Groups of order 28

This article gives information about, and links to more details on, groups of order 28
See pages on algebraic structures of order 28 | See pages on groups of a particular order

There are, up to isomorphism, four possibilities for a group of order 28.

The classification follows from the classification of groups of order four times a prime congruent to 3 modulo 4, since $28=4\cdot 7,7\equiv 3\mod 4$.

The groups are:

Group	GAP ID (second part)	Abelian?	Defining feature
Dicyclic group:Dic28	1	No	Semidirect product $\mathbb {Z} _{7}\rtimes \mathbb {Z} _{4}$
cyclic group:Z28	2	Yes
dihedral group:D28	3	No
direct product of Z2 and Z14	4	Yes

Minimal order attaining number

$28$ is the smallest number such that there are precisely $4$ groups of that order up to isomorphism. That is, the value of the minimal order attaining function at $4$ is $28$.