G is the group 64gp90
The Hall-Senior number of this group is 123.
G has 3 minimal generators, rank 4 and exponent 4. The centre has rank 2.
The 7 maximal subgroups are: 32gp22 (2x), 32gp46, 32gp6 (4x).
There are 2 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 4, 4.
At present no information on the cohomology ring.