About this representation

Group He
Group generators Standard generators
Number of points 2058
Primitivity information Primitive
Transitivity degree 1
Rank 5
Suborbit lengths 1, 1362, 425, 1360
Character 1 + 51ab + 680 + 1275a
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 2058
2A 154 2952
2B 42 21008
3A 42 3672
3B 0 3686
4A 14 270, 4476
4B 18 212, 4504
4C 2 220, 4504
5A 8 5410
6A 10 216, 348, 6312
6B 0 314, 6336
7A 0 7294
7B 0 7294
7C 0 7294
7D 0 7294
7E 0 7294
8A 2 410, 8252
10A 4 22, 530, 10190
12A 2 24, 34, 48, 622, 12156
12B 0 36, 64, 12168
14A 0 722, 14136
14B 0 722, 14136
14C 0 76, 14144
14D 0 76, 14144
15A 2 32, 58, 15134
17A 1 17121
17B 1 17121
21A 0 76, 2196
21B 0 76, 2196
21C 0 2198
21D 0 2198
28A 0 72, 1410, 2868
28B 0 72, 1410, 2868

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