Groups of Order 4

For Order 4 there are basically two types of group. Klien 4 and Cyclic Group of order 4. In Klien 4 each element is its own inverse. In cyclic group there are two elements which are inverse of each other and there are two which are their own inverses. The two which are inverse of each other are also the generator of this cyclic group.

S4 and Dihedral Group group D4

Dihedral group of Square

S3 Symmetric Group and its Cayley Table

Symmetric Group 3 with non abelian subgroup of order 3