/* Group 192.521 downloaded from the LMFDB on 16 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, -3, 14, 590, 58, 675, 80, 1699, 124, 1588]); a,b,c := Explode([GPC.1, GPC.3, GPC.6]); AssignNames(~GPC, ["a", "a2", "b", "b2", "b4", "c", "c2"]);
GPerm := PermutationGroup< 17 | (1,2,4,6,3,5,7,8)(12,13), (1,3)(2,5)(4,7)(6,8)(9,10), (1,2)(3,5)(4,8)(6,7)(9,10)(14,15,16,17), (14,16)(15,17), (1,4,3,7)(2,6,5,8), (1,3)(2,5)(4,7)(6,8), (11,12,13) >;
GLZN := MatrixGroup< 2, Integers(40) | [[9, 5, 28, 1], [1, 10, 0, 1], [9, 0, 0, 9], [33, 24, 8, 1], [1, 20, 0, 1], [21, 0, 0, 21], [27, 25, 0, 37]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_192_521 := 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, a^2>,< 2, 1, c^3>,< 2, 1, b^4*c^3>,< 2, 1, a^2*c^3>,< 2, 1, a^2*b^4>,< 2, 1, a^2*b^4*c^3>,< 2, 1, b^4>,< 3, 2, c^2>,< 4, 2, b^2>,< 4, 2, b^6*c^3>,< 4, 2, a^2*b^6>,< 4, 2, a^2*b^6*c^3>,< 4, 4, a^3>,< 4, 4, a>,< 4, 4, a^3*c^3>,< 4, 4, a*c^3>,< 4, 12, a*b>,< 4, 12, a^3*b>,< 4, 12, a*b*c>,< 4, 12, a^3*b*c>,< 6, 2, c>,< 6, 2, b^4*c>,< 6, 2, a^2*c>,< 6, 2, a^2*b^4*c^2>,< 6, 2, a^2*b^4*c>,< 6, 2, b^4*c^4>,< 6, 2, a^2*c^4>,< 8, 6, b>,< 8, 6, b^5>,< 8, 6, b*c>,< 8, 6, b^5*c>,< 8, 6, a^2*b>,< 8, 6, a^2*b^5>,< 8, 6, a^2*b*c>,< 8, 6, a^2*b^5*c>,< 12, 4, b^2*c^2>,< 12, 4, b^2*c>,< 12, 4, a^2*b^2*c^2>,< 12, 4, a^2*b^2*c>,< 12, 4, a*c^2>,< 12, 4, a^3*c^4>,< 12, 4, a*c^4>,< 12, 4, a^3*c^2>,< 12, 4, a*c>,< 12, 4, a^3*b^2*c>,< 12, 4, a*b^2*c>,< 12, 4, a^3*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, 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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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*K.1,K.1,-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,K.1,-1,-1*K.1,-1,K.1,-1*K.1,-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(4: Sparse := true);
S := [ K |1,-1,-1,-1,1,-1,1,1,1,1,-1,-1,1,K.1,-1*K.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,-1*K.1,-1,K.1,-1,-1*K.1,K.1,K.1,1,-1*K.1,K.1,-1*K.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*K.1,K.1,-1*K.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,K.1,-1,-1*K.1,-1,K.1,-1*K.1,-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(4: Sparse := true);
S := [ K |1,-1,-1,-1,1,-1,1,1,1,1,-1,-1,1,K.1,-1*K.1,K.1,-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,-1*K.1,-1,K.1,-1,-1*K.1,K.1,K.1,1,-1*K.1,K.1,-1*K.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*K.1,-1*K.1,K.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,-1*K.1,1,-1*K.1,-1,K.1,K.1,-1*K.1,1,K.1,K.1,-1*K.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,K.1,K.1,-1*K.1,-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,K.1,1,K.1,-1,-1*K.1,-1*K.1,K.1,1,-1*K.1,-1*K.1,K.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*K.1,-1*K.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,-1*K.1,1,-1*K.1,-1,K.1,K.1,-1*K.1,1,K.1,K.1,-1*K.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,K.1,K.1,-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,K.1,1,K.1,-1,-1*K.1,-1*K.1,K.1,1,-1*K.1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 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!\[2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -2, 2, -2, 2, -1, 2, -2, 2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, 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!\[2, 2, -2, -2, -2, 2, -2, 2, -1, 2, -2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, 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!\[2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 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!\[2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,-2,2,2,2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,-2,-2,2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,-2,-2,2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,-2,-2,2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,-2,-2,2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,-2,-2,2,-2,2,2,-1,2,-2,-2,2,-2*K.1,2*K.1,-2*K.1,2*K.1,0,0,0,0,1,1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,-1,-1*K.1,1,K.1,1,-1*K.1,K.1,K.1,-1,-1*K.1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,-2,-2,2,-2,2,2,-1,2,-2,-2,2,2*K.1,-2*K.1,2*K.1,-2*K.1,0,0,0,0,1,1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,-1,K.1,1,-1*K.1,1,K.1,-1*K.1,-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(4: Sparse := true);
S := [ K |2,-2,2,2,-2,-2,-2,2,-1,2,2,-2,-2,-2*K.1,-2*K.1,2*K.1,2*K.1,0,0,0,0,-1,-1,1,1,-1,1,1,0,0,0,0,0,0,0,0,1,K.1,-1,K.1,1,-1*K.1,-1*K.1,K.1,-1,-1*K.1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,2,-2,-2,-2,2,-1,2,2,-2,-2,2*K.1,2*K.1,-2*K.1,-2*K.1,0,0,0,0,-1,-1,1,1,-1,1,1,0,0,0,0,0,0,0,0,1,-1*K.1,-1,-1*K.1,1,K.1,K.1,-1*K.1,-1,K.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 |2,2,-2,-2,-2,2,-2,2,-1,-2,2,-2,2,0,0,0,0,0,0,0,0,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,-1,-1-2*K.1,-1,-1-2*K.1,1,1+2*K.1,1+2*K.1,1+2*K.1,1,-1-2*K.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,-2,2,-2,2,-1,-2,2,-2,2,0,0,0,0,0,0,0,0,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,-1,1+2*K.1,-1,1+2*K.1,1,-1-2*K.1,-1-2*K.1,-1-2*K.1,1,1+2*K.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 |2,2,2,2,2,2,2,2,-1,-2,-2,-2,-2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,-1-2*K.1,1,1+2*K.1,1,-1-2*K.1,1+2*K.1,-1-2*K.1,1,1+2*K.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 |2,2,2,2,2,2,2,2,-1,-2,-2,-2,-2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1+2*K.1,1,-1-2*K.1,1,1+2*K.1,-1-2*K.1,1+2*K.1,1,-1-2*K.1,1+2*K.1,-1-2*K.1]; 
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,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,-2,-2,2,-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,-2,-2,2,-2,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.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,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,-2,2,-2,-1*K.1-K.1^-1,K.1+K.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,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,-2,2,-2,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,-2,-2,2,-2,2,2,-1,-2,2,2,-2,0,0,0,0,0,0,0,0,1,1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,1,-1*K.1-K.1^-1,-1,-1*K.1-K.1^-1,-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,-2,-2,2,-2,2,2,-1,-2,2,2,-2,0,0,0,0,0,0,0,0,1,1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,1,K.1+K.1^-1,-1,K.1+K.1^-1,-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,2,-2,-2,-2,2,-1,-2,-2,2,2,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,1,1,0,0,0,0,0,0,0,0,-1,-1*K.1-K.1^-1,1,K.1+K.1^-1,-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,2,-2,-2,-2,2,-1,-2,-2,2,2,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,1,1,0,0,0,0,0,0,0,0,-1,K.1+K.1^-1,1,-1*K.1-K.1^-1,-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 4, 4, -4, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -4, 4, 4, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, 4, -4, -4, 4, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, -4, 4, -4, -4, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_192_521:= KnownIrreducibles(CR);