The formula for this classes is obtained by the Orbit-Stabilizer lemma applied for Sn with the action of conjugation.
For a partition p this formula is n!/(∏i (λi )!iλi, where λi denotes the number of parts in p that are equal to i.
i1 : p1 = new Partition from {3,2,1} o1 = Partition{3, 2, 1} o1 : Partition |
i2 : cardinalityOfConjugacyClass p1 o2 = 120 |
i3 : p2 = new Partition from {1,1,1,1,1} o3 = Partition{1, 1, 1, 1, 1} o3 : Partition |
i4 : cardinalityOfConjugacyClass p2 o4 = 1 |