A Module Construction for a Class Function On a Finite Group

For a finite group G and an arbitrary subgroup H≤G,it is proved that |C(x)| is a factor of |G∶H‖C(x)∩H|,where x∈G and C(x) is the G-conjugacy class containing x.Furthermore,a class function which turn out to be a character is defined and its representation module is constructed.