# Group cohomology of elementary abelian group:E16

From Groupprops

This article gives specific information, namely, group cohomology, about a particular group, namely: elementary abelian group:E16.

View group cohomology of particular groups | View other specific information about elementary abelian group:E16

## Family contexts

Family | Parameter values | Information on group cohomology of family |
---|---|---|

elementary abelian group of order for a prime | group cohomology of elementary abelian groups | |

elementary abelian group of prime-fourth order for a prime | group cohomology of elementary abelian group of prime-fourth order |

## 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 2-group | -- | 4 | 6 | 14 | 21 | 35 | 49 | 71 | 94 |