Order of cyclic subgroups in symmetric groups

Question

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 $(1\ 2\ 3\ 4\ 5\ 6)$?

Answer 1

Hint:

1. The order of a cyclic subgroup is the order of any of its generators.
2. The order of an element of $S_n$ is the lcm of the lengths of the cycles in its disjoint cycle decomposition.

Example: in $S_7$ you have a cyclic subgroup of order $10=2\times 5$ generated by $(1\ 2)(3\ 4\ 5\ 6\ 7)$.