  For $N\ge 3$ there are $S_N$ and $D_N$ actions on the space of solutions of
the first nontrivial equation in the $SL(N) MKdV hierarchy, generalizing the
two $Z_2$ actions on the space of solutions of the standard MKdV equation.
These actions survive scaling reduction, and give rise to transformation groups
for certain (systems of) ODEs, including the second, fourth and fifth
Painlev\'e equations.
