G is the group 243gp28
G has 2 minimal generators, rank 2 and exponent 9. The centre has rank 1.
The 4 maximal subgroups are: 81gp10, 81gp4, Syl3(U3(8)) (2x).
There are 3 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 2, 2, 2.
At present no information on the cohomology ring.