Small group number 55 of order 64

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

The Hall-Senior number of this group is 5.

This cohomology ring calculation is complete.

Ring structure

The cohomology ring has 6 generators:

• y₁ in degree 1
• y₂ in degree 1
• y₃ in degree 1
• x₁ in degree 2
• x₂ in degree 2
• x₃ in degree 2

There are 3 minimal relations:

• y₃² = 0
• y₂² = 0
• y₁² = 0

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