  We consider the maximally symmetric $(2,3,5)$-distribution given by the
An-Nurowski circle twistor bundle over the product of an An-Nurowski surface
and the plane. This circle twistor distribution encodes the configuration space
of an An-Nurowski surface rolling without slipping or twisting on the plane. We
calculate the vector fields associated to this maximally symmetric
$(2,3,5)$-distribution that define a split $\frak{g}_2$ Lie algebra and by
projection we obtain an action of $SL(3,\mathbb{R})$ on the submanifold
$\mathbb{R}^2\times \mathbb{S}^1$ (the configuration space without a surface).
