G is the group 128gp859
G has 3 minimal generators, rank 4 and exponent 4. The centre has rank 1.
The 7 maximal subgroups are: 64gp216, 64gp34 (2x), 64gp35 (2x), 64gp90 (2x).
There are 3 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 4, 4.
At present no information on the cohomology ring.