//C2.C(2,3) //C(2,3) FScale:=CreateBaseFld(Group("C(2,3)")); FScale:=Compositum(FScale,CyclotomicField(8:Sparse:=true)); F:=FScale; Z3:=F.2^3; isq3:=2*F.2^3+1; G:=MatrixGroup<4,F| [1,0,0,0, 0,0,1,0, 0,0,0,1, 0,1,0,0], [1,0,0,0, 0,1,0,0, 0,0,Z3,0, 0,0,0,Z3^2], [Z3,0,0,0, 0,Z3,0,0, 0,0,Z3,0, 0,0,0,1], [1,0,0,0, 0,1/isq3,1/isq3,1/isq3, 0,1/isq3,Z3/isq3,Z3^2/isq3, 0,1/isq3,Z3^2/isq3,Z3/isq3], [0,0,-1,0, 0,1,0,0, -1,0,0,0, 0,0,0,-1]>; 1 1 C1 C(2,3) 3 [] 1 2 C2 SL(2,3):A4 2 <<1>> 1 3 C2 A4:C4 2 <<1>> 1 4 C3 SU(3,2).C3 2 <<1>> 1 4 C3 SU(3,2).C3 2 <<2>> 1 5 C3 C3*S3^2 2 <<1>> 1 7 C5 C5 0 <<2>, <2>, <4>> 1 8 C4 SL(2,3):C2 1 <<2>, <3>> 1 8 C4 SL(2,3):C2 1 <<1>, <1>> 1 15 C6 C3*SL(2,3) 1 <<1>, <2>> 1 15 C6 C3*SL(2,3) 1 <<3>, <5>> 1 15 C6 C3*SL(2,3) 1 <<1>, <3>> 1 20 C6 C6 0 <<1>, <3>, <4>> -1 23 C3^2 C3^2 1 <<0, 2>, <2, 0>> 1 23 C3^2 C3^2*S3 1 <<1, 0>, <2, 1>> 1 23 C3^2 C3^2*S3 1 <<0, 1>, <1, 2>> -1 24 C9 C9 0 <<6>, <6>, <8>> -1 24 C9 C9 0 <<3>, <3>, <8>> 1 24 C9 C9 0 <<2>, <6>, <6>> 1 24 C9 C9 0 <<4>, <7>, <8>> 1 24 C9 C9 0 <<3>, <3>, <5>> 1 30 C2*C4 C2*C4 0 <<0, 3>, <1, 1>, <1, 2>> -1 40 C12 C12 0 <<5>, <6>, <9>> -1 40 C12 C12 0 <<3>, <3>, <11>> -3 40 C12 C12 0 <<6>, <8>, <9>> 1 40 C12 C12 0 <<1>, <4>, <5>> -1 40 C12 C12 0 <<3>, <6>, <11>> 1 40 C12 C12 0 <<1>, <3>, <6>> 1 40 C12 C12 0 <<8>, <9>, <9>> 1 40 C12 C12 0 <<3>, <5>, <6>> -1 48 C3*C6 C3*C6 0 <<0, 5>, <1, 0>, <1, 3>> -3 48 C3*C6 C3*C6 0 <<0, 3>, <2, 0>, <2, 5>> -4 48 C3*C6 C3*C6 0 <<0, 3>, <2, 2>, <2, 3>> -1 48 C3*C6 C3*C6 0 <<1, 0>, <2, 2>, <2, 3>> -1 48 C3*C6 C3*C6 0 <<0, 3>, <0, 5>, <1, 3>> -1 48 C3*C6 C3*C6 0 <<0, 3>, <2, 3>, <2, 5>> -5 48 C3*C6 C3*C6 0 <<0, 3>, <2, 0>, <2, 2>> -3 48 C3*C6 C3*C6 0 <<0, 1>, <0, 3>, <2, 2>> -2 48 C3*C6 C3*C6 0 <<0, 3>, <0, 5>, <2, 3>> -3 48 C3*C6 C3*C6 0 <<1, 0>, <1, 3>, <2, 2>> -1 48 C3*C6 C3*C6 0 <<0, 5>, <1, 3>, <2, 0>> -1 48 C3*C6 C3*C6 0 <<0, 3>, <1, 4>, <2, 3>> 1 48 C3*C6 C3*C6 0 <<0, 1>, <1, 0>, <1, 3>> 1 48 C3*C6 C3*C6 0 <<0, 5>, <1, 0>, <2, 3>> 1 48 C3*C6 C3*C6 0 <<0, 3>, <1, 3>, <2, 2>> 1 48 C3*C6 C3*C6 0 <<1, 3>, <2, 0>, <2, 2>> -1 50 C3^3 C3^3 0 <<0, 0, 2>, <0, 2, 2>, <1, 2, 0>> -3 50 C3^3 C3^3 0 <<0, 0, 2>, <0, 2, 1>, <1, 0, 2>> -1 50 C3^3 C3^3 0 <<0, 0, 2>, <0, 2, 2>, <2, 1, 0>> 1 50 C3^3 C3^3 0 <<0, 0, 1>, <0, 1, 1>, <2, 0, 1>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<2>> ]>> <6, <[ <<1>>, <<2>> ]>> <7, <[ <<2>, <2>, <4>>, <<1>, <1>, <2>>, <<1>, <3>, <3>>, <<3>, <4>, <4>> ]>> <8, <[ <<2>, <3>>, <<1>, <2>> ]>> <9, <[ <<1>, <1>>, <<3>, <3>> ]>> <10, <[ <<1>, <2>> ]>> <11, <[ <<3>, <5>> ]>> <12, <[ <<1>, <3>> ]>> <13, <[ <<1>, <3>, <4>>, <<2>, <3>, <5>> ]>> <14, <[ <<0, 2>, <2, 0>>, <<1, 0>, <1, 2>> ]>> <15, <[ <<1, 0>, <2, 1>>, <<0, 1>, <2, 0>> ]>> <16, <[ <<0, 1>, <1, 2>>, <<0, 2>, <2, 1>> ]>> <17, <[ <<6>, <6>, <8>>, <<2>, <6>, <6>>, <<5>, <6>, <6>> ]>> <18, <[ <<3>, <3>, <8>>, <<2>, <3>, <3>>, <<3>, <3>, <5>> ]>> <19, <[ <<2>, <6>, <6>>, <<5>, <6>, <6>>, <<6>, <6>, <8>> ]>> <20, <[ <<4>, <7>, <8>>, <<1>, <2>, <4>>, <<1>, <5>, <7>> ]>> <21, <[ <<3>, <3>, <5>>, <<3>, <3>, <8>>, <<2>, <3>, <3>> ]>> <22, <[ <<0, 3>, <1, 1>, <1, 2>>, <<0, 3>, <1, 0>, <1, 3>>, <<0, 1>, <1, 0>, <1, 1>>, <<0, 1>, <1, 2>, <1, 3>> ]>> <23, <[ <<5>, <6>, <9>>, <<3>, <6>, <11>> ]>> <24, <[ <<3>, <3>, <11>>, <<5>, <9>, <9>> ]>> <25, <[ <<6>, <8>, <9>>, <<3>, <6>, <8>> ]>> <26, <[ <<1>, <4>, <5>>, <<4>, <7>, <11>> ]>> <27, <[ <<3>, <6>, <11>>, <<5>, <6>, <9>> ]>> <28, <[ <<1>, <3>, <6>>, <<6>, <7>, <9>> ]>> <29, <[ <<8>, <9>, <9>>, <<3>, <3>, <8>> ]>> <30, <[ <<3>, <5>, <6>>, <<6>, <9>, <11>> ]>> <31, <[ <<0, 5>, <1, 0>, <1, 3>>, <<0, 1>, <1, 1>, <1, 4>> ]>> <32, <[ <<0, 3>, <2, 0>, <2, 5>>, <<0, 3>, <2, 2>, <2, 3>> ]>> <33, <[ <<0, 3>, <2, 2>, <2, 3>>, <<0, 3>, <2, 0>, <2, 5>> ]>> <34, <[ <<1, 0>, <2, 2>, <2, 3>>, <<1, 4>, <2, 0>, <2, 5>> ]>> <35, <[ <<0, 3>, <0, 5>, <1, 3>>, <<0, 1>, <0, 3>, <1, 1>> ]>> <36, <[ <<0, 3>, <2, 3>, <2, 5>> ]>> <37, <[ <<0, 3>, <2, 0>, <2, 2>> ]>> <38, <[ <<0, 1>, <0, 3>, <2, 2>>, <<0, 3>, <0, 5>, <2, 0>> ]>> <39, <[ <<0, 3>, <0, 5>, <2, 3>>, <<0, 1>, <0, 3>, <2, 5>> ]>> <40, <[ <<1, 0>, <1, 3>, <2, 2>>, <<1, 1>, <1, 4>, <2, 0>> ]>> <41, <[ <<0, 5>, <1, 3>, <2, 0>>, <<0, 1>, <1, 1>, <2, 2>> ]>> <42, <[ <<0, 3>, <1, 4>, <2, 3>>, <<0, 3>, <1, 0>, <2, 5>> ]>> <43, <[ <<0, 1>, <1, 0>, <1, 3>>, <<0, 5>, <1, 1>, <1, 4>> ]>> <44, <[ <<0, 5>, <1, 0>, <2, 3>>, <<0, 1>, <1, 4>, <2, 5>> ]>> <45, <[ <<0, 3>, <1, 3>, <2, 2>>, <<0, 3>, <1, 1>, <2, 0>> ]>> <46, <[ <<1, 3>, <2, 0>, <2, 2>>, <<1, 1>, <2, 0>, <2, 2>> ]>> <47, <[ <<0, 0, 2>, <0, 2, 2>, <1, 2, 0>>, <<0, 0, 2>, <1, 2, 0>, <2, 0, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 0, 2>>, <<0, 0, 1>, <0, 2, 1>, <1, 2, 1>>, <<0, 2, 1>, <2, 1, 0>, <2, 1, 2>>, <<0, 1, 1>, <1, 0, 2>, <2, 1, 0>>, <<0, 2, 2>, <2, 1, 0>, <2, 1, 2>>, <<0, 1, 1>, <0, 1, 2>, <1, 2, 0>>, <<0, 0, 1>, <1, 2, 1>, <2, 0, 1>>, <<0, 1, 1>, <0, 1, 2>, <1, 2, 1>>, <<0, 0, 2>, <0, 2, 1>, <1, 0, 2>>, <<0, 0, 1>, <0, 2, 2>, <1, 0, 2>>, <<0, 0, 2>, <0, 1, 2>, <1, 0, 2>>, <<0, 1, 2>, <1, 0, 2>, <2, 1, 2>>, <<0, 1, 1>, <0, 2, 1>, <1, 2, 0>>, <<0, 1, 1>, <2, 0, 1>, <2, 1, 0>>, <<0, 0, 2>, <2, 0, 1>, <2, 1, 0>>, <<0, 2, 1>, <1, 2, 0>, <2, 1, 2>>, <<0, 0, 1>, <0, 2, 2>, <1, 2, 0>>, <<0, 0, 2>, <0, 2, 1>, <1, 2, 1>>, <<0, 1, 2>, <0, 2, 2>, <1, 2, 1>>, <<0, 1, 2>, <2, 0, 1>, <2, 1, 2>>, <<0, 0, 1>, <2, 0, 1>, <2, 1, 2>>, <<0, 2, 2>, <1, 2, 1>, <2, 1, 0>> ]>> <48, <[ <<0, 0, 2>, <0, 2, 1>, <1, 0, 2>>, <<0, 1, 1>, <0, 2, 1>, <1, 2, 0>>, <<0, 1, 1>, <0, 1, 2>, <1, 2, 0>>, <<0, 0, 1>, <0, 2, 2>, <1, 0, 2>>, <<0, 1, 1>, <2, 0, 1>, <2, 1, 0>>, <<0, 0, 2>, <0, 1, 2>, <1, 0, 2>>, <<0, 1, 2>, <2, 0, 1>, <2, 1, 2>>, <<0, 1, 2>, <1, 0, 2>, <2, 1, 2>>, <<0, 1, 2>, <0, 2, 2>, <1, 2, 1>>, <<0, 1, 1>, <1, 0, 2>, <2, 1, 0>>, <<0, 2, 1>, <1, 2, 0>, <2, 1, 2>>, <<0, 2, 2>, <1, 2, 1>, <2, 1, 0>>, <<0, 1, 1>, <0, 1, 2>, <1, 2, 1>>, <<0, 0, 1>, <0, 1, 1>, <1, 0, 2>>, <<0, 0, 2>, <0, 2, 1>, <1, 2, 1>>, <<0, 0, 1>, <2, 0, 1>, <2, 1, 2>>, <<0, 2, 2>, <2, 1, 0>, <2, 1, 2>>, <<0, 0, 2>, <0, 2, 2>, <1, 2, 0>>, <<0, 0, 1>, <1, 2, 1>, <2, 0, 1>>, <<0, 0, 2>, <1, 2, 0>, <2, 0, 1>>, <<0, 0, 1>, <0, 2, 2>, <1, 2, 0>>, <<0, 0, 2>, <2, 0, 1>, <2, 1, 0>>, <<0, 2, 1>, <2, 1, 0>, <2, 1, 2>>, <<0, 0, 1>, <0, 2, 1>, <1, 2, 1>> ]>> <49, <[ <<0, 0, 2>, <0, 2, 2>, <2, 1, 0>>, <<0, 0, 1>, <1, 2, 0>, <2, 0, 1>>, <<0, 0, 1>, <0, 1, 1>, <2, 0, 1>>, <<0, 0, 1>, <0, 2, 1>, <2, 1, 2>>, <<0, 2, 1>, <1, 2, 1>, <2, 1, 0>>, <<0, 2, 2>, <1, 0, 2>, <2, 1, 0>>, <<0, 2, 2>, <1, 2, 0>, <2, 1, 2>>, <<0, 1, 2>, <0, 2, 2>, <1, 2, 0>>, <<0, 0, 2>, <1, 2, 1>, <2, 0, 1>>, <<0, 1, 1>, <0, 2, 1>, <1, 2, 1>>, <<0, 0, 1>, <0, 2, 1>, <1, 0, 2>>, <<0, 0, 2>, <0, 2, 2>, <1, 0, 2>>, <<0, 0, 2>, <0, 1, 2>, <2, 0, 1>>, <<0, 2, 1>, <1, 0, 2>, <2, 1, 2>>, <<0, 1, 1>, <0, 2, 1>, <2, 1, 0>>, <<0, 1, 1>, <1, 2, 0>, <2, 0, 1>>, <<0, 0, 2>, <1, 0, 2>, <2, 1, 0>>, <<0, 1, 2>, <1, 2, 0>, <2, 1, 2>>, <<0, 0, 1>, <0, 1, 1>, <1, 2, 0>>, <<0, 0, 2>, <0, 1, 2>, <1, 2, 1>>, <<0, 1, 2>, <0, 2, 2>, <2, 1, 2>>, <<0, 1, 2>, <1, 2, 1>, <2, 0, 1>>, <<0, 0, 1>, <1, 0, 2>, <2, 1, 2>>, <<0, 1, 1>, <1, 2, 1>, <2, 1, 0>> ]>> <50, <[ <<0, 0, 1>, <0, 1, 1>, <2, 0, 1>>, <<0, 2, 2>, <1, 0, 2>, <2, 1, 0>>, <<0, 0, 2>, <0, 2, 2>, <2, 1, 0>>, <<0, 0, 2>, <0, 1, 2>, <2, 0, 1>>, <<0, 1, 2>, <0, 2, 2>, <1, 2, 0>>, <<0, 0, 1>, <1, 2, 0>, <2, 0, 1>>, <<0, 1, 1>, <0, 2, 1>, <1, 2, 1>>, <<0, 2, 1>, <1, 2, 1>, <2, 1, 0>>, <<0, 2, 1>, <1, 0, 2>, <2, 1, 2>>, <<0, 2, 2>, <1, 2, 0>, <2, 1, 2>>, <<0, 1, 2>, <1, 2, 1>, <2, 0, 1>>, <<0, 1, 1>, <1, 2, 0>, <2, 0, 1>>, <<0, 0, 1>, <0, 2, 1>, <2, 1, 2>>, <<0, 0, 2>, <1, 2, 1>, <2, 0, 1>>, <<0, 1, 2>, <0, 2, 2>, <2, 1, 2>>, <<0, 0, 2>, <0, 2, 2>, <1, 0, 2>>, <<0, 0, 1>, <0, 1, 1>, <1, 2, 0>>, <<0, 1, 1>, <1, 2, 1>, <2, 1, 0>>, <<0, 0, 2>, <1, 0, 2>, <2, 1, 0>>, <<0, 0, 1>, <1, 0, 2>, <2, 1, 2>>, <<0, 1, 1>, <0, 2, 1>, <2, 1, 0>>, <<0, 0, 1>, <0, 2, 1>, <1, 0, 2>>, <<0, 0, 2>, <0, 1, 2>, <1, 2, 1>>, <<0, 1, 2>, <1, 2, 0>, <2, 1, 2>> ]>>