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?
$A_4=\{(12)(34),(13)(24),(14)(23),(123),(124),(132),(134),(142),(143),(234),(243)$
$|A_4|=11$

As $A_n$ is a subgroup of $S_n$, there should be identity and identity is a even permutation.
identity $e=(13)(13)$
