"Source: Text/Group/GrpData.text";
"Line: 2861";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpData.text, line: 2861
// Example: H73E17 ()
print "Example: H73E17";
ei := GetEchoInput();
SetEchoInput(true);
D:= IntegralMatrixGroupDatabase();
#D;
assert $1 eq 222;
G:= Group(D, 8, 7); Construction(D, 8, 7);
DQ:= RationalMatrixGroupDatabase();
H:= Group(DQ, 8, 3); L:= Lattice(DQ, 8, 3);
F:= PositiveDefiniteForm(G);
for s in Sublattices(G) do
  B:= BasisMatrix(s);
  FF:= B * F * Transpose(B);
  ok, T:= IsIsometric(LatticeWithGram(FF div GCD(Eltseq(FF))), L);
  if ok then break; end if;
end for;
assert ok;
T:= Matrix(Rationals(), T*B);
[Matrix(Integers(), T*Matrix(G.i)*T^-1) in H : i in [1..Ngens(G)]];
SetEchoInput(ei);
