G is the group 243gp7
G has 2 minimal generators, rank 3 and exponent 9. The centre has rank 2.
The 4 maximal subgroups are: M27xC3 (2x), 81gp3 (2x).
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.