# Upper bound on size of Schur multiplier for group of prime power order based on prime-base logarithm of order

From Groupprops

## Statement

Suppose is a prime number and is a finite p-group of order . Then, the Schur multiplier of is also a finite -group and its order is at most . In fact, we can say something stronger:

where denotes the derived subgroup of .

## Related facts

- Upper bound on size of second cohomology group for groups of prime power order is roughly equivalent in power.