click for screenshots


Visual Group Theory

A book designed to be used alone or in conjunction with Group Explorer, giving a thoroughly visual introduction to group theory, building strong intuition for the mathematical objects called groups.

JOMA Article on GE 1.5.8

Online article introducing the classroom utility of group theory visualization using Group Explorer 1.5.8.

Data file generator

A student and professor from Tokyo created a program to turn arbitrary group definitions into Group Explorer data files! You can read about it and download it for free.

GE has a wiki, so contribute!

Classroom Resources and Homework Assignments

These resources were contributed to the old version's homepage, but are still relevant and usable, perhaps with some tweaking.

Locations of visitors to this page
See previous years' maps

Current Features

Primary features listed here, or read the version 2.2 release notes.

  • Displays Cayley diagrams, multiplication tables, cycle graphs, and objects with symmetry
  • Many common group-theoretic computations can be done visually
  • Compare groups and subgroups via morphisms (see illustration below)
  • Browsable, searchable group library
  • Integrated help system (which you can preview on the web)
  • Save and print images at any scale and quality

Windows XP and Mac OS X users:

Linux users:

Group Explorer Overview

For information beyond the above features list, follow this link to an introduction to all Group Explorer features and visualizations, including multiplication tables, Cayley diagrams, cycle graphs, objects with symmetry, and sheets, including homomorphisms.

The following shareware clearinghouses have found and included Group Explorer, but they only include the Windows version.
Mac and Linux users should use the SourceForge download link.

Want to code on this project?

There is a tracker for bug reports. Solve some and send me an email!

click for screenshots

Spins 3D

Try a free group-theory-based puzzle game for the iPhone/iPod Touch, Spins 3D (link goes to the App Store). It is not part of Group Explorer, but is written by the same developer.


May 29, 2009: New version! To accompany the recent release of the book Visual Group Theory, Group Explorer v2.2 is out! This update includes bug fixes, user interface enhancements, a universal binary on the Mac, and makes it easier for Linux users to build (and use undo/redo support). Let me know of any issues you find. Enjoy!

Summer 2009: The book Visual Group Theory is out! Order one today!

Spring 2008: from Nathan's talk at the 2008 Joint Math Meetings, A Talk Without Words: Visualizing Group Theory (PPT format, 2.4MB, download starts immediately).

Fall 2007: Cayley diagrams of the symmetric groups up to S5, of order 5!=120.