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Dear Mrs. and Mr. Forum,

Jacob Hirbawi writes

I'm trying to look at the restriction of characters of a group on all of

its subgroups. The function "Restricted" seems like the logical choice, but

for some reason I can't get it to work.

Probably the GAP manual does not tell enough details about this problem.

Here is a solution.

# Define the parent group.

group:= PrimitiveGroup( 8, 3 );# Compute representatives of conjugacy classes of subgroups,

# and their character tables.

subgroups:= List( ConjugacyClassesSubgroups( group ), Representative );;

tables:= List( subgroups, CharTable );;# Compute (and store) the class fusions into 'group'.

List( subgroups, s -> FusionConjugacyClasses( s, group ) );;# Compute the restricted characters.

groupchar:= CharTable( group );

restricted:= List( tables,

t -> Restricted( groupchar, t, groupchar.irreducibles ) );# Example: Compute the decomposition into irreducibles for one subgroup.

subt:= CharTable( subgroups[11] );;

MatScalarProducts( subt, subt.irreducibles, restricted[11] );

Your last sentence indicates that you are aware of the fact that the update

GAP-3.4.2 has been released.

However, the above also works in GAP-3.4.0.

Kind regards

Thomas Breuer

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