Exercise 7. If H C G is a normal subgroup of order 2, show that H is contained in the center of G. Exercise 8. The subgroup H = {6, (1 2)(34), (1 3)(2 4), (1 4)(2 3)} C S4 is normal (you may assume this). List the cosets of H, and nd the order of each coset viewed as an element of the quotient S4 / H