2-Sylow subgroup of general linear group:GL(2,3)

Definition
$$G$$ is the general linear group of degree two over field:F3. In other words, it is the group of invertible $$2 \times 2$$ matrices with entries over the field of three elements. The field has elements $$0,1,2$$ with $$2 = -1$$.

$$H$$ is one of the 2-Sylow subgroups of $$G$$, i.e.:

$$H$$ is isomorphic to semidihedral group:SD16.

Sylow and corollaries
The subgroup is a 3-Sylow subgroup, so many properties follow as a corollary of that.