//D4.C2^3.S5 //C2^4.S5 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], [Z8,0,0,0, 0,Z8,0,0, 0,0,Z8,0, 0,0,0,-Z8]>; 1 1 C1 C2^4.S5 3 [] 1 2 C2 D4.D4 2 <<1>> 3 3 C2 C2*S4 2 <<1>> 1 4 C2 C2*D4 2 <<1>> 1 5 C3 C6 1 <<1>, <1>> 1 5 C3 C6 1 <<2>, <2>> 1 6 C5 C5 0 <<2>, <2>, <4>> 1 12 C4 C4wrC2 1 <<2>, <3>> 1 12 C4 C4wrC2 1 <<3>, <3>> -1 17 C2^2 C2^3 1 <<0, 1>, <1, 0>> 2 17 C2^2 C2*D4 1 <<1, 0>, <1, 1>> 1 17 C2^2 C2*D4 1 <<0, 1>, <1, 1>> -1 20 C2^2 C2^2 1 <<0, 1>, <1, 1>> 2 20 C2^2 C2^3 1 <<1, 0>, <1, 1>> 1 20 C2^2 C2^3 1 <<0, 1>, <1, 1>> -1 22 C6 C6 0 <<4>, <4>, <5>> -1 22 C6 C6 0 <<2>, <2>, <5>> 1 22 C6 C6 0 <<3>, <5>, <5>> 1 22 C6 C6 0 <<1>, <4>, <4>> 1 22 C6 C6 0 <<1>, <2>, <2>> -3 25 C2^3 C2^3 0 <<0, 0, 1>, <0, 1, 0>, <1, 1, 1>> -6 33 C2^3 C2^3 0 <<0, 1, 1>, <1, 0, 1>, <1, 1, 1>> -1 33 C2^3 C2^3 0 <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>> -1 33 C2^3 C2^3 0 <<0, 1, 0>, <0, 1, 1>, <1, 0, 1>> 1 33 C2^3 C2^3 0 <<0, 1, 0>, <1, 0, 0>, <1, 1, 1>> -3 33 C2^3 C2^3 0 <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>> -4 33 C2^3 C2^3 0 <<0, 1, 0>, <1, 0, 0>, <1, 0, 1>> -2 33 C2^3 C2^3 0 <<0, 1, 0>, <0, 1, 1>, <1, 0, 0>> 1 33 C2^3 C2^3 0 <<0, 1, 1>, <1, 0, 0>, <1, 0, 1>> 1 33 C2^3 C2^3 0 <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>> 1 36 C8 C8 0 <<1>, <3>, <6>> 1 36 C8 C8 0 <<1>, <4>, <5>> -1 38 C2*C4 C2*C4 0 <<0, 2>, <0, 3>, <1, 3>> -1 38 C2*C4 C2*C4 0 <<0, 1>, <0, 2>, <1, 0>> -1 38 C2*C4 C2*C4 0 <<0, 1>, <0, 1>, <1, 1>> 1 38 C2*C4 C2*C4 0 <<0, 2>, <0, 3>, <1, 1>> -2 38 C2*C4 C2*C4 0 <<0, 2>, <1, 0>, <1, 1>> -1 38 C2*C4 C2*C4 0 <<0, 2>, <0, 3>, <1, 0>> 1 38 C2*C4 C2*C4 0 <<0, 1>, <0, 2>, <1, 3>> 1 38 C2*C4 C2*C4 0 <<0, 1>, <0, 1>, <1, 0>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<1>, <1>>, <<2>, <2>> ]>> <6, <[ <<2>, <2>>, <<1>, <1>> ]>> <7, <[ <<2>, <2>, <4>>, <<1>, <3>, <3>>, <<3>, <4>, <4>>, <<1>, <1>, <2>> ]>> <8, <[ <<2>, <3>>, <<1>, <2>> ]>> <9, <[ <<3>, <3>>, <<1>, <1>> ]>> <10, <[ <<0, 1>, <1, 0>>, <<0, 1>, <1, 1>> ]>> <11, <[ <<1, 0>, <1, 1>> ]>> <12, <[ <<0, 1>, <1, 1>>, <<0, 1>, <1, 0>> ]>> <13, <[ <<0, 1>, <1, 1>>, <<0, 1>, <1, 0>> ]>> <14, <[ <<1, 0>, <1, 1>> ]>> <15, <[ <<0, 1>, <1, 1>>, <<0, 1>, <1, 0>> ]>> <16, <[ <<4>, <4>, <5>>, <<1>, <2>, <2>> ]>> <17, <[ <<2>, <2>, <5>>, <<1>, <4>, <4>> ]>> <18, <[ <<3>, <5>, <5>>, <<1>, <1>, <3>> ]>> <19, <[ <<1>, <4>, <4>>, <<2>, <2>, <5>> ]>> <20, <[ <<1>, <2>, <2>>, <<4>, <4>, <5>> ]>> <21, <[ <<0, 0, 1>, <0, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 0>, <1, 0, 1>>, <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>>, <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>>, <<0, 1, 0>, <1, 0, 0>, <1, 1, 1>>, <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>>, <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 0>, <1, 0, 1>, <1, 1, 0>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>>, <<0, 0, 1>, <0, 1, 0>, <1, 0, 0>>, <<0, 0, 1>, <0, 1, 0>, <1, 1, 0>> ]>> <22, <[ <<0, 1, 1>, <1, 0, 1>, <1, 1, 1>>, <<0, 1, 0>, <1, 0, 1>, <1, 1, 0>>, <<0, 1, 1>, <1, 0, 0>, <1, 1, 0>>, <<0, 1, 0>, <1, 0, 0>, <1, 1, 1>> ]>> <23, <[ <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>>, <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>> ]>> <24, <[ <<0, 1, 0>, <0, 1, 1>, <1, 0, 1>>, <<0, 1, 0>, <0, 1, 1>, <1, 1, 1>>, <<0, 1, 0>, <0, 1, 1>, <1, 1, 0>>, <<0, 1, 0>, <0, 1, 1>, <1, 0, 0>> ]>> <25, <[ <<0, 1, 0>, <1, 0, 0>, <1, 1, 1>>, <<0, 1, 0>, <1, 0, 1>, <1, 1, 0>>, <<0, 1, 1>, <1, 0, 0>, <1, 1, 0>>, <<0, 1, 1>, <1, 0, 1>, <1, 1, 1>> ]>> <26, <[ <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>>, <<1, 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>> ]>> <27, <[ <<0, 1, 0>, <1, 0, 0>, <1, 0, 1>>, <<0, 1, 0>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 1>, <1, 0, 0>, <1, 0, 1>>, <<0, 1, 1>, <1, 1, 0>, <1, 1, 1>> ]>> <28, <[ <<0, 1, 0>, <0, 1, 1>, <1, 0, 0>>, <<0, 1, 0>, <0, 1, 1>, <1, 1, 0>>, <<0, 1, 0>, <0, 1, 1>, <1, 1, 1>>, <<0, 1, 0>, <0, 1, 1>, <1, 0, 1>> ]>> <29, <[ <<0, 1, 1>, <1, 0, 0>, <1, 0, 1>>, <<0, 1, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 0>, <1, 0, 0>, <1, 0, 1>>, <<0, 1, 0>, <1, 1, 0>, <1, 1, 1>> ]>> <30, <[ <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>>, <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>>, <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>> ]>> <31, <[ <<1>, <3>, <6>>, <<5>, <6>, <7>>, <<1>, <2>, <3>>, <<2>, <5>, <7>> ]>> <32, <[ <<1>, <4>, <5>>, <<3>, <4>, <7>> ]>> <33, <[ <<0, 2>, <0, 3>, <1, 3>>, <<0, 1>, <0, 2>, <1, 1>> ]>> <34, <[ <<0, 1>, <0, 2>, <1, 0>>, <<0, 2>, <1, 0>, <1, 1>>, <<0, 2>, <1, 0>, <1, 3>>, <<0, 2>, <0, 3>, <1, 0>> ]>> <35, <[ <<0, 1>, <0, 1>, <1, 1>>, <<0, 1>, <1, 1>, <1, 1>>, <<0, 3>, <1, 3>, <1, 3>>, <<0, 3>, <0, 3>, <1, 3>> ]>> <36, <[ <<0, 2>, <0, 3>, <1, 1>>, <<0, 1>, <0, 2>, <1, 3>> ]>> <37, <[ <<0, 2>, <1, 0>, <1, 1>>, <<0, 1>, <0, 2>, <1, 0>>, <<0, 2>, <0, 3>, <1, 0>>, <<0, 2>, <1, 0>, <1, 3>> ]>> <38, <[ <<0, 2>, <0, 3>, <1, 0>>, <<0, 2>, <1, 0>, <1, 3>>, <<0, 2>, <1, 0>, <1, 1>>, <<0, 1>, <0, 2>, <1, 0>> ]>> <39, <[ <<0, 1>, <0, 2>, <1, 3>>, <<0, 2>, <0, 3>, <1, 1>> ]>> <40, <[ <<0, 1>, <0, 1>, <1, 0>>, <<1, 0>, <1, 1>, <1, 1>>, <<1, 0>, <1, 3>, <1, 3>>, <<0, 3>, <0, 3>, <1, 0>> ]>>