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 experimentalinvestigations. This study considers the symmetry of small fullerenes cage C24 and C28. UsingPM3 program for C24 and C28 fullerenes, Oh and Td symmetry were confirmed, respectively. Thementioned algorithm to compute the automorphism group of these fullerenes with connectivityand geometry of their symmetry point groupswas improved . Here, we computedthe symmetryof 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 C24and 24 which has 5 conjugacy classes for C28, respectively. t ,Alsohe conjugacy classes andcharacter table were computed.