# Revision history [back]

You are confusing rows and columns of the character table.

• The rows correspond to the irreducible representations
• The columns correspond to the conjugacy classes

For example:

sage: G = DihedralGroup(3)
sage: G.character_table()
[ 1 -1  1]
[ 2  0 -1]
[ 1  1  1]


So the last row in the character table is the trivial representation, which is the same ordering as

 sage: G.irreducible_characters()[-1] == G.trivial_character()
True


We also see that the trivial conjugacy class is the first column in the character table. For this, recall that the character evaluated at the trivial conjugacy class is just the dimension of the representation. As you already remarked, this is the same ordering that Sage (actually, GAP) returns the conjugacy classes in:

sage: G.conjugacy_classes_representatives()
[(), (1,2), (1,2,3)]