About this representation
| Group | J4 |
|---|---|
| Group generators | Type I standard generators |
| Dimension | 112 |
| Ring | GF(2) |
| Characteristic | 2 |
| Irreducibility information | Absolutely irreducible |
| Indicator | + |
| Character | φ2 |
| Character ring | Z[b33, c31, *3, c43, *3] |
| Schur index | 1 |
| Dimension of 1-cohomology | 0 |
| Notes | Invariant quadratic form is of plus type. Λ2(112) = 1.1220a.3774.1220b.1 (uniserial). S2(112) = (112 + 1).1220a.3774.1220b.1 (with just the 8 visible submodules). The modules 1, 112, 1220a, 1220b, 3774 are all absolutely irreducible GF(2)-modules of J4. |
| Contributed by | Not recorded |
Download
This representation is available in the following formats:
| MeatAxe | a | b |
| MeatAxe binary | a | b |
| GAP | a | b |
| GAP | a, b | |
| Magma | a, b | |
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 6, 2006 | irr.pl v0.2 | Pass |