G is the group 128gp742
G has 3 minimal generators, rank 4 and exponent 8. The centre has rank 1.
The 7 maximal subgroups are: 64gp102 (2x), 64gp18, 64gp206 (2x), 64gp256, 64gp88.
There are 3 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 4.
At present no information on the cohomology ring.