G is the group 128gp646
G has 3 minimal generators, rank 4 and exponent 8. The centre has rank 1.
The 7 maximal subgroups are: 64gp216, 64gp249, 64gp25 (2x), 64gp92 (2x), 64gp94.
There are 4 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 4, 4.
At present no information on the cohomology ring.