68.3 Comparison of Class Functions

With respect to \= and \<, class functions behave equally to their lists of values (see ValuesOfClassFunction). So two class functions are equal if and only if their lists of values are equal, no matter whether they are class functions of the same character table, of the same group but w.r.t. different class ordering, or of different groups.

gap> grps:= Filtered( AllSmallGroups( 8 ), g -> not IsAbelian( g ) );
[ <pc group of size 8 with 3 generators>, 
  <pc group of size 8 with 3 generators> ]
gap> t1:= CharacterTable( grps[1] );  SetName( t1, "t1" );
CharacterTable( <pc group of size 8 with 3 generators> )
gap> t2:= CharacterTable( grps[2] );  SetName( t2, "t2" );
CharacterTable( <pc group of size 8 with 3 generators> )
gap> irr1:= Irr( grps[1] );
[ Character( t1, [ 1, 1, 1, 1, 1 ] ), Character( t1, [ 1, 1, -1, 1, -1 ] ), 
  Character( t1, [ 1, -1, 1, 1, -1 ] ), Character( t1, [ 1, -1, -1, 1, 1 ] ),
  Character( t1, [ 2, 0, 0, -2, 0 ] ) ]
gap> irr2:= Irr( grps[2] );
[ Character( t2, [ 1, 1, 1, 1, 1 ] ), Character( t2, [ 1, 1, -1, 1, -1 ] ), 
  Character( t2, [ 1, -1, 1, 1, -1 ] ), Character( t2, [ 1, -1, -1, 1, 1 ] ), 
  Character( t2, [ 2, 0, 0, -2, 0 ] ) ]
gap> irr1 = irr2;
true
gap> IsSSortedList( irr1 );
false
gap> irr1[1] < irr1[2];
false
gap> irr1[3] < irr1[2];
true

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