5. The permutations(124)(35) and b = (12)(3)(4)(5) generate a group (G, *) of order 12.a = (a) Construct the Cayley table of (G, *). Provide an explanation of how you

constructed theCayley table, being clear about how all elements were obtained. (b) Construct a Cayley digraph for your table in part (a), using the elements a and b. (c) Construct the lattice diagram of this group. Provide an explanation of how you con-structed the lattice diagram, being clear about how each subgroup was obtained. (d) For each subgroup identified in part (b) determine if the subgroup is normal or not,providing an explanation of your answer. e) Let Z be the normal subgroup of G defined as follows: Z=\{g \in G \mid g h=h g \text { for all } h \in G\} Write down the elements of Z. Write down the elements of G/Z and construct the grouptable for G/Z.