G = Z12 × Z18, N = D[6]12, [12]18E, g = [3]12, [2]18.
(i) Find |N| and |G/N|, and write the elements of N.
(ii) Find the order of g in G and find the order of gN in the quotient group G/N.
(iii) Showthath18 ∈N forallh∈G.
(iv) Show the quotient group G/N is not cyclic.