Consider a necklace that can be rotated and turned over. It is a circular necklace with 12 identical beads. Let G denote the symmetry group.

1) How many of the reflections in G fix at least one bead?

2) Find the cycle index of G.

3) Suppose we are now given p distinct colors C1,C2, ..., Cp. Find the number of G-inequivalent ways to color the beads with these colors. Express your answer in terms of p.