A necklace is to be made out of 6 beads evenly spaced on a loop of string.

(a) What is the group of symmetries of a necklace like this?

(b) If there are k types of bead, how many different types of necklace can be made (where two necklaces are of the same type if you can turn one into the other by applying one of the elements of the symmetry group in part (a)).