G is the group 64gp216
The Hall-Senior number of this group is 170.
G has 4 minimal generators, rank 4 and exponent 4. The centre has rank 2.
The 15 maximal subgroups are: 32gp24, 32gp27 (4x), 32gp28 (4x), 32gp31 (2x), 32gp34 (2x), 32gp46, 32gp48.
There are 4 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 4, 4.
At present no information on the cohomology ring.