Small group number 5 of order 81

G = Ab(27,3) is Abelian group C₂₇ x C₃

This cohomology ring calculation is complete.

Ring structure

The cohomology ring has 4 generators:

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