G is the group 128gp780
G has 3 minimal generators, rank 4 and exponent 8. The centre has rank 1.
The 7 maximal subgroups are: 64gp102, 64gp111, 64gp25, 64gp254, 64gp92, 64gp94, 64gp99.
There are 2 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 4.
At present no information on the cohomology ring.