# Difference between revisions of "Group cohomology of dihedral group:D16"

From Groupprops

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This article describes the homology and cohomology group of [[dihedral group:D16]], the dihedral group of order 16 and degree 8. | This article describes the homology and cohomology group of [[dihedral group:D16]], the dihedral group of order 16 and degree 8. | ||

+ | ==Family contexts== | ||

+ | |||

+ | {| class="sortable" border="1" | ||

+ | ! Family name !! Parameter value !! Information on group cohomology of family | ||

+ | |- | ||

+ | | [[dihedral group]] <math>D_{2n}</math> of degree <math>n</math>, order <math>2n</math> || degree <math>n = 8</math>, order <math>2n = 16</math> || [[group cohomology of dihedral groups]] | ||

+ | |} | ||

==Homology groups for trivial group action== | ==Homology groups for trivial group action== | ||

## Latest revision as of 04:05, 16 January 2013

This article gives specific information, namely, group cohomology, about a particular group, namely: dihedral group:D16.

View group cohomology of particular groups | View other specific information about dihedral group:D16

This article describes the homology and cohomology group of dihedral group:D16, the dihedral group of order 16 and degree 8.

## Family contexts

Family name | Parameter value | Information on group cohomology of family |
---|---|---|

dihedral group of degree , order | degree , order | group cohomology of dihedral groups |

## 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 integers are given as follows:

The first few homology groups are as follows: