/* Group 768.1089108 downloaded from the LMFDB on 05 February 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([9, 2, 2, 2, 3, 2, 2, 2, 2, 2, 542, 74, 579, 11884, 3802, 2056, 1229, 30246, 7584, 3057, 5641, 1546, 2059, 916, 214, 1970, 4895]); a,b,c,d,e,f,g := Explode([GPC.1, GPC.2, GPC.3, GPC.5, GPC.6, GPC.7, GPC.8]); AssignNames(~GPC, ["a", "b", "c", "c2", "d", "e", "f", "g", "g2"]);
GPerm := PermutationGroup< 12 | (1,2)(3,8)(4,7)(5,6)(9,10)(11,12), (9,11)(10,12), (9,10)(11,12), (1,2)(3,7)(4,8)(5,6)(9,12)(10,11), (3,4,5)(6,7,8), (1,3)(2,6)(4,5)(7,8), (1,4)(2,7)(3,5)(6,8), (1,4)(2,8)(3,5)(6,7), (1,5)(2,6)(3,4)(7,8) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_768_1089108 := 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 := true,
solvable := true,
supersolvable := false>; 

 
/* Character Table */
G:= GPerm;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, G!(9,12)(10,11)>,< 2, 1, G!(9,10)(11,12)>,< 2, 1, G!(9,11)(10,12)>,< 2, 3, G!(1,3)(2,7)(4,5)(6,8)(9,10)(11,12)>,< 2, 3, G!(1,3)(2,7)(4,5)(6,8)(9,11)(10,12)>,< 2, 3, G!(1,3)(2,7)(4,5)(6,8)(9,12)(10,11)>,< 2, 3, G!(1,3)(2,7)(4,5)(6,8)>,< 2, 4, G!(1,8)(2,4)(3,6)(5,7)(9,12)(10,11)>,< 2, 4, G!(1,8)(2,4)(3,6)(5,7)>,< 2, 4, G!(1,7)(2,3)(4,6)(5,8)(9,11)(10,12)>,< 2, 4, G!(1,6)(2,5)(3,8)(4,7)(9,10)(11,12)>,< 2, 6, G!(2,6)(7,8)(9,10)(11,12)>,< 2, 6, G!(2,6)(7,8)(9,11)(10,12)>,< 2, 6, G!(2,6)(7,8)(9,12)(10,11)>,< 2, 6, G!(1,3)(2,6)(4,5)(7,8)(9,10)(11,12)>,< 2, 6, G!(1,3)(2,6)(4,5)(7,8)(9,11)(10,12)>,< 2, 6, G!(1,3)(2,6)(4,5)(7,8)(9,12)(10,11)>,< 2, 6, G!(2,7)(6,8)>,< 2, 6, G!(1,3)(2,6)(4,5)(7,8)>,< 2, 12, G!(4,5)(6,8)>,< 2, 12, G!(4,5)(6,8)(9,10)(11,12)>,< 2, 12, G!(4,5)(6,8)(9,11)(10,12)>,< 2, 12, G!(4,5)(6,8)(9,12)(10,11)>,< 2, 12, G!(1,2)(3,6)(4,8)(5,7)>,< 2, 12, G!(1,2)(3,6)(4,8)(5,7)(9,10)(11,12)>,< 2, 12, G!(1,2)(3,6)(4,8)(5,7)(9,11)(10,12)>,< 2, 12, G!(1,2)(3,6)(4,8)(5,7)(9,12)(10,11)>,< 3, 32, G!(1,4,5)(2,8,6)>,< 4, 12, G!(1,2,3,7)(4,6,5,8)>,< 4, 12, G!(1,2,3,7)(4,6,5,8)(9,10)(11,12)>,< 4, 12, G!(1,2,3,7)(4,6,5,8)(9,11)(10,12)>,< 4, 12, G!(1,2,3,7)(4,6,5,8)(9,12)(10,11)>,< 4, 12, G!(1,2,3,7)(4,8,5,6)>,< 4, 12, G!(1,2,3,7)(4,8,5,6)(9,10)(11,12)>,< 4, 12, G!(1,2,3,7)(4,8,5,6)(9,11)(10,12)>,< 4, 12, G!(1,2,3,7)(4,8,5,6)(9,12)(10,11)>,< 4, 12, G!(1,3,4,5)(2,6,8,7)>,< 4, 12, G!(1,3,4,5)(2,6,8,7)(9,10)(11,12)>,< 4, 12, G!(1,3,4,5)(2,6,8,7)(9,11)(10,12)>,< 4, 12, G!(1,3,4,5)(2,6,8,7)(9,12)(10,11)>,< 4, 24, G!(2,6,7,8)(4,5)>,< 4, 24, G!(2,6,7,8)(4,5)(9,10)(11,12)>,< 4, 24, G!(2,6,7,8)(4,5)(9,11)(10,12)>,< 4, 24, G!(2,6,7,8)(4,5)(9,12)(10,11)>,< 4, 24, G!(1,2,3,6)(4,8,5,7)>,< 4, 24, G!(1,2,3,6)(4,8,5,7)(9,10)(11,12)>,< 4, 24, G!(1,2,3,6)(4,8,5,7)(9,11)(10,12)>,< 4, 24, G!(1,2,3,6)(4,8,5,7)(9,12)(10,11)>,< 6, 32, G!(1,5,4)(2,6,8)(9,12)(10,11)>,< 6, 32, G!(3,4,5)(6,7,8)(9,10)(11,12)>,< 6, 32, G!(1,4,3)(6,7,8)(9,11)(10,12)>,< 6, 32, G!(1,6,5,8,3,7)(2,4)(9,12)(10,11)>,< 6, 32, G!(1,2,5,8,4,7)(3,6)>,< 6, 32, G!(1,8,3,7,5,2)(4,6)(9,11)(10,12)>,< 6, 32, G!(1,8,5,6,3,2)(4,7)(9,10)(11,12)>]); 
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!\[1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, -2, 0, 0, 2, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 2, 0, 0, -2, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, -2, 0, 0, 2, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 2, 0, 0, -2, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, -2, 0, 0, -2, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 2, 0, 0, 2, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, -2, 0, 0, -2, 0, -2, 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!\[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -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, -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, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -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, 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, -3, -3, 3, -3, 3, 1, -1, -1, 1, -1, -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, -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, -3, -3, 3, -3, 3, 1, -1, -1, 1, -1, -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, 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, -3, 3, -3, 3, -3, 1, -1, -1, 1, -1, -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, 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, -3, 3, -3, 3, -3, 1, -1, -1, 1, -1, -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, -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, 3, -3, -3, 3, 3, 1, 1, -1, 1, 1, -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, 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, 3, -3, -3, 3, 3, 1, 1, -1, 1, 1, -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, -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, 3, 3, 3, -3, -3, 1, 1, -1, 1, 1, -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, -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, 3, 3, 3, -3, -3, 1, 1, -1, 1, 1, -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, 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, -3, -3, 3, 3, -3, -1, 1, -1, -1, 1, -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, 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, -3, -3, 3, 3, -3, -1, 1, -1, -1, 1, -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, -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, -3, 3, -3, -3, 3, -1, 1, -1, -1, 1, -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, -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, -3, 3, -3, -3, 3, -1, 1, -1, -1, 1, -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, 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, 3, -3, -3, -3, -3, -1, -1, -1, -1, -1, -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, -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, 3, -3, -3, -3, -3, -1, -1, -1, -1, -1, -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, 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, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, -2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 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, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, -2, 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, -2, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, -2, 2, 0, 0, -2, 0, -2, -2, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 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, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 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, 2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 0, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 2, 0, 2, 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, 2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, -2, 0, -2, 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, 2, -2, -2, 2, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, 2, -2, 0, 0, -2, 0, -2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, 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, 2, -2, -2, 2, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, 2, -2, 0, 0, 2, 0, 2, -2, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 2, 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, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, 2, -2, -2, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 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, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, 2, -2, 2, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, -2, 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, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, -2, 2, 0, 0, -2, 0, 2, -2, 0, 2, 0, 2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 2, 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, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, -2, 2, 0, 0, 2, 0, -2, 2, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 2, 0, 0, -2, 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, -2, 2, -2, 2, 0, 0, 0, 0, -2, 2, -2, 2, -2, 2, 2, -2, 0, 0, -2, 0, 2, 2, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 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, -2, 2, -2, 2, 0, 0, 0, 0, -2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 2, 0, -2, -2, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 2, 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, -2, 2, -2, 2, 0, 0, 0, 0, 2, -2, 2, -2, 2, -2, -2, 2, -2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 2, 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, -2, 2, -2, 2, 0, 0, 0, 0, 2, -2, 2, -2, 2, -2, -2, 2, 2, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, -2, 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_1089108:= KnownIrreducibles(CR);