About this representation

Group He
Group generators Standard generators
Number of points 29155
Primitivity information Primitive
Transitivity degree 1
Rank 12
Suborbit lengths 1, 90, 120, 384, 9602, 1440, 2160, 28802, 5760, 11520
Character 1 + 51ab + 680 + 2.1275a + 1920 + 4352 + 7650a + 11900
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 29155
2A 651 214252
2B 147 214504
3A 112 39681
3B 7 39716
4A 35 2308, 47126
4B 19 264, 47252
4C 7 270, 47252
5A 5 55830
6A 12 250, 3213, 64734
6B 3 22, 348, 64834
7A 0 74165
7B 0 74165
7C 0 74165
7D 0 74165
7E 0 74165
8A 1 23, 435, 83626
10A 1 22, 5130, 102850
12A 2 25, 311, 425, 6101, 122367
12B 1 2, 36, 4, 621, 122417
14A 0 793, 142036
14B 0 793, 142036
14C 0 721, 142072
14D 0 721, 142072
15A 2 3, 522, 151936
17A 0 171715
17B 0 171715
21A 0 716, 211383
21B 0 716, 211383
21C 0 7, 211388
21D 0 7, 211388
28A 0 75, 1444, 281018
28B 0 75, 1444, 281018

Checks applied

Check Description Date Checked by Result
Presentation Check against the relations in a presentation. If this test passes, then the group is of the correct isomorphism type, and the generators are those stated. Note that the presentation itself is not checked here. Aug 2, 2006 certify.pl version 0.05 Pass
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 18, 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