Order of Irreducible Representation Characters wrong in Sage?

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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)]

Definition:     H.conjugacy_classes_representatives(self)
Docstring:
       Returns a complete list of representatives of conjugacy classes in
       a permutation group G. The ordering is that given by GAP.


Definition:     H.character_table(self)
Docstring:
       Returns the matrix of values of the irreducible characters of a
       permutation group G at the conjugacy classes of G. The columns
       represent the conjugacy classes of G and the rows represent the
       different irreducible characters in the ordering given by GAP.

So it seems that the rows correspond to characters only, and perhaps they aren't guaranteed to be in the same order as the conjugacy classes. After all, in your example above, which of the two 3-dimensional reps should correspond to which order 9 conjugacy class? And I do get the same order for the irreducible characters as in the table with H.irreducible_characters().