About this representation

Group He
Group generators Standard generators
Number of points 244800
Primitivity information Primitive
Transitivity degree 1
Rank 36
Suborbit lengths 1, 16, 1122, 3432, 7844, 1029, 1372, 2352, 548813, 1646410
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 244800
2A 0 2122400
2B 64 2122368
3A 0 381600
3B 84 381572
4A 0 461200
4B 0 232, 461184
4C 16 224, 461184
5A 0 548960
6A 0 640800
6B 4 240, 320, 640776
7A 24 734968
7B 24 734968
7C 45 734965
7D 3 734971
7E 3 734971
8A 4 26, 412, 830592
10A 0 1024480
12A 0 1220400
12B 0 22, 420, 610, 1220388
14A 0 212, 1417484
14B 0 212, 1417484
14C 1 2, 79, 1417481
14D 1 2, 79, 1417481
15A 0 1516320
17A 0 1714400
17B 0 1714400
21A 0 315, 2111655
21B 0 315, 2111655
21C 0 38, 712, 2111652
21D 0 38, 712, 2111652
28A 0 46, 288742
28B 0 46, 288742

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 20, 2006 permanalyse version 0.03 Check did not complete
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