The MultiplicityFree Permutation Characters
of the Sporadic Simple Groups
and their Automorphism Groups
The purpose of this page is to provide online access to the information
that was published in the following paper.
Thomas Breuer
and Klaus Lux.
The multiplicityfree Permutation Characters of the Sporadic Simple
Groups and their Automorphism Groups.
Comm. Algebra, 24(7):22932316, 1996.

Errata
The following errors in the paper mentioned above have been found.
 M_{12}.2

In the last character (of degree 990), replace the constituent 45a^{+}
by 45a^{}.
 HS

In the second degree 352 character, replace the constituent 154b by 154c.
(Note that this character is the image of the first degree 352 character
under the outer automorphism of HS.)
 HS.2

In the last degree 2200 character,
replace the entry A_{8}.2 in the first column by
A_{8}.2 <= A_{8}.2 x 2 .
 ON

In the third and fourth character, replace the constituent 32395a by 32395b.
(Note that these characters are the images of the first two characters
under the outer automorphism of ON.)
We thank Jürgen Müller for pointing out these errors.
GAP Code
The file for accessing the database
of multiplicityfree permutation characters of sporadic simple groups
and their automorphism groups
contains the following GAP objects.
 MULTFREEINFO

is the global variable that encodes the faithful multiplicityfree
permutation characters of the sporadic simple groups and their
automorphism groups, as classified in the paper mentioned above
(modulo the bug fixes).
 MultFreePermChars

is a function that can be used for computing more detailed data
about the permutation characters from the compact information
stored in MULTFREEINFO.
The file for computing multiplicityfree
possible permutation characters
contains the following GAP objects.
 MultFreeFromTOM

is a function that computes the multiplicityfree permutation
characters of a character table from the table of marks of the group.
 MultFree

is a function that can be used for computing multiplicityfree
characters that are possible permutation characters,
relative to a given table of a subgroup.
The functions MultFreeFromTOM and
MultFree are GAP 4 versions of the
GAP 3 functions with the same names that have been printed in the paper
mentioned above.
Examples
A few examples how to use the database in GAP are provided
in DVI format and
in HTML format.
Feedback
Any comments about the theory, the database, and the GAP functions
are very welcome.
If you have found important features missing or if there is a bug,
let us know and we will try to address it in an improved version.
Messages should be sent to
Thomas Breuer
or Klaus Lux.
Related Links
[GAP Home (Aachen)]
[GAP Home (St Andrews)]
[Examples on Permutation Characters]
[The GAP Character Table Library]
File created on 19Sep2000 by Thomas Breuer.
Last modified on 08Dec2001 by Thomas Breuer.