  A classical result of F.Klein states that, given a finite primitive group
$G\subseteq SL_2(\mathbb{C})$, there exists a hypergeometric equation such that
any second order LODE whose differential Galois group is isomorphic to $G$ is
projectively equivalent to the pullback by a rational map of this
hypergeometric equation. In this paper, we generalize this result. We show
that, given a finite primitive group $G\subseteq SL_n(\mathbb{C})$, there exist
a positive integer $d=d(G)$ and a standard equation such that any LODE whose
differential Galois group is isomorphic to $G$ is gauge equivalent, over a
field extension $F$ of degree $d$, to an equation projectively equivalent to
the pullback by a map in $F$ of this standard equation. For $n=3$, these
standard equations can be chosen to be hypergeometric.
