Konjugation/Klassengleichung/Fakt

Klassengleichung (Konjugation)

Sei ${}G$ eine endliche Gruppe und seien ${}K_{1},\ldots ,K_{r}$ die Konjugationsklassen von ${}G$ mit mindestens zwei Elementen.

Dann ist

${}\operatorname {ord} _{}^{}{\left(G\right)}=\operatorname {ord} _{}^{}{\left(Z(G)\right)}+\sum _{i=1}^{r}{\#\left(K_{i}\right)}\,.$

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