About this representation
| Group
| He
|
| Group generators
| Standard generators
|
| Number of points
| 2058
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 5
|
| Suborbit lengths
| 1, 1362, 425, 1360
|
| Character
| 1 + 51ab + 680 + 1275a
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 2058
|
|
| 2A
| 154
| 2952
|
| 2B
| 42
| 21008
|
| 3A
| 42
| 3672
|
| 3B
| 0
| 3686
|
| 4A
| 14
| 270, 4476
|
| 4B
| 18
| 212, 4504
|
| 4C
| 2
| 220, 4504
|
| 5A
| 8
| 5410
|
| 6A
| 10
| 216, 348, 6312
|
| 6B
| 0
| 314, 6336
|
| 7A
| 0
| 7294
|
| 7B
| 0
| 7294
|
| 7C
| 0
| 7294
|
| 7D
| 0
| 7294
|
| 7E
| 0
| 7294
|
| 8A
| 2
| 410, 8252
|
| 10A
| 4
| 22, 530, 10190
|
| 12A
| 2
| 24, 34, 48, 622, 12156
|
| 12B
| 0
| 36, 64, 12168
|
| 14A
| 0
| 722, 14136
|
| 14B
| 0
| 722, 14136
|
| 14C
| 0
| 76, 14144
|
| 14D
| 0
| 76, 14144
|
| 15A
| 2
| 32, 58, 15134
|
| 17A
| 1
| 17121
|
| 17B
| 1
| 17121
|
| 21A
| 0
| 76, 2196
|
| 21B
| 0
| 76, 2196
|
| 21C
| 0
| 2198
|
| 21D
| 0
| 2198
|
| 28A
| 0
| 72, 1410, 2868
|
| 28B
| 0
| 72, 1410, 2868
|
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
|