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I was asked how to compute the decomposition of a permutation character for

Fi_{24}' into irreducible ones. I don't really see whether there are

appropriate function(s) to do it. Could somebody give an advise how to do it

in GAP, if it's possible?

It rather depends on the form in which you have the permutation

character. If it's actually as a character with the classes in the

standard order then this should be easy, just recover the character

table with

ct := CharTable("F3+");;

And then you can take inner products:

For example:

List([1..Length(ct.irreducibles)],i->ScalarProduct(ct, permchar,i));

Will return a list giving the multiples of the irreducibles which

contribute to permchar.

If you have explicit permutations for your permutation character

then

a) It must be one of a handfull of known permutation characters

because all the others are too big. You can probably look up the

answer.

b) Otherwise you need to identify the classes of elements in your

permutation group with the standard named classes in F24'. This

problem has been discussed on this forum before. There is no totally

generic simple way, but it's not usually too hard in any particular

case.

Finally, if you just have the subgroup whose cosets you are

permuting (in some sense) your best bet is probably to work out it's

character table (though this is non-trivial for the larger ones) and

then induce the trivial character.

If you are doing a lot of computing in this group, you might want to

get in touch with me directly. I have some special-purpose programs

for computing efficiently in groups of this size, and I have quite a

lot of experience with this particular group.

Steve

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