/* Group 864.3015 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([8, 2, 2, 3, 2, 3, 2, 2, 3, 16, 194, 22659, 5587, 91, 19204, 756, 38021, 1317, 2045, 141, 40326, 166, 36871]); a,b,c,d := Explode([GPC.1, GPC.3, GPC.4, GPC.6]); AssignNames(~GPC, ["a", "a2", "b", "c", "c2", "d", "d2", "d4"]);
GPerm := PermutationGroup< 18 | (1,2)(3,4)(5,6)(10,11)(12,13,14,15)(17,18), (12,14)(13,15), (3,4,8)(5,6,7)(9,10,11)(16,17,18), (9,10,11)(16,17,18), (16,18,17), (1,3,2,5)(4,8,6,7), (1,4,2,6)(3,7,5,8), (1,2)(3,5)(4,6)(7,8) >;
GLZN := MatrixGroup< 2, Integers(30) | [[1, 20, 20, 11], [1, 10, 0, 1], [3, 10, 7, 7], [16, 15, 15, 1], [11, 0, 0, 11], [11, 20, 20, 1], [19, 0, 0, 19], [13, 12, 6, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_864_3015 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, a^2>,< 2, 1, a^2*d^6>,< 2, 1, d^6>,< 3, 2, d^8>,< 3, 2, c^4>,< 3, 2, c^4*d^8>,< 3, 2, c^4*d^4>,< 3, 8, b^2*d^4>,< 3, 8, b^2*c^3*d^2>,< 3, 8, b^2*c^4>,< 3, 8, b^2*c^5*d^3>,< 3, 8, b^2>,< 3, 8, b^2*c^4*d^8>,< 3, 8, b^2*c^5*d^11>,< 3, 8, b^2*c^4*d^4>,< 3, 8, b^2*c^2*d^10>,< 4, 6, d^3>,< 4, 6, a^2*d^3>,< 4, 108, a*d^8>,< 4, 108, a^3*d^8>,< 6, 2, a^2*d^4>,< 6, 2, a^2*d^2>,< 6, 2, a^2*c^2>,< 6, 2, a^2*c^4>,< 6, 2, a^2*c^2*d^4>,< 6, 2, a^2*c^2*d^2>,< 6, 2, a^2*c^2*d^8>,< 6, 2, a^2*c^4*d^8>,< 6, 2, d^2>,< 6, 2, c^2>,< 6, 2, c^4*d^2>,< 6, 2, c^2*d^8>,< 6, 8, b*d^2>,< 6, 8, b*d>,< 6, 8, b*c^2>,< 6, 8, b*c>,< 6, 8, a^2*b>,< 6, 8, b*d^6>,< 6, 8, b*c^2*d^4>,< 6, 8, b*c*d^4>,< 6, 8, a^2*b*d^4>,< 6, 8, a^2*b*d^2>,< 6, 8, a^2*b*d>,< 6, 8, a^2*b*c^2>,< 6, 8, a^2*b*c>,< 6, 8, b*c^2*d^8>,< 6, 8, b*c^4*d^2>,< 6, 8, a^2*b*d^8>,< 6, 8, a^2*b*c^4>,< 6, 8, a^2*b^2*c>,< 6, 8, a^2*b*d^6>,< 6, 8, a^2*b*c^2*d^4>,< 6, 8, a^2*b*c^2*d^2>,< 6, 8, a^2*b*c^2*d>,< 6, 8, a^2*b*c*d^4>,< 6, 8, a^2*b*c*d^2>,< 6, 8, a^2*b*c*d>,< 6, 8, a^2*b*c^2*d^8>,< 6, 8, a^2*b*c^4*d^2>,< 8, 54, a^3*c^3*d^5>,< 8, 54, a*c^3*d^2>,< 8, 54, a*c^3*d^8>,< 8, 54, a^3*c^3*d^11>,< 12, 12, d>,< 12, 12, c>,< 12, 12, c^2*d>,< 12, 12, c*d^4>,< 12, 12, a^2*d>,< 12, 12, a^2*c>,< 12, 12, a^2*c^2*d>,< 12, 12, a^2*c*d^4>]); 
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, 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, 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(4: Sparse := true);
S := [ K |1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1*K.1,K.1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,-1,1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,K.1,-1*K.1,-1*K.1,K.1,1,-1,-1,1,1,-1,1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,K.1,-1*K.1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,-1,1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1*K.1,K.1,K.1,-1*K.1,1,-1,-1,1,1,-1,1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, 2, 2, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, 2, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -1, 2, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, 2, -1, 2, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, 0, 0, 0, 0, -1, 2, -1, 2, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 0, 0, 0, 0, -1, 2, -1, 2, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, 2, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, 2, -1, -1, 2, -1, 0, 0, 0, 0, 2, -1, -1, -1, -1, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, 2, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 0, 0, 0, 0, 2, -1, -1, -1, -1, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 0, 0, 0, 0, 2, -1, -1, -1, -1, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, 2, 2, 0, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, 2, -1, -1, -1, 2, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, 2, 0, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, 2, 2, 0, 0, 0, 0, -1, -1, 2, -1, -1, -1, 2, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, 0, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 0, 0, 0, 0, -1, -1, 2, -1, -1, -1, 2, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, 2, -2, 0, 0, -1, 1, 1, -2, 2, -1, -1, 1, -2, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, -1, 2, -1, 1, 1, 1, -1, -2, 1, 2, 1, -2, 2, -1, 1, 1, -1, -1, -2, 1, 0, 0, 0, 0, -1, 1, 1, -1, 2, 1, -1, -2]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -2, 0, 0, -1, 1, 1, -2, 2, -1, -1, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 2, -1, 2, -2, -2, -2, -1, 1, -2, -1, 1, 1, -1, 2, 1, -2, -1, -1, 1, 1, 0, 0, 0, 0, -1, 1, 1, -1, 2, 1, -1, -2]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -2, 0, 0, -1, 1, 1, -2, 2, -1, -1, 1, -2, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, -1, -1, -1, 1, 1, 1, 2, 1, 1, -1, -2, 1, -1, -1, -2, 1, 2, 2, 1, -2, 0, 0, 0, 0, -1, 1, 1, -1, 2, 1, -1, -2]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -2, 0, 0, -1, 1, 1, 1, -1, -1, 2, 1, 1, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, -1, -1, -1, 1, -2, 1, 2, 1, 1, 2, -2, 1, -1, 2, -2, 1, -1, -1, 1, 1, 0, 0, 0, 0, -1, -2, 1, 2, -1, 1, -1, 1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, -2, 0, 0, -1, 1, 1, 1, -1, -1, 2, 1, 1, -2, -2, 1, 1, -2, 1, -2, 1, 1, 1, 2, -1, -1, 1, 1, 1, -1, -2, -2, -1, 1, 1, 2, -1, 1, -2, 2, -1, 1, -2, 0, 0, 0, 0, -1, -2, 1, 2, -1, 1, -1, 1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -2, 0, 0, -1, 1, 1, 1, -1, -1, 2, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1, -2, -1, 2, 2, -2, 1, -2, -1, 1, 1, -1, 1, -2, -1, -1, 1, 1, -1, 2, -2, 1, 0, 0, 0, 0, -1, -2, 1, 2, -1, 1, -1, 1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, -2, 0, 0, -1, 1, -2, 1, -1, 2, -1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, 2, 2, -1, 1, 1, 1, 2, 1, -2, -1, -2, -2, -1, -1, -2, -2, -1, -1, -2, 1, 0, 0, 0, 0, 2, 1, 1, -1, -1, -2, -1, 1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -2, 0, 0, -1, 1, -2, 1, -1, 2, -1, 1, 1, 1, 1, -2, -2, 1, -2, -2, 1, 1, 1, -1, -1, 2, -2, 1, -2, -1, 1, 1, 2, 1, 1, -1, -1, 1, 1, 2, -1, 1, -2, 0, 0, 0, 0, 2, 1, 1, -1, -1, -2, -1, 1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -2, 0, 0, -1, 1, -2, 1, -1, 2, -1, 1, 1, 1, 1, -2, 1, -2, 1, 1, -2, -2, -2, -1, -1, -1, 1, -2, 1, -1, -2, 1, -1, 1, 1, 2, 2, 1, 1, -1, 2, 1, 1, 0, 0, 0, 0, 2, 1, 1, -1, -1, -2, -1, 1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, 2, -2, 0, 0, 2, -2, 1, 1, -1, -1, -1, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -1, -1, 2, -2, 1, -2, 2, -2, 1, -1, -2, 1, 2, -1, -2, 1, -1, -1, 1, 1, 0, 0, 0, 0, -1, 1, -2, -1, -1, 1, 2, 1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, -2, 0, 0, 2, -2, 1, 1, -1, -1, -1, -2, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, 1, -1, 2, -1, 1, -2, 1, -1, 1, 1, -1, 1, -2, -1, 2, 1, 1, 2, -1, -2, -2, 0, 0, 0, 0, -1, 1, -2, -1, -1, 1, 2, 1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -2, 0, 0, 2, -2, 1, 1, -1, -1, -1, -2, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, -2, 2, -1, -1, 1, 1, 1, -1, 1, -2, 2, 1, 1, -1, -1, 1, -2, -1, 2, 1, 1, 0, 0, 0, 0, -1, 1, -2, -1, -1, 1, 2, 1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -2, 0, 0, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 2, -2]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,-2,-2,2,2,-2,-2,-2,2,-2,2,-2,-2,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,1,1,-1,1,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,-2,-2,2,2,-2,-2,-2,2,-2,2,-2,-2,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,1,1,-1,1,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,-2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,-2,2,-2,-2,-2,-2,-2,-2,2,-2,2,2,-1,1,1,1,1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,-1,1,1,1,-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,-2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,-2,2,-2,-2,-2,-2,-2,-2,2,-2,2,2,-1,1,1,1,1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,-1,1,1,1,-1,K.1+K.1^-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 0, 0, 0, -1, -1, -1, -1, -1, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,-3,3,3,3,3,0,0,0,0,0,0,0,0,0,-1,1,-1*K.1,K.1,3,-3,-3,-3,3,3,3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1,K.1,K.1,-1*K.1,-1,1,1,-1,-1,1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,-3,3,3,3,3,0,0,0,0,0,0,0,0,0,-1,1,K.1,-1*K.1,3,-3,-3,-3,3,3,3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1,-1*K.1,-1*K.1,K.1,-1,1,1,-1,-1,1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, -4, 4, -4, 4, -4, -4, -1, 1, 1, 1, 1, -1, -1, -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, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, -4, 4, -4, -4, -4, -4, -4, -4, 4, -4, 4, 4, 1, -1, -1, -1, -1, 1, 1, -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, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -2, -2, -2, 4, -2, -2, 1, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 2, 2, -2, 4, -4, 2, 2, -2, -4, -2, 2, 2, -1, 1, 1, -2, -2, -1, 2, -1, -1, -1, -1, 1, 1, 2, -1, 1, -1, -2, -1, -1, -1, 2, -1, 2, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -2, -2, -2, 4, 1, 1, -2, 1, 1, 1, -2, 1, -2, 0, 0, 0, 0, 2, 2, -2, 4, -4, 2, 2, -2, -4, -2, 2, 2, -1, 1, 1, 1, 1, 2, -1, 2, -1, 2, 2, -2, -2, -1, -1, -2, -1, 1, -1, -1, 2, -1, 2, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -2, -2, -2, 4, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, 0, 0, 2, 2, -2, 4, -4, 2, 2, -2, -4, -2, 2, 2, 2, -2, -2, 1, 1, -1, -1, -1, 2, -1, -1, 1, 1, -1, 2, 1, 2, 1, 2, 2, -1, -1, -1, -1, -1, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -2, -2, 4, -2, -2, 1, 1, 1, -2, 1, -2, 1, 1, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, -4, -2, 2, 4, -4, 2, -1, 1, 1, 1, -2, -1, 2, -1, 2, 2, 2, 1, -2, -1, -1, 1, -1, 1, 2, -1, -1, -1, -1, -1, 2, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -2, -2, 4, -2, 1, -2, -2, 1, 1, 1, 1, -2, 1, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, -4, -2, 2, 4, -4, 2, -1, -2, 1, -2, 1, -1, -1, 2, -1, -1, -1, 1, 1, -1, 2, -2, -1, 1, -1, 2, -1, -1, 2, 2, -1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -2, -2, 4, -2, 1, 1, 1, -2, 1, -2, 1, 1, -2, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, -4, -2, 2, 4, -4, 2, 2, 1, -2, 1, 1, 2, -1, -1, -1, -1, -1, -2, 1, 2, -1, 1, 2, -2, -1, -1, 2, 2, -1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -2, 4, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, 0, 0, 2, 2, 4, -2, 2, -4, 2, -2, 2, -2, 2, -4, -1, -2, 1, 1, -2, 2, 2, -1, -1, -1, -1, -2, 1, -1, 2, 1, -1, 1, -1, 2, 2, -1, -1, -1, 2, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -2, 4, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 2, 2, 4, -2, 2, -4, 2, -2, 2, -2, 2, -4, 2, 1, -2, -2, 1, -1, -1, -1, -1, 2, 2, 1, -2, -1, -1, 1, 2, 1, -1, -1, -1, -1, -1, 2, -1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -2, 4, -2, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 0, 0, 0, 0, 2, 2, 4, -2, 2, -4, 2, -2, 2, -2, 2, -4, -1, 1, 1, 1, 1, -1, -1, 2, 2, -1, -1, 1, 1, 2, -1, -2, -1, -2, 2, -1, -1, 2, 2, -1, -1, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 4, -2, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, -4, -4, -2, -2, 2, 2, 2, 4, 2, -2, 2, 2, 2, 1, -2, 1, -2, -1, 2, 2, -1, -1, -1, 1, 1, -1, -1, -2, 2, 1, -1, -1, -1, -1, 2, -1, 2, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 4, -2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, -2, 0, 0, 0, 0, -4, -4, -2, -2, 2, 2, 2, 4, 2, -2, 2, 2, -1, 1, 1, -2, 1, 2, -1, -1, 2, -1, -1, -2, 1, -1, -1, 1, -1, 1, 2, -1, 2, -1, -1, 2, -1, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 4, -2, -2, -2, 1, 1, 1, 1, 1, -2, -2, -2, 1, 0, 0, 0, 0, -4, -4, -2, -2, 2, 2, 2, 4, 2, -2, 2, 2, -1, -2, 1, 1, 1, -1, -1, -1, -1, 2, 2, 1, -2, 2, 2, 1, -1, -2, -1, 2, -1, 2, -1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, -2, -2, -2, 4, -2, -2, 1, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 2, -2, 2, -4, -4, 2, 2, 2, 4, 2, -2, -2, 1, -1, -1, 2, 2, 1, -2, -1, -1, -1, 1, -1, -1, 2, 1, -1, -1, 2, 1, -1, -1, -2, 1, 2, 2, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, -2, -2, -2, 4, 1, 1, -2, 1, 1, 1, -2, 1, -2, 0, 0, 0, 0, 2, -2, 2, -4, -4, 2, 2, 2, 4, 2, -2, -2, 1, -1, -1, -1, -1, -2, 1, 2, -1, 2, -2, 2, 2, -1, 1, 2, -1, -1, 1, -1, 2, 1, -2, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, -2, -2, -2, 4, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, 0, 0, 2, -2, 2, -4, -4, 2, 2, 2, 4, 2, -2, -2, -2, 2, 2, -1, -1, 1, 1, -1, 2, -1, 1, -1, -1, -1, -2, -1, 2, -1, -2, 2, -1, 1, 1, -1, -1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, -2, -2, 4, -2, -2, 1, 1, 1, -2, 1, -2, 1, 1, 0, 0, 0, 0, 2, -2, 2, 2, 2, 2, -4, 2, -2, -4, 4, -2, 1, -1, -1, -1, 2, 1, -2, -1, 2, 2, -2, -1, 2, -1, 1, -1, -1, -1, -2, -1, -1, 1, 1, -1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, -2, -2, 4, -2, 1, -2, -2, 1, 1, 1, 1, -2, 1, 0, 0, 0, 0, 2, -2, 2, 2, 2, 2, -4, 2, -2, -4, 4, -2, 1, 2, -1, 2, -1, 1, 1, 2, -1, -1, 1, -1, -1, -1, -2, 2, -1, -1, 1, 2, -1, 1, -2, 2, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, -2, -2, 4, -2, 1, 1, 1, -2, 1, -2, 1, 1, -2, 0, 0, 0, 0, 2, -2, 2, 2, 2, 2, -4, 2, -2, -4, 4, -2, -2, -1, 2, -1, -1, -2, 1, -1, -1, -1, 1, 2, -1, 2, 1, -1, 2, 2, 1, -1, 2, -2, 1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, -2, 4, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, 0, 0, 2, -2, -4, 2, 2, -4, 2, 2, -2, 2, -2, 4, 1, 2, -1, -1, 2, -2, -2, -1, -1, -1, 1, 2, -1, -1, -2, -1, -1, -1, 1, 2, 2, 1, 1, -1, 2, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, -2, 4, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 2, -2, -4, 2, 2, -4, 2, 2, -2, 2, -2, 4, -2, -1, 2, 2, -1, 1, 1, -1, -1, 2, -2, -1, 2, -1, 1, -1, 2, -1, 1, -1, -1, 1, 1, 2, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, -2, 4, -2, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 0, 0, 0, 0, 2, -2, -4, 2, 2, -4, 2, 2, -2, 2, -2, 4, 1, -1, -1, -1, -1, 1, 1, 2, 2, -1, 1, -1, -1, 2, 1, 2, -1, 2, -2, -1, -1, -2, -2, -1, -1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 4, -2, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, -4, 4, 2, 2, 2, 2, 2, -4, -2, 2, -2, -2, -2, -1, 2, -1, 2, 1, -2, 2, -1, -1, 1, -1, -1, -1, 1, 2, 2, -1, 1, -1, -1, 1, -2, -1, 2, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 4, -2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, -2, 0, 0, 0, 0, -4, 4, 2, 2, 2, 2, 2, -4, -2, 2, -2, -2, 1, -1, -1, 2, -1, -2, 1, -1, 2, -1, 1, 2, -1, -1, 1, -1, -1, -1, -2, -1, 2, 1, 1, 2, -1, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 4, -2, -2, -2, 1, 1, 1, 1, 1, -2, -2, -2, 1, 0, 0, 0, 0, -4, 4, 2, 2, 2, 2, 2, -4, -2, 2, -2, -2, 1, 2, -1, -1, -1, 1, 1, -1, -1, 2, -2, -1, 2, 2, -2, -1, -1, 2, 1, 2, -1, -2, 1, -1, -1, -1, 1, 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, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -3, -3, -3, 6, 6, -3, -3, -3, 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, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -2, 1, 1, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -3, -3, -3, -3, -3, -3, 6, -3, -3, 6, 6, -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, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, -3, 6, 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, 0, 0, 0, 0, 0, -2, 1, 1, 1, 1, -2, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 6, 6, -3, -3, -3, -3, -3, 6, -3, -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, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 1, 1, -2, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -3, 3, 3, -6, 6, -3, -3, 3, -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, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -2, -1, 1, 2]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -3, 3, 3, 3, -3, -3, 6, 3, 3, -6, -6, 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, 0, 0, 0, 0, 0, 0, 0, 1, 2, -1, -2, 1, -1, 1, -1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -3, 3, -6, 3, -3, 6, -3, 3, 3, 3, 3, -6, 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, 0, 0, 0, 0, 0, -2, -1, -1, 1, 1, 2, 1, -1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 6, -6, 3, 3, -3, -3, -3, -6, 3, 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, 0, 0, 0, 0, 0, 0, 0, 1, -1, 2, 1, 1, -1, -2, -1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_864_3015:= KnownIrreducibles(CR);