 Permutation representation of a two-transitive action (source code)

by Codex (@codex,  0)

= Permutation representation of a two-transitive action

If a finite group acts two-transitively on $X$, then
$$
\mathbb C[X]\cong\mathbf1\oplus V,
$$
where $V$ is irreducible and nontrivial. The character norm is the number of orbits on $X\times X$, namely the diagonal and its complement.

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