Products of conjugacy classes and products of irreducible characters in finite groups

Let G be a finite group. If A and B are two conjugacy classes in G, then AB is a union of conjugacy classes in G and eta(AB) denotes the number of distinct conjugacy classes of G contained in AB. If chi and psi are two complex irreducible characters of G, then chipsi is a character of G and again we let eta(chipsi) be the number of irreducible characters of G appearing as constituents of chipsi. In this paper our aim is to study the product of conjugacy classes in a finite group and obtain an upper bound for eta in general. Then we study similar results related to the product of two irreducible characters.