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

From Groupprops

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The first few homology groups are as follows: | The first few homology groups are as follows: | ||

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

+ | ! <math>q</math> !! <math>0</math> !! <math>1</math> !! <math>2</math> !! <math>3</math> !! <math>4</math> !! <math>5</math> !! <math>6</math> !! <math>7</math> !! <math>8</math> | ||

+ | |- | ||

+ | | <math>H_q</math> || <math>\mathbb{Z}</math> || <math>\mathbb{Z}/2\mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z}</math> || <math>\mathbb{Z}/2\mathbb{Z}</math> || <math>\mathbb{Z}/2\mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z} \oplus \mathbb{Z}/8\mathbb{Z}</math> || <math>\mathbb{Z}/2\mathbb{Z} \oplus \mathbb{Z}/2\mathbb{Z}</math> || <math>(\mathbb{Z}/2\mathbb{Z})^4</math> || <math>(\mathbb{Z}/2\mathbb{Z})^3</math> || <math>(\mathbb{Z}/2\mathbb{Z})^4 \oplus \mathbb{Z}/8\mathbb{Z}</math> || <math>(\mathbb{Z}/2\mathbb{Z})^4</math> | ||

+ | |} |

## Revision as of 03:47, 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.

## 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: