What is the order of the alternating group $A_4$? When I write out all the elements of $S_4$, I count only 11 transpositions. But in my text, the order of $A_4$ is $12$. What am I missing?
$A_4=\{(12)(34),(13)(24),(14)(23),(123),(124),(132),(134),(142),(143),(234),(243)$
$|A_4|=11$

The order of $A_n$ is always half the order of $S_n$, consider the bijective map from the even permutations to the odd permutations where $\varphi(\pi)=(12)\pi $. This is a bijection since the inverse is the map from the odd permutations to the even permutations $\varphi^{-1}(\pi)=(12)\pi$.
