(1)If $\,H ≤ G\,$, the factor group $\,N_G(H)⁄C_G(H)\,$ is isomorphic to a subgroup of $\,\operatorname{Aut}(H)\,$ using in the proof group action
(2)Let $\,H\leq G\,$ . The centralizer of $\,H\,$ is the set $\,C_G(H):=\{g∈G:hg=gh\;\; ∀h∈H\}\,$.Show that $\,C_G(H)\leq N_G(H)$