Conjugacy classes of rotational symmetry tetrahedron

Question

I am struggling with this question, as I don't know how to give a "short proof" as requested by our professor, as a non-graded exercise. Especially, since we have to do this without using any shapes, and just using our head!!

Problem: Let T be the tetrahedral rotation group. Give a short proof that the elements of order 3 are NOT all conjugate to each other in T.

Any help would be appreciated.

Thanks.

Answer 1

Hint: Number of elements in a conjugacy class must divide the order of the group.