What is the largest possible order of a cyclic subgroup of $S_7$?
What's an example of this?
I really just need a better understanding of cyclic subgroups of symmetric groups. I know that the largest possible subgroup of $S_7$ is of size $7$. And I know all the possible cycle structures. Would it be $6$ because $\left<(1 2 3 4 5 6 )\right>$ is a cyclic subgroup generated by the size of $S_6$ or the element $(1\ 2\ 3\ 4\ 5\ 6)$?