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 


Groups32 resides on a public account on the server As of 10/28/04 the server no longer will accept access via Telnet.  Use of Telnet access has been replaced by SSH.  Groups32 can now be run by:

Use groups32  as login and password from a SSH client program     OR
If your operating system or browser supports SSH, you can enter
  on the command line and give groups32 as password

If you experience difficulty accessing Groups32 using SSH please report to

It is recommended that users new to Groups32 read the sample session file (pdf format) while using Groups32 for the first time.   View or download Sample Session




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.

              IDENTIFY COMMAND
This is a  new command added July 2004 on an experimental basis.  It  is mostly useful for finding the built-in group isomorphic to an  imported group (e.g. from PERMGRP).





    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).
Unix/Linux 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.
Web/Java 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.