Let S5 be the symmetric group of permutations of five numbers. (a) Determine the order of all elements of S5. Give an example of elements and in S5, such that |a| = |B|=2 and | a|= 3. (b) (c) (d) Let D60 be the dihedral group of symmetries of regular 60-sided polygon. Determine whether S5 is isomorphic to D60- A group is simple if its only normal subgroups are the identity subgroup and the group itself. Explain whether S5 is simple.