Irreducible characters of the icosahedral group

To study point groups, their irreducible characters are essential. The table of irreducible characters of the icosahedral group $A_5$ is usually obtained by using its duality to the dodecahedral group. It seems that there is no literature which gives a routine computational way to complete it. In the works of Harter and Allen, a computational method is given and the character table up to the tetrahedral group $A_4$ using the group algebra table and linear algebra. In this paper, we employ their method with the aid of computer programming to complete the table. The method is applicable to any other more complicated groups.