7.66 PermutationCharacter

PermutationCharacter( G, U )

computes the permutation character of the operation of G on the cosets of U. The permutation character is returned as list of integers such that the i.th position contains the value of the permutation character on the i.th conjugacy class of G (see ConjugacyClasses).

The value of the permutation character of U in G on a class c of G is the number of right cosets invariant under the action of an element of c.

    gap> G := SymmetricPermGroup(5);;
    gap> PermutationCharacter( G, SylowSubgroup(G,2) );
    [ 15, 3, 3, 0, 0, 1, 0 ] 

For small groups the default function GroupOps.PermutationCharacter calculates the permutation character by inducing the trivial character of U. For large groups it counts the fixed points by examining double cosets of U and the subgroup generated by a class element.

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