Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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. :) – Babak S. Aug 4 '13 at 10:39

Hint #2: It suffices to consider disjoint cycle decompositions for which every cycle is of length 2,4 or 8.

share|cite|improve this answer

Hint: Consider cycle decompositions.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.