"Source: Text/LieTheory/GrpLie.text";
"Line: 672";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/GrpLie.text, line: 672
// Example: H113E5 ()
print "Example: H113E5";
ei := GetEchoInput();
SetEchoInput(true);
q := 5; k := GF(q); K := GF(q^2);
G := GroupOfLieType( "A3", K );
A := AutomorphismGroup(G);
AGRP := GammaGroup( k, A );
c := OneCocycle( AGRP, [GraphAutomorphism(G, Sym(3)!(1,3))] );
T := TwistedGroupOfLieType(c);
T eq TwistedGroupOfLieType(RootDatum("A3":Twist:=2),k,K);
assert $1;
G eq UntwistedOvergroup(T);
assert $1;
x := Random(G); x in T;
x := RelativeRootElement(T,2,[Random(K)]); x;
x in T;
assert $1;
SetEchoInput(ei);
