Chapter 4.6, Problem 2E

In Exercises $1-6$, $H$ is a normal subgroup of the group $G$. Find the order of the quotient group $G/H$. Write out the distinct elements of $G/H$ and construct a multiplication table for $G/H$.

The octic group $D_4=\{e,\alpha ,{\alpha }^2,{\alpha }^3,\beta ,\gamma ,\Delta ,\theta \}$

; $H=\{e,\beta ,\Delta ,{\alpha }^2\}$.