This question tests your ability to describe symmetries
geometrically and to represent them as permutations in cycle
form. It also tests your understanding of conjugacy classes and
their relationship to normal subgroups.  The figure for this
question is prism with three identical rectangular faces and an
equilateral triangle at the top and base. The locations of the
faces of the prism (numbered 1, 4 at the top and base and each
side 2, 3 and 5, 5 being the back face) have been numbered so
that we may represent the group G of all symmetries of the prism
as permutations of the set {1,2,3,4,5}.  a) Describe
geometrically the symmetries of the prism represented in cycle
form by (14)(23) and (25).  b) Write down all the symmetries of
the prism in cycle form as permutations of {1,2,3,4,5}, and
describe each symmetry geometrically.  c) Write down the
conjugacy classes of G.  d) Determine a subgroup of G of order
2, a subgroup of order 3, and a subgroup of order 4. In each
case, state whether or not your choice of su