//D4.C2^3.A6.C2 //C2^4.A6.C2 FScale:=CyclotomicField(240:Sparse:=true); F:=FScale; Z4:=F.1^4; Z8:=F.1^2; sq2:=Z8+Z8^7; G:=MatrixGroup<4,F| [1,0,0,0, 0,1,0,0, 0,0,-1,0, 0,0,0,-1], [1,0,0,0, 0,-1,0,0, 0,0,-1,0, 0,0,0,1], [0,1,0,0, 1,0,0,0, 0,0,0,1, 0,0,1,0], [0,0,1,0, 0,0,0,1, 1,0,0,0, 0,1,0,0], [-Z4*(1+Z4)/2,0,0,Z4*(1+Z4)/2, 0,(1+Z4)/2,(1+Z4)/2,0, (1+Z4)/2,0,0,(1+Z4)/2, 0,-Z4*(1+Z4)/2,Z4*(1+Z4)/2,0], [Z4*Z8,0,0,0, 0,Z4*Z8,0,0, 0,0,Z8,0, 0,0,0,Z8]>; 1 1 C1 C2^4.A6.C2 3 [] 2 3 C2 C2*C4^2:C3:C2 2 <<1>> 1 4 C2 C2*S4 2 <<1>> 1 5 C2 C2^2:D4 2 <<1>> 1 6 C3 C3*S4 2 <<2>> 2 7 C3 C3*S3 1 <<1>, <1>> 1 8 C5 C5 0 <<1>, <1>, <2>> 1 10 C4 Q8:C2^2.D6 2 <<3>> -1 25 C2^2 C2^2 1 <<0, 1>, <1, 1>> 1 25 C2^2 C2^2*C4 1 <<0, 1>, <1, 0>> 1 25 C2^2 C2^2*C4 1 <<1, 0>, <1, 1>> 1 34 C6 C6 0 <<2>, <3>, <5>> -2 36 C6 C6 0 <<1>, <4>, <4>> 1 36 C6 C6 0 <<3>, <5>, <5>> 1 36 C6 C6 0 <<4>, <4>, <5>> 1 38 C3^2 C3^2 0 <<1, 0>, <1, 1>, <2, 1>> -1 60 C2*C4 C2*C4 1 <<1, 1>, <1, 2>> 1 60 C2*C4 C2*C4wrC2 1 <<1, 2>, <1, 3>> 1 60 C2*C4 C2*C4wrC2 1 <<0, 1>, <1, 1>> 1 100 C12 C12 0 <<1>, <8>, <9>> 1 100 C12 C12 0 <<8>, <9>, <11>> -3 157 C2^2*C4 C2^2*C4 0 <<0, 0, 3>, <1, 0, 2>, <1, 1, 1>> -1 157 C2^2*C4 C2^2*C4 0 <<1, 0, 2>, <1, 0, 3>, <1, 1, 2>> -1 157 C2^2*C4 C2^2*C4 0 <<0, 0, 1>, <0, 1, 3>, <1, 0, 1>> -3 157 C2^2*C4 C2^2*C4 0 <<1, 0, 1>, <1, 0, 2>, <1, 1, 1>> -3 157 C2^2*C4 C2^2*C4 0 <<0, 1, 3>, <1, 0, 1>, <1, 1, 3>> -3 157 C2^2*C4 C2^2*C4 0 <<1, 0, 2>, <1, 1, 2>, <1, 1, 3>> -3 157 C2^2*C4 C2^2*C4 0 <<0, 1, 3>, <1, 1, 2>, <1, 1, 3>> -1 157 C2^2*C4 C2^2*C4 0 <<1, 0, 1>, <1, 0, 2>, <1, 1, 3>> 1 157 C2^2*C4 C2^2*C4 0 <<1, 0, 1>, <1, 1, 2>, <1, 1, 3>> 1 157 C2^2*C4 C2^2*C4 0 <<0, 0, 1>, <1, 0, 1>, <1, 1, 1>> 1 157 C2^2*C4 C2^2*C4 0 <<1, 0, 2>, <1, 1, 1>, <1, 1, 2>> -1 193 C2*C8 C2*C8 0 <<0, 4>, <0, 7>, <1, 1>> -1 193 C2*C8 C2*C8 0 <<0, 3>, <1, 5>, <1, 7>> -1 193 C2*C8 C2*C8 0 <<0, 4>, <0, 5>, <1, 2>> -3 193 C2*C8 C2*C8 0 <<0, 3>, <0, 4>, <1, 2>> 1 193 C2*C8 C2*C8 0 <<0, 1>, <0, 3>, <1, 2>> 1 193 C2*C8 C2*C8 0 <<0, 1>, <0, 4>, <1, 1>> -3 230 C2*C4^2 C2*C4^2 0 <<0, 2, 1>, <0, 3, 1>, <1, 0, 1>> -1 230 C2*C4^2 C2*C4^2 0 <<0, 1, 2>, <0, 2, 3>, <1, 1, 0>> 1 230 C2*C4^2 C2*C4^2 0 <<0, 3, 1>, <1, 1, 0>, <1, 1, 1>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<2>>, <<1>> ]>> <6, <[ <<1>, <1>>, <<2>, <2>> ]>> <7, <[ <<1>, <1>, <2>>, <<1>, <3>, <3>>, <<3>, <4>, <4>>, <<2>, <2>, <4>> ]>> <8, <[ <<3>>, <<1>> ]>> <9, <[ <<0, 1>, <1, 1>>, <<0, 1>, <1, 0>> ]>> <10, <[ <<0, 1>, <1, 0>>, <<0, 1>, <1, 1>> ]>> <11, <[ <<1, 0>, <1, 1>> ]>> <12, <[ <<2>, <3>, <5>>, <<1>, <3>, <4>> ]>> <13, <[ <<1>, <4>, <4>>, <<2>, <2>, <5>> ]>> <14, <[ <<3>, <5>, <5>>, <<1>, <1>, <3>> ]>> <15, <[ <<4>, <4>, <5>>, <<1>, <2>, <2>> ]>> <16, <[ <<1, 0>, <1, 1>, <2, 1>>, <<1, 1>, <1, 2>, <2, 0>>, <<0, 2>, <2, 0>, <2, 1>>, <<0, 2>, <1, 0>, <1, 2>>, <<0, 1>, <2, 0>, <2, 1>>, <<1, 2>, <2, 0>, <2, 2>>, <<1, 0>, <2, 1>, <2, 2>>, <<0, 1>, <1, 0>, <1, 2>> ]>> <17, <[ <<1, 1>, <1, 2>>, <<0, 3>, <1, 2>> ]>> <18, <[ <<1, 2>, <1, 3>>, <<0, 1>, <1, 2>> ]>> <19, <[ <<0, 1>, <1, 1>>, <<0, 3>, <1, 3>> ]>> <20, <[ <<1>, <8>, <9>>, <<4>, <5>, <9>>, <<3>, <4>, <11>>, <<3>, <7>, <8>> ]>> <21, <[ <<8>, <9>, <11>>, <<4>, <7>, <9>>, <<1>, <3>, <4>>, <<3>, <5>, <8>> ]>> <22, <[ <<0, 0, 3>, <1, 0, 2>, <1, 1, 1>>, <<0, 1, 1>, <1, 1, 2>, <1, 1, 3>>, <<0, 1, 3>, <1, 0, 1>, <1, 0, 2>>, <<0, 0, 1>, <1, 0, 3>, <1, 1, 2>> ]>> <23, <[ <<1, 0, 2>, <1, 0, 3>, <1, 1, 2>>, <<0, 0, 3>, <1, 0, 2>, <1, 1, 2>>, <<1, 0, 2>, <1, 1, 2>, <1, 1, 3>>, <<0, 1, 1>, <1, 0, 2>, <1, 1, 2>>, <<1, 0, 2>, <1, 1, 1>, <1, 1, 2>>, <<0, 0, 1>, <1, 0, 2>, <1, 1, 2>>, <<0, 1, 3>, <1, 0, 2>, <1, 1, 2>>, <<1, 0, 1>, <1, 0, 2>, <1, 1, 2>> ]>> <24, <[ <<0, 0, 1>, <0, 1, 3>, <1, 0, 1>>, <<0, 0, 1>, <1, 0, 3>, <1, 1, 1>>, <<0, 0, 3>, <0, 1, 1>, <1, 1, 1>>, <<0, 1, 3>, <1, 0, 1>, <1, 1, 3>>, <<0, 0, 3>, <0, 1, 1>, <1, 1, 3>>, <<0, 0, 3>, <1, 0, 3>, <1, 1, 1>>, <<0, 1, 1>, <1, 0, 1>, <1, 1, 3>>, <<0, 0, 1>, <0, 1, 3>, <1, 0, 3>> ]>> <25, <[ <<1, 0, 1>, <1, 0, 2>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 1, 2>>, <<0, 0, 3>, <0, 1, 3>, <1, 0, 2>>, <<1, 0, 3>, <1, 1, 2>, <1, 1, 3>> ]>> <26, <[ <<0, 1, 3>, <1, 0, 1>, <1, 1, 3>>, <<0, 0, 1>, <0, 1, 3>, <1, 0, 3>>, <<0, 0, 3>, <1, 0, 3>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 3>, <1, 0, 1>>, <<0, 1, 1>, <1, 0, 1>, <1, 1, 3>>, <<0, 0, 3>, <0, 1, 1>, <1, 1, 1>>, <<0, 0, 3>, <0, 1, 1>, <1, 1, 3>>, <<0, 0, 1>, <1, 0, 3>, <1, 1, 1>> ]>> <27, <[ <<1, 0, 2>, <1, 1, 2>, <1, 1, 3>>, <<0, 1, 3>, <1, 0, 2>, <1, 1, 2>>, <<1, 0, 2>, <1, 0, 3>, <1, 1, 2>>, <<0, 0, 1>, <1, 0, 2>, <1, 1, 2>>, <<1, 0, 1>, <1, 0, 2>, <1, 1, 2>>, <<0, 1, 1>, <1, 0, 2>, <1, 1, 2>>, <<0, 0, 3>, <1, 0, 2>, <1, 1, 2>>, <<1, 0, 2>, <1, 1, 1>, <1, 1, 2>> ]>> <28, <[ <<0, 1, 3>, <1, 1, 2>, <1, 1, 3>>, <<0, 1, 3>, <1, 0, 2>, <1, 0, 3>>, <<0, 0, 3>, <1, 0, 3>, <1, 1, 2>>, <<0, 0, 1>, <1, 0, 1>, <1, 1, 2>>, <<0, 1, 1>, <1, 0, 1>, <1, 0, 2>>, <<0, 1, 1>, <1, 1, 1>, <1, 1, 2>>, <<0, 0, 3>, <1, 0, 2>, <1, 1, 3>>, <<0, 0, 1>, <1, 0, 2>, <1, 1, 1>> ]>> <29, <[ <<1, 0, 1>, <1, 0, 2>, <1, 1, 3>>, <<0, 0, 1>, <0, 1, 3>, <1, 1, 2>>, <<1, 0, 2>, <1, 0, 3>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 3>, <1, 0, 2>>, <<1, 0, 1>, <1, 1, 2>, <1, 1, 3>>, <<0, 0, 3>, <0, 1, 1>, <1, 0, 2>>, <<0, 0, 3>, <0, 1, 1>, <1, 1, 2>>, <<1, 0, 3>, <1, 1, 1>, <1, 1, 2>> ]>> <30, <[ <<1, 0, 1>, <1, 1, 2>, <1, 1, 3>>, <<0, 0, 1>, <0, 1, 3>, <1, 0, 2>>, <<1, 0, 3>, <1, 1, 1>, <1, 1, 2>>, <<0, 0, 1>, <0, 1, 3>, <1, 1, 2>>, <<1, 0, 1>, <1, 0, 2>, <1, 1, 3>>, <<0, 0, 3>, <0, 1, 1>, <1, 1, 2>>, <<0, 0, 3>, <0, 1, 1>, <1, 0, 2>>, <<1, 0, 2>, <1, 0, 3>, <1, 1, 1>> ]>> <31, <[ <<0, 0, 1>, <1, 0, 1>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 1, 1>>, <<0, 1, 1>, <1, 0, 1>, <1, 1, 1>>, <<0, 0, 3>, <0, 1, 3>, <1, 1, 3>>, <<0, 0, 3>, <1, 0, 3>, <1, 1, 3>>, <<0, 0, 3>, <0, 1, 3>, <1, 0, 3>>, <<0, 0, 1>, <0, 1, 1>, <1, 0, 1>>, <<0, 1, 3>, <1, 0, 3>, <1, 1, 3>> ]>> <32, <[ <<1, 0, 2>, <1, 1, 1>, <1, 1, 2>>, <<0, 1, 1>, <1, 0, 2>, <1, 1, 2>>, <<1, 0, 1>, <1, 0, 2>, <1, 1, 2>>, <<0, 0, 3>, <1, 0, 2>, <1, 1, 2>>, <<1, 0, 2>, <1, 0, 3>, <1, 1, 2>>, <<0, 1, 3>, <1, 0, 2>, <1, 1, 2>>, <<0, 0, 1>, <1, 0, 2>, <1, 1, 2>>, <<1, 0, 2>, <1, 1, 2>, <1, 1, 3>> ]>> <33, <[ <<0, 4>, <0, 7>, <1, 1>>, <<0, 3>, <0, 4>, <1, 5>> ]>> <34, <[ <<0, 3>, <1, 5>, <1, 7>>, <<0, 1>, <0, 3>, <1, 5>>, <<0, 5>, <0, 7>, <1, 1>>, <<0, 7>, <1, 1>, <1, 3>> ]>> <35, <[ <<0, 4>, <0, 5>, <1, 2>>, <<0, 4>, <1, 3>, <1, 6>>, <<0, 4>, <1, 6>, <1, 7>>, <<0, 1>, <0, 4>, <1, 2>> ]>> <36, <[ <<0, 3>, <0, 4>, <1, 2>>, <<0, 4>, <1, 5>, <1, 6>>, <<0, 4>, <1, 1>, <1, 6>>, <<0, 4>, <0, 7>, <1, 2>> ]>> <37, <[ <<0, 1>, <0, 3>, <1, 2>>, <<1, 5>, <1, 6>, <1, 7>>, <<1, 1>, <1, 3>, <1, 6>>, <<0, 5>, <0, 7>, <1, 2>> ]>> <38, <[ <<0, 1>, <0, 4>, <1, 1>>, <<0, 4>, <0, 7>, <1, 7>>, <<0, 3>, <0, 4>, <1, 3>>, <<0, 4>, <0, 5>, <1, 5>> ]>> <39, <[ <<0, 2, 1>, <0, 3, 1>, <1, 0, 1>>, <<0, 1, 3>, <0, 2, 1>, <1, 0, 1>>, <<0, 2, 3>, <1, 0, 3>, <1, 3, 3>>, <<0, 1, 2>, <0, 3, 1>, <1, 1, 0>>, <<0, 1, 2>, <0, 2, 3>, <1, 0, 1>>, <<0, 2, 3>, <1, 0, 3>, <1, 1, 1>>, <<0, 3, 2>, <1, 3, 0>, <1, 3, 3>>, <<0, 2, 3>, <0, 3, 2>, <1, 0, 1>>, <<0, 2, 1>, <1, 0, 3>, <1, 1, 0>>, <<0, 1, 2>, <0, 3, 1>, <1, 3, 3>>, <<0, 2, 1>, <1, 0, 3>, <1, 3, 0>>, <<0, 3, 1>, <0, 3, 2>, <1, 3, 3>>, <<0, 1, 3>, <1, 1, 1>, <1, 3, 0>>, <<0, 3, 1>, <1, 0, 1>, <1, 1, 1>>, <<0, 1, 3>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 3>, <0, 2, 3>, <1, 3, 3>>, <<0, 1, 2>, <0, 1, 3>, <1, 1, 0>>, <<0, 3, 2>, <1, 1, 1>, <1, 3, 0>>, <<0, 1, 3>, <0, 2, 1>, <1, 3, 3>>, <<0, 3, 1>, <1, 0, 3>, <1, 1, 1>>, <<0, 1, 2>, <1, 0, 1>, <1, 3, 0>>, <<0, 1, 2>, <1, 0, 3>, <1, 3, 0>>, <<0, 2, 1>, <0, 3, 2>, <1, 1, 0>>, <<0, 2, 3>, <0, 3, 2>, <1, 1, 0>> ]>> <40, <[ <<0, 1, 2>, <0, 2, 3>, <1, 1, 0>>, <<0, 1, 2>, <1, 0, 3>, <1, 1, 0>>, <<0, 3, 2>, <1, 0, 1>, <1, 3, 0>>, <<0, 2, 1>, <1, 0, 1>, <1, 3, 0>>, <<0, 2, 1>, <0, 3, 1>, <1, 3, 3>>, <<0, 2, 1>, <0, 3, 2>, <1, 3, 0>>, <<0, 2, 3>, <1, 0, 3>, <1, 1, 0>>, <<0, 3, 1>, <1, 0, 3>, <1, 3, 3>>, <<0, 1, 3>, <1, 0, 1>, <1, 1, 1>>, <<0, 2, 3>, <1, 0, 1>, <1, 1, 1>>, <<0, 1, 3>, <0, 2, 3>, <1, 1, 1>>, <<0, 1, 3>, <0, 2, 3>, <1, 0, 1>>, <<0, 2, 1>, <0, 3, 1>, <1, 0, 3>>, <<0, 1, 2>, <1, 3, 0>, <1, 3, 3>>, <<0, 2, 1>, <1, 0, 3>, <1, 3, 3>>, <<0, 3, 1>, <0, 3, 2>, <1, 1, 0>>, <<0, 2, 1>, <0, 3, 2>, <1, 0, 1>>, <<0, 1, 2>, <0, 2, 3>, <1, 0, 3>>, <<0, 3, 2>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 2>, <0, 1, 3>, <1, 3, 0>>, <<0, 3, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 3, 1>, <0, 3, 2>, <1, 1, 1>>, <<0, 1, 2>, <0, 1, 3>, <1, 3, 3>>, <<0, 1, 3>, <1, 3, 0>, <1, 3, 3>> ]>> <41, <[ <<0, 3, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 2>, <0, 1, 3>, <1, 3, 3>>, <<0, 1, 3>, <1, 3, 0>, <1, 3, 3>>, <<0, 2, 1>, <0, 3, 1>, <1, 3, 3>>, <<0, 1, 2>, <1, 3, 0>, <1, 3, 3>>, <<0, 3, 1>, <0, 3, 2>, <1, 1, 1>>, <<0, 3, 1>, <1, 0, 3>, <1, 3, 3>>, <<0, 3, 1>, <0, 3, 2>, <1, 1, 0>>, <<0, 3, 2>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 2>, <0, 2, 3>, <1, 1, 0>>, <<0, 1, 2>, <0, 1, 3>, <1, 3, 0>>, <<0, 3, 2>, <1, 0, 1>, <1, 3, 0>>, <<0, 2, 1>, <0, 3, 2>, <1, 3, 0>>, <<0, 2, 1>, <1, 0, 1>, <1, 3, 0>>, <<0, 1, 2>, <1, 0, 3>, <1, 1, 0>>, <<0, 2, 3>, <1, 0, 3>, <1, 1, 0>>, <<0, 1, 3>, <1, 0, 1>, <1, 1, 1>>, <<0, 1, 3>, <0, 2, 3>, <1, 1, 1>>, <<0, 2, 1>, <0, 3, 2>, <1, 0, 1>>, <<0, 1, 2>, <0, 2, 3>, <1, 0, 3>>, <<0, 2, 3>, <1, 0, 1>, <1, 1, 1>>, <<0, 2, 1>, <0, 3, 1>, <1, 0, 3>>, <<0, 2, 1>, <1, 0, 3>, <1, 3, 3>>, <<0, 1, 3>, <0, 2, 3>, <1, 0, 1>> ]>>