[GAP Forum] Group representations over finite fields

[Francois Le Gall]

Dear Forum,

I am currently investigating the dimensions of the irreducible representations of a (small) finite group G over the finite field GF(p) when p does not divide the order of G, along with their multiplicities in the regular representation of G. This is the first time I use GAP for representation theory over finite fields, and I would be very happy to know if there is a simple way to obtain this information.

I read the MeatAxe documentation and tried the following commands

R:=RegularModule(G,GF(p));
MTX.CollectedFactors(R[2]);

but I suspect that this is different from what I am looking for (specifically, for G:=AbelianGroup([8,4]) and p:=3, each call to MTX.CollectedFactors(R[2]) seems to give a different answer).

Thank you in advance.

Sincerely,

Francois Le Gall