G is the group 243gp24
G has 2 minimal generators, rank 2 and exponent 81. The centre has rank 1.
The 4 maximal subgroups are: Ab(27,3), C81 (3x).
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 2.
At present no information on the cohomology ring.