Groups of order 4

There are, up to isomorphism, two possibilities for a group of order 4. Both of these are abelian groups and, in particular are abelian of prime power order.

The classification can be done by hand using multiplication tables, but it also follows more generally from the classification of groups of prime-square order.

See also groups of prime-square order for side-by-side comparison with the situation for other primes.

The groups are: