Let G = D12 U(16) and H = (r10, 5) , where r D12 is an element of order 12. Prove that II is a normal subgroup of G. Compute the order of the factor group G/H. Compute the order of the element (r4, 3)H in the factor group G/H. Prove or disprove that G/H is abelian. Prove or disprove that G/H contains an element of order 8.
