Full Non-Rigid Group Theory for Hexamethylethane

Abstract

The non-rigid molecule group theory in which the dynamical symmetry operations are defined as physical operations is applied to deduce the character table of the full non-rigid molecule group (f-NRG) of hexamethylethane. The f-NRG of this molecule is seen to be isomorphic to the group (Z₃ × Z₃ × Z₃ × Z₃ × Z₃ × Z₃) Λ G₁₂ of order 8748 which has 174 conjugacy classes. Here (Z₃ × Z₃ × Z₃ × Z₃ × Z₃ × Z₃) Λ G₁₂ denotes the semi direct product of the direct products of 6 copies of the cyclic group Z₃ by the dihedral group of order 12. Using some results in finite group theory and GAP system, we find the complex character table of this group.