(15 points) Consider the group U(15) = {1, 2, 4, 7, 8, 11, 13, 14} with multiplication modulo 15 and let H = {1, 11}. (a) Show that H is a normal subgroup of G. (b) List the distinct elements of the factor group G/H. Make sure your solution includes justification for why you have a complete list of all elements of G/H. (c) Construct the Cayley table for the factor group G/H. Make sure your Cayley table clearly shows that G/H is a group. (No justification necessary.) (d) What group is G/H isomorphic to? Provide a complete justification