Isoclinic groups and certain automorphisms of groups

Let G be a group and Aut_pwi(G), Aut_k-pwi(G) and D*(G) denote the group of all pointwise inner automorphisms, the group of all gk(G)-pointwise inner automorphisms and the group of all derival automorphisms of G that fix the center elementwise, respectively. We know that for finite groups, if G and H are two finite non-abelian isoclinic groups then Aut_pwi(G) ≈ Aut_pwi(H). Th is result is true for infinite groups. In this paper we prove that the group D*(G), Aut_pwi(G) and Aut_k-pwi(G) are independent of the choice of the group G in its isoclinism class. Also we show that this result is not true for D(G), Autc(G), C*(G) and A (G).