I was told that there were types of finite groups of lie types, such as $A_l,l\geq 1$, $^2A_l, l \geq 2$, $B_l, l \geq 2$, $^2B_2$ and so on.
My problem is that if there are any concrete examples of groups of various types. I mean, what do they consist of as a group. More precisely, are there any examples of finite groups of types $A_2$ or $^2A_2$?
In addition, what are the differences between $A_l$ and $^2A_l$, or between $B_l$ and $^2B_l$?
Thanks to everyone.
Added More precisely, let $k$ be the algebraic closure of the field with 5 elements, and $G = \{ (a_{ij})_{3 \times 3} | a_{ij} \in k, a_{ij}^5 =a_{ij}, 1 \leq i,j \leq 3, \det ((a_{ij})_{3 \times 3}) = 1 \}$. Then is $G$ a finite group of Lie type? If it is, is it of type $A_2$? If it is of type $A_2$, what is the group of type $^2A_2$?