# F:=Rationals();
local result, l;
result:= rec();
result.comment:=
"2a\"M20 = 2^5:A5 as 10 x 10 monomial matrices over Z.\n\
Representation 10b.\n\
Absolutely irreducible representation.\n\
Schur Index 1.\n\
\n\
SEED:\n\
Nonzero v negated by x and fixed by y*x*y*x*y^-1*x*y^-1\n\
where <x,y*x*y*x*y^-1*x*y^-1> = 2^5:S3.\n\
v has 2 x 10 = 20 images under G; <v> has 10 images under G.\n\
BASIS:\n\
NSB([x,y]) with above v.\n\
\n\
Possible matrix entries are in {-1,0,1}.\n\
\n\
Average number of nonzero entries for any element of the group:\n\
10  (exactly 10%).\n\
\n\
Entry  Av/Mat  %Av/Mat\n\
    0      90       90\n\
   ±1      10       10\n\
    1       5        5\n\
   -1       5        5\n\
";
result.symmetricforms:= [];
result.antisymmetricforms:= [];
result.hermitianforms:= [];
result.centralizeralgebra:= [];
result.generators:= List( [ [
-1,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,
0,-1,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,-1,0,0]
,[
0,1,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,1,0,0,
0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,1]
], l -> List( [ 0 .. 9 ],
i -> l{ [ i*10+1 .. (i+1)*10 ] } ) );


Add( result.symmetricforms, IdentityMat(10) );


Add( result.centralizeralgebra, IdentityMat(10) );
return result;