Q-conjugacy Character Table for Nonrigid Group Tetramethylethylene

The maturated and unmaturated groups were introduced by Japanese chemist Shinsaku Fujita who used them in Q-conjugacy character table of a finite group. Then he applied his results in this area of research to enumerate isomers of molecules. Using non-rigid group theory, it was shown by the second and third authors that the full non-rigid (f-NRG) group of tetramethylethylen is isomorphic to the group the C3 ∿ (C2 × C2) of order 324, where ∿ and × denote respectively, “wreath” and “direct” products of groups, furthermore Cn is the cyclic group of order n. In this paper we will show that this group has 29 dominant classes (similarly, Q-conjugacy characters) and that 16 of them are unmatured (similarly, Q-conjugacy characters such that they are sum of two irreducible characters). Then Q-conjugacy character table of the unmatured full non-rigid group tetramethylethylen is derived, at the end of this article a conjecture for simple method to specify how a given finite group is unmaturated is offered