Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups

We study some families of finite groups having inner class-preservingautomorphisms. In particular, let G be a finite group and S be asemidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is nota homomorphic image of G and \(Z(S) < Z(G)\) $Z(S)<Z(G)$ or G is nilpotent-by-nilpotent, wehave that all the Coleman automorphisms of G are inner. As a consequence, thesegroups satisfy the normalizer problem.