# To find Brauer Character for the special linear group SL(2,5) in GAP.

As suggest by Alexander Konovalov I load LoadPackage("ctbllib") and them worked for symmetric group $$S5$$. It worked for me as

gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]


But i tried same for Special linear group $$SL(2,5)$$, it does not works

true

gap> m:=SL(2,5);

SL(2,5)

gap> t:=CharacterTable("m") mod 2;

fail

gap>

• The package did load. It returned true. Commented Dec 25, 2018 at 8:43
• @Shaun Thanks for edit... Commented Dec 25, 2018 at 8:43
• @Shaun But not working to find Brauer Character... Commented Dec 25, 2018 at 8:44
• I don't know how to fix that, @neelkanth; I'm just saying that the problem doesn't seem to be with the package loading, as the title suggests. Commented Dec 25, 2018 at 8:45
• ok then i change the title.... Commented Dec 25, 2018 at 8:45

You are mixing up the (string) names of groups in the library and variables you choose to assign a group to. The group "M" in the libary is the monster simple group, and for it the Brauer table is not known.

The ATLAS name of $$SL(2,5)$$ is 2.L2(5), indeed we can get the table for it as

gap> t:=CharacterTable("2.L2(5)") mod 3;
BrauerTable( "2.A5", 3 )


Note that all of this is about pre-computed Brauer tables from the character table library. If you wanted to compute the Brauer table for an arbitrary finite group, you would have to find all irreducible modules (e.g. by splitting up the regular module), and then lift the Brauer character values appropriately (there currently is no pre-defined function which does so automatically).

• Ok thanks sir.... i will try this way and will tell you ..... Commented Dec 25, 2018 at 9:18
• Yes Sir now it is working....thanks... Commented Dec 25, 2018 at 9:22
• But How i will know in future about The ATLAS name of any other group.... Commented Dec 25, 2018 at 9:23
• @neelkanth If you are working with simple groups and their relatives, you might want to read through the preface of the ATLAS, as these names have become kind of standard. If you require the Brauer tables for other groups (and need to compute from scratch) I recommend the textbook by Lux and Pahlings published by Cambridge U.P. which contains GAP examples. Commented Dec 25, 2018 at 9:57
• @ahulpkr thanks sir I will purchase this book ... Commented Dec 25, 2018 at 12:27