11.2.2. For N = 12, consider the FFT based on the subgroup chain $C_1 \le C_3 \le C_6 \le C_{12}$ \\
(so n = 3). Let $\omega = e^{2\pi i/12}$. \\
(a) In terms of $\omega$, find generators for each $H_i$ and transversals for each inclusion $H_{i-1}$ in \\
$H_i$. \\
(b) Compute the FFT from start to finish, and verify that the end result is the same as \\
the result of the DFT for N = 12.
