local result, l, i; i:= Sqrt(-1); result:= rec(); result.comment:= "G has 160 images of v = V.1.\n\ \n\ 0 296 0 74 0\n\ -1 17 1/2 4 3/8\n\ 1 17 1/2 4 3/8\n\ -i - 1 8 1/2 2 1/8\n\ -i 17 1/2 4 3/8\n\ -i + 1 8 1/2 2 1/8\n\ i - 1 8 1/2 2 1/8\n\ i 17 1/2 4 3/8\n\ i + 1 8 1/2 2 1/8\n\ "; result.symmetricforms:= []; result.antisymmetricforms:= []; result.hermitianforms:= []; result.centralizeralgebra:= []; result.generators:= List( [ [ -1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,-i,0,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,-i,0,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,i-1,1,-i,-i-1,-1,1,0,-i-1,0,0,-i,i+1,0,0,i-1,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0, -1,-i,0,0,0,1,-i,i,i,0,i,0,0,0,0,1,-i,0,0,0, 0,0,0,-i+1,-i+1,0,0,i-1,0,i-1,0,-i+1,i,i+1,0,-i,0,-i,0,0, 0,i-1,-i+1,-i+1,0,-1,0,0,0,-1,0,-i,i+1,i+1,0,0,0,-i+1,0,0, 0,-i+1,-1,i,i+1,i+1,0,-1,0,0,0,i+1,-i-1,0,0,-i+1,0,0,0,0, 0,-i,i,0,1,-i+1,i-1,1,i+1,0,0,0,0,0,i,-i-1,0,0,-i-1,-i+1, 0,0,0,0,0,0,0,0,0,0,0,-i,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0, 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,-i,0,0,0,1,0,0,0,0,1,0,0,-1,0,0,-i-1,1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-i,0] ,[ 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,i-1,0,1,0,0,0,0,1,0,-i,0,-i,0,0, 0,0,0,-i-1,-i-1,0,0,i+1,0,i+1,0,-i-1,1,-i+1,0,-1,0,-1,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-i,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,-1,0,-i,i,-1,1,0,0,0,0,-i,0,0,i,1,i, 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,i,0,-1,1,i,0,0,-1,1,0,i,0,0,0,-i,1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, i,0,0,0,i-1,0,-i-1,i+1,i,0,1,0,0,0,-1,-i+1,-i-1,0,-i+1,i, 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,-i,0,0,0,1,0,0,0,0,1,0,0,-1,0,0,-i-1,1, 0,i+1,-i,-1,i-1,i,-i,0,i-1,0,0,-1,-i+1,0,0,i+1,0,0,0,0, i+1,0,0,i,i+1,0,i-1,-i,-i+1,0,-i,i+1,-1,0,0,-i,i-1,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0] ], l -> List( [ 0 .. 19 ], i -> l{ [ i*20+1 .. (i+1)*20 ] } ) ); l:= [ 6,-i,i,-i,-i,0,-i,i,1,-i-1,1,i-1,0,1,0,i+1,-i+1,0,i,1, i,6,1,1,0,-i,0,1,-i,-i,i+1,-i,i,0,1,-1,-i-1,1,i,0, -i,1,6,0,1,1,-i,0,0,i,1,i,-i,-i,-1,-i,i+1,-1,0,i, i,1,0,6,-1,i,-1,0,0,1,1,-1,-i,-i,-1,i,0,-1,i-1,-i, i,0,1,-1,6,-1,-i+1,1,-1,1,0,-1,1,0,-1,i,-i-1,i,1,i-1, 0,i,1,-i,-1,6,i,-i,-i+1,0,-i+1,0,1,i,0,i,1,1,1,i-1, i,0,i,-1,i+1,-i,6,1,i+1,1,-i,-1,0,i+1,-1,-i+1,i,-i+1,1,1, -i,1,0,0,1,i,1,6,-i-1,-1,i,1,-1,i,1,1,i+1,-i,i+1,-1, 1,i,0,0,-1,i+1,-i+1,i-1,6,0,-1,-i+1,1,-1,-1,i,1,i,1,1, i-1,i,-i,1,1,0,1,-1,0,6,-i+1,0,i,i,i-1,1,-i,-i,-1,-i+1, 1,-i+1,1,1,0,i+1,i,-i,-1,i+1,6,0,i,-i+1,1,i,1,1,0,0, -i-1,i,-i,-1,-1,0,-1,1,i+1,0,0,6,1,-i,i+1,i,1,-1,1,0, 0,-i,i,i,1,1,0,-1,1,-i,-i,1,6,-1,-i-1,0,-1,0,i+1,-1, 1,0,i,i,0,-i,-i+1,-i,-1,-i,i+1,i,-1,6,i,i,0,i,-i,0, 0,1,-1,-1,-1,0,-1,1,-1,-i-1,1,-i+1,i-1,-i,6,0,0,-i+1,1,1, -i+1,-1,i,-i,-i,-i,i+1,1,-i,1,-i,-i,0,-i,0,6,i,0,-i-1,1, i+1,i-1,-i+1,0,i-1,1,-i,-i+1,1,i,1,1,-1,0,0,-i,6,-1,-1,i, 0,1,-1,-1,-i,1,i+1,i,-i,i,1,-1,0,-i,i+1,0,-1,6,0,i, -i,-i,0,-i-1,1,1,1,-i+1,1,-1,0,1,-i+1,i,1,i-1,-1,0,6,-i+1, 1,0,-i,i,-i-1,-i-1,1,-1,1,i+1,0,0,-1,0,1,1,-i,-i,i+1,6]; Add( result.hermitianforms, List( [ 0 .. 19 ], i -> l{ [ i*20+1 .. (i+1)*20 ] } ) ); Add( result.centralizeralgebra, IdentityMat(20) ); return result;