Group Theory for Tetramethylethylene 

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(Z2Z2), 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