About this representation

Group J2
Group generators Standard generators
Number of points 840
Primitivity information Primitive
Transitivity degree 1
Rank 7
Suborbit lengths 1, 15, 20, 24, 180, 240, 360
Character 1 + 63 + 90 + 126 + 160 + 175 + 225
Point stabiliser A4 × A5
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 840
2A 40 2400
2B 16 2412
3A 12 3276
3B 9 3277
4A 0 220, 4200
5A 5 5167
5B 5 5167
5C 0 5168
5D 0 5168
6A 4 24, 312, 6132
6B 1 24, 35, 6136
7A 0 7120
8A 0 410, 8100
10A 1 22, 53, 1082
10B 1 22, 53, 1082
10C 0 58, 1080
10D 0 58, 1080
12A 0 22, 42, 66, 1266
15A 2 3, 52, 1555
15B 2 3, 52, 1555

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