**Group Theory for Tetramethylethylene, II **

**Mohammad Reza Darafsheh ^{1,}*, Ali Moghani^{2} and Soroor
Naghdi Sedeh^{2}**

^{1} School of Mathematics, College of Science, University of
Tehran, 14174 Tehran, Iran

^{2} Department of Color Physics, Institute for Colorant, Paint and
Coating (ICPC), 16765 Tehran, Iran

* Corresponding author: E-mail:
darafsheh@ut.ac.ir

**Abstract
**The maturated and unmaturated groups have been introduced by S. Fujita who
used them in the markaracter table and the Q-conjugacy character table of a
finite group. Fujita introduced more concise forms called the Q-conjugacy
characters with integer-valued of the irreducible characters of finite groups
and applied his results in this area of research to enumerate isomers of
molecules. In this paper using GAP program all integer-valued characters of the
full non-rigid group (f-NRG) of tetramethylethylene (2,3-dimethylbut-2-ene) is
calculated by the Q-conjugacy relationships. It is shown that this group has 29
dominant classes (similarly, Q-conjugacy characters) such that 16 of them are
unmaturated (similarly, Q-conjugacy characters such that they are the sum of two
irreducible characters). Then the markaracter table and Q-conjugacy character
table of the f-NRG of tetramethylethylene are derived for the first time.

**Keywords:** Full non-rigid group, markaracter table, Q-conjugacy
character table, tetramethylethylene (2,3-dimethylbut-2-ene).