Groups of order 124

This article gives information about, and links to more details on, groups of order 124
See pages on algebraic structures of order 124 | See pages on groups of a particular order

There are, up to isomorphism, four possibilities for a group of order 124.

The classification follows from the classification of groups of order four times a prime congruent to 3 modulo 4, since $124=4\cdot 31,31\equiv 3\mod 4$.

The groups are:

Group	GAP ID (second part)	Abelian?	Defining feature
Dicyclic group:Dic124	1	No	Semidirect product $\mathbb {Z} _{31}\rtimes \mathbb {Z} _{4}$
cyclic group:Z124	2	Yes
dihedral group:D124	3	No
direct product of Z2 and Z62	4	Yes