Groups of order 125

Statistics at a glance
Since $$125 = 5^3$$ is a prime power and prime power order implies nilpotent, all groups of this order are nilpotent groups.

GAP implementation
gap> SmallGroupsInformation(125);

There are 5 groups of order 125. 1 is of type c125. 2 is of type 5x25. 3 is of type 5^2:5. 4 is of type 25:5. 5 is of type 5^3.

The groups whose order factorises in at most 3 primes have been classified by O. Hoelder. This classification is used in the SmallGroups library.

This size belongs to layer 1 of the SmallGroups library. IdSmallGroup is available for this size.