G is the group 243gp56
G has 3 minimal generators, rank 3 and exponent 9. The centre has rank 1.
The 13 maximal subgroups are: E27xC3 (2x), M27xC3 (2x), Syl3(A9) (9x).
There are 5 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3, 3, 3.
At present no information on the cohomology ring.