G is the group 128gp560
G has 3 minimal generators, rank 4 and exponent 4. The centre has rank 1.
The 7 maximal subgroups are: 64gp199, 64gp23 (4x), 64gp90 (2x).
There are 2 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 4, 4.
At present no information on the cohomology ring.