21.13 PermGroupOps.Indices

PermGroupOps.Indices( G )

PermGroupOps.Indices returns a list l of indices of the permutation group G with respect to a stabilizer chain of G, i.e., l[i] is the index of G^{(i+1)} in G^{(i)}. Thus the size of G is the product of all indices in l. If a stabilizer chain for G is already known, PermGroupOps.Indices returns the indices corresponding to this stabilizer chain. Otherwise a stabilizer chain with the lexicographically smallest reduced base is computed and the indices corresponding to this chain are returned (see Stabilizer Chains).

    gap> s4 := Group( (1,2,3,4), (1,2) );;
    gap> PermGroupOps.Indices( s4 );
    [ 4, 3, 2 ]    # note that for s4 the indices are
                   # actually independent of the base 

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