How should I write down the alternating group $A_3$? I didn't understand how to write down the alternating group A3. 
Is this the group consisting of only the even permutations? Also, what familiar group is this isomorphic to?

Its elements are the  $3$-cycles and the identity
$\begin{cases}
f(1)=2, f(2)=3, f(3)=1 \\
g(1)=3, g(2)=1, g(3)=2 \\
Id
\end{cases}$.
