"Source: Text/Group/GrpMatInf.text";
"Line: 1062";
"Date: Thu Apr  1 11:57:57 2021";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatInf.text, line: 1062
// Example: H68E9 ()
print "Example: H68E9";
ei := GetEchoInput();
SetEchoInput(true);
G := MatrixGroup<10, K | [
    Matrix(SparseMatrix(K, 10, 10, [
    <1, 3, -1>, <2, 1, 1>, <2, 2, 1>, <2, 3, 1>, <2, 4, 1>, <2, 5, 1>, 
    <3, 4, -1>, <4, 5, -1>, <5, 2, -1>, <6, 8, -1>, <7, 6, 1>, 
    <7, 7, 1>, <7, 8, 1>, 
    <7, 9, 1>, <7, 10, 1>, <8, 9, -1>, <9, 10, -1>, <10, 7, -1>])),
    Matrix(SparseMatrix(K, 10, 10, [
    <1, 2, 1>, <2, 3, 1>, <3, 1, -1>, <3, 2, -1>, <3, 3, -1>, <3, 4, -1>, 
    <3, 5, -1>, <4, 4, 1>, <5, 1, 1>, <6, 7, 1>, <7, 8, 1>, <8, 6, -1>, 
    <8, 7, -1>, <8,8, -1>, <8, 9, -1>, <8, 10, -1>, <9, 9, 1>, <10, 6, 1>])),
    ScalarMatrix(K, 10, -1),
    Matrix(SparseMatrix(K, 10, 10, [
    <1, 6, 1>, <2, 7, 1>, <3, 8, 1>, <4, 9, 1>, <5, 10, 1>, <6, 1, w + 3>, 
    <7, 2, w + 3>, <8, 3, w + 3>, <9, 4, w + 3>, <10, 5, w + 3>])),
    Matrix(SparseMatrix(K, 10, 10, [
    <1, 6, 1>, <2, 7, 1>, <3, 8, 1>, <4, 9, 1>, <5, 10, 1>, 
    <6, 1, 1/5*(5*w - 7)>, <7, 2, 1/5*(5*w - 7)>, <8, 3, 1/5*(5*w - 7)>, 
    <9, 4, 1/5*(5*w - 7)>, <10, 5, 1/5*(5*w - 7)>]))
]> where w := K.1 where K := ext<K|Polynomial(K, [1, 0, 1])> where K is 
RationalField();

IsIrreducible (GModule (G));
assert $1;
IsSolubleByFinite (G);
assert $1;

flag := HasFiniteRank (G);
"G has finite rank?", flag;

h := HirschNumber(G);
"Hirsch number of G is ", h;

H := sub<G | G.2 * G.1 * G.2, G.3 * G.4, G.5>;
HasFiniteIndex (G, H);
assert $1;
SetEchoInput(ei);
