G is the group 128gp836
G has 3 minimal generators, rank 4 and exponent 4. The centre has rank 1.
The 7 maximal subgroups are: 64gp23 (7x).
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.