G = Syl5(Co1) is Sylow 5-subgroup of Co_1
G has 2 minimal generators, rank 3 and exponent 5. The centre has rank 1.
The 6 maximal subgroups are: E125 (5x), V125.
There are 6 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 2, 2, 2, 2, 2, 3.
At present no information on the cohomology ring.