In the permutations group S4, let H be the cyclic group the is generated by the cycle

(1 2 3 4).

A. Prove that the centralizer C(H) of H is excatly H ( C(H)={g in G|gh=hg for every h in H} )-I've managed to prove this one...

Can't understand how to prove this one:

B. Prove that the normalizer of H is a 2-sylow group of S4.

TNX to all the helpers!