Small group number 31 of order 243

G = Ab(9,9,3) is Abelian group C₉ x C₉ x C₃

This cohomology ring calculation is complete.

Ring structure

The cohomology ring has 6 generators:

• y₁ in degree 1, a nilpotent element
• y₂ in degree 1, a nilpotent element
• y₃ in degree 1, a nilpotent element
• 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.