It is easy to see that G is to for the order of an element of this group if the lcm(a,b), where has elements of order 9,3,1 (order of elements divides order of group, since cyclic these are the only 3 possible). So since is cyclic, if has generators, or elements of order 9. So basically 6 * 3, elements of would be of the form (a,9), lcm(a,9) = 9. so 6*3 = 18 elements of order 9. 1 element of order 1, so 27-19, elements of order 3 (the only other possible order). or 8 elements of order 3.