Groups of order 2^m.3^n

This article discusses groups whose order has prime factors in the set $$\{ 2, 3 \}$$ and no others. Another way of putting this is that the article discusses finite $$\pi$$-groups where $$\pi = \{ 2, 3\}$$.

Orders of interest
The clickable links in the table are to pages devoted to groups of that order.

The rows represent values of $$m$$ and corresponding values of $$2^m$$. The columns represent values of $$n$$ and corresponding values of $$3^n$$.

Counts of all groups
The rows give values of $$m, 2^m$$ and the columns give values of $$n, 2^n$$. Each cell value is the total number of isomorphism classes of groups of order $$2^m \cdot 3^n$$.

Note that for small values of $$m,n$$, the order of magnitude of the values depends roughly on $$m + n$$ (so it is roughly of the same order of magnitude as we move along a north-east-to-south-west diagonal). This fails to hold for larger values of $$m,n$$.

Counts of nilpotent groups
Thus, the number of nilpotent groups of order $$2^m \cdot 3^n$$ = (number of groups of order $$2^m$$) $$\times$$ (number of groups of order $$3^n$$)