The Multiplicity-Free 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.

The following errors in the paper mentioned above have been found.

M₁₂.2

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 A₈.2 in the first column by A₈.2 <= A₈.2 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.

The file for accessing the database of multiplicity-free permutation characters of sporadic simple groups and their automorphism groups contains the following GAP objects.

MULTFREEINFO

is the global variable that encodes the faithful multiplicity-free 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 multiplicity-free possible permutation characters contains the following GAP objects.

MultFreeFromTOM

is a function that computes the multiplicity-free permutation characters of a character table from the table of marks of the group.

MultFree

is a function that can be used for computing multiplicity-free 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.

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.

File created on 19-Sep-2000 by Thomas Breuer.
Last modified on 08-Dec-2001 by Thomas Breuer.