G is the group 128gp561
G has 3 minimal generators, rank 4 and exponent 8. The centre has rank 1.
The 7 maximal subgroups are: 64gp199, 64gp25 (4x), 64gp92 (2x).
There are 2 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 4, 4.
At present no information on the cohomology ring.