Groups of order 561

This article gives information about, and links to more details on, groups of order 561
See pages on algebraic structures of order 561 | See pages on groups of a particular order

Up to isomorphism, there is a unique group of order 561, namely cyclic group:Z561.

The fact of uniqueness follows from:

1. $561$ is a cyclicity-forcing number, i.e., any group of order 561 is cyclic. See the classification of cyclicity-forcing numbers to see the necessary and sufficient condition for a natural number to be cyclicity-forcing. This is perhaps an easier to compute and more well-known result than the pqr classification:
2. the classification of groups of order a product of three distinct primes. Use $561=3\cdot 11\cdot 17$, and you will observe $561$ falls into a one isomorphism class case.