A Module Construction for a Class Function on a Finite Group

For a finite group G, f is a function on G, whose value at an element q of G is the number of elements (a, b, c) ¿ G × G × G satisfying abcb^-1a^-1c^-1. By computing the inner products of / with the irreducible characters of G, we prove that f is a character of G, by the regular representation of the center of the complex group algebra, a module construction of f is obtained.