The symmetries of five-dimensional minimal supergravity reduced to three dimensions

The 14 Killing vectors of the target space for five-dimensional minimal supergravity reduced to three dimensions are explicitly constructed in terms of the original field variables. These vectors generate the Lie algebra of $G_2$. We also construct a symmetrical $7\times 7$ matrix representative of the coset $G_{2(+2)}\mathrm{/}((SL(2,R)\times SL(2,R))$ as a function of the same fields.