/* Group 1152.156080 downloaded from the LMFDB on 01 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, -2, -3, -2, 2, -3, 1838, 1037, 74, 1443, 1020, 102, 3604, 130, 3461, 36294, 9096, 5325, 2310, 1374, 62215, 19033, 7810, 1339, 1996, 214, 15578]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.3, GPC.7, GPC.8]); AssignNames(~GPC, ["a", "b", "c", "c2", "c4", "c8", "d", "e", "e2"]);
GPerm := PermutationGroup< 15 | (1,2,4,7)(3,5,8,6)(10,11), (13,15), (2,5)(3,8)(6,7), (1,3,4,8)(2,6,7,5), (1,4)(2,7)(3,8)(5,6), (13,14,15), (9,10,11), (12,13)(14,15), (12,14)(13,15) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1152_156080 := 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, c^12>,< 2, 3, d*e^3>,< 2, 3, c^12*d>,< 2, 4, b>,< 2, 6, a>,< 2, 6, a*c^4>,< 2, 12, b*e^3>,< 2, 24, a*b>,< 3, 2, e^4>,< 3, 8, c^16>,< 3, 16, c^16*e^4>,< 4, 2, c^18>,< 4, 6, a*d>,< 4, 6, c^18*e^3>,< 4, 6, a*c^4*d*e^3>,< 4, 12, a*c^14>,< 4, 12, a*c^14*d*e^3>,< 4, 12, b*c^15>,< 4, 24, a*b*d>,< 4, 36, b*c^3*d*e^3>,< 4, 72, a*b*c^19*e^3>,< 4, 72, a*b*c^13*d*e>,< 6, 2, c^12*e^4>,< 6, 4, b*e^2>,< 6, 4, b*e^4>,< 6, 6, d*e^5>,< 6, 6, c^12*d*e^2>,< 6, 8, c^20*d>,< 6, 12, a*e^2>,< 6, 12, a*c^4*e^2>,< 6, 12, b*e>,< 6, 12, b*d*e^2>,< 6, 16, c^4*e^4>,< 6, 24, a*b*e^2>,< 6, 24, a*b*e^4>,< 6, 32, b*c^8>,< 6, 32, b*c^8*e^2>,< 6, 32, b*c^8*e>,< 8, 6, c^9>,< 8, 6, c^15>,< 8, 18, c^9*e>,< 8, 18, c^21*e>,< 8, 36, a*c^5*d*e^2>,< 8, 36, a*c^11*d*e^2>,< 8, 36, a*c^21*d>,< 8, 36, a*c^3*e^3>,< 12, 4, c^6*e^2>,< 12, 12, a*e>,< 12, 12, c^6*e>,< 12, 12, a*c^4*d*e^2>,< 12, 16, c^22*e^3>,< 12, 24, a*c^2*e^2>,< 12, 24, a*c^2*e>,< 12, 24, a*b*e>,< 12, 24, a*b*d*e^2>,< 12, 32, c^2*e^2>,< 12, 96, b*c^11*e^3>,< 24, 48, c^11*d>,< 24, 48, c^13*e^3>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 0, 0, 2, 0, 2, -1, -1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, -1, 2, 2, 0, 0, -1, 0, 0, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, -1, 0, 0, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, -1, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, -2, -2, 0, 0, 2, 2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, 2, 2, 0, -2, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, -2, 0, -2, -2, 0, -2, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, -2, -2, 2, -1, 2, -1, 2, -2, -2, 2, -2, -2, 0, 2, 0, 0, 0, -1, 1, 1, -1, -1, 2, 1, 1, 1, 1, -1, -1, -1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 2, -1, 1, 1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, 0, 0, -2, 0, 2, -1, -1, 2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 2, -2, -2, 2, 2, -1, -2, -2, 0, 0, -1, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, -1, 0, 0, 0, 0, -1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, 0, 0, -2, 0, 2, -1, -1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, -2, -2, 2, 2, -1, -2, -2, 0, 0, -1, 0, 0, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 2, 0, 2, 0, -1, 0, 0, 0, 0, -1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, 2, 2, -2, -2, -1, 2, -1, 2, 2, 2, 2, 2, 2, 0, -2, 0, 0, 0, -1, 1, 1, -1, -1, 2, 1, 1, -1, -1, -1, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, 1, -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, 2, -2, -1, 2, -1, 2, -2, -2, 2, -2, -2, 0, -2, 0, 0, 0, -1, -1, -1, -1, -1, 2, -1, -1, 1, 1, -1, 1, 1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 2, 1, 1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 0, 0, 2, 0, 2, -1, -1, 2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 2, 2, 2, 2, 2, -1, 2, 2, 0, 0, -1, 0, 0, -1, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, 2, 0, 2, 0, -1, 0, 0, 0, 0, -1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,-2,2,0,0,2,2,2,0,2,-2,0,0,0,0,0,0,0,0,-2,0,0,2,-2,-2,0,0,2,-2,-2,0,0,0,0,0,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,-2,0,2,0,0,0,0,0,0,0,-1*K.1-K.1^3,K.1+K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,-2,2,0,0,2,2,2,0,2,-2,0,0,0,0,0,0,0,0,-2,0,0,2,-2,-2,0,0,2,-2,-2,0,0,0,0,0,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,-2,0,2,0,0,0,0,0,0,0,K.1+K.1^3,-1*K.1-K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,2,-2,0,0,2,2,2,0,-2,2,0,0,0,0,0,0,0,0,-2,0,0,2,-2,-2,0,0,-2,2,-2,0,0,0,0,0,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,2,0,-2,0,0,0,0,0,0,0,-1*K.1-K.1^3,K.1+K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,2,-2,0,0,2,2,2,0,-2,2,0,0,0,0,0,0,0,0,-2,0,0,2,-2,-2,0,0,-2,2,-2,0,0,0,0,0,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,2,0,-2,0,0,0,0,0,0,0,K.1+K.1^3,-1*K.1-K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,0,-2,-2,0,0,-1,2,-1,-2,-2,-2,-2,2,2,0,0,0,0,0,-1,-1-2*K.1,1+2*K.1,-1,-1,2,-1-2*K.1,1+2*K.1,1,1,-1,1+2*K.1,-1-2*K.1,0,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,1,1,1,1,-2,-1-2*K.1,-1,-1,1+2*K.1,1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,0,-2,-2,0,0,-1,2,-1,-2,-2,-2,-2,2,2,0,0,0,0,0,-1,1+2*K.1,-1-2*K.1,-1,-1,2,1+2*K.1,-1-2*K.1,1,1,-1,-1-2*K.1,1+2*K.1,0,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,1,1,1,1,-2,1+2*K.1,-1,-1,-1-2*K.1,1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,0,2,2,0,0,-1,2,-1,-2,2,2,-2,-2,-2,0,0,0,0,0,-1,-1-2*K.1,1+2*K.1,-1,-1,2,-1-2*K.1,1+2*K.1,-1,-1,-1,-1-2*K.1,1+2*K.1,0,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,1,-1,1,-1,-2,1+2*K.1,1,1,-1-2*K.1,1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,0,2,2,0,0,-1,2,-1,-2,2,2,-2,-2,-2,0,0,0,0,0,-1,1+2*K.1,-1-2*K.1,-1,-1,2,1+2*K.1,-1-2*K.1,-1,-1,-1,1+2*K.1,-1-2*K.1,0,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,1,-1,1,-1,-2,-1-2*K.1,1,1,1+2*K.1,1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, 3, 1, 1, -1, 1, 3, 0, 0, 3, -1, -1, -1, 1, -1, 3, -1, -1, 1, -1, 3, 3, 3, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, 0, 0, 0, 3, 3, -1, -1, 1, 1, -1, -1, 3, -1, -1, -1, 0, -1, 1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, 3, -1, -1, -1, -1, 3, 0, 0, 3, 1, 1, -1, -1, 1, 3, 1, -1, -1, 1, 3, 3, 3, -1, -1, 0, -1, -1, -1, -1, 0, -1, -1, 0, 0, 0, 3, 3, -1, -1, -1, -1, 1, 1, 3, 1, -1, 1, 0, 1, -1, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -3, -1, -1, 1, 1, 3, 0, 0, 3, 1, 1, -1, -1, 1, -3, -1, 1, 1, -1, 3, -3, -3, -1, -1, 0, 1, 1, -1, -1, 0, 1, 1, 0, 0, 0, 3, 3, -1, -1, -1, -1, 1, 1, 3, 1, -1, 1, 0, -1, -1, 1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -3, -1, -1, 1, 1, 3, 0, 0, 3, 1, 1, -1, -1, 1, 3, -1, -1, -1, 1, 3, -3, -3, -1, -1, 0, 1, 1, -1, -1, 0, 1, 1, 0, 0, 0, -3, -3, 1, 1, 1, 1, -1, -1, 3, 1, -1, 1, 0, -1, -1, 1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -3, 1, 1, 1, -1, 3, 0, 0, 3, -1, -1, -1, 1, -1, -3, 1, 1, -1, 1, 3, -3, -3, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, 0, 0, 0, 3, 3, -1, -1, 1, 1, -1, -1, 3, -1, -1, -1, 0, 1, 1, -1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -3, 1, 1, 1, -1, 3, 0, 0, 3, -1, -1, -1, 1, -1, 3, 1, -1, 1, -1, 3, -3, -3, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, 0, 0, 0, -3, -3, 1, 1, -1, -1, 1, 1, 3, -1, -1, -1, 0, 1, 1, -1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, 3, -1, -1, -1, -1, 3, 0, 0, 3, 1, 1, -1, -1, 1, -3, 1, 1, 1, -1, 3, 3, 3, -1, -1, 0, -1, -1, -1, -1, 0, -1, -1, 0, 0, 0, -3, -3, 1, 1, 1, 1, -1, -1, 3, 1, -1, 1, 0, 1, -1, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, 3, 1, 1, -1, 1, 3, 0, 0, 3, -1, -1, -1, 1, -1, -3, -1, 1, -1, 1, 3, 3, 3, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, 0, 0, 0, -3, -3, 1, 1, -1, -1, 1, 1, 3, -1, -1, -1, 0, -1, 1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 0, 0, 4, 0, -2, -2, 1, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 1, 0, 0, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 1, 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, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, -4, 0, 0, -4, 0, -2, -2, 1, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, -2, 2, 2, 0, 0, 1, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 0, -4, 4, 0, 0, -2, 4, -2, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 2, -4, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 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, 4, -4, 0, 0, -2, 4, -2, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 2, -4, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,0,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,4,-4,2,0,0,0,0,2,0,0,0,0,0,-2*K.1-2*K.1^3,2*K.1+2*K.1^3,-2*K.1-2*K.1^3,2*K.1+2*K.1^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^3,-1*K.1-K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,0,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,4,-4,2,0,0,0,0,2,0,0,0,0,0,2*K.1+2*K.1^3,-2*K.1-2*K.1^3,2*K.1+2*K.1^3,-2*K.1-2*K.1^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^3,K.1+K.1^3]; 
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,-2,1,-4,0,0,-4,0,0,0,0,0,0,0,-2,-2-4*K.1,2+4*K.1,-2,-2,-2,-2-4*K.1,2+4*K.1,0,0,1,0,0,0,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,2,0,2,0,2,0,0,0,0,-1,0,0,0]; 
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,-2,1,-4,0,0,-4,0,0,0,0,0,0,0,-2,2+4*K.1,-2-4*K.1,-2,-2,-2,2+4*K.1,-2-4*K.1,0,0,1,0,0,0,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,2,0,2,0,2,0,0,0,0,-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 6, 2, 2, -2, 2, -3, 0, 0, 6, -2, -2, -2, 2, -2, 0, -2, 0, 0, 0, -3, -3, -3, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 1, 1, 1, 0, 1, -1, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 0, -2, -2, 0, 0, 6, 0, 0, -6, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 6, 0, 0, -2, -2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 2, 2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 0, 2, 2, 0, 0, 6, 0, 0, -6, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 6, 0, 0, -2, -2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -2, 2, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 6, -2, -2, -2, -2, -3, 0, 0, 6, 2, 2, -2, -2, 2, 0, 2, 0, 0, 0, -3, -3, -3, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -1, 1, -1, 0, -1, 1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, -6, -2, -2, 2, 2, -3, 0, 0, 6, 2, 2, -2, -2, 2, 0, -2, 0, 0, 0, -3, 3, 3, 1, 1, 0, -1, -1, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -1, 1, -1, 0, 1, 1, -1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, -6, 2, 2, 2, -2, -3, 0, 0, 6, -2, -2, -2, 2, -2, 0, 2, 0, 0, 0, -3, 3, 3, 1, 1, 0, -1, -1, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 1, 1, 1, 0, -1, -1, 1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |6,-6,-2,2,0,-2,2,0,0,6,0,0,0,-2,2,0,0,0,0,0,0,0,0,-6,0,0,-2,2,0,0,0,2,-2,0,0,0,0,0,0,-3*K.1-3*K.1^3,3*K.1+3*K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,2,0,-2,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |6,-6,-2,2,0,-2,2,0,0,6,0,0,0,-2,2,0,0,0,0,0,0,0,0,-6,0,0,-2,2,0,0,0,2,-2,0,0,0,0,0,0,3*K.1+3*K.1^3,-3*K.1-3*K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,2,0,-2,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |6,-6,-2,2,0,2,-2,0,0,6,0,0,0,2,-2,0,0,0,0,0,0,0,0,-6,0,0,-2,2,0,0,0,-2,2,0,0,0,0,0,0,-3*K.1-3*K.1^3,3*K.1+3*K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,-2,0,2,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |6,-6,-2,2,0,2,-2,0,0,6,0,0,0,2,-2,0,0,0,0,0,0,0,0,-6,0,0,-2,2,0,0,0,-2,2,0,0,0,0,0,0,3*K.1+3*K.1^3,-3*K.1-3*K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,-2,0,2,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,6,-2,-2,0,-2,-2,0,0,-3,0,0,-6,2,2,2,2,-2,0,0,0,0,0,-3,-3-6*K.1,3+6*K.1,1,1,0,1+2*K.1,-1-2*K.1,1,1,0,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,0,0,0,3,-1,-1,-1,0,1+2*K.1,-1,1,-1-2*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,6,-2,-2,0,-2,-2,0,0,-3,0,0,-6,2,2,2,2,-2,0,0,0,0,0,-3,3+6*K.1,-3-6*K.1,1,1,0,-1-2*K.1,1+2*K.1,1,1,0,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,0,0,0,3,-1,-1,-1,0,-1-2*K.1,-1,1,1+2*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,6,-2,-2,0,2,2,0,0,-3,0,0,-6,-2,-2,2,-2,2,0,0,0,0,0,-3,-3-6*K.1,3+6*K.1,1,1,0,1+2*K.1,-1-2*K.1,-1,-1,0,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,0,0,0,3,1,-1,1,0,-1-2*K.1,1,-1,1+2*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,6,-2,-2,0,2,2,0,0,-3,0,0,-6,-2,-2,2,-2,2,0,0,0,0,0,-3,3+6*K.1,-3-6*K.1,1,1,0,-1-2*K.1,1+2*K.1,-1,-1,0,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,0,0,0,3,1,-1,1,0,1+2*K.1,1,-1,-1-2*K.1,0,0,0,0]; 
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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 4, 4, 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, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[12, -12, -4, 4, 0, -4, 4, 0, 0, -6, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 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, 4, -4, 0, 0, -6, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_1152_156080:= KnownIrreducibles(CR);