G is the group 32gp5
The Hall-Senior number of this group is 20.
G has 2 minimal generators, rank 3 and exponent 8. The centre has rank 2.
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 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 4 minimal relations:
This minimal generating set constitutes a Gröbner basis for the relations ideal.
This cohomology ring was obtained from a calculation out to degree 8. The cohomology ring approximation is stable from degree 4 onwards, and Benson's tests detect stability from degree 4 onwards.
This cohomology ring has dimension 3 and depth 2. Here is a homogeneous system of parameters:
The first 2 terms h1, h2 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.
A basis for AnnR/(h1, h2)(h3) is as follows.
(1 + 2t + t2) / (1 - t2)3