Groups of order 64

Numbers of groups
Since $$64= 2^6$$ is a prime power, and prime power order implies nilpotent, all groups of this order are nilpotent groups.

Summary information
Here, the rows are arithmetic functions that take values between $$0$$ and $$6$$, and the columns give the possible values of these functions. The entry in each cell is the number of isomorphism classes of groups for which the row arithmetic function takes the column value. Note that all the row value sums must equal $$267$$, which is the total number of groups of order $$64$$.

GAP implementation
gap> SmallGroupsInformation(64);

There are 267 groups of order 64. They are sorted by their ranks. 1 is cyclic. 2 - 54 have rank 2. 55 - 191 have rank 3. 192 - 259 have rank 4. 260 - 266 have rank 5. 267 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.</pre.