Groups of order 16807

Statistics at a glance
Since $$16807 = 7^5$$ is a prime power, and prime power order implies nilpotent, all groups of this order are nilpotent groups.

GAP implementation
gap> SmallGroupsInformation(16807);

There are 83 groups of order 16807. They are sorted by their ranks. 1 is cyclic. 2 - 42 have rank 2. 43 - 76 have rank 3. 77 - 82 have rank 4. 83 is elementary abelian.

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