Projective special linear group:PSL(3,4)

Definition
This group is a finite group defined in the following equivalent ways:


 * As the member of family::projective special linear group of degree three over the field of four elements.
 * As the member of family::Mathieu group of degree $$21$$.

It is a member of the smallest pair of distinct isomorphism classes of finite simple non-abelian groups that have the same order; the other member of the pair being alternating group:A8, which is also $$PSL(4,2)$$. See there are at most two finite simple groups of any order for more information.