© 2015 American Physical Society. We studied transition rates for the lowest 1/2+ and 5/2+ excited states of C17 through lifetime measurements with the GRETINA array using the recoil-distance method. The present measurements provide a model-independent determination of transition strengths giving the values of B(M1;1/2+→3/2g.s.+)=1.04-0.12+0.03×10-2μN2 and B(M1;5/2+→3/2g.s.+)=7.12-0.96+1.27×10-2μN2. The quenched M1 transition strength for the 1/2+→3/2g.s.+ transition, with respect to the 5/2+→3/2g.s.+ transition, has been confirmed with greater precision. The current data are compared to importance-truncated no-core shell model calculations addressing effects due to continuum and three-body forces.