Data from e(+)e(-) annihilation into hadrons, taken with the ALEPH detector at the Z resonance, are analyzed. The four-jet rate is studied as a function of the resolution parameter and compared to next-to-leading order calculations combined with resummation of large logarithms. Angular correlations in four-jet events are measured and compared to next-to-leading order QCD predictions. With these observables two different measurements are performed. In a first analysis the strong coupling constant is measured from the four-jet rate yielding alpha(S)(M(Z)) = 0.1170 +/- 0.0001(stat) +/- 0.0013(sys). In a second measurement the strong coupling constant and the QCD colour factors are determined simultaneously from a fit to the four-jet rate and the four-jet angular correlations, giving a(S)(M(Z)) = 0.119 +/- 0.006(stat) +/- 0.026(sys) C(A) = 2.93 +/- 0.14(stat) +/- 0.58(sys) C(F) = 1.35 +/- 0.07(stat) +/- 0.26(sys) in good agreement with the expectation from QCD.