I have seen this question already a few times, but I still do not understand the actual answer. I have to prove the isomorphism between $S_n$ and the semidirect product of $\{1,-1\}$ and $A_n$. I am a bit new to the semidirect product, hence my confusion.
So far I figured I have to do something with the parity of the permutations in $S_n$. And I need to definie a homomorphism $\rho: \{1,-1\} \to \text{Aut($A_n$)}$, I really do not know where to start.
Any tips?