Sp(4,2) is isomorphic to S6

Statement
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 $$PSp(4,2) \cong S_6$$.

Opposite facts

 * PGL(2,9) is not isomorphic to S6