Struct/The symmetric group of order six

=Definition=

There is a unique nonabelian group, up to isomorphism, with six elements. One example is the group $S_3$ of permutations of the three-element set $\{ 1,2,3 \}$.

=Properties=


 * The group $S_3$ is a non-abelian group.
 * Every non-abelian group of order $6$ is isomorphic to $S_3$.
 * The group $S_3$ is isomorphic to $D_6$, the symmetry group of a regular triangle.