GAP Manual: 50.1. ScalarProduct

ScalarProduct( tbl, character1, character2 )

returns the scalar product of character1 and character2, regarded as characters of the character table tbl.

    gap> t:= CharTable( "A5" );;
    gap> ScalarProduct( t, t.irreducibles[1], [ 5, 1, 2, 0, 0 ] );
    1
    gap> ScalarProduct( t, [ 4, 0, 1, -1, -1 ], [ 5, -1, 1, 0, 0 ] );
    2/3