About this representation

Group He
Group generators Standard generators
Number of points 8330
Primitivity information Primitive
Transitivity degree 1
Rank 7
Suborbit lengths 1, 105, 720, 8402, 1344, 4480
Character 1 + 51ab + 680 + 1275a + 1920 + 4352
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 8330
2A 346 23992
2B 42 24144
3A 77 32751
3B 8 32774
4A 22 2162, 41996
4B 18 212, 42072
4C 2 220, 42072
5A 5 51665
6A 13 232, 3111, 61320
6B 0 24, 314, 61380
7A 7 71189
7B 7 71189
7C 0 71190
7D 0 71190
7E 0 71190
8A 2 410, 81036
10A 1 22, 569, 10798
12A 1 26, 37, 416, 652, 12660
12B 0 36, 42, 64, 12690
14A 3 22, 749, 14570
14B 3 22, 749, 14570
14C 0 76, 14592
14D 0 76, 14592
15A 2 3, 515, 15550
17A 0 17490
17B 0 17490
21A 0 711, 21393
21B 0 711, 21393
21C 1 32, 7, 21396
21D 1 32, 7, 21396
28A 1 2, 4, 73, 1423, 28285
28B 1 2, 4, 73, 1423, 28285

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