About this representation

Group J2
Group generators Standard generators
Number of points 1008
Primitivity information Primitive
Transitivity degree 1
Rank 11
Suborbit lengths 1, 12, 25, 50, 602, 1002, 1502, 300
Character 1 + 14ab + 2.90 + 126 + 160 + 225 + 288
Point stabiliser A5 × D10
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 1008
2A 16 2496
2B 36 2486
3A 36 3324
3B 0 3336
4A 0 28, 4248
5A 13 5199
5B 13 5199
5C 3 5201
5D 3 5201
6A 4 216, 34, 6160
6B 0 312, 6162
7A 0 7144
8A 0 44, 8124
10A 1 26, 57, 1096
10B 1 26, 57, 1096
10C 1 2, 53, 1099
10D 1 2, 53, 1099
12A 0 22, 48, 62, 1280
15A 1 34, 57, 1564
15B 1 34, 57, 1564

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