There is a fibrationformula_28giving the long exact sequenceformula_29which computes the low order homotopy groups of formula_30 for formula_31, since formula_32 is formula_33-connected. In particular, there is a fibrationformula_34whose lower homotopy groups can be computed explicitly. Since formula_35, and there is the fibration formula_36we have formula_37 for formula_38. Using this, and the fact that formula_39, which can be computed using the Postnikov system, we have the long exact sequenceformula_40Since formula_41 we have formula_42. Also, the middle row gives formula_43 since the connecting map formula_44 is trivial. Also, we can know formula_45 has two-torsion.