###################################################
##
## The Schur index is a measure of the size of
## the smallest field a matrix representation 
## can be defined over relative to the field 
## generated by the character values of that 
## representation.
## The program below uses some theorems to give an upper
## bound only. (But when the Schur index is 1, this
## is often sufficient.)
## See the test in Corollary 31 of chapter 22 of 
## Berkovich+Zhmud, Characters of Finite Groups, vol 2. 
##
##4-2004,wdj
####################################################

SchurIndexBound:=function(chi)
local G,H,IrrH,CG,n,i,L,B;
G:=UnderlyingGroup(chi);
L:=[DegreeOfCharacter(chi)];
CG:=ConjugacyClassesSubgroups(G);
n:=Length(CG);
for i in [2..(n-1)] do
 H:=Representative(CG[i]);
 IrrH:=Irr(H);
 L:=Union(L,[ScalarProduct(RestrictedClassFunction(chi,H),IrrH[1])]);
od;
B:=Gcd(L);
Print(L," \n"); 
return(B);
end;