  When $n$ M5 branes coincide on an A type singularity,
$\mathbb{C}^2/\mathbb{Z}_k$, there is a multitude of tensionless strings which
arise in the spectrum. The low energy theory when all M5 branes are separated
at the singularity is given by a linear quiver with parameters $n$ and $k$. The
theory has a multitude of phases, as many as partitions of $n$, each
characterized by a different Higgs branch. Each such Higgs branch can be
described by a Coulomb branch of a 3d $\mathcal{N}=4$ quiver. For example, at
finite coupling, when all branes are separated, the quiver has a bouquet of $n$
$U(1)$ nodes connected to a single node. There is a natural discrete non
Abelian $S_n$ global symmetry which acts in the theory by permuting $n$
identical objects. It acts in particular on the Higgs branch at the above
finite coupling phase. It is conjectured that at the coincident point this
discrete $S_n$ flavor symmetry is gauged, and at partial coincidence the
corresponding subgroup of $S_n$ is gauged. This elegant and simple effect
solves several problems which are raised recently on the physics of multiple M5
branes on an A type singularity. Similar results on multitude of phases are
concluded for a system of $n$ M5 branes on an A type singularity next to an M9
plane.
