G is the group 64gp111
The Hall-Senior number of this group is 121.
G has 3 minimal generators, rank 3 and exponent 8. The centre has rank 1.
The 7 maximal subgroups are: 32gp15 (4x), 32gp37 (3x).
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.