G is the group 243gp34
G has 3 minimal generators, rank 3 and exponent 9. The centre has rank 2.
The 13 maximal subgroups are: Ab(9,3,3), Ab(9,9) (3x), 81gp3 (3x), 81gp4 (6x).
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.