\( \mathcal{N} \) = 5 SCFTs and quaternionic reflection groups

It was previously noted that for 3d SCFTs with $\mathcal{N}$ \( \mathcal{N} \) ≥ 6 the moduli space has the form of ℂ^4r/Γ, where Γ is a complex reflection group, at least following suitable gauging of finite symmetries. Here we argue that this observation can be extended also to 3d SCFTs with $\mathcal{N}$ \( \mathcal{N} \) ≥ 5 SUSY, where Γ is now a quaternionic reflection group. To do this, we study the moduli space of the known 3d $\mathcal{N}$ \( \mathcal{N} \) = 5 SCFTs. For Lagrangian cases, the results for the moduli space are further checked using the superconformal index.