"Source: Text/Group/GrpMatInf.text";
"Line: 1165";
"Date: Thu Apr  1 11:57:57 2021";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatInf.text, line: 1165
// Example: H68E11 ()
print "Example: H68E11";
ei := GetEchoInput();
SetEchoInput(true);
// irreducible but (evidently) imprimitive
K<w> := QuadraticField (2);
G := MatrixGroup< 8, K |                  
    [1/2*w,1/2*w,0,0,0,0,0,0,-1/2*w,1/2*w,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
     0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
     0,0,0,1],                                                            
    [1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
     0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],        
    [0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0, 
    0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0] >;
G;                                                                        
IsIrreducibleFiniteNilpotent(G);
assert $1;
r, B := IsPrimitiveFiniteNilpotent(G);
r;
assert not $1;
#B;
assert $1 eq 2;
SetEchoInput(ei);
