The Standard Model gauge group has an ambiguity in its global form, which is closely related to a Z_6 one-form global symmetry. In this talk, we will discuss how this ambiguity affects the simplest model of QCD axions - a single axion coupled to the Standard Model. Assuming the absence of axion domain wall problem, we derive a lower bound on the axion-photon coupling. We will then discuss the fate of this Z_6 one-form global symmetry in the axion Standard Model. Depending on the details, the symmetry can be part of a higher-group or a non-invertible symmetry. Using this symmetry, we argue for a lower bound on the hypercharge magnetic monopole mass and the axion string tension.