G is the group 128gp1753
G has 4 minimal generators, rank 4 and exponent 8. The centre has rank 1.
The 15 maximal subgroups are: 64gp102 (2x), Syl2(M12) (4x), 64gp135 (4x), 64gp216, 64gp254 (2x), 64gp266, 64gp94.
There are 9 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3, 3, 3, 3, 3, 3, 4.
At present no information on the cohomology ring.