Mohammad Reza Darafsheh,a*
Ali Reza Ashrafi,b and Arash Darafshehc
a Department of Mathematics, Statistics and Computer Science, Faculty
of Science, University of Tehran, Tehran, Iran. E-mail:
darafsheh@ut.ac.ir
b Department of Mathematics, Faculty of Science, University of Kashan,
Kashan, Iran
c Faculty of Science, Shahid Beheshti University, Tehran, Iran
Abstract
The non-rigid molecule group theory in which the dynamical symmetry operations
are defined as physical operations is applied to determine the character table
for the full non-rigid molecule group (f-NRG) of tetramethylethylene. We show
that the f-NRG of this molecule is a group of order 324, the structure of which
is formed as the wreath product Z3∿(Z2×Z2),
in which Z3 is the cyclic group of order 3 and Z2 denotes
the cyclic group of order two. Using the group theory package GAP, we calculate
the conjugacy classes and character table of this molecule.
Key words: non-rigid molecule group, tetramethylethylene, wreath product, character table