53.5 ClassFunction

ClassFunction( G, values )

returns the class function of the group G with values list values.

ClassFunction( G, chi )

returns the class function of G corresponding to the class function chi of H. The group H can be a factor group of G, or G can be a subgroup or factor group of H.

    gap> phi:= ClassFunction( S4, [ 1, -1, 0, 2, -2 ] );
    ClassFunction( S4, [ 1, -1, 0, 2, -2 ] )
    gap> coeff:= List( irr, x -> ScalarProduct( x, phi ) );
    [ -1/12, -1/12, -1/6, 5/4, -3/4 ]
    gap> ClassFunction( S4, coeff );
    ClassFunction( S4, [ -1/12, -1/12, -1/6, 5/4, -3/4 ] )
    gap> syl2:= SylowSubgroup( S4, 2 );;
    gap> ClassFunction( syl2, phi );
    ClassFunction( D8, [ 1, -1, -1, 2, -2 ] ) 

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