/* Group 972.469 downloaded from the LMFDB on 21 July 2026. */
 
/* 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([7, -2, -2, -3, -3, -3, -3, -3, 141, 36, 170, 5386, 353, 25204, 12611, 6003, 18156, 166, 15889]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.4, GPC.5, GPC.6]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "e", "e3"]);
GPerm := PermutationGroup< 27 | (4,7)(5,8)(6,9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27), (2,3)(5,6)(8,9)(10,20)(11,19)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27), (1,2,3)(10,11,12)(19,20,21), (1,20,11,2,21,12,3,19,10)(4,23,14,5,24,15,6,22,13)(7,26,17,8,27,18,9,25,16), (1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,25,22)(20,26,23)(21,27,24), (1,2,3)(7,9,8)(10,11,12)(16,18,17)(19,20,21)(25,27,26), (1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,27,26) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_972_469 := 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, 9, a>,< 2, 81, a*b^5>,< 2, 81, b^3*d*e^3>,< 3, 2, e^3>,< 3, 6, c^2>,< 3, 6, c^2*e^6>,< 3, 6, c^2*e^3>,< 3, 6, d>,< 3, 18, b^4*e^3>,< 3, 36, b^2*c^2*d^2*e^8>,< 6, 18, a*c>,< 6, 18, a*c*e^3>,< 6, 18, a*c*e^6>,< 6, 18, a*e^3>,< 6, 162, a*b^5*d^2>,< 6, 162, b^5*d*e^6>,< 9, 2, e^2>,< 9, 2, e^4>,< 9, 2, e^8>,< 9, 6, c^2*e^2>,< 9, 6, c*e^4>,< 9, 6, c^2*e^8>,< 9, 6, c^2*e^4>,< 9, 6, c*e^8>,< 9, 6, c^2*e^7>,< 9, 12, d*e>,< 9, 36, b^2*c^2*d^2*e^4>,< 9, 36, b^2*c*d^2*e^3>,< 9, 36, b^4*d*e>,< 18, 18, a*e>,< 18, 18, a*e^4>,< 18, 18, a*e^2>,< 18, 18, a*c*e>,< 18, 18, a*c*e^4>,< 18, 18, a*c^2*e^2>,< 18, 18, a*c*e^2>,< 18, 18, a*c^2*e>,< 18, 18, a*c*e^5>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, 0, 0, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, 2, 0, 0, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -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, 2, -1, -1, 2, -1, 1, 1, 1, -2, 0, 0, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, 1, 1, -2, -2, -2, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 0, 2, -1, 2, -1, -1, 2, -1, 1, 1, 1, -2, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 1, 1, 1, 1, 1, -2, -2, 1, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 0, 2, -1, 2, -1, -1, 2, 2, 1, 1, 1, -2, 0, 0, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -2, -2, 1, 1, 1, 1, 1, -2, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -1, -2, -2, -2, -2, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 0, 0, -2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 0, 0, 0, 4, -2, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 4, -2, 4, -2, 4, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 0, 0, 0, 4, -2, 4, -2, -2, -2, 1, 0, 0, 0, 0, 0, 0, -2, -2, -2, 4, -2, 4, -2, 4, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 0, 0, 0, 4, -2, 4, -2, -2, -2, 1, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 0, 0, 0, 4, 4, 4, 4, 4, -2, 1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 0, 2, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 0, -2, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,2,0,0,-3,-3,0,3,0,0,0,-1,2,-1,-1,0,0,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,0,0,0,0,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,2,0,0,-3,-3,0,3,0,0,0,-1,2,-1,-1,0,0,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,0,0,0,0,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,2,0,0,-3,-3,0,3,0,0,0,-1,2,-1,-1,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,2,0,0,-3,0,0,-3,3,0,0,-1,-1,2,-1,0,0,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,2,0,0,-3,0,0,-3,3,0,0,-1,-1,2,-1,0,0,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,0,0,0,0,K.1^4+K.1^-4,K.1+K.1^-1,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,2,0,0,-3,0,0,-3,3,0,0,-1,-1,2,-1,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,0,0,0,0,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1^4+K.1^-4,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,2,0,0,-3,3,0,0,-3,0,0,2,-1,-1,-1,0,0,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,2*K.1-2*K.1^2+K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,0,0,0,0,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,2,0,0,-3,3,0,0,-3,0,0,2,-1,-1,-1,0,0,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,2,0,0,-3,3,0,0,-3,0,0,2,-1,-1,-1,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,0,0,0,0,K.1^4+K.1^-4,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-2,0,0,-3,-3,0,3,0,0,0,1,-2,1,1,0,0,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,0,0,0,0,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-2,0,0,-3,-3,0,3,0,0,0,1,-2,1,1,0,0,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-2,0,0,-3,-3,0,3,0,0,0,1,-2,1,1,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-2,0,0,-3,0,0,-3,3,0,0,1,1,-2,1,0,0,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-2,0,0,-3,0,0,-3,3,0,0,1,1,-2,1,0,0,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,0,0,0,0,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-2,0,0,-3,0,0,-3,3,0,0,1,1,-2,1,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-2,0,0,-3,3,0,0,-3,0,0,-2,1,1,1,0,0,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,2*K.1-2*K.1^2+K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*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(9: Sparse := true);
S := [ K |6,-2,0,0,-3,3,0,0,-3,0,0,-2,1,1,1,0,0,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,3*K.1+3*K.1^-1,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-2,0,0,-3,3,0,0,-3,0,0,-2,1,1,1,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^4+3*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,0,0,0,0,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 0, 0, 0, 12, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 0, 0, 0, 0, 0, 0, 3, 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_972_469:= KnownIrreducibles(CR);