Groups of order 21

This article gives information about, and links to more details on, groups of order 21
See pages on algebraic structures of order 21 | See pages on groups of a particular order

Statistics at a glance

Quantity	Value	Explanation
Total number of groups	2
Number of abelian groups	1

The groups

There are, up to isomorphism, two groups of order 21, indicated in the table below:

Group	GAP ID (second part)	Abelian?
General semilinear group:GammaL(1,8)	1	No
cyclic group:Z21	2	Yes

This is classified by the classification of groups of order a product of two distinct primes in the case with two isomorphism classes since $21=3\cdot 7$, with $3\mid 7-1$.

Z7⋊Z3 is the smallest non-abelian group of odd order.