These tables will be included in future versions of GAPs character table
library CTblLib. But note
that then the classes and characters will be reordered according to the
conventions of that library.
We give the following information: each row stands for a set of classes
which have representatives with the same centralizer in G. The column "#
classes" tells how many classes are in this set. The column "|C(su)(q)|,
q=2" tells the order of the centralizer of elements in these classes. The
next two columns describe the centralizer of the semisimple part s of an
element in these classes; "type of C(s)" gives the semisimple part of the
centralizer of s in G under the restricted Frobenius morphism, and
"|Z0(C(s))(q)|" gives the number of rational points in the
radical of the centralizer of s (generically, as polynomial in q (= 2), the
polynomials are factorized into cyclotomic polynomials, phiN means the
evaluation of the N-th cyclotomic polynomial at q). Finally, in column "type
of u" a label for the class of the unipotent part u is given; we don't give
precise explanations of that labeling here.
There are 346 conjugacy classes.
| # classes | |C(su)(q)|, q=2 |
type of C(s) |
|Z0(C(s))(q)| | type of u |
1 |
3 |
2^36*3^10*5^2*7^2*11*13*17*19 |
2E6(q) |
1 |
- |
2 |
3 |
2^36*3^7*5*7*11 |
2E6(q) |
1 |
A1 |
3 |
3 |
2^33*3^5*5*7 |
2E6(q) |
1 |
2A1 |
4 |
3 |
2^31*3^4 |
2E6(q) |
1 |
3A1 |
5 |
3 |
2^27*3^6 |
2E6(q) |
1 |
A2 |
6 |
3 |
2^27*3^3*5*7 |
2E6(q) |
1 |
A2 |
7 |
3 |
2^26*3^4 |
2E6(q) |
1 |
A2+A1 |
8 |
3 |
2^22*3^4*7 |
2E6(q) |
1 |
2A2 |
9 |
3 |
2^22*3^4*7 |
2E6(q) |
1 |
2A2 |
10 |
3 |
2^22*3^4*7 |
2E6(q) |
1 |
2A2 |
11 |
3 |
2^25*3^2 |
2E6(q) |
1 |
A2+2A1 |
12 |
3 |
2^19*3^3*5 |
2E6(q) |
1 |
A3 |
13 |
3 |
2^22*3^2 |
2E6(q) |
1 |
2A2+A1 |
14 |
3 |
2^22*3^2 |
2E6(q) |
1 |
2A2+A1 |
15 |
3 |
2^22*3^2 |
2E6(q) |
1 |
2A2+A1 |
16 |
3 |
2^19*3^2 |
2E6(q) |
1 |
A3+A1 |
17 |
3 |
2^19*3^3 |
2E6(q) |
1 |
D4(a1) |
18 |
3 |
2^19*3 |
2E6(q) |
1 |
D4(a1) |
19 |
3 |
2^18*3^2 |
2E6(q) |
1 |
D4(a1) |
20 |
3 |
2^15*3^2 |
2E6(q) |
1 |
A4 |
21 |
3 |
2^14*3^3 |
2E6(q) |
1 |
D4 |
22 |
3 |
2^14*3^3 |
2E6(q) |
1 |
D4 |
23 |
3 |
2^15*3 |
2E6(q) |
1 |
A4+A1 |
24 |
3 |
2^13*3 |
2E6(q) |
1 |
D5(a1) |
25 |
3 |
2^12*3^2 |
2E6(q) |
1 |
A5 |
26 |
3 |
2^12*3^2 |
2E6(q) |
1 |
A5 |
27 |
3 |
2^12*3^2 |
2E6(q) |
1 |
A5 |
28 |
3 |
2^13*3 |
2E6(q) |
1 |
A5+A1 |
29 |
3 |
2^13*3 |
2E6(q) |
1 |
A5+A1 |
30 |
3 |
2^13*3 |
2E6(q) |
1 |
A5+A1 |
31 |
3 |
2^13*3 |
2E6(q) |
1 |
A5+A1 |
32 |
3 |
2^13*3 |
2E6(q) |
1 |
A5+A1 |
33 |
3 |
2^13*3 |
2E6(q) |
1 |
A5+A1 |
34 |
3 |
2^10*3 |
2E6(q) |
1 |
D5 |
35 |
3 |
2^10*3 |
2E6(q) |
1 |
D5 |
36 |
3 |
2^8*3 |
2E6(q) |
1 |
E6(a1) |
37 |
3 |
2^8*3 |
2E6(q) |
1 |
E6(a1) |
38 |
3 |
2^8*3 |
2E6(q) |
1 |
E6(a1) |
39 |
3 |
2^7*3 |
2E6(q) |
1 |
E6 |
40 |
3 |
2^7*3 |
2E6(q) |
1 |
E6 |
41 |
3 |
2^7*3 |
2E6(q) |
1 |
E6 |
42 |
3 |
2^7*3 |
2E6(q) |
1 |
E6 |
43 |
3 |
2^7*3 |
2E6(q) |
1 |
E6 |
44 |
3 |
2^7*3 |
2E6(q) |
1 |
E6 |
45 |
1 |
2^9*3^9 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ] ] |
46 |
1 |
2^9*3^7 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 1, 1, 1 ], [ 2, 1 ] ] |
47 |
1 |
2^8*3^6 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 1, 1, 1 ], [ 3 ] ] |
48 |
1 |
2^9*3^7 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 2, 1 ], [ 1, 1, 1 ] ] |
49 |
1 |
2^9*3^5 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 2, 1 ], [ 2, 1 ] ] |
50 |
1 |
2^8*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 2, 1 ], [ 3 ] ] |
51 |
1 |
2^8*3^6 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 3 ], [ 1, 1, 1 ] ] |
52 |
1 |
2^8*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 3 ], [ 2, 1 ] ] |
53 |
1 |
2^7*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 3 ], [ 3 ] ] |
54 |
1 |
2^7*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 3 ], [ 3 ] ] |
55 |
1 |
2^7*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 1, 1, 1 ], [ 3 ], [ 3 ] ] |
56 |
1 |
2^9*3^7 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ] ] |
57 |
1 |
2^9*3^5 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 1, 1, 1 ], [ 2, 1 ] ] |
58 |
1 |
2^8*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 1, 1, 1 ], [ 3 ] ] |
59 |
1 |
2^9*3^5 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 2, 1 ], [ 1, 1, 1 ] ] |
60 |
1 |
2^9*3^3 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 2, 1 ], [ 2, 1 ] ] |
61 |
1 |
2^8*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 2, 1 ], [ 3 ] ] |
62 |
1 |
2^8*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 3 ], [ 1, 1, 1 ] ] |
63 |
1 |
2^8*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 3 ], [ 2, 1 ] ] |
64 |
1 |
2^7*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 3 ], [ 3 ] ] |
65 |
1 |
2^7*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 3 ], [ 3 ] ] |
66 |
1 |
2^7*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 2, 1 ], [ 3 ], [ 3 ] ] |
67 |
1 |
2^8*3^6 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 1, 1, 1 ], [ 1, 1, 1 ] ] |
68 |
1 |
2^8*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 1, 1, 1 ], [ 2, 1 ] ] |
69 |
1 |
2^7*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 1, 1, 1 ], [ 3 ] ] |
70 |
1 |
2^7*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 1, 1, 1 ], [ 3 ] ] |
71 |
1 |
2^7*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 1, 1, 1 ], [ 3 ] ] |
72 |
1 |
2^8*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 2, 1 ], [ 1, 1, 1 ] ] |
73 |
1 |
2^8*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 2, 1 ], [ 2, 1 ] ] |
74 |
1 |
2^7*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 2, 1 ], [ 3 ] ] |
75 |
1 |
2^7*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 2, 1 ], [ 3 ] ] |
76 |
1 |
2^7*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 2, 1 ], [ 3 ] ] |
77 |
1 |
2^7*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 1, 1, 1 ] ] |
78 |
1 |
2^7*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 1, 1, 1 ] ] |
79 |
1 |
2^7*3^4 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 1, 1, 1 ] ] |
80 |
1 |
2^7*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 2, 1 ] ] |
81 |
1 |
2^7*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 2, 1 ] ] |
82 |
1 |
2^7*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 2, 1 ] ] |
83 |
1 |
2^6*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 3 ] ] |
84 |
1 |
2^6*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 3 ] ] |
85 |
1 |
2^6*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 3 ] ] |
86 |
1 |
2^6*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 3 ] ] |
87 |
1 |
2^6*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 3 ] ] |
88 |
1 |
2^6*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 3 ] ] |
89 |
1 |
2^6*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 3 ] ] |
90 |
1 |
2^6*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 3 ] ] |
91 |
1 |
2^6*3^2 |
2A2(q) + 2A2(q) + 2A2(q) |
1 |
[ [ 3 ], [ 3 ], [ 3 ] ] |
92 |
3 |
2^15*3^8*5*7*11 |
2A5(q) |
phi2 |
[ 1, 1, 1, 1, 1, 1 ] |
93 |
3 |
2^15*3^6*5 |
2A5(q) |
phi2 |
[ 2, 1, 1, 1, 1 ] |
94 |
3 |
2^14*3^4 |
2A5(q) |
phi2 |
[ 2, 2, 1, 1 ] |
95 |
3 |
2^12*3^4 |
2A5(q) |
phi2 |
[ 2, 2, 2 ] |
96 |
3 |
2^11*3^5 |
2A5(q) |
phi2 |
[ 3, 1, 1, 1 ] |
97 |
3 |
2^11*3^3 |
2A5(q) |
phi2 |
[ 3, 2, 1 ] |
98 |
3 |
2^9*3^3 |
2A5(q) |
phi2 |
[ 3, 3 ] |
99 |
3 |
2^9*3^3 |
2A5(q) |
phi2 |
[ 3, 3 ] |
100 |
3 |
2^9*3^3 |
2A5(q) |
phi2 |
[ 3, 3 ] |
101 |
3 |
2^8*3^3 |
2A5(q) |
phi2 |
[ 4, 1, 1 ] |
102 |
3 |
2^8*3^2 |
2A5(q) |
phi2 |
[ 4, 2 ] |
103 |
3 |
2^6*3^2 |
2A5(q) |
phi2 |
[ 5, 1 ] |
104 |
3 |
2^5*3^2 |
2A5(q) |
phi2 |
[ 6 ] |
105 |
3 |
2^5*3^2 |
2A5(q) |
phi2 |
[ 6 ] |
106 |
3 |
2^5*3^2 |
2A5(q) |
phi2 |
[ 6 ] |
107 |
3 |
2^6*3^3*5*7^2 |
A2(q2) |
phi3 |
[ 1, 1, 1 ] |
108 |
3 |
2^6*3*7 |
A2(q2) |
phi3 |
[ 2, 1 ] |
109 |
3 |
2^4*3*7 |
A2(q2) |
phi3 |
[ 3 ] |
110 |
3 |
2^4*3*7 |
A2(q2) |
phi3 |
[ 3 ] |
111 |
3 |
2^4*3*7 |
A2(q2) |
phi3 |
[ 3 ] |
112 |
1 |
2^12*3^7*5^2*7 |
D4(q) |
phi2^2 |
[ [ 1, 1, 1, 1, 1, 1, 1, 1 ], [ -1 ] ] |
113 |
1 |
2^12*3^5 |
D4(q) |
phi2^2 |
[ [ 2, 2, 1, 1, 1, 1 ], [ -1, 0 ] ] |
114 |
1 |
2^10*3^4*5 |
D4(q) |
phi2^2 |
[ [ 2, 2, 1, 1, 1, 1 ], [ -1, 1 ] ] |
115 |
1 |
2^10*3^4*5 |
D4(q) |
phi2^2 |
[ [ 2, 2, 2, 2 ], [ -1, 0 ], '+' ] |
116 |
1 |
2^10*3^4*5 |
D4(q) |
phi2^2 |
[ [ 2, 2, 2, 2 ], [ -1, 0 ], '-' ] |
117 |
1 |
2^10*3^3 |
D4(q) |
phi2^2 |
[ [ 2, 2, 2, 2 ], [ -1, 1 ] ] |
118 |
1 |
2^9*3^2 |
D4(q) |
phi2^2 |
[ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ] |
119 |
1 |
2^9*3^4 |
D4(q) |
phi2^2 |
[ [ 3, 3, 1, 1 ], [ -1, -1, -1 ] ] |
120 |
1 |
2^6*3^3 |
D4(q) |
phi2^2 |
[ [ 4, 2, 1, 1 ], [ -1, 1, -1, 1 ] ] |
121 |
1 |
2^6*3^3 |
D4(q) |
phi2^2 |
[ [ 4, 4 ], [ -1, -1, -1, 0 ], '+' ] |
122 |
1 |
2^6*3^3 |
D4(q) |
phi2^2 |
[ [ 4, 4 ], [ -1, -1, -1, 0 ], '-' ] |
123 |
1 |
2^6*3^2 |
D4(q) |
phi2^2 |
[ [ 4, 4 ], [ -1, -1, -1, 1 ] ] |
124 |
1 |
2^5*3^2 |
D4(q) |
phi2^2 |
[ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ] |
125 |
1 |
2^5*3^2 |
D4(q) |
phi2^2 |
[ [ 6, 2 ], [ -1, 1, -1, -1, -1, 1 ] ] |
126 |
3 |
2^6*3^3*5^2*7 |
A3(q) |
phi2 phi4 |
[ 1, 1, 1, 1 ] |
127 |
3 |
2^6*3^2*5 |
A3(q) |
phi2 phi4 |
[ 2, 1, 1 ] |
128 |
3 |
2^5*3^2*5 |
A3(q) |
phi2 phi4 |
[ 2, 2 ] |
129 |
3 |
2^4*3*5 |
A3(q) |
phi2 phi4 |
[ 3, 1 ] |
130 |
3 |
2^3*3*5 |
A3(q) |
phi2 phi4 |
[ 4 ] |
131 |
3 |
2^2*3^5 |
A1(q) + A1(q) |
phi2^2 phi6 |
[ [ 1, 1 ], [ 1, 1 ] ] |
132 |
3 |
2^2*3^4 |
A1(q) + A1(q) |
phi2^2 phi6 |
[ [ 1, 1 ], [ 2 ] ] |
133 |
3 |
2^2*3^4 |
A1(q) + A1(q) |
phi2^2 phi6 |
[ [ 2 ], [ 1, 1 ] ] |
134 |
3 |
2^2*3^3 |
A1(q) + A1(q) |
phi2^2 phi6 |
[ [ 2 ], [ 2 ] ] |
135 |
3 |
2^2*3^3*5^2 |
A1(q2) |
phi2^2 phi4 |
[ 1, 1 ] |
136 |
3 |
2^2*3^2*5 |
A1(q2) |
phi2^2 phi4 |
[ 2 ] |
137 |
3 |
2^3*3^2*7^2 |
A2(q) |
phi3 phi6 |
[ 1, 1, 1 ] |
138 |
3 |
2^3*3*7 |
A2(q) |
phi3 phi6 |
[ 2, 1 ] |
139 |
3 |
2^2*3*7 |
A2(q) |
phi3 phi6 |
[ 3 ] |
140 |
3 |
2*3^3*5 |
A1(q) |
phi1 phi2^2 phi4 |
[ 1, 1 ] |
141 |
3 |
2*3^2*5 |
A1(q) |
phi1 phi2^2 phi4 |
[ 2 ] |
142 |
6 |
2*3^2*11 |
A1(q) |
phi2 phi10 |
[ 1, 1 ] |
143 |
6 |
2*3*11 |
A1(q) |
phi2 phi10 |
[ 2 ] |
144 |
1 |
2*3^4 |
A1(q) |
phi2 phi6^2 |
[ 1, 1 ] |
145 |
1 |
2*3^3 |
A1(q) |
phi2 phi6^2 |
[ 2 ] |
146 |
6 |
3^2*11 |
A0(q) |
phi2^2 phi10 |
[ [ 1 ], 1 ] |
147 |
1 |
3^2*7 |
A0(q) |
phi1^2 phi2^2 phi3 |
[ [ 1 ], 1 ] |
148 |
6 |
3*19 |
A0(q) |
phi18 |
[ [ 1 ], 1 ] |
149 |
3 |
3*13 |
A0(q) |
phi6 phi12 |
[ [ 1 ], 1 ] |
150 |
3 |
3^2*7 |
A0(q) |
phi1 phi2 phi3 phi6 |
[ [ 1 ], 1 ] |
151 |
6 |
3*17 |
A0(q) |
phi1 phi2 phi8 |
[ [ 1 ], 1 ] |
152 |
6 |
3*5*7 |
A0(q) |
phi1 phi2 phi3 phi4 |
[ [ 1 ], 1 ] |
There are 346 irreducible characters.