Groups of order 256

Statistics at a glance
Note that since prime power order implies nilpotent, and $$256 = 2^8$$ is a prime power, all groups of order 256 are nilpotent.

GAP implementation
gap> SmallGroupsInformation(256);

There are 56092 groups of order 256. They are sorted by their ranks. 1 is cyclic. 2 - 541 have rank 2. 542 - 6731 have rank 3. 6732 - 26972 have rank 4. 26973 - 55625 have rank 5. 55626 - 56081 have rank 6. 56082 - 56091 have rank 7. 56092 is elementary abelian.

For the selection functions the values of the following attributes are precomputed and stored: IsAbelian, PClassPGroup, RankPGroup, FrattinifactorSize and FrattinifactorId.

This size belongs to layer 2 of the SmallGroups library. IdSmallGroup is available for this size.