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Dear GAP Forum,

Dima Pasechnik wrote

Looking at the field "text" of CharTable("3^(1+10):U5(2):2"), on sees the following: "table computed with CliffordTable( U5(2).2 -> 3^10:U5(2).2 -> 3^1+10:U5(2).2 )"So it seems that this table was computed using a

(semi) automated procedure.

In fact, GAP has the function CliffordTable, unfortunately

undocumented, AFAIK.Could perhaps someone who knows about this functions

be so kind to explain how it can be used (or at least tell,

who is to ask) ? As a matter of

fact, we need to compute the character table of

3^1+10:(2xU5(2).2), so we are wondering if

CliffordTable is the right thing to look at in this

respect.

Indeed the character table of 3^(1+10):U5(2):2 has been

computed using Clifford matrices

(also called Fischer matrices by some authors).

The ideas of this approach can be found in

@proceedings{MR91, title = "Representation theory of finite groups and finite--dimensional algebras", booktitle = "Representation theory of finite groups and finite--dimensional algebras", editor = "G.~O. Michler and C.~R. Ringel", series = "Progress in Mathematics", volume = "95", year = "1991", publisher = Birkhaeus, }

Although there are GAP functions that help to construct

character tables along these lines (We would not call the

procedure semi-automated, at most semi-semi-automated),

this code is not documented because it has not been tested

thoroughly enough.

The Clifford matrices method would in principle be the right

method to compute a table such as that of 3^1+10:(2xU5(2).2),

but we cannot recommend the GAP code mentioned above for use.

So if one really wants to compute this character table,

it is perhaps worth a try to use the Dixon-Schneider method,

since computers are getting faster and larger.

More precisely, one could follow use the functions described

in the manual section ``Advanced Methods for Dixon-Schneider

Calculations'' (and the example in the following section).

Another question is whether one needs to compute the

character table at all.

Probably the group in question is the 3B normalizer in the

Fischer group Fi24, and if one would be interested for example

only in the permutation character of Fi24 corresponding to the

action on the cosets of the 3B normalizer

then the known table of the intersection with the simple group

Fi24' would suffice.

Thomas Breuer and Alexander Hulpke

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