(4) (25 points) Consider the permutations A, B, C, D E S(4) defined by 1 2 3 4 1 2 3 4 1 2 3 4 A = 1 2 3 4 , B = 214 , C = 3 4 1 2 ' 1 2 3 4 D = 1 4 3 2 The set G = {A, B, C, D}, equipped with the usual multiplication of permutations, is a group. (a) Give the multiplication table for the group G. (b) Is G an abelian group, or a non-abelian group