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I was wondering whether or not there was an online encyclopedia of groups--finite or infinite. If there isn't, would you suppose that such a thing would be useful?

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You may also want to read a nice article of Conway, Dietrich and O'Brien http://www.math.auckland.ac.nz/~obrien/research/gnu.pdf

And also the paper of Besche, Eick and O'Brien http://www.math.auckland.ac.nz/~obrien/research/2000.pdf which contains a table of the number of groups of order $n < 2001$.

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  • $\begingroup$ These papers look very interesting. I'll read them when I get the time. $\endgroup$ – RougeSegwayUser Apr 13 '12 at 0:11
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Groups of order less than 30 are at http://opensourcemath.org/gap/small_groups.html

Also, http://world.std.com/~jmccarro/math/SmallGroups/SmallGroups.html goes up to order 32.

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Depending on your needs, Wolphram|Alpha or Mathematica itself might be helpful. See here for the computational overview, and here for the data function (open up the "More Information" for the sorts of things you can search.)

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Another older reference is Marshall Hall, Jr, and James K. Senior, The groups of order $2^n\ \ (n < 6)$ (Macmillan, New York, 1964).

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