# question regarding group permutation computation

In S6, let $\alpha=(135)(156)(135)$ how do I compute $\alpha^{24}$? I'm given the hint that I first have to express alpha as a product of disjoint cycles which I computed as (15)(36) and then I have to find $\alpha^2$.

Hint: $\alpha^{24}=(\alpha^2)^{12}$
Alternative hint: Don't even rewrite $\alpha$ as product of disjoint cycle. Just note that it is a permutation of $\{1,3,5,6\}$ only and that $|S_4|=24$.