Write the dihedral group D8 as {R0, R45, R90, R135, R180, R225, R270, R315, F1, F2, F3, F4, F5, F6, F7, F8} and let N = {R0, R90, R180, R270}. Prove that N is normal in D8. Given that F1N 5 {F1, F4, F3, F2}, determine whether D8/N is cyclic.
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