Suppose G is a group of order 48 (centre consisting identity only). Show it has a conjugacy class of order 3.
I know that the size of the conjugacy classes are limited to divisors of 48: 1,2,3,4,6,8,12,16,24, and 48. These classes also partition G so their sizes must sum to the order of G (so I cannot use 48 and have to include 1). I am not sure how to continue from here.