4. Construct each of the semidirect products below via our \"inflation process\"\
(i) $D_3 \times C_2$
(ii) $D_3 \rtimes C_2$
(iii) $V_4 \times C_3$
(iv) $C_3 \rtimes V_4$.
Make sure you define the labeling maps $\theta: B \to Aut(A)$. Then determine, with justi-
fication, what each group is isomorphic to. Use $D_3 = \langle a, b \mid a^2 = b^2 = (ab)^3 = 1 \rangle$,
$V_4 = \langle a, b \mid a^2 = b^2 = 1 \rangle$, and $C_n = \langle c \mid c^n = 1 \rangle$ for the individual factors, and Cayley
diagrams corresponding to these generating sets.
