# Group cohomology of elementary abelian group of prime-fourth order

From Groupprops

This article gives specific information, namely, group cohomology, about a family of groups, namely: elementary abelian group of prime-fourth order.

View group cohomology of group families | View other specific information about elementary abelian group of prime-fourth order

Suppose is a prime number. We are interested in the elementary abelian group of prime-fourth order

## Particular cases

## Homology groups for trivial group action

FACTS TO CHECK AGAINST(homology group for trivial group action):

First homology group: first homology group for trivial group action equals tensor product with abelianization

Second homology group: formula for second homology group for trivial group action in terms of Schur multiplier and abelianization|Hopf's formula for Schur multiplier

General: universal coefficients theorem for group homology|homology group for trivial group action commutes with direct product in second coordinate|Kunneth formula for group homology

### Over the integers

The homology groups over the integers are given as follows:

The first few homology groups are given as follows:

rank of as an elementary abelian -group | -- | 4 | 6 | 14 | 21 | 35 | 49 | 71 | 94 |