//SL(2,3):A4 //A4^2 FScale:=CreateBaseFld(SmallGroup(288,860)); F:=FScale; Z4:=F.1; 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-Z4)/2,0,(-1-Z4)/2,0, 0,(1+Z4)/2,0,(1+Z4)/2, (-1+Z4)/2,0,(1-Z4)/2,0, 0,(1-Z4)/2,0,(-1+Z4)/2], [(-1-Z4)/2,(-1-Z4)/2,0,0, (-1+Z4)/2,(1-Z4)/2,0,0, 0,0,(1+Z4)/2,(1+Z4)/2, 0,0,(1-Z4)/2,(-1+Z4)/2], [-1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,-1]>; 1 1 C1 A4^2 3 [] 1 2 C2 C2*A4 2 <<1>> 1 3 C2 C2*A4 2 <<1>> 1 4 C2 C2^3 2 <<1>> 1 5 C3 C3*A4 2 <<2>> 1 5 C3 C3*A4 2 <<1>> 1 6 C3 C3*A4 2 <<2>> 1 6 C3 C3*A4 2 <<1>> 2 7 C3 C3^2 1 <<1>, <1>> 2 7 C3 C3^2 1 <<2>, <2>> 2 8 C3 C3^2 1 <<1>, <1>> 2 8 C3 C3^2 1 <<2>, <2>> 1 16 C6 C6 0 <<1>, <3>, <4>> 1 16 C6 C6 0 <<2>, <3>, <5>> 1 17 C6 C6 0 <<1>, <3>, <4>> 1 17 C6 C6 0 <<2>, <3>, <5>> 1 18 C3^2 C3^2 0 <<1, 0>, <1, 2>, <2, 2>> 1 18 C3^2 C3^2 0 <<1, 0>, <2, 1>, <2, 2>> 1 18 C3^2 C3^2 0 <<0, 1>, <2, 0>, <2, 2>> 1 18 C3^2 C3^2 0 <<0, 2>, <2, 0>, <2, 2>> 1 18 C3^2 C3^2 0 <<1, 1>, <1, 2>, <2, 0>> 1 18 C3^2 C3^2 0 <<1, 1>, <2, 0>, <2, 1>> 1 18 C3^2 C3^2 0 <<0, 1>, <1, 0>, <1, 1>> 1 18 C3^2 C3^2 0 <<0, 2>, <1, 0>, <1, 1>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<2>> ]>> <6, <[ <<1>> ]>> <7, <[ <<2>> ]>> <8, <[ <<1>> ]>> <9, <[ <<1>, <1>> ]>> <10, <[ <<2>, <2>> ]>> <11, <[ <<1>, <1>> ]>> <12, <[ <<2>, <2>> ]>> <13, <[ <<1>, <3>, <4>> ]>> <14, <[ <<2>, <3>, <5>> ]>> <15, <[ <<1>, <3>, <4>> ]>> <16, <[ <<2>, <3>, <5>> ]>> <17, <[ <<1, 0>, <1, 2>, <2, 2>> ]>> <18, <[ <<1, 0>, <2, 1>, <2, 2>> ]>> <19, <[ <<0, 1>, <2, 0>, <2, 2>> ]>> <20, <[ <<0, 2>, <2, 0>, <2, 2>> ]>> <21, <[ <<1, 1>, <1, 2>, <2, 0>> ]>> <22, <[ <<1, 1>, <2, 0>, <2, 1>> ]>> <23, <[ <<0, 1>, <1, 0>, <1, 1>> ]>> <24, <[ <<0, 2>, <1, 0>, <1, 1>> ]>> Reduced: 1 1 C1 A4^2 3 [] 1 2 C2 C2*A4 2 <<1>> 1 3 C2 C2*A4 2 <<1>> 1 4 C2 C2^3 2 <<1>> 1 5 C3 C3*A4 2 <<2>> 1 5 C3 C3*A4 2 <<1>> 1 6 C3 C3*A4 2 <<2>> 1 6 C3 C3*A4 2 <<1>> 2 7 C3 C3^2 1 <<1>, <1>> 2 7 C3 C3^2 1 <<2>, <2>> 2 8 C3 C3^2 1 <<1>, <1>> 2 8 C3 C3^2 1 <<2>, <2>> 1 18 C3^2 C3^2 0 <<1, 0>, <1, 2>, <2, 2>> 1 18 C3^2 C3^2 0 <<1, 0>, <2, 1>, <2, 2>> 1 18 C3^2 C3^2 0 <<0, 1>, <2, 0>, <2, 2>> 1 18 C3^2 C3^2 0 <<0, 2>, <2, 0>, <2, 2>> 1 18 C3^2 C3^2 0 <<1, 1>, <1, 2>, <2, 0>> 1 18 C3^2 C3^2 0 <<1, 1>, <2, 0>, <2, 1>> 1 18 C3^2 C3^2 0 <<0, 1>, <1, 0>, <1, 1>> 1 18 C3^2 C3^2 0 <<0, 2>, <1, 0>, <1, 1>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<2>> ]>> <6, <[ <<1>> ]>> <7, <[ <<2>> ]>> <8, <[ <<1>> ]>> <9, <[ <<1>, <1>> ]>> <10, <[ <<2>, <2>> ]>> <11, <[ <<1>, <1>> ]>> <12, <[ <<2>, <2>> ]>> <13, <[ <<1, 0>, <1, 2>, <2, 2>> ]>> <14, <[ <<1, 0>, <2, 1>, <2, 2>> ]>> <15, <[ <<0, 1>, <2, 0>, <2, 2>> ]>> <16, <[ <<0, 2>, <2, 0>, <2, 2>> ]>> <17, <[ <<1, 1>, <1, 2>, <2, 0>> ]>> <18, <[ <<1, 1>, <2, 0>, <2, 1>> ]>> <19, <[ <<0, 1>, <1, 0>, <1, 1>> ]>> <20, <[ <<0, 2>, <1, 0>, <1, 1>> ]>>