On representation zeta function of special linear groups over finite principal ideal local rings

We show that the group algebras $\mathbb{C}[{\text{SL}}_3({\mathbb{F}}_3[t]\mathrm{/}(t^3))]$ and $\mathbb{C}[{\text{SL}}_3(\mathbb{Z}\mathrm{/}27)]$ are not isomorphic, as well as $\mathbb{C}[{\text{SL}}_4({\mathbb{F}}_2[t]\mathrm{/}(t^3))]$ and $\mathbb{C}[{\text{SL}}_4(\mathbb{Z}\mathrm{/}8)]$, by computing the number of conjugacy classes in those groups using MAGMA’s calculator. Similarly, we reproduce special cases of a recent result by Hassain and Singla, showing that $\mathbb{C}[{\text{SL}}_2({\mathbb{F}}_2[t]\mathrm{/}(t^k))]≆\mathbb{C}[{\text{SL}}_2(\mathbb{Z}\mathrm{/}{2}^k)]$ for $3\le k\le 8$.