Technical report: character table of symmetric group S₃ using permutation module / Ain Natasha Mohd Zaini and Mariam Jamilah R.Azmi

The aim of this project is to describe the conjugacy classes and the irreducible representation of finite group together with character table of symmetric group (Sₙ). The irreducible character of symmetric group (Sₙ) was determined by using permutation module and the representation of Young tableux is used to obtain an irreducible representations. A character table of Sn are constructed in this project is for symmetric group of order 3. Hence, the partition of S₃ was generated in order to determine the conjugacy classes as well as the cycle shape of the par­titions. Permutation module, Mλ was used to find the character entries in character table of S₃. However, this method does not produce irreducible characters, then the method of permutation matrix together with the definition of Fixed-Point formula was applied to find the irreducible characters in character table S₃. Finally, the conjugacy classes and irreducible characters of S₃ is obtained in order to construct character table of S₃.