/* Group 96.9 downloaded from the LMFDB on 02 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([6, -2, -2, -2, -2, -2, -3, 12, 31, 963, 69, 2404, 88, 2309]); a,b := Explode([GPC.1, GPC.4]); AssignNames(~GPC, ["a", "a2", "a4", "b", "b2", "b4"]);
GPerm := PermutationGroup< 15 | (1,2,3,5,4,6,7,8)(10,11)(12,13,15,14), (12,14,15,13), (1,3,4,7)(2,5,6,8)(12,15)(13,14), (12,15)(13,14), (1,4)(2,6)(3,7)(5,8), (9,10,11) >;
GLZ := MatrixGroup< 6, Integers() | [[1, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [-1, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0]] >;
GLFp := MatrixGroup< 3, GF(5) | [[3, 0, 0, 0, 3, 0, 0, 0, 3], [2, 3, 0, 0, 1, 4, 1, 1, 0], [4, 1, 3, 1, 3, 1, 3, 1, 4], [1, 1, 3, 1, 0, 1, 3, 1, 1], [2, 1, 2, 1, 4, 3, 2, 3, 3], [4, 0, 0, 0, 4, 0, 0, 0, 4]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_96_9 := rec< RF |  
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
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^4>,< 2, 1, b^6>,< 2, 1, a^4*b^6>,< 3, 2, b^4>,< 4, 1, a^2>,< 4, 1, a^6>,< 4, 1, a^2*b^6>,< 4, 1, a^6*b^6>,< 4, 1, b^3>,< 4, 1, b^9>,< 4, 1, a^4*b^3>,< 4, 1, a^4*b^9>,< 4, 1, a^6*b^3>,< 4, 1, a^2*b^9>,< 4, 1, a^2*b^3>,< 4, 1, a^6*b^9>,< 6, 2, b^2>,< 6, 2, a^4*b^8>,< 6, 2, a^4*b^2>,< 8, 3, a>,< 8, 3, a^7>,< 8, 3, a^3>,< 8, 3, a^5>,< 8, 3, a*b^2>,< 8, 3, a^7*b^2>,< 8, 3, a^3*b^2>,< 8, 3, a^5*b^2>,< 8, 3, a*b>,< 8, 3, a^7*b^3>,< 8, 3, a^3*b^3>,< 8, 3, a^5*b>,< 8, 3, a*b^3>,< 8, 3, a^7*b>,< 8, 3, a^3*b>,< 8, 3, a^5*b^3>,< 12, 2, b>,< 12, 2, b^7>,< 12, 2, a^4*b>,< 12, 2, a^4*b^7>,< 12, 2, a^2*b^4>,< 12, 2, a^6*b^4>,< 12, 2, a^2*b^2>,< 12, 2, a^6*b^2>,< 12, 2, a^2*b>,< 12, 2, a^6*b^7>,< 12, 2, a^6*b>,< 12, 2, a^2*b^7>]); 
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; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,1,-1*K.1,-1,K.1,-1*K.1,-1,K.1,1,-1*K.1,1,-1*K.1,K.1,K.1,-1,-1,1,-1*K.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,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1,1,-1,1,-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,K.1,-1,-1*K.1,K.1,-1,-1*K.1,1,K.1,1,K.1,-1*K.1,-1*K.1,-1,-1,1,K.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*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,-1,1,-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*K.1,-1,K.1,-1*K.1,-1,K.1,1,-1*K.1,1,-1*K.1,K.1,K.1,-1,-1,1,K.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,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1,1,-1,1,-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,K.1,-1,-1*K.1,K.1,-1,-1*K.1,1,K.1,1,K.1,-1*K.1,-1*K.1,-1,-1,1,-1*K.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,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,-1,1,-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*K.1,1,-1*K.1,K.1,1,K.1,-1,K.1,-1,-1*K.1,-1*K.1,K.1,-1,-1,1,-1,K.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,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,1,-1,1,-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,K.1,1,K.1,-1*K.1,1,-1*K.1,-1,-1*K.1,-1,K.1,K.1,-1*K.1,-1,-1,1,-1,-1*K.1,-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*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,1,-1,1,-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*K.1,1,-1*K.1,K.1,1,K.1,-1,K.1,-1,-1*K.1,-1*K.1,K.1,-1,-1,1,1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,K.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,-1,1,-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,K.1,1,K.1,-1*K.1,1,-1*K.1,-1,-1*K.1,-1,K.1,K.1,-1*K.1,-1,-1,1,1,K.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*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,1,-1,1,-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,K.1,-1*K.1,-1*K.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,-1*K.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,K.1,K.1,-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,K.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,K.1,K.1,-1*K.1,K.1,K.1,-1*K.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]; 
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,K.1,-1*K.1,-1*K.1,K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,1,-1*K.1^2,-1*K.1^2,-1,1,K.1^2,-1*K.1^2,-1*K.1^2,-1,K.1^2,K.1^2,1,K.1^2,1,-1,-1,-1*K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^3,K.1^3,-1*K.1^3,-1*K.1,K.1,-1*K.1^3,K.1^3,K.1,1,K.1^2,1,-1*K.1^2,-1,-1*K.1^2,-1,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,1,K.1^2,K.1^2,-1,1,-1*K.1^2,K.1^2,K.1^2,-1,-1*K.1^2,-1*K.1^2,1,-1*K.1^2,1,-1,-1,K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,-1*K.1,-1*K.1,K.1,K.1^3,-1*K.1^3,K.1,-1*K.1,-1*K.1^3,1,-1*K.1^2,1,K.1^2,-1,K.1^2,-1,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,1,-1*K.1^2,-1*K.1^2,-1,1,K.1^2,-1*K.1^2,-1*K.1^2,-1,K.1^2,K.1^2,1,K.1^2,1,-1,-1,K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^3,-1*K.1^3,K.1^3,K.1,-1*K.1,K.1^3,-1*K.1^3,-1*K.1,1,K.1^2,1,-1*K.1^2,-1,-1*K.1^2,-1,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,1,K.1^2,K.1^2,-1,1,-1*K.1^2,K.1^2,K.1^2,-1,-1*K.1^2,-1*K.1^2,1,-1*K.1^2,1,-1,-1,-1*K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,K.1,K.1,-1*K.1,-1*K.1^3,K.1^3,-1*K.1,K.1,K.1^3,1,-1*K.1^2,1,K.1^2,-1,K.1^2,-1,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,1,-1*K.1^2,K.1^2,1,-1,-1*K.1^2,-1*K.1^2,K.1^2,1,-1*K.1^2,K.1^2,-1,K.1^2,1,-1,-1,K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1,K.1^3,-1*K.1^3,K.1,-1*K.1,-1*K.1^3,-1,K.1^2,-1,-1*K.1^2,1,-1*K.1^2,1,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,1,K.1^2,-1*K.1^2,1,-1,K.1^2,K.1^2,-1*K.1^2,1,K.1^2,-1*K.1^2,-1,-1*K.1^2,1,-1,-1,-1*K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1,K.1,-1*K.1^3,K.1^3,K.1,-1,-1*K.1^2,-1,K.1^2,1,K.1^2,1,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,1,-1*K.1^2,K.1^2,1,-1,-1*K.1^2,-1*K.1^2,K.1^2,1,-1*K.1^2,K.1^2,-1,K.1^2,1,-1,-1,-1*K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,-1*K.1,K.1,-1*K.1,-1*K.1^3,K.1^3,-1*K.1,K.1,K.1^3,-1,K.1^2,-1,-1*K.1^2,1,-1*K.1^2,1,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,1,K.1^2,-1*K.1^2,1,-1,K.1^2,K.1^2,-1*K.1^2,1,K.1^2,-1*K.1^2,-1,-1*K.1^2,1,-1,-1,K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,K.1,-1*K.1,K.1^3,-1*K.1^3,-1*K.1,-1,-1*K.1^2,-1,K.1^2,1,K.1^2,1,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,-1,-1*K.1^2,K.1^2,K.1^2,K.1^2,1,K.1^2,-1*K.1^2,-1*K.1^2,1,-1*K.1^2,-1,-1,1,-1,-1*K.1,-1*K.1,K.1^3,-1*K.1^3,K.1,K.1^3,-1*K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^3,K.1,K.1^2,-1,-1*K.1^2,-1,-1*K.1^2,1,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,-1,K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^2,1,-1*K.1^2,K.1^2,K.1^2,1,K.1^2,-1,-1,1,-1,K.1^3,K.1^3,-1*K.1,K.1,-1*K.1^3,-1*K.1,K.1,-1*K.1^3,K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1^2,-1,K.1^2,-1,K.1^2,1,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,-1,-1*K.1^2,K.1^2,K.1^2,K.1^2,1,K.1^2,-1*K.1^2,-1*K.1^2,1,-1*K.1^2,-1,-1,1,-1,K.1,K.1,-1*K.1^3,K.1^3,-1*K.1,-1*K.1^3,K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^3,-1*K.1,K.1^2,-1,-1*K.1^2,-1,-1*K.1^2,1,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,-1,K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^2,1,-1*K.1^2,K.1^2,K.1^2,1,K.1^2,-1,-1,1,-1,-1*K.1^3,-1*K.1^3,K.1,-1*K.1,K.1^3,K.1,-1*K.1,K.1^3,-1*K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^2,-1,K.1^2,-1,K.1^2,1,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,1,-1*K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1,K.1^2,K.1^2,-1*K.1^2,-1,K.1^2,1,-1,1,-1,-1*K.1,K.1,-1*K.1^3,K.1^3,-1*K.1,-1*K.1^3,K.1^3,-1*K.1,K.1,-1*K.1^3,K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^3,K.1,-1*K.1^2,1,K.1^2,1,K.1^2,-1,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,1,K.1^2,K.1^2,K.1^2,-1*K.1^2,-1,-1*K.1^2,-1*K.1^2,K.1^2,-1,-1*K.1^2,1,-1,1,-1,K.1^3,-1*K.1^3,K.1,-1*K.1,K.1^3,K.1,-1*K.1,K.1^3,-1*K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^2,1,-1*K.1^2,1,-1*K.1^2,-1,K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,1,-1*K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1,K.1^2,K.1^2,-1*K.1^2,-1,K.1^2,1,-1,1,-1,K.1,-1*K.1,K.1^3,-1*K.1^3,K.1,K.1^3,-1*K.1^3,K.1,-1*K.1,K.1^3,-1*K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1^2,1,K.1^2,1,K.1^2,-1,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,1,K.1^2,K.1^2,K.1^2,-1*K.1^2,-1,-1*K.1^2,-1*K.1^2,K.1^2,-1,-1*K.1^2,1,-1,1,-1,-1*K.1^3,K.1^3,-1*K.1,K.1,-1*K.1^3,-1*K.1,K.1,-1*K.1^3,K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^3,-1*K.1,K.1,K.1^3,K.1^2,1,-1*K.1^2,1,-1*K.1^2,-1,K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, -2, 2, -2, -2, 2, -2, 2, -2, 2, -2, -2, -2, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, -2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, -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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, 2, -2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 2, -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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,-2,-1,-2*K.1,-2,2*K.1,-2*K.1,-2,2*K.1,2,-2*K.1,2,-2*K.1,2*K.1,2*K.1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,1,-1,1,-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,-1,2*K.1,-2,-2*K.1,2*K.1,-2,-2*K.1,2,2*K.1,2,2*K.1,-2*K.1,-2*K.1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,1,-1,1,-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,-1,-2*K.1,2,-2*K.1,2*K.1,2,2*K.1,-2,2*K.1,-2,-2*K.1,-2*K.1,2*K.1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1,1,-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,-1,2*K.1,2,2*K.1,-2*K.1,2,-2*K.1,-2,-2*K.1,-2,2*K.1,2*K.1,-2*K.1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1,1,-1,1,-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,-1,-2*K.1,-2*K.1,-2,2,2*K.1,-2*K.1,-2*K.1,-2,2*K.1,2*K.1,2,2*K.1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1*K.1,-1,K.1,1,K.1,1,-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 |2,-2,-2,2,-1,2*K.1,2*K.1,-2,2,-2*K.1,2*K.1,2*K.1,-2,-2*K.1,-2*K.1,2,-2*K.1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,K.1,-1,-1*K.1,1,-1*K.1,1,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,-1,-2*K.1,2*K.1,2,-2,-2*K.1,-2*K.1,2*K.1,2,-2*K.1,2*K.1,-2,2*K.1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1,1,K.1,-1,K.1,-1,K.1,K.1,-1*K.1,-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,-1,2*K.1,-2*K.1,2,-2,2*K.1,2*K.1,-2*K.1,2,2*K.1,-2*K.1,-2,-2*K.1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,K.1,1,-1*K.1,-1,-1*K.1,-1,-1*K.1,-1*K.1,K.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,-1,-2,-2*K.1,2*K.1,2*K.1,2*K.1,2,2*K.1,-2*K.1,-2*K.1,2,-2*K.1,-2,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1,1,K.1,1,K.1,-1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,-2,-1,-2,2*K.1,-2*K.1,-2*K.1,-2*K.1,2,-2*K.1,2*K.1,2*K.1,2,2*K.1,-2,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1,1,-1*K.1,1,-1*K.1,-1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,-2,-1,2,-2*K.1,-2*K.1,-2*K.1,2*K.1,-2,2*K.1,2*K.1,-2*K.1,-2,2*K.1,2,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1,-1,-1*K.1,-1,-1*K.1,1,K.1,-1*K.1,K.1,K.1,-1*K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,-2,-1,2,2*K.1,2*K.1,2*K.1,-2*K.1,-2,-2*K.1,-2*K.1,2*K.1,-2,-2*K.1,2,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1,-1,K.1,-1,K.1,1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_96_9:= KnownIrreducibles(CR);