proposition: Lemma charSG1 X : X \in irr 'SG_1 -> X = 1.
proof: Proof. move/irrP => [[i Hi] ->{X}]. apply/eqP; rewrite irr_eq1 -val_eqE /=. by move: Hi; rewrite NirrSn card_intpartn -[intpartn_nb 1%N]/1%N ltnS leqn0. Qed.
imports: mathcomp(all_ssreflect) mathcomp(fingroup perm ssralg morphism perm action) mathcomp(zmodp) mathcomp(vector matrix mxalgebra ssrnum algC) mathcomp(mxrepresentation classfun character) permcomp tools partition congr cycles cycletype presentSn