G is the group 128gp932
G has 3 minimal generators, rank 4 and exponent 8. The centre has rank 1.
The 7 maximal subgroups are: Syl2(M12), 64gp138, 64gp139, 64gp241, 64gp32, 64gp33, 64gp34.
There are 5 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3, 3, 4.
At present no information on the cohomology ring.