$A_4$ is not isomorphic to $D_6$

Question

How do i show that $D_6$ has an element of order 6 but $A_4$ has only elements of order 3 and 2 and thus, $A_4$ is not isomorphic to $D_6$? Can someone explain to me? Thanks!

Answer 1

$D_6$ is the group of symmetries of the hexagon. The $60$-degree rotation is in $D_6$ and has order $6$.

However, no element of $S_4$ has order $6$. See also Element structure of symmetric group:S4.