Projective special linear group

Particular cases

Finite fields

For $q=2$, $PSL(n,q)=SL(n,q)=PGL(n,q)=GL(n,q)$. For $q$ a power of two, $PSL(n,q)=SL(n,q)$ but this is not equal to $GL(n,q)$.

Size of field	Order of matrices	Common name for the projective special linear group
$q$	1	Trivial group
2	2	Symmetric group:S3
3	2	Alternating group:A4
4	2	Alternating group:A5
5	2	Alternating group:A5
7	2	Projective special linear group:PSL(3,2)
9	2	Alternating group:A6
2	3	Projective special linear group:PSL(3,2)
3	3	Projective special linear group:PSL(3,3)