Small group number 1 of order 243

G = C243 is Cyclic group of order 243

This cohomology ring calculation is complete.

Ring structure

The cohomology ring has 2 generators:

• y in degree 1, a nilpotent element
• x in degree 2

There is one minimal relation:

• y² = 0

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