G is the group 243gp3
G has 2 minimal generators, rank 3 and exponent 9. The centre has rank 2.
The 4 maximal subgroups are: E27xC3 (2x), 81gp3 (2x).
There are 3 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3.
At present no information on the cohomology ring.