G is the group 64gp261
The Hall-Senior number of this group is 12.
G has 5 minimal generators, rank 5 and exponent 4. The centre has rank 4.
There are 2 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 5, 5.
This cohomology ring calculation is complete.
Ring structure | Completion information | Koszul information | Restriction information | Poincaré series
The cohomology ring has 6 generators:
There is one minimal relation:
This minimal generating set constitutes a Gröbner basis for the relations ideal.
This cohomology ring was obtained from a calculation out to degree 12. The cohomology ring approximation is stable from degree 2 onwards, and Benson's tests detect stability from degree 5 onwards.
This cohomology ring has dimension 5 and depth 5. Here is a homogeneous system of parameters:
The first 5 terms h1, h2, h3, h4, h5 form a regular sequence of maximum length.
The first 4 terms h1, h2, h3, h4 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, h4, h5) is as follows.
(1 + 2t + t2) / (1 - t)3 (1 - t2)2