About this representation

Group HS
Group generators Standard generators
Number of points 100
Primitivity information Primitive
Transitivity degree 1
Rank 3
Suborbit lengths 1, 22, 77
Character 1 + 22 + 77
Point stabiliser M22
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 100
2A 20 240
2B 0 250
3A 10 330
4A 0 210, 420
4B 8 26, 420
4C 4 28, 420
5A 0 520
5B 0 520
5C 5 519
6A 0 25, 615
6B 2 24, 36, 612
7A 2 714
8A 2 23, 43, 810
8B 0 22, 44, 810
8C 0 22, 44, 810
10A 0 54, 108
10B 0 1010
11A 1 119
11B 1 119
12A 0 2, 42, 63, 126
15A 0 52, 156
20A 0 102, 204
20B 0 102, 204

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