Homotopy type of gauge groups of quaternionic line bundles over spheres

Let P be a principal S3-bundle over a sphere Sn, with n⩾4. Let GP be the gauge group of P. The homotopy type of GP when n=4 was studied by A. Kono in [A. Kono, A note on the homotopy type of certain gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 117 (1991) 295–297]. In this paper we extend his result and we study the homotopy type of the gauge group of these bundles for all n⩽25.