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


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