 8 ],
[ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ], [ 16, 11, 7, 6 ], [ 16, 11, 9, 4 ],
[ 16, 11, 10, 16 ], [ 16, 12, 7, 8 ], [ 16, 13, 4, 12 ], [ 16, 13, 8, 8 ],
[ 16, 14, 2, 4 ], [ 16, 14, 6, 16 ], [ 16, 15, 4, 4 ], [ 16, 15, 8, 8 ],
[ 16, 16, 4, 4 ], [ 16, 16, 8, 8 ], [ 16, 17, 3, 4 ], [ 16, 17, 6, 16 ],
[ 21, 1, 8, 16 ], [ 21, 2, 3, 8 ], [ 21, 2, 5, 12 ], [ 21, 2, 7, 4 ],
[ 21, 2, 10, 8 ], [ 21, 3, 2, 8 ], [ 21, 3, 4, 8 ], [ 21, 4, 5, 8 ],
[ 21, 5, 3, 4 ], [ 21, 5, 4, 4 ], [ 21, 5, 5, 6 ], [ 21, 5, 7, 2 ],
[ 21, 5, 10, 4 ], [ 21, 6, 2, 8 ], [ 21, 6, 4, 8 ], [ 21, 6, 10, 8 ],
[ 21, 7, 3, 8 ], [ 21, 7, 5, 8 ], [ 22, 1, 10, 16 ], [ 22, 2, 9, 8 ],
[ 22, 2, 10, 8 ], [ 22, 4, 9, 4 ], [ 22, 4, 10, 8 ], [ 27, 1, 11, 32 ],
[ 27, 2, 5, 16 ], [ 27, 2, 20, 32 ], [ 27, 3, 5, 8 ], [ 27, 3, 18, 16 ],
[ 27, 3, 23, 16 ], [ 27, 3, 25, 16 ], [ 27, 4, 19, 16 ], [ 27, 5, 20, 16 ],
[ 27, 6, 5, 8 ], [ 27, 6, 19, 8 ], [ 27, 6, 20, 16 ], [ 27, 7, 5, 8 ],
[ 27, 7, 20, 16 ], [ 27, 8, 5, 12 ], [ 27, 8, 18, 8 ], [ 27, 8, 23, 16 ],
[ 27, 8, 25, 24 ], [ 27, 9, 5, 4 ], [ 27, 9, 16, 8 ], [ 27, 9, 18, 8 ],
[ 27, 10, 7, 8 ], [ 27, 10, 14, 8 ], [ 27, 10, 18, 16 ], [ 27, 11, 5, 4 ],
[ 27, 11, 18, 8 ], [ 27, 11, 23, 16 ], [ 27, 11, 25, 8 ],
[ 27, 12, 15, 16 ], [ 27, 12, 19, 16 ], [ 27, 13, 4, 8 ], [ 27, 13, 17, 8 ],
[ 27, 13, 19, 16 ], [ 27, 14, 4, 4 ], [ 27, 14, 18, 8 ], [ 27, 14, 23, 16 ],
[ 27, 14, 25, 8 ], [ 30, 4, 23, 16 ], [ 30, 8, 20, 8 ], [ 30, 12, 23, 16 ],
[ 31, 9, 24, 16 ], [ 31, 10, 30, 16 ], [ 31, 10, 32, 16 ],
[ 31, 11, 27, 32 ], [ 31, 13, 35, 32 ], [ 31, 14, 24, 32 ],
[ 31, 15, 30, 16 ], [ 31, 16, 26, 16 ], [ 31, 21, 32, 16 ],
[ 31, 23, 24, 32 ], [ 31, 29, 41, 32 ] ]
k = 26: F-action on Pi is () [31,2,26]
Dynkin type is (A_0(q) + T(phi1 phi2^3 phi4)).2
Order of center |Z^F|: phi1 phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1^2 phi2 ( 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 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 6 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 3 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 3 ], [ 7, 1, 1, 4 ],
[ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ],
[ 7, 2, 2, 6 ], [ 7, 2, 3, 2 ], [ 7, 2, 4, 6 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 10 ], [ 7, 3, 3, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 1, 6 ],
[ 7, 4, 2, 6 ], [ 7, 4, 3, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 1, 3 ],
[ 7, 5, 2, 9 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 3 ], [ 12, 1, 4, 4 ],
[ 12, 1, 5, 4 ], [ 12, 2, 3, 4 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ],
[ 12, 3, 2, 4 ], [ 12, 3, 3, 2 ], [ 12, 3, 4, 6 ], [ 12, 4, 3, 6 ],
[ 12, 4, 4, 3 ], [ 12, 4, 5, 2 ], [ 16, 1, 2, 8 ], [ 16, 1, 4, 8 ],
[ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 2, 8, 16 ], [ 16, 3, 2, 4 ],
[ 16, 3, 4, 4 ], [ 16, 4, 2, 4 ], [ 16, 4, 4, 12 ], [ 16, 8, 2, 4 ],
[ 16, 8, 3, 4 ], [ 16, 8, 6, 12 ], [ 16, 8, 7, 4 ], [ 16, 8, 8, 8 ],
[ 16, 9, 2, 2 ], [ 16, 9, 4, 6 ], [ 16, 9, 8, 8 ], [ 16, 10, 7, 8 ],
[ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ], [ 16, 11, 7, 6 ], [ 16, 11, 9, 4 ],
[ 16, 11, 10, 16 ], [ 16, 13, 2, 4 ], [ 16, 13, 4, 12 ], [ 16, 14, 2, 2 ],
[ 16, 14, 3, 6 ], [ 16, 14, 6, 8 ], [ 16, 15, 2, 4 ], [ 16, 15, 4, 4 ],
[ 16, 16, 2, 4 ], [ 16, 16, 4, 4 ], [ 16, 17, 2, 6 ], [ 16, 17, 3, 2 ],
[ 16, 17, 6, 8 ], [ 21, 1, 6, 8 ], [ 21, 1, 8, 8 ], [ 21, 2, 4, 8 ],
[ 21, 2, 5, 12 ], [ 21, 2, 7, 4 ], [ 21, 3, 4, 4 ], [ 21, 3, 5, 8 ],
[ 21, 3, 9, 4 ], [ 21, 3, 10, 8 ], [ 21, 4, 5, 4 ], [ 21, 4, 7, 4 ],
[ 21, 5, 3, 4 ], [ 21, 5, 4, 4 ], [ 21, 5, 5, 6 ], [ 21, 5, 7, 2 ],
[ 21, 5, 10, 4 ], [ 21, 6, 2, 4 ], [ 21, 6, 4, 4 ], [ 21, 6, 5, 12 ],
[ 21, 6, 8, 4 ], [ 21, 6, 10, 4 ], [ 21, 7, 3, 4 ], [ 21, 7, 5, 4 ],
[ 21, 7, 7, 4 ], [ 21, 7, 10, 12 ], [ 27, 1, 9, 16 ], [ 27, 2, 5, 8 ],
[ 27, 2, 7, 24 ], [ 27, 2, 20, 16 ], [ 27, 3, 5, 8 ], [ 27, 3, 9, 8 ],
[ 27, 3, 24, 16 ], [ 27, 3, 25, 16 ], [ 27, 4, 4, 8 ], [ 27, 4, 9, 8 ],
[ 27, 5, 5, 8 ], [ 27, 6, 5, 4 ], [ 27, 6, 7, 12 ], [ 27, 6, 15, 8 ],
[ 27, 6, 18, 8 ], [ 27, 6, 20, 8 ], [ 27, 7, 5, 4 ], [ 27, 7, 7, 12 ],
[ 27, 7, 20, 8 ], [ 27, 8, 5, 12 ], [ 27, 8, 9, 8 ], [ 27, 8, 24, 8 ],
[ 27, 8, 25, 24 ], [ 27, 9, 5, 4 ], [ 27, 9, 16, 8 ], [ 27, 9, 18, 8 ],
[ 27, 10, 7, 4 ], [ 27, 10, 8, 12 ], [ 27, 10, 18, 8 ], [ 27, 10, 19, 8 ],
[ 27, 10, 20, 8 ], [ 27, 11, 5, 4 ], [ 27, 11, 9, 8 ], [ 27, 11, 24, 8 ],
[ 27, 11, 25, 8 ], [ 27, 12, 4, 8 ], [ 27, 12, 9, 8 ], [ 27, 12, 15, 8 ],
[ 27, 12, 20, 24 ], [ 27, 13, 4, 4 ], [ 27, 13, 9, 12 ], [ 27, 13, 15, 8 ],
[ 27, 13, 19, 8 ], [ 27, 13, 20, 8 ], [ 27, 14, 4, 4 ], [ 27, 14, 9, 8 ],
[ 27, 14, 24, 8 ], [ 27, 14, 25, 8 ], [ 31, 9, 25, 16 ], [ 31, 10, 30, 16 ],
[ 31, 10, 34, 16 ], [ 31, 11, 26, 16 ], [ 31, 14, 22, 48 ],
[ 31, 14, 24, 16 ], [ 31, 15, 45, 16 ], [ 31, 15, 47, 16 ],
[ 31, 16, 24, 16 ], [ 31, 21, 30, 16 ], [ 31, 21, 35, 16 ],
[ 31, 23, 27, 16 ] ]
k = 27: F-action on Pi is () [31,2,27]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2
Order of center |Z^F|: phi1^2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 phi2 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1 phi2 ( q^2-8*q+15 )
Fusion of maximal tori of C^F in those of G^F:
[ 6 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 2, 8 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 6 ],
[ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 3 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 3 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 4 ],
[ 7, 1, 3, 16 ], [ 7, 2, 3, 12 ], [ 7, 2, 4, 4 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 2 ], [ 7, 3, 3, 10 ], [ 7, 3, 4, 2 ], [ 7, 4, 1, 4 ],
[ 7, 4, 3, 12 ], [ 7, 5, 1, 3 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 9 ],
[ 7, 5, 4, 3 ], [ 9, 1, 3, 16 ], [ 9, 2, 3, 8 ], [ 9, 3, 3, 8 ],
[ 9, 4, 3, 8 ], [ 9, 5, 3, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 5, 4 ],
[ 12, 2, 1, 4 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ], [ 12, 3, 1, 8 ],
[ 12, 3, 4, 4 ], [ 12, 4, 1, 6 ], [ 12, 4, 4, 3 ], [ 12, 4, 5, 2 ],
[ 13, 2, 1, 4 ], [ 13, 2, 3, 4 ], [ 16, 1, 4, 8 ], [ 16, 1, 6, 32 ],
[ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 2, 6, 16 ], [ 16, 3, 4, 4 ],
[ 16, 3, 6, 16 ], [ 16, 4, 4, 12 ], [ 16, 4, 6, 16 ], [ 16, 5, 5, 16 ],
[ 16, 6, 5, 16 ], [ 16, 7, 5, 16 ], [ 16, 8, 5, 24 ], [ 16, 8, 6, 8 ],
[ 16, 9, 2, 2 ], [ 16, 9, 4, 6 ], [ 16, 9, 6, 8 ], [ 16, 10, 5, 8 ],
[ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ], [ 16, 11, 6, 16 ], [ 16, 11, 7, 6 ],
[ 16, 11, 9, 4 ], [ 16, 12, 5, 8 ], [ 16, 13, 4, 12 ], [ 16, 13, 6, 8 ],
[ 16, 14, 3, 4 ], [ 16, 14, 5, 16 ], [ 16, 15, 4, 4 ], [ 16, 15, 6, 8 ],
[ 16, 16, 4, 4 ], [ 16, 16, 6, 8 ], [ 16, 17, 2, 4 ], [ 16, 17, 5, 16 ],
[ 21, 1, 6, 16 ], [ 21, 2, 1, 8 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 12 ],
[ 21, 2, 8, 8 ], [ 21, 3, 7, 8 ], [ 21, 3, 9, 8 ], [ 21, 4, 7, 8 ],
[ 21, 5, 1, 4 ], [ 21, 5, 5, 2 ], [ 21, 5, 6, 4 ], [ 21, 5, 7, 6 ],
[ 21, 5, 8, 4 ], [ 21, 6, 1, 8 ], [ 21, 6, 6, 8 ], [ 21, 6, 8, 8 ],
[ 21, 7, 6, 8 ], [ 21, 7, 7, 8 ], [ 22, 1, 8, 16 ], [ 22, 2, 7, 8 ],
[ 22, 2, 8, 8 ], [ 22, 4, 7, 4 ], [ 22, 4, 8, 8 ], [ 27, 1, 7, 32 ],
[ 27, 2, 7, 16 ], [ 27, 2, 12, 32 ], [ 27, 3, 5, 8 ], [ 27, 3, 15, 16 ],
[ 27, 3, 16, 16 ], [ 27, 3, 21, 16 ], [ 27, 4, 14, 16 ], [ 27, 5, 13, 16 ],
[ 27, 6, 7, 8 ], [ 27, 6, 11, 8 ], [ 27, 6, 12, 16 ], [ 27, 7, 7, 8 ],
[ 27, 7, 12, 16 ], [ 27, 8, 5, 12 ], [ 27, 8, 15, 24 ], [ 27, 8, 16, 8 ],
[ 27, 8, 21, 16 ], [ 27, 9, 5, 4 ], [ 27, 9, 13, 8 ], [ 27, 9, 14, 8 ],
[ 27, 10, 8, 8 ], [ 27, 10, 13, 8 ], [ 27, 10, 17, 16 ], [ 27, 11, 5, 4 ],
[ 27, 11, 15, 8 ], [ 27, 11, 16, 8 ], [ 27, 11, 21, 16 ],
[ 27, 12, 12, 16 ], [ 27, 12, 14, 16 ], [ 27, 13, 9, 8 ], [ 27, 13, 12, 8 ],
[ 27, 13, 14, 16 ], [ 27, 14, 4, 4 ], [ 27, 14, 14, 8 ], [ 27, 14, 17, 8 ],
[ 27, 14, 21, 16 ], [ 30, 4, 9, 16 ], [ 30, 8, 4, 8 ], [ 30, 12, 9, 16 ],
[ 31, 9, 26, 16 ], [ 31, 10, 9, 16 ], [ 31, 10, 26, 16 ],
[ 31, 11, 25, 32 ], [ 31, 13, 33, 32 ], [ 31, 14, 21, 32 ],
[ 31, 15, 22, 16 ], [ 31, 16, 25, 16 ], [ 31, 21, 26, 16 ],
[ 31, 23, 26, 32 ], [ 31, 29, 37, 32 ] ]
k = 28: F-action on Pi is () [31,2,28]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2^2
Fusion of maximal tori of C^F in those of G^F:
[ 12 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 2 ],
[ 3, 2, 2, 2 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 1 ], [ 3, 5, 2, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 7, 1, 1, 4 ],
[ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 1, 2 ],
[ 7, 2, 2, 2 ], [ 7, 2, 3, 2 ], [ 7, 2, 4, 2 ], [ 7, 3, 1, 2 ],
[ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ], [ 7, 3, 4, 2 ], [ 7, 4, 1, 2 ],
[ 7, 4, 2, 2 ], [ 7, 4, 3, 2 ], [ 7, 4, 4, 2 ], [ 7, 5, 1, 1 ],
[ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ], [ 7, 5, 4, 1 ], [ 12, 1, 4, 4 ],
[ 12, 1, 5, 4 ], [ 12, 2, 2, 2 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ],
[ 12, 3, 3, 2 ], [ 12, 3, 4, 2 ], [ 12, 4, 2, 2 ], [ 12, 4, 4, 1 ],
[ 12, 4, 5, 2 ], [ 16, 1, 2, 8 ], [ 16, 1, 4, 8 ], [ 16, 2, 2, 4 ],
[ 16, 2, 4, 4 ], [ 16, 2, 7, 8 ], [ 16, 3, 2, 4 ], [ 16, 3, 4, 4 ],
[ 16, 4, 2, 4 ], [ 16, 4, 4, 4 ], [ 16, 4, 11, 8 ], [ 16, 8, 2, 4 ],
[ 16, 8, 3, 4 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ], [ 16, 9, 2, 2 ],
[ 16, 9, 4, 2 ], [ 16, 9, 7, 4 ], [ 16, 9, 11, 4 ], [ 16, 10, 6, 4 ],
[ 16, 10, 8, 4 ], [ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ], [ 16, 11, 7, 2 ],
[ 16, 11, 8, 8 ], [ 16, 11, 9, 4 ], [ 16, 13, 2, 4 ], [ 16, 13, 4, 4 ],
[ 16, 13, 11, 8 ], [ 16, 14, 2, 2 ], [ 16, 14, 3, 2 ], [ 16, 14, 7, 8 ],
[ 16, 14, 10, 8 ], [ 16, 15, 2, 4 ], [ 16, 15, 4, 4 ], [ 16, 16, 2, 4 ],
[ 16, 16, 4, 4 ], [ 16, 17, 2, 2 ], [ 16, 17, 3, 2 ], [ 21, 1, 6, 8 ],
[ 21, 1, 8, 8 ], [ 21, 2, 5, 4 ], [ 21, 2, 7, 4 ], [ 21, 3, 3, 4 ],
[ 21, 3, 4, 4 ], [ 21, 3, 8, 4 ], [ 21, 3, 9, 4 ], [ 21, 4, 5, 4 ],
[ 21, 4, 7, 4 ], [ 21, 5, 2, 2 ], [ 21, 5, 5, 2 ], [ 21, 5, 7, 2 ],
[ 21, 5, 9, 2 ], [ 21, 6, 3, 4 ], [ 21, 6, 4, 4 ], [ 21, 6, 8, 4 ],
[ 21, 6, 9, 4 ], [ 21, 7, 2, 4 ], [ 21, 7, 5, 4 ], [ 21, 7, 7, 4 ],
[ 21, 7, 9, 4 ], [ 27, 1, 9, 16 ], [ 27, 2, 5, 8 ], [ 27, 2, 7, 8 ],
[ 27, 3, 5, 8 ], [ 27, 3, 9, 8 ], [ 27, 3, 19, 8 ], [ 27, 3, 20, 8 ],
[ 27, 4, 4, 8 ], [ 27, 4, 9, 8 ], [ 27, 5, 5, 8 ], [ 27, 6, 5, 4 ],
[ 27, 6, 7, 4 ], [ 27, 6, 14, 4 ], [ 27, 6, 17, 4 ], [ 27, 7, 5, 4 ],
[ 27, 7, 7, 4 ], [ 27, 8, 5, 4 ], [ 27, 8, 9, 8 ], [ 27, 8, 19, 8 ],
[ 27, 8, 20, 8 ], [ 27, 9, 5, 4 ], [ 27, 9, 15, 4 ], [ 27, 9, 17, 4 ],
[ 27, 10, 7, 4 ], [ 27, 10, 8, 4 ], [ 27, 10, 15, 4 ], [ 27, 10, 16, 4 ],
[ 27, 11, 5, 4 ], [ 27, 11, 9, 8 ], [ 27, 11, 19, 8 ], [ 27, 11, 20, 8 ],
[ 27, 12, 4, 8 ], [ 27, 12, 9, 8 ], [ 27, 12, 13, 8 ], [ 27, 12, 18, 8 ],
[ 27, 13, 4, 4 ], [ 27, 13, 9, 4 ], [ 27, 13, 13, 4 ], [ 27, 13, 18, 4 ],
[ 27, 14, 4, 4 ], [ 27, 14, 9, 8 ], [ 27, 14, 20, 8 ], [ 27, 14, 22, 8 ],
[ 31, 9, 28, 8 ], [ 31, 10, 17, 8 ], [ 31, 10, 21, 8 ], [ 31, 11, 29, 8 ],
[ 31, 14, 25, 16 ], [ 31, 14, 26, 16 ], [ 31, 15, 15, 16 ],
[ 31, 15, 17, 16 ], [ 31, 16, 28, 8 ], [ 31, 21, 29, 16 ],
[ 31, 21, 33, 16 ], [ 31, 23, 28, 8 ] ]
k = 29: F-action on Pi is () [31,2,29]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^3 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^3 phi2
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, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 2, 1, 2 ], [ 3, 2, 2, 2 ], [ 3, 5, 1, 1 ],
[ 3, 5, 2, 1 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 7, 3, 1, 2 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 2 ],
[ 7, 3, 4, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 2, 1 ], [ 7, 5, 3, 1 ],
[ 7, 5, 4, 1 ], [ 9, 1, 3, 8 ], [ 9, 1, 4, 8 ], [ 9, 2, 3, 4 ],
[ 9, 2, 4, 4 ], [ 9, 3, 3, 4 ], [ 9, 3, 4, 4 ], [ 9, 4, 3, 4 ],
[ 9, 4, 4, 4 ], [ 9, 5, 3, 2 ], [ 9, 5, 4, 2 ], [ 12, 1, 2, 4 ],
[ 12, 1, 5, 4 ], [ 12, 2, 2, 2 ], [ 12, 2, 4, 2 ], [ 12, 2, 5, 2 ],
[ 12, 4, 2, 2 ], [ 12, 4, 4, 1 ], [ 12, 4, 5, 2 ], [ 13, 2, 1, 2 ],
[ 13, 2, 2, 2 ], [ 13, 2, 3, 2 ], [ 13, 2, 4, 2 ], [ 16, 1, 4, 8 ],
[ 16, 1, 7, 16 ], [ 16, 2, 2, 4 ], [ 16, 2, 4, 4 ], [ 16, 2, 7, 8 ],
[ 16, 2, 11, 8 ], [ 16, 3, 4, 4 ], [ 16, 3, 7, 8 ], [ 16, 4, 4, 4 ],
[ 16, 4, 7, 8 ], [ 16, 5, 6, 8 ], [ 16, 5, 8, 8 ], [ 16, 6, 6, 8 ],
[ 16, 6, 8, 8 ], [ 16, 7, 6, 8 ], [ 16, 7, 8, 8 ], [ 16, 9, 2, 2 ],
[ 16, 9, 4, 2 ], [ 16, 9, 7, 4 ], [ 16, 9, 11, 4 ], [ 16, 10, 6, 4 ],
[ 16, 10, 8, 4 ], [ 16, 11, 2, 2 ], [ 16, 11, 4, 4 ], [ 16, 11, 7, 2 ],
[ 16, 11, 8, 8 ], [ 16, 11, 9, 4 ], [ 16, 12, 6, 4 ], [ 16, 12, 8, 4 ],
[ 16, 13, 4, 4 ], [ 16, 13, 7, 4 ], [ 16, 15, 4, 4 ], [ 16, 15, 7, 4 ],
[ 16, 16, 4, 4 ], [ 16, 16, 7, 4 ], [ 21, 2, 2, 4 ], [ 21, 2, 5, 4 ],
[ 21, 2, 7, 4 ], [ 21, 2, 9, 4 ], [ 21, 5, 2, 2 ], [ 21, 5, 5, 2 ],
[ 21, 5, 7, 2 ], [ 21, 5, 9, 2 ], [ 22, 1, 8, 8 ], [ 22, 1, 10, 8 ],
[ 22, 2, 7, 4 ], [ 22, 2, 8, 4 ], [ 22, 2, 9, 4 ], [ 22, 2, 10, 4 ],
[ 22, 4, 7, 2 ], [ 22, 4, 8, 4 ], [ 22, 4, 9, 2 ], [ 22, 4, 10, 4 ],
[ 27, 1, 13, 16 ], [ 27, 3, 5, 8 ], [ 27, 3, 17, 8 ], [ 27, 3, 20, 8 ],
[ 27, 3, 22, 8 ], [ 27, 5, 19, 8 ], [ 27, 8, 5, 4 ], [ 27, 8, 17, 4 ],
[ 27, 8, 20, 8 ], [ 27, 8, 22, 8 ], [ 27, 9, 5, 4 ], [ 27, 9, 15, 4 ],
[ 27, 9, 17, 4 ], [ 27, 9, 20, 8 ], [ 27, 11, 5, 4 ], [ 27, 11, 17, 4 ],
[ 27, 11, 20, 8 ], [ 27, 11, 22, 8 ], [ 27, 14, 4, 4 ], [ 27, 14, 16, 4 ],
[ 27, 14, 19, 8 ], [ 27, 14, 20, 8 ], [ 30, 4, 9, 8 ], [ 30, 4, 23, 8 ],
[ 30, 8, 4, 4 ], [ 30, 8, 20, 4 ], [ 30, 12, 9, 8 ], [ 30, 12, 23, 8 ],
[ 31, 9, 29, 8 ], [ 31, 10, 21, 8 ], [ 31, 10, 29, 8 ], [ 31, 11, 28, 16 ],
[ 31, 13, 34, 16 ], [ 31, 13, 36, 16 ], [ 31, 16, 29, 8 ],
[ 31, 23, 29, 16 ], [ 31, 29, 39, 16 ], [ 31, 29, 43, 16 ] ]
k = 30: F-action on Pi is () [31,2,30]
Dynkin type is (A_0(q) + T(phi1 phi2^5)).2
Order of center |Z^F|: phi2^4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/384 phi1 ( q^3-7*q^2-5*q+75 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/384 phi2^2 ( q^2-10*q+21 )
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, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 2, 16 ],
[ 3, 2, 2, 8 ], [ 3, 3, 2, 8 ], [ 3, 4, 2, 8 ], [ 3, 5, 2, 4 ],
[ 4, 1, 2, 8 ], [ 4, 2, 2, 4 ], [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ],
[ 7, 1, 4, 64 ], [ 7, 2, 4, 32 ], [ 7, 3, 4, 32 ], [ 7, 4, 4, 32 ],
[ 7, 5, 4, 16 ], [ 8, 1, 2, 16 ], [ 9, 1, 2, 96 ], [ 9, 2, 2, 48 ],
[ 9, 3, 2, 48 ], [ 9, 4, 2, 48 ], [ 9, 5, 2, 24 ], [ 12, 1, 3, 48 ],
[ 12, 2, 2, 2 ], [ 12, 2, 3, 24 ], [ 12, 3, 2, 24 ], [ 12, 4, 2, 2 ],
[ 12, 4, 3, 12 ], [ 13, 1, 4, 96 ], [ 13, 2, 4, 48 ], [ 14, 1, 2, 64 ],
[ 14, 2, 2, 32 ], [ 15, 1, 3, 96 ], [ 16, 1, 5, 192 ], [ 16, 2, 3, 24 ],
[ 16, 2, 5, 96 ], [ 16, 3, 5, 96 ], [ 16, 4, 5, 96 ], [ 16, 5, 3, 96 ],
[ 16, 6, 3, 96 ], [ 16, 7, 3, 96 ], [ 16, 8, 4, 96 ], [ 16, 9, 3, 12 ],
[ 16, 9, 5, 48 ], [ 16, 10, 2, 12 ], [ 16, 10, 3, 48 ], [ 16, 10, 4, 12 ],
[ 16, 11, 3, 24 ], [ 16, 11, 5, 48 ], [ 16, 12, 3, 48 ], [ 16, 13, 5, 48 ],
[ 16, 14, 4, 48 ], [ 16, 15, 5, 48 ], [ 16, 16, 5, 48 ], [ 16, 17, 4, 48 ],
[ 21, 1, 4, 192 ], [ 21, 2, 10, 96 ], [ 21, 3, 8, 16 ], [ 21, 3, 10, 96 ],
[ 21, 4, 10, 96 ], [ 21, 5, 9, 8 ], [ 21, 5, 10, 48 ], [ 21, 6, 9, 16 ],
[ 21, 6, 10, 48 ], [ 21, 7, 9, 16 ], [ 21, 7, 10, 48 ], [ 22, 1, 6, 192 ],
[ 22, 2, 5, 48 ], [ 22, 2, 6, 96 ], [ 22, 3, 4, 96 ], [ 22, 4, 5, 48 ],
[ 22, 4, 6, 48 ], [ 23, 2, 6, 16 ], [ 23, 2, 8, 16 ], [ 23, 6, 6, 8 ],
[ 23, 6, 8, 8 ], [ 27, 1, 5, 384 ], [ 27, 2, 10, 192 ], [ 27, 3, 8, 96 ],
[ 27, 3, 13, 192 ], [ 27, 4, 10, 192 ], [ 27, 5, 11, 192 ],
[ 27, 6, 9, 48 ], [ 27, 6, 10, 96 ], [ 27, 7, 10, 96 ], [ 27, 8, 8, 96 ],
[ 27, 8, 13, 96 ], [ 27, 9, 7, 48 ], [ 27, 9, 12, 96 ], [ 27, 10, 6, 48 ],
[ 27, 10, 10, 96 ], [ 27, 11, 8, 96 ], [ 27, 11, 13, 96 ],
[ 27, 12, 8, 96 ], [ 27, 12, 10, 96 ], [ 27, 13, 8, 48 ],
[ 27, 13, 10, 96 ], [ 27, 14, 10, 96 ], [ 27, 14, 13, 96 ],
[ 28, 2, 9, 64 ], [ 28, 5, 9, 32 ], [ 28, 6, 9, 64 ], [ 29, 4, 10, 96 ],
[ 29, 4, 12, 96 ], [ 29, 9, 10, 48 ], [ 29, 9, 12, 48 ], [ 29, 12, 6, 48 ],
[ 29, 12, 8, 48 ], [ 30, 4, 27, 192 ], [ 30, 8, 30, 96 ],
[ 30, 11, 26, 96 ], [ 30, 11, 28, 96 ], [ 30, 12, 27, 96 ],
[ 30, 13, 19, 192 ], [ 31, 9, 30, 192 ], [ 31, 10, 24, 192 ],
[ 31, 11, 35, 192 ], [ 31, 12, 27, 192 ], [ 31, 12, 41, 192 ],
[ 31, 13, 23, 192 ], [ 31, 14, 48, 384 ], [ 31, 15, 20, 384 ],
[ 31, 16, 35, 192 ], [ 31, 21, 49, 384 ], [ 31, 23, 35, 192 ],
[ 31, 29, 52, 192 ] ]
k = 31: F-action on Pi is () [31,2,31]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1^2 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/128 phi1^2 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/128 ( q^4-12*q^3+46*q^2-60*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, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 7 ],
[ 2, 2, 2, 8 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 3, 2, 1, 12 ],
[ 3, 2, 2, 8 ], [ 3, 3, 1, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 1, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 6 ], [ 3, 5, 2, 4 ], [ 4, 1, 1, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 4 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 4 ], [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ], [ 7, 1, 3, 16 ],
[ 7, 1, 4, 16 ], [ 7, 2, 1, 8 ], [ 7, 2, 2, 16 ], [ 7, 2, 3, 8 ],
[ 7, 2, 4, 16 ], [ 7, 3, 1, 8 ], [ 7, 3, 2, 24 ], [ 7, 3, 3, 8 ],
[ 7, 3, 4, 16 ], [ 7, 4, 1, 24 ], [ 7, 4, 2, 24 ], [ 7, 4, 3, 16 ],
[ 7, 4, 4, 16 ], [ 7, 5, 1, 12 ], [ 7, 5, 2, 24 ], [ 7, 5, 3, 8 ],
[ 7, 5, 4, 16 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 24 ],
[ 9, 2, 2, 8 ], [ 9, 2, 4, 16 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 12 ], [ 9, 5, 2, 4 ],
[ 9, 5, 4, 8 ], [ 12, 1, 1, 8 ], [ 12, 1, 3, 8 ], [ 12, 1, 4, 16 ],
[ 12, 2, 1, 4 ], [ 12, 2, 3, 8 ], [ 12, 2, 4, 8 ], [ 12, 3, 1, 4 ],
[ 12, 3, 2, 12 ], [ 12, 3, 3, 8 ], [ 12, 3, 4, 16 ], [ 12, 4, 1, 2 ],
[ 12, 4, 3, 12 ], [ 12, 4, 4, 8 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ],
[ 13, 2, 2, 8 ], [ 13, 2, 3, 16 ], [ 13, 2, 4, 8 ], [ 15, 1, 4, 16 ],
[ 16, 1, 1, 32 ], [ 16, 1, 2, 32 ], [ 16, 1, 5, 32 ], [ 16, 2, 1, 16 ],
[ 16, 2, 2, 16 ], [ 16, 2, 5, 32 ], [ 16, 2, 8, 32 ], [ 16, 3, 1, 16 ],
[ 16, 3, 2, 16 ], [ 16, 3, 5, 16 ], [ 16, 4, 1, 48 ], [ 16, 4, 2, 48 ],
[ 16, 4, 5, 16 ], [ 16, 4, 8, 32 ], [ 16, 5, 1, 16 ], [ 16, 5, 3, 16 ],
[ 16, 6, 1, 16 ], [ 16, 6, 3, 16 ], [ 16, 7, 1, 16 ], [ 16, 7, 3, 16 ],
[ 16, 8, 1, 16 ], [ 16, 8, 2, 32 ], [ 16, 8, 3, 16 ], [ 16, 8, 4, 32 ],
[ 16, 8, 6, 48 ], [ 16, 8, 7, 16 ], [ 16, 8, 8, 32 ], [ 16, 9, 1, 24 ],
[ 16, 9, 2, 24 ], [ 16, 9, 5, 16 ], [ 16, 9, 8, 32 ], [ 16, 10, 1, 8 ],
[ 16, 10, 3, 16 ], [ 16, 10, 7, 16 ], [ 16, 11, 1, 8 ], [ 16, 11, 2, 16 ],
[ 16, 11, 5, 32 ], [ 16, 11, 7, 24 ], [ 16, 11, 10, 48 ], [ 16, 12, 1, 24 ],
[ 16, 12, 3, 8 ], [ 16, 12, 7, 16 ], [ 16, 13, 1, 24 ], [ 16, 13, 2, 48 ],
[ 16, 13, 5, 8 ], [ 16, 13, 8, 16 ], [ 16, 14, 1, 24 ], [ 16, 14, 2, 24 ],
[ 16, 14, 3, 48 ], [ 16, 14, 4, 24 ], [ 16, 14, 6, 48 ], [ 16, 15, 1, 8 ],
[ 16, 15, 2, 16 ], [ 16, 15, 5, 8 ], [ 16, 16, 1, 8 ], [ 16, 16, 2, 16 ],
[ 16, 16, 5, 8 ], [ 16, 17, 1, 8 ], [ 16, 17, 2, 24 ], [ 16, 17, 3, 16 ],
[ 16, 17, 4, 24 ], [ 16, 17, 6, 32 ], [ 21, 1, 2, 32 ], [ 21, 1, 3, 32 ],
[ 21, 2, 3, 16 ], [ 21, 2, 4, 48 ], [ 21, 2, 6, 16 ], [ 21, 2, 8, 32 ],
[ 21, 2, 10, 16 ], [ 21, 3, 2, 16 ], [ 21, 3, 5, 32 ], [ 21, 3, 6, 16 ],
[ 21, 3, 7, 16 ], [ 21, 3, 10, 16 ], [ 21, 4, 3, 16 ], [ 21, 4, 6, 16 ],
[ 21, 5, 3, 16 ], [ 21, 5, 4, 24 ], [ 21, 5, 6, 8 ], [ 21, 5, 8, 16 ],
[ 21, 5, 10, 16 ], [ 21, 6, 2, 24 ], [ 21, 6, 5, 48 ], [ 21, 6, 6, 16 ],
[ 21, 6, 7, 8 ], [ 21, 6, 10, 24 ], [ 21, 7, 3, 16 ], [ 21, 7, 6, 8 ],
[ 21, 7, 10, 24 ], [ 22, 1, 3, 32 ], [ 22, 1, 4, 32 ], [ 22, 2, 3, 32 ],
[ 22, 2, 4, 16 ], [ 22, 2, 6, 16 ], [ 22, 3, 2, 48 ], [ 22, 3, 3, 16 ],
[ 22, 3, 7, 32 ], [ 22, 4, 3, 48 ], [ 22, 4, 4, 8 ], [ 22, 4, 6, 8 ],
[ 22, 4, 9, 16 ], [ 27, 1, 3, 64 ], [ 27, 2, 3, 32 ], [ 27, 2, 6, 96 ],
[ 27, 2, 18, 64 ], [ 27, 3, 3, 32 ], [ 27, 3, 4, 32 ], [ 27, 3, 11, 64 ],
[ 27, 3, 13, 32 ], [ 27, 3, 24, 64 ], [ 27, 4, 2, 32 ], [ 27, 4, 5, 32 ],
[ 27, 5, 3, 32 ], [ 27, 6, 3, 32 ], [ 27, 6, 4, 16 ], [ 27, 6, 6, 48 ],
[ 27, 6, 8, 48 ], [ 27, 6, 10, 16 ], [ 27, 6, 15, 32 ], [ 27, 6, 18, 64 ],
[ 27, 6, 19, 32 ], [ 27, 7, 3, 16 ], [ 27, 7, 6, 48 ], [ 27, 7, 18, 32 ],
[ 27, 8, 3, 16 ], [ 27, 8, 4, 48 ], [ 27, 8, 11, 96 ], [ 27, 8, 13, 16 ],
[ 27, 8, 18, 32 ], [ 27, 8, 24, 96 ], [ 27, 9, 3, 32 ], [ 27, 9, 4, 16 ],
[ 27, 9, 12, 32 ], [ 27, 9, 16, 32 ], [ 27, 10, 2, 48 ], [ 27, 10, 3, 16 ],
[ 27, 10, 4, 48 ], [ 27, 10, 9, 32 ], [ 27, 10, 10, 16 ],
[ 27, 10, 14, 32 ], [ 27, 10, 19, 32 ], [ 27, 10, 20, 64 ],
[ 27, 11, 3, 16 ], [ 27, 11, 4, 16 ], [ 27, 11, 11, 32 ],
[ 27, 11, 13, 16 ], [ 27, 11, 24, 32 ], [ 27, 12, 2, 16 ],
[ 27, 12, 5, 32 ], [ 27, 12, 10, 48 ], [ 27, 12, 15, 32 ],
[ 27, 12, 20, 96 ], [ 27, 13, 2, 16 ], [ 27, 13, 5, 32 ], [ 27, 13, 6, 48 ],
[ 27, 13, 7, 48 ], [ 27, 13, 10, 16 ], [ 27, 13, 15, 32 ],
[ 27, 13, 17, 32 ], [ 27, 13, 20, 64 ], [ 27, 14, 2, 16 ],
[ 27, 14, 5, 16 ], [ 27, 14, 11, 32 ], [ 27, 14, 13, 16 ],
[ 27, 14, 24, 32 ], [ 29, 4, 7, 32 ], [ 29, 9, 7, 16 ], [ 30, 4, 14, 64 ],
[ 30, 4, 19, 64 ], [ 30, 8, 16, 64 ], [ 30, 8, 21, 32 ], [ 30, 11, 11, 32 ],
[ 30, 11, 19, 32 ], [ 30, 12, 14, 32 ], [ 30, 12, 19, 32 ],
[ 30, 13, 10, 96 ], [ 30, 13, 13, 32 ], [ 31, 9, 31, 64 ],
[ 31, 10, 13, 64 ], [ 31, 10, 27, 64 ], [ 31, 10, 54, 128 ],
[ 31, 11, 30, 64 ], [ 31, 12, 45, 64 ], [ 31, 13, 47, 64 ],
[ 31, 13, 53, 64 ], [ 31, 14, 34, 64 ], [ 31, 14, 37, 192 ],
[ 31, 15, 43, 64 ], [ 31, 15, 46, 64 ], [ 31, 16, 30, 64 ],
[ 31, 21, 10, 64 ], [ 31, 21, 25, 64 ], [ 31, 23, 30, 64 ],
[ 31, 29, 9, 64 ], [ 31, 29, 47, 64 ] ]
k = 32: F-action on Pi is () [31,2,32]
Dynkin type is (A_0(q) + T(phi2^2 phi4^2)).2
Order of center |Z^F|: phi2^2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 phi2^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1^2 phi2^2
Fusion of maximal tori of C^F in those of G^F:
[ 14 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 1, 8 ], [ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ],
[ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ], [ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ],
[ 5, 1, 2, 4 ], [ 7, 1, 2, 16 ], [ 7, 2, 2, 8 ], [ 7, 3, 2, 8 ],
[ 7, 4, 2, 8 ], [ 7, 5, 2, 4 ], [ 9, 1, 4, 16 ], [ 9, 2, 4, 8 ],
[ 9, 2, 5, 8 ], [ 9, 2, 7, 8 ], [ 9, 3, 4, 8 ], [ 9, 4, 4, 8 ],
[ 9, 5, 4, 4 ], [ 9, 5, 5, 4 ], [ 9, 5, 7, 4 ], [ 12, 1, 3, 8 ],
[ 12, 1, 5, 4 ], [ 12, 2, 3, 4 ], [ 12, 2, 5, 4 ], [ 12, 3, 2, 4 ],
[ 12, 4, 3, 2 ], [ 12, 4, 5, 4 ], [ 16, 1, 4, 8 ], [ 16, 1, 8, 32 ],
[ 16, 2, 4, 8 ], [ 16, 2, 8, 16 ], [ 16, 3, 4, 4 ], [ 16, 3, 8, 16 ],
[ 16, 4, 4, 4 ], [ 16, 4, 8, 16 ], [ 16, 4, 12, 16 ], [ 16, 5, 7, 16 ],
[ 16, 6, 7, 16 ], [ 16, 7, 7, 16 ], [ 16, 8, 8, 16 ], [ 16, 9, 4, 4 ],
[ 16, 9, 8, 8 ], [ 16, 9, 12, 8 ], [ 16, 10, 7, 8 ], [ 16, 11, 4, 8 ],
[ 16, 11, 9, 8 ], [ 16, 11, 10, 8 ], [ 16, 12, 7, 8 ], [ 16, 12, 10, 8 ],
[ 16, 12, 14, 8 ], [ 16, 13, 4, 4 ], [ 16, 13, 8, 8 ], [ 16, 13, 12, 8 ],
[ 16, 14, 6, 8 ], [ 16, 14, 8, 16 ], [ 16, 15, 4, 4 ], [ 16, 15, 8, 8 ],
[ 16, 16, 4, 4 ], [ 16, 16, 8, 8 ], [ 16, 17, 6, 8 ], [ 21, 1, 8, 16 ],
[ 21, 2, 5, 8 ], [ 21, 3, 4, 16 ], [ 21, 4, 5, 8 ], [ 21, 5, 5, 8 ],
[ 21, 6, 4, 16 ], [ 21, 7, 5, 16 ], [ 22, 1, 10, 16 ], [ 22, 2, 10, 16 ],
[ 22, 4, 10, 16 ], [ 27, 1, 11, 32 ], [ 27, 2, 20, 16 ], [ 27, 3, 10, 8 ],
[ 27, 3, 23, 32 ], [ 27, 3, 25, 16 ], [ 27, 4, 19, 16 ], [ 27, 5, 20, 16 ],
[ 27, 6, 20, 16 ], [ 27, 7, 20, 8 ], [ 27, 8, 10, 8 ], [ 27, 8, 23, 32 ],
[ 27, 8, 25, 8 ], [ 27, 9, 8, 8 ], [ 27, 9, 18, 16 ], [ 27, 10, 18, 16 ],
[ 27, 11, 10, 8 ], [ 27, 11, 23, 32 ], [ 27, 11, 25, 8 ],
[ 27, 12, 19, 32 ], [ 27, 13, 19, 16 ], [ 27, 14, 7, 8 ],
[ 27, 14, 23, 32 ], [ 27, 14, 25, 8 ], [ 30, 4, 21, 16 ], [ 30, 8, 29, 16 ],
[ 30, 12, 21, 16 ], [ 31, 9, 33, 16 ], [ 31, 10, 36, 16 ],
[ 31, 10, 37, 32 ], [ 31, 11, 32, 32 ], [ 31, 13, 43, 32 ],
[ 31, 14, 35, 32 ], [ 31, 15, 40, 32 ], [ 31, 16, 32, 16 ],
[ 31, 21, 34, 32 ], [ 31, 23, 31, 32 ], [ 31, 29, 42, 32 ] ]
k = 33: F-action on Pi is () [31,2,33]
Dynkin type is (A_0(q) + T(phi1^2 phi4^2)).2
Order of center |Z^F|: phi1^2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1^2 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 1, 2, 8 ], [ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ],
[ 5, 1, 1, 4 ], [ 7, 1, 3, 16 ], [ 7, 2, 3, 8 ], [ 7, 3, 3, 8 ],
[ 7, 4, 3, 8 ], [ 7, 5, 3, 4 ], [ 9, 1, 3, 16 ], [ 9, 2, 3, 8 ],
[ 9, 2, 6, 8 ], [ 9, 2, 8, 8 ], [ 9, 3, 3, 8 ], [ 9, 4, 3, 8 ],
[ 9, 5, 3, 4 ], [ 9, 5, 6, 4 ], [ 9, 5, 8, 4 ], [ 12, 1, 1, 8 ],
[ 12, 1, 5, 4 ], [ 12, 2, 1, 4 ], [ 12, 2, 5, 4 ], [ 12, 3, 1, 4 ],
[ 12, 4, 1, 2 ], [ 12, 4, 5, 4 ], [ 16, 1, 4, 8 ], [ 16, 1, 6, 32 ],
[ 16, 2, 4, 8 ], [ 16, 2, 6, 16 ], [ 16, 3, 4, 4 ], [ 16, 3, 6, 16 ],
[ 16, 4, 4, 4 ], [ 16, 4, 6, 16 ], [ 16, 4, 13, 16 ], [ 16, 5, 5, 16 ],
[ 16, 6, 5, 16 ], [ 16, 7, 5, 16 ], [ 16, 8, 5, 16 ], [ 16, 9, 4, 4 ],
[ 16, 9, 6, 8 ], [ 16, 9, 13, 8 ], [ 16, 10, 5, 8 ], [ 16, 11, 4, 8 ],
[ 16, 11, 6, 8 ], [ 16, 11, 9, 8 ], [ 16, 12, 5, 8 ], [ 16, 12, 11, 8 ],
[ 16, 12, 15, 8 ], [ 16, 13, 4, 4 ], [ 16, 13, 6, 8 ], [ 16, 13, 13, 8 ],
[ 16, 14, 5, 8 ], [ 16, 14, 9, 16 ], [ 16, 15, 4, 4 ], [ 16, 15, 6, 8 ],
[ 16, 16, 4, 4 ], [ 16, 16, 6, 8 ], [ 16, 17, 5, 8 ], [ 21, 1, 6, 16 ],
[ 21, 2, 7, 8 ], [ 21, 3, 9, 16 ], [ 21, 4, 7, 8 ], [ 21, 5, 7, 8 ],
[ 21, 6, 8, 16 ], [ 21, 7, 7, 16 ], [ 22, 1, 8, 16 ], [ 22, 2, 8, 16 ],
[ 22, 4, 8, 16 ], [ 27, 1, 7, 32 ], [ 27, 2, 12, 16 ], [ 27, 3, 10, 8 ],
[ 27, 3, 15, 16 ], [ 27, 3, 21, 32 ], [ 27, 4, 14, 16 ], [ 27, 5, 13, 16 ],
[ 27, 6, 12, 16 ], [ 27, 7, 12, 8 ], [ 27, 8, 10, 8 ], [ 27, 8, 15, 8 ],
[ 27, 8, 21, 32 ], [ 27, 9, 8, 8 ], [ 27, 9, 14, 16 ], [ 27, 10, 17, 16 ],
[ 27, 11, 10, 8 ], [ 27, 11, 15, 8 ], [ 27, 11, 21, 32 ],
[ 27, 12, 14, 32 ], [ 27, 13, 14, 16 ], [ 27, 14, 7, 8 ], [ 27, 14, 17, 8 ],
[ 27, 14, 21, 32 ], [ 30, 4, 7, 16 ], [ 30, 8, 13, 16 ], [ 30, 12, 7, 16 ],
[ 31, 9, 32, 16 ], [ 31, 10, 10, 16 ], [ 31, 10, 33, 32 ],
[ 31, 11, 31, 32 ], [ 31, 13, 41, 32 ], [ 31, 14, 36, 32 ],
[ 31, 15, 32, 32 ], [ 31, 16, 31, 16 ], [ 31, 21, 28, 32 ],
[ 31, 23, 32, 32 ], [ 31, 29, 38, 32 ] ]
k = 34: F-action on Pi is () [31,2,34]
Dynkin type is (A_0(q) + T(phi1 phi2 phi4^2)).2
Order of center |Z^F|: phi1 phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2^2 ( q-3 )
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, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 1 ],
[ 2, 2, 2, 2 ], [ 3, 2, 3, 4 ], [ 3, 2, 4, 4 ], [ 3, 5, 3, 2 ],
[ 3, 5, 4, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 3, 8 ],
[ 9, 1, 4, 8 ], [ 9, 2, 3, 4 ], [ 9, 2, 4, 4 ], [ 9, 2, 5, 4 ],
[ 9, 2, 6, 4 ], [ 9, 2, 7, 4 ], [ 9, 2, 8, 4 ], [ 9, 3, 3, 4 ],
[ 9, 3, 4, 4 ], [ 9, 4, 3, 4 ], [ 9, 4, 4, 4 ], [ 9, 5, 3, 2 ],
[ 9, 5, 4, 2 ], [ 9, 5, 5, 2 ], [ 9, 5, 6, 2 ], [ 9, 5, 7, 2 ],
[ 9, 5, 8, 2 ], [ 12, 1, 2, 4 ], [ 12, 1, 5, 4 ], [ 12, 2, 2, 2 ],
[ 12, 2, 5, 4 ], [ 12, 4, 2, 2 ], [ 12, 4, 5, 4 ], [ 16, 1, 4, 8 ],
[ 16, 1, 7, 16 ], [ 16, 2, 4, 8 ], [ 16, 2, 7, 8 ], [ 16, 2, 10, 8 ],
[ 16, 3, 4, 4 ], [ 16, 3, 7, 8 ], [ 16, 4, 4, 4 ], [ 16, 4, 7, 8 ],
[ 16, 4, 9, 8 ], [ 16, 4, 10, 8 ], [ 16, 4, 14, 8 ], [ 16, 5, 6, 8 ],
[ 16, 5, 8, 8 ], [ 16, 6, 6, 8 ], [ 16, 6, 8, 8 ], [ 16, 7, 6, 8 ],
[ 16, 7, 8, 8 ], [ 16, 9, 4, 4 ], [ 16, 9, 7, 4 ], [ 16, 9, 9, 4 ],
[ 16, 9, 10, 8 ], [ 16, 9, 14, 4 ], [ 16, 10, 6, 4 ], [ 16, 10, 8, 4 ],
[ 16, 11, 4, 8 ], [ 16, 11, 8, 8 ], [ 16, 11, 9, 8 ], [ 16, 12, 6, 4 ],
[ 16, 12, 8, 4 ], [ 16, 12, 9, 4 ], [ 16, 12, 12, 4 ], [ 16, 12, 13, 4 ],
[ 16, 12, 16, 4 ], [ 16, 13, 4, 4 ], [ 16, 13, 7, 4 ], [ 16, 13, 9, 4 ],
[ 16, 13, 10, 8 ], [ 16, 13, 14, 4 ], [ 16, 15, 4, 4 ], [ 16, 15, 7, 4 ],
[ 16, 16, 4, 4 ], [ 16, 16, 7, 4 ], [ 22, 1, 8, 8 ], [ 22, 1, 10, 8 ],
[ 22, 2, 8, 8 ], [ 22, 2, 10, 8 ], [ 22, 4, 8, 8 ], [ 22, 4, 10, 8 ],
[ 27, 1, 13, 16 ], [ 27, 3, 10, 8 ], [ 27, 3, 20, 8 ], [ 27, 3, 22, 16 ],
[ 27, 5, 19, 8 ], [ 27, 8, 10, 8 ], [ 27, 8, 20, 8 ], [ 27, 8, 22, 16 ],
[ 27, 9, 8, 8 ], [ 27, 9, 17, 8 ], [ 27, 9, 20, 8 ], [ 27, 11, 10, 8 ],
[ 27, 11, 20, 8 ], [ 27, 11, 22, 16 ], [ 27, 14, 7, 8 ], [ 27, 14, 19, 16 ],
[ 27, 14, 20, 8 ], [ 30, 4, 7, 8 ], [ 30, 4, 21, 8 ], [ 30, 8, 13, 8 ],
[ 30, 8, 29, 8 ], [ 30, 12, 7, 8 ], [ 30, 12, 21, 8 ], [ 31, 9, 34, 8 ],
[ 31, 10, 22, 8 ], [ 31, 10, 35, 16 ], [ 31, 11, 33, 16 ],
[ 31, 13, 42, 16 ], [ 31, 13, 44, 16 ], [ 31, 16, 33, 8 ],
[ 31, 23, 33, 16 ], [ 31, 29, 40, 16 ], [ 31, 29, 44, 16 ] ]
k = 35: F-action on Pi is () [31,2,35]
Dynkin type is (A_0(q) + T(phi1^5 phi2)).2
Order of center |Z^F|: phi1^4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/384 phi1^2 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/384 phi2 ( q^3-17*q^2+91*q-147 )
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, 14 ], [ 2, 2, 1, 7 ], [ 3, 1, 1, 16 ],
[ 3, 2, 1, 8 ], [ 3, 3, 1, 8 ], [ 3, 4, 1, 8 ], [ 3, 5, 1, 4 ],
[ 4, 1, 1, 8 ], [ 4, 2, 1, 4 ], [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ],
[ 7, 1, 1, 64 ], [ 7, 2, 1, 32 ], [ 7, 3, 1, 32 ], [ 7, 4, 1, 32 ],
[ 7, 5, 1, 16 ], [ 8, 1, 1, 16 ], [ 9, 1, 1, 96 ], [ 9, 2, 1, 48 ],
[ 9, 3, 1, 48 ], [ 9, 4, 1, 48 ], [ 9, 5, 1, 24 ], [ 12, 1, 1, 48 ],
[ 12, 2, 1, 24 ], [ 12, 2, 2, 2 ], [ 12, 3, 1, 24 ], [ 12, 4, 1, 12 ],
[ 12, 4, 2, 2 ], [ 13, 1, 1, 96 ], [ 13, 2, 1, 48 ], [ 14, 1, 1, 64 ],
[ 14, 2, 1, 32 ], [ 15, 1, 1, 96 ], [ 16, 1, 1, 192 ], [ 16, 2, 1, 96 ],
[ 16, 2, 3, 24 ], [ 16, 3, 1, 96 ], [ 16, 4, 1, 96 ], [ 16, 5, 1, 96 ],
[ 16, 6, 1, 96 ], [ 16, 7, 1, 96 ], [ 16, 8, 1, 96 ], [ 16, 9, 1, 48 ],
[ 16, 9, 3, 12 ], [ 16, 10, 1, 48 ], [ 16, 10, 2, 12 ], [ 16, 10, 4, 12 ],
[ 16, 11, 1, 48 ], [ 16, 11, 3, 24 ], [ 16, 12, 1, 48 ], [ 16, 13, 1, 48 ],
[ 16, 14, 1, 48 ], [ 16, 15, 1, 48 ], [ 16, 16, 1, 48 ], [ 16, 17, 1, 48 ],
[ 21, 1, 1, 192 ], [ 21, 2, 1, 96 ], [ 21, 3, 1, 96 ], [ 21, 3, 3, 16 ],
[ 21, 4, 1, 96 ], [ 21, 5, 1, 48 ], [ 21, 5, 2, 8 ], [ 21, 6, 1, 48 ],
[ 21, 6, 3, 16 ], [ 21, 7, 1, 48 ], [ 21, 7, 2, 16 ], [ 22, 1, 1, 192 ],
[ 22, 2, 1, 96 ], [ 22, 2, 2, 48 ], [ 22, 3, 1, 96 ], [ 22, 4, 1, 48 ],
[ 22, 4, 2, 48 ], [ 23, 2, 2, 16 ], [ 23, 2, 4, 16 ], [ 23, 6, 2, 8 ],
[ 23, 6, 4, 8 ], [ 27, 1, 1, 384 ], [ 27, 2, 1, 192 ], [ 27, 3, 1, 192 ],
[ 27, 3, 6, 96 ], [ 27, 4, 1, 192 ], [ 27, 5, 1, 192 ], [ 27, 6, 1, 96 ],
[ 27, 6, 2, 48 ], [ 27, 7, 1, 96 ], [ 27, 8, 1, 96 ], [ 27, 8, 6, 96 ],
[ 27, 9, 1, 96 ], [ 27, 9, 2, 48 ], [ 27, 10, 1, 96 ], [ 27, 10, 5, 48 ],
[ 27, 11, 1, 96 ], [ 27, 11, 6, 96 ], [ 27, 12, 1, 96 ], [ 27, 12, 3, 96 ],
[ 27, 13, 1, 96 ], [ 27, 13, 3, 48 ], [ 27, 14, 1, 96 ], [ 27, 14, 8, 96 ],
[ 28, 2, 2, 64 ], [ 28, 5, 2, 32 ], [ 28, 6, 2, 64 ], [ 29, 4, 2, 96 ],
[ 29, 4, 4, 96 ], [ 29, 9, 2, 48 ], [ 29, 9, 4, 48 ], [ 29, 12, 2, 48 ],
[ 29, 12, 4, 48 ], [ 30, 4, 3, 192 ], [ 30, 8, 3, 96 ], [ 30, 11, 2, 96 ],
[ 30, 11, 4, 96 ], [ 30, 12, 3, 96 ], [ 30, 13, 2, 192 ],
[ 31, 9, 35, 192 ], [ 31, 10, 2, 192 ], [ 31, 11, 34, 192 ],
[ 31, 12, 15, 192 ], [ 31, 12, 29, 192 ], [ 31, 13, 13, 192 ],
[ 31, 14, 45, 384 ], [ 31, 15, 11, 384 ], [ 31, 16, 34, 192 ],
[ 31, 21, 3, 384 ], [ 31, 23, 34, 192 ], [ 31, 29, 2, 192 ] ]
k = 36: F-action on Pi is () [31,2,36]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^3-3*q^2-9*q+27 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^3-3*q^2-9*q+27 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 1, 4 ],
[ 3, 5, 1, 2 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 4 ],
[ 7, 3, 1, 8 ], [ 7, 5, 1, 4 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ],
[ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 8 ],
[ 9, 3, 1, 8 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ],
[ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ], [ 12, 1, 2, 8 ], [ 12, 2, 1, 4 ],
[ 12, 2, 2, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 4 ], [ 13, 2, 1, 8 ],
[ 13, 2, 2, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 8 ],
[ 15, 1, 4, 8 ], [ 16, 1, 3, 32 ], [ 16, 2, 1, 16 ], [ 16, 2, 3, 16 ],
[ 16, 2, 13, 16 ], [ 16, 3, 3, 16 ], [ 16, 4, 3, 16 ], [ 16, 5, 2, 16 ],
[ 16, 5, 4, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 4, 16 ], [ 16, 7, 2, 16 ],
[ 16, 7, 4, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 3, 8 ], [ 16, 9, 13, 8 ],
[ 16, 10, 1, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 4, 8 ], [ 16, 10, 11, 8 ],
[ 16, 10, 15, 8 ], [ 16, 11, 1, 8 ], [ 16, 11, 3, 16 ], [ 16, 12, 2, 8 ],
[ 16, 12, 4, 8 ], [ 16, 13, 3, 8 ], [ 16, 15, 3, 8 ], [ 16, 16, 3, 8 ],
[ 21, 2, 2, 16 ], [ 21, 5, 2, 8 ], [ 22, 1, 2, 16 ], [ 22, 1, 5, 16 ],
[ 22, 2, 1, 16 ], [ 22, 2, 2, 8 ], [ 22, 2, 4, 16 ], [ 22, 2, 5, 8 ],
[ 22, 4, 1, 8 ], [ 22, 4, 2, 8 ], [ 22, 4, 4, 8 ], [ 22, 4, 5, 8 ],
[ 23, 2, 1, 8 ], [ 23, 2, 5, 8 ], [ 23, 6, 1, 4 ], [ 23, 6, 5, 4 ],
[ 27, 1, 12, 32 ], [ 27, 3, 2, 32 ], [ 27, 3, 7, 16 ], [ 27, 5, 8, 16 ],
[ 27, 8, 2, 16 ], [ 27, 8, 7, 16 ], [ 27, 9, 2, 16 ], [ 27, 9, 6, 8 ],
[ 27, 9, 10, 16 ], [ 27, 11, 2, 16 ], [ 27, 11, 7, 16 ], [ 27, 14, 3, 16 ],
[ 27, 14, 6, 16 ], [ 29, 4, 1, 16 ], [ 29, 4, 5, 16 ], [ 29, 4, 9, 16 ],
[ 29, 4, 13, 32 ], [ 29, 9, 1, 8 ], [ 29, 9, 5, 8 ], [ 29, 9, 9, 8 ],
[ 29, 9, 13, 16 ], [ 29, 12, 1, 8 ], [ 29, 12, 5, 8 ], [ 29, 12, 9, 16 ],
[ 29, 12, 13, 16 ], [ 30, 4, 8, 32 ], [ 30, 4, 22, 32 ], [ 30, 8, 3, 16 ],
[ 30, 8, 19, 16 ], [ 30, 11, 6, 16 ], [ 30, 11, 15, 16 ],
[ 30, 11, 22, 16 ], [ 30, 11, 31, 16 ], [ 30, 12, 8, 16 ],
[ 30, 12, 22, 16 ], [ 31, 9, 36, 32 ], [ 31, 10, 7, 32 ],
[ 31, 11, 36, 32 ], [ 31, 12, 5, 32 ], [ 31, 12, 7, 32 ],
[ 31, 12, 10, 32 ], [ 31, 12, 14, 32 ], [ 31, 13, 6, 32 ],
[ 31, 13, 8, 32 ], [ 31, 16, 38, 32 ], [ 31, 23, 38, 32 ],
[ 31, 29, 17, 32 ], [ 31, 29, 25, 32 ] ]
k = 37: F-action on Pi is () [31,2,37]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2
Order of center |Z^F|: phi1 phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q^2-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q^2-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 2, 1, 4 ], [ 12, 4, 1, 2 ],
[ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 16, 2, 13, 8 ], [ 16, 9, 13, 4 ],
[ 16, 10, 11, 4 ], [ 16, 10, 15, 4 ], [ 23, 2, 1, 4 ], [ 23, 2, 5, 4 ],
[ 23, 6, 1, 2 ], [ 23, 6, 5, 2 ], [ 27, 1, 19, 8 ], [ 27, 5, 6, 4 ],
[ 27, 9, 9, 4 ], [ 29, 4, 13, 8 ], [ 29, 4, 17, 8 ], [ 29, 9, 13, 4 ],
[ 29, 9, 17, 4 ], [ 29, 12, 9, 4 ], [ 29, 12, 13, 4 ], [ 31, 9, 38, 8 ],
[ 31, 11, 39, 8 ], [ 31, 12, 8, 8 ], [ 31, 12, 11, 8 ], [ 31, 16, 41, 8 ],
[ 31, 23, 41, 8 ] ]
k = 38: F-action on Pi is () [31,2,38]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q^2-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q^2-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 4, 4 ],
[ 3, 5, 4, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 16, 2, 14, 8 ],
[ 16, 9, 14, 4 ], [ 16, 10, 12, 4 ], [ 16, 10, 13, 4 ], [ 23, 2, 2, 4 ],
[ 23, 2, 6, 4 ], [ 23, 6, 2, 2 ], [ 23, 6, 6, 2 ], [ 27, 1, 19, 8 ],
[ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ], [ 29, 4, 14, 8 ], [ 29, 4, 18, 8 ],
[ 29, 9, 14, 4 ], [ 29, 9, 18, 4 ], [ 29, 12, 10, 4 ], [ 29, 12, 14, 4 ],
[ 31, 9, 40, 8 ], [ 31, 11, 40, 8 ], [ 31, 12, 22, 8 ], [ 31, 12, 25, 8 ],
[ 31, 16, 39, 8 ], [ 31, 23, 39, 8 ] ]
k = 39: F-action on Pi is () [31,2,39]
Dynkin type is (A_0(q) + T(phi1 phi2^3 phi4)).2
Order of center |Z^F|: phi1 phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q^2-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q^2-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 4, 2, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 2, 3, 4 ], [ 12, 4, 3, 2 ],
[ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 16, 2, 12, 8 ], [ 16, 9, 12, 4 ],
[ 16, 10, 10, 4 ], [ 16, 10, 14, 4 ], [ 23, 2, 3, 4 ], [ 23, 2, 7, 4 ],
[ 23, 6, 3, 2 ], [ 23, 6, 7, 2 ], [ 27, 1, 19, 8 ], [ 27, 5, 6, 4 ],
[ 27, 9, 9, 4 ], [ 29, 4, 15, 8 ], [ 29, 4, 19, 8 ], [ 29, 9, 15, 4 ],
[ 29, 9, 19, 4 ], [ 29, 12, 11, 4 ], [ 29, 12, 15, 4 ], [ 31, 9, 37, 8 ],
[ 31, 11, 37, 8 ], [ 31, 12, 50, 8 ], [ 31, 12, 53, 8 ], [ 31, 16, 42, 8 ],
[ 31, 23, 42, 8 ] ]
k = 40: F-action on Pi is () [31,2,40]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q^2-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q^2-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 2, 3, 4 ],
[ 3, 5, 3, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 12, 2, 2, 2 ],
[ 12, 4, 2, 2 ], [ 15, 1, 2, 4 ], [ 15, 1, 5, 4 ], [ 16, 2, 9, 8 ],
[ 16, 9, 9, 4 ], [ 16, 10, 9, 4 ], [ 16, 10, 16, 4 ], [ 23, 2, 4, 4 ],
[ 23, 2, 8, 4 ], [ 23, 6, 4, 2 ], [ 23, 6, 8, 2 ], [ 27, 1, 19, 8 ],
[ 27, 5, 6, 4 ], [ 27, 9, 9, 4 ], [ 29, 4, 16, 8 ], [ 29, 4, 20, 8 ],
[ 29, 9, 16, 4 ], [ 29, 9, 20, 4 ], [ 29, 12, 12, 4 ], [ 29, 12, 16, 4 ],
[ 31, 9, 39, 8 ], [ 31, 11, 38, 8 ], [ 31, 12, 36, 8 ], [ 31, 12, 39, 8 ],
[ 31, 16, 40, 8 ], [ 31, 23, 40, 8 ] ]
k = 41: F-action on Pi is () [31,2,41]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^3-3*q^2-17*q+51 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^3-3*q^2-17*q+51 )
Fusion of maximal tori of C^F in those of G^F:
[ 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 4, 8 ],
[ 3, 5, 4, 4 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 4 ], [ 8, 1, 1, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ],
[ 9, 2, 2, 8 ], [ 9, 2, 6, 16 ], [ 9, 2, 7, 16 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 4 ], [ 9, 5, 6, 8 ], [ 9, 5, 7, 8 ], [ 12, 1, 2, 8 ],
[ 12, 2, 2, 6 ], [ 12, 4, 2, 6 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 16 ],
[ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 3, 32 ], [ 16, 2, 3, 24 ],
[ 16, 2, 14, 16 ], [ 16, 3, 3, 16 ], [ 16, 4, 3, 16 ], [ 16, 4, 14, 32 ],
[ 16, 5, 2, 16 ], [ 16, 5, 4, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 4, 16 ],
[ 16, 7, 2, 16 ], [ 16, 7, 4, 16 ], [ 16, 9, 3, 12 ], [ 16, 9, 14, 24 ],
[ 16, 10, 2, 12 ], [ 16, 10, 4, 12 ], [ 16, 10, 12, 8 ], [ 16, 10, 13, 8 ],
[ 16, 11, 3, 24 ], [ 16, 12, 2, 8 ], [ 16, 12, 4, 8 ], [ 16, 12, 12, 16 ],
[ 16, 12, 13, 16 ], [ 16, 13, 3, 8 ], [ 16, 13, 14, 16 ], [ 16, 15, 3, 8 ],
[ 16, 16, 3, 8 ], [ 22, 1, 2, 16 ], [ 22, 1, 5, 16 ], [ 22, 2, 2, 16 ],
[ 22, 2, 5, 16 ], [ 22, 4, 2, 16 ], [ 22, 4, 5, 16 ], [ 23, 2, 2, 8 ],
[ 23, 2, 6, 8 ], [ 23, 6, 2, 4 ], [ 23, 6, 6, 4 ], [ 27, 1, 12, 32 ],
[ 27, 3, 7, 32 ], [ 27, 5, 8, 16 ], [ 27, 8, 7, 32 ], [ 27, 9, 6, 24 ],
[ 27, 9, 10, 16 ], [ 27, 11, 7, 32 ], [ 27, 14, 6, 32 ], [ 29, 4, 2, 16 ],
[ 29, 4, 8, 16 ], [ 29, 4, 10, 16 ], [ 29, 4, 14, 32 ], [ 29, 9, 2, 8 ],
[ 29, 9, 8, 8 ], [ 29, 9, 10, 8 ], [ 29, 9, 14, 16 ], [ 29, 12, 2, 8 ],
[ 29, 12, 6, 8 ], [ 29, 12, 10, 16 ], [ 29, 12, 14, 16 ], [ 30, 4, 6, 32 ],
[ 30, 4, 25, 32 ], [ 30, 8, 12, 32 ], [ 30, 8, 31, 32 ], [ 30, 11, 5, 16 ],
[ 30, 11, 13, 16 ], [ 30, 11, 24, 16 ], [ 30, 11, 32, 16 ],
[ 30, 12, 6, 16 ], [ 30, 12, 25, 16 ], [ 31, 9, 41, 32 ],
[ 31, 10, 20, 64 ], [ 31, 11, 45, 32 ], [ 31, 12, 21, 32 ],
[ 31, 12, 24, 32 ], [ 31, 12, 28, 32 ], [ 31, 12, 33, 32 ],
[ 31, 13, 20, 32 ], [ 31, 13, 26, 32 ], [ 31, 16, 46, 32 ],
[ 31, 23, 45, 32 ], [ 31, 29, 20, 32 ], [ 31, 29, 26, 32 ] ]
k = 42: F-action on Pi is () [31,2,42]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1^2 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^3-3*q^2-9*q+27 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^3-3*q^2-9*q+27 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 2, 4 ],
[ 3, 5, 2, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 4 ],
[ 7, 3, 4, 8 ], [ 7, 5, 4, 4 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ],
[ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 8 ],
[ 9, 3, 1, 8 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ],
[ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ], [ 12, 1, 2, 8 ], [ 12, 2, 2, 4 ],
[ 12, 2, 3, 4 ], [ 12, 4, 2, 4 ], [ 12, 4, 3, 2 ], [ 13, 2, 3, 8 ],
[ 13, 2, 4, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 16 ], [ 15, 1, 3, 8 ],
[ 15, 1, 4, 8 ], [ 16, 1, 3, 32 ], [ 16, 2, 3, 16 ], [ 16, 2, 5, 16 ],
[ 16, 2, 12, 16 ], [ 16, 3, 3, 16 ], [ 16, 4, 3, 16 ], [ 16, 5, 2, 16 ],
[ 16, 5, 4, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 4, 16 ], [ 16, 7, 2, 16 ],
[ 16, 7, 4, 16 ], [ 16, 9, 3, 8 ], [ 16, 9, 5, 8 ], [ 16, 9, 12, 8 ],
[ 16, 10, 2, 8 ], [ 16, 10, 3, 8 ], [ 16, 10, 4, 8 ], [ 16, 10, 10, 8 ],
[ 16, 10, 14, 8 ], [ 16, 11, 3, 16 ], [ 16, 11, 5, 8 ], [ 16, 12, 2, 8 ],
[ 16, 12, 4, 8 ], [ 16, 13, 3, 8 ], [ 16, 15, 3, 8 ], [ 16, 16, 3, 8 ],
[ 21, 2, 9, 16 ], [ 21, 5, 9, 8 ], [ 22, 1, 2, 16 ], [ 22, 1, 5, 16 ],
[ 22, 2, 2, 8 ], [ 22, 2, 3, 16 ], [ 22, 2, 5, 8 ], [ 22, 2, 6, 16 ],
[ 22, 4, 2, 8 ], [ 22, 4, 3, 8 ], [ 22, 4, 5, 8 ], [ 22, 4, 6, 8 ],
[ 23, 2, 3, 8 ], [ 23, 2, 7, 8 ], [ 23, 6, 3, 4 ], [ 23, 6, 7, 4 ],
[ 27, 1, 12, 32 ], [ 27, 3, 7, 16 ], [ 27, 3, 12, 32 ], [ 27, 5, 8, 16 ],
[ 27, 8, 7, 16 ], [ 27, 8, 12, 16 ], [ 27, 9, 6, 8 ], [ 27, 9, 7, 16 ],
[ 27, 9, 10, 16 ], [ 27, 11, 7, 16 ], [ 27, 11, 12, 16 ], [ 27, 14, 6, 16 ],
[ 27, 14, 12, 16 ], [ 29, 4, 3, 16 ], [ 29, 4, 7, 16 ], [ 29, 4, 11, 16 ],
[ 29, 4, 15, 32 ], [ 29, 9, 3, 8 ], [ 29, 9, 7, 8 ], [ 29, 9, 11, 8 ],
[ 29, 9, 15, 16 ], [ 29, 12, 3, 8 ], [ 29, 12, 7, 8 ], [ 29, 12, 11, 16 ],
[ 29, 12, 15, 16 ], [ 30, 4, 10, 32 ], [ 30, 4, 24, 32 ], [ 30, 8, 14, 16 ],
[ 30, 8, 30, 16 ], [ 30, 11, 7, 16 ], [ 30, 11, 14, 16 ],
[ 30, 11, 23, 16 ], [ 30, 11, 30, 16 ], [ 30, 12, 10, 16 ],
[ 30, 12, 24, 16 ], [ 31, 9, 42, 32 ], [ 31, 10, 19, 32 ],
[ 31, 11, 41, 32 ], [ 31, 12, 47, 32 ], [ 31, 12, 49, 32 ],
[ 31, 12, 52, 32 ], [ 31, 12, 56, 32 ], [ 31, 13, 50, 32 ],
[ 31, 13, 52, 32 ], [ 31, 16, 43, 32 ], [ 31, 23, 43, 32 ],
[ 31, 29, 19, 32 ], [ 31, 29, 27, 32 ] ]
k = 43: F-action on Pi is () [31,2,43]
Dynkin type is (A_0(q) + T(phi1^5 phi2)).2
Order of center |Z^F|: phi1^3 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^3-9*q^2+19*q+5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^3-9*q^2+19*q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 7 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 8 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 4 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 4 ], [ 5, 1, 1, 6 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 16 ], [ 7, 2, 1, 16 ], [ 7, 3, 1, 16 ],
[ 7, 4, 1, 16 ], [ 7, 5, 1, 16 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 24 ],
[ 9, 1, 2, 8 ], [ 9, 2, 1, 20 ], [ 9, 2, 2, 12 ], [ 9, 3, 1, 12 ],
[ 9, 3, 2, 4 ], [ 9, 4, 1, 12 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 10 ],
[ 9, 5, 2, 6 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ], [ 12, 2, 1, 8 ],
[ 12, 2, 2, 2 ], [ 12, 3, 1, 12 ], [ 12, 4, 1, 12 ], [ 12, 4, 2, 2 ],
[ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 2, 1, 16 ], [ 13, 2, 2, 8 ],
[ 14, 1, 1, 16 ], [ 14, 2, 1, 24 ], [ 15, 1, 1, 16 ], [ 15, 1, 4, 8 ],
[ 16, 1, 1, 32 ], [ 16, 1, 3, 16 ], [ 16, 2, 1, 32 ], [ 16, 2, 3, 8 ],
[ 16, 3, 1, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 1, 16 ], [ 16, 4, 3, 24 ],
[ 16, 5, 1, 16 ], [ 16, 5, 2, 8 ], [ 16, 5, 4, 8 ], [ 16, 6, 1, 16 ],
[ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 1, 16 ], [ 16, 7, 2, 8 ],
[ 16, 7, 4, 8 ], [ 16, 8, 1, 32 ], [ 16, 9, 1, 16 ], [ 16, 9, 3, 12 ],
[ 16, 10, 1, 16 ], [ 16, 10, 2, 4 ], [ 16, 10, 4, 4 ], [ 16, 11, 1, 32 ],
[ 16, 11, 3, 8 ], [ 16, 12, 1, 8 ], [ 16, 12, 2, 12 ], [ 16, 12, 4, 12 ],
[ 16, 13, 1, 8 ], [ 16, 13, 3, 12 ], [ 16, 14, 1, 24 ], [ 16, 15, 1, 8 ],
[ 16, 15, 3, 4 ], [ 16, 16, 1, 8 ], [ 16, 16, 3, 4 ], [ 16, 17, 1, 24 ],
[ 21, 1, 5, 16 ], [ 21, 2, 1, 16 ], [ 21, 2, 2, 16 ], [ 21, 3, 1, 16 ],
[ 21, 3, 3, 8 ], [ 21, 4, 2, 8 ], [ 21, 5, 1, 16 ], [ 21, 5, 2, 8 ],
[ 21, 6, 1, 24 ], [ 21, 6, 3, 8 ], [ 21, 7, 1, 24 ], [ 21, 7, 2, 8 ],
[ 22, 1, 1, 16 ], [ 22, 1, 2, 16 ], [ 22, 1, 4, 16 ], [ 22, 2, 1, 32 ],
[ 22, 2, 2, 8 ], [ 22, 2, 4, 16 ], [ 22, 3, 1, 24 ], [ 22, 3, 3, 24 ],
[ 22, 4, 1, 32 ], [ 22, 4, 2, 8 ], [ 22, 4, 4, 24 ], [ 23, 2, 1, 16 ],
[ 23, 6, 1, 8 ], [ 27, 1, 6, 32 ], [ 27, 2, 2, 48 ], [ 27, 3, 1, 32 ],
[ 27, 3, 2, 32 ], [ 27, 3, 6, 16 ], [ 27, 4, 3, 16 ], [ 27, 5, 2, 16 ],
[ 27, 6, 1, 16 ], [ 27, 6, 2, 24 ], [ 27, 7, 2, 24 ], [ 27, 8, 1, 16 ],
[ 27, 8, 2, 48 ], [ 27, 8, 6, 16 ], [ 27, 9, 1, 32 ], [ 27, 9, 2, 16 ],
[ 27, 10, 1, 16 ], [ 27, 10, 5, 24 ], [ 27, 11, 1, 16 ], [ 27, 11, 2, 16 ],
[ 27, 11, 6, 16 ], [ 27, 12, 1, 48 ], [ 27, 12, 3, 16 ], [ 27, 13, 1, 16 ],
[ 27, 13, 3, 24 ], [ 27, 14, 1, 16 ], [ 27, 14, 3, 16 ], [ 27, 14, 8, 16 ],
[ 28, 2, 1, 32 ], [ 28, 5, 1, 16 ], [ 28, 6, 1, 48 ], [ 29, 4, 1, 32 ],
[ 29, 4, 5, 16 ], [ 29, 9, 1, 16 ], [ 29, 9, 5, 8 ], [ 29, 12, 1, 16 ],
[ 30, 4, 1, 32 ], [ 30, 4, 8, 32 ], [ 30, 4, 15, 32 ], [ 30, 8, 1, 32 ],
[ 30, 8, 3, 16 ], [ 30, 8, 17, 32 ], [ 30, 11, 1, 16 ], [ 30, 11, 6, 16 ],
[ 30, 11, 15, 16 ], [ 30, 11, 17, 16 ], [ 30, 12, 1, 16 ],
[ 30, 12, 8, 16 ], [ 30, 12, 15, 16 ], [ 30, 13, 1, 48 ],
[ 30, 13, 11, 48 ], [ 31, 9, 43, 32 ], [ 31, 10, 2, 32 ], [ 31, 10, 6, 64 ],
[ 31, 11, 44, 32 ], [ 31, 12, 2, 32 ], [ 31, 12, 4, 32 ], [ 31, 13, 2, 32 ],
[ 31, 13, 4, 32 ], [ 31, 13, 5, 32 ], [ 31, 14, 41, 96 ], [ 31, 15, 2, 32 ],
[ 31, 16, 48, 32 ], [ 31, 21, 11, 32 ], [ 31, 23, 37, 32 ],
[ 31, 29, 4, 32 ], [ 31, 29, 10, 32 ], [ 31, 29, 13, 32 ] ]
k = 44: F-action on Pi is () [31,2,44]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1 phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1^2 ( q^2-4*q-1 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 phi2 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 2, 2, 2, 4 ],
[ 3, 1, 2, 8 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 2, 4 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 6 ],
[ 6, 1, 2, 8 ], [ 7, 1, 4, 16 ], [ 7, 2, 3, 8 ], [ 7, 2, 4, 8 ],
[ 7, 3, 1, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 2, 8 ], [ 7, 4, 4, 8 ],
[ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ],
[ 8, 1, 2, 8 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 24 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 12 ], [ 9, 2, 3, 8 ], [ 9, 2, 4, 8 ], [ 9, 3, 1, 4 ],
[ 9, 3, 2, 12 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 6 ], [ 9, 5, 3, 4 ], [ 9, 5, 4, 4 ], [ 12, 1, 2, 4 ],
[ 12, 1, 3, 8 ], [ 12, 2, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 2, 3, 4 ],
[ 12, 3, 2, 4 ], [ 12, 3, 3, 8 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ],
[ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ],
[ 13, 2, 1, 4 ], [ 13, 2, 2, 12 ], [ 13, 2, 3, 4 ], [ 13, 2, 4, 4 ],
[ 14, 1, 2, 16 ], [ 14, 2, 2, 8 ], [ 14, 2, 4, 16 ], [ 15, 1, 3, 16 ],
[ 15, 1, 4, 8 ], [ 16, 1, 3, 16 ], [ 16, 1, 5, 32 ], [ 16, 2, 1, 16 ],
[ 16, 2, 3, 8 ], [ 16, 2, 5, 16 ], [ 16, 3, 3, 8 ], [ 16, 3, 5, 16 ],
[ 16, 4, 3, 8 ], [ 16, 4, 5, 16 ], [ 16, 4, 7, 16 ], [ 16, 5, 2, 8 ],
[ 16, 5, 3, 16 ], [ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ], [ 16, 6, 3, 16 ],
[ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ], [ 16, 7, 3, 16 ], [ 16, 7, 4, 8 ],
[ 16, 8, 3, 16 ], [ 16, 8, 4, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 3, 4 ],
[ 16, 9, 5, 8 ], [ 16, 9, 7, 8 ], [ 16, 10, 1, 8 ], [ 16, 10, 2, 4 ],
[ 16, 10, 3, 8 ], [ 16, 10, 4, 4 ], [ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ],
[ 16, 11, 3, 8 ], [ 16, 11, 5, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 3, 8 ],
[ 16, 12, 4, 4 ], [ 16, 12, 6, 8 ], [ 16, 12, 8, 8 ], [ 16, 13, 3, 4 ],
[ 16, 13, 5, 8 ], [ 16, 13, 7, 8 ], [ 16, 14, 2, 8 ], [ 16, 14, 4, 8 ],
[ 16, 15, 3, 4 ], [ 16, 15, 5, 8 ], [ 16, 16, 3, 4 ], [ 16, 16, 5, 8 ],
[ 16, 17, 2, 8 ], [ 16, 17, 4, 8 ], [ 21, 1, 7, 16 ], [ 21, 2, 2, 8 ],
[ 21, 2, 3, 16 ], [ 21, 2, 9, 8 ], [ 21, 3, 6, 16 ], [ 21, 3, 8, 8 ],
[ 21, 4, 9, 8 ], [ 21, 5, 2, 4 ], [ 21, 5, 3, 8 ], [ 21, 5, 8, 8 ],
[ 21, 5, 9, 4 ], [ 21, 6, 2, 8 ], [ 21, 6, 7, 8 ], [ 21, 6, 9, 8 ],
[ 21, 7, 6, 8 ], [ 21, 7, 9, 8 ], [ 22, 1, 3, 16 ], [ 22, 1, 5, 16 ],
[ 22, 1, 6, 16 ], [ 22, 2, 1, 8 ], [ 22, 2, 3, 8 ], [ 22, 2, 4, 24 ],
[ 22, 2, 5, 8 ], [ 22, 2, 6, 8 ], [ 22, 3, 2, 8 ], [ 22, 3, 4, 8 ],
[ 22, 3, 6, 16 ], [ 22, 3, 8, 16 ], [ 22, 4, 1, 4 ], [ 22, 4, 3, 4 ],
[ 22, 4, 4, 12 ], [ 22, 4, 5, 8 ], [ 22, 4, 6, 4 ], [ 22, 4, 7, 8 ],
[ 22, 4, 9, 8 ], [ 23, 2, 5, 16 ], [ 23, 6, 5, 8 ], [ 27, 1, 10, 32 ],
[ 27, 2, 9, 16 ], [ 27, 2, 14, 32 ], [ 27, 3, 2, 16 ], [ 27, 3, 3, 32 ],
[ 27, 3, 8, 16 ], [ 27, 3, 12, 16 ], [ 27, 4, 8, 16 ], [ 27, 5, 9, 16 ],
[ 27, 6, 8, 16 ], [ 27, 6, 9, 8 ], [ 27, 6, 14, 16 ], [ 27, 7, 9, 8 ],
[ 27, 7, 14, 16 ], [ 27, 8, 2, 8 ], [ 27, 8, 3, 16 ], [ 27, 8, 8, 16 ],
[ 27, 8, 12, 8 ], [ 27, 8, 17, 16 ], [ 27, 9, 2, 8 ], [ 27, 9, 3, 16 ],
[ 27, 9, 7, 8 ], [ 27, 10, 2, 16 ], [ 27, 10, 6, 8 ], [ 27, 10, 15, 16 ],
[ 27, 11, 2, 8 ], [ 27, 11, 3, 16 ], [ 27, 11, 8, 16 ], [ 27, 11, 12, 8 ],
[ 27, 12, 2, 16 ], [ 27, 12, 8, 16 ], [ 27, 13, 6, 16 ], [ 27, 13, 8, 8 ],
[ 27, 13, 13, 16 ], [ 27, 14, 3, 8 ], [ 27, 14, 5, 16 ], [ 27, 14, 10, 16 ],
[ 27, 14, 12, 8 ], [ 28, 2, 8, 32 ], [ 28, 5, 8, 16 ], [ 28, 6, 6, 16 ],
[ 29, 4, 5, 16 ], [ 29, 4, 9, 32 ], [ 29, 9, 5, 8 ], [ 29, 9, 9, 16 ],
[ 29, 12, 5, 16 ], [ 30, 4, 12, 32 ], [ 30, 4, 22, 32 ], [ 30, 4, 26, 32 ],
[ 30, 8, 5, 16 ], [ 30, 8, 19, 16 ], [ 30, 8, 21, 16 ], [ 30, 11, 9, 16 ],
[ 30, 11, 22, 16 ], [ 30, 11, 25, 16 ], [ 30, 11, 31, 16 ],
[ 30, 12, 12, 16 ], [ 30, 12, 22, 16 ], [ 30, 12, 26, 16 ],
[ 30, 13, 6, 16 ], [ 30, 13, 16, 16 ], [ 31, 9, 44, 32 ], [ 31, 10, 8, 32 ],
[ 31, 10, 12, 32 ], [ 31, 11, 47, 32 ], [ 31, 12, 6, 32 ],
[ 31, 12, 12, 32 ], [ 31, 13, 7, 32 ], [ 31, 13, 10, 32 ],
[ 31, 13, 12, 32 ], [ 31, 14, 43, 32 ], [ 31, 15, 9, 32 ],
[ 31, 16, 44, 32 ], [ 31, 21, 17, 32 ], [ 31, 23, 48, 32 ],
[ 31, 29, 21, 32 ], [ 31, 29, 48, 32 ], [ 31, 29, 54, 32 ] ]
k = 45: F-action on Pi is () [31,2,45]
Dynkin type is (A_0(q) + T(phi1 phi2^5)).2
Order of center |Z^F|: phi1 phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1^2 ( q^2-4*q-1 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 phi2 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 7 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 8 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 4 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 6 ],
[ 6, 1, 2, 8 ], [ 7, 1, 4, 16 ], [ 7, 2, 4, 16 ], [ 7, 3, 4, 16 ],
[ 7, 4, 4, 16 ], [ 7, 5, 4, 16 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 8 ],
[ 9, 1, 2, 24 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 20 ], [ 9, 3, 1, 4 ],
[ 9, 3, 2, 12 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 6 ],
[ 9, 5, 2, 10 ], [ 12, 1, 2, 4 ], [ 12, 1, 3, 8 ], [ 12, 2, 2, 2 ],
[ 12, 2, 3, 8 ], [ 12, 3, 2, 12 ], [ 12, 4, 2, 2 ], [ 12, 4, 3, 12 ],
[ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], [ 13, 2, 3, 8 ], [ 13, 2, 4, 16 ],
[ 14, 1, 2, 16 ], [ 14, 2, 2, 24 ], [ 15, 1, 3, 16 ], [ 15, 1, 4, 8 ],
[ 16, 1, 3, 16 ], [ 16, 1, 5, 32 ], [ 16, 2, 3, 8 ], [ 16, 2, 5, 32 ],
[ 16, 3, 3, 8 ], [ 16, 3, 5, 16 ], [ 16, 4, 3, 24 ], [ 16, 4, 5, 16 ],
[ 16, 5, 2, 8 ], [ 16, 5, 3, 16 ], [ 16, 5, 4, 8 ], [ 16, 6, 2, 8 ],
[ 16, 6, 3, 16 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ], [ 16, 7, 3, 16 ],
[ 16, 7, 4, 8 ], [ 16, 8, 4, 32 ], [ 16, 9, 3, 12 ], [ 16, 9, 5, 16 ],
[ 16, 10, 2, 4 ], [ 16, 10, 3, 16 ], [ 16, 10, 4, 4 ], [ 16, 11, 3, 8 ],
[ 16, 11, 5, 32 ], [ 16, 12, 2, 12 ], [ 16, 12, 3, 8 ], [ 16, 12, 4, 12 ],
[ 16, 13, 3, 12 ], [ 16, 13, 5, 8 ], [ 16, 14, 4, 24 ], [ 16, 15, 3, 4 ],
[ 16, 15, 5, 8 ], [ 16, 16, 3, 4 ], [ 16, 16, 5, 8 ], [ 16, 17, 4, 24 ],
[ 21, 1, 7, 16 ], [ 21, 2, 9, 16 ], [ 21, 2, 10, 16 ], [ 21, 3, 8, 8 ],
[ 21, 3, 10, 16 ], [ 21, 4, 9, 8 ], [ 21, 5, 9, 8 ], [ 21, 5, 10, 16 ],
[ 21, 6, 9, 8 ], [ 21, 6, 10, 24 ], [ 21, 7, 9, 8 ], [ 21, 7, 10, 24 ],
[ 22, 1, 3, 16 ], [ 22, 1, 5, 16 ], [ 22, 1, 6, 16 ], [ 22, 2, 3, 16 ],
[ 22, 2, 5, 8 ], [ 22, 2, 6, 32 ], [ 22, 3, 2, 24 ], [ 22, 3, 4, 24 ],
[ 22, 4, 3, 24 ], [ 22, 4, 5, 8 ], [ 22, 4, 6, 32 ], [ 23, 2, 7, 16 ],
[ 23, 6, 7, 8 ], [ 27, 1, 10, 32 ], [ 27, 2, 9, 48 ], [ 27, 3, 8, 16 ],
[ 27, 3, 12, 32 ], [ 27, 3, 13, 32 ], [ 27, 4, 8, 16 ], [ 27, 5, 9, 16 ],
[ 27, 6, 9, 24 ], [ 27, 6, 10, 16 ], [ 27, 7, 9, 24 ], [ 27, 8, 8, 16 ],
[ 27, 8, 12, 48 ], [ 27, 8, 13, 16 ], [ 27, 9, 7, 16 ], [ 27, 9, 12, 32 ],
[ 27, 10, 6, 24 ], [ 27, 10, 10, 16 ], [ 27, 11, 8, 16 ],
[ 27, 11, 12, 16 ], [ 27, 11, 13, 16 ], [ 27, 12, 8, 16 ],
[ 27, 12, 10, 48 ], [ 27, 13, 8, 24 ], [ 27, 13, 10, 16 ],
[ 27, 14, 10, 16 ], [ 27, 14, 12, 16 ], [ 27, 14, 13, 16 ],
[ 28, 2, 10, 32 ], [ 28, 5, 10, 16 ], [ 28, 6, 10, 48 ], [ 29, 4, 7, 16 ],
[ 29, 4, 11, 32 ], [ 29, 9, 7, 8 ], [ 29, 9, 11, 16 ], [ 29, 12, 7, 16 ],
[ 30, 4, 14, 32 ], [ 30, 4, 24, 32 ], [ 30, 4, 28, 32 ], [ 30, 8, 16, 32 ],
[ 30, 8, 30, 16 ], [ 30, 8, 32, 32 ], [ 30, 11, 11, 16 ],
[ 30, 11, 23, 16 ], [ 30, 11, 27, 16 ], [ 30, 11, 30, 16 ],
[ 30, 12, 14, 16 ], [ 30, 12, 24, 16 ], [ 30, 12, 28, 16 ],
[ 30, 13, 10, 48 ], [ 30, 13, 20, 48 ], [ 31, 9, 45, 32 ],
[ 31, 10, 24, 32 ], [ 31, 10, 55, 64 ], [ 31, 11, 46, 32 ],
[ 31, 12, 48, 32 ], [ 31, 12, 54, 32 ], [ 31, 13, 51, 32 ],
[ 31, 13, 54, 32 ], [ 31, 13, 56, 32 ], [ 31, 14, 44, 96 ],
[ 31, 15, 49, 32 ], [ 31, 16, 37, 32 ], [ 31, 21, 20, 32 ],
[ 31, 23, 44, 32 ], [ 31, 29, 23, 32 ], [ 31, 29, 50, 32 ],
[ 31, 29, 56, 32 ] ]
k = 46: F-action on Pi is () [31,2,46]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1^2 ( q^2-2*q-7 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi2^2 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 3, 2, 1, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 1, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 1, 4 ],
[ 3, 4, 2, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ],
[ 4, 1, 2, 4 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 4 ], [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ], [ 7, 1, 3, 16 ],
[ 7, 1, 4, 16 ], [ 7, 2, 1, 8 ], [ 7, 2, 2, 8 ], [ 7, 2, 3, 8 ],
[ 7, 2, 4, 8 ], [ 7, 3, 1, 8 ], [ 7, 3, 2, 8 ], [ 7, 3, 3, 8 ],
[ 7, 3, 4, 8 ], [ 7, 4, 1, 8 ], [ 7, 4, 2, 8 ], [ 7, 4, 3, 8 ],
[ 7, 4, 4, 8 ], [ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ],
[ 7, 5, 4, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ],
[ 9, 2, 2, 8 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ], [ 12, 1, 1, 8 ],
[ 12, 1, 3, 8 ], [ 12, 1, 4, 16 ], [ 12, 2, 1, 4 ], [ 12, 2, 2, 2 ],
[ 12, 2, 3, 4 ], [ 12, 2, 4, 8 ], [ 12, 3, 1, 4 ], [ 12, 3, 2, 4 ],
[ 12, 3, 3, 8 ], [ 12, 3, 4, 8 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ],
[ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ],
[ 13, 2, 2, 8 ], [ 13, 2, 3, 8 ], [ 15, 1, 4, 16 ], [ 16, 1, 1, 32 ],
[ 16, 1, 2, 32 ], [ 16, 1, 5, 32 ], [ 16, 2, 1, 16 ], [ 16, 2, 2, 16 ],
[ 16, 2, 3, 8 ], [ 16, 2, 5, 16 ], [ 16, 2, 7, 16 ], [ 16, 3, 1, 16 ],
[ 16, 3, 2, 16 ], [ 16, 3, 5, 16 ], [ 16, 4, 1, 16 ], [ 16, 4, 2, 16 ],
[ 16, 4, 5, 16 ], [ 16, 5, 1, 16 ], [ 16, 5, 3, 16 ], [ 16, 6, 1, 16 ],
[ 16, 6, 3, 16 ], [ 16, 7, 1, 16 ], [ 16, 7, 3, 16 ], [ 16, 8, 1, 16 ],
[ 16, 8, 2, 16 ], [ 16, 8, 3, 16 ], [ 16, 8, 4, 16 ], [ 16, 8, 6, 16 ],
[ 16, 8, 7, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 2, 8 ], [ 16, 9, 3, 4 ],
[ 16, 9, 5, 8 ], [ 16, 9, 7, 8 ], [ 16, 10, 1, 8 ], [ 16, 10, 2, 4 ],
[ 16, 10, 3, 8 ], [ 16, 10, 4, 4 ], [ 16, 10, 6, 8 ], [ 16, 10, 8, 8 ],
[ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ], [ 16, 11, 3, 8 ], [ 16, 11, 5, 8 ],
[ 16, 11, 7, 8 ], [ 16, 11, 8, 16 ], [ 16, 12, 1, 8 ], [ 16, 12, 3, 8 ],
[ 16, 13, 1, 8 ], [ 16, 13, 2, 16 ], [ 16, 13, 5, 8 ], [ 16, 14, 1, 8 ],
[ 16, 14, 2, 8 ], [ 16, 14, 3, 8 ], [ 16, 14, 4, 8 ], [ 16, 15, 1, 8 ],
[ 16, 15, 2, 16 ], [ 16, 15, 5, 8 ], [ 16, 16, 1, 8 ], [ 16, 16, 2, 16 ],
[ 16, 16, 5, 8 ], [ 16, 17, 1, 8 ], [ 16, 17, 2, 8 ], [ 16, 17, 3, 8 ],
[ 16, 17, 4, 8 ], [ 21, 1, 2, 32 ], [ 21, 1, 3, 32 ], [ 21, 2, 3, 16 ],
[ 21, 2, 4, 16 ], [ 21, 2, 6, 16 ], [ 21, 2, 8, 16 ], [ 21, 3, 2, 16 ],
[ 21, 3, 3, 8 ], [ 21, 3, 5, 16 ], [ 21, 3, 6, 16 ], [ 21, 3, 7, 16 ],
[ 21, 3, 8, 8 ], [ 21, 4, 3, 16 ], [ 21, 4, 6, 16 ], [ 21, 5, 2, 4 ],
[ 21, 5, 3, 8 ], [ 21, 5, 4, 8 ], [ 21, 5, 6, 8 ], [ 21, 5, 8, 8 ],
[ 21, 5, 9, 4 ], [ 21, 6, 2, 8 ], [ 21, 6, 3, 8 ], [ 21, 6, 5, 8 ],
[ 21, 6, 6, 8 ], [ 21, 6, 7, 8 ], [ 21, 6, 9, 8 ], [ 21, 7, 2, 8 ],
[ 21, 7, 3, 8 ], [ 21, 7, 6, 8 ], [ 21, 7, 9, 8 ], [ 22, 1, 3, 32 ],
[ 22, 1, 4, 32 ], [ 22, 2, 2, 8 ], [ 22, 2, 3, 16 ], [ 22, 2, 4, 16 ],
[ 22, 2, 5, 8 ], [ 22, 3, 2, 16 ], [ 22, 3, 3, 16 ], [ 22, 4, 2, 8 ],
[ 22, 4, 3, 8 ], [ 22, 4, 4, 8 ], [ 22, 4, 5, 8 ], [ 27, 1, 3, 64 ],
[ 27, 2, 3, 32 ], [ 27, 2, 6, 32 ], [ 27, 3, 3, 32 ], [ 27, 3, 4, 32 ],
[ 27, 3, 6, 16 ], [ 27, 3, 8, 16 ], [ 27, 3, 11, 32 ], [ 27, 3, 19, 32 ],
[ 27, 4, 2, 32 ], [ 27, 4, 5, 32 ], [ 27, 5, 3, 32 ], [ 27, 6, 2, 8 ],
[ 27, 6, 3, 16 ], [ 27, 6, 4, 16 ], [ 27, 6, 6, 16 ], [ 27, 6, 8, 16 ],
[ 27, 6, 9, 8 ], [ 27, 6, 14, 16 ], [ 27, 6, 17, 16 ], [ 27, 7, 3, 16 ],
[ 27, 7, 6, 16 ], [ 27, 8, 3, 16 ], [ 27, 8, 4, 16 ], [ 27, 8, 6, 16 ],
[ 27, 8, 8, 16 ], [ 27, 8, 11, 16 ], [ 27, 8, 19, 32 ], [ 27, 9, 2, 8 ],
[ 27, 9, 3, 16 ], [ 27, 9, 4, 16 ], [ 27, 9, 7, 8 ], [ 27, 9, 15, 16 ],
[ 27, 10, 2, 16 ], [ 27, 10, 3, 16 ], [ 27, 10, 4, 16 ], [ 27, 10, 5, 8 ],
[ 27, 10, 6, 8 ], [ 27, 10, 9, 16 ], [ 27, 10, 15, 16 ], [ 27, 10, 16, 16 ],
[ 27, 11, 3, 16 ], [ 27, 11, 4, 16 ], [ 27, 11, 6, 16 ], [ 27, 11, 8, 16 ],
[ 27, 11, 11, 16 ], [ 27, 11, 19, 32 ], [ 27, 12, 2, 16 ],
[ 27, 12, 3, 16 ], [ 27, 12, 5, 16 ], [ 27, 12, 8, 16 ], [ 27, 12, 13, 32 ],
[ 27, 12, 18, 32 ], [ 27, 13, 2, 16 ], [ 27, 13, 3, 8 ], [ 27, 13, 5, 16 ],
[ 27, 13, 6, 16 ], [ 27, 13, 7, 16 ], [ 27, 13, 8, 8 ], [ 27, 13, 13, 16 ],
[ 27, 13, 18, 16 ], [ 27, 14, 2, 16 ], [ 27, 14, 5, 16 ], [ 27, 14, 8, 16 ],
[ 27, 14, 10, 16 ], [ 27, 14, 11, 16 ], [ 27, 14, 22, 32 ],
[ 29, 4, 6, 16 ], [ 29, 4, 8, 16 ], [ 29, 9, 6, 8 ], [ 29, 9, 8, 8 ],
[ 30, 4, 13, 32 ], [ 30, 4, 17, 32 ], [ 30, 8, 14, 16 ], [ 30, 8, 19, 16 ],
[ 30, 11, 10, 16 ], [ 30, 11, 12, 16 ], [ 30, 11, 18, 16 ],
[ 30, 11, 20, 16 ], [ 30, 12, 13, 16 ], [ 30, 12, 17, 16 ],
[ 30, 13, 9, 32 ], [ 30, 13, 12, 32 ], [ 31, 9, 46, 32 ],
[ 31, 10, 12, 32 ], [ 31, 10, 15, 32 ], [ 31, 10, 16, 32 ],
[ 31, 11, 42, 32 ], [ 31, 12, 17, 32 ], [ 31, 12, 31, 32 ],
[ 31, 13, 15, 32 ], [ 31, 13, 21, 32 ], [ 31, 14, 46, 64 ],
[ 31, 14, 47, 64 ], [ 31, 15, 13, 64 ], [ 31, 15, 16, 64 ],
[ 31, 16, 36, 32 ], [ 31, 21, 9, 64 ], [ 31, 21, 23, 64 ],
[ 31, 23, 36, 32 ], [ 31, 29, 8, 32 ], [ 31, 29, 46, 32 ] ]
k = 47: F-action on Pi is () [31,2,47]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^3-3*q^2-17*q+51 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^3-3*q^2-17*q+51 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 2, 3, 8 ],
[ 3, 5, 3, 4 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 4 ], [ 8, 1, 1, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 8 ],
[ 9, 2, 2, 8 ], [ 9, 2, 5, 16 ], [ 9, 2, 8, 16 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 4 ], [ 9, 5, 5, 8 ], [ 9, 5, 8, 8 ], [ 12, 1, 2, 8 ],
[ 12, 2, 2, 6 ], [ 12, 4, 2, 6 ], [ 15, 1, 1, 8 ], [ 15, 1, 2, 16 ],
[ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 1, 3, 32 ], [ 16, 2, 3, 24 ],
[ 16, 2, 9, 16 ], [ 16, 3, 3, 16 ], [ 16, 4, 3, 16 ], [ 16, 4, 9, 32 ],
[ 16, 5, 2, 16 ], [ 16, 5, 4, 16 ], [ 16, 6, 2, 16 ], [ 16, 6, 4, 16 ],
[ 16, 7, 2, 16 ], [ 16, 7, 4, 16 ], [ 16, 9, 3, 12 ], [ 16, 9, 9, 24 ],
[ 16, 10, 2, 12 ], [ 16, 10, 4, 12 ], [ 16, 10, 9, 8 ], [ 16, 10, 16, 8 ],
[ 16, 11, 3, 24 ], [ 16, 12, 2, 8 ], [ 16, 12, 4, 8 ], [ 16, 12, 9, 16 ],
[ 16, 12, 16, 16 ], [ 16, 13, 3, 8 ], [ 16, 13, 9, 16 ], [ 16, 15, 3, 8 ],
[ 16, 16, 3, 8 ], [ 22, 1, 2, 16 ], [ 22, 1, 5, 16 ], [ 22, 2, 2, 16 ],
[ 22, 2, 5, 16 ], [ 22, 4, 2, 16 ], [ 22, 4, 5, 16 ], [ 23, 2, 4, 8 ],
[ 23, 2, 8, 8 ], [ 23, 6, 4, 4 ], [ 23, 6, 8, 4 ], [ 27, 1, 12, 32 ],
[ 27, 3, 7, 32 ], [ 27, 5, 8, 16 ], [ 27, 8, 7, 32 ], [ 27, 9, 6, 24 ],
[ 27, 9, 10, 16 ], [ 27, 11, 7, 32 ], [ 27, 14, 6, 32 ], [ 29, 4, 4, 16 ],
[ 29, 4, 6, 16 ], [ 29, 4, 12, 16 ], [ 29, 4, 16, 32 ], [ 29, 9, 4, 8 ],
[ 29, 9, 6, 8 ], [ 29, 9, 12, 8 ], [ 29, 9, 16, 16 ], [ 29, 12, 4, 8 ],
[ 29, 12, 8, 8 ], [ 29, 12, 12, 16 ], [ 29, 12, 16, 16 ], [ 30, 4, 11, 32 ],
[ 30, 4, 20, 32 ], [ 30, 8, 15, 32 ], [ 30, 8, 28, 32 ], [ 30, 11, 8, 16 ],
[ 30, 11, 16, 16 ], [ 30, 11, 21, 16 ], [ 30, 11, 29, 16 ],
[ 30, 12, 11, 16 ], [ 30, 12, 20, 16 ], [ 31, 9, 47, 32 ],
[ 31, 10, 18, 64 ], [ 31, 11, 43, 32 ], [ 31, 12, 19, 32 ],
[ 31, 12, 35, 32 ], [ 31, 12, 38, 32 ], [ 31, 12, 42, 32 ],
[ 31, 13, 18, 32 ], [ 31, 13, 28, 32 ], [ 31, 16, 47, 32 ],
[ 31, 23, 46, 32 ], [ 31, 29, 18, 32 ], [ 31, 29, 28, 32 ] ]
k = 48: F-action on Pi is () [31,2,48]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^3 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^3-9*q^2+19*q+5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^3-9*q^2+19*q-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 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 2, 2, 2, 4 ],
[ 3, 1, 1, 8 ], [ 3, 2, 1, 4 ], [ 3, 2, 2, 4 ], [ 3, 3, 1, 4 ],
[ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 4 ],
[ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 6 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 2, 2, 8 ],
[ 7, 3, 1, 8 ], [ 7, 3, 4, 8 ], [ 7, 4, 1, 8 ], [ 7, 4, 3, 8 ],
[ 7, 5, 1, 4 ], [ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ],
[ 8, 1, 1, 8 ], [ 9, 1, 1, 24 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 12 ],
[ 9, 2, 2, 4 ], [ 9, 2, 3, 8 ], [ 9, 2, 4, 8 ], [ 9, 3, 1, 12 ],
[ 9, 3, 2, 4 ], [ 9, 4, 1, 12 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 6 ],
[ 9, 5, 2, 2 ], [ 9, 5, 3, 4 ], [ 9, 5, 4, 4 ], [ 12, 1, 1, 8 ],
[ 12, 1, 2, 4 ], [ 12, 2, 1, 4 ], [ 12, 2, 2, 2 ], [ 12, 2, 3, 4 ],
[ 12, 3, 1, 4 ], [ 12, 3, 4, 8 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ],
[ 12, 4, 3, 2 ], [ 12, 4, 4, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ],
[ 13, 2, 1, 4 ], [ 13, 2, 2, 4 ], [ 13, 2, 3, 12 ], [ 13, 2, 4, 4 ],
[ 14, 1, 1, 16 ], [ 14, 2, 1, 8 ], [ 14, 2, 3, 16 ], [ 15, 1, 1, 16 ],
[ 15, 1, 4, 8 ], [ 16, 1, 1, 32 ], [ 16, 1, 3, 16 ], [ 16, 2, 1, 16 ],
[ 16, 2, 3, 8 ], [ 16, 2, 5, 16 ], [ 16, 3, 1, 16 ], [ 16, 3, 3, 8 ],
[ 16, 4, 1, 16 ], [ 16, 4, 3, 8 ], [ 16, 4, 7, 16 ], [ 16, 5, 1, 16 ],
[ 16, 5, 2, 8 ], [ 16, 5, 4, 8 ], [ 16, 6, 1, 16 ], [ 16, 6, 2, 8 ],
[ 16, 6, 4, 8 ], [ 16, 7, 1, 16 ], [ 16, 7, 2, 8 ], [ 16, 7, 4, 8 ],
[ 16, 8, 1, 16 ], [ 16, 8, 2, 16 ], [ 16, 9, 1, 8 ], [ 16, 9, 3, 4 ],
[ 16, 9, 5, 8 ], [ 16, 9, 7, 8 ], [ 16, 10, 1, 8 ], [ 16, 10, 2, 4 ],
[ 16, 10, 3, 8 ], [ 16, 10, 4, 4 ], [ 16, 11, 1, 8 ], [ 16, 11, 2, 8 ],
[ 16, 11, 3, 8 ], [ 16, 11, 5, 8 ], [ 16, 12, 1, 8 ], [ 16, 12, 2, 4 ],
[ 16, 12, 4, 4 ], [ 16, 12, 6, 8 ], [ 16, 12, 8, 8 ], [ 16, 13, 1, 8 ],
[ 16, 13, 3, 4 ], [ 16, 13, 7, 8 ], [ 16, 14, 1, 8 ], [ 16, 14, 3, 8 ],
[ 16, 15, 1, 8 ], [ 16, 15, 3, 4 ], [ 16, 16, 1, 8 ], [ 16, 16, 3, 4 ],
[ 16, 17, 1, 8 ], [ 16, 17, 3, 8 ], [ 21, 1, 5, 16 ], [ 21, 2, 2, 8 ],
[ 21, 2, 8, 16 ], [ 21, 2, 9, 8 ], [ 21, 3, 3, 8 ], [ 21, 3, 5, 16 ],
[ 21, 4, 2, 8 ], [ 21, 5, 2, 4 ], [ 21, 5, 3, 8 ], [ 21, 5, 8, 8 ],
[ 21, 5, 9, 4 ], [ 21, 6, 3, 8 ], [ 21, 6, 5, 8 ], [ 21, 6, 6, 8 ],
[ 21, 7, 2, 8 ], [ 21, 7, 3, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 16 ],
[ 22, 1, 4, 16 ], [ 22, 2, 1, 8 ], [ 22, 2, 2, 8 ], [ 22, 2, 3, 24 ],
[ 22, 2, 4, 8 ], [ 22, 2, 6, 8 ], [ 22, 3, 1, 8 ], [ 22, 3, 3, 8 ],
[ 22, 3, 5, 16 ], [ 22, 3, 7, 16 ], [ 22, 4, 1, 4 ], [ 22, 4, 2, 8 ],
[ 22, 4, 3, 12 ], [ 22, 4, 4, 4 ], [ 22, 4, 6, 4 ], [ 22, 4, 7, 8 ],
[ 22, 4, 9, 8 ], [ 23, 2, 3, 16 ], [ 23, 6, 3, 8 ], [ 27, 1, 6, 32 ],
[ 27, 2, 2, 16 ], [ 27, 2, 17, 32 ], [ 27, 3, 2, 16 ], [ 27, 3, 6, 16 ],
[ 27, 3, 11, 32 ], [ 27, 3, 12, 16 ], [ 27, 4, 3, 16 ], [ 27, 5, 2, 16 ],
[ 27, 6, 2, 8 ], [ 27, 6, 3, 16 ], [ 27, 6, 17, 16 ], [ 27, 7, 2, 8 ],
[ 27, 7, 17, 16 ], [ 27, 8, 2, 8 ], [ 27, 8, 6, 16 ], [ 27, 8, 11, 16 ],
[ 27, 8, 12, 8 ], [ 27, 8, 17, 16 ], [ 27, 9, 2, 8 ], [ 27, 9, 3, 16 ],
[ 27, 9, 7, 8 ], [ 27, 10, 5, 8 ], [ 27, 10, 9, 16 ], [ 27, 10, 16, 16 ],
[ 27, 11, 2, 8 ], [ 27, 11, 6, 16 ], [ 27, 11, 11, 16 ], [ 27, 11, 12, 8 ],
[ 27, 12, 3, 16 ], [ 27, 12, 5, 16 ], [ 27, 13, 3, 8 ], [ 27, 13, 5, 16 ],
[ 27, 13, 18, 16 ], [ 27, 14, 3, 8 ], [ 27, 14, 8, 16 ], [ 27, 14, 11, 16 ],
[ 27, 14, 12, 8 ], [ 28, 2, 3, 32 ], [ 28, 5, 3, 16 ], [ 28, 6, 3, 16 ],
[ 29, 4, 3, 32 ], [ 29, 4, 7, 16 ], [ 29, 9, 3, 16 ], [ 29, 9, 7, 8 ],
[ 29, 12, 3, 16 ], [ 30, 4, 5, 32 ], [ 30, 4, 10, 32 ], [ 30, 4, 19, 32 ],
[ 30, 8, 5, 16 ], [ 30, 8, 14, 16 ], [ 30, 8, 21, 16 ], [ 30, 11, 3, 16 ],
[ 30, 11, 7, 16 ], [ 30, 11, 14, 16 ], [ 30, 11, 19, 16 ],
[ 30, 12, 5, 16 ], [ 30, 12, 10, 16 ], [ 30, 12, 19, 16 ],
[ 30, 13, 3, 16 ], [ 30, 13, 13, 16 ], [ 31, 9, 48, 32 ], [ 31, 10, 8, 32 ],
[ 31, 10, 15, 32 ], [ 31, 11, 48, 32 ], [ 31, 12, 44, 32 ],
[ 31, 12, 46, 32 ], [ 31, 13, 46, 32 ], [ 31, 13, 48, 32 ],
[ 31, 13, 49, 32 ], [ 31, 14, 42, 32 ], [ 31, 15, 42, 32 ],
[ 31, 16, 45, 32 ], [ 31, 21, 15, 32 ], [ 31, 23, 47, 32 ],
[ 31, 29, 6, 32 ], [ 31, 29, 12, 32 ], [ 31, 29, 15, 32 ] ]
k = 49: F-action on Pi is () [31,2,49]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1 phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q^2-9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q^3-3*q^2-5*q+15 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 2, 8 ],
[ 3, 2, 2, 4 ], [ 3, 3, 2, 4 ], [ 3, 4, 2, 4 ], [ 3, 5, 2, 2 ],
[ 4, 1, 2, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 6 ],
[ 6, 1, 2, 8 ], [ 7, 1, 4, 16 ], [ 7, 2, 4, 8 ], [ 7, 3, 4, 8 ],
[ 7, 4, 4, 8 ], [ 7, 5, 4, 4 ], [ 8, 1, 2, 8 ], [ 9, 1, 1, 8 ],
[ 9, 1, 2, 24 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 12 ], [ 9, 2, 5, 8 ],
[ 9, 2, 7, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 12 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 12 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 6 ], [ 9, 5, 5, 4 ],
[ 9, 5, 7, 4 ], [ 12, 1, 2, 4 ], [ 12, 1, 3, 8 ], [ 12, 2, 2, 4 ],
[ 12, 2, 3, 4 ], [ 12, 3, 2, 4 ], [ 12, 4, 2, 4 ], [ 12, 4, 3, 2 ],
[ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], [ 13, 2, 3, 4 ], [ 13, 2, 4, 4 ],
[ 14, 1, 2, 16 ], [ 14, 2, 2, 8 ], [ 15, 1, 3, 16 ], [ 15, 1, 4, 8 ],
[ 16, 1, 3, 16 ], [ 16, 1, 5, 32 ], [ 16, 2, 3, 16 ], [ 16, 2, 5, 16 ],
[ 16, 3, 3, 8 ], [ 16, 3, 5, 16 ], [ 16, 4, 3, 8 ], [ 16, 4, 5, 16 ],
[ 16, 4, 12, 16 ], [ 16, 5, 2, 8 ], [ 16, 5, 3, 16 ], [ 16, 5, 4, 8 ],
[ 16, 6, 2, 8 ], [ 16, 6, 3, 16 ], [ 16, 6, 4, 8 ], [ 16, 7, 2, 8 ],
[ 16, 7, 3, 16 ], [ 16, 7, 4, 8 ], [ 16, 8, 4, 16 ], [ 16, 9, 3, 8 ],
[ 16, 9, 5, 8 ], [ 16, 9, 12, 8 ], [ 16, 10, 2, 8 ], [ 16, 10, 3, 8 ],
[ 16, 10, 4, 8 ], [ 16, 11, 3, 16 ], [ 16, 11, 5, 8 ], [ 16, 12, 2, 4 ],
[ 16, 12, 3, 8 ], [ 16, 12, 4, 4 ], [ 16, 12, 10, 8 ], [ 16, 12, 14, 8 ],
[ 16, 13, 3, 4 ], [ 16, 13, 5, 8 ], [ 16, 13, 12, 8 ], [ 16, 14, 4, 8 ],
[ 16, 14, 8, 16 ], [ 16, 15, 3, 4 ], [ 16, 15, 5, 8 ], [ 16, 16, 3, 4 ],
[ 16, 16, 5, 8 ], [ 16, 17, 4, 8 ], [ 21, 1, 7, 16 ], [ 21, 2, 9, 8 ],
[ 21, 3, 8, 16 ], [ 21, 4, 9, 8 ], [ 21, 5, 9, 8 ], [ 21, 6, 9, 16 ],
[ 21, 7, 9, 16 ], [ 22, 1, 3, 16 ], [ 22, 1, 5, 16 ], [ 22, 1, 6, 16 ],
[ 22, 2, 2, 4 ], [ 22, 2, 3, 8 ], [ 22, 2, 5, 20 ], [ 22, 2, 6, 8 ],
[ 22, 3, 2, 8 ], [ 22, 3, 4, 8 ], [ 22, 4, 2, 4 ], [ 22, 4, 3, 4 ],
[ 22, 4, 5, 20 ], [ 22, 4, 6, 4 ], [ 23, 2, 6, 8 ], [ 23, 2, 8, 8 ],
[ 23, 6, 6, 4 ], [ 23, 6, 8, 4 ], [ 27, 1, 10, 32 ], [ 27, 2, 9, 16 ],
[ 27, 3, 7, 8 ], [ 27, 3, 8, 32 ], [ 27, 3, 12, 16 ], [ 27, 4, 8, 16 ],
[ 27, 5, 9, 16 ], [ 27, 6, 9, 16 ], [ 27, 7, 9, 8 ], [ 27, 8, 7, 8 ],
[ 27, 8, 8, 32 ], [ 27, 8, 12, 8 ], [ 27, 9, 6, 8 ], [ 27, 9, 7, 16 ],
[ 27, 10, 6, 16 ], [ 27, 11, 7, 8 ], [ 27, 11, 8, 32 ], [ 27, 11, 12, 8 ],
[ 27, 12, 8, 32 ], [ 27, 13, 8, 16 ], [ 27, 14, 6, 8 ], [ 27, 14, 10, 32 ],
[ 27, 14, 12, 8 ], [ 28, 2, 9, 16 ], [ 28, 5, 9, 8 ], [ 28, 6, 9, 16 ],
[ 29, 4, 6, 8 ], [ 29, 4, 8, 8 ], [ 29, 4, 10, 16 ], [ 29, 4, 12, 16 ],
[ 29, 9, 6, 4 ], [ 29, 9, 8, 4 ], [ 29, 9, 10, 8 ], [ 29, 9, 12, 8 ],
[ 29, 12, 6, 8 ], [ 29, 12, 8, 8 ], [ 30, 4, 13, 16 ], [ 30, 4, 20, 16 ],
[ 30, 4, 25, 16 ], [ 30, 4, 27, 16 ], [ 30, 8, 14, 8 ], [ 30, 8, 28, 16 ],
[ 30, 8, 30, 8 ], [ 30, 8, 31, 16 ], [ 30, 11, 10, 8 ], [ 30, 11, 12, 8 ],
[ 30, 11, 21, 8 ], [ 30, 11, 24, 8 ], [ 30, 11, 26, 8 ], [ 30, 11, 28, 8 ],
[ 30, 11, 29, 8 ], [ 30, 11, 32, 8 ], [ 30, 12, 13, 8 ], [ 30, 12, 20, 8 ],
[ 30, 12, 25, 8 ], [ 30, 12, 27, 8 ], [ 30, 13, 9, 16 ], [ 30, 13, 19, 16 ],
[ 31, 9, 52, 16 ], [ 31, 10, 19, 16 ], [ 31, 10, 23, 32 ],
[ 31, 11, 49, 16 ], [ 31, 12, 20, 16 ], [ 31, 12, 26, 16 ],
[ 31, 12, 34, 16 ], [ 31, 12, 40, 16 ], [ 31, 13, 19, 16 ],
[ 31, 13, 22, 16 ], [ 31, 13, 24, 16 ], [ 31, 13, 27, 16 ],
[ 31, 14, 50, 32 ], [ 31, 15, 19, 32 ], [ 31, 16, 52, 16 ],
[ 31, 21, 19, 32 ], [ 31, 23, 51, 16 ], [ 31, 29, 22, 16 ],
[ 31, 29, 24, 16 ], [ 31, 29, 49, 16 ], [ 31, 29, 55, 16 ] ]
k = 50: F-action on Pi is () [31,2,50]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^3 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/96 phi1 ( q^3-15*q^2+71*q-105 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/96 phi1 ( q^3-15*q^2+71*q-105 )
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, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 7 ],
[ 2, 2, 2, 8 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 12 ], [ 3, 2, 1, 8 ],
[ 3, 2, 2, 12 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 6 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 6 ], [ 3, 5, 1, 4 ], [ 3, 5, 2, 6 ], [ 4, 1, 1, 6 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 4 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 12 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 4 ], [ 7, 1, 3, 36 ],
[ 7, 1, 4, 12 ], [ 7, 2, 1, 8 ], [ 7, 2, 2, 4 ], [ 7, 2, 3, 24 ],
[ 7, 2, 4, 12 ], [ 7, 3, 1, 12 ], [ 7, 3, 2, 8 ], [ 7, 3, 3, 24 ],
[ 7, 3, 4, 12 ], [ 7, 4, 1, 24 ], [ 7, 4, 2, 8 ], [ 7, 4, 3, 36 ],
[ 7, 4, 4, 12 ], [ 7, 5, 1, 16 ], [ 7, 5, 2, 8 ], [ 7, 5, 3, 24 ],
[ 7, 5, 4, 12 ], [ 9, 1, 3, 48 ], [ 9, 2, 1, 24 ], [ 9, 2, 3, 48 ],
[ 9, 3, 3, 24 ], [ 9, 4, 3, 24 ], [ 9, 5, 1, 12 ], [ 9, 5, 3, 24 ],
[ 12, 1, 1, 24 ], [ 12, 1, 4, 12 ], [ 12, 2, 1, 12 ], [ 12, 2, 4, 8 ],
[ 12, 3, 1, 18 ], [ 12, 3, 2, 2 ], [ 12, 3, 3, 8 ], [ 12, 3, 4, 12 ],
[ 12, 4, 1, 12 ], [ 12, 4, 3, 2 ], [ 12, 4, 4, 8 ], [ 13, 1, 1, 24 ],
[ 13, 1, 3, 24 ], [ 13, 2, 1, 24 ], [ 13, 2, 3, 24 ], [ 14, 1, 3, 16 ],
[ 14, 2, 1, 8 ], [ 14, 2, 3, 16 ], [ 16, 1, 2, 24 ], [ 16, 1, 6, 96 ],
[ 16, 2, 2, 24 ], [ 16, 2, 6, 48 ], [ 16, 3, 2, 12 ], [ 16, 3, 6, 48 ],
[ 16, 4, 1, 48 ], [ 16, 4, 2, 36 ], [ 16, 4, 6, 96 ], [ 16, 5, 5, 48 ],
[ 16, 6, 5, 48 ], [ 16, 7, 5, 48 ], [ 16, 8, 1, 12 ], [ 16, 8, 2, 24 ],
[ 16, 8, 3, 24 ], [ 16, 8, 4, 12 ], [ 16, 8, 5, 72 ], [ 16, 8, 6, 36 ],
[ 16, 8, 7, 12 ], [ 16, 9, 1, 24 ], [ 16, 9, 2, 24 ], [ 16, 9, 6, 48 ],
[ 16, 10, 5, 24 ], [ 16, 11, 1, 12 ], [ 16, 11, 2, 24 ], [ 16, 11, 5, 12 ],
[ 16, 11, 6, 48 ], [ 16, 11, 7, 24 ], [ 16, 12, 1, 24 ], [ 16, 12, 5, 48 ],
[ 16, 13, 1, 24 ], [ 16, 13, 2, 36 ], [ 16, 13, 6, 48 ], [ 16, 14, 1, 36 ],
[ 16, 14, 2, 24 ], [ 16, 14, 3, 36 ], [ 16, 14, 4, 12 ], [ 16, 14, 5, 72 ],
[ 16, 15, 2, 12 ], [ 16, 15, 6, 24 ], [ 16, 16, 2, 12 ], [ 16, 16, 6, 24 ],
[ 16, 17, 1, 12 ], [ 16, 17, 2, 24 ], [ 16, 17, 3, 12 ], [ 16, 17, 4, 12 ],
[ 16, 17, 5, 48 ], [ 21, 1, 1, 48 ], [ 21, 1, 2, 48 ], [ 21, 2, 1, 48 ],
[ 21, 2, 4, 12 ], [ 21, 2, 6, 36 ], [ 21, 2, 8, 48 ], [ 21, 3, 1, 24 ],
[ 21, 3, 2, 4 ], [ 21, 3, 6, 24 ], [ 21, 3, 7, 36 ], [ 21, 4, 1, 24 ],
[ 21, 4, 6, 24 ], [ 21, 5, 1, 24 ], [ 21, 5, 4, 8 ], [ 21, 5, 6, 24 ],
[ 21, 5, 8, 24 ], [ 21, 6, 1, 36 ], [ 21, 6, 2, 8 ], [ 21, 6, 5, 12 ],
[ 21, 6, 6, 36 ], [ 21, 6, 7, 24 ], [ 21, 7, 1, 12 ], [ 21, 7, 3, 4 ],
[ 21, 7, 6, 24 ], [ 22, 1, 7, 48 ], [ 22, 2, 7, 48 ], [ 22, 3, 1, 24 ],
[ 22, 3, 2, 24 ], [ 22, 3, 5, 48 ], [ 22, 3, 6, 48 ], [ 22, 4, 1, 24 ],
[ 22, 4, 3, 24 ], [ 22, 4, 7, 48 ], [ 27, 1, 2, 96 ], [ 27, 2, 1, 48 ],
[ 27, 2, 6, 48 ], [ 27, 2, 11, 96 ], [ 27, 2, 16, 96 ], [ 27, 3, 4, 24 ],
[ 27, 3, 14, 48 ], [ 27, 3, 16, 96 ], [ 27, 4, 11, 48 ], [ 27, 4, 12, 48 ],
[ 27, 5, 12, 48 ], [ 27, 6, 1, 24 ], [ 27, 6, 4, 12 ], [ 27, 6, 6, 36 ],
[ 27, 6, 8, 24 ], [ 27, 6, 11, 72 ], [ 27, 6, 13, 48 ], [ 27, 6, 16, 48 ],
[ 27, 7, 1, 24 ], [ 27, 7, 6, 24 ], [ 27, 7, 11, 48 ], [ 27, 7, 16, 48 ],
[ 27, 8, 1, 48 ], [ 27, 8, 4, 36 ], [ 27, 8, 11, 48 ], [ 27, 8, 14, 72 ],
[ 27, 8, 16, 96 ], [ 27, 9, 4, 24 ], [ 27, 9, 13, 48 ], [ 27, 10, 1, 24 ],
[ 27, 10, 2, 24 ], [ 27, 10, 3, 12 ], [ 27, 10, 4, 36 ], [ 27, 10, 11, 48 ],
[ 27, 10, 12, 48 ], [ 27, 10, 13, 72 ], [ 27, 11, 4, 12 ],
[ 27, 11, 14, 24 ], [ 27, 11, 16, 48 ], [ 27, 12, 2, 24 ],
[ 27, 12, 5, 24 ], [ 27, 12, 11, 24 ], [ 27, 12, 12, 72 ],
[ 27, 13, 1, 24 ], [ 27, 13, 2, 12 ], [ 27, 13, 6, 24 ], [ 27, 13, 7, 36 ],
[ 27, 13, 11, 48 ], [ 27, 13, 12, 72 ], [ 27, 13, 16, 48 ],
[ 27, 14, 2, 12 ], [ 27, 14, 14, 48 ], [ 27, 14, 15, 24 ], [ 28, 2, 4, 16 ],
[ 28, 5, 4, 16 ], [ 28, 6, 3, 16 ], [ 30, 4, 2, 48 ], [ 30, 8, 2, 48 ],
[ 30, 12, 2, 48 ], [ 30, 13, 3, 48 ], [ 30, 13, 6, 48 ], [ 31, 9, 51, 48 ],
[ 31, 10, 4, 48 ], [ 31, 10, 25, 96 ], [ 31, 11, 51, 96 ],
[ 31, 13, 29, 96 ], [ 31, 14, 27, 96 ], [ 31, 14, 39, 96 ],
[ 31, 15, 21, 48 ], [ 31, 15, 26, 48 ], [ 31, 16, 50, 48 ],
[ 31, 21, 2, 48 ], [ 31, 21, 6, 48 ], [ 31, 23, 50, 96 ],
[ 31, 29, 29, 96 ] ]
k = 51: F-action on Pi is () [31,2,51]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^3 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q^3-5*q^2-q+21 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^4-6*q^3+4*q^2+30*q-45 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 1, 1, 8 ],
[ 3, 2, 1, 4 ], [ 3, 3, 1, 4 ], [ 3, 4, 1, 4 ], [ 3, 5, 1, 2 ],
[ 4, 1, 1, 4 ], [ 4, 2, 1, 2 ], [ 5, 1, 1, 6 ], [ 5, 1, 2, 2 ],
[ 6, 1, 1, 8 ], [ 7, 1, 1, 16 ], [ 7, 2, 1, 8 ], [ 7, 3, 1, 8 ],
[ 7, 4, 1, 8 ], [ 7, 5, 1, 4 ], [ 8, 1, 1, 8 ], [ 9, 1, 1, 24 ],
[ 9, 1, 2, 8 ], [ 9, 2, 1, 12 ], [ 9, 2, 2, 4 ], [ 9, 2, 6, 8 ],
[ 9, 2, 8, 8 ], [ 9, 3, 1, 12 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 12 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 2 ], [ 9, 5, 6, 4 ],
[ 9, 5, 8, 4 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 4 ], [ 12, 2, 1, 4 ],
[ 12, 2, 2, 4 ], [ 12, 3, 1, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 4 ],
[ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 2, 1, 4 ], [ 13, 2, 2, 4 ],
[ 14, 1, 1, 16 ], [ 14, 2, 1, 8 ], [ 15, 1, 1, 16 ], [ 15, 1, 4, 8 ],
[ 16, 1, 1, 32 ], [ 16, 1, 3, 16 ], [ 16, 2, 1, 16 ], [ 16, 2, 3, 16 ],
[ 16, 3, 1, 16 ], [ 16, 3, 3, 8 ], [ 16, 4, 1, 16 ], [ 16, 4, 3, 8 ],
[ 16, 4, 13, 16 ], [ 16, 5, 1, 16 ], [ 16, 5, 2, 8 ], [ 16, 5, 4, 8 ],
[ 16, 6, 1, 16 ], [ 16, 6, 2, 8 ], [ 16, 6, 4, 8 ], [ 16, 7, 1, 16 ],
[ 16, 7, 2, 8 ], [ 16, 7, 4, 8 ], [ 16, 8, 1, 16 ], [ 16, 9, 1, 8 ],
[ 16, 9, 3, 8 ], [ 16, 9, 13, 8 ], [ 16, 10, 1, 8 ], [ 16, 10, 2, 8 ],
[ 16, 10, 4, 8 ], [ 16, 11, 1, 8 ], [ 16, 11, 3, 16 ], [ 16, 12, 1, 8 ],
[ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ], [ 16, 12, 11, 8 ], [ 16, 12, 15, 8 ],
[ 16, 13, 1, 8 ], [ 16, 13, 3, 4 ], [ 16, 13, 13, 8 ], [ 16, 14, 1, 8 ],
[ 16, 14, 9, 16 ], [ 16, 15, 1, 8 ], [ 16, 15, 3, 4 ], [ 16, 16, 1, 8 ],
[ 16, 16, 3, 4 ], [ 16, 17, 1, 8 ], [ 21, 1, 5, 16 ], [ 21, 2, 2, 8 ],
[ 21, 3, 3, 16 ], [ 21, 4, 2, 8 ], [ 21, 5, 2, 8 ], [ 21, 6, 3, 16 ],
[ 21, 7, 2, 16 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 16 ], [ 22, 1, 4, 16 ],
[ 22, 2, 1, 8 ], [ 22, 2, 2, 20 ], [ 22, 2, 4, 8 ], [ 22, 2, 5, 4 ],
[ 22, 3, 1, 8 ], [ 22, 3, 3, 8 ], [ 22, 4, 1, 4 ], [ 22, 4, 2, 20 ],
[ 22, 4, 4, 4 ], [ 22, 4, 5, 4 ], [ 23, 2, 2, 8 ], [ 23, 2, 4, 8 ],
[ 23, 6, 2, 4 ], [ 23, 6, 4, 4 ], [ 27, 1, 6, 32 ], [ 27, 2, 2, 16 ],
[ 27, 3, 2, 16 ], [ 27, 3, 6, 32 ], [ 27, 3, 7, 8 ], [ 27, 4, 3, 16 ],
[ 27, 5, 2, 16 ], [ 27, 6, 2, 16 ], [ 27, 7, 2, 8 ], [ 27, 8, 2, 8 ],
[ 27, 8, 6, 32 ], [ 27, 8, 7, 8 ], [ 27, 9, 2, 16 ], [ 27, 9, 6, 8 ],
[ 27, 10, 5, 16 ], [ 27, 11, 2, 8 ], [ 27, 11, 6, 32 ], [ 27, 11, 7, 8 ],
[ 27, 12, 3, 32 ], [ 27, 13, 3, 16 ], [ 27, 14, 3, 8 ], [ 27, 14, 6, 8 ],
[ 27, 14, 8, 32 ], [ 28, 2, 2, 16 ], [ 28, 5, 2, 8 ], [ 28, 6, 2, 16 ],
[ 29, 4, 2, 16 ], [ 29, 4, 4, 16 ], [ 29, 4, 6, 8 ], [ 29, 4, 8, 8 ],
[ 29, 9, 2, 8 ], [ 29, 9, 4, 8 ], [ 29, 9, 6, 4 ], [ 29, 9, 8, 4 ],
[ 29, 12, 2, 8 ], [ 29, 12, 4, 8 ], [ 30, 4, 3, 16 ], [ 30, 4, 6, 16 ],
[ 30, 4, 11, 16 ], [ 30, 4, 17, 16 ], [ 30, 8, 3, 8 ], [ 30, 8, 12, 16 ],
[ 30, 8, 15, 16 ], [ 30, 8, 19, 8 ], [ 30, 11, 2, 8 ], [ 30, 11, 4, 8 ],
[ 30, 11, 5, 8 ], [ 30, 11, 8, 8 ], [ 30, 11, 13, 8 ], [ 30, 11, 16, 8 ],
[ 30, 11, 18, 8 ], [ 30, 11, 20, 8 ], [ 30, 12, 3, 8 ], [ 30, 12, 6, 8 ],
[ 30, 12, 11, 8 ], [ 30, 12, 17, 8 ], [ 30, 13, 2, 16 ], [ 30, 13, 12, 16 ],
[ 31, 9, 50, 16 ], [ 31, 10, 7, 16 ], [ 31, 10, 14, 32 ],
[ 31, 11, 50, 16 ], [ 31, 12, 16, 16 ], [ 31, 12, 18, 16 ],
[ 31, 12, 30, 16 ], [ 31, 12, 32, 16 ], [ 31, 13, 14, 16 ],
[ 31, 13, 16, 16 ], [ 31, 13, 17, 16 ], [ 31, 13, 25, 16 ],
[ 31, 14, 49, 32 ], [ 31, 15, 12, 32 ], [ 31, 16, 49, 16 ],
[ 31, 21, 13, 32 ], [ 31, 23, 52, 16 ], [ 31, 29, 5, 16 ],
[ 31, 29, 11, 16 ], [ 31, 29, 14, 16 ], [ 31, 29, 16, 16 ] ]
k = 52: F-action on Pi is () [31,2,52]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1 phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/96 phi1 ( q^3-11*q^2+39*q-45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/96 phi1 ( q^3-11*q^2+39*q-45 )
Fusion of maximal tori of C^F in those of G^F:
[ 3 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 1, 2, 8 ], [ 2, 2, 1, 7 ],
[ 2, 2, 2, 8 ], [ 3, 1, 1, 12 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 12 ],
[ 3, 2, 2, 8 ], [ 3, 3, 1, 6 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 6 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 6 ], [ 3, 5, 2, 4 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 6 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 4 ], [ 5, 1, 2, 12 ],
[ 6, 1, 2, 8 ], [ 7, 1, 1, 12 ], [ 7, 1, 2, 36 ], [ 7, 1, 3, 4 ],
[ 7, 1, 4, 12 ], [ 7, 2, 1, 12 ], [ 7, 2, 2, 24 ], [ 7, 2, 3, 4 ],
[ 7, 2, 4, 8 ], [ 7, 3, 1, 12 ], [ 7, 3, 2, 24 ], [ 7, 3, 3, 8 ],
[ 7, 3, 4, 12 ], [ 7, 4, 1, 12 ], [ 7, 4, 2, 36 ], [ 7, 4, 3, 8 ],
[ 7, 4, 4, 24 ], [ 7, 5, 1, 12 ], [ 7, 5, 2, 24 ], [ 7, 5, 3, 8 ],
[ 7, 5, 4, 16 ], [ 9, 1, 4, 48 ], [ 9, 2, 2, 24 ], [ 9, 2, 4, 48 ],
[ 9, 3, 4, 24 ], [ 9, 4, 4, 24 ], [ 9, 5, 2, 12 ], [ 9, 5, 4, 24 ],
[ 12, 1, 3, 24 ], [ 12, 1, 4, 12 ], [ 12, 2, 3, 12 ], [ 12, 2, 4, 8 ],
[ 12, 3, 1, 2 ], [ 12, 3, 2, 18 ], [ 12, 3, 3, 12 ], [ 12, 3, 4, 8 ],
[ 12, 4, 1, 2 ], [ 12, 4, 3, 12 ], [ 12, 4, 4, 8 ], [ 13, 1, 2, 24 ],
[ 13, 1, 4, 24 ], [ 13, 2, 2, 24 ], [ 13, 2, 4, 24 ], [ 14, 1, 4, 16 ],
[ 14, 2, 2, 8 ], [ 14, 2, 4, 16 ], [ 16, 1, 2, 24 ], [ 16, 1, 8, 96 ],
[ 16, 2, 2, 24 ], [ 16, 2, 8, 48 ], [ 16, 3, 2, 12 ], [ 16, 3, 8, 48 ],
[ 16, 4, 2, 36 ], [ 16, 4, 5, 48 ], [ 16, 4, 8, 96 ], [ 16, 5, 7, 48 ],
[ 16, 6, 7, 48 ], [ 16, 7, 7, 48 ], [ 16, 8, 1, 12 ], [ 16, 8, 2, 24 ],
[ 16, 8, 3, 24 ], [ 16, 8, 4, 12 ], [ 16, 8, 6, 12 ], [ 16, 8, 7, 36 ],
[ 16, 8, 8, 72 ], [ 16, 9, 2, 24 ], [ 16, 9, 5, 24 ], [ 16, 9, 8, 48 ],
[ 16, 10, 7, 24 ], [ 16, 11, 1, 12 ], [ 16, 11, 2, 24 ], [ 16, 11, 5, 12 ],
[ 16, 11, 7, 24 ], [ 16, 11, 10, 48 ], [ 16, 12, 3, 24 ], [ 16, 12, 7, 48 ],
[ 16, 13, 2, 36 ], [ 16, 13, 5, 24 ], [ 16, 13, 8, 48 ], [ 16, 14, 1, 12 ],
[ 16, 14, 2, 36 ], [ 16, 14, 3, 24 ], [ 16, 14, 4, 36 ], [ 16, 14, 6, 72 ],
[ 16, 15, 2, 12 ], [ 16, 15, 8, 24 ], [ 16, 16, 2, 12 ], [ 16, 16, 8, 24 ],
[ 16, 17, 1, 12 ], [ 16, 17, 2, 12 ], [ 16, 17, 3, 24 ], [ 16, 17, 4, 12 ],
[ 16, 17, 6, 48 ], [ 21, 1, 3, 48 ], [ 21, 1, 4, 48 ], [ 21, 2, 3, 48 ],
[ 21, 2, 4, 36 ], [ 21, 2, 6, 12 ], [ 21, 2, 10, 48 ], [ 21, 3, 2, 36 ],
[ 21, 3, 5, 24 ], [ 21, 3, 7, 4 ], [ 21, 3, 10, 24 ], [ 21, 4, 3, 24 ],
[ 21, 4, 10, 24 ], [ 21, 5, 3, 24 ], [ 21, 5, 4, 24 ], [ 21, 5, 6, 8 ],
[ 21, 5, 10, 24 ], [ 21, 6, 2, 36 ], [ 21, 6, 5, 24 ], [ 21, 6, 6, 8 ],
[ 21, 6, 7, 12 ], [ 21, 6, 10, 36 ], [ 21, 7, 3, 24 ], [ 21, 7, 6, 4 ],
[ 21, 7, 10, 12 ], [ 22, 1, 9, 48 ], [ 22, 2, 9, 48 ], [ 22, 3, 3, 24 ],
[ 22, 3, 4, 24 ], [ 22, 3, 7, 48 ], [ 22, 3, 8, 48 ], [ 22, 4, 4, 24 ],
[ 22, 4, 6, 24 ], [ 22, 4, 9, 48 ], [ 27, 1, 4, 96 ], [ 27, 2, 3, 48 ],
[ 27, 2, 10, 48 ], [ 27, 2, 15, 96 ], [ 27, 2, 18, 96 ], [ 27, 3, 4, 24 ],
[ 27, 3, 18, 96 ], [ 27, 3, 24, 48 ], [ 27, 4, 15, 48 ], [ 27, 4, 20, 48 ],
[ 27, 5, 16, 48 ], [ 27, 6, 3, 24 ], [ 27, 6, 4, 36 ], [ 27, 6, 6, 12 ],
[ 27, 6, 10, 24 ], [ 27, 6, 15, 48 ], [ 27, 6, 18, 48 ], [ 27, 6, 19, 72 ],
[ 27, 7, 3, 24 ], [ 27, 7, 10, 24 ], [ 27, 7, 15, 48 ], [ 27, 7, 18, 48 ],
[ 27, 8, 3, 48 ], [ 27, 8, 4, 36 ], [ 27, 8, 13, 48 ], [ 27, 8, 18, 96 ],
[ 27, 8, 24, 72 ], [ 27, 9, 4, 24 ], [ 27, 9, 16, 48 ], [ 27, 10, 3, 36 ],
[ 27, 10, 4, 12 ], [ 27, 10, 9, 24 ], [ 27, 10, 10, 24 ],
[ 27, 10, 14, 72 ], [ 27, 10, 19, 48 ], [ 27, 10, 20, 48 ],
[ 27, 11, 4, 12 ], [ 27, 11, 18, 48 ], [ 27, 11, 24, 24 ],
[ 27, 12, 2, 24 ], [ 27, 12, 5, 24 ], [ 27, 12, 15, 72 ],
[ 27, 12, 20, 24 ], [ 27, 13, 2, 36 ], [ 27, 13, 5, 24 ], [ 27, 13, 7, 12 ],
[ 27, 13, 10, 24 ], [ 27, 13, 15, 48 ], [ 27, 13, 17, 72 ],
[ 27, 13, 20, 48 ], [ 27, 14, 2, 12 ], [ 27, 14, 18, 48 ],
[ 27, 14, 24, 24 ], [ 28, 2, 6, 16 ], [ 28, 5, 6, 16 ], [ 28, 6, 6, 16 ],
[ 30, 4, 16, 48 ], [ 30, 8, 18, 48 ], [ 30, 12, 16, 48 ],
[ 30, 13, 13, 48 ], [ 30, 13, 16, 48 ], [ 31, 9, 49, 48 ],
[ 31, 10, 27, 48 ], [ 31, 10, 31, 96 ], [ 31, 11, 52, 96 ],
[ 31, 13, 31, 96 ], [ 31, 14, 34, 96 ], [ 31, 14, 40, 96 ],
[ 31, 15, 25, 48 ], [ 31, 15, 28, 48 ], [ 31, 16, 51, 48 ],
[ 31, 21, 22, 48 ], [ 31, 21, 46, 48 ], [ 31, 23, 49, 96 ],
[ 31, 29, 33, 96 ] ]
k = 53: F-action on Pi is () [31,2,53]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^3 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^3 ( q-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 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 4 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 3, 2, 1, 4 ],
[ 3, 2, 2, 4 ], [ 3, 3, 1, 2 ], [ 3, 3, 2, 2 ], [ 3, 4, 1, 2 ],
[ 3, 4, 2, 2 ], [ 3, 5, 1, 2 ], [ 3, 5, 2, 2 ], [ 4, 1, 1, 2 ],
[ 4, 1, 2, 2 ], [ 4, 2, 1, 2 ], [ 4, 2, 2, 2 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 1, 4 ],
[ 7, 1, 2, 4 ], [ 7, 1, 3, 4 ], [ 7, 1, 4, 4 ], [ 7, 2, 1, 4 ],
[ 7, 2, 2, 4 ], [ 7, 2, 3, 4 ], [ 7, 2, 4, 4 ], [ 7, 3, 1, 4 ],
[ 7, 3, 2, 4 ], [ 7, 3, 3, 4 ], [ 7, 3, 4, 4 ], [ 7, 4, 1, 4 ],
[ 7, 4, 2, 4 ], [ 7, 4, 3, 4 ], [ 7, 4, 4, 4 ], [ 7, 5, 1, 4 ],
[ 7, 5, 2, 4 ], [ 7, 5, 3, 4 ], [ 7, 5, 4, 4 ], [ 9, 1, 3, 8 ],
[ 9, 1, 4, 8 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 4 ], [ 9, 2, 3, 8 ],
[ 9, 2, 4, 8 ], [ 9, 3, 3, 4 ], [ 9, 3, 4, 4 ], [ 9, 4, 3, 4 ],
[ 9, 4, 4, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 9, 5, 3, 4 ],
[ 9, 5, 4, 4 ], [ 12, 1, 2, 4 ], [ 12, 1, 4, 4 ], [ 12, 2, 2, 2 ],
[ 12, 2, 4, 4 ], [ 12, 3, 1, 2 ], [ 12, 3, 2, 2 ], [ 12, 3, 3, 4 ],
[ 12, 3, 4, 4 ], [ 12, 4, 1, 2 ], [ 12, 4, 2, 2 ], [ 12, 4, 3, 2 ],
[ 12, 4, 4, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ],
[ 13, 1, 4, 4 ], [ 13, 2, 1, 4 ], [ 13, 2, 2, 4 ], [ 13, 2, 3, 4 ],
[ 13, 2, 4, 4 ], [ 14, 1, 3, 8 ], [ 14, 1, 4, 8 ], [ 14, 2, 1, 4 ],
[ 14, 2, 2, 4 ], [ 14, 2, 3, 8 ], [ 14, 2, 4, 8 ], [ 16, 1, 2, 8 ],
[ 16, 1, 7, 16 ], [ 16, 2, 2, 8 ], [ 16, 2, 7, 8 ], [ 16, 3, 2, 4 ],
[ 16, 3, 7, 8 ], [ 16, 4, 2, 4 ], [ 16, 4, 3, 8 ], [ 16, 4, 7, 16 ],
[ 16, 5, 6, 8 ], [ 16, 5, 8, 8 ], [ 16, 6, 6, 8 ], [ 16, 6, 8, 8 ],
[ 16, 7, 6, 8 ], [ 16, 7, 8, 8 ], [ 16, 8, 1, 4 ], [ 16, 8, 2, 8 ],
[ 16, 8, 3, 8 ], [ 16, 8, 4, 4 ], [ 16, 8, 6, 4 ], [ 16, 8, 7, 4 ],
[ 16, 9, 2, 4 ], [ 16, 9, 3, 4 ], [ 16, 9, 7, 8 ], [ 16, 10, 6, 4 ],
[ 16, 10, 8, 4 ], [ 16, 11, 1, 4 ], [ 16, 11, 2, 8 ], [ 16, 11, 5, 4 ],
[ 16, 11, 7, 4 ], [ 16, 11, 8, 8 ], [ 16, 12, 2, 4 ], [ 16, 12, 4, 4 ],
[ 16, 12, 6, 8 ], [ 16, 12, 8, 8 ], [ 16, 13, 2, 4 ], [ 16, 13, 3, 4 ],
[ 16, 13, 7, 8 ], [ 16, 14, 1, 4 ], [ 16, 14, 2, 4 ], [ 16, 14, 3, 4 ],
[ 16, 14, 4, 4 ], [ 16, 15, 2, 4 ], [ 16, 15, 7, 4 ], [ 16, 16, 2, 4 ],
[ 16, 16, 7, 4 ], [ 16, 17, 1, 4 ], [ 16, 17, 2, 4 ], [ 16, 17, 3, 4 ],
[ 16, 17, 4, 4 ], [ 21, 1, 5, 8 ], [ 21, 1, 7, 8 ], [ 21, 2, 2, 8 ],
[ 21, 2, 4, 4 ], [ 21, 2, 6, 4 ], [ 21, 2, 9, 8 ], [ 21, 3, 2, 4 ],
[ 21, 3, 3, 4 ], [ 21, 3, 7, 4 ], [ 21, 3, 8, 4 ], [ 21, 4, 2, 4 ],
[ 21, 4, 9, 4 ], [ 21, 5, 2, 4 ], [ 21, 5, 4, 4 ], [ 21, 5, 6, 4 ],
[ 21, 5, 9, 4 ], [ 21, 6, 2, 4 ], [ 21, 6, 3, 4 ], [ 21, 6, 5, 4 ],
[ 21, 6, 6, 4 ], [ 21, 6, 7, 4 ], [ 21, 6, 9, 4 ], [ 21, 7, 2, 4 ],
[ 21, 7, 3, 4 ], [ 21, 7, 6, 4 ], [ 21, 7, 9, 4 ], [ 22, 1, 7, 8 ],
[ 22, 1, 9, 8 ], [ 22, 2, 7, 8 ], [ 22, 2, 9, 8 ], [ 22, 3, 1, 4 ],
[ 22, 3, 2, 4 ], [ 22, 3, 3, 4 ], [ 22, 3, 4, 4 ], [ 22, 3, 5, 8 ],
[ 22, 3, 6, 8 ], [ 22, 3, 7, 8 ], [ 22, 3, 8, 8 ], [ 22, 4, 1, 4 ],
[ 22, 4, 3, 4 ], [ 22, 4, 4, 4 ], [ 22, 4, 6, 4 ], [ 22, 4, 7, 8 ],
[ 22, 4, 9, 8 ], [ 27, 1, 8, 16 ], [ 27, 2, 2, 8 ], [ 27, 2, 9, 8 ],
[ 27, 2, 14, 16 ], [ 27, 2, 17, 16 ], [ 27, 3, 4, 8 ], [ 27, 3, 17, 16 ],
[ 27, 3, 19, 8 ], [ 27, 4, 13, 8 ], [ 27, 4, 18, 8 ], [ 27, 5, 15, 8 ],
[ 27, 6, 2, 4 ], [ 27, 6, 4, 4 ], [ 27, 6, 6, 4 ], [ 27, 6, 9, 4 ],
[ 27, 6, 14, 8 ], [ 27, 6, 17, 8 ], [ 27, 7, 2, 4 ], [ 27, 7, 9, 4 ],
[ 27, 7, 14, 8 ], [ 27, 7, 17, 8 ], [ 27, 8, 2, 8 ], [ 27, 8, 4, 4 ],
[ 27, 8, 12, 8 ], [ 27, 8, 17, 16 ], [ 27, 8, 19, 8 ], [ 27, 9, 4, 8 ],
[ 27, 9, 15, 8 ], [ 27, 10, 3, 4 ], [ 27, 10, 4, 4 ], [ 27, 10, 5, 4 ],
[ 27, 10, 6, 4 ], [ 27, 10, 15, 8 ], [ 27, 10, 16, 8 ], [ 27, 11, 4, 4 ],
[ 27, 11, 17, 8 ], [ 27, 11, 19, 8 ], [ 27, 12, 2, 8 ], [ 27, 12, 5, 8 ],
[ 27, 12, 13, 8 ], [ 27, 12, 18, 8 ], [ 27, 13, 2, 4 ], [ 27, 13, 3, 4 ],
[ 27, 13, 7, 4 ], [ 27, 13, 8, 4 ], [ 27, 13, 13, 8 ], [ 27, 13, 18, 8 ],
[ 27, 14, 2, 4 ], [ 27, 14, 16, 8 ], [ 27, 14, 22, 8 ], [ 28, 2, 4, 8 ],
[ 28, 2, 6, 8 ], [ 28, 5, 4, 8 ], [ 28, 5, 6, 8 ], [ 28, 6, 3, 8 ],
[ 28, 6, 6, 8 ], [ 30, 4, 2, 8 ], [ 30, 4, 16, 8 ], [ 30, 8, 2, 8 ],
[ 30, 8, 18, 8 ], [ 30, 12, 2, 8 ], [ 30, 12, 16, 8 ], [ 30, 13, 3, 8 ],
[ 30, 13, 6, 8 ], [ 30, 13, 13, 8 ], [ 30, 13, 16, 8 ], [ 31, 9, 53, 8 ],
[ 31, 10, 16, 8 ], [ 31, 10, 28, 16 ], [ 31, 11, 53, 16 ],
[ 31, 13, 30, 16 ], [ 31, 13, 32, 16 ], [ 31, 14, 42, 16 ],
[ 31, 14, 43, 16 ], [ 31, 15, 24, 8 ], [ 31, 15, 27, 8 ], [ 31, 16, 53, 8 ],
[ 31, 21, 12, 8 ], [ 31, 21, 16, 8 ], [ 31, 23, 53, 16 ],
[ 31, 29, 31, 16 ], [ 31, 29, 35, 16 ] ]
j = 7: Omega of order 2, action on Pi: <()>
k = 1: F-action on Pi is () [31,7,1]
Dynkin type is (A_0(q) + T(phi1^6)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/192 ( q^3-21*q^2+143*q-315 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/192 ( q^3-21*q^2+131*q-231 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 4, 1, 8 ],
[ 3, 5, 1, 4 ], [ 5, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ],
[ 9, 2, 1, 12 ], [ 9, 3, 1, 12 ], [ 9, 4, 1, 36 ], [ 9, 5, 1, 18 ],
[ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ], [ 11, 2, 1, 4 ], [ 15, 1, 1, 24 ],
[ 16, 5, 1, 48 ], [ 16, 10, 1, 24 ], [ 16, 12, 1, 24 ], [ 16, 15, 1, 48 ],
[ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ], [ 19, 3, 1, 32 ], [ 19, 5, 1, 16 ],
[ 20, 2, 1, 12 ], [ 23, 3, 1, 24 ], [ 23, 6, 1, 12 ], [ 25, 1, 1, 48 ],
[ 25, 2, 1, 24 ], [ 25, 3, 1, 24 ], [ 26, 2, 1, 24 ], [ 26, 3, 1, 48 ],
[ 29, 2, 1, 48 ], [ 29, 6, 1, 96 ], [ 29, 9, 1, 24 ], [ 29, 10, 1, 24 ],
[ 29, 11, 1, 48 ], [ 29, 12, 1, 48 ], [ 29, 13, 1, 48 ], [ 30, 6, 1, 96 ],
[ 30, 10, 1, 96 ], [ 30, 11, 1, 48 ], [ 31, 12, 1, 96 ], [ 31, 19, 1, 192 ],
[ 31, 22, 1, 96 ], [ 31, 24, 1, 96 ], [ 31, 28, 1, 96 ], [ 31, 31, 1, 96 ],
[ 31, 32, 1, 192 ] ]
k = 2: F-action on Pi is () [31,7,2]
Dynkin type is (A_0(q) + T(phi1^5 phi2)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-12*q+35 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-13*q^2+51*q-63 )
Fusion of maximal tori of C^F in those of G^F:
[ 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 9, 2, 1, 12 ], [ 9, 3, 1, 12 ],
[ 9, 4, 1, 12 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 4 ],
[ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ], [ 15, 1, 1, 24 ], [ 16, 5, 2, 16 ],
[ 16, 10, 2, 8 ], [ 16, 12, 2, 8 ], [ 16, 15, 3, 8 ], [ 18, 1, 1, 24 ],
[ 18, 2, 1, 12 ], [ 20, 2, 2, 4 ], [ 23, 3, 2, 8 ], [ 23, 6, 2, 4 ],
[ 25, 1, 1, 48 ], [ 25, 2, 1, 24 ], [ 25, 3, 1, 24 ], [ 26, 2, 2, 8 ],
[ 26, 3, 5, 16 ], [ 29, 2, 2, 16 ], [ 29, 2, 5, 16 ], [ 29, 6, 2, 32 ],
[ 29, 9, 2, 8 ], [ 29, 9, 5, 8 ], [ 29, 10, 2, 8 ], [ 29, 11, 2, 16 ],
[ 29, 12, 2, 16 ], [ 29, 13, 2, 16 ], [ 30, 6, 4, 32 ], [ 30, 6, 15, 32 ],
[ 30, 10, 3, 16 ], [ 30, 10, 17, 32 ], [ 30, 11, 2, 16 ],
[ 30, 11, 15, 16 ], [ 30, 11, 17, 16 ], [ 31, 12, 4, 32 ],
[ 31, 12, 15, 32 ], [ 31, 19, 2, 64 ], [ 31, 19, 5, 32 ], [ 31, 22, 2, 32 ],
[ 31, 24, 4, 32 ], [ 31, 24, 13, 32 ], [ 31, 28, 4, 32 ],
[ 31, 28, 29, 32 ], [ 31, 31, 17, 32 ], [ 31, 32, 2, 32 ],
[ 31, 32, 33, 64 ] ]
k = 3: F-action on Pi is () [31,7,3]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^2-10*q+21 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 4, 2, 8 ],
[ 3, 5, 2, 4 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ],
[ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ],
[ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 12 ],
[ 9, 4, 3, 16 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 6 ], [ 9, 5, 3, 8 ],
[ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ], [ 16, 5, 3, 16 ], [ 16, 5, 5, 32 ],
[ 16, 10, 3, 8 ], [ 16, 10, 5, 16 ], [ 16, 12, 3, 8 ], [ 16, 12, 5, 16 ],
[ 16, 15, 5, 16 ], [ 16, 15, 6, 32 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ],
[ 20, 2, 2, 4 ], [ 23, 3, 3, 8 ], [ 23, 6, 3, 4 ], [ 25, 1, 2, 16 ],
[ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ], [ 26, 2, 2, 8 ], [ 26, 3, 5, 16 ],
[ 29, 2, 3, 16 ], [ 29, 2, 5, 16 ], [ 29, 6, 3, 32 ], [ 29, 9, 3, 8 ],
[ 29, 9, 5, 8 ], [ 29, 10, 3, 8 ], [ 29, 11, 3, 16 ], [ 29, 12, 3, 16 ],
[ 29, 13, 3, 16 ], [ 30, 6, 3, 32 ], [ 30, 6, 15, 32 ], [ 30, 10, 5, 32 ],
[ 30, 10, 17, 32 ], [ 30, 11, 3, 16 ], [ 30, 11, 9, 16 ],
[ 30, 11, 17, 16 ], [ 31, 12, 3, 32 ], [ 31, 12, 43, 32 ],
[ 31, 19, 3, 64 ], [ 31, 19, 9, 64 ], [ 31, 22, 3, 32 ], [ 31, 24, 3, 32 ],
[ 31, 24, 9, 32 ], [ 31, 28, 3, 32 ], [ 31, 28, 43, 32 ],
[ 31, 31, 25, 32 ], [ 31, 32, 3, 64 ], [ 31, 32, 49, 64 ] ]
k = 4: F-action on Pi is () [31,7,4]
Dynkin type is (A_0(q) + T(phi1^5 phi2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^2-10*q+21 )
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 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 16 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 8 ], [ 9, 5, 2, 2 ],
[ 11, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ], [ 16, 5, 4, 16 ],
[ 16, 10, 4, 8 ], [ 16, 12, 4, 8 ], [ 16, 15, 3, 8 ], [ 18, 1, 2, 8 ],
[ 18, 2, 2, 4 ], [ 20, 2, 1, 12 ], [ 23, 3, 1, 16 ], [ 23, 3, 4, 8 ],
[ 23, 6, 1, 8 ], [ 23, 6, 4, 4 ], [ 25, 1, 2, 16 ], [ 25, 2, 2, 8 ],
[ 25, 3, 5, 8 ], [ 26, 2, 1, 24 ], [ 26, 3, 1, 16 ], [ 29, 2, 1, 32 ],
[ 29, 2, 4, 16 ], [ 29, 6, 4, 32 ], [ 29, 9, 1, 16 ], [ 29, 9, 4, 8 ],
[ 29, 10, 1, 16 ], [ 29, 10, 4, 8 ], [ 29, 11, 4, 16 ], [ 29, 12, 4, 16 ],
[ 29, 13, 4, 16 ], [ 30, 6, 1, 32 ], [ 30, 6, 2, 32 ], [ 30, 10, 1, 32 ],
[ 30, 10, 3, 16 ], [ 30, 11, 1, 16 ], [ 30, 11, 4, 16 ], [ 30, 11, 6, 16 ],
[ 31, 12, 2, 32 ], [ 31, 12, 29, 32 ], [ 31, 19, 4, 64 ], [ 31, 19, 5, 32 ],
[ 31, 22, 4, 32 ], [ 31, 24, 2, 32 ], [ 31, 24, 5, 32 ], [ 31, 28, 2, 32 ],
[ 31, 28, 15, 32 ], [ 31, 31, 9, 32 ], [ 31, 32, 2, 32 ],
[ 31, 32, 17, 64 ] ]
k = 5: F-action on Pi is () [31,7,5]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-12*q+35 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-13*q^2+51*q-63 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 9, 2, 1, 12 ], [ 9, 3, 1, 12 ],
[ 9, 4, 1, 12 ], [ 9, 4, 8, 8 ], [ 9, 5, 1, 6 ], [ 9, 5, 8, 4 ],
[ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ], [ 15, 1, 1, 24 ], [ 16, 5, 11, 16 ],
[ 16, 10, 11, 8 ], [ 16, 12, 11, 8 ], [ 16, 15, 13, 8 ], [ 18, 1, 1, 24 ],
[ 18, 2, 1, 12 ], [ 20, 2, 3, 4 ], [ 23, 3, 5, 8 ], [ 23, 6, 5, 4 ],
[ 25, 1, 1, 48 ], [ 25, 2, 1, 24 ], [ 25, 3, 1, 24 ], [ 26, 2, 5, 8 ],
[ 26, 3, 2, 16 ], [ 29, 2, 6, 16 ], [ 29, 2, 9, 16 ], [ 29, 6, 9, 32 ],
[ 29, 9, 6, 8 ], [ 29, 9, 9, 8 ], [ 29, 10, 5, 8 ], [ 29, 11, 9, 16 ],
[ 29, 12, 9, 16 ], [ 29, 13, 9, 16 ], [ 30, 6, 11, 32 ], [ 30, 6, 18, 32 ],
[ 30, 10, 15, 16 ], [ 30, 10, 19, 16 ], [ 30, 11, 16, 16 ],
[ 30, 11, 18, 16 ], [ 30, 11, 31, 16 ], [ 31, 12, 7, 32 ],
[ 31, 12, 18, 32 ], [ 31, 19, 6, 32 ], [ 31, 19, 21, 32 ],
[ 31, 22, 5, 32 ], [ 31, 24, 16, 32 ], [ 31, 24, 49, 32 ],
[ 31, 28, 14, 32 ], [ 31, 28, 32, 32 ], [ 31, 31, 3, 32 ],
[ 31, 32, 6, 32 ], [ 31, 32, 34, 32 ] ]
k = 6: F-action on Pi is () [31,7,6]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 4, 4, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 4, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ],
[ 16, 5, 6, 16 ], [ 16, 10, 6, 8 ], [ 16, 12, 6, 8 ], [ 16, 15, 7, 8 ],
[ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 20, 2, 3, 4 ], [ 23, 3, 5, 8 ],
[ 23, 6, 5, 4 ], [ 25, 1, 2, 16 ], [ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ],
[ 26, 2, 5, 8 ], [ 29, 2, 6, 8 ], [ 29, 2, 7, 8 ], [ 29, 2, 9, 16 ],
[ 29, 9, 6, 4 ], [ 29, 9, 7, 4 ], [ 29, 9, 9, 8 ], [ 29, 10, 5, 8 ],
[ 30, 6, 10, 16 ], [ 30, 6, 17, 16 ], [ 30, 6, 18, 16 ], [ 30, 10, 14, 8 ],
[ 30, 10, 19, 8 ], [ 30, 10, 21, 16 ], [ 30, 11, 10, 8 ], [ 30, 11, 14, 8 ],
[ 30, 11, 18, 8 ], [ 30, 11, 19, 8 ], [ 30, 11, 25, 8 ], [ 30, 11, 31, 8 ],
[ 31, 12, 6, 16 ], [ 31, 12, 17, 16 ], [ 31, 12, 46, 16 ],
[ 31, 19, 7, 16 ], [ 31, 19, 10, 32 ], [ 31, 19, 17, 16 ],
[ 31, 22, 6, 16 ], [ 31, 24, 12, 16 ], [ 31, 24, 15, 16 ],
[ 31, 24, 45, 16 ], [ 31, 28, 13, 16 ], [ 31, 28, 31, 16 ],
[ 31, 28, 46, 16 ], [ 31, 32, 7, 16 ], [ 31, 32, 35, 32 ],
[ 31, 32, 50, 16 ] ]
k = 7: F-action on Pi is () [31,7,7]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 4, 6, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 6, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ],
[ 16, 5, 15, 16 ], [ 16, 10, 15, 8 ], [ 16, 12, 15, 8 ], [ 16, 15, 13, 8 ],
[ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 20, 2, 2, 4 ], [ 23, 3, 2, 8 ],
[ 23, 6, 2, 4 ], [ 25, 1, 2, 16 ], [ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ],
[ 26, 2, 2, 8 ], [ 29, 2, 2, 16 ], [ 29, 2, 5, 8 ], [ 29, 2, 8, 8 ],
[ 29, 9, 2, 8 ], [ 29, 9, 5, 4 ], [ 29, 9, 8, 4 ], [ 29, 10, 2, 8 ],
[ 30, 6, 4, 16 ], [ 30, 6, 9, 16 ], [ 30, 6, 16, 16 ], [ 30, 10, 3, 8 ],
[ 30, 10, 12, 16 ], [ 30, 10, 19, 8 ], [ 30, 11, 2, 8 ], [ 30, 11, 5, 8 ],
[ 30, 11, 13, 8 ], [ 30, 11, 15, 8 ], [ 30, 11, 20, 8 ], [ 30, 11, 22, 8 ],
[ 31, 12, 5, 16 ], [ 31, 12, 16, 16 ], [ 31, 12, 32, 16 ],
[ 31, 19, 6, 16 ], [ 31, 19, 8, 16 ], [ 31, 19, 13, 32 ], [ 31, 22, 7, 16 ],
[ 31, 24, 8, 16 ], [ 31, 24, 14, 16 ], [ 31, 24, 25, 16 ],
[ 31, 28, 7, 16 ], [ 31, 28, 18, 16 ], [ 31, 28, 30, 16 ],
[ 31, 32, 8, 32 ], [ 31, 32, 18, 16 ], [ 31, 32, 34, 16 ] ]
k = 8: F-action on Pi is () [31,7,8]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ],
[ 9, 3, 6, 4 ], [ 9, 4, 6, 4 ], [ 9, 5, 6, 2 ], [ 10, 1, 1, 4 ],
[ 10, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 3, 4 ],
[ 18, 2, 1, 2 ], [ 18, 2, 3, 2 ], [ 25, 1, 5, 8 ], [ 25, 2, 3, 4 ],
[ 25, 3, 2, 4 ], [ 25, 3, 4, 4 ], [ 26, 2, 4, 4 ], [ 29, 2, 17, 8 ],
[ 29, 9, 17, 4 ], [ 30, 6, 5, 8 ], [ 30, 10, 7, 4 ], [ 31, 12, 11, 8 ],
[ 31, 19, 37, 8 ], [ 31, 22, 8, 8 ], [ 31, 24, 41, 8 ], [ 31, 28, 11, 8 ],
[ 31, 32, 10, 8 ] ]
k = 9: F-action on Pi is () [31,7,9]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 1, 4 ],
[ 3, 5, 1, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ], [ 9, 3, 6, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 6, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 6, 2 ],
[ 9, 5, 8, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ], [ 11, 2, 1, 2 ],
[ 15, 1, 2, 4 ], [ 16, 5, 1, 8 ], [ 16, 5, 11, 8 ], [ 16, 10, 1, 4 ],
[ 16, 10, 11, 4 ], [ 16, 12, 1, 4 ], [ 16, 12, 11, 4 ], [ 16, 15, 1, 8 ],
[ 16, 15, 13, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 1, 2 ],
[ 18, 2, 3, 2 ], [ 19, 3, 1, 8 ], [ 19, 5, 1, 4 ], [ 20, 2, 1, 2 ],
[ 20, 2, 3, 2 ], [ 23, 3, 1, 4 ], [ 23, 3, 5, 4 ], [ 23, 6, 1, 2 ],
[ 23, 6, 5, 2 ], [ 25, 1, 5, 8 ], [ 25, 2, 3, 4 ], [ 25, 3, 2, 4 ],
[ 25, 3, 4, 4 ], [ 26, 2, 3, 4 ], [ 26, 3, 1, 4 ], [ 26, 3, 2, 4 ],
[ 26, 3, 3, 4 ], [ 26, 3, 4, 4 ], [ 29, 2, 13, 8 ], [ 29, 6, 1, 8 ],
[ 29, 6, 5, 8 ], [ 29, 6, 9, 8 ], [ 29, 6, 13, 8 ], [ 29, 9, 13, 4 ],
[ 29, 10, 9, 4 ], [ 29, 10, 13, 4 ], [ 29, 11, 1, 4 ], [ 29, 11, 5, 4 ],
[ 29, 11, 9, 4 ], [ 29, 11, 13, 4 ], [ 29, 12, 1, 4 ], [ 29, 12, 5, 4 ],
[ 29, 12, 9, 4 ], [ 29, 12, 13, 4 ], [ 29, 13, 1, 4 ], [ 29, 13, 5, 4 ],
[ 29, 13, 9, 4 ], [ 29, 13, 13, 4 ], [ 30, 6, 6, 8 ], [ 30, 10, 9, 8 ],
[ 31, 12, 10, 8 ], [ 31, 19, 41, 16 ], [ 31, 22, 9, 8 ], [ 31, 24, 37, 8 ],
[ 31, 28, 9, 8 ], [ 31, 31, 2, 8 ], [ 31, 31, 4, 8 ], [ 31, 31, 6, 8 ],
[ 31, 31, 8, 8 ], [ 31, 32, 11, 16 ] ]
k = 10: F-action on Pi is () [31,7,10]
Dynkin type is (A_0(q) + T(phi1^2 phi4^2)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 2, 4 ],
[ 3, 5, 2, 2 ], [ 5, 1, 1, 2 ], [ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ],
[ 9, 3, 6, 4 ], [ 9, 4, 3, 4 ], [ 9, 4, 6, 8 ], [ 9, 5, 3, 2 ],
[ 9, 5, 6, 4 ], [ 15, 1, 5, 4 ], [ 16, 5, 5, 8 ], [ 16, 5, 15, 8 ],
[ 16, 10, 5, 4 ], [ 16, 10, 15, 4 ], [ 16, 12, 5, 4 ], [ 16, 12, 15, 4 ],
[ 16, 15, 6, 8 ], [ 16, 15, 13, 4 ], [ 25, 1, 6, 8 ], [ 25, 2, 4, 4 ],
[ 26, 2, 4, 4 ], [ 29, 2, 17, 8 ], [ 29, 9, 17, 4 ], [ 30, 6, 7, 8 ],
[ 30, 10, 10, 8 ], [ 31, 12, 9, 8 ], [ 31, 19, 45, 16 ], [ 31, 22, 10, 8 ],
[ 31, 24, 33, 8 ], [ 31, 28, 10, 8 ], [ 31, 32, 12, 16 ] ]
k = 11: F-action on Pi is () [31,7,11]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ], [ 9, 3, 6, 4 ], [ 9, 4, 6, 4 ],
[ 9, 5, 6, 2 ], [ 11, 2, 1, 2 ], [ 15, 1, 5, 4 ], [ 20, 2, 1, 2 ],
[ 20, 2, 3, 2 ], [ 23, 3, 1, 4 ], [ 23, 3, 5, 4 ], [ 23, 6, 1, 2 ],
[ 23, 6, 5, 2 ], [ 25, 1, 6, 8 ], [ 25, 2, 4, 4 ], [ 26, 2, 3, 4 ],
[ 29, 2, 13, 8 ], [ 29, 9, 13, 4 ], [ 29, 10, 9, 4 ], [ 29, 10, 13, 4 ],
[ 30, 6, 8, 8 ], [ 30, 10, 7, 4 ], [ 31, 12, 8, 8 ], [ 31, 19, 37, 8 ],
[ 31, 22, 11, 8 ], [ 31, 24, 29, 8 ], [ 31, 28, 8, 8 ], [ 31, 32, 10, 8 ] ]
k = 12: F-action on Pi is () [31,7,12]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-9*q^2+27*q-27 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 4, 1, 8 ],
[ 3, 5, 1, 4 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ],
[ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ],
[ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 12 ], [ 9, 4, 2, 8 ],
[ 9, 4, 4, 16 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 4 ], [ 9, 5, 4, 8 ],
[ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 5, 1, 16 ], [ 16, 5, 7, 32 ],
[ 16, 10, 1, 8 ], [ 16, 10, 7, 16 ], [ 16, 12, 1, 8 ], [ 16, 12, 7, 16 ],
[ 16, 15, 1, 16 ], [ 16, 15, 8, 32 ], [ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ],
[ 20, 2, 3, 4 ], [ 23, 3, 5, 8 ], [ 23, 6, 5, 4 ], [ 25, 1, 3, 16 ],
[ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ], [ 26, 2, 5, 8 ], [ 26, 3, 3, 16 ],
[ 29, 2, 7, 16 ], [ 29, 2, 9, 16 ], [ 29, 6, 5, 32 ], [ 29, 9, 7, 8 ],
[ 29, 9, 9, 8 ], [ 29, 10, 5, 8 ], [ 29, 11, 5, 16 ], [ 29, 12, 5, 16 ],
[ 29, 13, 5, 16 ], [ 30, 6, 13, 32 ], [ 30, 6, 17, 32 ], [ 30, 10, 16, 32 ],
[ 30, 10, 21, 32 ], [ 30, 11, 11, 16 ], [ 30, 11, 19, 16 ],
[ 30, 11, 25, 16 ], [ 31, 12, 13, 32 ], [ 31, 12, 45, 32 ],
[ 31, 19, 11, 64 ], [ 31, 19, 61, 64 ], [ 31, 22, 12, 32 ],
[ 31, 24, 11, 32 ], [ 31, 24, 53, 32 ], [ 31, 28, 12, 32 ],
[ 31, 28, 45, 32 ], [ 31, 31, 5, 32 ], [ 31, 32, 16, 64 ],
[ 31, 32, 51, 64 ] ]
k = 13: F-action on Pi is () [31,7,13]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 4, 3, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 9, 5, 3, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ],
[ 16, 5, 8, 16 ], [ 16, 10, 8, 8 ], [ 16, 12, 8, 8 ], [ 16, 15, 7, 8 ],
[ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ], [ 20, 2, 2, 4 ], [ 23, 3, 3, 8 ],
[ 23, 6, 3, 4 ], [ 25, 1, 3, 16 ], [ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ],
[ 26, 2, 2, 8 ], [ 29, 2, 3, 16 ], [ 29, 2, 5, 8 ], [ 29, 2, 8, 8 ],
[ 29, 9, 3, 8 ], [ 29, 9, 5, 4 ], [ 29, 9, 8, 4 ], [ 29, 10, 3, 8 ],
[ 30, 6, 3, 16 ], [ 30, 6, 12, 16 ], [ 30, 6, 16, 16 ], [ 30, 10, 5, 16 ],
[ 30, 10, 14, 8 ], [ 30, 10, 19, 8 ], [ 30, 11, 3, 8 ], [ 30, 11, 7, 8 ],
[ 30, 11, 9, 8 ], [ 30, 11, 12, 8 ], [ 30, 11, 20, 8 ], [ 30, 11, 22, 8 ],
[ 31, 12, 12, 16 ], [ 31, 12, 31, 16 ], [ 31, 12, 44, 16 ],
[ 31, 19, 7, 16 ], [ 31, 19, 12, 32 ], [ 31, 19, 17, 16 ],
[ 31, 22, 13, 16 ], [ 31, 24, 7, 16 ], [ 31, 24, 10, 16 ],
[ 31, 24, 21, 16 ], [ 31, 28, 6, 16 ], [ 31, 28, 17, 16 ],
[ 31, 28, 44, 16 ], [ 31, 32, 7, 16 ], [ 31, 32, 19, 32 ],
[ 31, 32, 50, 16 ] ]
k = 14: F-action on Pi is () [31,7,14]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-9*q^2+27*q-27 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 4, 8, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 9, 5, 8, 4 ], [ 11, 2, 1, 4 ], [ 15, 1, 3, 8 ],
[ 15, 1, 4, 8 ], [ 16, 5, 11, 16 ], [ 16, 10, 11, 8 ], [ 16, 12, 11, 8 ],
[ 16, 15, 13, 8 ], [ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ], [ 20, 2, 1, 12 ],
[ 23, 3, 1, 8 ], [ 23, 3, 4, 16 ], [ 23, 6, 1, 4 ], [ 23, 6, 4, 8 ],
[ 25, 1, 3, 16 ], [ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ], [ 26, 2, 1, 24 ],
[ 26, 3, 4, 16 ], [ 29, 2, 1, 16 ], [ 29, 2, 4, 32 ], [ 29, 6, 13, 32 ],
[ 29, 9, 1, 8 ], [ 29, 9, 4, 16 ], [ 29, 10, 1, 8 ], [ 29, 10, 4, 16 ],
[ 29, 11, 13, 16 ], [ 29, 12, 13, 16 ], [ 29, 13, 13, 16 ],
[ 30, 6, 2, 32 ], [ 30, 6, 14, 32 ], [ 30, 10, 3, 16 ], [ 30, 10, 15, 16 ],
[ 30, 11, 4, 16 ], [ 30, 11, 6, 16 ], [ 30, 11, 8, 16 ], [ 31, 12, 14, 32 ],
[ 31, 12, 30, 32 ], [ 31, 19, 8, 32 ], [ 31, 19, 21, 32 ],
[ 31, 22, 14, 32 ], [ 31, 24, 6, 32 ], [ 31, 24, 17, 32 ],
[ 31, 28, 5, 32 ], [ 31, 28, 16, 32 ], [ 31, 31, 7, 32 ], [ 31, 32, 6, 32 ],
[ 31, 32, 18, 32 ] ]
k = 15: F-action on Pi is () [31,7,15]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^2-10*q+21 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 4, 3, 8 ],
[ 3, 5, 3, 4 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ],
[ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ],
[ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ],
[ 9, 4, 5, 16 ], [ 9, 4, 8, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 2 ],
[ 9, 5, 5, 8 ], [ 9, 5, 8, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ],
[ 16, 5, 9, 16 ], [ 16, 5, 16, 32 ], [ 16, 10, 9, 8 ], [ 16, 10, 16, 16 ],
[ 16, 12, 9, 8 ], [ 16, 12, 16, 16 ], [ 16, 15, 9, 24 ], [ 18, 1, 2, 8 ],
[ 18, 2, 2, 4 ], [ 20, 2, 3, 4 ], [ 23, 3, 8, 8 ], [ 23, 6, 8, 4 ],
[ 25, 1, 2, 16 ], [ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ], [ 26, 2, 5, 8 ],
[ 26, 3, 2, 16 ], [ 29, 2, 6, 16 ], [ 29, 2, 12, 16 ], [ 29, 6, 12, 32 ],
[ 29, 9, 6, 8 ], [ 29, 9, 12, 8 ], [ 29, 10, 8, 8 ], [ 29, 11, 12, 16 ],
[ 29, 12, 12, 16 ], [ 29, 13, 12, 16 ], [ 30, 6, 11, 32 ],
[ 30, 6, 23, 32 ], [ 30, 10, 15, 16 ], [ 30, 10, 28, 32 ],
[ 30, 11, 16, 16 ], [ 30, 11, 21, 16 ], [ 30, 11, 29, 16 ],
[ 31, 12, 19, 32 ], [ 31, 12, 35, 32 ], [ 31, 19, 14, 64 ],
[ 31, 19, 24, 32 ], [ 31, 22, 15, 32 ], [ 31, 24, 28, 32 ],
[ 31, 24, 50, 32 ], [ 31, 28, 28, 32 ], [ 31, 28, 35, 32 ],
[ 31, 31, 11, 32 ], [ 31, 32, 22, 32 ], [ 31, 32, 40, 64 ] ]
k = 16: F-action on Pi is () [31,7,16]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q^2-6*q+9 )
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, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 4, 5, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 9, 5, 5, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ],
[ 16, 5, 14, 16 ], [ 16, 10, 14, 8 ], [ 16, 12, 14, 8 ], [ 16, 15, 12, 8 ],
[ 18, 1, 3, 8 ], [ 18, 2, 3, 4 ], [ 20, 2, 3, 4 ], [ 23, 3, 8, 8 ],
[ 23, 6, 8, 4 ], [ 25, 1, 3, 16 ], [ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ],
[ 26, 2, 5, 8 ], [ 29, 2, 6, 8 ], [ 29, 2, 7, 8 ], [ 29, 2, 12, 16 ],
[ 29, 9, 6, 4 ], [ 29, 9, 7, 4 ], [ 29, 9, 12, 8 ], [ 29, 10, 8, 8 ],
[ 30, 6, 10, 16 ], [ 30, 6, 23, 16 ], [ 30, 6, 26, 16 ], [ 30, 10, 14, 8 ],
[ 30, 10, 28, 16 ], [ 30, 10, 30, 8 ], [ 30, 11, 10, 8 ], [ 30, 11, 14, 8 ],
[ 30, 11, 21, 8 ], [ 30, 11, 23, 8 ], [ 30, 11, 28, 8 ], [ 30, 11, 29, 8 ],
[ 31, 12, 26, 16 ], [ 31, 12, 34, 16 ], [ 31, 12, 47, 16 ],
[ 31, 19, 15, 32 ], [ 31, 19, 18, 16 ], [ 31, 19, 20, 16 ],
[ 31, 22, 16, 16 ], [ 31, 24, 24, 16 ], [ 31, 24, 27, 16 ],
[ 31, 24, 46, 16 ], [ 31, 28, 27, 16 ], [ 31, 28, 34, 16 ],
[ 31, 28, 49, 16 ], [ 31, 32, 23, 16 ], [ 31, 32, 39, 16 ],
[ 31, 32, 56, 32 ] ]
k = 17: F-action on Pi is () [31,7,17]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-9*q^2+27*q-27 )
Fusion of maximal tori of C^F in those of G^F:
[ 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 4, 4, 8 ],
[ 3, 5, 4, 4 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ],
[ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ],
[ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ],
[ 9, 4, 6, 16 ], [ 9, 4, 7, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 4 ],
[ 9, 5, 6, 8 ], [ 9, 5, 7, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ],
[ 16, 5, 12, 16 ], [ 16, 5, 13, 32 ], [ 16, 10, 12, 8 ], [ 16, 10, 13, 16 ],
[ 16, 12, 12, 8 ], [ 16, 12, 13, 16 ], [ 16, 15, 14, 24 ], [ 18, 1, 3, 8 ],
[ 18, 2, 3, 4 ], [ 20, 2, 2, 4 ], [ 23, 3, 2, 8 ], [ 23, 6, 2, 4 ],
[ 25, 1, 3, 16 ], [ 25, 2, 5, 8 ], [ 25, 3, 3, 8 ], [ 26, 2, 2, 8 ],
[ 26, 3, 8, 16 ], [ 29, 2, 2, 16 ], [ 29, 2, 8, 16 ], [ 29, 6, 14, 32 ],
[ 29, 9, 2, 8 ], [ 29, 9, 8, 8 ], [ 29, 10, 2, 8 ], [ 29, 11, 14, 16 ],
[ 29, 12, 14, 16 ], [ 29, 13, 14, 16 ], [ 30, 6, 9, 32 ], [ 30, 6, 28, 32 ],
[ 30, 10, 12, 32 ], [ 30, 10, 31, 16 ], [ 30, 11, 5, 16 ],
[ 30, 11, 13, 16 ], [ 30, 11, 24, 16 ], [ 31, 12, 28, 32 ],
[ 31, 12, 33, 32 ], [ 31, 19, 16, 64 ], [ 31, 19, 22, 32 ],
[ 31, 22, 17, 32 ], [ 31, 24, 20, 32 ], [ 31, 24, 26, 32 ],
[ 31, 28, 21, 32 ], [ 31, 28, 33, 32 ], [ 31, 31, 23, 32 ],
[ 31, 32, 24, 64 ], [ 31, 32, 38, 32 ] ]
k = 18: F-action on Pi is () [31,7,18]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ],
[ 9, 3, 5, 4 ], [ 9, 4, 5, 4 ], [ 9, 5, 5, 2 ], [ 10, 1, 2, 4 ],
[ 10, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 4 ],
[ 18, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 25, 1, 7, 8 ], [ 25, 2, 6, 4 ],
[ 25, 3, 6, 4 ], [ 25, 3, 8, 4 ], [ 26, 2, 4, 4 ], [ 29, 2, 20, 8 ],
[ 29, 9, 20, 4 ], [ 30, 6, 5, 8 ], [ 30, 10, 7, 4 ], [ 31, 12, 39, 8 ],
[ 31, 19, 40, 8 ], [ 31, 22, 18, 8 ], [ 31, 24, 42, 8 ], [ 31, 28, 25, 8 ],
[ 31, 32, 26, 8 ] ]
k = 19: F-action on Pi is () [31,7,19]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 16 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 3, 4 ],
[ 3, 5, 3, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ], [ 9, 3, 5, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 5, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 5, 2 ],
[ 9, 5, 8, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ], [ 11, 2, 1, 2 ],
[ 15, 1, 2, 4 ], [ 16, 5, 4, 8 ], [ 16, 5, 9, 8 ], [ 16, 10, 4, 4 ],
[ 16, 10, 9, 4 ], [ 16, 12, 4, 4 ], [ 16, 12, 9, 4 ], [ 16, 15, 3, 4 ],
[ 16, 15, 9, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 2, 2 ],
[ 18, 2, 4, 2 ], [ 19, 3, 4, 8 ], [ 19, 5, 4, 4 ], [ 20, 2, 1, 2 ],
[ 20, 2, 3, 2 ], [ 23, 3, 4, 4 ], [ 23, 3, 8, 4 ], [ 23, 6, 4, 2 ],
[ 23, 6, 8, 2 ], [ 25, 1, 7, 8 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ],
[ 25, 3, 8, 4 ], [ 26, 2, 3, 4 ], [ 26, 3, 1, 4 ], [ 26, 3, 2, 4 ],
[ 26, 3, 3, 4 ], [ 26, 3, 4, 4 ], [ 29, 2, 16, 8 ], [ 29, 6, 4, 8 ],
[ 29, 6, 8, 8 ], [ 29, 6, 12, 8 ], [ 29, 6, 16, 8 ], [ 29, 9, 16, 4 ],
[ 29, 10, 12, 4 ], [ 29, 10, 16, 4 ], [ 29, 11, 4, 4 ], [ 29, 11, 8, 4 ],
[ 29, 11, 12, 4 ], [ 29, 11, 16, 4 ], [ 29, 12, 4, 4 ], [ 29, 12, 8, 4 ],
[ 29, 12, 12, 4 ], [ 29, 12, 16, 4 ], [ 29, 13, 4, 4 ], [ 29, 13, 8, 4 ],
[ 29, 13, 12, 4 ], [ 29, 13, 16, 4 ], [ 30, 6, 6, 8 ], [ 30, 10, 9, 8 ],
[ 31, 12, 38, 8 ], [ 31, 19, 44, 16 ], [ 31, 22, 19, 8 ], [ 31, 24, 38, 8 ],
[ 31, 28, 23, 8 ], [ 31, 31, 10, 8 ], [ 31, 31, 12, 8 ], [ 31, 31, 14, 8 ],
[ 31, 31, 16, 8 ], [ 31, 32, 27, 16 ] ]
k = 20: F-action on Pi is () [31,7,20]
Dynkin type is (A_0(q) + T(phi1 phi2 phi4^2)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
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, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 4, 4 ],
[ 3, 5, 4, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ],
[ 9, 3, 5, 4 ], [ 9, 4, 3, 4 ], [ 9, 4, 5, 4 ], [ 9, 4, 6, 4 ],
[ 9, 5, 3, 2 ], [ 9, 5, 5, 2 ], [ 9, 5, 6, 2 ], [ 15, 1, 5, 4 ],
[ 16, 5, 8, 8 ], [ 16, 5, 13, 8 ], [ 16, 10, 8, 4 ], [ 16, 10, 13, 4 ],
[ 16, 12, 8, 4 ], [ 16, 12, 13, 4 ], [ 16, 15, 7, 4 ], [ 16, 15, 14, 4 ],
[ 25, 1, 8, 8 ], [ 25, 2, 7, 4 ], [ 26, 2, 4, 4 ], [ 29, 2, 20, 8 ],
[ 29, 9, 20, 4 ], [ 30, 6, 7, 8 ], [ 30, 10, 10, 8 ], [ 31, 12, 37, 8 ],
[ 31, 19, 48, 16 ], [ 31, 22, 20, 8 ], [ 31, 24, 34, 8 ], [ 31, 28, 24, 8 ],
[ 31, 32, 28, 16 ] ]
k = 21: F-action on Pi is () [31,7,21]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ], [ 9, 3, 5, 4 ], [ 9, 4, 5, 4 ],
[ 9, 5, 5, 2 ], [ 11, 2, 1, 2 ], [ 15, 1, 5, 4 ], [ 20, 2, 1, 2 ],
[ 20, 2, 3, 2 ], [ 23, 3, 4, 4 ], [ 23, 3, 8, 4 ], [ 23, 6, 4, 2 ],
[ 23, 6, 8, 2 ], [ 25, 1, 8, 8 ], [ 25, 2, 7, 4 ], [ 26, 2, 3, 4 ],
[ 29, 2, 16, 8 ], [ 29, 9, 16, 4 ], [ 29, 10, 12, 4 ], [ 29, 10, 16, 4 ],
[ 30, 6, 8, 8 ], [ 30, 10, 7, 4 ], [ 31, 12, 36, 8 ], [ 31, 19, 40, 8 ],
[ 31, 22, 21, 8 ], [ 31, 24, 30, 8 ], [ 31, 28, 22, 8 ], [ 31, 32, 26, 8 ] ]
k = 22: F-action on Pi is () [31,7,22]
Dynkin type is (A_0(q) + T(phi1 phi2^5)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi2 ( q^2-8*q+15 )
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, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 6 ],
[ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 9, 2, 2, 12 ], [ 9, 3, 2, 12 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 6 ],
[ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ], [ 15, 1, 3, 24 ], [ 16, 5, 4, 16 ],
[ 16, 10, 4, 8 ], [ 16, 12, 4, 8 ], [ 16, 15, 3, 8 ], [ 18, 1, 4, 24 ],
[ 18, 2, 4, 12 ], [ 20, 2, 3, 4 ], [ 23, 3, 8, 8 ], [ 23, 6, 8, 4 ],
[ 25, 1, 4, 48 ], [ 25, 2, 8, 24 ], [ 25, 3, 7, 24 ], [ 26, 2, 5, 8 ],
[ 26, 3, 3, 16 ], [ 29, 2, 7, 16 ], [ 29, 2, 12, 16 ], [ 29, 6, 8, 32 ],
[ 29, 9, 7, 8 ], [ 29, 9, 12, 8 ], [ 29, 10, 8, 8 ], [ 29, 11, 8, 16 ],
[ 29, 12, 8, 16 ], [ 29, 13, 8, 16 ], [ 30, 6, 13, 32 ], [ 30, 6, 26, 32 ],
[ 30, 10, 16, 32 ], [ 30, 10, 30, 16 ], [ 30, 11, 11, 16 ],
[ 30, 11, 23, 16 ], [ 30, 11, 28, 16 ], [ 31, 12, 41, 32 ],
[ 31, 12, 54, 32 ], [ 31, 19, 19, 32 ], [ 31, 19, 64, 64 ],
[ 31, 22, 22, 32 ], [ 31, 24, 23, 32 ], [ 31, 24, 54, 32 ],
[ 31, 28, 26, 32 ], [ 31, 28, 48, 32 ], [ 31, 31, 13, 32 ],
[ 31, 32, 32, 64 ], [ 31, 32, 55, 32 ] ]
k = 23: F-action on Pi is () [31,7,23]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi2 ( q^2-8*q+15 )
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, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 6 ],
[ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 9, 2, 2, 12 ], [ 9, 3, 2, 12 ],
[ 9, 4, 2, 12 ], [ 9, 4, 7, 8 ], [ 9, 5, 2, 6 ], [ 9, 5, 7, 4 ],
[ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ], [ 15, 1, 3, 24 ], [ 16, 5, 10, 16 ],
[ 16, 10, 10, 8 ], [ 16, 12, 10, 8 ], [ 16, 15, 12, 8 ], [ 18, 1, 4, 24 ],
[ 18, 2, 4, 12 ], [ 20, 2, 2, 4 ], [ 23, 3, 3, 8 ], [ 23, 6, 3, 4 ],
[ 25, 1, 4, 48 ], [ 25, 2, 8, 24 ], [ 25, 3, 7, 24 ], [ 26, 2, 2, 8 ],
[ 26, 3, 8, 16 ], [ 29, 2, 3, 16 ], [ 29, 2, 8, 16 ], [ 29, 6, 15, 32 ],
[ 29, 9, 3, 8 ], [ 29, 9, 8, 8 ], [ 29, 10, 3, 8 ], [ 29, 11, 15, 16 ],
[ 29, 12, 15, 16 ], [ 29, 13, 15, 16 ], [ 30, 6, 12, 32 ],
[ 30, 6, 28, 32 ], [ 30, 10, 14, 16 ], [ 30, 10, 31, 16 ],
[ 30, 11, 7, 16 ], [ 30, 11, 12, 16 ], [ 30, 11, 24, 16 ],
[ 31, 12, 40, 32 ], [ 31, 12, 56, 32 ], [ 31, 19, 20, 32 ],
[ 31, 19, 23, 32 ], [ 31, 22, 23, 32 ], [ 31, 24, 19, 32 ],
[ 31, 24, 22, 32 ], [ 31, 28, 20, 32 ], [ 31, 28, 47, 32 ],
[ 31, 31, 31, 32 ], [ 31, 32, 23, 32 ], [ 31, 32, 54, 32 ] ]
k = 24: F-action on Pi is () [31,7,24]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/192 phi1 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/192 ( q^3-15*q^2+71*q-105 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 4, 3, 8 ],
[ 3, 5, 3, 4 ], [ 5, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ],
[ 9, 2, 2, 12 ], [ 9, 3, 2, 12 ], [ 9, 4, 2, 12 ], [ 9, 4, 8, 24 ],
[ 9, 5, 2, 6 ], [ 9, 5, 8, 12 ], [ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ],
[ 11, 2, 1, 4 ], [ 15, 1, 3, 24 ], [ 16, 5, 9, 48 ], [ 16, 10, 9, 24 ],
[ 16, 12, 9, 24 ], [ 16, 15, 9, 24 ], [ 18, 1, 4, 24 ], [ 18, 2, 4, 12 ],
[ 19, 3, 4, 32 ], [ 19, 5, 4, 16 ], [ 20, 2, 1, 12 ], [ 23, 3, 4, 24 ],
[ 23, 6, 4, 12 ], [ 25, 1, 4, 48 ], [ 25, 2, 8, 24 ], [ 25, 3, 7, 24 ],
[ 26, 2, 1, 24 ], [ 26, 3, 4, 48 ], [ 29, 2, 4, 48 ], [ 29, 6, 16, 96 ],
[ 29, 9, 4, 24 ], [ 29, 10, 4, 24 ], [ 29, 11, 16, 48 ], [ 29, 12, 16, 48 ],
[ 29, 13, 16, 48 ], [ 30, 6, 14, 96 ], [ 30, 10, 15, 48 ],
[ 30, 11, 8, 48 ], [ 31, 12, 42, 96 ], [ 31, 19, 24, 96 ],
[ 31, 22, 24, 96 ], [ 31, 24, 18, 96 ], [ 31, 28, 19, 96 ],
[ 31, 31, 15, 96 ], [ 31, 32, 22, 96 ] ]
k = 25: F-action on Pi is () [31,7,25]
Dynkin type is (A_0(q) + T(phi1 phi2 phi3 phi6)).2
Order of center |Z^F|: phi1 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 4, 4, 2 ], [ 3, 5, 4, 1 ], [ 10, 1, 1, 2 ],
[ 10, 2, 1, 1 ], [ 11, 2, 2, 1 ], [ 19, 3, 3, 2 ], [ 19, 5, 3, 1 ],
[ 25, 1, 9, 6 ], [ 25, 2, 9, 3 ], [ 26, 2, 7, 3 ], [ 31, 22, 25, 3 ] ]
k = 26: F-action on Pi is () [31,7,26]
Dynkin type is (A_0(q) + T(phi1^2 phi3^2)).2
Order of center |Z^F|: phi1 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 26 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 4, 1, 2 ], [ 3, 5, 1, 1 ], [ 10, 1, 1, 2 ],
[ 10, 2, 1, 1 ], [ 11, 2, 1, 1 ], [ 19, 3, 1, 2 ], [ 19, 5, 1, 1 ],
[ 25, 1, 9, 6 ], [ 25, 2, 9, 3 ], [ 26, 2, 6, 3 ], [ 31, 22, 26, 3 ] ]
k = 27: F-action on Pi is () [31,7,27]
Dynkin type is (A_0(q) + T(phi2^2 phi6^2)).2
Order of center |Z^F|: phi2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 27 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 4, 2, 2 ], [ 3, 5, 2, 1 ], [ 10, 1, 2, 2 ],
[ 10, 2, 2, 1 ], [ 11, 2, 2, 1 ], [ 19, 3, 2, 2 ], [ 19, 5, 2, 1 ],
[ 25, 1, 10, 6 ], [ 25, 2, 10, 3 ], [ 26, 2, 7, 3 ], [ 31, 22, 27, 3 ] ]
k = 28: F-action on Pi is () [31,7,28]
Dynkin type is (A_0(q) + T(phi1 phi2 phi3 phi6)).2
Order of center |Z^F|: phi2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 4, 3, 2 ], [ 3, 5, 3, 1 ], [ 10, 1, 2, 2 ],
[ 10, 2, 2, 1 ], [ 11, 2, 1, 1 ], [ 19, 3, 4, 2 ], [ 19, 5, 4, 1 ],
[ 25, 1, 10, 6 ], [ 25, 2, 10, 3 ], [ 26, 2, 6, 3 ], [ 31, 22, 28, 3 ] ]
k = 29: F-action on Pi is () [31,7,29]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ],
[ 9, 3, 6, 4 ], [ 9, 4, 6, 4 ], [ 9, 5, 6, 2 ], [ 10, 1, 1, 4 ],
[ 10, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 3, 4 ],
[ 18, 2, 1, 2 ], [ 18, 2, 3, 2 ], [ 25, 1, 5, 8 ], [ 25, 2, 3, 4 ],
[ 25, 3, 2, 4 ], [ 25, 3, 4, 4 ], [ 26, 2, 9, 4 ], [ 29, 2, 18, 8 ],
[ 29, 9, 18, 4 ], [ 30, 6, 19, 8 ], [ 30, 10, 23, 4 ], [ 31, 12, 25, 8 ],
[ 31, 19, 38, 8 ], [ 31, 22, 29, 8 ], [ 31, 24, 44, 8 ], [ 31, 28, 39, 8 ],
[ 31, 32, 42, 8 ] ]
k = 30: F-action on Pi is () [31,7,30]
Dynkin type is (A_0(q) + T(phi1 phi2^3 phi4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ],
[ 9, 3, 5, 4 ], [ 9, 4, 5, 4 ], [ 9, 5, 5, 2 ], [ 10, 1, 2, 4 ],
[ 10, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 4 ],
[ 18, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 25, 1, 7, 8 ], [ 25, 2, 6, 4 ],
[ 25, 3, 6, 4 ], [ 25, 3, 8, 4 ], [ 26, 2, 9, 4 ], [ 29, 2, 19, 8 ],
[ 29, 9, 19, 4 ], [ 30, 6, 19, 8 ], [ 30, 10, 23, 4 ], [ 31, 12, 53, 8 ],
[ 31, 19, 39, 8 ], [ 31, 22, 30, 8 ], [ 31, 24, 43, 8 ], [ 31, 28, 53, 8 ],
[ 31, 32, 58, 8 ] ]
k = 31: F-action on Pi is () [31,7,31]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 4, 4 ],
[ 3, 5, 4, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ], [ 9, 3, 6, 4 ], [ 9, 4, 2, 4 ],
[ 9, 4, 6, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 2, 2 ], [ 9, 5, 6, 2 ],
[ 9, 5, 7, 2 ], [ 10, 1, 1, 4 ], [ 10, 2, 1, 2 ], [ 11, 2, 2, 2 ],
[ 15, 1, 2, 4 ], [ 16, 5, 2, 8 ], [ 16, 5, 12, 8 ], [ 16, 10, 2, 4 ],
[ 16, 10, 12, 4 ], [ 16, 12, 2, 4 ], [ 16, 12, 12, 4 ], [ 16, 15, 3, 4 ],
[ 16, 15, 14, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 3, 4 ], [ 18, 2, 1, 2 ],
[ 18, 2, 3, 2 ], [ 19, 3, 3, 8 ], [ 19, 5, 3, 4 ], [ 20, 2, 2, 2 ],
[ 20, 2, 4, 2 ], [ 23, 3, 2, 4 ], [ 23, 3, 6, 4 ], [ 23, 6, 2, 2 ],
[ 23, 6, 6, 2 ], [ 25, 1, 5, 8 ], [ 25, 2, 3, 4 ], [ 25, 3, 2, 4 ],
[ 25, 3, 4, 4 ], [ 26, 2, 8, 4 ], [ 26, 3, 5, 4 ], [ 26, 3, 6, 4 ],
[ 26, 3, 7, 4 ], [ 26, 3, 8, 4 ], [ 29, 2, 14, 8 ], [ 29, 6, 2, 8 ],
[ 29, 6, 6, 8 ], [ 29, 6, 10, 8 ], [ 29, 6, 14, 8 ], [ 29, 9, 14, 4 ],
[ 29, 10, 10, 4 ], [ 29, 10, 14, 4 ], [ 29, 11, 2, 4 ], [ 29, 11, 6, 4 ],
[ 29, 11, 10, 4 ], [ 29, 11, 14, 4 ], [ 29, 12, 2, 4 ], [ 29, 12, 6, 4 ],
[ 29, 12, 10, 4 ], [ 29, 12, 14, 4 ], [ 29, 13, 2, 4 ], [ 29, 13, 6, 4 ],
[ 29, 13, 10, 4 ], [ 29, 13, 14, 4 ], [ 30, 6, 20, 8 ], [ 30, 10, 25, 8 ],
[ 31, 12, 24, 8 ], [ 31, 19, 42, 16 ], [ 31, 22, 31, 8 ], [ 31, 24, 40, 8 ],
[ 31, 28, 37, 8 ], [ 31, 31, 18, 8 ], [ 31, 31, 20, 8 ], [ 31, 31, 22, 8 ],
[ 31, 31, 24, 8 ], [ 31, 32, 43, 16 ] ]
k = 32: F-action on Pi is () [31,7,32]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 2, 4 ],
[ 3, 5, 2, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ], [ 9, 3, 5, 4 ], [ 9, 4, 2, 4 ],
[ 9, 4, 5, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 2, 2 ], [ 9, 5, 5, 2 ],
[ 9, 5, 7, 2 ], [ 10, 1, 2, 4 ], [ 10, 2, 2, 2 ], [ 11, 2, 2, 2 ],
[ 15, 1, 2, 4 ], [ 16, 5, 3, 8 ], [ 16, 5, 10, 8 ], [ 16, 10, 3, 4 ],
[ 16, 10, 10, 4 ], [ 16, 12, 3, 4 ], [ 16, 12, 10, 4 ], [ 16, 15, 5, 8 ],
[ 16, 15, 12, 4 ], [ 18, 1, 2, 4 ], [ 18, 1, 4, 4 ], [ 18, 2, 2, 2 ],
[ 18, 2, 4, 2 ], [ 19, 3, 2, 8 ], [ 19, 5, 2, 4 ], [ 20, 2, 2, 2 ],
[ 20, 2, 4, 2 ], [ 23, 3, 3, 4 ], [ 23, 3, 7, 4 ], [ 23, 6, 3, 2 ],
[ 23, 6, 7, 2 ], [ 25, 1, 7, 8 ], [ 25, 2, 6, 4 ], [ 25, 3, 6, 4 ],
[ 25, 3, 8, 4 ], [ 26, 2, 8, 4 ], [ 26, 3, 5, 4 ], [ 26, 3, 6, 4 ],
[ 26, 3, 7, 4 ], [ 26, 3, 8, 4 ], [ 29, 2, 15, 8 ], [ 29, 6, 3, 8 ],
[ 29, 6, 7, 8 ], [ 29, 6, 11, 8 ], [ 29, 6, 15, 8 ], [ 29, 9, 15, 4 ],
[ 29, 10, 11, 4 ], [ 29, 10, 15, 4 ], [ 29, 11, 3, 4 ], [ 29, 11, 7, 4 ],
[ 29, 11, 11, 4 ], [ 29, 11, 15, 4 ], [ 29, 12, 3, 4 ], [ 29, 12, 7, 4 ],
[ 29, 12, 11, 4 ], [ 29, 12, 15, 4 ], [ 29, 13, 3, 4 ], [ 29, 13, 7, 4 ],
[ 29, 13, 11, 4 ], [ 29, 13, 15, 4 ], [ 30, 6, 20, 8 ], [ 30, 10, 25, 8 ],
[ 31, 12, 52, 8 ], [ 31, 19, 43, 16 ], [ 31, 22, 32, 8 ], [ 31, 24, 39, 8 ],
[ 31, 28, 51, 8 ], [ 31, 31, 26, 8 ], [ 31, 31, 28, 8 ], [ 31, 31, 30, 8 ],
[ 31, 31, 32, 8 ], [ 31, 32, 59, 16 ] ]
k = 33: F-action on Pi is () [31,7,33]
Dynkin type is (A_0(q) + T(phi1 phi2 phi4^2)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
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, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 3, 4 ],
[ 3, 5, 3, 2 ], [ 5, 1, 1, 2 ], [ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ],
[ 9, 3, 6, 4 ], [ 9, 4, 4, 4 ], [ 9, 4, 5, 4 ], [ 9, 4, 6, 4 ],
[ 9, 5, 4, 2 ], [ 9, 5, 5, 2 ], [ 9, 5, 6, 2 ], [ 15, 1, 5, 4 ],
[ 16, 5, 6, 8 ], [ 16, 5, 16, 8 ], [ 16, 10, 6, 4 ], [ 16, 10, 16, 4 ],
[ 16, 12, 6, 4 ], [ 16, 12, 16, 4 ], [ 16, 15, 7, 4 ], [ 16, 15, 9, 4 ],
[ 25, 1, 6, 8 ], [ 25, 2, 4, 4 ], [ 26, 2, 9, 4 ], [ 29, 2, 18, 8 ],
[ 29, 9, 18, 4 ], [ 30, 6, 21, 8 ], [ 30, 10, 26, 8 ], [ 31, 12, 23, 8 ],
[ 31, 19, 46, 16 ], [ 31, 22, 33, 8 ], [ 31, 24, 36, 8 ], [ 31, 28, 38, 8 ],
[ 31, 32, 44, 16 ] ]
k = 34: F-action on Pi is () [31,7,34]
Dynkin type is (A_0(q) + T(phi2^2 phi4^2)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 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 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 4, 1, 4 ],
[ 3, 5, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ],
[ 9, 3, 5, 4 ], [ 9, 4, 4, 4 ], [ 9, 4, 5, 8 ], [ 9, 5, 4, 2 ],
[ 9, 5, 5, 4 ], [ 15, 1, 5, 4 ], [ 16, 5, 7, 8 ], [ 16, 5, 14, 8 ],
[ 16, 10, 7, 4 ], [ 16, 10, 14, 4 ], [ 16, 12, 7, 4 ], [ 16, 12, 14, 4 ],
[ 16, 15, 8, 8 ], [ 16, 15, 12, 4 ], [ 25, 1, 8, 8 ], [ 25, 2, 7, 4 ],
[ 26, 2, 9, 4 ], [ 29, 2, 19, 8 ], [ 29, 9, 19, 4 ], [ 30, 6, 21, 8 ],
[ 30, 10, 26, 8 ], [ 31, 12, 51, 8 ], [ 31, 19, 47, 16 ], [ 31, 22, 34, 8 ],
[ 31, 24, 35, 8 ], [ 31, 28, 52, 8 ], [ 31, 32, 60, 16 ] ]
k = 35: F-action on Pi is () [31,7,35]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 1, 6, 8 ], [ 9, 2, 6, 4 ], [ 9, 3, 6, 4 ], [ 9, 4, 6, 4 ],
[ 9, 5, 6, 2 ], [ 11, 2, 2, 2 ], [ 15, 1, 5, 4 ], [ 20, 2, 2, 2 ],
[ 20, 2, 4, 2 ], [ 23, 3, 2, 4 ], [ 23, 3, 6, 4 ], [ 23, 6, 2, 2 ],
[ 23, 6, 6, 2 ], [ 25, 1, 6, 8 ], [ 25, 2, 4, 4 ], [ 26, 2, 8, 4 ],
[ 29, 2, 14, 8 ], [ 29, 9, 14, 4 ], [ 29, 10, 10, 4 ], [ 29, 10, 14, 4 ],
[ 30, 6, 22, 8 ], [ 30, 10, 23, 4 ], [ 31, 12, 22, 8 ], [ 31, 19, 38, 8 ],
[ 31, 22, 35, 8 ], [ 31, 24, 32, 8 ], [ 31, 28, 36, 8 ], [ 31, 32, 42, 8 ] ]
k = 36: F-action on Pi is () [31,7,36]
Dynkin type is (A_0(q) + T(phi1 phi2^3 phi4)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 1, 5, 8 ], [ 9, 2, 5, 4 ], [ 9, 3, 5, 4 ], [ 9, 4, 5, 4 ],
[ 9, 5, 5, 2 ], [ 11, 2, 2, 2 ], [ 15, 1, 5, 4 ], [ 20, 2, 2, 2 ],
[ 20, 2, 4, 2 ], [ 23, 3, 3, 4 ], [ 23, 3, 7, 4 ], [ 23, 6, 3, 2 ],
[ 23, 6, 7, 2 ], [ 25, 1, 8, 8 ], [ 25, 2, 7, 4 ], [ 26, 2, 8, 4 ],
[ 29, 2, 15, 8 ], [ 29, 9, 15, 4 ], [ 29, 10, 11, 4 ], [ 29, 10, 15, 4 ],
[ 30, 6, 22, 8 ], [ 30, 10, 23, 4 ], [ 31, 12, 50, 8 ], [ 31, 19, 39, 8 ],
[ 31, 22, 36, 8 ], [ 31, 24, 31, 8 ], [ 31, 28, 50, 8 ], [ 31, 32, 58, 8 ] ]
k = 37: F-action on Pi is () [31,7,37]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/192 ( q^3-21*q^2+143*q-315 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/192 ( q^3-21*q^2+131*q-231 )
Fusion of maximal tori of C^F in those of G^F:
[ 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 4, 4, 8 ],
[ 3, 5, 4, 4 ], [ 5, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ],
[ 9, 2, 1, 12 ], [ 9, 3, 1, 12 ], [ 9, 4, 1, 12 ], [ 9, 4, 7, 24 ],
[ 9, 5, 1, 6 ], [ 9, 5, 7, 12 ], [ 10, 1, 1, 8 ], [ 10, 2, 1, 4 ],
[ 11, 2, 2, 4 ], [ 15, 1, 1, 24 ], [ 16, 5, 12, 48 ], [ 16, 10, 12, 24 ],
[ 16, 12, 12, 24 ], [ 16, 15, 14, 24 ], [ 18, 1, 1, 24 ], [ 18, 2, 1, 12 ],
[ 19, 3, 3, 32 ], [ 19, 5, 3, 16 ], [ 20, 2, 4, 12 ], [ 23, 3, 6, 24 ],
[ 23, 6, 6, 12 ], [ 25, 1, 1, 48 ], [ 25, 2, 1, 24 ], [ 25, 3, 1, 24 ],
[ 26, 2, 10, 24 ], [ 26, 3, 6, 48 ], [ 29, 2, 10, 48 ], [ 29, 6, 10, 96 ],
[ 29, 9, 10, 24 ], [ 29, 10, 6, 24 ], [ 29, 11, 10, 48 ],
[ 29, 12, 10, 48 ], [ 29, 13, 10, 48 ], [ 30, 6, 25, 96 ],
[ 30, 10, 31, 48 ], [ 30, 11, 32, 48 ], [ 31, 12, 21, 96 ],
[ 31, 19, 22, 96 ], [ 31, 22, 37, 96 ], [ 31, 24, 52, 96 ],
[ 31, 28, 42, 96 ], [ 31, 31, 19, 96 ], [ 31, 32, 38, 96 ] ]
k = 38: F-action on Pi is () [31,7,38]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^2-10*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, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 4, 7, 8 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 7, 4 ], [ 11, 2, 2, 4 ], [ 15, 1, 1, 8 ],
[ 15, 1, 4, 8 ], [ 16, 5, 10, 16 ], [ 16, 10, 10, 8 ], [ 16, 12, 10, 8 ],
[ 16, 15, 12, 8 ], [ 18, 1, 2, 8 ], [ 18, 2, 2, 4 ], [ 20, 2, 4, 12 ],
[ 23, 3, 6, 16 ], [ 23, 3, 7, 8 ], [ 23, 6, 6, 8 ], [ 23, 6, 7, 4 ],
[ 25, 1, 2, 16 ], [ 25, 2, 2, 8 ], [ 25, 3, 5, 8 ], [ 26, 2, 10, 24 ],
[ 26, 3, 6, 16 ], [ 29, 2, 10, 32 ], [ 29, 2, 11, 16 ], [ 29, 6, 11, 32 ],
[ 29, 9, 10, 16 ], [ 29, 9, 11, 8 ], [ 29, 10, 6, 16 ], [ 29, 10, 7, 8 ],
[ 29, 11, 11, 16 ], [ 29, 12, 11, 16 ], [ 29, 13, 11, 16 ],
[ 30, 6, 24, 32 ], [ 30, 6, 25, 32 ], [ 30, 10, 30, 16 ],
[ 30, 10, 31, 16 ], [ 30, 11, 26, 16 ], [ 30, 11, 30, 16 ],
[ 30, 11, 32, 16 ], [ 31, 12, 20, 32 ], [ 31, 12, 49, 32 ],
[ 31, 19, 18, 32 ], [ 31, 19, 23, 32 ], [ 31, 22, 38, 32 ],
[ 31, 24, 48, 32 ], [ 31, 24, 51, 32 ], [ 31, 28, 41, 32 ],
[ 31, 28, 56, 32 ], [ 31, 31, 27, 32 ], [ 31, 32, 39, 32 ],
[ 31, 32, 54, 32 ] ]
k = 39: F-action on Pi is () [31,7,39]
Dynkin type is (A_0(q) + T(phi1 phi2^5)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-9*q^2+27*q-27 )
Fusion of maximal tori of C^F in those of G^F:
[ 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 16 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 8 ],
[ 11, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 5, 2, 16 ],
[ 16, 10, 2, 8 ], [ 16, 12, 2, 8 ], [ 16, 15, 3, 8 ], [ 18, 1, 3, 8 ],
[ 18, 2, 3, 4 ], [ 20, 2, 4, 12 ], [ 23, 3, 6, 8 ], [ 23, 3, 7, 16 ],
[ 23, 6, 6, 4 ], [ 23, 6, 7, 8 ], [ 25, 1, 3, 16 ], [ 25, 2, 5, 8 ],
[ 25, 3, 3, 8 ], [ 26, 2, 10, 24 ], [ 26, 3, 7, 16 ], [ 29, 2, 10, 16 ],
[ 29, 2, 11, 32 ], [ 29, 6, 6, 32 ], [ 29, 9, 10, 8 ], [ 29, 9, 11, 16 ],
[ 29, 10, 6, 8 ], [ 29, 10, 7, 16 ], [ 29, 11, 6, 16 ], [ 29, 12, 6, 16 ],
[ 29, 13, 6, 16 ], [ 30, 6, 24, 32 ], [ 30, 6, 27, 32 ], [ 30, 10, 30, 16 ],
[ 30, 10, 32, 32 ], [ 30, 11, 26, 16 ], [ 30, 11, 27, 16 ],
[ 30, 11, 30, 16 ], [ 31, 12, 27, 32 ], [ 31, 12, 48, 32 ],
[ 31, 19, 19, 32 ], [ 31, 19, 62, 64 ], [ 31, 22, 39, 32 ],
[ 31, 24, 47, 32 ], [ 31, 24, 56, 32 ], [ 31, 28, 40, 32 ],
[ 31, 28, 55, 32 ], [ 31, 31, 21, 32 ], [ 31, 32, 48, 64 ],
[ 31, 32, 55, 32 ] ]
k = 40: F-action on Pi is () [31,7,40]
Dynkin type is (A_0(q) + T(phi2^6)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/192 phi1 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/192 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 4, 2, 8 ],
[ 3, 5, 2, 4 ], [ 5, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ],
[ 9, 2, 2, 12 ], [ 9, 3, 2, 12 ], [ 9, 4, 2, 36 ], [ 9, 5, 2, 18 ],
[ 10, 1, 2, 8 ], [ 10, 2, 2, 4 ], [ 11, 2, 2, 4 ], [ 15, 1, 3, 24 ],
[ 16, 5, 3, 48 ], [ 16, 10, 3, 24 ], [ 16, 12, 3, 24 ], [ 16, 15, 5, 48 ],
[ 18, 1, 4, 24 ], [ 18, 2, 4, 12 ], [ 19, 3, 2, 32 ], [ 19, 5, 2, 16 ],
[ 20, 2, 4, 12 ], [ 23, 3, 7, 24 ], [ 23, 6, 7, 12 ], [ 25, 1, 4, 48 ],
[ 25, 2, 8, 24 ], [ 25, 3, 7, 24 ], [ 26, 2, 10, 24 ], [ 26, 3, 7, 48 ],
[ 29, 2, 11, 48 ], [ 29, 6, 7, 96 ], [ 29, 9, 11, 24 ], [ 29, 10, 7, 24 ],
[ 29, 11, 7, 48 ], [ 29, 12, 7, 48 ], [ 29, 13, 7, 48 ], [ 30, 6, 27, 96 ],
[ 30, 10, 32, 96 ], [ 30, 11, 27, 48 ], [ 31, 12, 55, 96 ],
[ 31, 19, 63, 192 ], [ 31, 22, 40, 96 ], [ 31, 24, 55, 96 ],
[ 31, 28, 54, 96 ], [ 31, 31, 29, 96 ], [ 31, 32, 64, 192 ] ]
j = 8: Omega of order 2, action on Pi: <()>
k = 1: F-action on Pi is () [31,8,1]
Dynkin type is (A_0(q) + T(phi1^6)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/192 ( q^3-21*q^2+143*q-315 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/192 ( q^3-21*q^2+131*q-231 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 3, 1, 8 ],
[ 3, 5, 1, 4 ], [ 5, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ],
[ 9, 2, 1, 12 ], [ 9, 3, 1, 36 ], [ 9, 4, 1, 12 ], [ 9, 5, 1, 18 ],
[ 10, 2, 1, 4 ], [ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ], [ 15, 1, 1, 24 ],
[ 16, 6, 1, 48 ], [ 16, 10, 1, 24 ], [ 16, 12, 1, 24 ], [ 16, 16, 1, 48 ],
[ 18, 2, 1, 12 ], [ 19, 4, 1, 32 ], [ 19, 5, 1, 16 ], [ 20, 1, 1, 24 ],
[ 20, 2, 1, 12 ], [ 23, 4, 1, 24 ], [ 23, 6, 1, 12 ], [ 25, 2, 1, 24 ],
[ 25, 3, 1, 48 ], [ 26, 1, 1, 48 ], [ 26, 2, 1, 24 ], [ 26, 3, 1, 24 ],
[ 29, 3, 1, 48 ], [ 29, 7, 1, 96 ], [ 29, 9, 1, 24 ], [ 29, 10, 1, 48 ],
[ 29, 11, 1, 24 ], [ 29, 12, 1, 48 ], [ 29, 13, 1, 48 ], [ 30, 5, 1, 96 ],
[ 30, 9, 1, 96 ], [ 30, 11, 1, 48 ], [ 31, 12, 1, 96 ], [ 31, 20, 1, 192 ],
[ 31, 22, 1, 96 ], [ 31, 25, 1, 96 ], [ 31, 27, 1, 96 ], [ 31, 31, 1, 96 ],
[ 31, 33, 1, 192 ] ]
k = 2: F-action on Pi is () [31,8,2]
Dynkin type is (A_0(q) + T(phi1^5 phi2)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-12*q+35 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-13*q^2+51*q-63 )
Fusion of maximal tori of C^F in those of G^F:
[ 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 9, 2, 1, 12 ], [ 9, 3, 1, 12 ],
[ 9, 3, 2, 8 ], [ 9, 4, 1, 12 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 4 ],
[ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ], [ 15, 1, 1, 24 ], [ 16, 6, 4, 16 ],
[ 16, 10, 4, 8 ], [ 16, 12, 2, 8 ], [ 16, 16, 3, 8 ], [ 18, 2, 2, 4 ],
[ 20, 1, 1, 24 ], [ 20, 2, 1, 12 ], [ 23, 4, 4, 8 ], [ 23, 6, 4, 4 ],
[ 25, 2, 2, 8 ], [ 25, 3, 5, 16 ], [ 26, 1, 1, 48 ], [ 26, 2, 1, 24 ],
[ 26, 3, 1, 24 ], [ 29, 3, 4, 16 ], [ 29, 3, 5, 16 ], [ 29, 7, 4, 32 ],
[ 29, 9, 4, 8 ], [ 29, 9, 5, 8 ], [ 29, 10, 4, 16 ], [ 29, 11, 4, 8 ],
[ 29, 12, 4, 16 ], [ 29, 13, 4, 16 ], [ 30, 5, 2, 32 ], [ 30, 5, 15, 32 ],
[ 30, 9, 3, 16 ], [ 30, 9, 17, 32 ], [ 30, 11, 4, 16 ], [ 30, 11, 15, 16 ],
[ 30, 11, 17, 16 ], [ 31, 12, 4, 32 ], [ 31, 12, 29, 32 ],
[ 31, 20, 2, 64 ], [ 31, 20, 5, 32 ], [ 31, 22, 4, 32 ], [ 31, 25, 4, 32 ],
[ 31, 25, 5, 32 ], [ 31, 27, 4, 32 ], [ 31, 27, 15, 32 ], [ 31, 31, 9, 32 ],
[ 31, 33, 2, 32 ], [ 31, 33, 17, 64 ] ]
k = 3: F-action on Pi is () [31,8,3]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^2-10*q+21 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 3, 2, 8 ],
[ 3, 5, 2, 4 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ],
[ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ],
[ 9, 3, 1, 8 ], [ 9, 3, 2, 12 ], [ 9, 3, 3, 16 ], [ 9, 4, 1, 8 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 6 ], [ 9, 5, 3, 8 ],
[ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ], [ 16, 6, 3, 16 ], [ 16, 6, 5, 32 ],
[ 16, 10, 3, 8 ], [ 16, 10, 5, 16 ], [ 16, 12, 3, 8 ], [ 16, 12, 5, 16 ],
[ 16, 16, 5, 16 ], [ 16, 16, 6, 32 ], [ 18, 2, 2, 4 ], [ 20, 1, 2, 8 ],
[ 20, 2, 2, 4 ], [ 23, 4, 3, 8 ], [ 23, 6, 3, 4 ], [ 25, 2, 2, 8 ],
[ 25, 3, 5, 16 ], [ 26, 1, 2, 16 ], [ 26, 2, 2, 8 ], [ 26, 3, 5, 8 ],
[ 29, 3, 3, 16 ], [ 29, 3, 5, 16 ], [ 29, 7, 3, 32 ], [ 29, 9, 3, 8 ],
[ 29, 9, 5, 8 ], [ 29, 10, 3, 16 ], [ 29, 11, 3, 8 ], [ 29, 12, 3, 16 ],
[ 29, 13, 3, 16 ], [ 30, 5, 3, 32 ], [ 30, 5, 15, 32 ], [ 30, 9, 5, 32 ],
[ 30, 9, 17, 32 ], [ 30, 11, 3, 16 ], [ 30, 11, 9, 16 ], [ 30, 11, 17, 16 ],
[ 31, 12, 3, 32 ], [ 31, 12, 43, 32 ], [ 31, 20, 3, 64 ], [ 31, 20, 9, 64 ],
[ 31, 22, 3, 32 ], [ 31, 25, 3, 32 ], [ 31, 25, 9, 32 ], [ 31, 27, 3, 32 ],
[ 31, 27, 43, 32 ], [ 31, 31, 25, 32 ], [ 31, 33, 3, 64 ],
[ 31, 33, 49, 64 ] ]
k = 4: F-action on Pi is () [31,8,4]
Dynkin type is (A_0(q) + T(phi1^5 phi2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^2-10*q+21 )
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 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 16 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 8 ], [ 9, 5, 2, 2 ],
[ 10, 2, 1, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ], [ 16, 6, 2, 16 ],
[ 16, 10, 2, 8 ], [ 16, 12, 4, 8 ], [ 16, 16, 3, 8 ], [ 18, 2, 1, 12 ],
[ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ], [ 23, 4, 1, 16 ], [ 23, 4, 2, 8 ],
[ 23, 6, 1, 8 ], [ 23, 6, 2, 4 ], [ 25, 2, 1, 24 ], [ 25, 3, 1, 16 ],
[ 26, 1, 2, 16 ], [ 26, 2, 2, 8 ], [ 26, 3, 5, 8 ], [ 29, 3, 1, 32 ],
[ 29, 3, 2, 16 ], [ 29, 7, 2, 32 ], [ 29, 9, 1, 16 ], [ 29, 9, 2, 8 ],
[ 29, 10, 2, 16 ], [ 29, 11, 1, 16 ], [ 29, 11, 2, 8 ], [ 29, 12, 2, 16 ],
[ 29, 13, 2, 16 ], [ 30, 5, 1, 32 ], [ 30, 5, 4, 32 ], [ 30, 9, 1, 32 ],
[ 30, 9, 3, 16 ], [ 30, 11, 1, 16 ], [ 30, 11, 2, 16 ], [ 30, 11, 6, 16 ],
[ 31, 12, 2, 32 ], [ 31, 12, 15, 32 ], [ 31, 20, 4, 64 ], [ 31, 20, 5, 32 ],
[ 31, 22, 2, 32 ], [ 31, 25, 2, 32 ], [ 31, 25, 13, 32 ], [ 31, 27, 2, 32 ],
[ 31, 27, 29, 32 ], [ 31, 31, 17, 32 ], [ 31, 33, 2, 32 ],
[ 31, 33, 33, 64 ] ]
k = 5: F-action on Pi is () [31,8,5]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-12*q+35 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-13*q^2+51*q-63 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 6 ],
[ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ], [ 9, 2, 1, 12 ], [ 9, 3, 1, 12 ],
[ 9, 3, 6, 8 ], [ 9, 4, 1, 12 ], [ 9, 5, 1, 6 ], [ 9, 5, 6, 4 ],
[ 11, 1, 1, 8 ], [ 11, 2, 1, 4 ], [ 15, 1, 1, 24 ], [ 16, 6, 11, 16 ],
[ 16, 10, 11, 8 ], [ 16, 12, 15, 8 ], [ 16, 16, 13, 8 ], [ 18, 2, 3, 4 ],
[ 20, 1, 1, 24 ], [ 20, 2, 1, 12 ], [ 23, 4, 5, 8 ], [ 23, 6, 5, 4 ],
[ 25, 2, 5, 8 ], [ 25, 3, 2, 16 ], [ 26, 1, 1, 48 ], [ 26, 2, 1, 24 ],
[ 26, 3, 1, 24 ], [ 29, 3, 8, 16 ], [ 29, 3, 9, 16 ], [ 29, 7, 9, 32 ],
[ 29, 9, 8, 8 ], [ 29, 9, 9, 8 ], [ 29, 10, 9, 16 ], [ 29, 11, 5, 8 ],
[ 29, 12, 9, 16 ], [ 29, 13, 13, 16 ], [ 30, 5, 9, 32 ], [ 30, 5, 16, 32 ],
[ 30, 9, 12, 16 ], [ 30, 9, 19, 16 ], [ 30, 11, 13, 16 ],
[ 30, 11, 20, 16 ], [ 30, 11, 31, 16 ], [ 31, 12, 7, 32 ],
[ 31, 12, 32, 32 ], [ 31, 20, 6, 32 ], [ 31, 20, 13, 32 ],
[ 31, 22, 14, 32 ], [ 31, 25, 8, 32 ], [ 31, 25, 45, 32 ],
[ 31, 27, 14, 32 ], [ 31, 27, 18, 32 ], [ 31, 31, 4, 32 ],
[ 31, 33, 6, 32 ], [ 31, 33, 18, 32 ] ]
k = 6: F-action on Pi is () [31,8,6]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 3, 4, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 4, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ],
[ 16, 6, 8, 16 ], [ 16, 10, 8, 8 ], [ 16, 12, 6, 8 ], [ 16, 16, 7, 8 ],
[ 18, 2, 3, 4 ], [ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ], [ 23, 4, 5, 8 ],
[ 23, 6, 5, 4 ], [ 25, 2, 5, 8 ], [ 26, 1, 2, 16 ], [ 26, 2, 2, 8 ],
[ 26, 3, 5, 8 ], [ 29, 3, 7, 8 ], [ 29, 3, 8, 8 ], [ 29, 3, 9, 16 ],
[ 29, 9, 7, 4 ], [ 29, 9, 8, 4 ], [ 29, 9, 9, 8 ], [ 29, 11, 5, 8 ],
[ 30, 5, 10, 16 ], [ 30, 5, 16, 16 ], [ 30, 5, 17, 16 ], [ 30, 9, 14, 8 ],
[ 30, 9, 19, 8 ], [ 30, 9, 21, 16 ], [ 30, 11, 12, 8 ], [ 30, 11, 14, 8 ],
[ 30, 11, 19, 8 ], [ 30, 11, 20, 8 ], [ 30, 11, 25, 8 ], [ 30, 11, 31, 8 ],
[ 31, 12, 6, 16 ], [ 31, 12, 31, 16 ], [ 31, 12, 46, 16 ],
[ 31, 20, 7, 16 ], [ 31, 20, 10, 32 ], [ 31, 20, 17, 16 ],
[ 31, 22, 13, 16 ], [ 31, 25, 7, 16 ], [ 31, 25, 12, 16 ],
[ 31, 25, 49, 16 ], [ 31, 27, 13, 16 ], [ 31, 27, 17, 16 ],
[ 31, 27, 46, 16 ], [ 31, 33, 7, 16 ], [ 31, 33, 19, 32 ],
[ 31, 33, 50, 16 ] ]
k = 7: F-action on Pi is () [31,8,7]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 3, 8, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 8, 4 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ],
[ 16, 6, 15, 16 ], [ 16, 10, 15, 8 ], [ 16, 12, 11, 8 ], [ 16, 16, 13, 8 ],
[ 18, 2, 2, 4 ], [ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ], [ 23, 4, 4, 8 ],
[ 23, 6, 4, 4 ], [ 25, 2, 2, 8 ], [ 26, 1, 2, 16 ], [ 26, 2, 2, 8 ],
[ 26, 3, 5, 8 ], [ 29, 3, 4, 16 ], [ 29, 3, 5, 8 ], [ 29, 3, 6, 8 ],
[ 29, 9, 4, 8 ], [ 29, 9, 5, 4 ], [ 29, 9, 6, 4 ], [ 29, 11, 4, 8 ],
[ 30, 5, 2, 16 ], [ 30, 5, 11, 16 ], [ 30, 5, 18, 16 ], [ 30, 9, 3, 8 ],
[ 30, 9, 15, 16 ], [ 30, 9, 19, 8 ], [ 30, 11, 4, 8 ], [ 30, 11, 8, 8 ],
[ 30, 11, 15, 8 ], [ 30, 11, 16, 8 ], [ 30, 11, 18, 8 ], [ 30, 11, 22, 8 ],
[ 31, 12, 5, 16 ], [ 31, 12, 18, 16 ], [ 31, 12, 30, 16 ],
[ 31, 20, 6, 16 ], [ 31, 20, 8, 16 ], [ 31, 20, 21, 32 ], [ 31, 22, 7, 16 ],
[ 31, 25, 6, 16 ], [ 31, 25, 16, 16 ], [ 31, 25, 17, 16 ],
[ 31, 27, 7, 16 ], [ 31, 27, 16, 16 ], [ 31, 27, 32, 16 ],
[ 31, 33, 8, 32 ], [ 31, 33, 18, 16 ], [ 31, 33, 34, 16 ] ]
k = 8: F-action on Pi is () [31,8,8]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ],
[ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 8, 2 ], [ 11, 1, 1, 4 ],
[ 11, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 20, 1, 1, 4 ], [ 20, 1, 3, 4 ],
[ 20, 2, 1, 2 ], [ 20, 2, 3, 2 ], [ 25, 2, 4, 4 ], [ 26, 1, 5, 8 ],
[ 26, 2, 3, 4 ], [ 26, 3, 2, 4 ], [ 26, 3, 4, 4 ], [ 29, 3, 17, 8 ],
[ 29, 9, 17, 4 ], [ 30, 5, 5, 8 ], [ 30, 9, 6, 4 ], [ 31, 12, 11, 8 ],
[ 31, 20, 49, 8 ], [ 31, 22, 11, 8 ], [ 31, 25, 29, 8 ], [ 31, 27, 11, 8 ],
[ 31, 33, 10, 8 ] ]
k = 9: F-action on Pi is () [31,8,9]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 1, 4 ],
[ 3, 5, 1, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 6, 4 ],
[ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 6, 2 ],
[ 9, 5, 8, 2 ], [ 10, 2, 1, 2 ], [ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ],
[ 15, 1, 2, 4 ], [ 16, 6, 1, 8 ], [ 16, 6, 11, 8 ], [ 16, 10, 1, 4 ],
[ 16, 10, 11, 4 ], [ 16, 12, 1, 4 ], [ 16, 12, 15, 4 ], [ 16, 16, 1, 8 ],
[ 16, 16, 13, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 3, 2 ], [ 19, 4, 1, 8 ],
[ 19, 5, 1, 4 ], [ 20, 1, 1, 4 ], [ 20, 1, 3, 4 ], [ 20, 2, 1, 2 ],
[ 20, 2, 3, 2 ], [ 23, 4, 1, 4 ], [ 23, 4, 5, 4 ], [ 23, 6, 1, 2 ],
[ 23, 6, 5, 2 ], [ 25, 2, 3, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ],
[ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 26, 1, 5, 8 ], [ 26, 2, 3, 4 ],
[ 26, 3, 2, 4 ], [ 26, 3, 4, 4 ], [ 29, 3, 13, 8 ], [ 29, 7, 1, 8 ],
[ 29, 7, 5, 8 ], [ 29, 7, 9, 8 ], [ 29, 7, 13, 8 ], [ 29, 9, 13, 4 ],
[ 29, 10, 1, 4 ], [ 29, 10, 5, 4 ], [ 29, 10, 9, 4 ], [ 29, 10, 13, 4 ],
[ 29, 11, 9, 4 ], [ 29, 11, 13, 4 ], [ 29, 12, 1, 4 ], [ 29, 12, 5, 4 ],
[ 29, 12, 9, 4 ], [ 29, 12, 13, 4 ], [ 29, 13, 1, 4 ], [ 29, 13, 5, 4 ],
[ 29, 13, 9, 4 ], [ 29, 13, 13, 4 ], [ 30, 5, 6, 8 ], [ 30, 9, 8, 8 ],
[ 31, 12, 10, 8 ], [ 31, 20, 57, 16 ], [ 31, 22, 9, 8 ], [ 31, 25, 33, 8 ],
[ 31, 27, 9, 8 ], [ 31, 31, 2, 8 ], [ 31, 31, 3, 8 ], [ 31, 31, 6, 8 ],
[ 31, 31, 7, 8 ], [ 31, 33, 11, 16 ] ]
k = 10: F-action on Pi is () [31,8,10]
Dynkin type is (A_0(q) + T(phi1^2 phi4^2)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 11 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 2, 4 ],
[ 3, 5, 2, 2 ], [ 5, 1, 1, 2 ], [ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ],
[ 9, 3, 3, 4 ], [ 9, 3, 8, 8 ], [ 9, 4, 8, 4 ], [ 9, 5, 3, 2 ],
[ 9, 5, 8, 4 ], [ 15, 1, 5, 4 ], [ 16, 6, 5, 8 ], [ 16, 6, 15, 8 ],
[ 16, 10, 5, 4 ], [ 16, 10, 15, 4 ], [ 16, 12, 5, 4 ], [ 16, 12, 11, 4 ],
[ 16, 16, 6, 8 ], [ 16, 16, 13, 4 ], [ 25, 2, 4, 4 ], [ 26, 1, 6, 8 ],
[ 26, 2, 4, 4 ], [ 29, 3, 17, 8 ], [ 29, 9, 17, 4 ], [ 30, 5, 7, 8 ],
[ 30, 9, 11, 8 ], [ 31, 12, 9, 8 ], [ 31, 20, 53, 16 ], [ 31, 22, 10, 8 ],
[ 31, 25, 37, 8 ], [ 31, 27, 10, 8 ], [ 31, 33, 12, 16 ] ]
k = 11: F-action on Pi is () [31,8,11]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ],
[ 9, 5, 8, 2 ], [ 10, 2, 1, 2 ], [ 15, 1, 5, 4 ], [ 18, 2, 1, 2 ],
[ 18, 2, 3, 2 ], [ 23, 4, 1, 4 ], [ 23, 4, 5, 4 ], [ 23, 6, 1, 2 ],
[ 23, 6, 5, 2 ], [ 25, 2, 3, 4 ], [ 26, 1, 6, 8 ], [ 26, 2, 4, 4 ],
[ 29, 3, 13, 8 ], [ 29, 9, 13, 4 ], [ 29, 11, 9, 4 ], [ 29, 11, 13, 4 ],
[ 30, 5, 8, 8 ], [ 30, 9, 6, 4 ], [ 31, 12, 8, 8 ], [ 31, 20, 49, 8 ],
[ 31, 22, 8, 8 ], [ 31, 25, 41, 8 ], [ 31, 27, 8, 8 ], [ 31, 33, 10, 8 ] ]
k = 12: F-action on Pi is () [31,8,12]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-9*q^2+27*q-27 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 3, 1, 8 ],
[ 3, 5, 1, 4 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ],
[ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ],
[ 9, 3, 1, 12 ], [ 9, 3, 2, 8 ], [ 9, 3, 4, 16 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 8 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 4 ], [ 9, 5, 4, 8 ],
[ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 6, 1, 16 ], [ 16, 6, 7, 32 ],
[ 16, 10, 1, 8 ], [ 16, 10, 7, 16 ], [ 16, 12, 1, 8 ], [ 16, 12, 7, 16 ],
[ 16, 16, 1, 16 ], [ 16, 16, 8, 32 ], [ 18, 2, 3, 4 ], [ 20, 1, 3, 8 ],
[ 20, 2, 3, 4 ], [ 23, 4, 5, 8 ], [ 23, 6, 5, 4 ], [ 25, 2, 5, 8 ],
[ 25, 3, 3, 16 ], [ 26, 1, 3, 16 ], [ 26, 2, 5, 8 ], [ 26, 3, 3, 8 ],
[ 29, 3, 7, 16 ], [ 29, 3, 9, 16 ], [ 29, 7, 5, 32 ], [ 29, 9, 7, 8 ],
[ 29, 9, 9, 8 ], [ 29, 10, 5, 16 ], [ 29, 11, 5, 8 ], [ 29, 12, 5, 16 ],
[ 29, 13, 5, 16 ], [ 30, 5, 12, 32 ], [ 30, 5, 17, 32 ], [ 30, 9, 16, 32 ],
[ 30, 9, 21, 32 ], [ 30, 11, 11, 16 ], [ 30, 11, 19, 16 ],
[ 30, 11, 25, 16 ], [ 31, 12, 13, 32 ], [ 31, 12, 45, 32 ],
[ 31, 20, 11, 64 ], [ 31, 20, 61, 64 ], [ 31, 22, 12, 32 ],
[ 31, 25, 11, 32 ], [ 31, 25, 53, 32 ], [ 31, 27, 12, 32 ],
[ 31, 27, 45, 32 ], [ 31, 31, 5, 32 ], [ 31, 33, 16, 64 ],
[ 31, 33, 51, 64 ] ]
k = 13: F-action on Pi is () [31,8,13]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 3, 3, 8 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 9, 5, 3, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ],
[ 16, 6, 6, 16 ], [ 16, 10, 6, 8 ], [ 16, 12, 8, 8 ], [ 16, 16, 7, 8 ],
[ 18, 2, 2, 4 ], [ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 23, 4, 3, 8 ],
[ 23, 6, 3, 4 ], [ 25, 2, 2, 8 ], [ 26, 1, 3, 16 ], [ 26, 2, 5, 8 ],
[ 26, 3, 3, 8 ], [ 29, 3, 3, 16 ], [ 29, 3, 5, 8 ], [ 29, 3, 6, 8 ],
[ 29, 9, 3, 8 ], [ 29, 9, 5, 4 ], [ 29, 9, 6, 4 ], [ 29, 11, 3, 8 ],
[ 30, 5, 3, 16 ], [ 30, 5, 13, 16 ], [ 30, 5, 18, 16 ], [ 30, 9, 5, 16 ],
[ 30, 9, 14, 8 ], [ 30, 9, 19, 8 ], [ 30, 11, 3, 8 ], [ 30, 11, 7, 8 ],
[ 30, 11, 9, 8 ], [ 30, 11, 10, 8 ], [ 30, 11, 18, 8 ], [ 30, 11, 22, 8 ],
[ 31, 12, 12, 16 ], [ 31, 12, 17, 16 ], [ 31, 12, 44, 16 ],
[ 31, 20, 7, 16 ], [ 31, 20, 12, 32 ], [ 31, 20, 17, 16 ],
[ 31, 22, 6, 16 ], [ 31, 25, 10, 16 ], [ 31, 25, 15, 16 ],
[ 31, 25, 21, 16 ], [ 31, 27, 6, 16 ], [ 31, 27, 31, 16 ],
[ 31, 27, 44, 16 ], [ 31, 33, 7, 16 ], [ 31, 33, 35, 32 ],
[ 31, 33, 50, 16 ] ]
k = 14: F-action on Pi is () [31,8,14]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-9*q^2+27*q-27 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 3, 6, 8 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 9, 5, 6, 4 ], [ 10, 2, 1, 4 ], [ 15, 1, 3, 8 ],
[ 15, 1, 4, 8 ], [ 16, 6, 11, 16 ], [ 16, 10, 11, 8 ], [ 16, 12, 15, 8 ],
[ 16, 16, 13, 8 ], [ 18, 2, 1, 12 ], [ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ],
[ 23, 4, 1, 8 ], [ 23, 4, 2, 16 ], [ 23, 6, 1, 4 ], [ 23, 6, 2, 8 ],
[ 25, 2, 1, 24 ], [ 25, 3, 4, 16 ], [ 26, 1, 3, 16 ], [ 26, 2, 5, 8 ],
[ 26, 3, 3, 8 ], [ 29, 3, 1, 16 ], [ 29, 3, 2, 32 ], [ 29, 7, 13, 32 ],
[ 29, 9, 1, 8 ], [ 29, 9, 2, 16 ], [ 29, 10, 13, 16 ], [ 29, 11, 1, 8 ],
[ 29, 11, 2, 16 ], [ 29, 12, 13, 16 ], [ 29, 13, 9, 16 ], [ 30, 5, 4, 32 ],
[ 30, 5, 14, 32 ], [ 30, 9, 3, 16 ], [ 30, 9, 12, 16 ], [ 30, 11, 2, 16 ],
[ 30, 11, 5, 16 ], [ 30, 11, 6, 16 ], [ 31, 12, 14, 32 ],
[ 31, 12, 16, 32 ], [ 31, 20, 8, 32 ], [ 31, 20, 13, 32 ],
[ 31, 22, 5, 32 ], [ 31, 25, 14, 32 ], [ 31, 25, 25, 32 ],
[ 31, 27, 5, 32 ], [ 31, 27, 30, 32 ], [ 31, 31, 8, 32 ], [ 31, 33, 6, 32 ],
[ 31, 33, 34, 32 ] ]
k = 15: F-action on Pi is () [31,8,15]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/192 ( q^3-21*q^2+143*q-315 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/192 ( q^3-21*q^2+131*q-231 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 3, 3, 8 ],
[ 3, 5, 3, 4 ], [ 5, 1, 1, 6 ], [ 8, 1, 1, 12 ], [ 9, 1, 1, 24 ],
[ 9, 2, 1, 12 ], [ 9, 3, 1, 12 ], [ 9, 3, 5, 24 ], [ 9, 4, 1, 12 ],
[ 9, 5, 1, 6 ], [ 9, 5, 5, 12 ], [ 10, 2, 2, 4 ], [ 11, 1, 1, 8 ],
[ 11, 2, 1, 4 ], [ 15, 1, 1, 24 ], [ 16, 6, 9, 48 ], [ 16, 10, 9, 24 ],
[ 16, 12, 16, 24 ], [ 16, 16, 9, 24 ], [ 18, 2, 4, 12 ], [ 19, 4, 4, 32 ],
[ 19, 5, 4, 16 ], [ 20, 1, 1, 24 ], [ 20, 2, 1, 12 ], [ 23, 4, 8, 24 ],
[ 23, 6, 8, 12 ], [ 25, 2, 8, 24 ], [ 25, 3, 6, 48 ], [ 26, 1, 1, 48 ],
[ 26, 2, 1, 24 ], [ 26, 3, 1, 24 ], [ 29, 3, 12, 48 ], [ 29, 7, 12, 96 ],
[ 29, 9, 12, 24 ], [ 29, 10, 12, 48 ], [ 29, 11, 8, 24 ],
[ 29, 12, 12, 48 ], [ 29, 13, 16, 48 ], [ 30, 5, 23, 96 ],
[ 30, 9, 28, 48 ], [ 30, 11, 29, 48 ], [ 31, 12, 35, 96 ],
[ 31, 20, 14, 96 ], [ 31, 22, 24, 96 ], [ 31, 25, 48, 96 ],
[ 31, 27, 28, 96 ], [ 31, 31, 12, 96 ], [ 31, 33, 22, 96 ] ]
k = 16: F-action on Pi is () [31,8,16]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^2-10*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, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ],
[ 9, 3, 5, 8 ], [ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ],
[ 9, 5, 2, 2 ], [ 9, 5, 5, 4 ], [ 10, 2, 2, 4 ], [ 15, 1, 1, 8 ],
[ 15, 1, 4, 8 ], [ 16, 6, 10, 16 ], [ 16, 10, 10, 8 ], [ 16, 12, 14, 8 ],
[ 16, 16, 12, 8 ], [ 18, 2, 4, 12 ], [ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ],
[ 23, 4, 7, 8 ], [ 23, 4, 8, 16 ], [ 23, 6, 7, 4 ], [ 23, 6, 8, 8 ],
[ 25, 2, 8, 24 ], [ 25, 3, 6, 16 ], [ 26, 1, 2, 16 ], [ 26, 2, 2, 8 ],
[ 26, 3, 5, 8 ], [ 29, 3, 11, 16 ], [ 29, 3, 12, 32 ], [ 29, 7, 11, 32 ],
[ 29, 9, 11, 8 ], [ 29, 9, 12, 16 ], [ 29, 10, 11, 16 ], [ 29, 11, 7, 8 ],
[ 29, 11, 8, 16 ], [ 29, 12, 11, 16 ], [ 29, 13, 15, 16 ],
[ 30, 5, 23, 32 ], [ 30, 5, 24, 32 ], [ 30, 9, 28, 16 ], [ 30, 9, 30, 16 ],
[ 30, 11, 28, 16 ], [ 30, 11, 29, 16 ], [ 30, 11, 30, 16 ],
[ 31, 12, 34, 32 ], [ 31, 12, 49, 32 ], [ 31, 20, 15, 32 ],
[ 31, 20, 18, 32 ], [ 31, 22, 23, 32 ], [ 31, 25, 47, 32 ],
[ 31, 25, 52, 32 ], [ 31, 27, 27, 32 ], [ 31, 27, 56, 32 ],
[ 31, 31, 28, 32 ], [ 31, 33, 23, 32 ], [ 31, 33, 54, 32 ] ]
k = 17: F-action on Pi is () [31,8,17]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-10*q+25 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi1 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 3, 4, 8 ],
[ 3, 5, 4, 4 ], [ 5, 1, 1, 4 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 4 ],
[ 9, 1, 1, 16 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 8 ], [ 9, 2, 2, 4 ],
[ 9, 3, 1, 8 ], [ 9, 3, 2, 4 ], [ 9, 3, 6, 8 ], [ 9, 3, 7, 16 ],
[ 9, 4, 1, 8 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 2 ],
[ 9, 5, 6, 4 ], [ 9, 5, 7, 8 ], [ 15, 1, 1, 8 ], [ 15, 1, 4, 8 ],
[ 16, 6, 12, 16 ], [ 16, 6, 13, 32 ], [ 16, 10, 12, 8 ], [ 16, 10, 13, 16 ],
[ 16, 12, 12, 16 ], [ 16, 12, 13, 8 ], [ 16, 16, 14, 24 ], [ 18, 2, 3, 4 ],
[ 20, 1, 2, 8 ], [ 20, 2, 2, 4 ], [ 23, 4, 6, 8 ], [ 23, 6, 6, 4 ],
[ 25, 2, 5, 8 ], [ 25, 3, 2, 16 ], [ 26, 1, 2, 16 ], [ 26, 2, 2, 8 ],
[ 26, 3, 5, 8 ], [ 29, 3, 8, 16 ], [ 29, 3, 10, 16 ], [ 29, 7, 10, 32 ],
[ 29, 9, 8, 8 ], [ 29, 9, 10, 8 ], [ 29, 10, 10, 16 ], [ 29, 11, 6, 8 ],
[ 29, 12, 10, 16 ], [ 29, 13, 14, 16 ], [ 30, 5, 9, 32 ], [ 30, 5, 25, 32 ],
[ 30, 9, 12, 16 ], [ 30, 9, 31, 32 ], [ 30, 11, 13, 16 ],
[ 30, 11, 24, 16 ], [ 30, 11, 32, 16 ], [ 31, 12, 21, 32 ],
[ 31, 12, 33, 32 ], [ 31, 20, 16, 32 ], [ 31, 20, 22, 64 ],
[ 31, 22, 17, 32 ], [ 31, 25, 20, 32 ], [ 31, 25, 46, 32 ],
[ 31, 27, 21, 32 ], [ 31, 27, 42, 32 ], [ 31, 31, 20, 32 ],
[ 31, 33, 24, 64 ], [ 31, 33, 38, 32 ] ]
k = 18: F-action on Pi is () [31,8,18]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ],
[ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 8, 2 ], [ 11, 1, 1, 4 ],
[ 11, 2, 1, 2 ], [ 15, 1, 2, 4 ], [ 20, 1, 1, 4 ], [ 20, 1, 3, 4 ],
[ 20, 2, 1, 2 ], [ 20, 2, 3, 2 ], [ 25, 2, 7, 4 ], [ 26, 1, 5, 8 ],
[ 26, 2, 3, 4 ], [ 26, 3, 2, 4 ], [ 26, 3, 4, 4 ], [ 29, 3, 20, 8 ],
[ 29, 9, 20, 4 ], [ 30, 5, 19, 8 ], [ 30, 9, 22, 4 ], [ 31, 12, 39, 8 ],
[ 31, 20, 50, 8 ], [ 31, 22, 21, 8 ], [ 31, 25, 32, 8 ], [ 31, 27, 25, 8 ],
[ 31, 33, 26, 8 ] ]
k = 19: F-action on Pi is () [31,8,19]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1^2 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 ( q^2-6*q+9 )
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, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 3, 4 ],
[ 3, 5, 3, 2 ], [ 5, 1, 1, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ], [ 9, 3, 2, 4 ], [ 9, 3, 5, 4 ],
[ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ], [ 9, 5, 2, 2 ], [ 9, 5, 5, 2 ],
[ 9, 5, 8, 2 ], [ 10, 2, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 2, 1, 2 ],
[ 15, 1, 2, 4 ], [ 16, 6, 4, 8 ], [ 16, 6, 9, 8 ], [ 16, 10, 4, 4 ],
[ 16, 10, 9, 4 ], [ 16, 12, 2, 4 ], [ 16, 12, 16, 4 ], [ 16, 16, 3, 4 ],
[ 16, 16, 9, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 19, 4, 4, 8 ],
[ 19, 5, 4, 4 ], [ 20, 1, 1, 4 ], [ 20, 1, 3, 4 ], [ 20, 2, 1, 2 ],
[ 20, 2, 3, 2 ], [ 23, 4, 4, 4 ], [ 23, 4, 8, 4 ], [ 23, 6, 4, 2 ],
[ 23, 6, 8, 2 ], [ 25, 2, 6, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ],
[ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 26, 1, 5, 8 ], [ 26, 2, 3, 4 ],
[ 26, 3, 2, 4 ], [ 26, 3, 4, 4 ], [ 29, 3, 16, 8 ], [ 29, 7, 4, 8 ],
[ 29, 7, 8, 8 ], [ 29, 7, 12, 8 ], [ 29, 7, 16, 8 ], [ 29, 9, 16, 4 ],
[ 29, 10, 4, 4 ], [ 29, 10, 8, 4 ], [ 29, 10, 12, 4 ], [ 29, 10, 16, 4 ],
[ 29, 11, 12, 4 ], [ 29, 11, 16, 4 ], [ 29, 12, 4, 4 ], [ 29, 12, 8, 4 ],
[ 29, 12, 12, 4 ], [ 29, 12, 16, 4 ], [ 29, 13, 4, 4 ], [ 29, 13, 8, 4 ],
[ 29, 13, 12, 4 ], [ 29, 13, 16, 4 ], [ 30, 5, 20, 8 ], [ 30, 9, 24, 8 ],
[ 31, 12, 38, 8 ], [ 31, 20, 58, 16 ], [ 31, 22, 19, 8 ], [ 31, 25, 36, 8 ],
[ 31, 27, 23, 8 ], [ 31, 31, 10, 8 ], [ 31, 31, 11, 8 ], [ 31, 31, 14, 8 ],
[ 31, 31, 15, 8 ], [ 31, 33, 27, 16 ] ]
k = 20: F-action on Pi is () [31,8,20]
Dynkin type is (A_0(q) + T(phi1 phi2 phi4^2)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
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, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 4, 4 ],
[ 3, 5, 4, 2 ], [ 5, 1, 1, 2 ], [ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ],
[ 9, 3, 4, 4 ], [ 9, 3, 7, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ],
[ 9, 5, 4, 2 ], [ 9, 5, 7, 2 ], [ 9, 5, 8, 2 ], [ 15, 1, 5, 4 ],
[ 16, 6, 8, 8 ], [ 16, 6, 13, 8 ], [ 16, 10, 8, 4 ], [ 16, 10, 13, 4 ],
[ 16, 12, 6, 4 ], [ 16, 12, 12, 4 ], [ 16, 16, 7, 4 ], [ 16, 16, 14, 4 ],
[ 25, 2, 7, 4 ], [ 26, 1, 6, 8 ], [ 26, 2, 4, 4 ], [ 29, 3, 20, 8 ],
[ 29, 9, 20, 4 ], [ 30, 5, 21, 8 ], [ 30, 9, 27, 8 ], [ 31, 12, 37, 8 ],
[ 31, 20, 54, 16 ], [ 31, 22, 20, 8 ], [ 31, 25, 40, 8 ], [ 31, 27, 24, 8 ],
[ 31, 33, 28, 16 ] ]
k = 21: F-action on Pi is () [31,8,21]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 phi2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 32 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 1, 2 ],
[ 9, 1, 8, 8 ], [ 9, 2, 8, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 8, 4 ],
[ 9, 5, 8, 2 ], [ 10, 2, 2, 2 ], [ 15, 1, 5, 4 ], [ 18, 2, 2, 2 ],
[ 18, 2, 4, 2 ], [ 23, 4, 4, 4 ], [ 23, 4, 8, 4 ], [ 23, 6, 4, 2 ],
[ 23, 6, 8, 2 ], [ 25, 2, 6, 4 ], [ 26, 1, 6, 8 ], [ 26, 2, 4, 4 ],
[ 29, 3, 16, 8 ], [ 29, 9, 16, 4 ], [ 29, 11, 12, 4 ], [ 29, 11, 16, 4 ],
[ 30, 5, 22, 8 ], [ 30, 9, 22, 4 ], [ 31, 12, 36, 8 ], [ 31, 20, 50, 8 ],
[ 31, 22, 18, 8 ], [ 31, 25, 44, 8 ], [ 31, 27, 22, 8 ], [ 31, 33, 26, 8 ] ]
k = 22: F-action on Pi is () [31,8,22]
Dynkin type is (A_0(q) + T(phi1 phi2^5)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-9*q^2+27*q-27 )
Fusion of maximal tori of C^F in those of G^F:
[ 9 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 16 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 8 ],
[ 10, 2, 2, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ], [ 16, 6, 4, 16 ],
[ 16, 10, 4, 8 ], [ 16, 12, 2, 8 ], [ 16, 16, 3, 8 ], [ 18, 2, 4, 12 ],
[ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 23, 4, 7, 16 ], [ 23, 4, 8, 8 ],
[ 23, 6, 7, 8 ], [ 23, 6, 8, 4 ], [ 25, 2, 8, 24 ], [ 25, 3, 7, 16 ],
[ 26, 1, 3, 16 ], [ 26, 2, 5, 8 ], [ 26, 3, 3, 8 ], [ 29, 3, 11, 32 ],
[ 29, 3, 12, 16 ], [ 29, 7, 8, 32 ], [ 29, 9, 11, 16 ], [ 29, 9, 12, 8 ],
[ 29, 10, 8, 16 ], [ 29, 11, 7, 16 ], [ 29, 11, 8, 8 ], [ 29, 12, 8, 16 ],
[ 29, 13, 8, 16 ], [ 30, 5, 24, 32 ], [ 30, 5, 26, 32 ], [ 30, 9, 30, 16 ],
[ 30, 9, 32, 32 ], [ 30, 11, 27, 16 ], [ 30, 11, 28, 16 ],
[ 30, 11, 30, 16 ], [ 31, 12, 41, 32 ], [ 31, 12, 48, 32 ],
[ 31, 20, 19, 32 ], [ 31, 20, 62, 64 ], [ 31, 22, 22, 32 ],
[ 31, 25, 51, 32 ], [ 31, 25, 56, 32 ], [ 31, 27, 26, 32 ],
[ 31, 27, 55, 32 ], [ 31, 31, 13, 32 ], [ 31, 33, 32, 64 ],
[ 31, 33, 55, 32 ] ]
k = 23: F-action on Pi is () [31,8,23]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q^2-6*q+9 )
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, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ],
[ 9, 3, 7, 8 ], [ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ],
[ 9, 5, 2, 4 ], [ 9, 5, 7, 4 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ],
[ 16, 6, 14, 16 ], [ 16, 10, 14, 8 ], [ 16, 12, 10, 8 ], [ 16, 16, 12, 8 ],
[ 18, 2, 3, 4 ], [ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 23, 4, 6, 8 ],
[ 23, 6, 6, 4 ], [ 25, 2, 5, 8 ], [ 26, 1, 3, 16 ], [ 26, 2, 5, 8 ],
[ 26, 3, 3, 8 ], [ 29, 3, 7, 8 ], [ 29, 3, 8, 8 ], [ 29, 3, 10, 16 ],
[ 29, 9, 7, 4 ], [ 29, 9, 8, 4 ], [ 29, 9, 10, 8 ], [ 29, 11, 6, 8 ],
[ 30, 5, 10, 16 ], [ 30, 5, 25, 16 ], [ 30, 5, 27, 16 ], [ 30, 9, 14, 8 ],
[ 30, 9, 30, 8 ], [ 30, 9, 31, 16 ], [ 30, 11, 12, 8 ], [ 30, 11, 14, 8 ],
[ 30, 11, 23, 8 ], [ 30, 11, 24, 8 ], [ 30, 11, 26, 8 ], [ 30, 11, 32, 8 ],
[ 31, 12, 20, 16 ], [ 31, 12, 40, 16 ], [ 31, 12, 47, 16 ],
[ 31, 20, 18, 16 ], [ 31, 20, 20, 16 ], [ 31, 20, 23, 32 ],
[ 31, 22, 16, 16 ], [ 31, 25, 19, 16 ], [ 31, 25, 24, 16 ],
[ 31, 25, 50, 16 ], [ 31, 27, 20, 16 ], [ 31, 27, 41, 16 ],
[ 31, 27, 49, 16 ], [ 31, 33, 23, 16 ], [ 31, 33, 39, 16 ],
[ 31, 33, 56, 32 ] ]
k = 24: F-action on Pi is () [31,8,24]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1 ( q^2-8*q+15 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 ( q^3-9*q^2+27*q-27 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 3, 3, 8 ],
[ 3, 5, 3, 4 ], [ 5, 1, 1, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ],
[ 9, 1, 1, 8 ], [ 9, 1, 2, 16 ], [ 9, 2, 1, 4 ], [ 9, 2, 2, 8 ],
[ 9, 3, 1, 4 ], [ 9, 3, 2, 8 ], [ 9, 3, 5, 8 ], [ 9, 3, 8, 16 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 8 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 4 ],
[ 9, 5, 5, 4 ], [ 9, 5, 8, 8 ], [ 15, 1, 3, 8 ], [ 15, 1, 4, 8 ],
[ 16, 6, 9, 16 ], [ 16, 6, 16, 32 ], [ 16, 10, 9, 8 ], [ 16, 10, 16, 16 ],
[ 16, 12, 9, 16 ], [ 16, 12, 16, 8 ], [ 16, 16, 9, 24 ], [ 18, 2, 2, 4 ],
[ 20, 1, 3, 8 ], [ 20, 2, 3, 4 ], [ 23, 4, 4, 8 ], [ 23, 6, 4, 4 ],
[ 25, 2, 2, 8 ], [ 25, 3, 8, 16 ], [ 26, 1, 3, 16 ], [ 26, 2, 5, 8 ],
[ 26, 3, 3, 8 ], [ 29, 3, 4, 16 ], [ 29, 3, 6, 16 ], [ 29, 7, 16, 32 ],
[ 29, 9, 4, 8 ], [ 29, 9, 6, 8 ], [ 29, 10, 16, 16 ], [ 29, 11, 4, 8 ],
[ 29, 12, 16, 16 ], [ 29, 13, 12, 16 ], [ 30, 5, 11, 32 ],
[ 30, 5, 28, 32 ], [ 30, 9, 15, 32 ], [ 30, 9, 28, 16 ], [ 30, 11, 8, 16 ],
[ 30, 11, 16, 16 ], [ 30, 11, 21, 16 ], [ 31, 12, 19, 32 ],
[ 31, 12, 42, 32 ], [ 31, 20, 14, 32 ], [ 31, 20, 24, 64 ],
[ 31, 22, 15, 32 ], [ 31, 25, 18, 32 ], [ 31, 25, 28, 32 ],
[ 31, 27, 19, 32 ], [ 31, 27, 35, 32 ], [ 31, 31, 16, 32 ],
[ 31, 33, 22, 32 ], [ 31, 33, 40, 64 ] ]
k = 25: F-action on Pi is () [31,8,25]
Dynkin type is (A_0(q) + T(phi1 phi2 phi3 phi6)).2
Order of center |Z^F|: phi1 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 37 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 3, 3, 2 ], [ 3, 5, 3, 1 ], [ 10, 2, 2, 1 ],
[ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 19, 4, 4, 2 ], [ 19, 5, 4, 1 ],
[ 25, 2, 10, 3 ], [ 26, 1, 9, 6 ], [ 26, 2, 6, 3 ], [ 31, 22, 28, 3 ] ]
k = 26: F-action on Pi is () [31,8,26]
Dynkin type is (A_0(q) + T(phi2^2 phi6^2)).2
Order of center |Z^F|: phi2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 27 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 3, 2, 2 ], [ 3, 5, 2, 1 ], [ 10, 2, 2, 1 ],
[ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 19, 4, 2, 2 ], [ 19, 5, 2, 1 ],
[ 25, 2, 10, 3 ], [ 26, 1, 10, 6 ], [ 26, 2, 7, 3 ], [ 31, 22, 27, 3 ] ]
k = 27: F-action on Pi is () [31,8,27]
Dynkin type is (A_0(q) + T(phi1^2 phi3^2)).2
Order of center |Z^F|: phi1 phi3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 26 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 3, 1, 2 ], [ 3, 5, 1, 1 ], [ 10, 2, 1, 1 ],
[ 11, 1, 1, 2 ], [ 11, 2, 1, 1 ], [ 19, 4, 1, 2 ], [ 19, 5, 1, 1 ],
[ 25, 2, 9, 3 ], [ 26, 1, 9, 6 ], [ 26, 2, 6, 3 ], [ 31, 22, 26, 3 ] ]
k = 28: F-action on Pi is () [31,8,28]
Dynkin type is (A_0(q) + T(phi1 phi2 phi3 phi6)).2
Order of center |Z^F|: phi2 phi6 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/6 q phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/6 q phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 36 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 3, 4, 2 ], [ 3, 5, 4, 1 ], [ 10, 2, 1, 1 ],
[ 11, 1, 2, 2 ], [ 11, 2, 2, 1 ], [ 19, 4, 3, 2 ], [ 19, 5, 3, 1 ],
[ 25, 2, 9, 3 ], [ 26, 1, 10, 6 ], [ 26, 2, 7, 3 ], [ 31, 22, 25, 3 ] ]
k = 29: F-action on Pi is () [31,8,29]
Dynkin type is (A_0(q) + T(phi1 phi2^3 phi4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ],
[ 9, 3, 7, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 7, 2 ], [ 11, 1, 2, 4 ],
[ 11, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 20, 1, 2, 4 ], [ 20, 1, 4, 4 ],
[ 20, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 25, 2, 7, 4 ], [ 26, 1, 7, 8 ],
[ 26, 2, 8, 4 ], [ 26, 3, 6, 4 ], [ 26, 3, 8, 4 ], [ 29, 3, 19, 8 ],
[ 29, 9, 19, 4 ], [ 30, 5, 19, 8 ], [ 30, 9, 22, 4 ], [ 31, 12, 53, 8 ],
[ 31, 20, 51, 8 ], [ 31, 22, 36, 8 ], [ 31, 25, 31, 8 ], [ 31, 27, 53, 8 ],
[ 31, 33, 58, 8 ] ]
k = 30: F-action on Pi is () [31,8,30]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ],
[ 9, 3, 7, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 7, 2 ], [ 11, 1, 2, 4 ],
[ 11, 2, 2, 2 ], [ 15, 1, 2, 4 ], [ 20, 1, 2, 4 ], [ 20, 1, 4, 4 ],
[ 20, 2, 2, 2 ], [ 20, 2, 4, 2 ], [ 25, 2, 4, 4 ], [ 26, 1, 7, 8 ],
[ 26, 2, 8, 4 ], [ 26, 3, 6, 4 ], [ 26, 3, 8, 4 ], [ 29, 3, 18, 8 ],
[ 29, 9, 18, 4 ], [ 30, 5, 5, 8 ], [ 30, 9, 6, 4 ], [ 31, 12, 25, 8 ],
[ 31, 20, 52, 8 ], [ 31, 22, 35, 8 ], [ 31, 25, 30, 8 ], [ 31, 27, 39, 8 ],
[ 31, 33, 42, 8 ] ]
k = 31: F-action on Pi is () [31,8,31]
Dynkin type is (A_0(q) + T(phi2^2 phi4^2)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 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 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 1, 4 ],
[ 3, 5, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ],
[ 9, 3, 4, 4 ], [ 9, 3, 7, 8 ], [ 9, 4, 7, 4 ], [ 9, 5, 4, 2 ],
[ 9, 5, 7, 4 ], [ 15, 1, 5, 4 ], [ 16, 6, 7, 8 ], [ 16, 6, 14, 8 ],
[ 16, 10, 7, 4 ], [ 16, 10, 14, 4 ], [ 16, 12, 7, 4 ], [ 16, 12, 10, 4 ],
[ 16, 16, 8, 8 ], [ 16, 16, 12, 4 ], [ 25, 2, 7, 4 ], [ 26, 1, 8, 8 ],
[ 26, 2, 9, 4 ], [ 29, 3, 19, 8 ], [ 29, 9, 19, 4 ], [ 30, 5, 21, 8 ],
[ 30, 9, 27, 8 ], [ 31, 12, 51, 8 ], [ 31, 20, 55, 16 ], [ 31, 22, 34, 8 ],
[ 31, 25, 39, 8 ], [ 31, 27, 52, 8 ], [ 31, 33, 60, 16 ] ]
k = 32: F-action on Pi is () [31,8,32]
Dynkin type is (A_0(q) + T(phi1 phi2 phi4^2)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
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, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 3, 4 ],
[ 3, 5, 3, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ],
[ 9, 3, 3, 4 ], [ 9, 3, 7, 4 ], [ 9, 3, 8, 4 ], [ 9, 4, 7, 4 ],
[ 9, 5, 3, 2 ], [ 9, 5, 7, 2 ], [ 9, 5, 8, 2 ], [ 15, 1, 5, 4 ],
[ 16, 6, 6, 8 ], [ 16, 6, 16, 8 ], [ 16, 10, 6, 4 ], [ 16, 10, 16, 4 ],
[ 16, 12, 8, 4 ], [ 16, 12, 9, 4 ], [ 16, 16, 7, 4 ], [ 16, 16, 9, 4 ],
[ 25, 2, 4, 4 ], [ 26, 1, 8, 8 ], [ 26, 2, 9, 4 ], [ 29, 3, 18, 8 ],
[ 29, 9, 18, 4 ], [ 30, 5, 7, 8 ], [ 30, 9, 11, 8 ], [ 31, 12, 23, 8 ],
[ 31, 20, 56, 16 ], [ 31, 22, 33, 8 ], [ 31, 25, 38, 8 ], [ 31, 27, 38, 8 ],
[ 31, 33, 44, 16 ] ]
k = 33: F-action on Pi is () [31,8,33]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 13 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 2, 4 ],
[ 3, 5, 2, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ], [ 9, 3, 2, 4 ], [ 9, 3, 5, 4 ],
[ 9, 3, 7, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 2, 2 ], [ 9, 5, 5, 2 ],
[ 9, 5, 7, 2 ], [ 10, 2, 2, 2 ], [ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ],
[ 15, 1, 2, 4 ], [ 16, 6, 3, 8 ], [ 16, 6, 10, 8 ], [ 16, 10, 3, 4 ],
[ 16, 10, 10, 4 ], [ 16, 12, 3, 4 ], [ 16, 12, 14, 4 ], [ 16, 16, 5, 8 ],
[ 16, 16, 12, 4 ], [ 18, 2, 2, 2 ], [ 18, 2, 4, 2 ], [ 19, 4, 2, 8 ],
[ 19, 5, 2, 4 ], [ 20, 1, 2, 4 ], [ 20, 1, 4, 4 ], [ 20, 2, 2, 2 ],
[ 20, 2, 4, 2 ], [ 23, 4, 3, 4 ], [ 23, 4, 7, 4 ], [ 23, 6, 3, 2 ],
[ 23, 6, 7, 2 ], [ 25, 2, 6, 4 ], [ 25, 3, 5, 4 ], [ 25, 3, 6, 4 ],
[ 25, 3, 7, 4 ], [ 25, 3, 8, 4 ], [ 26, 1, 7, 8 ], [ 26, 2, 8, 4 ],
[ 26, 3, 6, 4 ], [ 26, 3, 8, 4 ], [ 29, 3, 15, 8 ], [ 29, 7, 3, 8 ],
[ 29, 7, 7, 8 ], [ 29, 7, 11, 8 ], [ 29, 7, 15, 8 ], [ 29, 9, 15, 4 ],
[ 29, 10, 3, 4 ], [ 29, 10, 7, 4 ], [ 29, 10, 11, 4 ], [ 29, 10, 15, 4 ],
[ 29, 11, 11, 4 ], [ 29, 11, 15, 4 ], [ 29, 12, 3, 4 ], [ 29, 12, 7, 4 ],
[ 29, 12, 11, 4 ], [ 29, 12, 15, 4 ], [ 29, 13, 3, 4 ], [ 29, 13, 7, 4 ],
[ 29, 13, 11, 4 ], [ 29, 13, 15, 4 ], [ 30, 5, 20, 8 ], [ 30, 9, 24, 8 ],
[ 31, 12, 52, 8 ], [ 31, 20, 59, 16 ], [ 31, 22, 32, 8 ], [ 31, 25, 35, 8 ],
[ 31, 27, 51, 8 ], [ 31, 31, 26, 8 ], [ 31, 31, 27, 8 ], [ 31, 31, 30, 8 ],
[ 31, 31, 31, 8 ], [ 31, 33, 59, 16 ] ]
k = 34: F-action on Pi is () [31,8,34]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi1 phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 3, 4, 4 ],
[ 3, 5, 4, 2 ], [ 5, 1, 2, 2 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ],
[ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 6, 4 ],
[ 9, 3, 7, 4 ], [ 9, 4, 7, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 6, 2 ],
[ 9, 5, 7, 2 ], [ 10, 2, 1, 2 ], [ 11, 1, 2, 4 ], [ 11, 2, 2, 2 ],
[ 15, 1, 2, 4 ], [ 16, 6, 2, 8 ], [ 16, 6, 12, 8 ], [ 16, 10, 2, 4 ],
[ 16, 10, 12, 4 ], [ 16, 12, 4, 4 ], [ 16, 12, 13, 4 ], [ 16, 16, 3, 4 ],
[ 16, 16, 14, 4 ], [ 18, 2, 1, 2 ], [ 18, 2, 3, 2 ], [ 19, 4, 3, 8 ],
[ 19, 5, 3, 4 ], [ 20, 1, 2, 4 ], [ 20, 1, 4, 4 ], [ 20, 2, 2, 2 ],
[ 20, 2, 4, 2 ], [ 23, 4, 2, 4 ], [ 23, 4, 6, 4 ], [ 23, 6, 2, 2 ],
[ 23, 6, 6, 2 ], [ 25, 2, 3, 4 ], [ 25, 3, 1, 4 ], [ 25, 3, 2, 4 ],
[ 25, 3, 3, 4 ], [ 25, 3, 4, 4 ], [ 26, 1, 7, 8 ], [ 26, 2, 8, 4 ],
[ 26, 3, 6, 4 ], [ 26, 3, 8, 4 ], [ 29, 3, 14, 8 ], [ 29, 7, 2, 8 ],
[ 29, 7, 6, 8 ], [ 29, 7, 10, 8 ], [ 29, 7, 14, 8 ], [ 29, 9, 14, 4 ],
[ 29, 10, 2, 4 ], [ 29, 10, 6, 4 ], [ 29, 10, 10, 4 ], [ 29, 10, 14, 4 ],
[ 29, 11, 10, 4 ], [ 29, 11, 14, 4 ], [ 29, 12, 2, 4 ], [ 29, 12, 6, 4 ],
[ 29, 12, 10, 4 ], [ 29, 12, 14, 4 ], [ 29, 13, 2, 4 ], [ 29, 13, 6, 4 ],
[ 29, 13, 10, 4 ], [ 29, 13, 14, 4 ], [ 30, 5, 6, 8 ], [ 30, 9, 8, 8 ],
[ 31, 12, 24, 8 ], [ 31, 20, 60, 16 ], [ 31, 22, 31, 8 ], [ 31, 25, 34, 8 ],
[ 31, 27, 37, 8 ], [ 31, 31, 18, 8 ], [ 31, 31, 19, 8 ], [ 31, 31, 22, 8 ],
[ 31, 31, 23, 8 ], [ 31, 33, 43, 16 ] ]
k = 35: F-action on Pi is () [31,8,35]
Dynkin type is (A_0(q) + T(phi1 phi2^3 phi4)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 30 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ], [ 9, 3, 7, 4 ], [ 9, 4, 7, 4 ],
[ 9, 5, 7, 2 ], [ 10, 2, 2, 2 ], [ 15, 1, 5, 4 ], [ 18, 2, 2, 2 ],
[ 18, 2, 4, 2 ], [ 23, 4, 3, 4 ], [ 23, 4, 7, 4 ], [ 23, 6, 3, 2 ],
[ 23, 6, 7, 2 ], [ 25, 2, 6, 4 ], [ 26, 1, 8, 8 ], [ 26, 2, 9, 4 ],
[ 29, 3, 15, 8 ], [ 29, 9, 15, 4 ], [ 29, 11, 11, 4 ], [ 29, 11, 15, 4 ],
[ 30, 5, 22, 8 ], [ 30, 9, 22, 4 ], [ 31, 12, 50, 8 ], [ 31, 20, 51, 8 ],
[ 31, 22, 30, 8 ], [ 31, 25, 43, 8 ], [ 31, 27, 50, 8 ], [ 31, 33, 58, 8 ] ]
k = 36: F-action on Pi is () [31,8,36]
Dynkin type is (A_0(q) + T(phi1^2 phi2^2 phi4)).2
Order of center |Z^F|: phi2 phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi1^2 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 31 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 5, 1, 2, 2 ],
[ 9, 1, 7, 8 ], [ 9, 2, 7, 4 ], [ 9, 3, 7, 4 ], [ 9, 4, 7, 4 ],
[ 9, 5, 7, 2 ], [ 10, 2, 1, 2 ], [ 15, 1, 5, 4 ], [ 18, 2, 1, 2 ],
[ 18, 2, 3, 2 ], [ 23, 4, 2, 4 ], [ 23, 4, 6, 4 ], [ 23, 6, 2, 2 ],
[ 23, 6, 6, 2 ], [ 25, 2, 3, 4 ], [ 26, 1, 8, 8 ], [ 26, 2, 9, 4 ],
[ 29, 3, 14, 8 ], [ 29, 9, 14, 4 ], [ 29, 11, 10, 4 ], [ 29, 11, 14, 4 ],
[ 30, 5, 8, 8 ], [ 30, 9, 6, 4 ], [ 31, 12, 22, 8 ], [ 31, 20, 52, 8 ],
[ 31, 22, 29, 8 ], [ 31, 25, 42, 8 ], [ 31, 27, 36, 8 ], [ 31, 33, 42, 8 ] ]
k = 37: F-action on Pi is () [31,8,37]
Dynkin type is (A_0(q) + T(phi1 phi2^5)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi2 ( q^2-8*q+15 )
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, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 6 ],
[ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 9, 2, 2, 12 ], [ 9, 3, 1, 8 ],
[ 9, 3, 2, 12 ], [ 9, 4, 2, 12 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 6 ],
[ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ], [ 15, 1, 3, 24 ], [ 16, 6, 2, 16 ],
[ 16, 10, 2, 8 ], [ 16, 12, 4, 8 ], [ 16, 16, 3, 8 ], [ 18, 2, 3, 4 ],
[ 20, 1, 4, 24 ], [ 20, 2, 4, 12 ], [ 23, 4, 6, 8 ], [ 23, 6, 6, 4 ],
[ 25, 2, 5, 8 ], [ 25, 3, 3, 16 ], [ 26, 1, 4, 48 ], [ 26, 2, 10, 24 ],
[ 26, 3, 7, 24 ], [ 29, 3, 7, 16 ], [ 29, 3, 10, 16 ], [ 29, 7, 6, 32 ],
[ 29, 9, 7, 8 ], [ 29, 9, 10, 8 ], [ 29, 10, 6, 16 ], [ 29, 11, 6, 8 ],
[ 29, 12, 6, 16 ], [ 29, 13, 6, 16 ], [ 30, 5, 12, 32 ], [ 30, 5, 27, 32 ],
[ 30, 9, 16, 32 ], [ 30, 9, 30, 16 ], [ 30, 11, 11, 16 ],
[ 30, 11, 23, 16 ], [ 30, 11, 26, 16 ], [ 31, 12, 27, 32 ],
[ 31, 12, 54, 32 ], [ 31, 20, 19, 32 ], [ 31, 20, 64, 64 ],
[ 31, 22, 39, 32 ], [ 31, 25, 23, 32 ], [ 31, 25, 54, 32 ],
[ 31, 27, 40, 32 ], [ 31, 27, 48, 32 ], [ 31, 31, 21, 32 ],
[ 31, 33, 48, 64 ], [ 31, 33, 55, 32 ] ]
k = 38: F-action on Pi is () [31,8,38]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/64 phi1^2 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/64 phi2 ( q^2-8*q+15 )
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, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 6 ],
[ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ], [ 9, 2, 2, 12 ], [ 9, 3, 2, 12 ],
[ 9, 3, 5, 8 ], [ 9, 4, 2, 12 ], [ 9, 5, 2, 6 ], [ 9, 5, 5, 4 ],
[ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ], [ 15, 1, 3, 24 ], [ 16, 6, 10, 16 ],
[ 16, 10, 10, 8 ], [ 16, 12, 14, 8 ], [ 16, 16, 12, 8 ], [ 18, 2, 2, 4 ],
[ 20, 1, 4, 24 ], [ 20, 2, 4, 12 ], [ 23, 4, 3, 8 ], [ 23, 6, 3, 4 ],
[ 25, 2, 2, 8 ], [ 25, 3, 8, 16 ], [ 26, 1, 4, 48 ], [ 26, 2, 10, 24 ],
[ 26, 3, 7, 24 ], [ 29, 3, 3, 16 ], [ 29, 3, 6, 16 ], [ 29, 7, 15, 32 ],
[ 29, 9, 3, 8 ], [ 29, 9, 6, 8 ], [ 29, 10, 15, 16 ], [ 29, 11, 3, 8 ],
[ 29, 12, 15, 16 ], [ 29, 13, 11, 16 ], [ 30, 5, 13, 32 ],
[ 30, 5, 28, 32 ], [ 30, 9, 14, 16 ], [ 30, 9, 28, 16 ], [ 30, 11, 7, 16 ],
[ 30, 11, 10, 16 ], [ 30, 11, 21, 16 ], [ 31, 12, 26, 32 ],
[ 31, 12, 56, 32 ], [ 31, 20, 15, 32 ], [ 31, 20, 20, 32 ],
[ 31, 22, 38, 32 ], [ 31, 25, 22, 32 ], [ 31, 25, 27, 32 ],
[ 31, 27, 34, 32 ], [ 31, 27, 47, 32 ], [ 31, 31, 32, 32 ],
[ 31, 33, 39, 32 ], [ 31, 33, 54, 32 ] ]
k = 39: F-action on Pi is () [31,8,39]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/192 phi1 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/192 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 15 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 3, 4, 8 ],
[ 3, 5, 4, 4 ], [ 5, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ],
[ 9, 2, 2, 12 ], [ 9, 3, 2, 12 ], [ 9, 3, 6, 24 ], [ 9, 4, 2, 12 ],
[ 9, 5, 2, 6 ], [ 9, 5, 6, 12 ], [ 10, 2, 1, 4 ], [ 11, 1, 2, 8 ],
[ 11, 2, 2, 4 ], [ 15, 1, 3, 24 ], [ 16, 6, 12, 48 ], [ 16, 10, 12, 24 ],
[ 16, 12, 13, 24 ], [ 16, 16, 14, 24 ], [ 18, 2, 1, 12 ], [ 19, 4, 3, 32 ],
[ 19, 5, 3, 16 ], [ 20, 1, 4, 24 ], [ 20, 2, 4, 12 ], [ 23, 4, 2, 24 ],
[ 23, 6, 2, 12 ], [ 25, 2, 1, 24 ], [ 25, 3, 4, 48 ], [ 26, 1, 4, 48 ],
[ 26, 2, 10, 24 ], [ 26, 3, 7, 24 ], [ 29, 3, 2, 48 ], [ 29, 7, 14, 96 ],
[ 29, 9, 2, 24 ], [ 29, 10, 14, 48 ], [ 29, 11, 2, 24 ], [ 29, 12, 14, 48 ],
[ 29, 13, 10, 48 ], [ 30, 5, 14, 96 ], [ 30, 9, 12, 48 ], [ 30, 11, 5, 48 ],
[ 31, 12, 28, 96 ], [ 31, 20, 16, 96 ], [ 31, 22, 37, 96 ],
[ 31, 25, 26, 96 ], [ 31, 27, 33, 96 ], [ 31, 31, 24, 96 ],
[ 31, 33, 38, 96 ] ]
k = 40: F-action on Pi is () [31,8,40]
Dynkin type is (A_0(q) + T(phi2^6)).2
Order of center |Z^F|: phi2^3 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/192 phi1 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/192 ( q^3-15*q^2+71*q-105 )
Fusion of maximal tori of C^F in those of G^F:
[ 4 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 3, 3, 2, 8 ],
[ 3, 5, 2, 4 ], [ 5, 1, 2, 6 ], [ 8, 1, 2, 12 ], [ 9, 1, 2, 24 ],
[ 9, 2, 2, 12 ], [ 9, 3, 2, 36 ], [ 9, 4, 2, 12 ], [ 9, 5, 2, 18 ],
[ 10, 2, 2, 4 ], [ 11, 1, 2, 8 ], [ 11, 2, 2, 4 ], [ 15, 1, 3, 24 ],
[ 16, 6, 3, 48 ], [ 16, 10, 3, 24 ], [ 16, 12, 3, 24 ], [ 16, 16, 5, 48 ],
[ 18, 2, 4, 12 ], [ 19, 4, 2, 32 ], [ 19, 5, 2, 16 ], [ 20, 1, 4, 24 ],
[ 20, 2, 4, 12 ], [ 23, 4, 7, 24 ], [ 23, 6, 7, 12 ], [ 25, 2, 8, 24 ],
[ 25, 3, 7, 48 ], [ 26, 1, 4, 48 ], [ 26, 2, 10, 24 ], [ 26, 3, 7, 24 ],
[ 29, 3, 11, 48 ], [ 29, 7, 7, 96 ], [ 29, 9, 11, 24 ], [ 29, 10, 7, 48 ],
[ 29, 11, 7, 24 ], [ 29, 12, 7, 48 ], [ 29, 13, 7, 48 ], [ 30, 5, 26, 96 ],
[ 30, 9, 32, 96 ], [ 30, 11, 27, 48 ], [ 31, 12, 55, 96 ],
[ 31, 20, 63, 192 ], [ 31, 22, 40, 96 ], [ 31, 25, 55, 96 ],
[ 31, 27, 54, 96 ], [ 31, 31, 29, 96 ], [ 31, 33, 64, 192 ] ]
j = 12: Omega of order 4, action on Pi: <(), ()>
k = 1: F-action on Pi is () [31,12,1]
Dynkin type is (A_0(q) + T(phi1^6)).2.2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 ( q^2-14*q+45 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 5, 1, 4 ],
[ 5, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ],
[ 9, 3, 1, 8 ], [ 9, 4, 1, 8 ], [ 9, 5, 1, 12 ], [ 15, 1, 1, 8 ],
[ 16, 10, 1, 8 ], [ 16, 12, 1, 16 ], [ 23, 6, 1, 4 ], [ 29, 9, 1, 8 ],
[ 29, 12, 1, 16 ], [ 30, 11, 1, 16 ] ]
k = 2: F-action on Pi is () [31,12,2]
Dynkin type is (A_0(q) + T(phi1^5 phi2)).2.2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 6 ], [ 9, 5, 2, 2 ], [ 15, 1, 4, 4 ],
[ 16, 12, 4, 8 ], [ 23, 6, 1, 4 ], [ 29, 9, 1, 8 ], [ 30, 11, 1, 8 ],
[ 30, 11, 6, 8 ] ]
k = 3: F-action on Pi is () [31,12,3]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2.2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 5, 2, 4 ],
[ 5, 1, 1, 2 ], [ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ],
[ 9, 2, 1, 4 ], [ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ],
[ 9, 4, 1, 4 ], [ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 6 ],
[ 9, 5, 3, 4 ], [ 15, 1, 4, 4 ], [ 16, 10, 5, 8 ], [ 16, 12, 3, 8 ],
[ 16, 12, 5, 8 ], [ 29, 9, 5, 4 ], [ 30, 11, 9, 8 ], [ 30, 11, 17, 8 ] ]
k = 4: F-action on Pi is () [31,12,4]
Dynkin type is (A_0(q) + T(phi1^5 phi2)).2.2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 5 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 9, 5, 2, 4 ], [ 15, 1, 1, 8 ],
[ 16, 12, 2, 8 ], [ 29, 9, 5, 4 ], [ 30, 11, 15, 8 ], [ 30, 11, 17, 8 ] ]
k = 5: F-action on Pi is () [31,12,5]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2.2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 15, 1, 4, 4 ],
[ 16, 10, 15, 8 ], [ 29, 9, 5, 4 ], [ 30, 11, 15, 8 ], [ 30, 11, 22, 8 ] ]
k = 6: F-action on Pi is () [31,12,6]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2.2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 7 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 9, 5, 4, 4 ],
[ 15, 1, 4, 4 ], [ 16, 12, 6, 8 ], [ 23, 6, 5, 4 ], [ 29, 9, 9, 8 ],
[ 30, 11, 25, 8 ], [ 30, 11, 31, 8 ] ]
k = 7: F-action on Pi is () [31,12,7]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2.2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 10, 11, 8 ],
[ 23, 6, 5, 4 ], [ 29, 9, 9, 8 ], [ 29, 12, 9, 16 ], [ 30, 11, 31, 16 ] ]
k = 8: F-action on Pi is () [31,12,8]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2.2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 15, 1, 5, 4 ],
[ 23, 6, 1, 2 ], [ 23, 6, 5, 2 ], [ 29, 9, 13, 4 ] ]
k = 9: F-action on Pi is () [31,12,9]
Dynkin type is (A_0(q) + T(phi1^2 phi4^2)).2.2
Order of center |Z^F|: phi4 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 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 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 2, 2 ],
[ 15, 1, 5, 4 ], [ 16, 10, 5, 4 ], [ 16, 10, 15, 4 ], [ 29, 9, 17, 4 ] ]
k = 10: F-action on Pi is () [31,12,10]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2.2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 ( q-3 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 3, 5, 1, 2 ],
[ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 16, 10, 1, 4 ],
[ 16, 10, 11, 4 ], [ 23, 6, 1, 2 ], [ 23, 6, 5, 2 ], [ 29, 9, 13, 4 ],
[ 29, 12, 1, 4 ], [ 29, 12, 5, 4 ], [ 29, 12, 9, 4 ], [ 29, 12, 13, 4 ] ]
k = 11: F-action on Pi is () [31,12,11]
Dynkin type is (A_0(q) + T(phi1^3 phi2 phi4)).2.2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/8 phi1 phi2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/8 phi1 phi2
Fusion of maximal tori of C^F in those of G^F:
[ 28 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 2, 1, 1 ], [ 8, 1, 1, 2 ],
[ 8, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 29, 9, 17, 4 ] ]
k = 12: F-action on Pi is () [31,12,12]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2.2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-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 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 9, 5, 3, 4 ], [ 15, 1, 3, 8 ],
[ 16, 12, 8, 8 ], [ 29, 9, 5, 4 ], [ 30, 11, 9, 8 ], [ 30, 11, 22, 8 ] ]
k = 13: F-action on Pi is () [31,12,13]
Dynkin type is (A_0(q) + T(phi1^2 phi2^4)).2.2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
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, 6 ], [ 2, 2, 1, 3 ], [ 3, 5, 1, 4 ],
[ 5, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ],
[ 9, 3, 2, 8 ], [ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 9, 5, 4, 8 ],
[ 15, 1, 3, 8 ], [ 16, 10, 1, 8 ], [ 16, 12, 7, 16 ], [ 23, 6, 5, 4 ],
[ 29, 9, 9, 8 ], [ 29, 12, 5, 16 ], [ 30, 11, 25, 16 ] ]
k = 14: F-action on Pi is () [31,12,14]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2.2
Order of center |Z^F|: phi2^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 phi2 ( q-3 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 2, 4 ],
[ 8, 1, 2, 4 ], [ 9, 1, 2, 16 ], [ 9, 2, 2, 8 ], [ 9, 3, 2, 8 ],
[ 9, 4, 2, 8 ], [ 9, 5, 2, 4 ], [ 15, 1, 3, 8 ], [ 16, 10, 11, 8 ],
[ 23, 6, 1, 4 ], [ 29, 9, 1, 8 ], [ 29, 12, 13, 16 ], [ 30, 11, 6, 16 ] ]
k = 15: F-action on Pi is () [31,12,15]
Dynkin type is (A_0(q) + T(phi1^5 phi2)).2.2
Order of center |Z^F|: phi1^2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/32 phi1 ( q-5 )
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/32 ( q^2-10*q+21 )
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 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 4 ],
[ 8, 1, 1, 4 ], [ 9, 1, 1, 16 ], [ 9, 2, 1, 8 ], [ 9, 3, 1, 8 ],
[ 9, 4, 1, 8 ], [ 9, 5, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 10, 2, 8 ],
[ 23, 6, 2, 4 ], [ 29, 9, 2, 8 ], [ 29, 12, 2, 16 ], [ 30, 11, 2, 16 ] ]
k = 16: F-action on Pi is () [31,12,16]
Dynkin type is (A_0(q) + T(phi1^4 phi2^2)).2.2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 ( q^2-6*q+9 )
Fusion of maximal tori of C^F in those of G^F:
[ 10 ]
elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 2, 2, 1, 3 ], [ 5, 1, 1, 2 ],
[ 5, 1, 2, 2 ], [ 9, 1, 1, 8 ], [ 9, 1, 2, 8 ], [ 9, 2, 1, 4 ],
[ 9, 2, 2, 4 ], [ 9, 3, 1, 4 ], [ 9, 3, 2, 4 ], [ 9, 4, 1, 4 ],
[ 9, 4, 2, 4 ], [ 9, 5, 1, 2 ], [ 9, 5, 2, 2 ], [ 9, 5, 6, 4 ],
[ 15, 1, 4, 4 ], [ 16, 12, 15, 8 ], [ 23, 6, 2, 4 ], [ 29, 9, 2, 8 ],
[ 30, 11, 2, 8 ], [ 30, 11, 5, 8 ] ]
k = 17: F-action on Pi is () [31,12,17]
Dynkin type is (A_0(q) + T(phi1^3 phi2^3)).2.2
Order of center |Z^F|: phi1 phi2 times
1, q congruent 0 modulo 2
2, q congruent 1 modulo 2
Numbers of classes in class type:
q congruent 0 modulo 4: 0
q congruent 1 modulo 4: 1/16 phi1^2
q congruent 2 modulo 4: 0
q congruent 3 modulo 4: 1/16 phi2 ( q-3 )
Fusion of maximal tori of C^F i