Finite matrix group SL_2(3)

The finite matrix group $\mathrm{SL}_2(3)$ consists of determinant-one $2\times2$ matrices over the field $\mathbb F_3$ , with matrix multiplication.

Order and nonsimplicity

The determinant divides the general linear group order by $3-1$ , giving $24$ elements. The scalar matrices $\{I,-I\}$ form a proper nontrivial center, so this group is not simple.

References

Peter J. Cameron, Notes on Classical Groups, §2.1, Theorems 2.2–2.3, pp. 15–16: orders, determinant and scalar kernels; §2.4, Theorem 2.10, pp. 20–22: simplicity.