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Using $Version == "12.3.0 for Mac OS X x86 (64-bit) (May 10, 2021)" and executing

Select[FiniteGroupData[All], 
    And[Not[MissingQ[#]], Not@SquareMatrixQ[#]] &@
    FiniteGroupData[#, "CharacterTable"] &]

I found that both {"PointGroup","Oh"} and {"PointGroup","I"} have character tables that are not square. It is a theorem that they must be square. In fact, the reason they are not square is that in both cases one of the rows is shorter than the others.

Using

\[Chi] = FiniteGroupData[{"PointGroup", "Oh"}, "CharacterTable"];
Length /@ \[Chi]
TableForm@\[Chi]

we can see that the 2nd row is 1 entry short. Comparing to https://www.webqc.org/symmetrypointgroup-oh.html it's clear that all the other irreps are correct, and that the A2g is incorrect; it has a 0 where +1, -1 should be. I conjecture this is due to a missing comma in Mathematica's internals, giving 1-1=0.

Similarly,

\[Chi]I = FiniteGroupData[{"PointGroup", "I"}, "CharacterTable"];
Length /@ \[Chi]I
TableForm@\[Chi]I

shows that the trivial irrep is one entry short. I conjecture this is due to a similar missing comma, giving implied multiplication 1 1 = 1.

Whatever the cause, this is certainly a bug, and I have opened an issue with Wolfram.

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1
  • $\begingroup$ Wolfram support reproduces and confirms this is a bug. $\endgroup$
    – evanb
    Aug 3, 2021 at 7:09

1 Answer 1

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This bug was resolved in version 13.0 ($Version == "13.0.0 for Mac OS X x86 (64-bit) (December 3, 2021)").

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