We present a conjectural description of the space of local operators on a
stack of finitely many fivebranes in $M$ theory at the level of the holomorphic
twist. Our approach is through the lens of twisted holography and utilizes a
description of the minimal twist of eleven-dimensional supergravity. We find
that the spaces of local operators are modules for the exceptional linearly
compact super Lie algebra $E(3|6)$. From the conjectural description of local
operators we deduce closed formulas for the superconformal index of
six-dimensional $\mathcal{N}=(2,0)$ theories of type $A_{N-1}$.
