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Can somebody explain to me the combinatorics calculation of the order of the conjugacy classes in the group of permutations $S_n$. I saw an example of $S_4$ and $S_5$ but I still don't understand the algorithm in generally or the way of choosing and then multiplying by the amount of options.

Can somebody write the general formule for the order of conjugacy class of a permutation in $S_n$ that written in general by different k-permutations of length $r_1, r_2, ... , r_k$. or for example what is the algorithm to calculate the order of the conjugacy classe of the following permutations in $S_10$,for example $$(a,b,c)(d,e,f)(g,h,i)$$ $$(a,b)(e,f,g,h)(c,d)$$ $$(a,b)(e,f,g,h)(c,d)(i,j)$$ And so on, how do I calculate these?

Ilya.K.
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    What is meant by order of Conjugacy classes? Do you mean total number of conjugacy classes? Or do you mean number of elements in the conjugacy class of an element? – Babai Sep 30 '15 at 09:14
  • The second, numbers of elements of the same k-permutation form. – Ilya.K. Sep 30 '15 at 09:15
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    you should probably look here - http://math.stackexchange.com/questions/449041/counting-the-number-of-elements-in-a-conjugacy-class-of-s-n – Babai Sep 30 '15 at 09:19
  • Yes, a very good explanation. – Ilya.K. Sep 30 '15 at 09:32

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