# More than 99% of groups of order less than 2000 are of order 1024?

In Algebra: Chapter 0, the author made a remark (footnote on page 82), saying that more than 99% of groups of order less than 2000 are of order 1024.

Is this for real? How can one deduce this result? Is there a nice way or do we just check all finite groups up to isomorphism?

Thanks!

Here is a list of the number of groups of order $$nn$$ for $$n=1,…,2015n=1,\ldots,2015$$. If you add up the number of groups of order other than $$10241024$$, you get $$423,164,062423{,}164{,}062$$. There are $$49,487,365,42249{,}487{,}365{,}422$$ groups of order $$10241024$$, so you can see the assertion is true. (In fact the percentage is about $$99.15%99.15\%$$.)
As far as I know there is no reasonable way to deduce a priori the number of isomorphism classes of groups of a given order, though I believe that combinatorial group theory has some methods for specific cases. A general rule of thumb is that there are a ton of $$22$$-groups, and in fact I have heard it said that “almost all finite groups are $$22$$-groups” (though I cannot cite a reference for this statement).
EDIT: As pointed out in the comments, “almost all finite groups are $$22$$-groups” is still a conjecture. There is an asymptotic bound on the number of $$pp$$-groups of order $$pnp^n$$, however. Denoting by $$μ(p,n)\mu(p,n)$$ the number of groups of order $$pnp^n$$, $$μ(p,n)=p(227+O(n−1/3))n3,\mu(p,n)=p^{\left(\frac{2}{27}+O(n^{-1/3})\right)n^3},$$ which is proven here. This colossal growth along with the results of Besche, Eick & O’Brien seem to be what primarily motivated the conjecture.