Small group number 45 of order 32

G = Ab(4,2,2,2) is Abelian group C₄ x C₂ x C₂ x C₂

The Hall-Senior number of this group is 2.

This cohomology ring calculation is complete.

Ring structure

The cohomology ring has 5 generators:

• y₁ in degree 1
• y₂ in degree 1
• y₃ in degree 1
• y₄ in degree 1
• x in degree 2

There is one minimal relation:

• y₁² = 0

This minimal generating set constitutes a Gröbner basis for the relations ideal.