G is the group 243gp50
G has 3 minimal generators, rank 2 and exponent 27. The centre has rank 1.
The 13 maximal subgroups are: E27*C9, Ab(27,3) (4x), 81gp6 (8x).
There are 4 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 2, 2, 2, 2.
At present no information on the cohomology ring.