/* Group 1344.108 downloaded from the LMFDB on 04 October 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, -3, -2, -2, -7, 192, 16353, 41, 674, 66, 91, 34565, 3469, 5205, 7229, 1333, 141, 8078, 12118, 7422, 3062, 166, 18447, 6167, 6175, 1575]); a,b,c := Explode([GPC.1, GPC.2, GPC.6]); AssignNames(~GPC, ["a", "b", "b2", "b4", "b8", "c", "c2", "c4"]);
GPerm := PermutationGroup< 23 | (1,2,5,8,6,3,4,7)(10,13)(11,15)(14,16)(18,19)(20,21)(22,23), (1,3,6,2)(4,7,5,8)(9,10)(11,16)(12,14)(13,15), (18,20,22)(19,21,23), (1,4,6,5)(2,7,3,8)(9,11,12,15)(10,13,14,16), (1,5,6,4)(2,8,3,7), (9,12)(10,14)(11,15)(13,16), (1,6)(2,3)(4,5)(7,8), (17,18,20,23,22,21,19) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1344_108 := 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, c^14>,< 2, 1, b^12>,< 2, 1, b^12*c^14>,< 3, 7, b^8*c^8>,< 3, 7, b^16*c^24>,< 4, 2, c^7>,< 4, 2, b^6*c^14>,< 4, 2, b^6>,< 4, 2, b^12*c^21>,< 4, 4, b^6*c^7>,< 4, 8, a*b^12>,< 4, 8, a*b^12*c^21>,< 6, 7, b^16*c^10>,< 6, 7, b^8*c^22>,< 6, 7, b^4*c^20>,< 6, 7, b^20*c^16>,< 6, 7, b^4*c^10>,< 6, 7, b^20*c^22>,< 7, 6, c^4>,< 8, 28, b^3>,< 8, 28, b^21>,< 8, 28, b^9>,< 8, 28, b^15>,< 8, 28, a*b^21*c^7>,< 8, 28, a*b^9*c^14>,< 8, 28, a*b^9>,< 8, 28, a*b^21*c^21>,< 12, 14, b^8*c>,< 12, 14, b^16*c>,< 12, 14, b^2*c^2>,< 12, 14, b^10*c^2>,< 12, 14, b^2>,< 12, 14, b^22>,< 12, 14, b^20*c^7>,< 12, 14, b^4*c^21>,< 12, 28, b^2*c>,< 12, 28, b^10*c>,< 12, 56, a*b^8>,< 12, 56, a*b^4>,< 12, 56, a*b^8*c^27>,< 12, 56, a*b^4*c^11>,< 14, 6, c^2>,< 14, 6, b^12*c^8>,< 14, 6, b^12*c^2>,< 24, 28, b>,< 24, 28, b^17*c>,< 24, 28, b^5>,< 24, 28, b^19>,< 24, 28, b*c>,< 24, 28, b^17>,< 24, 28, b^5*c>,< 24, 28, b^13>,< 24, 28, a*b>,< 24, 28, a*b^5*c>,< 24, 28, a*b^5*c^2>,< 24, 28, a*b*c^3>,< 24, 28, a*b*c>,< 24, 28, a*b^5>,< 24, 28, a*b^5*c^3>,< 24, 28, a*b*c^2>,< 28, 12, c>,< 28, 12, b^12*c>,< 28, 12, b^6*c^4>,< 28, 12, b^6*c^2>,< 28, 12, b^6*c>,< 28, 12, b^18*c>,< 28, 24, a*c^4>,< 28, 24, a*c^12>,< 28, 24, a*c>,< 28, 24, a*c^5>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,K.1^-1,K.1,1,1,1,1,1,1,1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,1,1,1,1,1,1,1,1,1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.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,K.1,K.1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1^-1,K.1,K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,K.1,K.1^-1,1,1,1,1,1,1,1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,1,1,1,1,1,1,1,1,1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,1,1,1,K.1^-1,K.1^-1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1,K.1,K.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,-1*K.1,K.1,K.1,K.1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,1,1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,K.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]; 
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,K.1,-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,-1,1,1,1,1,-1*K.1,K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-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]; 
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,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,K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,-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]; 
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,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*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,K.1^-1,K.1,1,1,1,1,1,-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,K.1,K.1,K.1,K.1^-1,K.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*K.1^-1,1,1,1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,K.1^-1,K.1^-1,K.1,K.1,-1*K.1^-1,K.1^-1,-1*K.1^-1,K.1^-1,-1*K.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(3: Sparse := true);
S := [ K |1,1,1,1,K.1,K.1^-1,1,1,1,1,1,-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,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1,K.1^-1,K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,1,1,1,-1*K.1^-1,K.1^-1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,K.1,K.1,K.1^-1,K.1^-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,K.1^-1,K.1,1,1,1,1,1,-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,K.1,K.1,K.1,K.1^-1,K.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*K.1^-1,1,1,1,K.1,-1*K.1,-1*K.1,K.1,K.1,K.1^-1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,K.1^-1,-1*K.1^-1,K.1^-1,-1*K.1^-1,K.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(3: Sparse := true);
S := [ K |1,1,1,1,K.1,K.1^-1,1,1,1,1,1,-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,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1,K.1^-1,K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,1,1,1,K.1^-1,-1*K.1^-1,-1*K.1^-1,K.1^-1,K.1^-1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1^-1,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,K.1^-1,K.1,1,1,1,1,1,1,1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,1,-1,-1,-1,-1,-1,-1,-1,-1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.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*K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.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(3: Sparse := true);
S := [ K |1,1,1,1,K.1,K.1^-1,1,1,1,1,1,1,1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,1,-1,-1,-1,-1,-1,-1,-1,-1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.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*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |1,1,1,1,-1*K.1^2,K.1^4,-1,-1,-1,-1,1,-1,1,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,1,-1*K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,K.1^3,K.1^3,-1*K.1^4,-1*K.1^4,-1*K.1^4,K.1^2,K.1^2,K.1^2,-1*K.1^4,K.1^2,-1*K.1^2,K.1^4,K.1^4,-1*K.1^4,K.1^2,-1*K.1^2,1,1,1,-1*K.1,K.1,K.1,-1*K.1,K.1,K.1^5,-1*K.1^5,-1*K.1^5,K.1^5,-1*K.1,-1*K.1,-1*K.1^5,-1*K.1^5,K.1^5,K.1^5,K.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(12: Sparse := true);
S := [ K |1,1,1,1,K.1^4,-1*K.1^2,-1,-1,-1,-1,1,-1,1,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,1,K.1^3,K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1^3,-1*K.1^3,K.1^2,K.1^2,K.1^2,-1*K.1^4,-1*K.1^4,-1*K.1^4,K.1^2,-1*K.1^4,K.1^4,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^4,K.1^4,1,1,1,K.1^5,-1*K.1^5,-1*K.1^5,K.1^5,-1*K.1^5,-1*K.1,K.1,K.1,-1*K.1,K.1^5,K.1^5,K.1,K.1,-1*K.1,-1*K.1,-1*K.1^5,-1,1,-1,-1,1,-1,1,1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |1,1,1,1,-1*K.1^2,K.1^4,-1,-1,-1,-1,1,-1,1,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,1,K.1^3,K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1^3,-1*K.1^3,-1*K.1^4,-1*K.1^4,-1*K.1^4,K.1^2,K.1^2,K.1^2,-1*K.1^4,K.1^2,-1*K.1^2,K.1^4,K.1^4,-1*K.1^4,K.1^2,-1*K.1^2,1,1,1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1^5,K.1^5,K.1^5,-1*K.1^5,K.1,K.1,K.1^5,K.1^5,-1*K.1^5,-1*K.1^5,-1*K.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(12: Sparse := true);
S := [ K |1,1,1,1,K.1^4,-1*K.1^2,-1,-1,-1,-1,1,-1,1,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,1,-1*K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,K.1^3,K.1^3,K.1^2,K.1^2,K.1^2,-1*K.1^4,-1*K.1^4,-1*K.1^4,K.1^2,-1*K.1^4,K.1^4,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^4,K.1^4,1,1,1,-1*K.1^5,K.1^5,K.1^5,-1*K.1^5,K.1^5,K.1,-1*K.1,-1*K.1,K.1,-1*K.1^5,-1*K.1^5,-1*K.1,-1*K.1,K.1,K.1,K.1^5,-1,1,-1,-1,1,-1,1,1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |1,1,1,1,-1*K.1^2,K.1^4,-1,-1,-1,-1,1,1,-1,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,-1*K.1^4,-1*K.1^4,-1*K.1^4,K.1^2,K.1^2,K.1^2,-1*K.1^4,K.1^2,-1*K.1^2,K.1^4,-1*K.1^4,K.1^4,-1*K.1^2,K.1^2,1,1,1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1^5,-1*K.1^5,K.1^5,-1*K.1^5,K.1,K.1,-1*K.1^5,K.1^5,K.1^5,-1*K.1^5,K.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(12: Sparse := true);
S := [ K |1,1,1,1,K.1^4,-1*K.1^2,-1,-1,-1,-1,1,1,-1,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,K.1^3,-1*K.1^3,K.1^2,K.1^2,K.1^2,-1*K.1^4,-1*K.1^4,-1*K.1^4,K.1^2,-1*K.1^4,K.1^4,-1*K.1^2,K.1^2,-1*K.1^2,K.1^4,-1*K.1^4,1,1,1,K.1^5,K.1^5,K.1^5,K.1^5,-1*K.1^5,-1*K.1,K.1,-1*K.1,K.1,-1*K.1^5,-1*K.1^5,K.1,-1*K.1,-1*K.1,K.1,-1*K.1^5,-1,1,-1,-1,1,-1,-1,-1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |1,1,1,1,-1*K.1^2,K.1^4,-1,-1,-1,-1,1,1,-1,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,K.1^3,-1*K.1^3,-1*K.1^4,-1*K.1^4,-1*K.1^4,K.1^2,K.1^2,K.1^2,-1*K.1^4,K.1^2,-1*K.1^2,K.1^4,-1*K.1^4,K.1^4,-1*K.1^2,K.1^2,1,1,1,K.1,K.1,K.1,K.1,-1*K.1,-1*K.1^5,K.1^5,-1*K.1^5,K.1^5,-1*K.1,-1*K.1,K.1^5,-1*K.1^5,-1*K.1^5,K.1^5,-1*K.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(12: Sparse := true);
S := [ K |1,1,1,1,K.1^4,-1*K.1^2,-1,-1,-1,-1,1,1,-1,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,-1*K.1^2,K.1^4,1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,K.1^2,K.1^2,K.1^2,-1*K.1^4,-1*K.1^4,-1*K.1^4,K.1^2,-1*K.1^4,K.1^4,-1*K.1^2,K.1^2,-1*K.1^2,K.1^4,-1*K.1^4,1,1,1,-1*K.1^5,-1*K.1^5,-1*K.1^5,-1*K.1^5,K.1^5,K.1,-1*K.1,K.1,-1*K.1,K.1^5,K.1^5,-1*K.1,K.1,K.1,-1*K.1,K.1^5,-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, 0, 0, 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, 0, 0, 0, 0, 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, 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, 0, 0, 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, 0, 0, 0, 0, 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, 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,-2,0,2,0,0,0,0,-2,2,-2,-2,2,-2,2,0,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-2,2,0,-2,0,0,2,0,0,0,0,0,0,-2,-2,2,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,K.1+K.1^-1,0,K.1+K.1^-1,0,0,0,-2,0,0,2,0,0,0,0]; 
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,-2,0,2,0,0,0,0,-2,2,-2,-2,2,-2,2,0,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,-2,2,0,-2,0,0,2,0,0,0,0,0,0,-2,-2,2,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,0,0,0,-2,0,0,2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,2,2,2,0,-2,0,0,0,0,-2,2,-2,-2,2,-2,2,0,-1*K.1-K.1^3,0,0,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,0,2,-2,0,2,0,0,-2,0,0,0,0,0,0,-2,-2,2,0,K.1+K.1^3,-1*K.1-K.1^3,0,0,0,0,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,-1*K.1-K.1^3,0,K.1+K.1^3,0,0,0,2,0,0,-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,2,2,2,0,-2,0,0,0,0,-2,2,-2,-2,2,-2,2,0,K.1+K.1^3,0,0,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,0,2,-2,0,2,0,0,-2,0,0,0,0,0,0,-2,-2,2,0,-1*K.1-K.1^3,K.1+K.1^3,0,0,0,0,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,K.1+K.1^3,0,-1*K.1-K.1^3,0,0,0,2,0,0,-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,2,2,0,2,0,-2,0,0,0,-2,-2,2,-2,-2,2,2,-1*K.1-K.1^3,0,K.1+K.1^3,-1*K.1-K.1^3,0,0,0,K.1+K.1^3,-2,0,0,-2,0,2,2,0,0,0,0,0,0,0,-2,2,-2,-1*K.1-K.1^3,0,0,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,0,0,0,0,K.1+K.1^3,0,K.1+K.1^3,0,-1*K.1-K.1^3,2,0,0,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,2,2,0,2,0,-2,0,0,0,-2,-2,2,-2,-2,2,2,K.1+K.1^3,0,-1*K.1-K.1^3,K.1+K.1^3,0,0,0,-1*K.1-K.1^3,-2,0,0,-2,0,2,2,0,0,0,0,0,0,0,-2,2,-2,K.1+K.1^3,0,0,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,0,0,0,0,-1*K.1-K.1^3,0,-1*K.1-K.1^3,0,K.1+K.1^3,2,0,0,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,2*K.1^-1,2*K.1,-2,2,-2,2,-2,0,0,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,2,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,-2*K.1,2*K.1^-1,-2*K.1^-1,2*K.1^-1,2*K.1,-2*K.1^-1,-2*K.1^-1,-2*K.1,0,0,0,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,-2,-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,2*K.1,2*K.1^-1,-2,2,-2,2,-2,0,0,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,2,0,0,0,0,0,0,0,0,2*K.1^-1,-2*K.1^-1,-2*K.1^-1,2*K.1,-2*K.1,2*K.1,2*K.1^-1,-2*K.1,-2*K.1,-2*K.1^-1,0,0,0,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,-2,-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,2*K.1^-1,2*K.1,2,-2,2,-2,-2,0,0,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,2,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,2*K.1,-2*K.1^-1,2*K.1^-1,-2*K.1^-1,-2*K.1,2*K.1^-1,-2*K.1^-1,-2*K.1,0,0,0,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,-2,-2,2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,2*K.1,2*K.1^-1,2,-2,2,-2,-2,0,0,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,2,0,0,0,0,0,0,0,0,-2*K.1^-1,2*K.1^-1,2*K.1^-1,-2*K.1,2*K.1,-2*K.1,-2*K.1^-1,2*K.1,-2*K.1,-2*K.1^-1,0,0,0,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,-2,-2,2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,2,2,0,-2,0,2,0,0,0,-2,-2,2,-2,-2,2,2,-1*K.1-K.1^-1,0,K.1+K.1^-1,K.1+K.1^-1,0,0,0,-1*K.1-K.1^-1,2,0,0,2,0,-2,-2,0,0,0,0,0,0,0,-2,2,-2,K.1+K.1^-1,0,0,-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,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,-2,0,0,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,2,2,0,-2,0,2,0,0,0,-2,-2,2,-2,-2,2,2,K.1+K.1^-1,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,K.1+K.1^-1,2,0,0,2,0,-2,-2,0,0,0,0,0,0,0,-2,2,-2,-1*K.1-K.1^-1,0,0,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,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,-2,0,0,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,-2,2,-2,-2*K.1^4,2*K.1^8,-2,0,2,0,0,0,0,-2*K.1^8,-2*K.1^4,-2*K.1^8,2*K.1^4,2*K.1^8,2*K.1^4,2,0,-1*K.1^3-K.1^-3,0,0,K.1^3+K.1^-3,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,0,0,-2*K.1^8,2*K.1^8,0,2*K.1^4,0,0,-2*K.1^4,0,0,0,0,0,0,-2,-2,2,0,-1*K.1^3+K.1^5+K.1^7,K.1^3-K.1^5-K.1^7,0,0,0,0,K.1+K.1^7,K.1+K.1^7,K.1^3-K.1^5-K.1^7,-1*K.1^3+K.1^5+K.1^7,0,-1*K.1-K.1^7,0,-1*K.1-K.1^7,0,0,0,-2,0,0,2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,-2,2,-2,2*K.1^8,-2*K.1^4,-2,0,2,0,0,0,0,2*K.1^4,2*K.1^8,2*K.1^4,-2*K.1^8,-2*K.1^4,-2*K.1^8,2,0,-1*K.1^3-K.1^-3,0,0,K.1^3+K.1^-3,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,0,0,2*K.1^4,-2*K.1^4,0,-2*K.1^8,0,0,2*K.1^8,0,0,0,0,0,0,-2,-2,2,0,-1*K.1-K.1^7,K.1+K.1^7,0,0,0,0,K.1^3-K.1^5-K.1^7,K.1^3-K.1^5-K.1^7,K.1+K.1^7,-1*K.1-K.1^7,0,-1*K.1^3+K.1^5+K.1^7,0,-1*K.1^3+K.1^5+K.1^7,0,0,0,-2,0,0,2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,-2,2,-2,-2*K.1^4,2*K.1^8,-2,0,2,0,0,0,0,-2*K.1^8,-2*K.1^4,-2*K.1^8,2*K.1^4,2*K.1^8,2*K.1^4,2,0,K.1^3+K.1^-3,0,0,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,K.1^3+K.1^-3,0,0,-2*K.1^8,2*K.1^8,0,2*K.1^4,0,0,-2*K.1^4,0,0,0,0,0,0,-2,-2,2,0,K.1^3-K.1^5-K.1^7,-1*K.1^3+K.1^5+K.1^7,0,0,0,0,-1*K.1-K.1^7,-1*K.1-K.1^7,-1*K.1^3+K.1^5+K.1^7,K.1^3-K.1^5-K.1^7,0,K.1+K.1^7,0,K.1+K.1^7,0,0,0,-2,0,0,2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,-2,2,-2,2*K.1^8,-2*K.1^4,-2,0,2,0,0,0,0,2*K.1^4,2*K.1^8,2*K.1^4,-2*K.1^8,-2*K.1^4,-2*K.1^8,2,0,K.1^3+K.1^-3,0,0,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,K.1^3+K.1^-3,0,0,2*K.1^4,-2*K.1^4,0,-2*K.1^8,0,0,2*K.1^8,0,0,0,0,0,0,-2,-2,2,0,K.1+K.1^7,-1*K.1-K.1^7,0,0,0,0,-1*K.1^3+K.1^5+K.1^7,-1*K.1^3+K.1^5+K.1^7,-1*K.1-K.1^7,K.1+K.1^7,0,K.1^3-K.1^5-K.1^7,0,K.1^3-K.1^5-K.1^7,0,0,0,-2,0,0,2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,-2,2,-2,-2*K.1^4,2*K.1^8,2,0,-2,0,0,0,0,-2*K.1^8,-2*K.1^4,-2*K.1^8,2*K.1^4,2*K.1^8,2*K.1^4,2,0,K.1-K.1^3-K.1^5,0,0,-1*K.1+K.1^3+K.1^5,K.1-K.1^3-K.1^5,-1*K.1+K.1^3+K.1^5,0,0,2*K.1^8,-2*K.1^8,0,-2*K.1^4,0,0,2*K.1^4,0,0,0,0,0,0,-2,-2,2,0,-1*K.1^3-K.1^5+K.1^7,K.1^3+K.1^5-K.1^7,0,0,0,0,K.1-K.1^7,-1*K.1+K.1^7,-1*K.1^3-K.1^5+K.1^7,K.1^3+K.1^5-K.1^7,0,-1*K.1+K.1^7,0,K.1-K.1^7,0,0,0,2,0,0,-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,-2,2,-2,2*K.1^8,-2*K.1^4,2,0,-2,0,0,0,0,2*K.1^4,2*K.1^8,2*K.1^4,-2*K.1^8,-2*K.1^4,-2*K.1^8,2,0,-1*K.1+K.1^3+K.1^5,0,0,K.1-K.1^3-K.1^5,-1*K.1+K.1^3+K.1^5,K.1-K.1^3-K.1^5,0,0,-2*K.1^4,2*K.1^4,0,2*K.1^8,0,0,-2*K.1^8,0,0,0,0,0,0,-2,-2,2,0,-1*K.1+K.1^7,K.1-K.1^7,0,0,0,0,K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^5+K.1^7,-1*K.1+K.1^7,K.1-K.1^7,0,-1*K.1^3-K.1^5+K.1^7,0,K.1^3+K.1^5-K.1^7,0,0,0,2,0,0,-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,-2,2,-2,-2*K.1^4,2*K.1^8,2,0,-2,0,0,0,0,-2*K.1^8,-2*K.1^4,-2*K.1^8,2*K.1^4,2*K.1^8,2*K.1^4,2,0,-1*K.1+K.1^3+K.1^5,0,0,K.1-K.1^3-K.1^5,-1*K.1+K.1^3+K.1^5,K.1-K.1^3-K.1^5,0,0,2*K.1^8,-2*K.1^8,0,-2*K.1^4,0,0,2*K.1^4,0,0,0,0,0,0,-2,-2,2,0,K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^5+K.1^7,0,0,0,0,-1*K.1+K.1^7,K.1-K.1^7,K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^5+K.1^7,0,K.1-K.1^7,0,-1*K.1+K.1^7,0,0,0,2,0,0,-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,-2,2,-2,2*K.1^8,-2*K.1^4,2,0,-2,0,0,0,0,2*K.1^4,2*K.1^8,2*K.1^4,-2*K.1^8,-2*K.1^4,-2*K.1^8,2,0,K.1-K.1^3-K.1^5,0,0,-1*K.1+K.1^3+K.1^5,K.1-K.1^3-K.1^5,-1*K.1+K.1^3+K.1^5,0,0,-2*K.1^4,2*K.1^4,0,2*K.1^8,0,0,-2*K.1^8,0,0,0,0,0,0,-2,-2,2,0,K.1-K.1^7,-1*K.1+K.1^7,0,0,0,0,-1*K.1^3-K.1^5+K.1^7,K.1^3+K.1^5-K.1^7,K.1-K.1^7,-1*K.1+K.1^7,0,K.1^3+K.1^5-K.1^7,0,-1*K.1^3-K.1^5+K.1^7,0,0,0,2,0,0,-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,2,-2,-2,-2*K.1^4,2*K.1^8,0,2,0,-2,0,0,0,-2*K.1^8,2*K.1^4,2*K.1^8,2*K.1^4,-2*K.1^8,-2*K.1^4,2,K.1-K.1^3-K.1^5,0,-1*K.1+K.1^3+K.1^5,K.1-K.1^3-K.1^5,0,0,0,-1*K.1+K.1^3+K.1^5,-2*K.1^8,0,0,2*K.1^4,0,-2*K.1^4,2*K.1^8,0,0,0,0,0,0,0,-2,2,-2,K.1^3+K.1^5-K.1^7,0,0,-1*K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^5+K.1^7,-1*K.1+K.1^7,-1*K.1+K.1^7,0,0,0,0,K.1-K.1^7,0,K.1-K.1^7,0,K.1^3+K.1^5-K.1^7,2,0,0,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,2,-2,-2,2*K.1^8,-2*K.1^4,0,2,0,-2,0,0,0,2*K.1^4,-2*K.1^8,-2*K.1^4,-2*K.1^8,2*K.1^4,2*K.1^8,2,-1*K.1+K.1^3+K.1^5,0,K.1-K.1^3-K.1^5,-1*K.1+K.1^3+K.1^5,0,0,0,K.1-K.1^3-K.1^5,2*K.1^4,0,0,-2*K.1^8,0,2*K.1^8,-2*K.1^4,0,0,0,0,0,0,0,-2,2,-2,K.1-K.1^7,0,0,-1*K.1+K.1^7,-1*K.1+K.1^7,-1*K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^5+K.1^7,0,0,0,0,K.1^3+K.1^5-K.1^7,0,K.1^3+K.1^5-K.1^7,0,K.1-K.1^7,2,0,0,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,2,-2,-2,-2*K.1^4,2*K.1^8,0,2,0,-2,0,0,0,-2*K.1^8,2*K.1^4,2*K.1^8,2*K.1^4,-2*K.1^8,-2*K.1^4,2,-1*K.1+K.1^3+K.1^5,0,K.1-K.1^3-K.1^5,-1*K.1+K.1^3+K.1^5,0,0,0,K.1-K.1^3-K.1^5,-2*K.1^8,0,0,2*K.1^4,0,-2*K.1^4,2*K.1^8,0,0,0,0,0,0,0,-2,2,-2,-1*K.1^3-K.1^5+K.1^7,0,0,K.1^3+K.1^5-K.1^7,K.1^3+K.1^5-K.1^7,K.1-K.1^7,K.1-K.1^7,0,0,0,0,-1*K.1+K.1^7,0,-1*K.1+K.1^7,0,-1*K.1^3-K.1^5+K.1^7,2,0,0,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,2,-2,-2,2*K.1^8,-2*K.1^4,0,2,0,-2,0,0,0,2*K.1^4,-2*K.1^8,-2*K.1^4,-2*K.1^8,2*K.1^4,2*K.1^8,2,K.1-K.1^3-K.1^5,0,-1*K.1+K.1^3+K.1^5,K.1-K.1^3-K.1^5,0,0,0,-1*K.1+K.1^3+K.1^5,2*K.1^4,0,0,-2*K.1^8,0,2*K.1^8,-2*K.1^4,0,0,0,0,0,0,0,-2,2,-2,-1*K.1+K.1^7,0,0,K.1-K.1^7,K.1-K.1^7,K.1^3+K.1^5-K.1^7,K.1^3+K.1^5-K.1^7,0,0,0,0,-1*K.1^3-K.1^5+K.1^7,0,-1*K.1^3-K.1^5+K.1^7,0,-1*K.1+K.1^7,2,0,0,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,2,-2,-2,-2*K.1^4,2*K.1^8,0,-2,0,2,0,0,0,-2*K.1^8,2*K.1^4,2*K.1^8,2*K.1^4,-2*K.1^8,-2*K.1^4,2,-1*K.1^3-K.1^-3,0,K.1^3+K.1^-3,K.1^3+K.1^-3,0,0,0,-1*K.1^3-K.1^-3,2*K.1^8,0,0,-2*K.1^4,0,2*K.1^4,-2*K.1^8,0,0,0,0,0,0,0,-2,2,-2,-1*K.1^3+K.1^5+K.1^7,0,0,K.1^3-K.1^5-K.1^7,-1*K.1^3+K.1^5+K.1^7,K.1+K.1^7,-1*K.1-K.1^7,0,0,0,0,K.1+K.1^7,0,-1*K.1-K.1^7,0,K.1^3-K.1^5-K.1^7,-2,0,0,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,2,-2,-2,2*K.1^8,-2*K.1^4,0,-2,0,2,0,0,0,2*K.1^4,-2*K.1^8,-2*K.1^4,-2*K.1^8,2*K.1^4,2*K.1^8,2,-1*K.1^3-K.1^-3,0,K.1^3+K.1^-3,K.1^3+K.1^-3,0,0,0,-1*K.1^3-K.1^-3,-2*K.1^4,0,0,2*K.1^8,0,-2*K.1^8,2*K.1^4,0,0,0,0,0,0,0,-2,2,-2,-1*K.1-K.1^7,0,0,K.1+K.1^7,-1*K.1-K.1^7,K.1^3-K.1^5-K.1^7,-1*K.1^3+K.1^5+K.1^7,0,0,0,0,K.1^3-K.1^5-K.1^7,0,-1*K.1^3+K.1^5+K.1^7,0,K.1+K.1^7,-2,0,0,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,2,-2,-2,-2*K.1^4,2*K.1^8,0,-2,0,2,0,0,0,-2*K.1^8,2*K.1^4,2*K.1^8,2*K.1^4,-2*K.1^8,-2*K.1^4,2,K.1^3+K.1^-3,0,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,0,0,0,K.1^3+K.1^-3,2*K.1^8,0,0,-2*K.1^4,0,2*K.1^4,-2*K.1^8,0,0,0,0,0,0,0,-2,2,-2,K.1^3-K.1^5-K.1^7,0,0,-1*K.1^3+K.1^5+K.1^7,K.1^3-K.1^5-K.1^7,-1*K.1-K.1^7,K.1+K.1^7,0,0,0,0,-1*K.1-K.1^7,0,K.1+K.1^7,0,-1*K.1^3+K.1^5+K.1^7,-2,0,0,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |2,2,-2,-2,2*K.1^8,-2*K.1^4,0,-2,0,2,0,0,0,2*K.1^4,-2*K.1^8,-2*K.1^4,-2*K.1^8,2*K.1^4,2*K.1^8,2,K.1^3+K.1^-3,0,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,0,0,0,K.1^3+K.1^-3,-2*K.1^4,0,0,2*K.1^8,0,-2*K.1^8,2*K.1^4,0,0,0,0,0,0,0,-2,2,-2,K.1+K.1^7,0,0,-1*K.1-K.1^7,K.1+K.1^7,-1*K.1^3+K.1^5+K.1^7,K.1^3-K.1^5-K.1^7,0,0,0,0,-1*K.1^3+K.1^5+K.1^7,0,K.1^3-K.1^5-K.1^7,0,-1*K.1-K.1^7,-2,0,0,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 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, 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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,-4,4,4*K.1^-1,4*K.1,0,0,0,0,0,0,0,4*K.1,-4*K.1^-1,-4*K.1,4*K.1^-1,-4*K.1,-4*K.1^-1,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,-4,4,4*K.1,4*K.1^-1,0,0,0,0,0,0,0,4*K.1^-1,-4*K.1,-4*K.1^-1,4*K.1,-4*K.1^-1,-4*K.1,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, -1, 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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, -1, 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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 0, 0, -6, -6, -6, -6, 6, -6, 6, 0, 0, 0, 0, 0, 0, -1, 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, 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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 0, 0, -6, -6, -6, -6, 6, 6, -6, 0, 0, 0, 0, 0, 0, -1, 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, 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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |6,6,6,6,0,0,-6,6,-6,6,-6,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,1,-1-2*K.1-2*K.1^2-2*K.1^-3,1+2*K.1+2*K.1^2+2*K.1^-3,-1-2*K.1-2*K.1^2-2*K.1^-3,1+2*K.1+2*K.1^2+2*K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |6,6,6,6,0,0,-6,6,-6,6,-6,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,1,1+2*K.1+2*K.1^2+2*K.1^-3,-1-2*K.1-2*K.1^2-2*K.1^-3,1+2*K.1+2*K.1^2+2*K.1^-3,-1-2*K.1-2*K.1^2-2*K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |6,6,6,6,0,0,6,-6,6,-6,-6,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,1,1,-1,-1-2*K.1-2*K.1^2-2*K.1^-3,1+2*K.1+2*K.1^2+2*K.1^-3,1+2*K.1+2*K.1^2+2*K.1^-3,-1-2*K.1-2*K.1^2-2*K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |6,6,6,6,0,0,6,-6,6,-6,-6,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,1,1,-1,1+2*K.1+2*K.1^2+2*K.1^-3,-1-2*K.1-2*K.1^2-2*K.1^-3,-1-2*K.1-2*K.1^2-2*K.1^-3,1+2*K.1+2*K.1^2+2*K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[12, -12, 12, -12, 0, 0, -12, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, -12, 12, -12, 0, 0, 12, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[12, 12, -12, -12, 0, 0, 0, 12, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, -12, -12, 0, 0, 0, -12, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |12,-12,-12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2-4*K.1-4*K.1^2-4*K.1^-3,0,0,2+4*K.1+4*K.1^2+4*K.1^-3,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |12,-12,-12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2+4*K.1+4*K.1^2+4*K.1^-3,0,0,-2-4*K.1-4*K.1^2-4*K.1^-3,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_1344_108:= KnownIrreducibles(CR);