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 );;
MatScalarProducts( subt, subt.irreducibles, restricted );
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.