where each A is an irreducible character of some elementary subgroup (si of (M, ip* designates the character of (M induced by AXv , and where the ai belong to the ring Z of rational integers. Here, an elementary group is defined as a group which is the direct product of a cyclic group and a p-group for some prime number p. By a generalized character of 5, we shall mean the difference of two characters of 5. Thus, if xI, X2, * * , Xk are the irreducible characters of 5, the generalized characters have the form