  In the Standard Model the hypercharges of quarks and leptons are not
determined by the gauge group itself. In a recent paper [C. Hattori et al.
Phys. Rev. D83, 015009 (2011)] it is shown that, if the direct product gauge
group G_SM is slightly modified to the semidirect product group G'_SM,
hypercharges are restricted to quantized values as n/6 mod Z (n = 0,1,3,4). In
this brief paper, we examine all of the compact Lie groups locally isomorphic
to G_SM, and show that G'_SM (or its isomorphisms) is the unique possibility
that yields the correct hypercharge quantization.
