What does the order of a permutation say about it's cycle lengths?

Question

Say we have a Permutation $a$ of $S_5$.

We know that a is of order 6. Since the order is the least common multiple of a permutation, $a$ probably looks something like this:

$(a_1, a_2, a_3)(a_4, a_5)$

My question is whether you can always determine the length of the disjunct cycle when you only have the order and the number of elements i.e. 5.

Answer 1

The lcm of the lengths of the cycles in its cycle decomposition is equal to the order. That's about all you can say.