This is the problem:
Exhibit three reductive groups of dimension $4$ and semisimple rank $1$ which are pairwise nonisomorphic (as algebraic groups).
I know that for any reductive group $G$ of semisimple rank $1$, $G = (G,G)Z$, where $(G, G)$, the derived subgroup of $G$ is semisimple, of dimension $3$, and $Z$ is the identity component of the centre of $G$.
As the dimension of $G$ is $4$, it is clear that the dimension of its cetre is $1$.
I think $GL(2,\mathbb{C})$ is an easy example. Other such groups might also appear as matrix groups. But I have no idea as to how to construct them.
Would you please tell me a method or give me some advice? Thanks in advance~