G is the group 243gp22
G has 2 minimal generators, rank 2 and exponent 27. The centre has rank 1.
The 4 maximal subgroups are: 81gp4, 81gp6 (3x).
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.