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).