Using data from e+e- annihilation into hadrons, taken with the OPAL detector at LEP at the Z pole between 1991 and 1995, we performed a simultaneous measurement of the colour factors of the underlying gauge group of the strong interaction, CF and CA, and the strong coupling, alpha(s). The measurement was carried out by fitting next-to-leading order perturbative predictions to measured angular correlations of 4-jet events together with multi-jet related variables. Our results, CA = 3.02 +/- 0.25 (stat.) +/- 0.49 (syst.), CF = 1.34 +/- 0.13 (stat.) +/- 0.22 (syst.), alpha(s)(M_Z) = 0.120 +/- 0.011 (stat.) +/- 0.020 (syst.), provide a test of perturbative QCD in which the only assumptions are non-abelian gauge symmetry and standard hadronization models. The measurements are in agreement with SU(3) expectations for CF and CA and the world average of alpha(s)(M_Z).