In this post, we look for the existing atlas-like websites providing well-presented classifications or database about some specific areas of mathematics. Here are some examples:
Finite groups of order ≤500, group names, extensions, presentations,
properties and character tables.
- Atlas of Finite Group Representations: http://brauer.maths.qmul.ac.uk/Atlas/v3/
This ATLAS of Group Representations has been prepared by Robert
Wilson, Peter Walsh, Jonathan Tripp, Ibrahim Suleiman, Richard Parker,
Simon Norton, Simon Nickerson, Steve Linton, John Bray, and Rachel
Abbott (in reverse alphabetical order, because I'm fed up with always
being last!). It currently contains information (including 5215
representations) on about 716 groups [mainly finite simple groups or almost simple].
- Atlas of subgroup lattice of finite almost simple groups: http://homepages.ulb.ac.be/~dleemans/atlaslat/
This atlas contains all subgroup lattices of almost simple groups $G$
such that $S≤G≤Aut(S)$ and $S$ is a simple group of order less than 1
million appearing in the Atlas of Finite Groups by Conway et al. Some
simple groups and almost simple groups or order larger than 1 million
have also been included, but not in a systematic way.
- The L-functions and Modular Forms Database: https://www.lmfdb.org/
Welcome to the LMFDB, the database of L-functions, modular forms, and
related objects. These pages are intended to be a modern handbook
including tables, formulas, links, and references for L-functions and
their underlying objects [like field extensions and polynomial Galois groups].
- The Inverse Symbolic Calculator: https://isc.carma.newcastle.edu.au/
The Inverse Symbolic Calculator (ISC) uses a combination of lookup
tables and integer relation algorithms in order to associate a closed
form representation with a user-defined, truncated decimal expansion
(written as a floating point expression). The lookup tables include a
substantial data set compiled by S. Plouffe both before and during his
period as an employee at CECM.
If you know such a website on any area of mathematics, please put it as an answer (with a short description).
Best Answer
This catalogue of mathematical datasets could be of some interest to you - at least some of the entries are atlas-like websites. It includes several of the websites mentioned above, and I'm slowly adding more to it.