/* Group 384.2611 downloaded from the LMFDB on 29 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, 2, -2, -3, -2, 2, -2, 530, 66, 1283, 91, 1284, 2901, 2038, 2046, 166]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.3, GPC.6, GPC.7]); AssignNames(~GPC, ["a", "b", "c", "c2", "c4", "d", "e", "e2"]);
GPerm := PermutationGroup< 15 | (2,5,6,8)(3,7)(9,10,11,12), (1,2)(3,5)(4,6)(7,8), (1,3)(2,5)(4,7)(6,8)(10,12)(14,15), (1,3)(2,5)(4,7)(6,8), (1,4)(2,6)(3,7)(5,8)(9,11)(10,12), (2,6)(5,8)(9,11)(10,12), (1,4)(2,6)(3,7)(5,8), (13,14,15) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_384_2611 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
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, e^2>,< 2, 1, b>,< 2, 1, b*e^2>,< 2, 2, d>,< 2, 2, b*c^6>,< 2, 2, b*d>,< 2, 2, b*c^6*d>,< 2, 2, c^6>,< 2, 2, c^6*d*e^2>,< 2, 4, c^6*e>,< 2, 4, b*c^6*e>,< 2, 6, a>,< 2, 6, a*e^2>,< 2, 6, a*d>,< 2, 6, a*d*e^2>,< 2, 12, a*c^2>,< 2, 12, a*c^2*e>,< 2, 12, a*c^2*d>,< 2, 12, a*c^2*d*e>,< 3, 2, c^8>,< 4, 4, e^3>,< 4, 4, b*e^3>,< 4, 8, c^3>,< 4, 8, c^9>,< 4, 8, c^3*d*e>,< 4, 8, c^9*e>,< 4, 12, a*e>,< 4, 12, a*d*e>,< 4, 24, a*c^9*e>,< 4, 24, a*b*c^3*d*e>,< 4, 24, a*b*c^3>,< 4, 24, a*c^9>,< 6, 2, b*c^4>,< 6, 2, b*c^4*e^2>,< 6, 2, c^8*e^2>,< 6, 4, c^4*d>,< 6, 4, b*c^2>,< 6, 4, b*c^4*d>,< 6, 4, b*c^2*d>,< 6, 4, c^2>,< 6, 4, c^2*d*e^2>,< 6, 8, c^2*e>,< 6, 8, b*c^2*e>,< 12, 8, c^4*e>,< 12, 8, b*c^4*e>,< 12, 8, c>,< 12, 8, c^11>,< 12, 8, c^5>,< 12, 8, c^7>,< 12, 8, c*e>,< 12, 8, c^11*e>,< 12, 8, c^5*e>,< 12, 8, c^7*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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1*K.1,K.1,-1*K.1,K.1,-1,-1,-1*K.1,K.1,K.1,-1*K.1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1*K.1,K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,1,-1*K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,K.1,-1*K.1,K.1,-1*K.1,-1,-1,K.1,-1*K.1,-1*K.1,K.1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,1,K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1*K.1,K.1,-1*K.1,K.1,1,1,K.1,-1*K.1,-1*K.1,K.1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1*K.1,K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,1,-1*K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,K.1,-1*K.1,K.1,-1*K.1,1,1,-1*K.1,K.1,K.1,-1*K.1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,1,K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,-1*K.1,K.1,K.1,-1*K.1,1,1,-1*K.1,K.1,-1*K.1,K.1,1,1,1,-1,-1,1,1,-1,-1,1,1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1,K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,K.1,-1*K.1,-1*K.1,K.1,1,1,K.1,-1*K.1,K.1,-1*K.1,1,1,1,-1,-1,1,1,-1,-1,1,1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,K.1,-1,-1*K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,-1*K.1,K.1,K.1,-1*K.1,-1,-1,K.1,-1*K.1,K.1,-1*K.1,1,1,1,-1,-1,1,1,-1,-1,1,1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1,K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,K.1,-1*K.1,-1*K.1,K.1,-1,-1,-1*K.1,K.1,-1*K.1,K.1,1,1,1,-1,-1,1,1,-1,-1,1,1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,K.1,-1,-1*K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -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, -2, 2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 2, -2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 2, -2, 2, 2, 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, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, -2, -2, 2, 2, 2, -2, -2, -2, 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, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, -2, -2, 2, 2, 2, -2, -2, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 0, 0, -2, -2, 2, 2, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 2, -2, -2, 2, -2, 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, 0, 0, 2, 2, -2, -2, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 2, -2, -2, 2, -2, 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, 0, 0, -2, -2, 2, 2, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 2, 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, 0, 0, 2, 2, -2, -2, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -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, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -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, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -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; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,2,-2,-2,-2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,-1,2,2,-2*K.1,2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,-1,-1,-1,1,1,-1,-1,1,1,1,1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,-1,K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,2,-2,-2,-2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,-1,2,2,2*K.1,-2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,-1,-1,-1,1,1,-1,-1,1,1,1,1,-1*K.1,K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1,-1*K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,2,-2,-2,-2,-2,2,2,2,2,0,0,0,0,0,0,0,0,-1,-2,-2,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,K.1,1,-1*K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,2,-2,-2,-2,-2,2,2,2,2,0,0,0,0,0,0,0,0,-1,-2,-2,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,1,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,-2,2,-2,2,-2,2,-2,-2,2,0,0,0,0,0,0,0,0,-1,2,-2,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,1,-1,-1,1,1,-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,1,K.1+K.1^-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,-2,2,-2,-2,2,0,0,0,0,0,0,0,0,-1,2,-2,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,1,-1,-1,1,1,-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,1,-1*K.1-K.1^-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,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,-1,-2,2,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,1,-1,-1,1,-1,1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1,K.1+K.1^-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,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,-1,-2,2,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,1,-1,-1,1,-1,1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1,-1*K.1-K.1^-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,-2,2,2,-2,-2,2,0,0,0,0,0,0,0,0,-1,-2,2,0,0,0,0,0,0,0,0,0,0,-1,1,1,1,-1,1,-1,1,-1,1,-1,-1-2*K.1,-1-2*K.1,1+2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,-1,1+2*K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,-2,2,2,-2,-2,2,0,0,0,0,0,0,0,0,-1,-2,2,0,0,0,0,0,0,0,0,0,0,-1,1,1,1,-1,1,-1,1,-1,1,-1,1+2*K.1,1+2*K.1,-1-2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,-1,-1-2*K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,-2,2,2,-2,2,-2,0,0,0,0,0,0,0,0,-1,2,-2,0,0,0,0,0,0,0,0,0,0,-1,1,1,1,-1,1,-1,1,-1,-1,1,-1-2*K.1,1+2*K.1,1+2*K.1,-1-2*K.1,-1-2*K.1,-1-2*K.1,1+2*K.1,1,1+2*K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,-2,2,2,-2,2,-2,0,0,0,0,0,0,0,0,-1,2,-2,0,0,0,0,0,0,0,0,0,0,-1,1,1,1,-1,1,-1,1,-1,-1,1,1+2*K.1,-1-2*K.1,-1-2*K.1,1+2*K.1,1+2*K.1,1+2*K.1,-1-2*K.1,1,-1-2*K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 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, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 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, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 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, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 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, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, -2, 2, -2, -2, 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, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, -2, 2, 2, 2, 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, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, -2, 2, 2, -2, 2, 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, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 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; 
_ := CharacterTable(G : Check := 0); 
chartbl_384_2611:= KnownIrreducibles(CR);