G is the group 128gp1759
G has 4 minimal generators, rank 4 and exponent 4. The centre has rank 1.
The 15 maximal subgroups are: 64gp138 (8x), 64gp216 (3x), 64gp266, 64gp91 (3x).
There are 12 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4.
At present no information on the cohomology ring.