A quick note about the homotopy groups of the Cayley plane. Mimura computed some of them. Specifically for *i*=8,9,10,...,23 he computed that $\pi_i\mathbf{CaP}^2$ equals **Z**, **Z**/2, **Z**/2, **Z**/24, 0, 0, **Z**/2, **Z**/120, (**Z**/2)$^{\oplus3}$, (**Z**/2)$^{\oplus4}$, **Z**/24$\oplus$ **Z**/2, **Z**/504$\oplus$ **Z**/2, 0, **Z**/6, **Z**/4, **Z**$\oplus$ **Z**/120$\oplus$ (**Z**/2)$^{\oplus2}$, respectively. See Theorem 7.2 of his 1967 paper *The homotopy groups of Lie groups of low rank*:<br>
&nbsp; http://www.ams.org/mathscinet-getitem?mr=206958<br>
&nbsp; http://projecteuclid.org/euclid.kjm/1250524375