Groups of order 87

This article gives information about, and links to more details on, groups of order 87
See pages on algebraic structures of order 87 | See pages on groups of a particular order

Up to isomorphism, there is a unique group of order 87, namely cyclic group:Z87, which is also the external direct product of cyclic group:Z3 and cyclic group:Z29.

The fact of uniqueness follows from the classification of groups of order a product of two distinct primes. Since $87=3\cdot 29$ and $3$ does not divide $(29-1)$, the number $87$ falls in the one isomorphism class case.

Another way of viewing this is that $87$ is a cyclicity-forcing number, i.e., any group of order 15 is cyclic. See the classification of cyclicity-forcing numbers to see the necessary and sufficient condition for a natural number to be cyclicity-forcing.