Is there any cyclic subgroup of order 6 in in $ S_6$?

Question

Is there any cyclic subgroup of order 6 in $ S_6$?

Attempt:

$|S_6|=6!=720$

Let $H$ be a subgroup of $S_6$ ,$H$ cyclic $\iff\langle H \rangle=\{e,h,h^2,...,h^{n-1}\}=S_6$

Answer 1

Yes: no need of great theorems. The subgroup generated by $(1,2,3,4,5,6)$ does the job.