"Source: Text/Group/GrpMatGen.text";
"Line: 1696";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatGen.text, line: 1696
// Example: H66E11 ()
print "Example: H66E11";
ei := GetEchoInput();
SetEchoInput(true);
F9<w> := GF(9);
y := w^6;  z := w^2;
J2A2 := MatrixGroup< 6, F9 | [y, 1-y, z,0,0,0, 1-y ,z, -1,0,0,0, z, -1,1+y, 
                              0,0,0,0,0,0, z, 1+y, y, 0,0,0,1+y, y, -1, 0,
                              0,0, y ,-1,1-y],
                             [1+y, z, y, 0,0,0, z, 1+y, z, 0,0,0, y, z, 1+y, 
                              0,0,0, z, 0,0,1-y, y, z, 0, z, 0, y, 1-y, y, 
                              0,0, z, z, y, 1-y],
                             [0,0,0,y, 0,0, 0,0,0,0,y, 0, 0,0,0,0,0,y,
                              y, 0,0,0,0,0, 0,y, 0,0,0,0, 0,0,y, 0,0,0] >;
J2A2;
Order(J2A2); 
assert $1 eq 1209600;
FactoredOrder(J2A2);
IsSoluble(J2A2);    
assert not $1;
IsPerfect(J2A2);
assert $1;
IsSimple(J2A2);
assert not $1;
S2 := SylowSubgroup(J2A2, 2);
IsAbelian(S2); 
assert not $1;
IsNilpotent(S2);
assert $1;
IsSpecial(S2);
assert not $1;
SetEchoInput(ei);
