  We study an algebraic structure of magical supergravities in three
dimensions. We show that if the commutation relations among the generators of
the quasi-conformal group in the super-Ehlers decomposition are in a particular
form, then one can always find a parameterization of the group element in terms
of various 3d bosonic fields that reproduces the 3d reduced Lagrangian of the
corresponding magical supergravity. This provides a unified treatment of all
the magical supergravity theories in finding explicit relations between the 3d
dimensionally reduced Lagrangians and particular coset nonlinear sigma models.
We also verify that the commutation relations of $E_{6(+2)}$, the
quasi-conformal group for $\mathbb{A}=\mathbb{C}$, indeed satisfy this
property, allowing the algebraic interpretation of the structure constants and
scalar field functions as was done in the $F_{4(+4)}$ magical supergravity.
