Sp(4,2) is isomorphic to S6

The symplectic group of degree four over field:F2, denoted $Sp(4,2)$ is isomorphic to symmetric group:S6.
Note that we already have that $Sp(4,2) \cong PSp(4,2)$, where the latter is the projective symplectic group of degree four. Thus, this establishes also that $PSp(4,2) \cong S_6$.