  We present a free field realisation for the vertex operator algebra
associated to the genus-two, class $\mathcal{S}$ superconformal field theory of
type $\mathfrak{a}_1$. The free field realisation is in the style of recent
work by the authors, and is formulated in terms of a one-dimensional isotropic
lattice vertex algebra along with two pairs of symplectic fermions. Our
realisation makes manifest an enhanced ${\rm USp}(4)$ outer automorphism group
of the VOA that is inherited from the symplectic fermion system. This extends
an ${\rm SU(2)}$ outer automorphism that has been observed in recent work of
Kiyoshige and Nishinaka and significantly simplifies the structure of the
algebra. Along the way, we also produce a realisation of the generic subregular
Drinfel'd-Sokolov $\mathcal{W}$ algebra of type $\mathcal{c}_2$ in terms of the
generic principle $\mathcal{W}$ algebra of type $\mathfrak{c}_2$ and a
one-dimensional isotropic lattice vertex algebra.

High Energy Physics - Theory;Quantum Algebra;Representation Theory