In this talk, we will exhibit a relationship between quantum permutation groups of finite sets and quantum automorphism groups of finite-dimensional C$^\ast$-algebras using 2-cocycle deformations. This leads to isomorphisms of the associated C$^\ast$-algebras and von Neumann algebras, up to crossed products by finite abelian groups. Using these results, we obtain strong 1-boundedness of the von Neumann algebras of some quantum permutation groups, and residual finite dimensionality results for the Hopf algebras of quantum automorphism groups. This is joint work with Floris Elzinga, Samuel Harris, and Makoto Yamashita.