G is the group 128gp1620
G has 4 minimal generators, rank 4 and exponent 8. The centre has rank 1.
The 15 maximal subgroups are: 64gp249 (2x), 64gp264, 64gp92 (6x), 64gp94 (6x).
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.