Full Non-Rigid Group of 1,3,5-Trimethyl-2,4,6-trinitrobenzene Using Wreath Product

Abstract

Using non-rigid group theory, it is shown that the full non-rigid (f-NRG) group of 1,3,5-trimethyl-2,4,6-trinitrobenzene is isomorphic to the group (C₂ × C₃) ∼ S₃ of order 1296, where ~ stands for wreath product, C₂ and C₃ are cyclic groups of order 2 and 3, respectively and S₃ is the symmetric group of order 6 on 3 letters. This group has 98 conjugacy classes and irreducible representations. Then the character table of the full non-rigid 1,3,5-trimethyl-2,4,6-trinitrobenzene is derived for the first time.