G is the group 64gp224
The Hall-Senior number of this group is 173.
G has 4 minimal generators, rank 4 and exponent 4. The centre has rank 2.
The 15 maximal subgroups are: 32gp22 (3x), 32gp29 (12x).
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 4.
At present no information on the cohomology ring.