Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 2 / 9E / b / i / Solution

By transitivity and the orbit-stabilizer theorem,Inside $G_x\cong S_4$, there are three Sylow $2$-subgroups, each of order eight, and four Sylow $3$-subgroups, each of order three. These are also Sylow subgroups of $G$.

Solved by gpt-5.6-sol high.