# Conjugacy Class of symmetry group $S_{10}$

Let $X=\{a\in S_{10} | ~~\text{order}(a)=8\}$. Determine how many conjugacy classes are in $X$.

How to do this question in general?

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Do you mean for arbitrary orders in arbitrary symmetric groups? Do you see how to do it in this case? – Tobias Kildetoft Aug 3 '13 at 19:12
No in this case. But the other question I'm trying to do is slightly different. – fjiao03 Aug 3 '13 at 19:18
In that case: Do you know what the conjugacy classes look like in the symmetric groups? Do you know what an element of order $8$ looks like? – Tobias Kildetoft Aug 3 '13 at 19:35
@Babak: GAP would tell you the answer to this question, but I think he wants to learn how the answer is calculated. – Derek Holt Aug 4 '13 at 9:50
@DerekHolt: Yes. In fact, I wanted the OP to examine the problem by GAP just to find and construct a theoretical idea. :) – S. Snape Aug 4 '13 at 10:39