G is the group 64gp191
The Hall-Senior number of this group is 245.
G has 3 minimal generators, rank 2 and exponent 16. The centre has rank 1.
There are 2 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 2, 2.
This cohomology ring calculation is complete.
Ring structure | Completion information | Koszul information | Restriction information | Poincaré series
The cohomology ring has 6 generators:
There are 9 minimal relations:
A minimal Gröbner basis for the relations ideal consists of this minimal generating set, together with the following redundant relations:
This cohomology ring was obtained from a calculation out to degree 12. The cohomology ring approximation is stable from degree 10 onwards, and Benson's tests detect stability from degree 10 onwards.
This cohomology ring has dimension 2 and depth 1. Here is a homogeneous system of parameters:
The first term h1 forms a regular sequence of maximum length.
The first term h1 forms a complete Duflot regular sequence. That is, its restriction to the greatest central elementary abelian subgroup forms a regular sequence of maximal length.
Data for Benson's test:
A basis for R/(h1, h2) is as follows.
A basis for AnnR/(h1)(h2) is as follows.
(1 + 3t + 4t2 + 3t3 + t4 + t5 + 3t6 + 3t7 + t8) / (1 - t2) (1 - t8)