I used Theorem 10.1.6 from the textbook (6th edition) with g=g'=7 to solve this problem.
More so, remember that with U(30), the group operation is multiplication, unlike with number 24 where it was addition. Thus, with ker = {1,11}, g = 7, g*ker = {7,77} but 77 = 17 in U(30). -K. Brumbaugh
Thanks for the explanation.
