Struct/The Klein group of order four

=Definition=

There is a unique non-cyclic group, up to isomorphism, with four elements. One example is the Klein group, displayed below.

=Properties=


 * The group $K_4$ is an abelian group.
 * It is not a cyclic group.
 * The group $K_4$ has automorphism group $S_3$, which acting by permutations on the set $\{ i,j,k \}$.
 * The group $K_4$ is isomorphic to the direct product $\ZZ / 2 \ZZ \times \ZZ / 2 \ZZ$.