G is the group 243gp29
G has 2 minimal generators, rank 2 and exponent 9. The centre has rank 1.
The 4 maximal subgroups are: 81gp10 (3x), 81gp4.
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 2.
At present no information on the cohomology ring.