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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/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.kjm/1250524375

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

A quick note about the homotopy groups of the Cayley plane: Mimura computed some of them. Specifically for i=8,9... 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/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.kjm/1250524375

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/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.kjm/1250524375

A quick note about the homotopy groups of the Cayley plane: Mimura computed some of them. Specifically for $i=8,9\dots$ he computed that $\pi_i(\mathbf{CaP}^2)$ equals $\mathbf{Z}$, $\mathbf{Z}/2$, $\mathbf{Z}/2$, $\mathbf{Z}/24$, $0$, $0$, $\mathbf{Z}/2$, $\mathbf{Z}/120$, $(\mathbf{Z}/2)^{\oplus3}$,$(\mathbf{Z}/2)^{\oplus4}$, $\mathbf{Z}/24\oplus \mathbf{Z}/2$, $\mathbf{Z}/504 \oplus \mathbf{Z}/2$, $0$, $\mathbf{Z}/6$, $\mathbf{Z}/4$, $\mathbf{Z} \oplus \mathbf{Z}/120 \oplus (\mathbf{Z}/2)^{\oplus2}$, 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/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.kjm/1250524375

A quick note about the homotopy groups of the Cayley plane: Mimura computed some of them. Specifically for i=8,9... 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/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.kjm/1250524375