It is known that for p-perfect groups G of finite virtual cohomological dimension and finite type mod-p cohomology, the p-completed classifying space BGandp has the property that ΩBGandp is a retract of the loop space on a simply-connected, [ ]p-finite, p-complete space. In this note we consider a particular example where this theorem applies, namely we study the homotopy type of BSL3(ℤ)and2. It particular we analyse ΩBSt3(ℤ)and2, a double cover of ΩBSL3(ℤ)and2, and obtain a splitting theorem for it in terms of 2-primary Moore spaces and fibres of degree 2r maps on spheres. We also give a formula for the Poincaré series of H∗(ΩBΓandp; [ ]p) for a general group Γ, as above, in terms of possibly simpler components. This formula is used to calculate the mod-2 homology of ΩBΓand2 for Γ=SL3(ℤ) or St3(ℤ) as modules over a certain tensor subalgebra.