Center of special linear group:SL(2,3)

Definition
$$G$$ is the special linear group:SL(2,3), i.e., the special linear group of degree two over field:F3. In other words, it is the group of invertible matrices of determinant 1 over the field with three elements. The field has elements 0,1,2, with $$2 = -1$$.

$$H$$ is the subgroup:

$$\{ \begin{pmatrix} 1 & 0 \\ 0 & 1 \\\end{pmatrix}, \begin{pmatrix} 2 & 0 \\ 0 & 2 \\\end{pmatrix} \}$$

$$H$$ is isomorphic to cyclic group:Z2. It is the center of $$G$$. The quotient group $$G/H$$ is the projective special linear group of degree two $$PSL(2,3)$$ over field:F3, which is isomorphic to alternating group:A4.

Subgroup-defining functions
The subgroup is a characteristic subgroup and arises as a result of many subgroup-defining functions, some of which are detailed below: