What is the percentage of known finite non-abelian groups to known finite abelian groups? I'm curious as to what the percentage of known finite non-abelian groups to known finite abelian groups is. Is there any research or hard data in this direction?
Edit: As we keep discovering more groups will non-abelian groups or abelian groups dominate the percentage?
 A: The vast majority of finite groups are 2-groups (that is groups whose order is a power of 2). The vast majority of those 2-groups are non-abelian. There is a classical result (see https://academic.oup.com/plms/article-abstract/s3-15/1/151/1534319 ) that the for any prime $p$, the number of groups of size $p^n$ is $p^{\frac{2n^3}{27}}$. It is not hard to see from this (and a little care with the error terms) that the vast majority of groups of size at most $m$ are contained in the $2$ groups. Note that this doesn't assert that they have density 1 (which is as far as I'm aware an open problem). Now, for any prime $p$ and $n$ the number of abelian groups of order $p^n$ is $P(n)$ where $P(n)$ is the number of partitions of $n$. The number of partitions of $n$ grows slower than exponential, and so the vast majority of finite groups are non-abelian 2-groups as long as one is counting how many groups there are of order $n$ for large $n$. 
Edit: The above isn't quite right it seems. See Verret's comment below. It appears that even the claim that a majority of groups are 2 groups is still open. 
