  We discuss heavy particles that can be used to pin down the faithful Standard
Model (SM) gauge group and their patterns in the SM effective field theory
(SMEFT). These heavy particles are not invariant under a specific
$\mathbb{Z}_6$ subgroup of $SU(3)_c\times SU(2)_L \times U(1)_Y$, which however
acts trivially on all the SM particles, hence the faithful SM gauge group
remains undetermined. Different realizations of the faithful SM gauge group
correspond to different spectra of heavy particles, and they also correspond to
distinct sets of line operators with one-form global symmetry acting on them.
We show that the heavy particles not invariant under the $\mathbb{Z}_6$ group
cannot appear in tree-level ultraviolet completions of SMEFT, this enforces us
to consider one-loop UV completions of SMEFT to identify the $\mathbb{Z}_6$
non-invariant heavy particles. We demonstrate with examples that correlations
between Wilson coefficients provide an efficient way to examine models with
$\mathbb{Z}_6$ non-invariant heavy particles. Finally, we prove that all the
scalars that can trigger electroweak symmetry breaking must be invariant under
the $\mathbb{Z}_6$ group, hence they cannot be used to probe the faithful SM
gauge group.
