Groups of order 25

This article gives information about, and links to more details on, groups of order 25
See pages on algebraic structures of order 25 | See pages on groups of a particular order

There are, up to isomorphism, two possibilities for a group of order 25. 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:Z25	1	unique cyclic group of order 25
elementary abelian group:E25	2	unique elementary abelian group of order 25; also a direct product of two copies of cyclic group:Z5.