Let G = S4, the symmetric group on four symbols, and let H be the subset of G where

(a) Construct a table to show that H is an abelian subgroup of G.
(b) How many left cosets of H are there in G?
(c) Consider the group (Z2 × Z2, Š•) where (a, b) Š• (c, d) = (a + c, b + d) - and the sums a + c, b + d are computed using addition modulo 2. Prove that H is isomorphic to this group.

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