Encyclopedia of Groups

Question

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?

Answer 1

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 $n < 2001$.

Answer 2

EDIT: Lance Pollard notes that the links below are broken. Groups of order up to 30 are (currently) available at https://en.wikipedia.org/wiki/List_of_small_groups and at http://www.math.ucsd.edu/~atparris/small_groups.html

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.

Answer 3

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

Answer 4

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.)

Answer 5

For smallish (up to order 500, with gaps for order 256 and 384) finite groups, this website of Tim Dokchitser might be of interest:

https://people.maths.bris.ac.uk/~matyd/GroupNames/index.html