"Source: Text/RepThy/Chtr.text";
"Line: 1079";
"Date: Fri Sep 26 12:10:12 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/RepThy/Chtr.text, line: 1079
// Example: H100E5 ()
print "Example: H100E5";
ei := GetEchoInput();
SetEchoInput(true);
G1 := Group<x, y|x^36, y^7, y^x = y^3>;
G, f := SolubleQuotient(G1, 36*7);
x := f(G1.1); y := f(G1.2);
C := sub<G|x^6,y>;
IsCyclic(C);
assert $1;
IsNormal(G, C);
assert $1;
Centralizer(G,C) eq C;
assert $1;
exists(l){l:l in LinearCharacters(C)|IsFaithful(l)};
c := Induction(l, G);
IsIrreducible(c);
assert $1;
Degree(c);
assert $1 eq 6;
CharacterField(c);
SchurIndex(c);
assert $1 eq 6;
SetEchoInput(ei);
