The specific heat Cp at constant pressure, the shear viscosity ns, and the mutual diffusion coefficient D of the 2,6-dimethylpyridine-water mixture of critical composition have been measured in the homogeneous phase at various temperatures near the lower critical demixing temperature Tc. The amplitude of the fluctuation correlation length xi0= 0.198±0.004 nm has been derived from a combined evaluation of the ns and D data. This value is in reasonable agreement with the one obtained from the amplitude A+= 0.26±0.01 J/ g K of the critical term in the specific heat, using the two-scale-factor universality relation. Within the limits of error the relaxation rate G of order parameter fluctuations follows power law with the theoretical universal exponent and with the amplitude G = 25±1 10^9 1/ s. No indications of interferences of the critical fluctuations with other elementary chemical reactions have been found. A noteworthy result is the agreement of the background viscosity nb, resulting from the treatment of ns and D data, with the viscosity ns(v=0) extrapolated from high-frequency viscosity data. The latter have been measured in the frequency range of 5Ð130 MHz using a novel shear impedance spectrometer.