can serve as generators in the above presentation. The Klein four-group is the smallest non-cyclic group. It is, however, an abelian group, and isomorphic to the dihedral group of order (cardinality) 4, symbolized (or , using the geometric convention); other than the group of order 2, it is the only dihedral group that is abelian.

The Klein four-group is also isomorphic to the direct sum