On IA-automorphisms that fix the centre element-wise

Let G be a group. An automorphism of G is called an IA-automorphism if it induces the identity mapping on G/gamma(2)(G), where gamma(2)(G) is the commutator sub-group of G. Let IAz(G) be the group of those IA-automorphisms, which fix the centre element-wise and let Autcent(G) be the group of central automorphisms, the automorphisms that induce the identity mapping on the central quotient. It can be observed that Autcent(G) = C-Aut(G)(IA(z)(G)). We prove that IA(z)(G) and IA(z)(H) are isomorphic for any two finite isoclinic groups G and H. Also, for a finite p-group G, we give a necessary and sufficient condition to ensure that IA(z)(G) = Autcent(G).