G is the group 243gp19
G has 2 minimal generators, rank 2 and exponent 27. The centre has rank 1.
The 4 maximal subgroups are: E27*C9, Ab(27,3), 81gp6 (2x).
There are 2 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 2, 2.
At present no information on the cohomology ring.