/* Group 972.453 downloaded from the LMFDB on 05 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([7, -2, -2, -3, -3, -3, -3, -3, 141, 36, 170, 1354, 605, 2524, 1271, 36293, 166, 31758]); 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< 18 | (3,7)(5,6)(8,9), (2,4)(3,7)(5,8)(6,9)(11,14)(12,13)(15,16)(17,18), (10,11,15,13,17,18,12,16,14), (1,2,4)(3,6,8)(5,9,7)(10,12,13)(11,16,17)(14,18,15), (2,5,6)(4,8,9), (10,13,12)(11,17,16)(14,15,18), (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_972_453 := 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, b^3>,< 2, 81, a*b^2*d^2*e^8>,< 2, 81, a*b^5>,< 3, 2, e^3>,< 3, 2, d>,< 3, 4, d*e^3>,< 3, 6, b^2>,< 3, 6, b^2*e^6>,< 3, 6, b^2*e^3>,< 3, 6, c*d>,< 3, 12, c*e^3>,< 3, 12, b^2*c>,< 3, 12, b^2*c*e^3>,< 3, 12, b^2*c*e^6>,< 6, 18, b>,< 6, 18, b*e^3>,< 6, 18, b*e^6>,< 6, 18, b^3*e^3>,< 6, 162, a*b^2*c^2*d*e^8>,< 6, 162, a*b^5*d^2>,< 9, 2, e^2>,< 9, 2, e^4>,< 9, 2, e^8>,< 9, 4, d*e>,< 9, 4, d*e^2>,< 9, 4, d*e^4>,< 9, 6, b^2*e^2>,< 9, 6, b^4*e^4>,< 9, 6, b^2*e^8>,< 9, 6, b^2*e^4>,< 9, 6, b^4*e^8>,< 9, 6, b^2*e^7>,< 9, 12, c*e>,< 9, 12, c*e^2>,< 9, 12, c*e^4>,< 9, 12, b^2*c*e>,< 9, 12, b^4*c*e^2>,< 9, 12, b^2*c*e^4>,< 9, 12, b^2*c*e^2>,< 9, 12, b^2*c*e^5>,< 9, 12, b^4*c*e>,< 18, 18, b*e>,< 18, 18, b*e^4>,< 18, 18, b*e^7>,< 18, 18, b*e^2>,< 18, 18, b^5*e>,< 18, 18, b*e^5>,< 18, 18, b^3*e>,< 18, 18, b^3*e^4>,< 18, 18, b^3*e^2>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 0, 2, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -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, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, 2, -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, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, 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, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, -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, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, 1, -2, 1, 1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, 2, -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, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, 1, -2, 1, 1, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -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, -1, -1, -1, 2, 2, -1, -1, -1, 1, -2, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, -1, -1, -1, -1, -1, -1, -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, -2, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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 |2,2,0,0,-1,2,-1,-1,-1,2,2,-1,-1,2,-1,2,-1,-1,-1,0,0,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.1^2+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,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,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,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 |2,2,0,0,-1,2,-1,-1,-1,2,2,-1,-1,2,-1,2,-1,-1,-1,0,0,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+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,K.1+K.1^-1,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.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,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 |2,2,0,0,-1,2,-1,-1,-1,2,2,-1,-1,2,-1,2,-1,-1,-1,0,0,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.1^4+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,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+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,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+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,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 |2,2,0,0,-1,2,-1,-1,2,-1,2,-1,-1,-1,2,-1,-1,-1,2,0,0,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,K.1^2+K.1^-2,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+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,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 |2,2,0,0,-1,2,-1,-1,2,-1,2,-1,-1,-1,2,-1,-1,-1,2,0,0,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,K.1+K.1^-1,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.1^4+K.1^-4,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,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.1^4+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 |2,2,0,0,-1,2,-1,-1,2,-1,2,-1,-1,-1,2,-1,-1,-1,2,0,0,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,K.1^4+K.1^-4,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.1^2+K.1^-2,K.1^2+K.1^-2,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+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^2+K.1^-2,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 |2,2,0,0,-1,2,-1,2,-1,-1,2,-1,2,-1,-1,-1,-1,2,-1,0,0,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.1^4+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.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,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+K.1^-1,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+K.1^-1,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 |2,2,0,0,-1,2,-1,2,-1,-1,2,-1,2,-1,-1,-1,-1,2,-1,0,0,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.1^2+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+K.1^-1,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,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.1^4+K.1^-4,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,K.1+K.1^-1,K.1^4+K.1^-4,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 |2,2,0,0,-1,2,-1,2,-1,-1,2,-1,2,-1,-1,-1,-1,2,-1,0,0,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+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.1^4+K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,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.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,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 |2,-2,0,0,-1,2,-1,-1,-1,2,2,-1,-1,2,-1,-2,1,1,1,0,0,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.1^2+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,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,-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.1^4-K.1^-4,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |2,-2,0,0,-1,2,-1,-1,-1,2,2,-1,-1,2,-1,-2,1,1,1,0,0,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+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,K.1+K.1^-1,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.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,-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.1^2-K.1^-2,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |2,-2,0,0,-1,2,-1,-1,-1,2,2,-1,-1,2,-1,-2,1,1,1,0,0,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.1^4+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,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+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,-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-K.1^-1,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |2,-2,0,0,-1,2,-1,-1,2,-1,2,-1,-1,-1,2,1,1,1,-2,0,0,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,K.1^2+K.1^-2,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+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-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.1^2-K.1^-2,-1*K.1-K.1^-1,-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 |2,-2,0,0,-1,2,-1,-1,2,-1,2,-1,-1,-1,2,1,1,1,-2,0,0,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,K.1+K.1^-1,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.1^4+K.1^-4,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-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-K.1^-1,-1*K.1^4-K.1^-4,-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 |2,-2,0,0,-1,2,-1,-1,2,-1,2,-1,-1,-1,2,1,1,1,-2,0,0,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,K.1^4+K.1^-4,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.1^2+K.1^-2,K.1^2+K.1^-2,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+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-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.1^4-K.1^-4,-1*K.1^2-K.1^-2,-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 |2,-2,0,0,-1,2,-1,2,-1,-1,2,-1,2,-1,-1,1,1,-2,1,0,0,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.1^4+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.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-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.1^2-K.1^-2,-1*K.1-K.1^-1,-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 |2,-2,0,0,-1,2,-1,2,-1,-1,2,-1,2,-1,-1,1,1,-2,1,0,0,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.1^2+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+K.1^-1,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1+K.1^-1,-1*K.1-K.1^-1,-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-K.1^-1,-1*K.1^4-K.1^-4,-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; 
K := CyclotomicField(9: Sparse := true);
S := [ K |2,-2,0,0,-1,2,-1,2,-1,-1,2,-1,2,-1,-1,1,1,-2,1,0,0,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+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.1^4+K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-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.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 4, 4, -2, 4, 1, 1, 1, -2, 1, -2, 1, -2, 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, 4, 4, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, 4, -2, 1, 1, -2, 1, -2, 1, 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, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, -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, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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 |4,0,0,0,-2,4,-2,-2,-2,4,-2,1,1,-2,1,0,0,0,0,0,0,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^4+2*K.1^-4,-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.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |4,0,0,0,-2,4,-2,-2,-2,4,-2,1,1,-2,1,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^4+2*K.1^-4,2*K.1^2+2*K.1^-2,-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.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |4,0,0,0,-2,4,-2,-2,-2,4,-2,1,1,-2,1,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-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-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |4,0,0,0,-2,4,-2,-2,4,-2,-2,1,1,1,-2,0,0,0,0,0,0,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-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.1^4-K.1^-4,-1*K.1^4-K.1^-4,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |4,0,0,0,-2,4,-2,-2,4,-2,-2,1,1,1,-2,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,-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.1^2-K.1^-2,-1*K.1^2-K.1^-2,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |4,0,0,0,-2,4,-2,-2,4,-2,-2,1,1,1,-2,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-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-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |4,0,0,0,-2,4,-2,4,-2,-2,-2,1,-2,1,1,0,0,0,0,0,0,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-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^-2,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |4,0,0,0,-2,4,-2,4,-2,-2,-2,1,-2,1,1,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-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^-1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |4,0,0,0,-2,4,-2,4,-2,-2,-2,1,-2,1,1,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-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^-4,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 0, 0, 2, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 6, 6, 6, -3, -3, -3, 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!\[6, 0, 0, -2, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 6, 6, -3, -3, -3, 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, 0, 0, 0, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 3, 3, 3, 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(9: Sparse := true);
S := [ K |12,0,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6*K.1^4+6*K.1^-4,6*K.1+6*K.1^-1,6*K.1^2+6*K.1^-2,-3*K.1^2-3*K.1^-2,-3*K.1^4-3*K.1^-4,-3*K.1-3*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |12,0,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6*K.1^2+6*K.1^-2,6*K.1^4+6*K.1^-4,6*K.1+6*K.1^-1,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,-3*K.1^4-3*K.1^-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |12,0,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6*K.1+6*K.1^-1,6*K.1^2+6*K.1^-2,6*K.1^4+6*K.1^-4,-3*K.1^4-3*K.1^-4,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_972_453:= KnownIrreducibles(CR);