G is the group 32gp34
The Hall-Senior number of this group is 34.
G has 3 minimal generators, rank 3 and exponent 4. The centre has rank 2.
There are 4 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3, 3.
This cohomology ring calculation is complete.
Ring structure | Completion information | Koszul information | Restriction information | Poincaré series
The cohomology ring has 5 generators:
There are 2 minimal relations:
A minimal Gröbner basis for the relations ideal consists of this minimal generating set, together with the following redundant relation:
This cohomology ring was obtained from a calculation out to degree 8. The cohomology ring approximation is stable from degree 2 onwards, and Benson's tests detect stability from degree 3 onwards.
This cohomology ring has dimension 3 and depth 3. Here is a homogeneous system of parameters:
The first 3 terms h1, h2, h3 form a regular sequence of maximum length.
The first 2 terms h1, h2 form a complete Duflot regular sequence. That is, their restrictions to the greatest central elementary abelian subgroup form a regular sequence of maximal length.
Data for Benson's test:
A basis for R/(h1, h2, h3) is as follows.
(1 + 3t + 3t2 + t3) / (1 - t2)3