# Groups of order 5

From Groupprops

This article gives information about, and links to more details on, groups of order 5

See pages on algebraic structures of order 5| See pages on groups of a particular order

There is, up to isomorphism, a unique group of order 5, namely cyclic group:Z5. This can be proved in many ways, including simply listing possible multiplication tables, but it also follows from the fact that 5 is a prime number and there is a *unique* isomorphism class of group of prime order, namely that of the cyclic group of prime order.