G = M243 is Extraspecial 3-group of order 243 and exponent 9
G has 4 minimal generators, rank 3 and exponent 9. The centre has rank 1.
The 40 maximal subgroups are: E27xC3, M27xC3 (12x), 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.