Let G = S3 and H = {(), (2 3)}. Find the left and the right cosets of H in G.

Let G = S3 and H = {(), (2 3)}. Find the left and the right cosets of H in G.

The three left cosets are
H = {(), (2 3)} = (2 3)H
(1 2)H = {(1 2), (1 2 3)} = (1 2 3)H
(1 3)H = {(1 3), (1 3 2)} = (1 3 2)H.
The three right cosets are
H = {(), (2 3)} = H(2 3)
H(1 2) = {(1 2), (1 3 2)} = H(1 3 2)
H(1 3) = {(1 3), (1 2 3)} = H(1 2 3).