David J. Green

Cohomology
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Cohomology of group number 51 of order 32

About the group

Ring generators

Ring relations

Back to groups of order 32

General information on the group

• The group has 5 minimal generators and exponent 2.
• It is abelian, isomorphic to C₂×C₂×C₂×C₂×C₂.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 5 and depth 5.
• The Poincaré series is

  − 1

  (t  −  1)5

• The a-invariants are -∞,-∞,-∞,-∞,-∞,-5.

About the group

Ring generators

Ring relations

Back to groups of order 32

Ring generators

The cohomology ring has 5 minimal generators of maximal degree 1:

1. c_1_0, an element of degree 1
2. c_1_1, an element of degree 1
3. c_1_2, an element of degree 1
4. c_1_3, an element of degree 1
5. c_1_4, an element of degree 1

About the group

Ring generators

Ring relations

Back to groups of order 32

Ring relations

There are no relations.

About the group

Ring generators

Ring relations

Back to groups of order 32