I have difficulty in solving the problem
Show that a solvable $4$-transitive permutation group $G$ is isomorphic to $S_4$. (Finite Group Theory by Isaacs, $8$A.$10$)
There's hint here: Show a minimal normal subgroup $N$ of $G$ is regular and consider the conjugation action of a point stablizer $G_\alpha$ on $N$.
Suppose $G$ acts on $\Omega$. Following the hint, I only know that if $N$ is regular, then the conjugation action of $G_\alpha$ on $N$ is isomorphic to the action of $G_\alpha$ on $\Omega-\{\alpha\}$, which is $3$-transitive.
Thanks a lot!