Groups of order 128

Statistics at a glance
Note that since prime power order implies nilpotent, and $$128 = 2^7$$ is a prime power, all groups of order 128 are nilpotent.

Summary information
Here, the rows are arithmetic functions that take values between $$0$$ and $$7$$, 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 $$2328$$, which is the total number of groups of order $$128$$.

GAP implementation
gap> SmallGroupsInformation(128);

There are 2328 groups of order 128. They are sorted by their ranks. 1 is cyclic. 2 - 163 have rank 2. 164 - 996 have rank 3. 997 - 2149 have rank 4. 2150 - 2318 have rank 5. 2319 - 2327 have rank 6. 2328 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.