G is the group 64gp36
The Hall-Senior number of this group is 254.
G has 2 minimal generators, rank 3 and exponent 8. The centre has rank 1.
The 3 maximal subgroups are: 32gp31, 32gp8 (2x).
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 3.
At present no information on the cohomology ring.