/* Group 320.1591 downloaded from the LMFDB on 13 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, -2, -2, -2, -2, -5, 36, 851, 1278, 102, 2028, 3043, 124, 4717, 3156]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.4, GPC.5]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "d2", "d4"]);
GPerm := PermutationGroup< 13 | (1,2)(3,4)(5,6)(7,8)(10,11,12,13), (1,3)(2,4)(5,7)(6,8), (1,3)(2,4)(5,8)(6,7), (1,4,3,2)(5,8)(6,7), (10,12)(11,13), (1,3)(2,4), (9,10,11,13,12) >;
GLZN := MatrixGroup< 2, Integers(20) | [[9, 0, 0, 1], [1, 10, 0, 1], [19, 10, 10, 3], [9, 0, 0, 9], [9, 3, 0, 3], [1, 4, 0, 1], [19, 0, 0, 19]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_320_1591 := 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, d^10>,< 2, 1, c>,< 2, 1, c*d^10>,< 2, 1, a>,< 2, 1, a*d^10>,< 2, 1, a*c>,< 2, 1, a*c*d^10>,< 2, 5, b^2*d^2>,< 2, 5, b^2*c>,< 2, 5, a*b^2>,< 2, 5, b^2*c*d^2>,< 2, 5, a*b^2*d^2>,< 2, 5, a*b^2*c>,< 2, 5, a*b^2*c*d^2>,< 2, 5, b^2>,< 4, 2, d^5>,< 4, 2, c*d^5>,< 4, 2, a*d^5>,< 4, 2, a*c*d^5>,< 4, 10, b^2*d>,< 4, 10, b^2*c*d>,< 4, 10, a*b^2*d>,< 4, 10, a*b^2*c*d>,< 4, 10, b>,< 4, 10, b^3>,< 4, 10, b*d>,< 4, 10, b^3*d>,< 4, 10, b*c>,< 4, 10, b^3*c>,< 4, 10, a*b>,< 4, 10, a*b^3>,< 4, 10, b*c*d>,< 4, 10, b^3*c*d>,< 4, 10, a*b*d>,< 4, 10, a*b^3*d>,< 4, 10, a*b*c>,< 4, 10, a*b^3*c>,< 4, 10, a*b*c*d>,< 4, 10, a*b^3*c*d>,< 5, 4, d^8>,< 10, 4, c*d^4>,< 10, 4, c*d^2>,< 10, 4, a*d^4>,< 10, 4, a*d^2>,< 10, 4, a*c*d^4>,< 10, 4, a*c*d^2>,< 10, 4, d^2>,< 20, 4, d>,< 20, 4, d^13>,< 20, 4, c*d>,< 20, 4, c*d^13>,< 20, 4, a*d>,< 20, 4, a*d^13>,< 20, 4, a*c*d>,< 20, 4, a*c*d^13>]); 
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; 
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,-1*K.1,K.1,1,-1*K.1,-1*K.1,-1*K.1,-1,K.1,-1*K.1,K.1,-1,1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,K.1,1,-1,-1,-1,-1,1,1,1,-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,-1,1,1,K.1,-1*K.1,1,K.1,K.1,K.1,-1,-1*K.1,K.1,-1*K.1,-1,1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,1,-1,-1,-1,-1,1,1,1,-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,-1,-1*K.1,-1*K.1,-1,-1*K.1,K.1,K.1,1,K.1,-1*K.1,K.1,1,-1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,1,-1,-1,-1,-1,1,1,1,1,-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,-1,K.1,K.1,-1,K.1,-1*K.1,-1*K.1,1,-1*K.1,K.1,-1*K.1,1,-1,K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,1,-1,-1,-1,-1,1,1,1,1,-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,-1,-1*K.1,K.1,1,-1*K.1,K.1,-1*K.1,1,-1*K.1,K.1,-1*K.1,-1,-1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,1,-1,1,-1,1,1,-1,-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,-1,K.1,-1*K.1,1,K.1,-1*K.1,K.1,1,K.1,-1*K.1,K.1,-1,-1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,1,-1,1,-1,1,1,-1,-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,-1,1,-1*K.1,-1*K.1,-1,-1*K.1,-1*K.1,K.1,-1,-1*K.1,K.1,-1*K.1,1,1,-1*K.1,K.1,-1*K.1,K.1,K.1,K.1,K.1,K.1,1,-1,1,-1,1,1,-1,-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,-1,1,K.1,K.1,-1,K.1,K.1,-1*K.1,-1,K.1,-1*K.1,K.1,1,1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,1,-1,1,-1,1,1,-1,-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,-1,1,-1*K.1,-1*K.1,1,K.1,-1*K.1,K.1,-1,-1*K.1,-1*K.1,K.1,1,-1,K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,1,1,-1,1,-1,1,-1,-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,-1,1,K.1,K.1,1,-1*K.1,K.1,-1*K.1,-1,K.1,K.1,-1*K.1,1,-1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,1,1,-1,1,-1,1,-1,-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,-1,-1*K.1,K.1,-1,K.1,K.1,-1*K.1,1,-1*K.1,-1*K.1,K.1,-1,1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,1,1,-1,1,-1,1,-1,-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,-1,K.1,-1*K.1,-1,-1*K.1,-1*K.1,K.1,1,K.1,K.1,-1*K.1,-1,1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,1,1,-1,1,-1,1,-1,-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,-1,-1*K.1,-1*K.1,1,K.1,K.1,K.1,1,K.1,K.1,-1*K.1,1,1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,1,1,1,1,1,1,1,1,-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,-1,K.1,K.1,1,-1*K.1,-1*K.1,-1*K.1,1,-1*K.1,-1*K.1,K.1,1,1,-1*K.1,K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,1,1,1,1,1,1,1,1,-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,-1,1,1,1,1,-1*K.1,K.1,-1,K.1,-1*K.1,-1*K.1,-1,K.1,K.1,-1*K.1,-1,-1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
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,-1,1,1,1,1,K.1,-1*K.1,-1,-1*K.1,K.1,K.1,-1,-1*K.1,-1*K.1,K.1,-1,-1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, -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, 2, -2, 2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 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, 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, -2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 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, 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, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 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, 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, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 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, 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, -2, 2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 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, 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, -2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 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, 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, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 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, 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, 2, -2, -2, 2, -2, 2, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 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, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, 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, -1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 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, 1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, -4, 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, 1, -1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 4, 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, -1, 1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 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, -1, -1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, 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, 1, 1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 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, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,-4,-4,4,-4,4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,1,-1,1,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,-4,-4,4,-4,4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,-1,1,1,-1,1,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,-4,-4,4,4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,-1,1,1,-1,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,-4,-4,4,4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,-1,1,1,-1,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,-4,4,-4,-4,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,-4,4,-4,-4,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,-1,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,-4,4,-4,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,1,-1,1,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,-4,4,-4,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,1,-1,1,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7,2*K.1^3-K.1^5+2*K.1^7,-2*K.1^3+K.1^5-2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_320_1591:= KnownIrreducibles(CR);