Constituents of a module

Construct a permutation group G.

> G := PermutationGroup<20 |
>     (1, 6, 11, 16)(2, 7, 12, 17)(3, 8, 13, 18)(4, 9, 14, 19)(5, 10, 15, 20),
>     (1, 6)(2, 7)(3, 8)(4, 9)(5, 10),
>     (1, 2, 3, 4, 5),
>     (1, 5)(2, 4)
> >;

Construct the permutation module of G over .

> P := PermutationModule(G, GF(7));
> P;
GModule P of dimension 20 with base ring GF(7)
>
> // Find the Composition factors of P.
> F := CompositionFactors(P);
[
    GModule of dimension 1 with base ring GF(7),
    GModule of dimension 3 with base ring GF(7),
    GModule of dimension 16 with base ring GF(7)
]

Form a tensor product.

> T := TensorProduct(F[3], F[3]);
> T;
GModule T of dimension 256 with base ring GF(7)
>
> CompositionFactors(T);
[
    GModule of dimension 48 with base ring GF(7),
    GModule of dimension 1 with base ring GF(7),
    GModule of dimension 16 with base ring GF(7),
    GModule of dimension 1 with base ring GF(7),
    GModule of dimension 48 with base ring GF(7),
    GModule of dimension 3 with base ring GF(7),
    GModule of dimension 48 with base ring GF(7),
    GModule of dimension 4 with base ring GF(7),
    GModule of dimension 4 with base ring GF(7),
    GModule of dimension 16 with base ring GF(7),
    GModule of dimension 16 with base ring GF(7),
    GModule of dimension 48 with base ring GF(7),
    GModule of dimension 3 with base ring GF(7)
]

Classify the modules up to isomorphism and select one module from each isomorphism class.

> Constituents(T);
[
    GModule of dimension 1 with base ring GF(7),
    GModule of dimension 3 with base ring GF(7),
    GModule of dimension 4 with base ring GF(7),
    GModule of dimension 16 with base ring GF(7),
    GModule of dimension 48 with base ring GF(7),
    GModule of dimension 48 with base ring GF(7),
    GModule of dimension 48 with base ring GF(7)
]

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