Thank you for your help. I need a solution of this problem ASAP. (AMS351 Book : Numbers, Groups & Codes six edition by Hemphreys & Prest)

Problem 1. Review the statement of Burnsides Theorem. For the set X = {1, 2, 3, 4}, for the dihedral subgroup D(4) of S(4) = S(X) generated by (1 2 3 4) and (14)(23), for every element D(4), compute the fixed set X^ . Confirm Burnsides Lemma in this case.