About this representation
| Group
| Th
|
| Group generators
| Standard generators
|
| Dimension
| 248
|
| Ring
| GF(19)
|
| Characteristic
| 19
|
| Irreducibility information
| Absolutely irreducible
|
| Indicator
| +
|
| Character
| φ2
|
| Character ring
| Z
|
| Schur index
| 1
|
| Dimension of 1-cohomology
| 0
|
| Dimension of 2-cohomology
| 0
|
| Notes
| Invariant quadratic form is of plus type.
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
Checks applied
| Check |
Description |
Date |
Checked by |
Result |
| 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
|
| Dimension/field
| Check the dimension and field/ring of the representation.
| 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
|
| Irreducibility
| Check the irreducibility type is correct.
| Jul 5, 2006
| irr.pl v0.2
| Pass
|