GAP homepage
(Groups, Algorithms and Programming)

GRAPE (GAP share package for graphs, geometries, groups) by
Leonard Soicher

Fundamental,
a program for computing fundamental groups and covers (uses GAP and GRAPE)

Overview
of MAGMA (Computational algebra system for algebra, number theory and
geometry)

Andries Brouwer's
DRG finder (instructions
here)

Bill Kocay's
Groups and
Graphs for Mac or Windows

PERMS 2.1, a Mathematica package for permutation groups by
Bernd Fiedler

SYMMETRICA, a program for algebraic combinatorics of the symmetric group,
from the University of Bayreuth

John Stembridge's
Maple packages: symmetric functions, posets, and Coxeter and Weyl groups
(with a
tutorial for Coxeter and Weyl)

Schur, a package for Lie groups
and symmetric polynomials by
Steven M. Christensen
and Associates, Inc.

PermGroup, an online permutation group calculator based on GAP4
