Mathematics:

Cohomology
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Jena:

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David Green

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Singular

Gap

Cohomology of group number 2328 of order 128

About the group

Ring generators

Ring relations

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General information on the group

• The group has 7 minimal generators and exponent 2.
• It is abelian, isomorphic to C₂×C₂×C₂×C₂×C₂×C₂×C₂.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 7 and depth 7.
• The Poincaré series is

  − 1

  (t  −  1)7

• The a-invariants are -∞,-∞,-∞,-∞,-∞,-∞,-∞,-7.

About the group

Ring generators

Ring relations

Back to groups of order 128

Ring generators

The cohomology ring has 7 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
6. c_1_5, an element of degree 1
7. c_1_6, an element of degree 1

About the group

Ring generators

Ring relations

Back to groups of order 128

Ring relations

There are no relations.

About the group

Ring generators

Ring relations

Back to groups of order 128