G is the group 64gp135
The Hall-Senior number of this group is 263.
G has 3 minimal generators, rank 3 and exponent 8. The centre has rank 1.
The 7 maximal subgroups are: 32gp11 (2x), 32gp31, 32gp43 (2x), E32-, 32gp8.
There are 3 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 2, 2, 3.
At present no information on the cohomology ring.