Consider the group S₄.

a)Prove that {(1,2)(3,4), (1,3)(2,4), (1,4)(2,3)}is an S₄ - conjugacy class.

b)Let V:={(1), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3)}. Prove that V is a normal abelian subgroup of S₄ isomorphic to the Klein 4-subroup V₄

c)Let H= {(1), (1, 2, 3), (1, 3, 2)}. Prove: VH is a normal subgroup of S₄ of cardinality 12, which is the union of three S₄ - conjugacy classes