5 Find all cosets of the subgroup H of the group G given bel

5. Find all cosets of the subgroup H of the group G given below. What fnitely generated abelian group is the factor group G/H isomorphic to?

<(3,2)> subgroup is of order 2

no. of cosets must be 3 as G has 6 elements

a) e*<(3,2)> = <(3,2)> = (3,2) * <(3,2)>

b) (1,2) *<(3,2)> = {(1,2,3),(1,2)} = (1,2,3) *<(3,2)>

c) (1,3) *<(3,2)> = {(1,3,2),(1,3)} = (1,3,2) *<(3,2)>

Well H is not normal subgroup