Distinct die labelings

You wipe the numbers off a 66-sided die and relabel its faces with 1166 (each once). How many distinct dice can you make, counting two labelings the same if one is a rotation of the other?

Show hints (2)+
  1. There are 6!6! labelings; the cube has 2424 rotational orientations.
  2. Distinct labels means no rotation fixes a labeling, so it's 6!/246!/24.

Answer

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30

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Asked at: Jane Street, Citadel

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