4th symmetric group, order

I have the following revision question:

Recall that (the fourth symmetric group) consists of the set of bijections The group operation is composition of functions. Let

Find the order of and write down all the elements of the cyclic subgroup .

I think that to find the order of I need to calculate i.e. and then the order is the

Then I think that if, for example, the order was 2 then but Im not sure.

Anyway my main problem is calculating . Can anyone please show me how this is done? Thanks