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**eXist** Find the number of cycles of each possible length in $\displaystyle S_5$. Then find all possible orders of elements of in $\displaystyle S_5$. (Do this without writing out all 120 possible permutations.

I'm a little confused as to what it's asking. I know the order of a cycle is the length of that cycle. I'm guessing their asking how many 1 cycles are there, how many 2 cycles are there, how many 3 cycles, etc.

For the second part when you have to find all possible orders of the elements, I'd say it was the LCM of all the cycles. So my answer is: 60, 20, 15, 12, 10, 6, 5, 4, 3, 2, 1. Not sure if that's right though. Any help is appreciated.