About this representation
| Group
| HS
|
| Group generators
| Standard generators
|
| Number of points
| 1100
|
| Distinguishing letter
| b
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 5
|
| Suborbit lengths
| 1, 28, 105, 336, 630
|
| Point stabiliser
| S8
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 1100
|
|
| 2A
| 60
| 2520
|
| 2B
| 32
| 2534
|
| 3A
| 11
| 3363
|
| 4A
| 40
| 210, 4260
|
| 4B
| 16
| 222, 4260
|
| 4C
| 4
| 228, 4260
|
| 5A
| 0
| 5220
|
| 5B
| 10
| 5218
|
| 5C
| 0
| 5220
|
| 6A
| 5
| 23, 39, 6177
|
| 6B
| 3
| 24, 319, 6172
|
| 7A
| 1
| 7157
|
| 8A
| 2
| 27, 411, 8130
|
| 8B
| 0
| 22, 414, 8130
|
| 8C
| 0
| 22, 414, 8130
|
| 10A
| 0
| 512, 10104
|
| 10B
| 2
| 24, 56, 10106
|
| 11A
| 0
| 11100
|
| 11B
| 0
| 11100
|
| 12A
| 1
| 2, 313, 42, 63, 1286
|
| 15A
| 1
| 33, 52, 1572
|
| 20A
| 0
| 58, 102, 2052
|
| 20B
| 0
| 58, 102, 2052
|
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
|