G is the group 128gp853
G has 3 minimal generators, rank 4 and exponent 8. The centre has rank 1.
The 7 maximal subgroups are: 64gp215, 64gp32 (2x), 64gp33 (2x), 64gp90, 64gp92.
There are 3 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 4, 4, 4.
At present no information on the cohomology ring.