**Group Theory for Tetramethylethylene ****Mohammad Reza Darafsheh,**^{a}***
Ali Reza Ashrafi,**^{b} and Arash Darafsheh^{c}^{
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 Z_{3}∿(Z_{2}×Z_{2}),
in which Z_{3} is the cyclic group of order 3 and Z_{2} 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