Group cohomology of semidihedral groups
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: