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

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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 5, 2006 irr.pl v0.2 Pass