G is the group 243gp13
G has 2 minimal generators, rank 4 and exponent 9. The centre has rank 2.
The 4 maximal subgroups are: 81gp3 (3x), V81.
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 4.
At present no information on the cohomology ring.