Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 18J / a / Solution

Up to conjugacy, the transitive subgroups of the symmetric group on four points areRepresentatives are $⟨(1234)⟩$, the normal Klein four group of double transpositions, $⟨(1234),(13)⟩$, $A_4$, and $S_4$.