THE Q-CONJUGACY CHARACTER TABLE OF DIHEDRAL GROUPS

Abstract

In a seminal paper published in 1998, Shinsaku Fujita introduced the concept of Q-conjugacy character table of a finite group. He applied this notion to solve some problems in combinatorial chemistry.  In this paper, the Q-conjugacy character table of dihedral groups is computed in general. As a consequence, Q-conjugacy character table of molecules with point group symmetries D₃ \(\cong\) C_3v \(\cong\) Dih₆, D₄ \(\cong\) D_2d \(\cong\) C_4v \(\cong\) Dih₈, D₅ \(\cong\) C_5v \(\cong\) Dih₁₀, D_3d \(\cong\) D_3h \(\cong\) D₆ \(\cong\) C_6v \(\cong\) Dih₁₂, D₂ \(\cong\) C_2v \(\cong\) Z₂ × Z₂ \(\cong\) Dih₂, D_4d \(\cong\) Dih₁₆, D_5d \(\cong\) D_5h \(\cong\) Dih₂₀, D_6d \(\cong\) Dih₂₄ are computed, where Z₂ denotes a cyclic group of order 2 and Dihn is the dihedral group of even order n.