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:
http://www.ams.org/mathscinet-getitem?mr=206958
http://projecteuclid.org/euclid.kjm/1250524375
Carl McTague
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