Originally Posted by

**steph3824** Let H be the group of the symmetries of a square. Denote by R reflection about the y-axis and by ρ the rotation by 90 degrees around the origin.

a)Give a representation of each of the 8 elements of H: e, ρ, ρ², ρ³, R, ρR, ρ²R, ρ³R as a permutation of {1,2,3,4}. We can therefore view H as a subgroup of S(4).

b) Construct all the left cosets of H in S(4).

c)Compute the right coset H(1,2) and compare it to the left coset (1,2)H. Are they equal?

I missed the class where all of this type of stuff was discussed, and am so lost. I've read through my book but it is just not very helpful and doesn't offer many examples. I would sooooo appreciate any help on this problem