Corollary 5: G is finite group of order $n$ and $p$ smallest prime divides $n$ then any subgroup of index $p$ is normal.
The book begins with let $H\leq G$ s.t. $|G:H|=p$ then let $K$ be the kernel of the action of G on the left cosets of H (action is left multiplication ) now it is clear that $G/H$ isomorphic to a subgroup of $S_p$ but why $G/K$ is also isomorphic to a subgroup of the same symmetric group. That's the question.