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.