# Group cohomology of dicyclic groups

From Groupprops

This article gives specific information, namely, group cohomology, about a family of groups, namely: dicyclic group.

View group cohomology of group families | View other specific information about dicyclic group

We consider here the dicyclic group of degree and 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 for odd degree

The homology groups with coefficients in the ring of integers are as follows when the degree is odd.

### Over the integers for even degree

The homology groups with coefficients in the ring of integers are as follows when the degree is even.