If H is a subgroup of G, the factor group N_G(H)/C_G(H) (see Exercise 4) is isomorphic to a subgroup of Aut H.

Data From Exercise 4

Let H be a subgroup of G. The centralizer of H is the set C_G(H) = {g ϵ G| hg = gh for all h ϵ H}. Show that C_G(H) is a subgroup of N_G (H).