On semicomplete finite p-groups

Let G be a finite group and N be a non-trivial proper normal subgroup of G. The pair (G, N) is called a Camina pair if xN subset of x(G) for all x is an element of G \ N, where x(G) denotes the conjugacy class of x in G. Also let Aut(G') (G) denote the group of all automorphisms of G fixing G/G' elementwise. A group G is called semicomplete if Aut(G') (G) = Inn(G). In this paper, using the notion of Frattinian groups, we give a necessary and sufficient condition for a finite p-group G such that (G, Z(G)) is a Camina pair to be semicomplete.