(a) Let $G$ be $S_{4}$, the symmetric group on four letters. Determine the character table of $G$.

[Begin by listing the conjugacy classes and their orders.]

(b) For each irreducible representation $V$ of $G=S_{4}$, decompose $\operatorname{Res}_{A_{4}}^{S_{4}}(V)$ into irreducible representations. You must justify your answer.