Automorphism group of a Reed-Muller code

We compute the automorphism group of the second-order Reed-Muller code of length 64.

> C := ReedMullerCode(2, 6);
> aut := AutomorphismGroup(C);
> FactoredOrder(aut);
[ <2, 21>, <3, 4>, <5, 1>, <7, 2>, <31, 1> ]
> CompositionFactors(aut);
    G
    |  A(5, 2)                = L(6, 2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1

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