/* Group 1728.46361 downloaded from the LMFDB on 09 November 2025. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation GPerm is permutation group 
	 GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups 
 
 Many characteristics of the group are stored as booleans in a record: 
	 Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, 
	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
	 solvable, supersolvable 
 
 The character table is stored as chartbl_n_i where n is the order of 
 the group and i is which group of that order it is. Conjugacy classes 
 are stored in the variable 'C' with elements from the group 'G'. 
*/
 
/* Constructions */
GPC := PCGroup([9, 2, 2, 2, 2, 3, 2, 3, 2, 3, 36, 46, 435, 732, 102, 733, 6512, 3119, 158, 1545, 103687, 15568, 14290, 5875, 214, 93320, 11699]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.8]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "d2", "e", "e2"]);
GPerm := PermutationGroup< 18 | (6,7)(9,12)(13,15), (8,9,11,12)(10,13,14,15)(17,18), (2,4)(8,10,11,14)(9,13,12,15), (8,11)(9,12)(10,14)(13,15), (2,3,4), (5,6,7), (16,17,18), (1,2)(3,4), (1,3)(2,4) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1728_46361 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, b^2>,< 2, 3, e^3>,< 2, 3, b^2*d^3>,< 2, 6, a*c^3>,< 2, 18, a*c^3*e^3>,< 2, 18, c^3>,< 2, 36, a*b>,< 2, 54, b^2*c^3*d^3*e^5>,< 3, 2, e^2>,< 3, 2, d^4>,< 3, 4, d^4*e^2>,< 3, 8, c^4>,< 3, 16, c^4*e^4>,< 3, 16, c^4*d^4>,< 3, 32, c^4*d^4*e^4>,< 4, 6, a*b^2>,< 4, 6, b^3>,< 4, 6, b>,< 4, 6, b^3*d^3*e^3>,< 4, 6, b*e^3>,< 4, 18, a*b^2*d^3>,< 4, 36, a*b*d^3*e>,< 4, 36, a*b^3*c>,< 4, 36, a*b^3*c*d^3>,< 4, 108, b^3*c^5*d^5*e^5>,< 4, 108, b^3*c^3*d^4>,< 6, 2, b^2*d^4>,< 6, 2, b^2*e^4>,< 6, 4, b^2*d^4*e^4>,< 6, 6, e>,< 6, 6, b^2*d^3*e^2>,< 6, 6, b^2*d^2*e^3>,< 6, 6, d>,< 6, 6, a*c^3*e^2>,< 6, 6, a*c^3*e^4>,< 6, 8, b^2*c^4*d^3*e^3>,< 6, 12, d^2*e>,< 6, 12, b^2*d*e^2>,< 6, 16, b^2*c^2*e^2>,< 6, 16, b^2*c^2*d^2>,< 6, 18, a*c^3*e>,< 6, 18, a*c^3*d*e^2>,< 6, 32, b^2*c^2*d^2*e^2>,< 6, 36, a*b*d^2>,< 6, 36, a*b*d>,< 6, 48, a*b^2*c*d^2>,< 6, 48, a*c^5*d^2*e^5>,< 6, 48, a*c*d^5*e>,< 6, 144, c^5>,< 12, 6, a*d^2>,< 12, 6, a*d^4>,< 12, 12, b*e^2>,< 12, 12, b^3*e^2>,< 12, 12, b*e>,< 12, 12, b^3*e>,< 12, 12, b*d^2>,< 12, 12, b^3*d^2>,< 12, 12, b*c^2*d>,< 12, 12, b^3*c^2*d>,< 12, 18, a*d>,< 12, 18, a*d^2*e>,< 12, 24, b*d^2*e^2>,< 12, 24, b^3*d^2*e^2>,< 12, 24, b*d^2*e>,< 12, 24, b^3*d^2*e>,< 12, 36, a*b*d^2*e>,< 12, 36, a*b*d*e>,< 12, 36, a*b*c*e^2>,< 12, 36, a*b*c*e^4>,< 12, 36, a*b*c*e>,< 12, 36, a*b*c*d*e^2>,< 12, 48, a*c^2*e>,< 12, 48, a*b^2*c^4*d^4*e^4>,< 12, 48, a*b^2*c^2*d^2*e^4>]); 
CR := CharacterRing(G);
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 2, 0, 2, -1, -1, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, -1, 2, -1, 2, 2, -1, 0, -1, 0, 2, -1, -1, 2, -1, 0, 0, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 0, 0, -1, 2, -1, 2, -1, 2, -1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, 0, 0, 2, -1, -1, 0, 0, 0, 2, 2, -1, -1, 2, -1, -1, 2, 0, 0, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, -1, -1, 2, 2, -1, 0, 0, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, -2, 0, -2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, 2, -2, -1, 2, 2, -1, -1, -2, -2, -1, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 0, 0, 0, -1, 2, -1, 2, -1, 2, -1, -2, -2, -2, 0, -2, 0, 2, 2, 0, 0, 0, 2, -1, -1, -1, -1, 2, 1, 2, 1, 2, -1, -1, -1, 2, 1, 1, -1, 0, 0, -2, 1, 1, 0, 0, 0, -2, -2, 1, 1, -2, 1, 1, -2, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 0, 0, 0, -1, 2, -1, 2, -1, 2, -1, 2, 2, 2, 0, 2, 0, -2, -2, 0, 0, 0, 2, -1, -1, -1, -1, 2, 1, 2, 1, 2, -1, -1, -1, 2, 1, 1, -1, 0, 0, -2, 1, 1, 0, 0, 0, 2, 2, -1, -1, 2, -1, -1, 2, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 2, 0, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, 2, -2, -1, 2, 2, -1, -1, -2, -2, -1, 0, 0, 1, 1, 1, -1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, -2, 0, 2, -1, -1, 2, 2, -1, -1, -2, -2, -2, 2, -2, 2, 0, 0, -2, 0, 0, -1, 2, -1, 2, 2, -1, 0, -1, 0, 2, -1, -1, 2, -1, 0, 0, -1, 1, 1, 0, 0, 0, 0, -1, -1, 1, 1, -2, -2, 1, -2, -2, 1, -1, -1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, -2, 0, 2, -1, -1, 2, 2, -1, -1, 2, 2, 2, -2, 2, -2, 0, 0, -2, 0, 0, -1, 2, -1, 2, 2, -1, 0, -1, 0, 2, -1, -1, 2, -1, 0, 0, -1, 1, 1, 0, 0, 0, 0, 1, 1, -1, -1, 2, 2, -1, 2, 2, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, -2, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 2, 0, 2, -1, -1, 2, 2, -1, -1, -2, -2, -2, -2, -2, -2, 0, 0, 2, 0, 0, -1, 2, -1, 2, 2, -1, 0, -1, 0, 2, -1, -1, 2, -1, 0, 0, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, -2, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, -2, 0, -2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, -1, -1, 2, 2, -1, 0, 0, -1, -1, -1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 0, 0, -1, 2, -1, 2, -1, 2, -1, -2, -2, -2, 0, -2, 0, -2, -2, 0, 0, 0, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, 0, 0, 2, -1, -1, 0, 0, 0, -2, -2, 1, 1, -2, 1, 1, -2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,2,2,2,2,2,2,2,-2*K.1,2*K.1,-2*K.1,0,2*K.1,0,0,0,0,0,0,-2,-2,-2,2,-2,-2,0,2,0,-2,2,-2,-2,-2,0,0,-2,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,2*K.1,-2*K.1,-2*K.1,-2*K.1,2*K.1,2*K.1,0,0,2*K.1,-2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,2,2,2,2,2,2,2,2*K.1,-2*K.1,2*K.1,0,-2*K.1,0,0,0,0,0,0,-2,-2,-2,2,-2,-2,0,2,0,-2,2,-2,-2,-2,0,0,-2,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,-2*K.1,2*K.1,2*K.1,2*K.1,-2*K.1,-2*K.1,0,0,-2*K.1,2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,-1,2,-1,2,-1,2,-1,-2*K.1^3,2*K.1^3,-2*K.1^3,0,2*K.1^3,0,0,0,0,0,0,-2,1,1,-1,1,-2,1-2*K.1^2,2,-1+2*K.1^2,-2,-1,1,1,-2,1-2*K.1^2,-1+2*K.1^2,1,0,0,0,-1+2*K.1^2,1-2*K.1^2,0,0,0,-2*K.1^3,2*K.1^3,-1*K.1^3,K.1^3,-2*K.1^3,K.1^3,-1*K.1^3,2*K.1^3,0,0,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,-1,2,-1,2,-1,2,-1,2*K.1^3,-2*K.1^3,2*K.1^3,0,-2*K.1^3,0,0,0,0,0,0,-2,1,1,-1,1,-2,-1+2*K.1^2,2,1-2*K.1^2,-2,-1,1,1,-2,-1+2*K.1^2,1-2*K.1^2,1,0,0,0,1-2*K.1^2,-1+2*K.1^2,0,0,0,2*K.1^3,-2*K.1^3,K.1^3,-1*K.1^3,2*K.1^3,-1*K.1^3,K.1^3,-2*K.1^3,0,0,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,-1,2,-1,2,-1,2,-1,-2*K.1^3,2*K.1^3,-2*K.1^3,0,2*K.1^3,0,0,0,0,0,0,-2,1,1,-1,1,-2,-1+2*K.1^2,2,1-2*K.1^2,-2,-1,1,1,-2,-1+2*K.1^2,1-2*K.1^2,1,0,0,0,1-2*K.1^2,-1+2*K.1^2,0,0,0,-2*K.1^3,2*K.1^3,-1*K.1^3,K.1^3,-2*K.1^3,K.1^3,-1*K.1^3,2*K.1^3,0,0,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,-1,2,-1,2,-1,2,-1,2*K.1^3,-2*K.1^3,2*K.1^3,0,-2*K.1^3,0,0,0,0,0,0,-2,1,1,-1,1,-2,1-2*K.1^2,2,-1+2*K.1^2,-2,-1,1,1,-2,1-2*K.1^2,-1+2*K.1^2,1,0,0,0,-1+2*K.1^2,1-2*K.1^2,0,0,0,2*K.1^3,-2*K.1^3,K.1^3,-1*K.1^3,2*K.1^3,-1*K.1^3,K.1^3,-2*K.1^3,0,0,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,2,-1,-1,2,2,-1,-1,-2*K.1^3,2*K.1^3,-2*K.1^3,0,2*K.1^3,0,0,0,0,0,0,1,-2,1,2,-2,1,0,-1,0,-2,-1,1,-2,1,0,0,1,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^3,-1*K.1^3,2*K.1^3,-2*K.1^3,K.1^3,-2*K.1^3,2*K.1^3,-1*K.1^3,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,2,-1,-1,2,2,-1,-1,2*K.1^3,-2*K.1^3,2*K.1^3,0,-2*K.1^3,0,0,0,0,0,0,1,-2,1,2,-2,1,0,-1,0,-2,-1,1,-2,1,0,0,1,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^3,K.1^3,-2*K.1^3,2*K.1^3,-1*K.1^3,2*K.1^3,-2*K.1^3,K.1^3,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,2,-1,-1,2,2,-1,-1,-2*K.1^3,2*K.1^3,-2*K.1^3,0,2*K.1^3,0,0,0,0,0,0,1,-2,1,2,-2,1,0,-1,0,-2,-1,1,-2,1,0,0,1,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^3,-1*K.1^3,2*K.1^3,-2*K.1^3,K.1^3,-2*K.1^3,2*K.1^3,-1*K.1^3,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,2,-1,-1,2,2,-1,-1,2*K.1^3,-2*K.1^3,2*K.1^3,0,-2*K.1^3,0,0,0,0,0,0,1,-2,1,2,-2,1,0,-1,0,-2,-1,1,-2,1,0,0,1,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^3,K.1^3,-2*K.1^3,2*K.1^3,-1*K.1^3,2*K.1^3,-2*K.1^3,K.1^3,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, 3, -1, 3, 1, -1, 3, 3, 3, 0, 0, 0, 0, -1, 1, 1, 3, -1, -1, 1, -1, -1, -1, 1, 3, 3, 3, -1, -1, -1, 3, -1, 3, 0, -1, -1, 0, 0, -1, -1, 0, 1, 1, 0, 0, 0, 0, 3, 3, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, 3, -1, 3, -1, -1, 3, 3, 3, 0, 0, 0, 0, 1, -1, -1, 3, 1, -1, -1, 1, 1, 1, -1, 3, 3, 3, -1, -1, -1, 3, -1, 3, 0, -1, -1, 0, 0, -1, -1, 0, -1, -1, 0, 0, 0, 0, 3, 3, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -3, 1, -3, -1, 1, 3, 3, 3, 0, 0, 0, 0, 1, -1, -1, 3, 1, -1, 1, -1, 1, -1, 1, 3, 3, 3, -1, -1, -1, -3, -1, -3, 0, -1, -1, 0, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 3, 3, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -3, 1, -3, 1, 1, 3, 3, 3, 0, 0, 0, 0, -1, 1, 1, 3, -1, -1, -1, 1, -1, 1, -1, 3, 3, 3, -1, -1, -1, -3, -1, -3, 0, -1, -1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 3, 3, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -3, 1, 3, -1, -1, 3, 3, 3, 0, 0, 0, 0, -1, 1, 1, -3, -1, 1, -1, 1, 1, -1, 1, 3, 3, 3, -1, -1, -1, -3, -1, -3, 0, -1, -1, 0, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, -3, -3, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -3, 1, 3, 1, -1, 3, 3, 3, 0, 0, 0, 0, 1, -1, -1, -3, 1, 1, 1, -1, -1, 1, -1, 3, 3, 3, -1, -1, -1, -3, -1, -3, 0, -1, -1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, -3, -3, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, 3, -1, -3, -1, 1, 3, 3, 3, 0, 0, 0, 0, -1, 1, 1, -3, -1, 1, 1, -1, 1, 1, -1, 3, 3, 3, -1, -1, -1, 3, -1, 3, 0, -1, -1, 0, 0, -1, -1, 0, -1, -1, 0, 0, 0, 0, -3, -3, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, 3, -1, -3, 1, 1, 3, 3, 3, 0, 0, 0, 0, 1, -1, -1, -3, 1, 1, -1, 1, -1, -1, 1, 3, 3, 3, -1, -1, -1, 3, -1, 3, 0, -1, -1, 0, 0, -1, -1, 0, 1, 1, 0, 0, 0, 0, -3, -3, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, -2, -2, 1, -2, -2, -2, 0, -2, 0, 4, 1, 1, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, -2, 4, -2, 4, 4, -2, 0, -2, 0, -2, -2, -2, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 4, -2, 4, -2, -2, -2, -2, 1, -2, -2, -2, 1, 0, 0, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, -4, -4, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 4, 2, 4, 2, -2, -2, -2, 1, -2, 2, 2, 1, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, -4, -4, -4, 0, -4, 0, 0, 0, 0, 0, 0, -2, -2, 1, -2, -2, -2, 0, -2, 0, 4, 1, 1, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -2, 4, -2, 4, 4, -2, 0, -2, 0, -2, -2, -2, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 4, -4, -4, 0, 4, 0, 2, 4, -4, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,0,-2,4,-2,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,-4,2,2,-2,2,-4,-2-4*K.1,4,2+4*K.1,2,-2,2,-1,2,-2-4*K.1,2+4*K.1,-1,0,0,0,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,0,-2,4,-2,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,-4,2,2,-2,2,-4,2+4*K.1,4,-2-4*K.1,2,-2,2,-1,2,2+4*K.1,-2-4*K.1,-1,0,0,0,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,0,-2,-2,1,4,-2,-2,1,-4*K.1,4*K.1,-4*K.1,0,4*K.1,0,0,0,0,0,0,2,2,-1,-2,2,2,0,-2,0,-4,1,-1,2,2,0,0,-1,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,-2*K.1,2*K.1,2*K.1,2*K.1,-2*K.1,-2*K.1,0,0,K.1,-1*K.1,K.1,-1*K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,0,-2,-2,1,4,-2,-2,1,4*K.1,-4*K.1,4*K.1,0,-4*K.1,0,0,0,0,0,0,2,2,-1,-2,2,2,0,-2,0,-4,1,-1,2,2,0,0,-1,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,2*K.1,-2*K.1,-2*K.1,-2*K.1,2*K.1,2*K.1,0,0,-1*K.1,K.1,-1*K.1,K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,0,4,-2,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,2,-4,2,4,-4,2,0,-2,0,2,-2,2,2,-1,0,0,-1,0,0,0,0,0,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,0,4,-2,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,2,-4,2,4,-4,2,0,-2,0,2,-2,2,2,-1,0,0,-1,0,0,0,0,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 0, 0, 0, 2, 0, 6, -3, -3, 0, 0, 0, 0, -2, 2, 2, 6, -2, -2, 0, 0, -2, 0, 0, -3, 6, -3, -2, -2, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -3, -3, 1, -1, 2, 2, -1, -2, -2, 1, 1, 1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 6, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, -2, 2, 2, 0, -2, 0, 2, -2, 0, 0, 0, 6, -3, -3, 1, 1, -2, -3, -2, -3, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -1, -1, 2, 1, 1, -2, 0, 0, -1, -1, 1, 1, 0, 0, -1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 0, 0, 0, -2, 0, 6, -3, -3, 0, 0, 0, 0, 2, -2, -2, 6, 2, -2, 0, 0, 2, 0, 0, -3, 6, -3, -2, -2, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -3, -3, -1, 1, -2, -2, 1, 2, 2, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 6, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 2, -2, -2, 0, 2, 0, -2, 2, 0, 0, 0, 6, -3, -3, 1, 1, -2, -3, -2, -3, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, 1, -2, -1, -1, 2, 0, 0, 1, 1, -1, -1, 0, 0, 1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, -6, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, -2, 2, 2, 0, -2, 0, -2, 2, 0, 0, 0, 6, -3, -3, 1, 1, -2, 3, -2, 3, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -1, -1, 2, 1, 1, -2, 0, 0, -1, -1, 1, 1, 0, 0, 1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, -6, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 2, -2, -2, 0, 2, 0, 2, -2, 0, 0, 0, 6, -3, -3, 1, 1, -2, 3, -2, 3, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, 1, -2, -1, -1, 2, 0, 0, 1, 1, -1, -1, 0, 0, -1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 0, 0, 0, -2, 0, 6, -3, -3, 0, 0, 0, 0, -2, 2, 2, -6, -2, 2, 0, 0, 2, 0, 0, -3, 6, -3, -2, -2, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 3, 3, 1, -1, 2, 2, -1, -2, -2, 1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 0, 0, 0, 2, 0, 6, -3, -3, 0, 0, 0, 0, 2, -2, -2, -6, 2, 2, 0, 0, -2, 0, 0, -3, 6, -3, -2, -2, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 3, 3, -1, 1, -2, -2, 1, 2, 2, -1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,6,6,6,0,0,0,0,-2*K.1,-2*K.1,2*K.1,0,2*K.1,0,0,0,0,0,0,-6,-6,-6,-2,2,2,0,-2,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1,-2*K.1,2*K.1,2*K.1,-2*K.1,2*K.1,2*K.1,0,0,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,6,6,6,0,0,0,0,2*K.1,2*K.1,-2*K.1,0,-2*K.1,0,0,0,0,0,0,-6,-6,-6,-2,2,2,0,-2,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1,2*K.1,-2*K.1,-2*K.1,2*K.1,-2*K.1,-2*K.1,0,0,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,-3,6,-3,0,0,0,0,-2*K.1^3,-2*K.1^3,2*K.1^3,0,2*K.1^3,0,0,0,0,0,0,-6,3,3,1,-1,2,3-6*K.1^2,-2,-3+6*K.1^2,0,1,-1,0,0,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,0,0,0,0,0,-2*K.1^3,-2*K.1^3,K.1^3,-1*K.1^3,2*K.1^3,K.1^3,-1*K.1^3,2*K.1^3,0,0,K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,0,0,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,-3,6,-3,0,0,0,0,2*K.1^3,2*K.1^3,-2*K.1^3,0,-2*K.1^3,0,0,0,0,0,0,-6,3,3,1,-1,2,-3+6*K.1^2,-2,3-6*K.1^2,0,1,-1,0,0,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,0,0,0,0,0,2*K.1^3,2*K.1^3,-1*K.1^3,K.1^3,-2*K.1^3,-1*K.1^3,K.1^3,-2*K.1^3,0,0,-1*K.1^3,K.1^3,K.1^3,-1*K.1^3,0,0,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,-3,6,-3,0,0,0,0,-2*K.1^3,-2*K.1^3,2*K.1^3,0,2*K.1^3,0,0,0,0,0,0,-6,3,3,1,-1,2,-3+6*K.1^2,-2,3-6*K.1^2,0,1,-1,0,0,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,0,0,0,0,0,-2*K.1^3,-2*K.1^3,K.1^3,-1*K.1^3,2*K.1^3,K.1^3,-1*K.1^3,2*K.1^3,0,0,K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,-3,6,-3,0,0,0,0,2*K.1^3,2*K.1^3,-2*K.1^3,0,-2*K.1^3,0,0,0,0,0,0,-6,3,3,1,-1,2,3-6*K.1^2,-2,-3+6*K.1^2,0,1,-1,0,0,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,0,0,0,0,0,2*K.1^3,2*K.1^3,-1*K.1^3,K.1^3,-2*K.1^3,-1*K.1^3,K.1^3,-2*K.1^3,0,0,-1*K.1^3,K.1^3,K.1^3,-1*K.1^3,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,6,-3,-3,0,0,0,0,-2*K.1^3,-2*K.1^3,2*K.1^3,0,2*K.1^3,0,0,0,0,0,0,3,-6,3,-2,2,-1,0,1,0,0,1,-1,0,0,0,0,0,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,3*K.1+3*K.1^-1,-3*K.1-3*K.1^-1,K.1^3,K.1^3,-2*K.1^3,2*K.1^3,-1*K.1^3,-2*K.1^3,2*K.1^3,-1*K.1^3,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,6,-3,-3,0,0,0,0,2*K.1^3,2*K.1^3,-2*K.1^3,0,-2*K.1^3,0,0,0,0,0,0,3,-6,3,-2,2,-1,0,1,0,0,1,-1,0,0,0,0,0,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,3*K.1+3*K.1^-1,-3*K.1-3*K.1^-1,-1*K.1^3,-1*K.1^3,2*K.1^3,-2*K.1^3,K.1^3,2*K.1^3,-2*K.1^3,K.1^3,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^3,K.1^3,K.1^3,-1*K.1^3,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,6,-3,-3,0,0,0,0,-2*K.1^3,-2*K.1^3,2*K.1^3,0,2*K.1^3,0,0,0,0,0,0,3,-6,3,-2,2,-1,0,1,0,0,1,-1,0,0,0,0,0,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,-3*K.1-3*K.1^-1,3*K.1+3*K.1^-1,K.1^3,K.1^3,-2*K.1^3,2*K.1^3,-1*K.1^3,-2*K.1^3,2*K.1^3,-1*K.1^3,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,0,6,-3,-3,0,0,0,0,2*K.1^3,2*K.1^3,-2*K.1^3,0,-2*K.1^3,0,0,0,0,0,0,3,-6,3,-2,2,-1,0,1,0,0,1,-1,0,0,0,0,0,1-2*K.1^2,-1+2*K.1^2,0,0,0,0,-3*K.1-3*K.1^-1,3*K.1+3*K.1^-1,-1*K.1^3,-1*K.1^3,2*K.1^3,-2*K.1^3,K.1^3,2*K.1^3,-2*K.1^3,K.1^3,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^3,K.1^3,K.1^3,-1*K.1^3,-1+2*K.1^2,1-2*K.1^2,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, 8, 8, 8, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, -4, -4, -4, 0, -4, 0, -4, 2, 2, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 8, -8, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -4, 4, 4, 0, -4, 0, 4, 2, -2, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[12, 12, -4, -4, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, -4, 4, 4, 0, -4, 0, 0, 0, 0, 0, 0, -6, -6, 3, 2, 2, 2, 0, 2, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, -4, -4, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 4, -4, -4, 0, 4, 0, 0, 0, 0, 0, 0, -6, -6, 3, 2, 2, 2, 0, 2, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, -2, -2, -2, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |12,-12,-4,4,0,0,0,0,0,-6,-6,3,0,0,0,0,-4*K.1,-4*K.1,4*K.1,0,4*K.1,0,0,0,0,0,0,6,6,-3,2,-2,-2,0,2,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1,2*K.1,-2*K.1,-2*K.1,2*K.1,-2*K.1,-2*K.1,0,0,-1*K.1,K.1,K.1,-1*K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |12,-12,-4,4,0,0,0,0,0,-6,-6,3,0,0,0,0,4*K.1,4*K.1,-4*K.1,0,-4*K.1,0,0,0,0,0,0,6,6,-3,2,-2,-2,0,2,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1,-2*K.1,2*K.1,2*K.1,-2*K.1,2*K.1,2*K.1,0,0,K.1,-1*K.1,-1*K.1,K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_1728_46361:= KnownIrreducibles(CR);