Editing Character theory (section)

== Applications ==
Characters of [[irreducible representation]]s encode many important properties of a group and can thus be used to study its structure. Character theory is an essential tool in the [[classification of finite simple groups]]. Close to half of the [[mathematical proof|proof]] of the [[Feit–Thompson theorem]] involves intricate calculations with character values. Easier, but still essential, results that use character theory include [[Burnside's theorem]] (a purely group-theoretic proof of Burnside's theorem has since been found, but that proof came over half a century after Burnside's original proof), and a theorem of [[Richard Brauer]] and [[Michio Suzuki (mathematician)|Michio Suzuki]] stating that a finite [[simple group]] cannot have a [[generalized quaternion group]] as its [[Sylow theorems|Sylow {{math|2}}-subgroup]].