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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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Have you looked at – Gerry Myerson Apr 11 '12 at 4:24
Groups of order at most 12 are given at – Gerry Myerson Apr 11 '12 at 4:27
The GAP system for computational group theory has a number of data libraries, including an interface to the Atlas of Group Representations. Of course this is more in the way of a downloadable package than an online resource. – hardmath Apr 11 '12 at 4:35
Nobody yet has mentioned Groupprops, the group properties wiki – MJD Apr 11 '12 at 5:24
To expand on hardmath's comment, GAP (and anything that interfaces to GAP e.g. sage) has a SmallGroups library containing every group of order <=2000 except those of order 1024 --- this is over 400 million groups. It also has all groups of squarefree order, small cubefree order groups, all $p$-groups of order $\leq p^6$,... See It also has databases of primitive permutation groups, classical groups, finite perfect groups, and more: – m_t_ Apr 11 '12 at 6:47
up vote 6 down vote accepted

You may also want to read a nice article of Conway, Dietrich and O'Brien

And also the paper of Besche, Eick and O'Brien which contains a table of the number of groups of order $n < 2001$.

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These papers look very interesting. I'll read them when I get the time. – Chris Dugale Apr 13 '12 at 0:11

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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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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