
Encyclopaedia of DesignTheory: A character table 
Let G be the symmetric group of degree 3, the group of all permutations of the set {1,2,3}.
There are three conjugacy classes in G. The class C_{1} consists of the identity permutation, denoted (1). The class C_{2} consists of the two cyclic permutations (1,2,3) and (1,3,2). The class C_{3} consists of the three transpositions (1,2), (1,3) and (2,3).
The number of irreducible representations is the same, namely 3. They are as follows:
Thus the character table of G is as follows, where X_{i} is the character of the representation R_{i}:
C_{1}  C_{2}  C_{3}  
X_{1}  +1  +1  +1 
X_{2}  +1  +1  1 
X_{3}  +2  1  0 
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Peter J. Cameron
6 August 2002