Symplectic group is perfect

Statement
The symplectic group $$Sp(2m,k)$$ is a perfect group if either of these conditions hold:


 * $$k$$ has at least four elements.
 * $$m \ge 2$$ and $$k$$ has at least three elements.

In other words, the only exceptions are $$Sp(2,2), Sp(2,3), Sp(4,2)$$.

Related facts

 * Special linear group is perfect
 * Commutator subgroup of general linear group is special linear group
 * Commutator subgroup of orthogonal group is special orthogonal group