Homotopy type of gauge groups of -bundles over

Let P k be the principal SU ( 3 ) -bundle over S 6 with its Chern class c 3 ( P k ) = 2 k . The purpose of this paper is to show when two gauge groups G ( P k ) and G ( P k ′ ) have the same homotopy type. Namely, G ( P k ) ≃ G ( P k ′ ) , if and only if ( 120 , k ) = ( 120 , k ′ ) , where ( a , b ) denote the G.C.D. of a and b.