As the Bibliography shows,
GAP has been used in a wide variety of areas of
mathematics. On this page we first provide some direct links to
examples that are intended to give a flavour of the use of
GAP. Pointers to some further sources of examples are
Analyzing Rubik's Cube with GAP
An updated GAP 4 version of a GAP 3
example by Martin Schönert, 1993.
An almost classical permutation group of small degree is examined
with some elementary GAP commands.
Two fundamental groups from A. Cavicchioli
This example demonstrates some methods for the investigation of finitely
presented groups using two presentations of fundamental groups due to
Lifting a quotient of type McL of a finitely
An example by Alexander Hulpke
demonstrating how a known (non-solvable) quotient of a finitely
presented group can be extended with sovable normal subgroups.
Balanced presentations for covering
groups of simple groups
An example that demonstrates how the deficiency of some perfect
groups may be determined by a program PGRelFind using
GAP together with the
ACE package. 2001.
Quotients of Grigorchuk's group
Investigation of some factor groups of a group of automorphisms of
a binary tree defined by R. I. Grigorchuk.
A solvable subgroup of Fi23
In this example from the Diploma thesis of
Alexander Hulpke a solvable maximal
subgroup of Fi23 is constructed using information from
Constructing HS and Co3
This is a GAP 4 version of the last example in the paper
"Construction of Co3. An example of the use of an integrated system
for Computational Group Theory", Groups St Andrews 1997 in Bath,
by Alexander Hulpke and
A p-Group with Special Properties
Using a function provided by
Bettina Eick a p-group with rather
special properties of lower and upper central series, requested in
a Forum letter, is constructed and investigated, also using XGAP
to depict the lattice of its normal subgroups.
Further Sources of Examples
Alexander Hulpke keeps a
collection of worked-out
of problems raised in the GAP Forum.
In the section
of the home page for 'The Character Table Library'
Thomas Breuer provides a number of
examples from character and representation theory.
Götz Pfeiffer, in his paper
Character Tables of Weyl Groups in GAP,
gives a guideline for an implementation in GAP 3.
describes the use of a graphical interface for the investigation of
the subgroup structure of some groups aided by the graphical display
of parts of the subgroup lattice.
describes examples of the interactive use of coset table methods for
the investigation of finite fg groups.
Some other package manuals also contain rather extensive examples for
the use of the respective packages.
Further examples of the use of GAP can be
found in some discussions kept in the