G = (E27*C3)xC3 is Direct product E27*C3 x C_3
G has 4 minimal generators, rank 3 and exponent 9. The centre has rank 2.
The 40 maximal subgroups are: Ab(9,3,3) (4x), E27xC3, M27xC3 (8x), E27*C9 (27x).
There are 4 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3, 3.
At present no information on the cohomology ring.