  The gauge group of strong and electroweak interactions in Nature could be any
of the four that share the same Lie algebra, $SU(3)_c\times SU(2)_L\times
U(1)_Y/Z_p\equiv G_p$ with $Z_p=\left\{Z_6,Z_3,Z_2,Z_1\right\}$. Each of these
cases allows in its spectrum for the matter fields of the SM but also for new
distinctive representations, e.g. under the assumption that $q_L$ possesses the
minimum possible hypercharge in Nature, $G_p$ allows for particles with a
multiple of $p\,e/6$ for electric charge. This letter discusses how these new
possibilities in the spectrum could be used to tell the SM group apart.
