/* Group 256.5426 downloaded from the LMFDB on 19 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, 2, 2, 2, 2, 2273, 41, 3362, 66, 4355, 539, 2252, 116, 5389, 141, 5390, 166]); a,b,c := Explode([GPC.1, GPC.2, GPC.5]); AssignNames(~GPC, ["a", "b", "b2", "b4", "c", "c2", "c4", "c8"]);
GPerm := PermutationGroup< 32 | (3,4)(5,7)(6,8)(9,13)(10,14)(11,16)(12,15)(17,24)(18,23)(19,22)(20,21)(25,26)(29,32)(30,31), (1,23,7,19,3,22,6,18,2,24,8,20,4,21,5,17)(9,31,15,27,11,30,14,26,10,32,16,28,12,29,13,25), (1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32), (1,6,4,7,2,5,3,8)(9,14,12,15,10,13,11,16)(17,22,20,23,18,21,19,24)(25,30,28,31,26,29,27,32), (1,7,3,6,2,8,4,5)(9,13,12,16,10,14,11,15)(17,23,19,22,18,24,20,21)(25,29,28,32,26,30,27,31), (1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16)(17,19,18,20)(21,23,22,24)(25,27,26,28)(29,31,30,32), (1,4,2,3)(5,8,6,7)(9,11,10,12)(13,15,14,16)(17,20,18,19)(21,24,22,23)(25,27,26,28)(29,31,30,32), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_256_5426 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
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^8>,< 2, 2, b^4*c^4>,< 2, 8, a>,< 2, 32, a*b^7>,< 4, 2, b^4*c^8>,< 4, 2, c^4>,< 4, 4, b^2*c^2>,< 4, 4, b^2*c^10>,< 4, 8, a*c^4>,< 4, 32, a*b^7*c^7>,< 8, 2, c^2>,< 8, 2, c^6>,< 8, 2, b^2>,< 8, 2, b^6>,< 8, 4, b^2*c^4>,< 8, 4, b^4*c^2>,< 8, 8, a*c^2>,< 8, 8, a*c^6>,< 16, 2, c>,< 16, 2, c^9>,< 16, 2, c^5>,< 16, 2, c^13>,< 16, 4, b^4*c>,< 16, 4, b^4*c^5>,< 16, 4, b^2*c>,< 16, 4, b^2*c^9>,< 16, 4, b^2*c^13>,< 16, 4, b^2*c^5>,< 16, 8, a*c>,< 16, 8, a*b^2*c>,< 16, 8, a*c^3>,< 16, 8, a*c^5>,< 16, 16, b>,< 16, 16, b^5>,< 16, 16, b*c>,< 16, 16, b^5*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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, -2, 0, 2, 2, -2, -2, -2, 0, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 0, 0, 2, 2, -2, -2, 0, 0, -2, 2, 2, -2, -2, 2, 0, 0, -2, -2, -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, 0, 0, 2, 2, -2, -2, 0, 0, -2, 2, 2, -2, -2, 2, 0, 0, 2, 2, 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, 0, 2, 2, -2, -2, 2, 0, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,0,2,-2,0,0,2,0,2,0,0,2,-2,0,0,0,-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,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,0,2,-2,0,0,2,0,2,0,0,2,-2,0,0,0,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,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,0,-2,2,0,0,0,0,0,2,2,0,0,-2,0,0,-2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,0,-2,2,0,0,0,0,0,2,2,0,0,-2,0,0,-2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,0,-2,2,0,0,0,0,0,2,2,0,0,-2,0,0,2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-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,-2,0,0,-2,2,0,0,0,0,0,2,2,0,0,-2,0,0,2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.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(8: Sparse := true);
S := [ K |2,2,-2,2,0,2,-2,0,0,-2,0,2,0,0,2,-2,0,0,0,-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,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,2,0,2,-2,0,0,-2,0,2,0,0,2,-2,0,0,0,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,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,0,0,2,2,2,2,0,0,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,0,0,2,2,2,2,0,0,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,0,2,-2,0,0,0,0,-2,0,0,-2,2,0,-2*K.1^2,2*K.1^2,-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,-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.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,0,2,-2,0,0,0,0,-2,0,0,-2,2,0,2*K.1^2,-2*K.1^2,-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,-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.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,0,2,-2,0,0,0,0,-2,0,0,-2,2,0,-2*K.1^2,2*K.1^2,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,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.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,0,2,-2,0,0,0,0,-2,0,0,-2,2,0,2*K.1^2,-2*K.1^2,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,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.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, 0, 0, -4, 4, 0, 0, 0, 0, 0, -4, -4, 0, 0, 4, 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(8: Sparse := true);
S := [ K |4,4,4,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*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 |4,4,4,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*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(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,-2,2,0,0,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,0,-2*K.1-2*K.1^7,2*K.1^3+2*K.1^5,2*K.1+2*K.1^7,-2*K.1^3-2*K.1^5,0,0,K.1+K.1^3+K.1^5+K.1^7,-1*K.1+K.1^3+K.1^5-K.1^7,K.1-K.1^3-K.1^5+K.1^7,-1*K.1-K.1^3-K.1^5-K.1^7,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,-2,2,0,0,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,0,2*K.1+2*K.1^7,-2*K.1^3-2*K.1^5,-2*K.1-2*K.1^7,2*K.1^3+2*K.1^5,0,0,-1*K.1-K.1^3-K.1^5-K.1^7,K.1-K.1^3-K.1^5+K.1^7,-1*K.1+K.1^3+K.1^5-K.1^7,K.1+K.1^3+K.1^5+K.1^7,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,-2,2,0,0,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,0,-2*K.1^3-2*K.1^5,-2*K.1-2*K.1^7,2*K.1^3+2*K.1^5,2*K.1+2*K.1^7,0,0,-1*K.1+K.1^3+K.1^5-K.1^7,-1*K.1-K.1^3-K.1^5-K.1^7,K.1+K.1^3+K.1^5+K.1^7,K.1-K.1^3-K.1^5+K.1^7,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,-2,2,0,0,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,0,2*K.1^3+2*K.1^5,2*K.1+2*K.1^7,-2*K.1^3-2*K.1^5,-2*K.1-2*K.1^7,0,0,K.1-K.1^3-K.1^5+K.1^7,K.1+K.1^3+K.1^5+K.1^7,-1*K.1-K.1^3-K.1^5-K.1^7,-1*K.1+K.1^3+K.1^5-K.1^7,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,2,-2,0,0,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,0,-2*K.1^3-2*K.1^5,-2*K.1-2*K.1^7,2*K.1^3+2*K.1^5,2*K.1+2*K.1^7,0,0,K.1-K.1^3-K.1^5+K.1^7,K.1+K.1^3+K.1^5+K.1^7,-1*K.1-K.1^3-K.1^5-K.1^7,-1*K.1+K.1^3+K.1^5-K.1^7,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,2,-2,0,0,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,0,2*K.1^3+2*K.1^5,2*K.1+2*K.1^7,-2*K.1^3-2*K.1^5,-2*K.1-2*K.1^7,0,0,-1*K.1+K.1^3+K.1^5-K.1^7,-1*K.1-K.1^3-K.1^5-K.1^7,K.1+K.1^3+K.1^5+K.1^7,K.1-K.1^3-K.1^5+K.1^7,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,2,-2,0,0,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,0,-2*K.1-2*K.1^7,2*K.1^3+2*K.1^5,2*K.1+2*K.1^7,-2*K.1^3-2*K.1^5,0,0,-1*K.1-K.1^3-K.1^5-K.1^7,K.1-K.1^3-K.1^5+K.1^7,-1*K.1+K.1^3+K.1^5-K.1^7,K.1+K.1^3+K.1^5+K.1^7,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,2,-2,0,0,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,0,2*K.1+2*K.1^7,-2*K.1^3-2*K.1^5,-2*K.1-2*K.1^7,2*K.1^3+2*K.1^5,0,0,K.1+K.1^3+K.1^5+K.1^7,-1*K.1+K.1^3+K.1^5-K.1^7,K.1-K.1^3-K.1^5+K.1^7,-1*K.1-K.1^3-K.1^5-K.1^7,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_256_5426:= KnownIrreducibles(CR);