on automorphic classes of finite groups

Let g be a finite group and x ∈ g. cl_a(x) = {α(x)|α ∈ aut(g)} denotes the automorphic class of x in g. in this paper some properties of finite groups are described via automorphic class and it is shown that if the number of automorphic classes of a given lower autonilpotent group g, is even then |aut(g)| is also even.