In chapter three, p. 31, of this paper (https://arxiv.org/abs/0904.1556) Baez and Huerta show that the standard model's structure group contains, in a sense, superfluous parts.
They show that one can divide out the discrete subgroup $\mathbb{Z}_6$ (which is the multiplicative group of the sixth roots of unity) from $G_{SM}:=\text{SU}(3)_C\times\text{SU}(2)_L\times\text{U}(1)_Y$ to get the group $(\text{SU}(3)_C\times\text{SU}(2)_L\times\text{U}(1)_Y)/\mathbb{Z}_6$ and that this $\mathbb{Z}_6$ subgroup acts trivially on the standard model's fermions' representations.
Although they derive this fact while looking at an inclusion of $G_{SM}$ into $\text{SU}(5)$ in the context of grand unified theories, to my knowledge this result does not depend on actually "using" $\text{SU}(5)$ in any way, shape, or form.
In this related post Why is the "actual" gauge group of the standard model $SU(3) \times SU(2) \times U(1) /N$? people have already given explanations as to why this works mathematically (e.g. how one can check that $\mathbb{Z}_6$ acts trivially on the fermions' representations and how, since $\mathbb{Z}_6$ is in the centre of $G_{SM}$, it corresponds to a trivial representation in the adjoint representation under which the gauge bosons transform).
While it is quite obvious how this affects the search for possible GUT groups (we now only have to "fit" a "smaller" version of the standard model's structure group into a "larger" group which opens up more possibilities) I, however, have yet to see a satisfing answer as to what this means physically/from a physics standpoint for the standard model as it is.
So, here are my questions:
Does this affect any calculations? (I would think not because in these we are almost always dealing with the connected component of the identity since we are mostly working with Lie Algebras)
Does this result in any physical phenomenon that might be nonperturbative?
Is there any "nice" explanation as to what this symmetry means? I.e. in a way similar to that lepton and baryon number conservation stem from global $U(1)$-symmetries, even though, $\mathbb{Z}_6$ obviously is not a continuous symmetry and, therefore, does not "come" with an associated Noether charge.
How well known is this in the particle physics community and are people talking about this or is it a "nice to know but anyway" kind of result?
Edit: I have come up with a fifth question: Does dividing out the $\mathbb{Z}_6$ subgroup affect the global symmetries that ensure baryon and lepton number conservation in any way?
