G is the group 243gp60
G has 3 minimal generators, rank 3 and exponent 9. The centre has rank 1.
The 13 maximal subgroups are: 81gp10 (2x), M27xC3, E27*C9 (3x), Syl3(A9) (3x), 81gp8 (3x), Syl3(U3(8)).
There are 4 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 2, 2, 2, 3.
At present no information on the cohomology ring.