Small group number 83 of order 64

G = Ab(8,4,2) is Abelian group C₈ x C₄ x C₂

The Hall-Senior number of this group is 6.

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
• x₁ in degree 2
• x₂ in degree 2

There are 2 minimal relations:

• y₂² = 0
• y₁² = 0

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