About this representation

Group J2
Group generators Standard generators
Number of points 1800
Primitivity information Primitive
Transitivity degree 1
Rank 18
Suborbit lengths 1, 142, 21, 28, 423, 843, 1686, 336
Character 1 + 36 + 2.63 + 90 + 2.126 + 160 + 175 + 288 + 2.336
Point stabiliser L3(2):2
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 1800
2A 120 2840
2B 20 2890
3A 0 3600
3B 6 3598
4A 12 254, 4420
5A 0 5360
5B 0 5360
5C 0 5360
5D 0 5360
6A 0 340, 6280
6B 2 22, 36, 6296
7A 1 7257
8A 2 25, 427, 8210
10A 0 54, 10178
10B 0 54, 10178
10C 0 524, 10168
10D 0 524, 10168
12A 0 34, 618, 12140
15A 0 15120
15B 0 15120

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