Computational determination of character table and symmetry of fullerenes cage as C24 and C28

Fullerene chemistry is nowadays a well-established field of both theoretical and experimental investigations‎. This study considers the symmetry of small fullerenes cage C24 and C28‎. ‎Using PM3 program for C24 and C28 fullerenes, Oh and Td symmetry were confirmed, respectively‎. ‎ The mentioned algorithm to compute the automorphism group of these fullerenes with connectivity and geometry of their symmetry point groups‎ was improved. ‎Here‎, ‎we computed the symmetry of these small fullerenes by simple method such as Groups, Algorithms and Programming (‎GAP) system‎. ‎It was proved that there are groups of order 48 which has 10 conjugacy classes for C24 and 24 which has 5 conjugacy classes for C28, respectively‎. ‎Also, the conjugacy classes and character table were computed‎.