# Group cohomology of semidihedral groups

From Groupprops

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

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

We describe here the homology and cohomology groups of the semidihedral group of order , which is obtained as the external semidirect product of a cyclic group of order and cyclic group:Z2 where the non-identity element acts via multiplication by .

## 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 with coefficients in the ring of integers are given as follows: