4th symmetric group, order

I have the following revision question:

Recall that $\displaystyle S_4 $ (the fourth symmetric group) consists of the set of bijections $\displaystyle f: \{ 1,2,3,4 \} \rightarrow \{ 1,2,3,4 \}. $ The group operation is composition of functions. Let

$\displaystyle p = \begin{pmatrix} 1&2&3&4 \\ 4&2&1&3 \end{pmatrix} $

Find the order of $\displaystyle p $ and write down all the elements of the cyclic subgroup $\displaystyle <p> $.

I think that to find the order of $\displaystyle p $ I need to calculate $\displaystyle p^{something} = 1. $ i.e. $\displaystyle p^{something} = \begin{pmatrix} 1&2&3&4 \\ 1&2&3&4 \end{pmatrix} $ and then the order is the $\displaystyle something $

Then I think that if, for example, the order was 2 then $\displaystyle <p> = \{ p,p^1 \}.... $ but Im not sure.

Anyway my main problem is calculating $\displaystyle p^2, p^3, p^4, ect $. Can anyone please show me how this is done? Thanks