# Higman-Sims asymptotic formula on number of groups of prime power order

From Groupprops

## Statement

### Quick version

Let be a (fixed) prime number. Define as the number of groups of order (see also group of prime power order, number of groups of given order). Then:

### Full version

Let be a (fixed) prime number. Define as the number of groups of order (see also group of prime power order, number of groups of given order). Define:

Then:

Note that the big-O notation is with respect to (sending and not with respect to ). However, the constants under the big-O notation may depend on .