Let $V=\{V_i\}$, $i=1,\dots,m<n$ be a set of linearly independent vector fields on some $n$-dim manifold $M$. Let, furthermore, $l(V)$ be a nilpotent and hence finite-dimensional Lie algebra generated by $V$. By Lie's third theorem $l(V)$ gives rise to a finite-dimensional Lie group $L(V)$ acting on $M$.
How should I proceed to determine a (finite-dimensional) representation of $L(V)$?