//SL(2,3).A5 //A5*A4 FScale:=CyclotomicField(60:Sparse:=true); F:=FScale; Z4:=F.1; sq5:= 2*F.3^3 + 2*F.3^2 + 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)/4,(sq5+Z4)/4,(-1-Z4)/4,(sq5+Z4)/4, (1+Z4*sq5)/4,(1+Z4)/4,(1+Z4*sq5)/4,(1+Z4)/4, (-1+Z4)/4,(1-Z4*sq5)/4,(1-Z4)/4,(-1+Z4*sq5)/4, (sq5-Z4)/4,(1-Z4)/4,(-sq5+Z4)/4,(-1+Z4)/4], [(-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], [-1/2,(1+sq5)/4+Z4*(1-sq5)/4,0,0, (1+sq5)/4-Z4*(1-sq5)/4,1/2,0,0, 0,0,1/2,-(1+sq5)/4-Z4*(1-sq5)/4, 0,0,-(1+sq5)/4+Z4*(1-sq5)/4,-1/2], [-1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,-1]>; 1 1 C1 A5*A4 3 [] 1 2 C2 C2*A5 2 <<1>> 1 3 C2 C2*A4 2 <<1>> 1 4 C2 C2^3 2 <<1>> 1 5 C3 C3*A5 2 <<2>> 1 5 C3 C3*A5 2 <<1>> 1 6 C3 C3*A4 2 <<2>> 2 7 C3 C3^2 1 <<1>, <1>> 2 7 C3 C3^2 1 <<2>, <2>> 1 8 C5 C5*A4 2 <<3>> 1 17 C6 C6 0 <<2>, <3>, <5>> 1 19 C6 C6 0 <<2>, <3>, <5>> 1 19 C6 C6 0 <<1>, <3>, <4>> 1 20 C3^2 C3^2 0 <<1, 0>, <1, 2>, <2, 2>> 1 20 C3^2 C3^2 0 <<1, 0>, <2, 1>, <2, 2>> 1 20 C3^2 C3^2 0 <<0, 2>, <2, 0>, <2, 2>> 1 20 C3^2 C3^2 0 <<0, 1>, <2, 0>, <2, 2>> 1 22 C10 C10 0 <<2>, <5>, <7>> 1 24 C15 C15 0 <<1>, <5>, <6>> 1 24 C15 C15 0 <<5>, <6>, <14>> 1 24 C15 C15 0 <<4>, <6>, <10>> 1 24 C15 C15 0 <<6>, <10>, <11>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<2>> ]>> <6, <[ <<1>> ]>> <7, <[ <<2>>, <<1>> ]>> <8, <[ <<1>, <1>> ]>> <9, <[ <<2>, <2>> ]>> <10, <[ <<3>>, <<2>> ]>> <11, <[ <<2>, <3>, <5>>, <<1>, <3>, <4>> ]>> <12, <[ <<2>, <3>, <5>> ]>> <13, <[ <<1>, <3>, <4>> ]>> <14, <[ <<1, 0>, <1, 2>, <2, 2>>, <<0, 1>, <1, 0>, <1, 1>> ]>> <15, <[ <<1, 0>, <2, 1>, <2, 2>>, <<0, 2>, <1, 0>, <1, 1>> ]>> <16, <[ <<0, 2>, <2, 0>, <2, 2>>, <<1, 1>, <2, 0>, <2, 1>> ]>> <17, <[ <<0, 1>, <2, 0>, <2, 2>>, <<1, 1>, <1, 2>, <2, 0>> ]>> <18, <[ <<2>, <5>, <7>>, <<3>, <5>, <8>> ]>> <19, <[ <<1>, <5>, <6>>, <<4>, <5>, <9>> ]>> <20, <[ <<5>, <6>, <14>>, <<5>, <9>, <11>> ]>> <21, <[ <<4>, <6>, <10>>, <<1>, <9>, <10>> ]>> <22, <[ <<6>, <10>, <11>>, <<9>, <10>, <14>> ]>> Reduced: 1 1 C1 A4*A5 3 [] 1 2 C2 C2*A5 2 <<1>> 1 3 C2 C2*A4 2 <<1>> 1 4 C2 C2^3 2 <<1>> 1 5 C3 C3*A5 2 <<2>> 1 5 C3 C3*A5 2 <<1>> 1 6 C3 C3*A4 2 <<2>> 2 7 C3 C3^2 1 <<1>, <1>> 2 7 C3 C3^2 1 <<2>, <2>> 1 8 C5 C5*A4 2 <<3>> 1 20 C3^2 C3^2 0 <<1, 0>, <1, 2>, <2, 2>> 1 20 C3^2 C3^2 0 <<1, 0>, <2, 1>, <2, 2>> 1 20 C3^2 C3^2 0 <<0, 2>, <2, 0>, <2, 2>> 1 20 C3^2 C3^2 0 <<0, 1>, <2, 0>, <2, 2>> 1 24 C15 C15 0 <<1>, <5>, <6>> 1 24 C15 C15 0 <<5>, <6>, <14>> 1 24 C15 C15 0 <<4>, <6>, <10>> 1 24 C15 C15 0 <<6>, <10>, <11>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<2>> ]>> <6, <[ <<1>> ]>> <7, <[ <<2>>, <<1>> ]>> <8, <[ <<1>, <1>> ]>> <9, <[ <<2>, <2>> ]>> <10, <[ <<3>>, <<2>> ]>> <11, <[ <<1, 0>, <1, 2>, <2, 2>>, <<0, 1>, <1, 0>, <1, 1>> ]>> <12, <[ <<1, 0>, <2, 1>, <2, 2>>, <<0, 2>, <1, 0>, <1, 1>> ]>> <13, <[ <<0, 2>, <2, 0>, <2, 2>>, <<1, 1>, <2, 0>, <2, 1>> ]>> <14, <[ <<0, 1>, <2, 0>, <2, 2>>, <<1, 1>, <1, 2>, <2, 0>> ]>> <15, <[ <<1>, <5>, <6>>, <<4>, <5>, <9>> ]>> <16, <[ <<5>, <6>, <14>>, <<5>, <9>, <11>> ]>> <17, <[ <<4>, <6>, <10>>, <<1>, <9>, <10>> ]>> <18, <[ <<6>, <10>, <11>>, <<9>, <10>, <14>> ]>>