/* Group 768.1090187 downloaded from the LMFDB on 09 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([9, -2, -2, -2, -2, -3, -2, 2, -2, 2, 109, 46, 1443, 732, 102, 1444, 733, 7781, 3902, 1004, 365, 411, 609, 41479, 20752, 3490, 2635, 5867, 1016]); a,b,c,d,e,f,g := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.7, GPC.8, GPC.9]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "e", "f", "g"]);
F:=GF(4); al:=F.1; GLFq := MatrixGroup< 4, F | [[1, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, al^1], [0, 0, 0, 1]],[[0, al^1, al^2, al^2], [al^1, al^1, 1, 0], [al^2, 1, al^2, 1], [0, 0, 0, 1]],[[0, 1, al^1, al^1], [al^2, al^2, al^1, 0], [1, 1, 0, al^2], [0, 0, 0, al^2]],[[0, al^1, al^2, al^2], [al^1, al^1, 1, al^1], [al^2, 1, al^2, 0], [0, 0, 0, 1]],[[al^2, al^2, 1, 1], [0, 1, 0, 0], [al^2, 1, al^2, al^1], [0, 0, 0, 1]],[[0, al^1, al^2, al^2], [al^2, 0, al^1, al^2], [0, 0, 1, al^2], [0, 0, 0, 1]],[[0, al^1, al^2, al^2], [al^1, al^1, 1, 1], [al^2, 1, al^2, al^1], [0, 0, 0, 1]],[[0, al^2, 0, 0], [1, 1, al^1, 0], [al^2, al^1, 1, al^2], [al^2, 1, al^1, 0]],[[0, al^1, al^2, 1], [0, 1, 0, 0], [al^1, al^2, 0, al^1], [0, 0, 0, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_768_1090187 := 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:= GLFq;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Matrix(4, [0, -1, -1, -1, -1, 0, -1, -1, -1, -1, 0, -1, -1, -1, -1, 0])>,< 2, 1, Matrix(4, [0, -1, -1, 0, 0, 2, 2, -1, 2, 0, 2, 1, -1, -1, -1, 0])>,< 2, 1, Matrix(4, [0, -1, -1, 1, 1, 1, 0, -1, 0, 1, 1, 2, -1, -1, -1, 0])>,< 2, 1, Matrix(4, [0, -1, -1, 2, 2, -1, 1, -1, 1, 2, -1, 0, -1, -1, -1, 0])>,< 2, 2, Matrix(4, [0, -1, -1, 2, 1, 1, 0, -1, 0, 1, 1, 0, -1, -1, -1, 0])>,< 2, 2, Matrix(4, [0, -1, -1, 0, -1, 0, -1, -1, -1, -1, 0, 1, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [-1, 1, 2, 2, 2, -1, 1, 1, -1, -1, 0, -1, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [-1, 1, 2, 2, 2, -1, 1, 0, -1, -1, 0, 1, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [-1, 1, 2, 2, 2, -1, 1, 2, -1, -1, 0, 2, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [1, 0, 1, 1, 1, 1, 0, 0, -1, -1, 0, -1, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [-1, 1, 2, 1, 1, 1, 0, 0, 2, 0, 2, -1, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [1, 0, 1, 1, 1, 1, 0, 2, -1, -1, 0, 0, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [-1, 1, 2, -1, -1, 0, -1, 0, 1, 2, -1, 2, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [-1, 1, 2, -1, -1, 0, -1, 1, 1, 2, -1, 0, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [-1, 1, 2, -1, -1, 0, -1, 2, 1, 2, -1, 1, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [1, 0, 1, 0, 0, 2, 2, 2, 1, 2, -1, -1, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [2, 2, 0, 0, 0, 2, 2, 2, -1, -1, 0, -1, -1, -1, -1, 0])>,< 2, 3, Matrix(4, [1, 0, 1, 0, 0, 2, 2, 0, 1, 2, -1, 0, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, -1, -1, 0, -1, -1, 1, 2, -1, -1, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [0, -1, -1, 0, -1, 0, -1, 2, -1, -1, 0, -1, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, 0, -1, 0, -1, -1, 1, 2, -1, 1, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, 0, -1, 0, -1, 2, 1, 2, -1, -1, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, 1, 2, -1, 1, -1, -1, -1, 0, 2, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, 1, 2, -1, 1, 0, -1, -1, 0, -1, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, 2, 2, -1, 1, -1, -1, -1, 0, 0, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [0, -1, -1, 1, 2, -1, 1, 0, 1, 2, -1, -1, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, 0, -1, 0, -1, 0, 1, 2, -1, 0, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, 0, -1, 0, -1, 1, 1, 2, -1, 2, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, 1, 2, -1, 1, 1, -1, -1, 0, 1, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [-1, 1, 2, 1, 2, -1, 1, 2, -1, -1, 0, 0, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [0, -1, -1, 0, 0, 2, 2, 2, 2, 0, 2, -1, -1, -1, -1, 0])>,< 2, 6, Matrix(4, [0, -1, -1, 1, 1, 1, 0, 0, 0, 1, 1, -1, -1, -1, -1, 0])>,< 2, 24, Matrix(4, [-1, 0, -1, -1, 0, -1, -1, -1, 2, 1, -1, 1, 0, 1, 2, -1])>,< 2, 24, Matrix(4, [0, -1, 2, -1, 2, -1, -1, 1, -1, -1, 0, -1, 1, 2, 0, -1])>,< 3, 32, Matrix(4, [-1, 2, 0, -1, -1, 2, -1, 2, 0, 0, 0, 1, -1, -1, -1, 1])>,< 4, 24, Matrix(4, [-1, 0, -1, 0, 0, -1, -1, -1, 2, 1, -1, -1, 0, 1, 2, -1])>,< 4, 24, Matrix(4, [-1, 1, -1, -1, -1, 0, 1, -1, -1, -1, 0, 0, 1, 2, 0, -1])>,< 4, 24, Matrix(4, [-1, 2, -1, 1, 1, -1, -1, -1, 0, 0, -1, -1, 2, 0, 1, -1])>,< 4, 24, Matrix(4, [-1, 0, -1, -1, 0, -1, -1, 0, 2, 1, -1, 0, 0, 1, 2, -1])>,< 4, 24, Matrix(4, [-1, 0, -1, 2, 0, -1, -1, 0, 2, 1, -1, -1, 0, 1, 2, -1])>,< 4, 24, Matrix(4, [-1, 1, -1, 1, -1, 0, 1, 2, -1, -1, 0, -1, 1, 2, 0, -1])>,< 4, 24, Matrix(4, [-1, 1, -1, 1, 2, -1, -1, 2, 1, 2, -1, -1, 1, 2, 0, -1])>,< 4, 24, Matrix(4, [0, -1, 2, -1, 2, -1, -1, 0, -1, -1, 0, 1, 1, 2, 0, -1])>,< 4, 24, Matrix(4, [0, -1, 2, 0, 2, -1, -1, 0, -1, -1, 0, -1, 1, 2, 0, -1])>,< 4, 24, Matrix(4, [0, -1, 2, -1, -1, 0, 1, 1, 1, 2, -1, -1, 1, 2, 0, -1])>,< 4, 24, Matrix(4, [0, -1, 2, 0, 2, -1, -1, 1, -1, -1, 0, 1, 1, 2, 0, -1])>,< 4, 24, Matrix(4, [0, -1, 2, 1, 2, -1, -1, 0, -1, -1, 0, 0, 1, 2, 0, -1])>,< 4, 24, Matrix(4, [0, -1, 2, 1, 2, -1, -1, 1, -1, -1, 0, 2, 1, 2, 0, -1])>,< 4, 24, Matrix(4, [0, -1, 2, 2, 2, -1, -1, 0, -1, -1, 0, 2, 1, 2, 0, -1])>,< 6, 32, Matrix(4, [2, -1, -1, 0, 2, 2, 1, -1, -1, 2, 2, 1, -1, -1, -1, 2])>,< 6, 32, Matrix(4, [1, -1, -1, 0, 1, -1, 0, 2, 2, 1, -1, -1, -1, -1, -1, 1])>,< 6, 32, Matrix(4, [0, 0, 1, 1, 2, 1, 1, 2, 0, 0, 0, 0, -1, -1, -1, 1])>,< 6, 32, Matrix(4, [0, 2, 0, 1, 2, 2, 1, 2, 2, 1, 0, 0, -1, -1, -1, 2])>,< 6, 32, Matrix(4, [-1, 2, 0, 0, 0, 0, 2, 2, 1, -1, 2, -1, -1, -1, -1, 1])>,< 6, 32, Matrix(4, [-1, 0, 1, 2, -1, 1, -1, 2, 2, 1, 0, 2, -1, -1, -1, 2])>,< 6, 32, Matrix(4, [0, 0, 1, 1, -1, 2, -1, 2, 2, 1, -1, 0, -1, -1, -1, 1])>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, 0, 0, 2, 2, -2, 2, 2, -2, 2, -2, -2, 2, -2, -2, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, 0, 0, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 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, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, 2, 2, 2, -2, 2, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, 2, -2, -2, -2, -2, 2, -2, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,-2,2,0,0,2,2,-2,2,2,-2,2,-2,-2,2,-2,-2,2,0,-2,0,0,0,-2,0,0,0,0,2,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1-2*K.1,-1,1,1+2*K.1,1,1+2*K.1,-1-2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,-2,2,0,0,2,2,-2,2,2,-2,2,-2,-2,2,-2,-2,2,0,-2,0,0,0,-2,0,0,0,0,2,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1+2*K.1,-1,1,-1-2*K.1,1,-1-2*K.1,1+2*K.1]; 
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,-2,-2,2,-2,2,2,2,-2,2,2,-2,-2,2,0,-2,0,0,0,2,0,0,0,0,-2,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1-2*K.1,1,1,1+2*K.1,-1,-1-2*K.1,1+2*K.1]; 
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,-2,-2,2,-2,2,2,2,-2,2,2,-2,-2,2,0,-2,0,0,0,2,0,0,0,0,-2,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1+2*K.1,1,1,-1-2*K.1,-1,1+2*K.1,-1-2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, -1, -1, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, 3, -1, -1, -1, 1, 1, 0, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, 3, 1, 1, 0, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, -1, -1, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, 3, -1, -1, -1, -1, -1, 0, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, 0, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, -3, 3, -3, 1, -3, 1, -1, 1, -1, -1, 1, 3, -1, 3, -1, -1, -1, -1, 1, -1, 1, -1, -3, 1, 1, 1, 1, 3, -1, 1, 0, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, -3, 3, -3, 1, -3, 1, -1, 1, -1, -1, 1, 3, -1, 3, -1, -1, -1, -1, 1, -1, 1, -1, -3, 1, 1, 1, 1, 3, 1, -1, 0, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, -3, 3, 1, -3, 1, 1, -1, -3, 3, -1, 1, -1, 3, -1, -1, -1, -1, 3, -3, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 0, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, -3, 3, 1, -3, 1, 1, -1, -3, 3, -1, 1, -1, 3, -1, -1, -1, -1, 3, -3, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 0, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, -3, 3, 1, 1, 1, -3, 3, 1, -1, 3, -3, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 3, 1, 1, -3, 1, 1, -1, -1, 1, 0, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, -3, 3, 1, 1, 1, -3, 3, 1, -1, 3, -3, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 3, 1, 1, -3, 1, 1, -1, 1, -1, 0, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, 3, -3, -3, 1, -3, 1, -1, 1, -1, -1, 1, 3, -1, 3, -1, 1, -1, 1, -1, 1, 1, 1, 3, -1, -1, 1, -1, -3, -1, 1, 0, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, 3, -3, -3, 1, -3, 1, -1, 1, -1, -1, 1, 3, -1, 3, -1, 1, -1, 1, -1, 1, 1, 1, 3, -1, -1, 1, -1, -3, 1, -1, 0, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, 3, -3, 1, -3, 1, 1, -1, -3, 3, -1, 1, -1, 3, -1, -1, 1, -1, -3, 3, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 0, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, 3, -3, 1, -3, 1, 1, -1, -3, 3, -1, 1, -1, 3, -1, -1, 1, -1, -3, 3, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 0, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, 3, -3, 1, 1, 1, -3, 3, 1, -1, 3, -3, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -3, -1, -1, 3, 1, -1, 1, -1, 1, 0, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -3, 3, -3, 1, 1, 1, -3, 3, 1, -1, 3, -3, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -3, -1, -1, 3, 1, -1, 1, 1, -1, 0, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -3, -3, -1, -1, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -3, 1, 1, -3, -1, 1, 1, -1, -1, 0, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -3, -3, -1, -1, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -3, 1, 1, -3, -1, 1, 1, 1, 1, 0, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -3, -3, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, 1, -1, -3, -3, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 0, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -3, -3, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, 3, -1, -1, 1, -1, -3, -3, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 0, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -3, -3, 3, -1, 3, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, 1, -1, 1, 1, 1, -1, 1, -3, 1, 1, -1, 1, -3, -1, -1, 0, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -3, -3, 3, -1, 3, -1, -1, -1, -1, -1, -1, 3, -1, 3, -1, 1, -1, 1, 1, 1, -1, 1, -3, 1, 1, -1, 1, -3, 1, 1, 0, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 6, 6, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 2, -2, 2, 2, -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`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, -6, 6, 0, 0, -2, -2, 2, 6, 6, 2, -2, -6, -6, -2, 2, 2, -2, 0, 2, 0, 0, 0, 2, 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!\[6, -6, -6, 6, 0, 0, -2, 6, 2, -2, -2, -6, 6, 2, 2, -2, -6, 2, -2, 0, 2, 0, 0, 0, 2, 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!\[6, -6, -6, 6, 0, 0, 6, -2, -6, -2, -2, 2, -2, 2, 2, 6, 2, -6, -2, 0, 2, 0, 0, 0, 2, 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!\[6, -6, 6, -6, 0, 0, -6, 2, 6, 2, -2, -2, -2, 2, -2, 6, 2, -6, -2, 0, 2, 0, 0, 0, -2, 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!\[6, -6, 6, -6, 0, 0, 2, -6, -2, 2, -2, 6, 6, 2, -2, -2, -6, 2, -2, 0, 2, 0, 0, 0, -2, 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!\[6, -6, 6, -6, 0, 0, 2, 2, -2, -6, 6, -2, -2, -6, 6, -2, 2, 2, -2, 0, 2, 0, 0, 0, -2, 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!\[6, 6, -6, -6, -6, 6, 2, 2, 2, 2, -2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, 2, -2, -2, -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`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, 6, -6, 2, 2, 2, 2, -2, 2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 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`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, -6, -6, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 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`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, -6, 6, 0, 0, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 2, 2, 2, -4, -2, 0, 0, 4, -2, 0, 0, -4, 0, 2, 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, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, -6, 6, 0, 0, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 2, 2, 2, 4, -2, 0, 0, -4, -2, 0, 0, 4, 0, 2, -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, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, 6, -6, 0, 0, 2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 2, -4, -2, 0, 0, 4, 2, 0, 0, 4, 0, -2, -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, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, 6, -6, 0, 0, 2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 4, -2, 0, 0, -4, 2, 0, 0, -4, 0, -2, 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, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_768_1090187:= KnownIrreducibles(CR);