This is a computer program which computes information about the groups of orders 1-32.  You can find the orders of elements, list the subgroups, find cosets, search for a finitely presented group, work with permutations, and more.









John J Wavrik 

Dept of Math 
























An older version of the program is available online via ssh. 

From a ssh client program, type “ssh” and supply the password  “groups32”.


A new version of the Groups32 program can now be downloaded by clicking here.  This provides a .zip file that contains the executable Groups32.exe, an Introduction and Sample Session. This program is only for Windows.


Read the Sample Session (pdf format) while using Groups32 for the first time.   View or download Sample Session




An article about the development of Groups32 was published in the Journal of Online Mathematics and its Applications (JOMA) the online journal of the MAA.

The article, “Evolution of a Computer Application” is an attempt to combine exposition with access to a computer program. The executable files which originally accompanied the article can be obtained by clicking here. A new version of Groups32 can be obtained here.
















All files are in .pdf format and require Adobe Reader or equivalent



An introductory demonstration on Groups and the use of Groups32 

A script which presents an overview of most of the commands. Either print the script on paper or run the script and Groups32 in separate windows.


Click here  for information about the history and technical background of Groups32.


There is a file of  sample problems with solutions. These are taken from various parts of a course in modern algebra - they are intended to show how Groups32 can be used. They are not beginners exercises. 


Click here for a list of handouts for an undergraduate course in Applied Modern Algebra which used Groups32.



































    1. Tables / Backtracking Algorithms
    2. Cayley Tables
    3. Introduction to Groups32
    4. Sample Session - Groups32
    5. Greatest Common Divisor
    6. Permutations
    7. Normal Subgroups
    8. Quotient Groups
    9. Generators and Relations






Where can I get SSH for my personal computer?
this information was supplied by the UCSD Math Dept Computer Support
If the computer you're using does not already have a SSH client installed, the following SSH clients are available for free download and use:






SSH Secure Shell
for Workstations




The SSH Secure Shell for Workstations client has BOTH SSH remote terminal and SFTP secure file transfer capabilities built-in.

However, if you do not have local administrative privileges to install software on the PC you're using, then use the PuTTY client instead (SSH remote terminal only).

Mac OS X

Mac OS X comes with SSH pre-installed.

Go to Applications -> Utilities -> Terminal

At the prompt, type "ssh -l username"
OR "ssh"

Use Software Update to update to the latest SSH version.

For a graphical SFTP secure file transfer client, use Cyberduck or Fugu. Or use the pre-installed command-line "sftp" and "scp" clients.

To run Unix X11 graphical programs, use the Apple X11 client under Applications -> Utilities -> X11 (or download from Apple X11). At the prompt, type "ssh -X -l username" to login with automatic X11 port forwarding enabled.

Classic Mac OS
(9.x or older)


PPC or 68K

NiftyTelnet SSH


MacSSH and NiftyTelnet SSH only have SSH remote terminal capability.

For SFTP secure file transfer, use MacSFTP ($15 shareware).


Most Unix/Linux distributions now
come with SSH pre-installed.

At the prompt, type "ssh -l username"
OR "ssh"

If SSH is not installed, please consult your system documentation on how to update your system or ask your system administrator to install OpenSSH.

Use the command-line "sftp" or "scp" clients for secure file transfer.

To run Unix X11 graphical programs, type "ssh -X -l username" to login with automatic X11 port forwarding enabled.


If you have a Java-enabled web browser,
you can use the

MindTerm SSH Java Applet

To run MindTerm SSH properly, your web browser must use a recent Java Virtual Machine (JVM) runtime environment. If a working JVM is not already installed:

Microsoft Windows: Install the latest Sun J2SE JRE.
Mac OS X: Use Software Update to update to the latest Mac OS X Java.
Classic Mac OS: Install the latest Mac OS Runtime for Java (MRJ).
Unix/Linux: Install the latest Sun J2SE JRE.

For Classic Mac OS, you must install the latest MRJ and use Microsoft Internet Explorer 5.x to use MindTerm SSH. The internal JVM in Netscape Communicator 4.x lacks certain features needed to run MindTerm SSH successfully. It is recommended that Classic Mac OS users use the MacSSH or NiftyTelnet SSH clients instead.