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Definition:     H.conjugacy_classes_representatives(self)
       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)
       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().