REPRESENTATION THEORETIC INVESTIGATION ON THE NUMBER OF CONJUGACY CLASSES OF TWO FAMILIES OF GROUPS

In this paper, we will solve the problem of counting the number of conjugacy classes of groups  of order  with   distinct primes and the number of conjugacy classes of groups of order , where  is prime.  In general, Sylow Theory together with class equation for groups is used for solving these problems, but instead of it we have used representation theory to solve these problems.