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An irregular hexagon H has vertices (1, 0), (0, 1), (−2, 2), (−1, 0), (0,−1) and (2,−2).? a) Using standard notation, write down the elements of the symmetry group S(H) of H, giving a brief description of the geometric effect of each symmetry on points in the plane. b) Compile a Cayley table for S(H). c) Show that the set G = {3, 6, 9, 12, 15, 18} is a group under the operation ×21. You should state the inverse of each element in (G,×21)

An irregular hexagon H has vertices (1, 0), (0, 1), (−2, 2), (−1, 0), (0,−1) and (2,−2).?

a) Using standard notation, write down the elements of the

symmetry group S(H) of H, giving a brief description of the

geometric effect of each symmetry on points in the plane.

b) Compile a Cayley table for S(H).

c) Show that the set G = {3, 6, 9, 12, 15, 18} is a group under the

operation ×21. You should state the inverse of each element in

(G,×21)

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