List of small groups

G ⋊ H denotes a semidirect product where H acts on G; this may also depend on the choice of action of H on G. Abelian and simple groups are noted.

The identity element in the cycle graphs is represented by the black circle.

Angle brackets show the presentation of a group.

The numbers of non-abelian groups, by order, are counted by (sequence A060689 in the OEIS).

The smallest order for which the Small Groups library does not have information is 1024.