G is the group 64gp23
The Hall-Senior number of this group is 128.
G has 2 minimal generators, rank 4 and exponent 4. The centre has rank 2.
The 3 maximal subgroups are: 32gp22 (3x).
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.