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Dear GAP-Forum,

as far as I know, GAP should offer at least two ways to get the

character table of SL(2,5): visiting the GAP Character Table Libraries

by typing

CharTable( "SL", 2, 5 );

and pressing <ENTER> or making GAP calculate the character table.

However, what I received taking the latter way in GAP 3.4.4 follows:

gap> G := SpecialLinearGroup( 2, 5 );; G.name := "SL(2,5)";;

gap> CharTable( G );

Error, Record: element 'permDomain' must have an assigned value at

d := Permutation( d, G.permDomain ) ... in

arg[1].operations.RepresentativeOperation( arg[1], arg[2], arg[3],

OnPoints ) called from

RepresentativeOperation( C.group, g, C.representative ) called from

<elm> in <rec> called from

D.ClassElement( D, D.conjugacyClasses[nu].representative ^ power )

called from

DxPowerClass( D, i, -1 ) called from

...

brk>

Obviously, GAP prefers a permutation group presentation of SL(2,5) to

calculate the group's character table. As I found out by descending a

little deeper down to GAP's internal code, such a presentation is

computed by calling the function

G.operations.MakePermGroupP( <group> )

with the group G itself in place of the argument. For matrix groups G

like SL(2,5) this function sets a local variable P to

Size( G.field )^G.dimension

and decides how to continue by testing if P < 65536 or not. In both

cases the result --- G's permutation group presentation --- is bound

to the record component G.permGroupP, but a component

G.permDomain

is ONLY stored IF P >= 65536.

For the special linear group G=SL(2,5) is P=25 and hence accessing the

record component G.permDomain in the upper example will fail, of

course!

Now, here comes my question:

Is there any reason why G.permDomain is not bound by MakePermGroupP

whenever P is less than 65536 or is this a 'strange behaviour' ---

just to use Akihiro Munemasa's words (GAP-Forum, 12 May 93) ?

Mathias Kratzer

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