Abstract:

Jelten B. Naphtali has achieved the minimum number of irreducible representations of finite non abelian groups using the centre. Also, Naphtali et al have determined the representation of finite 2 – groups with minimum centre using the degree equation. In this paper we determine the irreducible representations of finite p – groups with maximum centre where p is prime. We consider this for finite abelian and finite non abelian groups both of prime power order. That is groups of order pn for , where n is an integer and p is fixed at p = 2. In this work we employ the class equation as the major theorem in proving our results.