G is the group 64gp91
The Hall-Senior number of this group is 126.
G has 3 minimal generators, rank 3 and exponent 4. The centre has rank 1.
The 7 maximal subgroups are: 32gp24 (2x), 32gp48, 32gp6 (4x).
There are 3 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3.
At present no information on the cohomology ring.