/* Group 1296.2039 downloaded from the LMFDB on 28 October 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([8, -2, -2, -3, -2, -2, -3, -3, -3, 161, 41, 1922, 450, 2123, 91, 2412, 116, 2317, 3390, 1382, 1222, 27663, 4639]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.4, GPC.7, GPC.8]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "c4", "d", "e"]);
GPerm := PermutationGroup< 20 | (10,11)(12,14)(13,15)(16,17)(19,20), (2,4)(3,7)(5,8)(6,9)(10,12,11,14)(13,17,15,16), (3,7)(5,6)(8,9)(10,13,11,15)(12,16,14,17), (10,11)(12,14)(13,15)(16,17), (1,2,4)(3,6,8)(5,9,7), (2,5,6)(4,8,9), (18,19,20), (1,3,7)(2,6,5)(4,8,9) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1296_2039 := 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 := true>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, c^6>,< 2, 3, a>,< 2, 3, a*b^2>,< 3, 2, e^2>,< 3, 2, b^4>,< 3, 4, b^4*e>,< 3, 6, d^2>,< 3, 6, c^8>,< 3, 12, c^4*d^2*e>,< 3, 12, b^2*c^10>,< 3, 12, b^4*d>,< 3, 24, b^4*c^8*d^2*e^2>,< 4, 18, c^3>,< 4, 18, b^3*c^6>,< 4, 18, b^3*c^7>,< 4, 54, a*b^3*c^6*e^2>,< 4, 54, a*b*c^7*d*e>,< 4, 54, a*b^2*c^3*e>,< 6, 2, c^6*e^2>,< 6, 2, b^2>,< 6, 4, b^2*e^2>,< 6, 6, a*e>,< 6, 6, a*b^2*e>,< 6, 6, c^2>,< 6, 6, c^6*d^2>,< 6, 12, c^2*d>,< 6, 12, b^4*c^2>,< 6, 12, b^2*d^2>,< 6, 18, a*d>,< 6, 18, a*c^4>,< 6, 18, a*c^2>,< 6, 18, a*b^2*d>,< 6, 24, b^2*c^4*d>,< 6, 36, a*c^4*d>,< 6, 36, a*c^2*d>,< 12, 18, c>,< 12, 18, c^5>,< 12, 18, b^3*d>,< 12, 18, b^3*d^2>,< 12, 18, b^3*c*e>,< 12, 18, b^3*c*d>,< 12, 36, b>,< 12, 36, b*c>,< 12, 36, b^2*c^3>,< 12, 36, b^2*c>,< 12, 36, b^4*c>,< 12, 36, b*d>,< 12, 36, b*d^2>,< 12, 36, b*c*e>,< 12, 36, b*c*d>,< 12, 54, a*b^3*d*e^2>,< 12, 54, a*b^3*d^2*e^2>,< 12, 54, a*b*c*d*e^2>,< 12, 54, a*b*c*d>,< 12, 54, a*b^2*c^5*e>,< 12, 54, a*b^2*c*e>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, -1, -1, 2, 2, 2, -1, -1, -1, 2, 2, 2, 0, 0, 0, 2, -1, -1, 0, 2, 0, 2, -1, 2, -1, 0, 0, 0, 0, -1, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, -1, 2, -1, 2, -1, -1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, 2, 2, -1, 2, -1, 2, -1, -1, 0, 0, -2, 0, 2, 0, 2, 2, 2, -2, 2, -2, -1, -1, -1, 2, 1, -2, -2, 1, -1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, 2, 2, -1, 2, -1, 2, -1, -1, 0, 0, 2, 0, -2, 0, 2, 2, 2, -2, 2, -2, -1, -1, -1, 2, 1, -2, -2, 1, -1, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 0, -2, 0, 2, 0, 0, 2, 2, 2, -2, -1, -2, 2, 2, -1, -1, -2, 1, 1, -2, -1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -1, 0, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 0, 2, 0, -2, 0, 0, 2, 2, 2, -2, -1, -2, 2, 2, -1, -1, -2, 1, 1, -2, -1, 1, 1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 1, 0, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, -1, -1, 2, 2, 2, -1, -1, -1, -2, -2, 2, 0, 0, 0, 2, -1, -1, 0, 2, 0, 2, -1, 2, -1, 0, 0, 0, 0, -1, 0, 0, -2, 2, 2, -2, -2, -2, 1, 1, 1, -1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, -1, -1, 2, 2, 2, -1, -1, -1, -2, 2, -2, 0, 0, 0, 2, -1, -1, 0, 2, 0, 2, -1, 2, -1, 0, 0, 0, 0, -1, 0, 0, -2, -2, -2, 2, -2, 2, -1, 1, 1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, -1, -1, 2, 2, 2, -1, -1, -1, 2, -2, -2, 0, 0, 0, 2, -1, -1, 0, 2, 0, 2, -1, 2, -1, 0, 0, 0, 0, -1, 0, 0, 2, -2, -2, -2, 2, -2, 1, -1, -1, 1, 1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, -1, 2, -1, 2, -1, -1, 0, 0, -2, 0, -2, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 0, -2, 0, -2, 0, 0, 2, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 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!\[2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, -2, 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(12: Sparse := true);
S := [ K |2,-2,-2,2,2,2,2,-1,2,-1,2,-1,-1,0,0,0,0,0,0,-2,-2,-2,2,-2,-2,1,1,1,-2,1,-2,2,-1,1,1,-1,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,K.1+K.1^-1,0,0,0,0,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,0,0,0,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,-2,2,2,2,2,-1,2,-1,2,-1,-1,0,0,0,0,0,0,-2,-2,-2,2,-2,-2,1,1,1,-2,1,-2,2,-1,1,1,-1,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,-1*K.1-K.1^-1,0,0,0,0,K.1+K.1^-1,0,K.1+K.1^-1,0,0,0,-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 |2,-2,-2,2,2,2,2,2,-1,-1,-1,2,-1,0,0,0,0,0,0,-2,-2,-2,2,1,-2,-2,-2,1,1,-2,1,-1,2,1,1,-1,0,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,-1*K.1-K.1^-1,0,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,-2,2,2,2,2,2,-1,-1,-1,2,-1,0,0,0,0,0,0,-2,-2,-2,2,1,-2,-2,-2,1,1,-2,1,-1,2,1,1,-1,0,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,K.1+K.1^-1,0,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,2,2,2,-1,2,-1,2,-1,-1,0,0,0,0,0,0,-2,-2,-2,-2,-2,2,1,1,1,-2,-1,2,-2,1,1,-1,1,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,K.1+K.1^-1,0,0,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,0,0,-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 |2,-2,2,-2,2,2,2,-1,2,-1,2,-1,-1,0,0,0,0,0,0,-2,-2,-2,-2,-2,2,1,1,1,-2,-1,2,-2,1,1,-1,1,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,-1*K.1-K.1^-1,0,0,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,0,0,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,2,2,2,2,-1,-1,-1,2,-1,0,0,0,0,0,0,-2,-2,-2,-2,1,2,-2,-2,1,1,2,-1,1,-2,1,-1,1,0,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,-1*K.1-K.1^-1,0,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,2,2,2,2,-1,-1,-1,2,-1,0,0,0,0,0,0,-2,-2,-2,-2,1,2,-2,-2,1,1,2,-1,1,-2,1,-1,1,0,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,K.1+K.1^-1,0,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 4, -2, -2, -2, 4, -2, -2, 1, 1, 0, 0, 4, 0, 0, 0, 4, -2, -2, 0, 4, 0, -2, 1, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 4, -2, -2, 4, -2, -2, 1, -2, 1, 0, 4, 0, 0, 0, 0, 4, -2, -2, 0, -2, 0, 4, -2, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, 1, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 4, -2, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, 4, -2, -2, 1, -2, -2, -2, -2, -2, 1, 1, 1, 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, 4, -2, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -2, -4, -2, -2, 1, -2, 2, 2, 2, 2, 1, -1, -1, 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, 0, 0, 4, -2, -2, -2, 4, -2, -2, 1, 1, 0, 0, -4, 0, 0, 0, 4, -2, -2, 0, 4, 0, -2, 1, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 4, -2, -2, 4, -2, -2, 1, -2, 1, 0, -4, 0, 0, 0, 0, 4, -2, -2, 0, -2, 0, 4, -2, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 0, 4, -2, -2, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, -4, 0, -4, 2, -4, 2, 0, 0, 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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 4, 4, 4, -2, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, 0, -4, -4, -4, 4, 2, -4, 2, 2, -1, 2, 2, 2, -2, -2, -1, -1, 1, 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, 4, -2, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 4, 2, 2, -1, 2, -2, -2, 2, 2, -1, 1, -1, 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(12: Sparse := true);
S := [ K |4,-4,0,0,4,-2,-2,-2,4,-2,-2,1,1,0,0,0,0,0,0,-4,2,2,0,-4,0,2,-1,2,2,0,0,0,0,-1,0,0,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,0,-1*K.1-K.1^-1,0,0,0,0,K.1+K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,0,0,4,-2,-2,-2,4,-2,-2,1,1,0,0,0,0,0,0,-4,2,2,0,-4,0,2,-1,2,2,0,0,0,0,-1,0,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,0,K.1+K.1^-1,0,0,0,0,-1*K.1-K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,0,0,4,-2,-2,4,-2,-2,1,-2,1,0,0,0,0,0,0,-4,2,2,0,2,0,-4,2,2,-1,0,0,0,0,-1,0,0,0,0,0,-2*K.1-2*K.1^-1,0,2*K.1+2*K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,K.1+K.1^-1,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,0,0,4,-2,-2,4,-2,-2,1,-2,1,0,0,0,0,0,0,-4,2,2,0,2,0,-4,2,2,-1,0,0,0,0,-1,0,0,0,0,0,2*K.1+2*K.1^-1,0,-2*K.1-2*K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,-1*K.1-K.1^-1,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, -3, 6, -3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -3, 6, -3, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -1, 2, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, -3, 6, -3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -3, 6, -3, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, -3, 6, -3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -3, 6, -3, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, -3, 6, -3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, -3, 6, -3, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -1, 2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-6,6,-3,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,3,-6,3,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,0,0,0,K.1+K.1^-1,0,0,K.1+K.1^-1,0,0,0,0,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,-6,6,-3,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,3,-6,3,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,0,0,0,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,0,0,0,K.1+K.1^-1,0,0,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,6,-6,-3,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,3,-6,3,3,0,-3,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,0,0,0,K.1+K.1^-1,0,0,K.1+K.1^-1,0,0,0,0,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |6,-6,6,-6,-3,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,3,-6,3,3,0,-3,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,0,0,0,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,0,0,0,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[8, 8, 0, 0, 8, -4, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 8, -4, -4, 0, -4, 0, -4, 2, 2, 2, 0, 0, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, 0, 8, -4, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, -8, 4, 4, 0, 4, 0, 4, -2, -2, -2, 0, 0, 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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[12, 12, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 1, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |12,-12,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,6,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,0,0,0,2*K.1+2*K.1^-1,0,0,-1*K.1-K.1^-1,0,0,0,0,K.1+K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |12,-12,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,6,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,0,0,0,-2*K.1-2*K.1^-1,0,0,K.1+K.1^-1,0,0,0,0,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_1296_2039:= KnownIrreducibles(CR);