About this representation

Group J2
Group generators Standard generators
Number of points 280
Primitivity information Primitive
Transitivity degree 1
Rank 4
Suborbit lengths 1, 36, 108, 135
Character 1 + 63 + 90 + 126
Point stabiliser 3.PGL2(9)
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 280
2A 40 2120
2B 12 2134
3A 1 393
3B 4 392
4A 4 218, 460
5A 10 554
5B 10 554
5C 0 556
5D 0 556
6A 1 313, 640
6B 0 22, 34, 644
7A 0 740
8A 2 2, 49, 830
10A 2 24, 52, 1026
10B 2 24, 52, 1026
10C 0 58, 1024
10D 0 58, 1024
12A 1 3, 66, 1220
15A 1 33, 1518
15B 1 33, 1518

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