InstallMethod( ClassPositionsOfCentre,
    "for a homogeneous list",
    [ IsHomogeneousList ],
    function( chi )
    local deg, mdeg, degsquare;

    deg:= chi[1];
    mdeg:= - deg;
    degsquare:= deg^2;

    return Filtered( [ 1 .. Length( chi ) ],
               i -> chi[i] = deg or chi[i] = mdeg or
                    ( IsCyc( chi[i] ) and IsCycInt( chi[i] )
                      and chi[i] * GaloisCyc( chi[i], -1 ) = degsquare ) );
    end );



list_max:=function(L)
	local i, K, S;
	K:=0;
	for i in [1..Length(L)] do
		if K<L[i] then 
			K:=L[i]; S:=i;
		fi;
	od;
	return [K, S];
end;

list_remoting:=function(L, K)
	local i, H;
	H:=[];
	for i in [1..Length(L)] do
		if i<K then Add(H, L[i]); else if i>K then Add(H, L[i]); fi; fi;		
	od; 
	return H;
end;

list_ordering:=function(L)
	local K, N,i;
	K:=[]; N:=L;
	for i in [1..Length(L)] do
		Add(K, list_max(N)[1]);
		N:=list_remoting(N,list_max(N)[2]);
		od;
	return K;
end;

		
Element_howmany_noncent_ConjugacyClasses:=function(G,K)
	local L, i, j;
	L:=list_ordering(SizesConjugacyClasses(CharacterTable(G)));
	j:=0;
	if K>0 then
	for i in [1..Length(L)] do
		j:=j+L[i];
		if j>=K then
			return i;
		fi;
	od;
	else return 0;
	fi;
end;

centreofcharacter:=function(f, G)
	local i,s;
	s:=0;
	for i in [1..NrConjugacyClasses(G)] do
		if f[1]=AbsoluteValue(f[i]) then 
			s:=s+Size(ConjugacyClasses(G)[i]); fi;
	od;	
	return s;
end;

Ga_not1:=function(n)
	local G,C,i,j,s,f;
	for i in [1..n] do
		G:=SymmetricGroup(i);
		C:=CharacterTable("symmetric", i);
		for j in [1..NrConjugacyClasses(G)] do
			f:=Irr(C)[j];	
			s:=Element_howmany_noncent_ConjugacyClasses(G,(DegreeOfCharacter(f)^2-1)*centreofcharacter(f,G));
			if s>1 
				then Print([i, s, CharacterParameters(C)[j]]); Print("\n ");
			fi;
		od;		
	od;
end;