G = E243 is Extraspecial 3-group of order 243 and exponent 3
G has 4 minimal generators, rank 3 and exponent 3. The centre has rank 1.
The 40 maximal subgroups are: E27xC3 (40x).
There are 40 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3.
At present no information on the cohomology ring.