G is the group 64gp249
The Hall-Senior number of this group is 109.
G has 4 minimal generators, rank 3 and exponent 8. The centre has rank 1.
The 15 maximal subgroups are: 32gp37 (6x), 32gp38 (8x), 32gp48.
There are 3 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3.
At present no information on the cohomology ring.