G is the group 243gp41
G has 3 minimal generators, rank 3 and exponent 9. The centre has rank 2.
The 13 maximal subgroups are: Ab(9,3,3), M27xC3, 81gp3 (2x), 81gp4 (9x).
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 3.
At present no information on the cohomology ring.