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The mixed valence Cr ^3+ /Cr ^4+ compound NaCr _2 O _4 , hosts a plethora of unconventional electronic properties. In the present study, muon spin rotation/relaxation ( $\mu^+$ SR) and high-resolution time-of-flight neutron powder diffraction measurements were carried out on high-quality samples to clarify the complex magnetic ground state of this unique material. We identified a commensurate canted antiferromagnetic order (C-AFM) with a canting angle of the Cr spin axial vector equal to $\theta_{\mathrm{c}} = (8.8\pm0.5)^{\circ}$ , and an estimated Cr moment $\mu^{\mathrm{C}}_{\mathrm{Cr}} \sim (4.30\pm0.01)\mu_\mathrm{B}$ . Such an unusually large value of $\mu^{\mathrm{C}}_{\mathrm{Cr}}$ is compatible with the existence of high-spin Cr sites created by the presence of an unconventional negative charge transfer state in NaCr _2 O _4 . In addition to the C-AFM structure, a novel magnetic supercell was also revealed. Such supercell display an incommensurate (IC)-AFM propagation vector (0 0 ${\textstyle \frac{1}{2}-}\delta$ ), having a Cr moment $\mu^{\mathrm{IC}}_{\mathrm{Cr}} = (2.20\pm0.03)\mu_\mathrm{B}$ . It is suggested that the C-AFM and IC-AFM modulations have two different electronic origins, being due to itinerant and localized contributions to the magnetic moment respectively. Finally, the direct measurement of the magnetic order parameter for the C-AFM structure provided a value of the critical exponent $\beta = 0.245 \approx \frac{1}{4}$ , suggesting a non conventional critical behavior for the magnetic phase transition in NaCr _2 O _4 .