//SL(2,3):A4.D4 //A4^2.D4 FScale:=CyclotomicField(24:Sparse:=true); F:=FScale; Z4:=F.1^2; sq2:=F.1+F.1^7; G:=MatrixGroup<4,F| [-Z4/2,-Z4/2,-Z4/2,-Z4/2, -1/2,1/2,-1/2,1/2, -1/2,-1/2,1/2,1/2, Z4/2,-Z4/2,-Z4/2,Z4/2], [-1/sq2,0,-1/sq2,0, 0,Z4/sq2,0,Z4/sq2, Z4/sq2,0,-Z4/sq2,0, 0,1/sq2,0,-1/sq2], [-1/sq2,-1/sq2,0,0, Z4/sq2,-Z4/sq2,0,0, 0,0,Z4/sq2,Z4/sq2, 0,0,1/sq2,-1/sq2], [Z4,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,-Z4], [Z4,0,0,0, 0,0,Z4,0, 0,Z4,0,0, 0,0,0,Z4]>; 1 1 C1 A4^2.D4 3 [] 1 3 C2 D4:D4 2 <<1>> 1 4 C2 C2*S4 2 <<1>> 4 5 C2 C2*S4 2 <<1>> 1 6 C2 C2*D4 2 <<1>> 1 7 C2 C2*D4 2 <<1>> 1 8 C3 C3*S4 2 <<2>> 1 9 C3 C3*S3 1 <<1>, <1>> 1 9 C3 C3*S3 1 <<2>, <2>> 1 13 C4 C4*S4 2 <<1>> 1 17 C4 C4wrC2 1 <<1>, <2>> 1 17 C4 C4wrC2 1 <<3>, <3>> -1 21 C2^2 C2^3 1 <<1, 0>, <1, 1>> -1 21 C2^2 C2^2 1 <<1, 0>, <1, 1>> 4 21 C2^2 C2*D4 1 <<0, 1>, <1, 1>> 1 21 C2^2 C2*D4 1 <<0, 1>, <1, 0>> -1 30 C2^2 C2^3 1 <<0, 1>, <1, 0>> -1 30 C2^2 C2^3 1 <<0, 1>, <1, 1>> 3 30 C2^2 C2^3 1 <<1, 0>, <1, 1>> 1 38 C6 C6 0 <<2>, <3>, <5>> -2 40 C6 C6 0 <<1>, <4>, <4>> 1 40 C6 C6 0 <<1>, <2>, <2>> 1 40 C6 C6 0 <<3>, <5>, <5>> 1 41 C3^2 C3^2 0 <<0, 1>, <1, 0>, <1, 2>> -1 44 C2^3 C2^3 0 <<0, 0, 1>, <0, 1, 0>, <1, 1, 0>> -3 44 C2^3 C2^3 0 <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>> 1 44 C2^3 C2^3 0 <<0, 1, 0>, <1, 0, 0>, <1, 0, 1>> -1 44 C2^3 C2^3 0 <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>> 1 44 C2^3 C2^3 0 <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>> -3 60 C2^3 C2^3 0 <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>> -1 60 C2^3 C2^3 0 <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>> -1 60 C2^3 C2^3 0 <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>> -2 60 C2^3 C2^3 0 <<0, 0, 1>, <1, 0, 1>, <1, 1, 1>> -7 60 C2^3 C2^3 0 <<0, 0, 1>, <0, 1, 1>, <1, 1, 0>> -4 60 C2^3 C2^3 0 <<0, 0, 1>, <0, 1, 1>, <1, 0, 1>> -3 60 C2^3 C2^3 0 <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>> -3 60 C2^3 C2^3 0 <<0, 1, 1>, <1, 0, 0>, <1, 0, 1>> -3 60 C2^3 C2^3 0 <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>> 1 60 C2^3 C2^3 0 <<0, 0, 1>, <0, 1, 1>, <1, 0, 0>> 1 65 C8 C8 0 <<1>, <3>, <6>> 1 65 C8 C8 0 <<4>, <7>, <7>> 1 78 C2*C4 C2*C4 0 <<0, 1>, <1, 2>, <1, 3>> -1 79 C2*C4 C2*C4 0 <<0, 2>, <0, 3>, <1, 3>> -2 79 C2*C4 C2*C4 0 <<0, 2>, <0, 3>, <1, 0>> -1 79 C2*C4 C2*C4 0 <<0, 3>, <0, 3>, <1, 3>> -4 79 C2*C4 C2*C4 0 <<0, 2>, <1, 0>, <1, 1>> 3 79 C2*C4 C2*C4 0 <<0, 1>, <0, 2>, <1, 3>> 1 79 C2*C4 C2*C4 0 <<1, 0>, <1, 3>, <1, 3>> 1 79 C2*C4 C2*C4 0 <<0, 1>, <0, 2>, <1, 0>> 1 92 C12 C12 0 <<4>, <7>, <9>> 1 92 C12 C12 0 <<4>, <5>, <9>> 1 107 C4^2 C4^2 0 <<0, 3>, <1, 1>, <3, 2>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<1>> ]>> <6, <[ <<1>> ]>> <7, <[ <<2>>, <<1>> ]>> <8, <[ <<1>, <1>>, <<2>, <2>> ]>> <9, <[ <<2>, <2>>, <<1>, <1>> ]>> <10, <[ <<1>>, <<3>> ]>> <11, <[ <<1>, <2>>, <<2>, <3>> ]>> <12, <[ <<3>, <3>>, <<1>, <1>> ]>> <13, <[ <<1, 0>, <1, 1>>, <<0, 1>, <1, 0>> ]>> <14, <[ <<1, 0>, <1, 1>>, <<0, 1>, <1, 0>> ]>> <15, <[ <<0, 1>, <1, 1>> ]>> <16, <[ <<0, 1>, <1, 0>>, <<1, 0>, <1, 1>> ]>> <17, <[ <<0, 1>, <1, 0>>, <<0, 1>, <1, 1>> ]>> <18, <[ <<0, 1>, <1, 1>>, <<0, 1>, <1, 0>> ]>> <19, <[ <<1, 0>, <1, 1>> ]>> <20, <[ <<2>, <3>, <5>>, <<1>, <3>, <4>> ]>> <21, <[ <<1>, <4>, <4>>, <<2>, <2>, <5>> ]>> <22, <[ <<1>, <2>, <2>>, <<4>, <4>, <5>> ]>> <23, <[ <<3>, <5>, <5>>, <<1>, <1>, <3>> ]>> <24, <[ <<0, 1>, <1, 0>, <1, 2>>, <<1, 0>, <2, 1>, <2, 2>>, <<1, 1>, <1, 2>, <2, 0>>, <<0, 2>, <1, 0>, <1, 2>>, <<0, 2>, <2, 0>, <2, 1>>, <<1, 2>, <2, 0>, <2, 2>>, <<1, 0>, <1, 1>, <2, 1>>, <<0, 1>, <2, 0>, <2, 1>> ]>> <25, <[ <<0, 0, 1>, <0, 1, 0>, <1, 1, 0>>, <<0, 0, 1>, <0, 1, 0>, <1, 0, 0>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>>, <<0, 1, 0>, <1, 0, 0>, <1, 1, 1>>, <<0, 1, 0>, <1, 0, 1>, <1, 1, 0>>, <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>>, <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>>, <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 0>, <1, 0, 1>> ]>> <26, <[ <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>>, <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>>, <<0, 0, 1>, <0, 1, 0>, <1, 1, 0>>, <<0, 0, 1>, <0, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>>, <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 0>, <1, 0, 1>, <1, 1, 0>>, <<0, 0, 1>, <0, 1, 0>, <1, 0, 0>>, <<0, 1, 0>, <1, 0, 0>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 0>, <1, 0, 1>> ]>> <27, <[ <<0, 1, 0>, <1, 0, 0>, <1, 0, 1>>, <<0, 1, 0>, <1, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <1, 0, 0>, <1, 1, 0>>, <<0, 0, 1>, <1, 0, 1>, <1, 1, 1>> ]>> <28, <[ <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>>, <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>>, <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 0>, <1, 1, 0>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 0>, <1, 0, 1>>, <<0, 1, 0>, <1, 0, 0>, <1, 1, 1>>, <<0, 1, 0>, <1, 0, 1>, <1, 1, 0>>, <<0, 0, 1>, <0, 1, 0>, <1, 0, 0>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>>, <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>> ]>> <29, <[ <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>>, <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>>, <<0, 0, 1>, <0, 1, 0>, <1, 1, 1>>, <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>>, <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 0>, <1, 0, 1>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>>, <<0, 1, 0>, <1, 0, 1>, <1, 1, 0>>, <<0, 1, 0>, <1, 0, 0>, <1, 1, 1>>, <<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>> ]>> <30, <[ <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>>, <<0, 1, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 1>, <1, 0, 0>, <1, 0, 1>>, <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>> ]>> <31, <[ <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 1>, <1, 0, 0>, <1, 1, 0>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>>, <<0, 0, 1>, <1, 0, 0>, <1, 1, 0>> ]>> <32, <[ <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 1, 0>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 0, 0>> ]>> <33, <[ <<0, 0, 1>, <1, 0, 1>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 0, 1>>, <<0, 1, 1>, <1, 0, 1>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 1, 1>> ]>> <34, <[ <<0, 0, 1>, <0, 1, 1>, <1, 1, 0>>, <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 0, 0>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>> ]>> <35, <[ <<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, 1>> ]>> <36, <[ <<1, 0, 0>, <1, 0, 1>, <1, 1, 0>>, <<0, 0, 1>, <1, 0, 0>, <1, 1, 0>>, <<1, 0, 0>, <1, 1, 0>, <1, 1, 1>>, <<0, 1, 1>, <1, 0, 0>, <1, 1, 0>> ]>> <37, <[ <<0, 1, 1>, <1, 0, 0>, <1, 0, 1>>, <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>>, <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>>, <<0, 1, 1>, <1, 1, 0>, <1, 1, 1>> ]>> <38, <[ <<0, 0, 1>, <1, 0, 0>, <1, 1, 1>>, <<0, 1, 1>, <1, 0, 0>, <1, 0, 1>>, <<0, 1, 1>, <1, 1, 0>, <1, 1, 1>>, <<0, 0, 1>, <1, 0, 1>, <1, 1, 0>> ]>> <39, <[ <<0, 0, 1>, <0, 1, 1>, <1, 0, 0>>, <<1, 0, 0>, <1, 0, 1>, <1, 1, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 1, 0>>, <<1, 0, 1>, <1, 1, 0>, <1, 1, 1>> ]>> <40, <[ <<1>, <3>, <6>>, <<5>, <6>, <7>>, <<2>, <5>, <7>>, <<1>, <2>, <3>> ]>> <41, <[ <<4>, <7>, <7>>, <<3>, <3>, <4>>, <<1>, <1>, <4>>, <<4>, <5>, <5>> ]>> <42, <[ <<0, 1>, <1, 2>, <1, 3>>, <<0, 3>, <1, 1>, <1, 2>> ]>> <43, <[ <<0, 2>, <0, 3>, <1, 3>>, <<0, 1>, <0, 2>, <1, 1>> ]>> <44, <[ <<0, 2>, <0, 3>, <1, 0>>, <<0, 1>, <0, 2>, <1, 0>>, <<0, 2>, <1, 0>, <1, 1>>, <<0, 2>, <1, 0>, <1, 3>> ]>> <45, <[ <<0, 3>, <0, 3>, <1, 3>>, <<0, 1>, <0, 1>, <1, 1>>, <<0, 1>, <1, 1>, <1, 1>>, <<0, 3>, <1, 3>, <1, 3>> ]>> <46, <[ <<0, 2>, <1, 0>, <1, 1>>, <<0, 2>, <1, 0>, <1, 3>>, <<0, 2>, <0, 3>, <1, 0>>, <<0, 1>, <0, 2>, <1, 0>> ]>> <47, <[ <<0, 1>, <0, 2>, <1, 3>>, <<0, 2>, <0, 3>, <1, 1>> ]>> <48, <[ <<1, 0>, <1, 3>, <1, 3>>, <<1, 0>, <1, 1>, <1, 1>>, <<0, 1>, <0, 1>, <1, 0>>, <<0, 3>, <0, 3>, <1, 0>> ]>> <49, <[ <<0, 1>, <0, 2>, <1, 0>>, <<0, 2>, <0, 3>, <1, 0>>, <<0, 2>, <1, 0>, <1, 3>>, <<0, 2>, <1, 0>, <1, 1>> ]>> <50, <[ <<4>, <7>, <9>>, <<1>, <3>, <4>>, <<8>, <9>, <11>>, <<3>, <5>, <8>> ]>> <51, <[ <<4>, <5>, <9>>, <<3>, <4>, <11>>, <<1>, <8>, <9>>, <<3>, <7>, <8>> ]>> <52, <[ <<0, 3>, <1, 1>, <3, 2>>, <<0, 1>, <3, 2>, <3, 3>>, <<0, 1>, <1, 1>, <3, 0>>, <<0, 1>, <1, 0>, <1, 1>>, <<0, 3>, <1, 0>, <3, 3>>, <<0, 1>, <1, 2>, <3, 3>>, <<0, 3>, <3, 0>, <3, 3>>, <<0, 3>, <1, 1>, <1, 2>> ]>>