An exhaustive analysis of the critical behavior of the nematic to isotropic (N-to-I) phase transition on the liquid crystal hexyloxycyanobiphenyl (6OCB) has been performed. To do so, the accurate evolution of various physical magnitudes (static dielectric permittivity data together with specific heat and volumetric determinations) around the N-to-I transition has been required. The specific heat data with the isobaric thermal expansion coefficient and the derivative of the static dielectric permittivity with temperature have been proven to be related to each other by a scaling relationship. However, some discrepancies have been observed for the dielectric data in relation to such a scaling relationship and the critical behavior of the N-to-I phase transition. All information has been used to get some insight on the strength of the first-order N-to-I phase transition of the 6OCB in relation to the other counterparts in the nOCB series of compounds.