G is the group 128gp1758
G has 4 minimal generators, rank 4 and exponent 4. The centre has rank 1.
The 15 maximal subgroups are: 64gp138 (4x), 64gp139 (4x), 64gp215 (3x), 64gp264, 64gp90 (3x).
There are 6 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 4, 4, 4, 4, 4, 4.
At present no information on the cohomology ring.