local result, l, i;
i:= Sqrt(-1);
result:= rec();
result.comment:=
"4b\"M20 as 4 x 4 matrices over Z[i].\n\
Absolutely irreducible representation.\n\
Schur Index 1.\n\
\n\
SEED:\n\
Nonzero v s.t. v.y = v and v.xyxy^-1x^-1 = i*v where <y,xyxy^-1x^-1> = 4.4^2:3.\n\
v has 4 x 20 = 80 images under G; <v> has 20 images under G.\n\
BASIS:\n\
All in v^G: {v,v*x,v*x*y,v*x*y^2}.\n\
\n\
Possible matrix entries for any element of the group:\n\
The 9 elements of {0,1,-1,i,-i,1+i,1-i,-1+i,-1-i} only.\n\
The possible norms are in {0,1,2} only.\n\
\n\
Average number of nonzero entries for any element of the group:\n\
11 + 1/5  (11.2; 70% exactly).\n\
\n\
Entry    Av/Mat  %Av/Mat\n\
   0      4.8     30\n\
   1      1.6     10\n\
  -1      1.6     10\n\
   i      1.6     10\n\
  -i      1.6     10\n\
 1+i      1.2      7.5\n\
 1-i      1.2      7.5\n\
-1+i      1.2      7.5\n\
-1-i      1.2      7.5\n\
Norm 0    4.8     30\n\
Norm 1    6.4     40\n\
Norm 2    4.8     30\n\
nonzero  11.2     70\n\
";
result.symmetricforms:= [];
result.antisymmetricforms:= [];
result.hermitianforms:= [];
result.centralizeralgebra:= [];
result.generators:= List( [ [
0,1,0,0,
-i,-i-1,-i+1,0,
0,0,i,0,
-1,-1,-1,-1]
,[
1,0,0,0,
0,0,1,0,
0,0,0,1,
0,1,0,0]
], l -> List( [ 0 .. 3 ],
i -> l{ [ i*4+1 .. (i+1)*4 ] } ) );


l:= [
2,-1,-1,-1,
-1,2,-i,i,
-1,i,2,-i,
-1,-i,i,2];
Add( result.hermitianforms, List( [ 0 .. 3 ],
i -> l{ [ i*4+1 .. (i+1)*4 ] } ) );

Add( result.centralizeralgebra, IdentityMat(4) );
return result;