G is the group 128gp527
G has 3 minimal generators, rank 4 and exponent 8. The centre has rank 1.
The 7 maximal subgroups are: 64gp102 (2x), 64gp264, 64gp91, 64gp94, 64gp99 (2x).
There are 3 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 4, 4, 4.
At present no information on the cohomology ring.