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?
Encyclopedia of Groups
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group-theory
soft-question
online-resources
reference-works
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1Have you looked at http://hobbes.la.asu.edu/groups/groups.html? – 2012-04-11
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0Groups of order at most 12 are given at http://web.science.mq.edu.au/~chris/groups/appendix.pdf – 2012-04-11
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0The [Atlas of Finite Group Representations](http://brauer.maths.qmul.ac.uk/Atlas/) looks relevant. – 2012-04-11
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1The [GAP system for computational group theory](http://www.gap-system.org/) has a number of [data libraries](http://www.gap-system.org/Datalib/datalib.html), 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. – 2012-04-11
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8Nobody yet has mentioned [Groupprops, the group properties wiki](http://groupprops.subwiki.org/wiki/Main_Page) – 2012-04-11
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6To 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 http://www.gap-system.org/Manuals/doc/htm/ref/CHAP048.htm#SECT007 It also has databases of primitive permutation groups, classical groups, finite perfect groups, and more: http://www.gap-system.org/Manuals/doc/htm/ref/CHAP048.htm – 2012-04-11
4 Answers
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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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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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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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0These papers look very interesting. I'll read them when I get the time. – 2012-04-13