Refer to Example 1 in this chapter and explain why it is unnecessary to compute the orde...

Refer to Example 1 in this chapter and explain why it is unnecessary to compute the orders of the last five elements listed to determine the isomorphism class of G.

Reference:

EXAMPLE 1 Let G = {1, 8, 12, 14, 18, 21, 27, 31, 34, 38, 44, 47, 51, 53, 57, 64} under multiplication modulo 65. Since G has order 16, we know it is isomorphic to one of

To decide which one, we dirty our hands to calculate the orders of the elements of G.