About this representation

Group J3
Group generators Standard generators
Number of points 6156
Primitivity information Primitive
Transitivity degree 1
Rank 8
Suborbit lengths 1, 85, 120, 510, 680, 13602, 2040
Character 1 + 323ab + 324 + 1140 + 1215ab + 1615
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 6156
2A 76 23040
3A 36 32040
3B 0 32052
4A 12 232, 41520
5A 1 51231
5B 1 51231
6A 4 216, 324, 61008
8A 0 26, 416, 8760
9A 0 9684
9B 0 9684
9C 0 9684
10A 1 515, 10608
10B 1 515, 10608
12A 0 22, 34, 48, 610, 12504
15A 1 57, 15408
15B 1 57, 15408
17A 2 17362
17B 2 17362
19A 0 19324
19B 0 19324

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