Groups of order 15625

Statistics at a glance
Since $$15625 = 5^6$$ is a prime power, and prime power order implies nilpotent, all groups of this order are nilpotent groups.

GAP implementation
gap> SmallGroupsInformation(15625);

There are 684 groups of order 15625.

Easterfield (1940) constructed a list of the groups of     order p^6 for p >= 5.

The database of parametrised presentations for the groups with order p^6 for p >= 5 is based on the Easterfield list, corrected by Newman, O'Brien and Vaughan-Lee (2004). It differs only in the addition of groups in isoclinism family $Phi_{13}$, in using the James (1980) presentations for the groups in $Phi_{19}$, and a small number of     typographical amendments. The linear ordering employed is     very close to that of Easterfield.

Each group with order $p^6$ is described by a power- commutator presentation on 6 generators and 21 relations: 15 are commutator relations and 6 are power relations. Each presentation has the prime $p$ as a parameter. The database contains about 500 parametrised presentations, most of these have $p$ as the only parameter.

This size belongs to layer 9 of the SmallGroups library. IdSmallGroup is not available for this size.