G = 81gp7xC3 is Direct product 81gp7 x C_3
G has 3 minimal generators, rank 4 and exponent 9. The centre has rank 2.
The 13 maximal subgroups are: E27xC3, M27xC3 (2x), Syl3(A9) (9x), V81.
There are 2 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 4.
At present no information on the cohomology ring.