Related to [A000679](http://www.oeis.org/A000679) (Number of groups of order $2^n$), how many non-Abelian groups of order $2^n$ are there?



Number of non-Abelian groups of order $2^n$
It is true that there is no known formula for the number of isomorphism classes of groups of order $n$, but there is a very nice asymptotic formula for $p$-groups.


In particular, the number of isomorphism classes of groups of order $p^n$ grows as $p^{\frac{2}{27}n^3 + O(n^{8/3})}$. This function grows very rapidly, and there is a folklore conjecture that 
"almost all groups are $2$-groups."


<http://en.wikipedia.org/wiki/P-group>


