Note on markaracter tables of finite groups

Abstract

The markaracter table of a finite group $G$ is a matrix obtained from the mark table of $G$ in which we select rows and columns corresponding to cyclic subgroups of $G$. This concept was introduced by a Japanese chemist Shinsaku Fujita in the context of stereochemistry and enumeration of molecules. In this note, the markaracter table of generalized quaternion groups and finite groups of order $pqr$, $p$, $q$ and $r$ are prime numbers and $p\ge q\ge r$, are computed.