G is the group 243gp59
G has 3 minimal generators, rank 3 and exponent 9. The centre has rank 1.
The 13 maximal subgroups are: 81gp10 (9x), M27xC3 (4x).
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.