There are essentially two groups with four elements. In other words, any group with four elements is isomorphic to one of these two. One is the cyclic group with four elements. The other is the Klein four-group. It is abelian, and may be written as a multiplicative group with elements e, a, b and c, where e is the identity element, a2=b2=c2=e, ab=c, bc=a and ca=b.