# F:=Rationals(); local result, l; result:= rec(); result.comment:= "2a\"M20 = 2^5:A5 as 6 x 6 monomial matrices over Z.\n\ Representation 6a.\n\ Absolutely irreducible representation.\n\ Schur Index 1.\n\ \n\ SEED:\n\ Nonzero v fixed by x and y*x*y^-1 where = 2^4:D10.\n\ v has 2 x 6 = 12 images under G; has 6 images under G.\n\ BASIS:\n\ NSB([y,x]) 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\ 6 (about 16.667%).\n\ \n\ Entry Av/Mat %Av/Mat\n\ 0 30 83.333 [83+1/3]\n\ ±1 6 16.667 [16+2/3]\n\ 1 3 8.333 [ 8+1/3]\n\ -1 3 8.333 [ 8+1/3]\n\ "; result.symmetricforms:= []; result.antisymmetricforms:= []; result.hermitianforms:= []; result.centralizeralgebra:= []; result.generators:= List( [ [ 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,0,1,0,0, 0,0,-1,0,0,0, 0,0,0,0,0,-1, 0,0,0,0,1,0] ,[ 0,1,0,0,0,0, 0,0,1,0,0,0, 1,0,0,0,0,0, 0,0,0,0,1,0, 0,0,0,0,0,1, 0,0,0,1,0,0] ], l -> List( [ 0 .. 5 ], i -> l{ [ i*6+1 .. (i+1)*6 ] } ) ); Add( result.symmetricforms, IdentityMat(6) ); Add( result.centralizeralgebra, IdentityMat(6) ); return result;