[GAP Forum] Group representations over finite fields

[Francois Le Gall]

Dear Juergen, Dear Forum,

Thank you very much for the very helpful explanations!
I will try to work out the details of the reduction from the ordinary character tables you suggested.

I now understand that MeatAxe procedures are randomized. There is nevertheless something that I feel very strange. 
When I run (using GAP 4.4.12 on Mac OS X 10.6.8)  several times the following commands 

G:=AbelianGroup([8,4]);
R:=RegularModule(G,GF(3));
F:=MTX.CollectedFactors(R[2]);

I obtain five kinds of outputs: 

(a) 4 irreducibles of dimension 1 (each with multiplicity 1) + 14 irreducibles of dimension 2 (each with multiplicity 1)
(b) 4 irreducibles of dimension 1 (each with multiplicity 1) + 13 irreducibles of dimension 2 (each with multiplicity 1) + 1 irreducibles of dimension 2 (with multiplicity 2)
(c) 4 irreducibles of dimension 1 (each with multiplicity 1) + 12 irreducibles of dimension 2 (each with multiplicity 1) + 2 irreducibles of dimension 2 (each with multiplicity 2)
(d) 4 irreducibles of dimension 1 (each with multiplicity 1) + 11 irreducibles of dimension 2 (each with multiplicity 1) + 3 irreducibles of dimension 2 (each with multiplicity 2)
(e) 4 irreducibles of dimension 1 (each with multiplicity 1) + 9 irreducibles of dimension 2 (each with multiplicity 1) + 5 irreducibles of dimension 2 (each with multiplicity 2)

Outputs (b) to (e) seem wrong (specifically, the sum of the products of dimensions by multiplicities does not match the order of the group). Does this mean that the command 
MTX.CollectedFactors outputs, with some probability, wrong multiplicities?

Best regards,

Francois Le Gall