Conjugacy class of permutatuion

Question

I have permutation $\partial$ = (1 10)(2 6 3 7 6 8 12)(4)(9 11) $\in S_{12}$ and i need to find number of elements in conjugacy class of permutation $\partial$ in group of all permutations. I dont understand how to solve this problem. How can i find conjugacy class if disjoint cycles have different length?

Answer 1

The conjugacy class of a permutation consists of all the permutations with the same cycle structure. How many of those are there in $S_{12}$ with structure $(xx)(xxxxxxx)(x)(xx)$?

Remember that disjoint cycles commute, so the order of the cycles doesn't matter, nor does the order of elements in each cycle.

Answer 2

$\frac{12!}{(2^2*2!)(7^1*1!)(3^1*1!)(1^1*1!)}$