//Q8.A4.C6 //A4*S4 FScale:=CreateBaseFld(SmallGroup(576,8273)); 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-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+Z4)/sq2,0,0,0, 0,(1+Z4)/sq2,0,0, 0,0,(1-Z4)/sq2,0, 0,0,0,(-1-Z4)/sq2]>; 1 1 C1 A4*S4 3 [] 1 2 C2 C2*S4 2 <<1>> 1 4 C2 C2*A4 2 <<1>> 1 5 C2 C2*D4 2 <<1>> 1 6 C2 C2^3 2 <<1>> 1 7 C3 C3*A4 2 <<2>> 1 8 C3 C3*S4 2 <<2>> 1 8 C3 C3*S4 2 <<1>> 2 9 C3 C3^2 1 <<1>, <1>> 2 9 C3 C3^2 1 <<2>, <2>> 1 12 C4 C4*A4 2 <<3>> 1 27 C6 C6 0 <<1>, <3>, <4>> 1 28 C6 C6 0 <<1>, <3>, <4>> 1 28 C6 C6 0 <<2>, <3>, <5>> 1 29 C3^2 C3^2 0 <<1, 2>, <2, 0>, <2, 2>> 1 29 C3^2 C3^2 0 <<1, 1>, <1, 2>, <2, 0>> 1 29 C3^2 C3^2 0 <<0, 2>, <1, 0>, <1, 2>> 1 29 C3^2 C3^2 0 <<0, 1>, <1, 0>, <1, 2>> 1 36 C2*C4 C2*C4 0 <<0, 3>, <1, 0>, <1, 3>> 1 51 C12 C12 0 <<3>, <4>, <11>> 1 51 C12 C12 0 <<1>, <3>, <4>> 1 51 C12 C12 0 <<3>, <7>, <8>> 1 51 C12 C12 0 <<3>, <5>, <8>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<1>> ]>> <6, <[ <<2>>, <<1>> ]>> <7, <[ <<2>> ]>> <8, <[ <<1>> ]>> <9, <[ <<1>, <1>> ]>> <10, <[ <<2>, <2>> ]>> <11, <[ <<3>>, <<1>> ]>> <12, <[ <<1>, <3>, <4>>, <<2>, <3>, <5>> ]>> <13, <[ <<1>, <3>, <4>> ]>> <14, <[ <<2>, <3>, <5>> ]>> <15, <[ <<1, 2>, <2, 0>, <2, 2>>, <<0, 1>, <2, 0>, <2, 1>> ]>> <16, <[ <<1, 1>, <1, 2>, <2, 0>>, <<0, 2>, <2, 0>, <2, 1>> ]>> <17, <[ <<0, 2>, <1, 0>, <1, 2>>, <<1, 0>, <1, 1>, <2, 1>> ]>> <18, <[ <<0, 1>, <1, 0>, <1, 2>>, <<1, 0>, <2, 1>, <2, 2>> ]>> <19, <[ <<0, 3>, <1, 0>, <1, 3>>, <<0, 1>, <1, 0>, <1, 1>> ]>> <20, <[ <<3>, <4>, <11>>, <<4>, <5>, <9>> ]>> <21, <[ <<1>, <3>, <4>>, <<4>, <7>, <9>> ]>> <22, <[ <<3>, <7>, <8>>, <<1>, <8>, <9>> ]>> <23, <[ <<3>, <5>, <8>>, <<8>, <9>, <11>> ]>> Reduced: 1 1 C1 A4*S4 3 [] 1 2 C2 C2*S4 2 <<1>> 1 4 C2 C2*A4 2 <<1>> 1 5 C2 C2*D4 2 <<1>> 1 6 C2 C2^3 2 <<1>> 1 7 C3 C3*A4 2 <<2>> 1 8 C3 C3*S4 2 <<2>> 1 8 C3 C3*S4 2 <<1>> 2 9 C3 C3^2 1 <<1>, <1>> 2 9 C3 C3^2 1 <<2>, <2>> 1 12 C4 C4*A4 2 <<3>> 1 29 C3^2 C3^2 0 <<1, 2>, <2, 0>, <2, 2>> 1 29 C3^2 C3^2 0 <<1, 1>, <1, 2>, <2, 0>> 1 29 C3^2 C3^2 0 <<0, 2>, <1, 0>, <1, 2>> 1 29 C3^2 C3^2 0 <<0, 1>, <1, 0>, <1, 2>> 1 51 C12 C12 0 <<3>, <4>, <11>> 1 51 C12 C12 0 <<1>, <3>, <4>> 1 51 C12 C12 0 <<3>, <7>, <8>> 1 51 C12 C12 0 <<3>, <5>, <8>> <2, <[ <<1>> ]>> <3, <[ <<1>> ]>> <4, <[ <<1>> ]>> <5, <[ <<1>> ]>> <6, <[ <<2>>, <<1>> ]>> <7, <[ <<2>> ]>> <8, <[ <<1>> ]>> <9, <[ <<1>, <1>> ]>> <10, <[ <<2>, <2>> ]>> <11, <[ <<3>>, <<1>> ]>> <12, <[ <<1, 2>, <2, 0>, <2, 2>>, <<0, 1>, <2, 0>, <2, 1>> ]>> <13, <[ <<1, 1>, <1, 2>, <2, 0>>, <<0, 2>, <2, 0>, <2, 1>> ]>> <14, <[ <<0, 2>, <1, 0>, <1, 2>>, <<1, 0>, <1, 1>, <2, 1>> ]>> <15, <[ <<0, 1>, <1, 0>, <1, 2>>, <<1, 0>, <2, 1>, <2, 2>> ]>> <16, <[ <<3>, <4>, <11>>, <<4>, <5>, <9>> ]>> <17, <[ <<1>, <3>, <4>>, <<4>, <7>, <9>> ]>> <18, <[ <<3>, <7>, <8>>, <<1>, <8>, <9>> ]>> <19, <[ <<3>, <5>, <8>>, <<8>, <9>, <11>> ]>>