A new example of a generic 2-distribution on a 5-manifold with large symmetry algebra

We discover a new example of a generic rank 2-distribution on a 5-manifold with a 6-dimensional transitive symmetry algebra, which is not present in Cartan's classical five variables paper. It corresponds to the Monge equation z' = y + (y'')^(1/3) with invariant quartic having root type [4], and a 6-dimensional non-solvable symmetry algebra isomorphic to the semidirect product of sl(2) and the 3-dimensional Heisenberg algebra.