Higman–Sims asymptotic formula

In finite group theory, the Higman–Sims asymptotic formula gives an asymptotic estimate on number of groups of prime power order.

Statement
Let $$p$$ be a (fixed) prime number. Define $$f(n,p)$$ as the number of isomorphism classes of groups of order $$p^n$$. Then:
 * $$f(n,p) = p^{\frac{2}{27}n^3 + \mathcal O(n^{8/3})}$$

Here, the big-O notation is with respect to $$n$$, not with respect to $$p$$ (the constant under the big-O notation may depend on $$p$$).