Question:

What are the orders of the Sylow p-subgroups of the symmetric group $\displaystyle S_6$?

Give the possible orders of each Sylow p-subgroup of $\displaystyle S_6$.

(N.B. If there are many possible orders, then give at least four).

Can anyone help me to understand what is meant by the above question please?

So far i understand that $\displaystyle S_6$ is the symmetric group of degree 6.

that is the symmetric group on {$\displaystyle {1,2,3,4,5,6}$ }

and i think that the order is given by $\displaystyle 6!$.

where do i go from there?