@paysmaths Also known as Burnside's Lemma, I did have to check "wait I recognise this" π For G acting on X giving a permutation character Ο, evaluating <1,Ο> counts the number of orbits of the action. If G acts 2-transitively then Ο-1 is thus an irreducible character as <Ο,Ο>=<1,Ο_{XX}>=2