/* Group 384.2088 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([8, -2, -2, -2, -2, -2, -2, -2, -3, 3105, 41, 3979, 91, 972, 116, 2270, 166, 2079]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.4, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "c4", "d", "d2"]);
GPerm := PermutationGroup< 19 | (1,2)(3,5)(4,6)(7,8)(12,13,14,16)(15,17,18,19), (1,3,8,6,4,7,5,2)(10,11)(12,14)(13,16)(15,18)(17,19), (1,4)(2,6)(3,7)(5,8)(13,17)(16,19), (1,5,4,8)(2,7,6,3), (12,15)(13,17)(14,18)(16,19), (12,14)(13,16)(15,18)(17,19), (1,4)(2,6)(3,7)(5,8), (9,10,11) >;
GLZN := MatrixGroup< 2, Integers(48) | [[1, 12, 0, 1], [25, 0, 0, 25], [1, 16, 0, 1], [1, 24, 0, 1], [13, 39, 42, 11], [7, 0, 0, 7], [13, 33, 30, 19], [25, 24, 24, 25]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_384_2088 := 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^3>,< 2, 1, c^4*d^3>,< 2, 1, b^2*c^4>,< 2, 1, b^2*c^4*d^3>,< 2, 1, c^4>,< 2, 1, b^2>,< 2, 1, b^2*d^3>,< 2, 2, a>,< 2, 2, a*c^4>,< 2, 2, a*b^2>,< 2, 2, a*b^2*c^4>,< 3, 2, d^2>,< 4, 2, c^2>,< 4, 2, c^6*d^3>,< 4, 2, b^2*c^6>,< 4, 2, b^2*c^6*d^3>,< 4, 2, a*c^6>,< 4, 2, a*c^2>,< 4, 2, a*b^2*c^6>,< 4, 2, a*b^2*c^2>,< 4, 8, b^3>,< 4, 8, b>,< 4, 8, a*b^3*d^3>,< 4, 8, a*b>,< 4, 24, a*b^3*c^7*d^3>,< 4, 24, a*b*c^7*d^3>,< 4, 24, b*c*d^4>,< 4, 24, b^3*c*d>,< 6, 2, d>,< 6, 2, c^4*d>,< 6, 2, b^2*c^4*d^2>,< 6, 2, b^2*c^4*d>,< 6, 2, c^4*d^4>,< 6, 2, b^2*d^4>,< 6, 2, b^2*d>,< 6, 4, a*d^2>,< 6, 4, a*c^4*d^2>,< 6, 4, a*b^2*d^2>,< 6, 4, a*b^2*c^4*d^2>,< 8, 6, a*c>,< 8, 6, a*c^5>,< 8, 6, a*c*d>,< 8, 6, a*c^5*d>,< 8, 6, a*b^2*c>,< 8, 6, a*b^2*c^5>,< 8, 6, a*b^2*c*d>,< 8, 6, a*b^2*c^5*d>,< 8, 6, c>,< 8, 6, c*d>,< 8, 6, c^3>,< 8, 6, c^5>,< 8, 6, b^2*c>,< 8, 6, b^2*c*d>,< 8, 6, b^2*c^3>,< 8, 6, b^2*c^5>,< 12, 4, c^2*d^2>,< 12, 4, c^2*d>,< 12, 4, b^2*c^2*d^2>,< 12, 4, b^2*c^2*d>,< 12, 4, a*c^2*d^2>,< 12, 4, a*c^2*d>,< 12, 4, a*b^2*c^2*d^2>,< 12, 4, a*b^2*c^2*d>,< 12, 8, b*d^2>,< 12, 8, b^3*d>,< 12, 8, b*d>,< 12, 8, b^3*d^2>,< 12, 8, a*b*d^2>,< 12, 8, a*b^3*d>,< 12, 8, a*b*d>,< 12, 8, a*b^3*d^2>]); 
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; 
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; 
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; 
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,-1,-1*K.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,-1,1,1,1,1,-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,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,-1,1,1,1,1,1,-1,-1,1,1,-1,-1,K.1,-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,-1,1,1,1,1,-1,-1,-1,1,1,-1,1,1,-1,1,1,-1,-1,1,-1,1,-1*K.1,K.1,K.1,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,-1,1,1,1,1,1,-1,-1,1,1,-1,-1,-1*K.1,K.1,-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,-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,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,-1,1,1,1,1,1,-1,-1,1,1,-1,-1,K.1,-1*K.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,-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,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,-1,1,1,1,-1,-1,-1,-1,1,1,-1*K.1,K.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,-1,1,1,1,-1,1,1,1,-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,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,-1,1,1,1,-1,-1,-1,-1,1,1,K.1,-1*K.1,-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,-1,1,1,1,-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,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,-1,1,1,1,-1,-1,-1,-1,1,1,-1*K.1,K.1,K.1,-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,-1,-1,1,-1,-1,-1,1,1,-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,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,-1,1,1,1,-1,-1,-1,-1,1,1,K.1,-1*K.1,-1*K.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,-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,K.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, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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!\[2, -2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 2, 0, 0, 0, -2, 2, 0, 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, 0, 0, 0, 0, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 0, 0, -2, 2, 0, 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, 0, 0, 0, 0, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0, -2, -2, 0, 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, 0, 0, 0, 0, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, -2, -2, 0, 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, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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, -1, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 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!\[2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -1, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 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!\[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 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!\[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, -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, 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, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -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, 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; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,2,-2,-2,2,-2,-2,-2,2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,-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,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,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,-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,-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,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,-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,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,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,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,-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,-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,-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,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,0,0,0,0,2,-2,2,2,-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,-2*K.1,-2*K.1,-2*K.1,2*K.1,2*K.1,-2*K.1,2*K.1,0,2*K.1,2,-2,0,0,0,2,-2,0,0,0,0,0,0,0,0,0]; 
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,-2,2,0,0,0,0,2,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1,2*K.1,-2*K.1,-2*K.1,2*K.1,-2*K.1,0,-2*K.1,2,-2,0,0,0,2,-2,0,0,0,0,0,0,0,0,0]; 
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,-2,0,0,0,0,2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,2*K.1,-2*K.1,2*K.1,-2*K.1,-2*K.1,0,2*K.1,-2,-2,0,0,0,2,2,0,0,0,0,0,0,0,0,0]; 
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,-2,0,0,0,0,2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,-2*K.1,2*K.1,-2*K.1,2*K.1,2*K.1,0,-2*K.1,-2,-2,0,0,0,2,2,0,0,0,0,0,0,0,0,0]; 
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,-2,-2,2,2,-1,2,2,-2,-2,2,2,-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,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,1,-1,1,-1,-1*K.1,K.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 |2,-2,-2,2,-2,2,2,-2,-2,-2,2,2,-1,2,2,-2,-2,2,2,-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,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,1,-1,1,-1,K.1,-1*K.1,-1*K.1,-1*K.1,K.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,-2,2,2,-2,-2,-1,2,2,-2,-2,-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,-1,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,-1,-1,1,1,-1*K.1,K.1,-1*K.1,K.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,-2,2,2,-2,-2,-1,2,2,-2,-2,-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,-1,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,-1,-1,1,1,K.1,-1*K.1,K.1,-1*K.1,-1*K.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,-2,-2,-2,-2,-1,-2,-2,-2,-2,2,2,2,2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,-1,1,1,-1,-1-2*K.1,1+2*K.1,-1-2*K.1,-1-2*K.1,1+2*K.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,-2,-2,-2,-2,-1,-2,-2,-2,-2,2,2,2,2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,-1,1,1,-1,1+2*K.1,-1-2*K.1,1+2*K.1,1+2*K.1,-1-2*K.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 |2,2,2,2,2,2,2,2,2,2,2,2,-1,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,-1-2*K.1,1+2*K.1,1+2*K.1,-1-2*K.1,-1-2*K.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 |2,2,2,2,2,2,2,2,2,2,2,2,-1,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1+2*K.1,-1-2*K.1,-1-2*K.1,1+2*K.1,1+2*K.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,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,-2,2,-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,-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,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,-2,2,-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,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,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,-2,2,-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,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,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,-2,2,-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,-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,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,-2,2,2,-1,-2,-2,2,2,-2,-2,2,2,0,0,0,0,0,0,0,0,1,1,1,-1,1,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,-1,1,-1,1,-1*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,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,-2,-2,2,2,-1,-2,-2,2,2,-2,-2,2,2,0,0,0,0,0,0,0,0,1,1,1,-1,1,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,-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,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; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,-2,2,-2,2,2,-2,2,2,-2,-2,-1,-2,-2,2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,1,1,1,-1,1,-1,-1,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,1,1,-1,-1,-1*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,-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,-2,2,2,-2,-2,-1,-2,-2,2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,1,1,1,-1,1,-1,-1,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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,-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(8: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,2,-2,0,0,0,0,2,0,0,0,0,-2*K.1^2,2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,0,0,2,-2,-2,-2,2,2,-2,0,0,0,0,-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,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^-1,-1*K.1-K.1^3,0,0,-2*K.1^2,2*K.1^2,-2*K.1^2,0,0,2*K.1^2,0,0,0,0,0,0,0,0]; 
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,-2,0,0,0,0,2,0,0,0,0,2*K.1^2,-2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,0,0,2,-2,-2,-2,2,2,-2,0,0,0,0,-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,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^-1,K.1+K.1^3,0,0,2*K.1^2,-2*K.1^2,2*K.1^2,0,0,-2*K.1^2,0,0,0,0,0,0,0,0]; 
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,-2,0,0,0,0,2,0,0,0,0,-2*K.1^2,2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,0,0,2,-2,-2,-2,2,2,-2,0,0,0,0,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,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^-1,K.1+K.1^3,0,0,-2*K.1^2,2*K.1^2,-2*K.1^2,0,0,2*K.1^2,0,0,0,0,0,0,0,0]; 
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,-2,0,0,0,0,2,0,0,0,0,2*K.1^2,-2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,0,0,2,-2,-2,-2,2,2,-2,0,0,0,0,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,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^-1,-1*K.1-K.1^3,0,0,2*K.1^2,-2*K.1^2,2*K.1^2,0,0,-2*K.1^2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,-2,-2,2,2,0,0,0,0,2,0,0,0,0,-2*K.1^2,2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,0,0,-2,2,2,-2,-2,2,-2,0,0,0,0,-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.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^-1,K.1+K.1^3,0,0,-2*K.1^2,-2*K.1^2,2*K.1^2,0,0,2*K.1^2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,-2,-2,2,2,0,0,0,0,2,0,0,0,0,2*K.1^2,-2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,0,0,-2,2,2,-2,-2,2,-2,0,0,0,0,-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,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^-1,-1*K.1-K.1^3,0,0,2*K.1^2,2*K.1^2,-2*K.1^2,0,0,-2*K.1^2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,-2,-2,2,2,0,0,0,0,2,0,0,0,0,-2*K.1^2,2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,0,0,-2,2,2,-2,-2,2,-2,0,0,0,0,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.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^-1,-1*K.1-K.1^3,0,0,-2*K.1^2,-2*K.1^2,2*K.1^2,0,0,2*K.1^2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,-2,-2,2,2,0,0,0,0,2,0,0,0,0,2*K.1^2,-2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,0,0,-2,2,2,-2,-2,2,-2,0,0,0,0,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,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,K.1+K.1^-1,K.1+K.1^3,0,0,2*K.1^2,2*K.1^2,-2*K.1^2,0,0,-2*K.1^2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, 4, -4, -4, -4, 4, 0, 0, 0, 0, -2, 4, -4, -4, 4, 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, 2, -2, 0, 0, 0, 2, -2, 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, 0, 0, 0, 0, -2, 4, -4, 4, -4, 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, -2, -2, 0, 0, 0, 2, 2, 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, 0, 0, 0, 0, -2, -4, 4, 4, -4, 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, -2, 2, 0, 0, 0, -2, 2, 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, 0, 0, 0, 0, -2, -4, 4, -4, 4, 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, 2, 2, 0, 0, 0, -2, -2, 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, -4, 4, -4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, 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, 4, -4, 4, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, 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, -4, 4, 4, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 4, -4, -4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,-4,4,-4,4,-4,4,-4,0,0,0,0,-2,0,0,0,0,-4*K.1,4*K.1,4*K.1,-4*K.1,0,0,0,0,0,0,0,0,-2,2,2,2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,-4,4,-4,4,-4,4,-4,0,0,0,0,-2,0,0,0,0,4*K.1,-4*K.1,-4*K.1,4*K.1,0,0,0,0,0,0,0,0,-2,2,2,2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,-2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,-4,-4,4,4,0,0,0,0,-2,0,0,0,0,-4*K.1,4*K.1,-4*K.1,4*K.1,0,0,0,0,0,0,0,0,2,-2,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1,-2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,-4,-4,4,4,0,0,0,0,-2,0,0,0,0,4*K.1,-4*K.1,4*K.1,-4*K.1,0,0,0,0,0,0,0,0,2,-2,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1,2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_384_2088:= KnownIrreducibles(CR);