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
|
Download
This representation is available in the following formats:
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
|