Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2015 / Paper 2 / 9 / c / Solution

The cycle type records the lengths of the disjoint cycles in a permutation, including fixed points as length-one cycles. The possibilities for three objects areThese exhaust the six elements of the symmetric group $S_3$, denoted ${\Sigma }_3$ in the source. They are also the conjugacy classes of the symmetric group on three letters.