Conjugacy classes of $A_7$

Question

What I have got is the following as the representatives of the conjugacy classes: $\mathrm{id}$, $(123)$, $(12345)$, $(12)(34)$, $(123)(456)$, $(1234)(56)$ which are the nonsplitting cases. The conjugacy class of $7$ cycles splits into two in $A_7$. So that gives me 8 conjugacy classes. But $A_7$ has 9. Which one am I missing?

Answer 1

You're missing $(123)(45)(67)$.