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Q-conjugacy character table for the non-rigid group of 2,3-dimethylbutane

Darafsheh Reza Mohammad (School of Mathematics, College of Science, Tehran, Iran)
Moghani Ali (Department of color physics, Institute for Colorants Paint and Coating (ICPC), Tehran, Iran)

Maturated and unmaturated groups were introduced by the Japanese chemist Shinsaku Fujita, who used them in the markaracter table and the Q-conjugacy character table of a finite group. He then applied his results in this area of research to enumerate isomers of molecules. Using the non-rigid group theory, it was shown by the second author that the full non-rigid (f-NRG) group of 2,3- -dimethylbutane is isomorphic to the group (Z3×Z3×Z3×Z3):Z2 of order 162 with 54 conjugacy classes. Here (Z3×Z3×Z3×Z3):Z2 denotes the semi direct product of four copies of Z3 by Z2, where Zn is a cyclic group of order n. In this paper, it is shown with the GAP program that this group has 30 dominant classes (similarly, Q-conjugacy characters) and that 24 of them are unmatured (similarly, Q-conjugacy characters such that they are the sum of two irreducible characters). Then, the Q-conjugacy character table of the unmatured full non-rigid group 2,3-dimethylbutane is derived.

Keywords: full non-rigid group, Q-conjugacy character, 2, 3-dimethylbutane