  The reasons behind the gauge symmetry of the Standard Model,
U(1)xSU(2)xSU(3), are still unsettled. One obvious feature is the low
dimensionality of all its subgroups. Under certain conditions, a negative
answer to the question "why not larger groups like SU(15), or for that matter,
SP(26) or E7?" is possible.
  We have recently observed that fermions charged under large groups acquire
much bigger dynamical masses, all things being equal at a high e.g. GUT scale,
than ordinary quarks. Should such multicharged fermions exist, they are just
too heavy to be observed today (and have either decayed early on if coupled to
the rest of the Standard Model, or become reliquial dark matter if uncoupled).
Their mass scale is dictated by strong antiscreening of the running coupling
for those larger groups (with an appropriately small number of flavors)
together with scaling properties of the Dyson-Schwinger equation for the
fermion mass.
  The generated fermion mass (assuming only few flavors, to avoid spoiling
antiscreening) grows exponentially with the number of colors as M(N_c) ~
exp(N_c) for scales much below the GUT scale. Large groups would be strongly
coupled already near the GUT scale and fermions charged thereunder have
correspondingly large masses.
