G is the group 243gp25
G has 2 minimal generators, rank 2 and exponent 9. The centre has rank 1.
The 4 maximal subgroups are: 81gp10 (2x), Ab(9,9), Syl3(U3(8)).
There are 2 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 2, 2.
At present no information on the cohomology ring.