Automorphism Group of Nonabelian Groups of Order p3

Let G be a nonabelian group of order p(3), where p is a prime number. Then G is a two generated group that its commutator, centre and Frattini subgroup coincide and are of order p. Hence, the quotient group of G over its centre and also Frattini quotient group of G, both are of order p(2). However, the first mentioned quotient is isomorphic to the inner group of G, which is a normal subgroup of automorphism group of G. Whereas, Frattini quotient group of G is an abelian elementary group that can be considered as a vector space of dimension two over Z(p), the field of integers modulo p. In this paper, we consider to apply these properties of G to characterize the automorphism group of G.