Am I right that conjugacy classes of group $A_n$ can be obtained from conjugacy classes of $S_n$ (which are in correspondence with Young diagrams). If class $$C(h)=\{\sigma h {\sigma}^{-1}|\sigma\in S_n\}$$ contains independent cycles of only odd length and length of all cycles are different then $C(h)$ in $A_n$ split to two classes $$C_1(h)=\{\sigma h {\sigma}^{-1}|\sigma\in A_n\}$$ $$C_2(h)=\{\sigma \tau h {\tau}^{-1} {\sigma}^{-1}|\sigma\in A_n\}.$$ I only interested in the answer.
Thanks a lot!