Groups of order 15

This article gives information about, and links to more details on, groups of order 15
See pages on algebraic structures of order 15 | See pages on groups of a particular order

Up to isomorphism, there is a unique group of order 15, namely cyclic group:Z15, which is also the external direct product of cyclic group:Z3 and cyclic group:Z5.

The fact of uniqueness follows from the classification of groups of order a product of two distinct primes. Since $15=3\cdot 5$ and $3\not \mid (5-1)$, the number $15$ falls in the one isomorphism class case.