Projective Symplectic Group

The projective symplectic group ${\it PSp}_n(q)$ is the Group obtained from the Symplectic Group ${\it Sp}_n(q)$ on factoring by the Scalar Matrices contained in that Group. ${\it PSp}_{2m}(q)$ is Simple except for

$${\it PSp}_2(2) = S_3$$

$${\it PSp}_2(3) = A_4$$

$${\it PSp}_4(2) = S_6,$$

so it is given the simpler name $S_{2m}(q)$, with $S_2(q)=L_2(q)$.

References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. ``The Groups ${\it Sp}_n(q)$ and ${\it PSp}_n(q)={\it S}_n(q)$.'' §2.3 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, pp. x-xi, 1985.