Groups of order 361

This article gives information about, and links to more details on, groups of order 361
See pages on algebraic structures of order 361 | See pages on groups of a particular order

There are, up to isomorphism, two possibilities for a group of order 361. Both of these are abelian groups and, in particular are abelian of prime power order.

The classification follows 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:

Group	GAP ID (second part)	Defining feature
cyclic group:Z361	1	unique cyclic group of order 361
elementary abelian group:E361	2	unique elementary abelian group of order 361; also a direct product of two copies of cyclic group:Z19.