/* Group 216.110 downloaded from the LMFDB on 11 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([6, -2, -3, -2, -3, -2, -3, 12, 1838, 710, 50, 4035, 1881, 5404, 88, 5189]); a,b,c := Explode([GPC.1, GPC.3, GPC.5]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "c2"]);
GPerm := PermutationGroup< 13 | (3,7)(5,6)(8,9)(10,11)(12,13), (10,12)(11,13), (10,13)(11,12), (1,2,4)(3,6,8)(5,9,7), (2,5,6)(4,8,9), (1,3,7)(2,6,5)(4,8,9) >;
GLFp := MatrixGroup< 4, GF(3) | [[0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 2, 1], [1, 1, 2, 2, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2], [2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2], [0, 2, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0], [2, 1, 2, 2, 1, 0, 0, 1, 0, 1, 1, 2, 1, 0, 1, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_216_110 := 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, c^3>,< 2, 1, b^3>,< 2, 1, b^3*c^3>,< 2, 9, a^3>,< 2, 9, a^3*c>,< 2, 9, a^3*b*c^4>,< 2, 9, a^3*b*c^5>,< 3, 2, c^2>,< 3, 3, a^4*c^2>,< 3, 3, a^2*c^4>,< 3, 6, b^2>,< 3, 6, a^4*b^2*c^2>,< 3, 6, a^2*b^4>,< 6, 2, c>,< 6, 2, b^3*c^2>,< 6, 2, b^3*c>,< 6, 3, a^2*c>,< 6, 3, a^4*c>,< 6, 3, a^2*b^3>,< 6, 3, a^4*b^3>,< 6, 3, a^2*b^3*c>,< 6, 3, a^4*b^3*c>,< 6, 6, b>,< 6, 6, b^2*c>,< 6, 6, b*c>,< 6, 6, a^2*b>,< 6, 6, a^4*b>,< 6, 6, a^2*b^2*c>,< 6, 6, a^4*b^2*c>,< 6, 6, a^2*b*c>,< 6, 6, a^4*b*c>,< 6, 9, a>,< 6, 9, a^5>,< 6, 9, a*c>,< 6, 9, a^5*c>,< 6, 9, a*b>,< 6, 9, a^5*b>,< 6, 9, a*b*c>,< 6, 9, a^5*b*c>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,K.1^-1,K.1,1,K.1^-1,K.1,1,1,1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,1,K.1^-1,1,K.1^-1,1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,K.1,K.1^-1,1,K.1,K.1^-1,1,1,1,K.1^-1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.1,1,K.1,1,K.1,1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,-1,1,-1,1,1,-1,1,K.1^-1,K.1,1,K.1^-1,K.1,-1,1,-1,-1*K.1,-1*K.1^-1,K.1^-1,-1*K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1,-1*K.1^-1,1,K.1^-1,-1,-1*K.1,K.1,-1*K.1,K.1^-1,-1*K.1^-1,K.1,-1*K.1,-1*K.1^-1,K.1^-1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,-1,1,-1,1,1,-1,1,K.1,K.1^-1,1,K.1,K.1^-1,-1,1,-1,-1*K.1^-1,-1*K.1,K.1,-1*K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1,-1*K.1,1,K.1,-1,-1*K.1^-1,K.1^-1,-1*K.1^-1,K.1,-1*K.1,K.1^-1,-1*K.1^-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(3: Sparse := true);
S := [ K |1,-1,-1,1,1,-1,-1,1,1,K.1^-1,K.1,1,K.1^-1,K.1,-1,1,-1,-1*K.1,-1*K.1^-1,K.1^-1,-1*K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1,-1*K.1^-1,1,K.1^-1,-1,-1*K.1,K.1,-1*K.1,-1*K.1^-1,K.1^-1,-1*K.1,K.1,K.1^-1,-1*K.1^-1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,-1,1,1,-1,-1,1,1,K.1,K.1^-1,1,K.1,K.1^-1,-1,1,-1,-1*K.1^-1,-1*K.1,K.1,-1*K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1,-1*K.1,1,K.1,-1,-1*K.1^-1,K.1^-1,-1*K.1^-1,-1*K.1,K.1,-1*K.1^-1,K.1^-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(3: Sparse := true);
S := [ K |1,-1,1,-1,-1,1,-1,1,1,K.1^-1,K.1,1,K.1^-1,K.1,1,-1,-1,-1*K.1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,K.1,-1*K.1^-1,1,K.1^-1,-1,-1*K.1^-1,-1,-1*K.1,-1*K.1,K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,K.1^-1,K.1^-1,K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,1,-1,-1,1,-1,1,1,K.1,K.1^-1,1,K.1,K.1^-1,1,-1,-1,-1*K.1^-1,K.1,-1*K.1,-1*K.1,-1*K.1^-1,K.1^-1,-1*K.1,1,K.1,-1,-1*K.1,-1,-1*K.1^-1,-1*K.1^-1,K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,K.1,K.1,K.1^-1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,1,-1,1,-1,1,-1,1,K.1^-1,K.1,1,K.1^-1,K.1,1,-1,-1,-1*K.1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,K.1,-1*K.1^-1,1,K.1^-1,-1,-1*K.1^-1,-1,-1*K.1,-1*K.1,K.1,K.1^-1,K.1^-1,K.1,K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,1,-1,1,-1,1,-1,1,K.1,K.1^-1,1,K.1,K.1^-1,1,-1,-1,-1*K.1^-1,K.1,-1*K.1,-1*K.1,-1*K.1^-1,K.1^-1,-1*K.1,1,K.1,-1,-1*K.1,-1,-1*K.1^-1,-1*K.1^-1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,-1*K.1,-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(3: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,1,1,1,K.1^-1,K.1,1,K.1^-1,K.1,-1,-1,1,K.1,-1*K.1^-1,-1*K.1^-1,K.1^-1,-1*K.1,-1*K.1,K.1^-1,-1,-1*K.1^-1,-1,-1*K.1^-1,1,K.1,-1*K.1,-1*K.1,K.1^-1,-1*K.1^-1,K.1,-1*K.1,K.1^-1,-1*K.1^-1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,1,1,1,K.1,K.1^-1,1,K.1,K.1^-1,-1,-1,1,K.1^-1,-1*K.1,-1*K.1,K.1,-1*K.1^-1,-1*K.1^-1,K.1,-1,-1*K.1,-1,-1*K.1,1,K.1^-1,-1*K.1^-1,-1*K.1^-1,K.1,-1*K.1,K.1^-1,-1*K.1^-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(3: Sparse := true);
S := [ K |1,1,-1,-1,1,1,-1,-1,1,K.1^-1,K.1,1,K.1^-1,K.1,-1,-1,1,K.1,-1*K.1^-1,-1*K.1^-1,K.1^-1,-1*K.1,-1*K.1,K.1^-1,-1,-1*K.1^-1,-1,-1*K.1^-1,1,K.1,-1*K.1,-1*K.1,-1*K.1^-1,K.1^-1,-1*K.1,K.1,-1*K.1^-1,K.1^-1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,-1,-1,1,1,-1,-1,1,K.1,K.1^-1,1,K.1,K.1^-1,-1,-1,1,K.1^-1,-1*K.1,-1*K.1,K.1,-1*K.1^-1,-1*K.1^-1,K.1,-1,-1*K.1,-1,-1*K.1,1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,K.1,-1*K.1^-1,K.1^-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(3: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,K.1^-1,K.1,1,K.1^-1,K.1,1,1,1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,1,K.1^-1,1,K.1^-1,1,K.1,K.1,K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,K.1,K.1^-1,1,K.1,K.1^-1,1,1,1,K.1^-1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.1,1,K.1,1,K.1,1,K.1^-1,K.1^-1,K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-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, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,0,0,0,0,2,2*K.1^-1,2*K.1,-1,-1*K.1^-1,-1*K.1,2,2,2,2*K.1,2*K.1^-1,2*K.1^-1,2*K.1^-1,2*K.1,2*K.1,-1*K.1^-1,-1,-1*K.1^-1,-1,-1*K.1^-1,-1,-1*K.1,-1*K.1,-1*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,0,0,0,0,2,2*K.1,2*K.1^-1,-1,-1*K.1,-1*K.1^-1,2,2,2,2*K.1^-1,2*K.1,2*K.1,2*K.1,2*K.1^-1,2*K.1^-1,-1*K.1,-1,-1*K.1,-1,-1*K.1,-1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,2,2*K.1^-1,2*K.1,-1,-1*K.1^-1,-1*K.1,-2,2,-2,-2*K.1,-2*K.1^-1,2*K.1^-1,-2*K.1^-1,2*K.1,-2*K.1,K.1^-1,1,K.1^-1,-1,-1*K.1^-1,1,K.1,-1*K.1,K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,2,2*K.1,2*K.1^-1,-1,-1*K.1,-1*K.1^-1,-2,2,-2,-2*K.1^-1,-2*K.1,2*K.1,-2*K.1,2*K.1^-1,-2*K.1^-1,K.1,1,K.1,-1,-1*K.1,1,K.1^-1,-1*K.1^-1,K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,2,2*K.1^-1,2*K.1,-1,-1*K.1^-1,-1*K.1,2,-2,-2,-2*K.1,2*K.1^-1,-2*K.1^-1,-2*K.1^-1,-2*K.1,2*K.1,K.1^-1,-1,-1*K.1^-1,1,K.1^-1,1,K.1,K.1,-1*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,2,2*K.1,2*K.1^-1,-1,-1*K.1,-1*K.1^-1,2,-2,-2,-2*K.1^-1,2*K.1,-2*K.1,-2*K.1,-2*K.1^-1,2*K.1^-1,K.1,-1,-1*K.1,1,K.1,1,K.1^-1,K.1^-1,-1*K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,2,2*K.1^-1,2*K.1,-1,-1*K.1^-1,-1*K.1,-2,-2,2,2*K.1,-2*K.1^-1,-2*K.1^-1,2*K.1^-1,-2*K.1,-2*K.1,-1*K.1^-1,1,K.1^-1,1,K.1^-1,-1,-1*K.1,K.1,K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,2,2*K.1,2*K.1^-1,-1,-1*K.1,-1*K.1^-1,-2,-2,2,2*K.1^-1,-2*K.1,-2*K.1,2*K.1,-2*K.1^-1,-2*K.1^-1,-1*K.1,1,K.1,1,K.1,-1,-1*K.1^-1,K.1^-1,K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, -6, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, 6, -6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_216_110:= KnownIrreducibles(CR);