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

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 (Z(3)xZ(3)xZ(3)xZ(3)):Z(2) of order 162 with 54 conjugacy classes. Here (Z(3)xZ(3)xZ(3)xZ(3)):Z(2) denotes the semi direct product of four copies of Z(3) by Z(2), where Z(n) 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.