About this representation

Group Suz
Group generators Standard generators
Number of points 1782
Primitivity information Primitive
Transitivity degree 1
Rank 3
Suborbit lengths 1, 416, 1365
Character 1 + 780 + 1001
Point stabiliser G2(4)
Contributed by Not recorded

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This representation is available in the following formats:

MeatAxe a b
MeatAxe binary a b
GAP a b
GAP a, b
Magma a, b

On conjugacy classes

Conjugacy class Fixed points Cycle type
1A 1782
2A 54 2864
2B 42 2870
3A 162 3540
3B 0 3594
3C 18 3588
4A 30 212, 4432
4B 6 224, 4432
4C 2 226, 4432
4D 0 221, 4435
5A 12 5354
5B 2 5356
6A 18 272, 312, 6264
6B 0 318, 6288
6C 0 318, 6288
6D 0 318, 6288
6E 6 26, 312, 6288
7A 4 7254
8A 6 212, 46, 8216
8B 2 22, 412, 8216
8C 0 2, 413, 8216
9A 0 9198
9B 0 9198
10A 4 24, 510, 10172
10B 2 58, 10174
11A 0 11162
12A 6 26, 38, 436, 62, 12132
12B 0 310, 64, 12144
12C 2 28, 436, 66, 12132
12D 0 23, 43, 66, 12144
12E 0 32, 68, 12144
13A 1 13137
13B 1 13137
14A 0 22, 76, 14124
15A 3 33, 53, 15117
15B 3 33, 53, 15117
15C 2 532, 15108
18A 0 96, 1896
18B 0 96, 1896
20A 0 22, 42, 56, 102, 2086
21A 1 3, 723, 2177
21B 1 3, 723, 2177
24A 0 23, 32, 43, 63, 818, 12, 2466

Checks applied

Check Description Date Checked by Result
Semi-presentation Check against a semi-presentation. If this fails, then the representation is not on standard generators, and may generate the wrong group. Note that the semi-presentation itself is not checked here. Jul 4, 2006 certify.pl version 0.05 Pass
Order Check that the elements generate a group of the correct order. Jul 4, 2006 permanalyse version 0.03 Pass
Number of points Check whether the permutation representation is acting on the stated number of points. Jul 4, 2006 certify.pl version 0.05 Pass
Files exist Check whether files exist (where stated). Jul 4, 2006 certify.pl version 0.05 Pass