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What are the most famous (or most beautiful, IYO) finite sets in mathematics? I'm especially looking for 'large' sets that contain more than $2^{10} \approx 1000$ but fewer than $2^{20} \approx 1{,}000{,}000$ elements.

I'll start the ball rolling with the five platonic solids. (Unfortunately not large.)

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    6 775 235 700 (http://en.wikipedia.org/wiki/World_population) is a bit bigger then 2^20, but still it is a finite set of such cardinality where all of us are elements.2011-10-19
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    @Gortaur: "in mathematics."2011-10-19
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    I can't wait until Asaf sees this question...2011-10-19
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    I wonder if the set of [reducible configurations in the first computer-assisted proof of four-color theorem](http://en.wikipedia.org/wiki/Four_color_theorem#Proof_by_computer) count. There were apparently 1936 of them. :)2011-10-19
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    I don't understand the motivation behind this question.2011-10-19
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    I think a good place to start would be the OEIS entries that have the "fini" keyword: http://oeis.org/search?q=keyword:fini2011-10-19
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    This is not actually a question in the sense of this site. It is a call for a discussion, or referendum, on people's tastes and preferences. I have voted to close.2011-10-19

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