/* Group 3888.jh downloaded from the LMFDB on 25 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([9, 2, 2, 3, 3, 2, 3, 2, 3, 3, 30456, 37549, 46, 218, 74739, 444, 30784, 7456, 130, 73877, 154230, 53313, 46518, 11940, 4956, 1374, 186, 259207, 20752, 9097, 3499, 3076, 286, 209960]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.4, GPC.5, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "d2", "e", "e2", "e6"]);
GPerm := PermutationGroup< 13 | (2,4)(3,6,7,9,5,8)(10,11,12,13), (1,2,4)(3,7,5)(6,9,8)(11,13), (1,3,4,7,2,5)(8,9)(10,12,13,11) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_3888_jh := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>; 

 
/* Character Table */
G:= GPerm;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 3, G!(10,12)(11,13)>,< 2, 6, G!(12,13)>,< 2, 27, G!(2,4)(3,8)(5,9)(6,7)>,< 2, 81, G!(1,3)(2,5)(4,7)(8,9)(10,12)(11,13)>,< 2, 162, G!(1,7)(2,3)(4,5)(8,9)(12,13)>,< 3, 2, G!(1,2,4)(3,7,5)(6,8,9)>,< 3, 3, G!(3,7,5)(6,9,8)>,< 3, 3, G!(3,5,7)(6,8,9)>,< 3, 6, G!(6,9,8)>,< 3, 6, G!(3,7,5)(6,8,9)>,< 3, 6, G!(1,4,2)(3,7,5)(6,9,8)>,< 3, 8, G!(10,12,13)>,< 3, 16, G!(1,2,4)(3,7,5)(6,8,9)(11,12,13)>,< 3, 18, G!(1,8,7)(2,9,5)(3,4,6)>,< 3, 24, G!(1,4,2)(6,8,9)(10,13,11)>,< 3, 24, G!(1,2,4)(6,9,8)(10,11,13)>,< 3, 48, G!(6,8,9)(11,12,13)>,< 3, 48, G!(3,5,7)(6,9,8)(11,12,13)>,< 3, 48, G!(1,2,4)(3,5,7)(6,8,9)(11,12,13)>,< 3, 144, G!(1,7,6)(2,5,8)(3,9,4)(10,13,11)>,< 4, 6, G!(10,13,12,11)>,< 4, 162, G!(1,9)(2,8)(3,7)(4,6)(10,11,12,13)>,< 6, 6, G!(1,2,4)(3,7,5)(6,8,9)(10,11)(12,13)>,< 6, 9, G!(3,7,5)(6,9,8)(10,12)(11,13)>,< 6, 9, G!(3,5,7)(6,8,9)(10,12)(11,13)>,< 6, 12, G!(1,4,2)(3,5,7)(6,9,8)(10,13)>,< 6, 18, G!(6,9,8)(10,12)(11,13)>,< 6, 18, G!(3,7,5)(6,8,9)(10,12)(11,13)>,< 6, 18, G!(1,4,2)(3,7,5)(6,9,8)(10,12)(11,13)>,< 6, 18, G!(3,5,7)(6,8,9)(12,13)>,< 6, 18, G!(3,7,5)(6,9,8)(12,13)>,< 6, 27, G!(2,4)(3,6,5,8,7,9)>,< 6, 27, G!(2,4)(3,6,7,9,5,8)>,< 6, 36, G!(6,8,9)(12,13)>,< 6, 36, G!(3,5,7)(6,9,8)(12,13)>,< 6, 36, G!(1,2,4)(3,5,7)(6,8,9)(12,13)>,< 6, 54, G!(1,7,8)(2,5,9)(3,6,4)(10,12)(11,13)>,< 6, 81, G!(1,5,4,3,2,7)(8,9)(10,12)(11,13)>,< 6, 81, G!(1,7,2,3,4,5)(8,9)(10,12)(11,13)>,< 6, 108, G!(1,9,5)(2,6,3)(4,8,7)(11,13)>,< 6, 162, G!(1,3,4,7,2,5)(8,9)(12,13)>,< 6, 162, G!(1,5,2,7,4,3)(8,9)(12,13)>,< 6, 216, G!(1,2)(3,8)(5,9)(6,7)(10,13,12)>,< 6, 216, G!(1,9,4,6,2,8)(3,7)(10,11,13)>,< 6, 216, G!(1,8,2,6,4,9)(3,7)(10,13,11)>,< 9, 18, G!(1,9,7,2,6,5,4,8,3)>,< 9, 18, G!(1,7,9,2,5,6,4,3,8)>,< 9, 144, G!(1,6,3,4,9,5,2,8,7)(10,11,13)>,< 9, 144, G!(1,9,3,2,6,7,4,8,5)(11,13,12)>,< 12, 12, G!(1,4,2)(3,5,7)(6,9,8)(10,13,11,12)>,< 12, 18, G!(3,5,7)(6,8,9)(10,11,12,13)>,< 12, 18, G!(3,7,5)(6,9,8)(10,11,12,13)>,< 12, 36, G!(6,8,9)(10,11,12,13)>,< 12, 36, G!(3,5,7)(6,9,8)(10,11,12,13)>,< 12, 36, G!(1,2,4)(3,5,7)(6,8,9)(10,11,12,13)>,< 12, 108, G!(1,8,7)(2,9,5)(3,4,6)(10,13,12,11)>,< 12, 162, G!(1,8,4,9,2,6)(3,7)(10,13,12,11)>,< 12, 162, G!(1,6,2,9,4,8)(3,7)(10,11,12,13)>,< 18, 54, G!(1,8,3,2,9,7,4,6,5)(10,11)(12,13)>,< 18, 54, G!(1,6,7,4,9,3,2,8,5)(10,12)(11,13)>,< 18, 108, G!(1,5,9,4,7,8,2,3,6)(10,13)>,< 18, 108, G!(1,6,7,4,9,3,2,8,5)(10,12)>,< 36, 108, G!(1,7,8,4,3,6,2,5,9)(10,12,11,13)>,< 36, 108, G!(1,3,6,2,7,8,4,5,9)(10,13,12,11)>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, 0, 2, 2, 2, 2, -1, -1, -1, 2, 2, 0, 0, -1, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 2, 2, -1, 2, 2, 2, -1, -1, -1, -1, 0, 0, -1, 2, -1, 2, -1, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, 0, 2, 2, 2, 2, -1, -1, -1, 2, 2, 0, 0, -1, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 2, -1, 2, -1, 2, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 0, 2, 2, 2, 2, -1, -1, -1, 2, 2, 0, 0, -1, -1, -1, 2, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, 0, 0, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, -1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, 0, 0, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -2, 0, 2, 2, 2, -2, -1, -1, -1, -2, -2, 0, 0, 1, 1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 2, 2, -1, -2, -2, -2, 1, 1, 1, 1, 0, 0, -1, 2, 1, -2, 1, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -2, 0, 2, 2, 2, -2, -1, -1, -1, -2, -2, 0, 0, 1, 1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 2, -1, -1, 2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 2, -1, -2, 1, -2, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, 2, -2, 0, 2, 2, 2, -2, -1, -1, -1, -2, -2, 0, 0, 1, 1, 1, 2, 0, 0, -2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -2, -2, -2, 1, 1, 1, -2, 0, 0, -1, -1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, -1, -2, 0, 2, 2, 2, -2, 2, 2, 2, -2, -2, 0, 0, -2, -2, -2, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, 1, 0, 0, -1, -1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, -2, -2, 0, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 2, -2, -2, 0, 0, 0, 1, 1, 1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, 1, 3, -1, 1, 3, 3, 3, 3, 3, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 3, 3, 1, 1, 1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 3, 3, 0, 0, -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!\[3, -1, -1, 3, -1, -1, 3, 3, 3, 3, 3, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 3, 3, 0, 0, 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!\[3, -1, -1, -3, 1, 1, 3, 3, 3, 3, 3, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -3, -3, -1, -1, -1, -1, 1, 1, -1, 1, 1, 0, 0, 0, 3, 3, 0, 0, 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!\[3, -1, 1, -3, 1, -1, 3, 3, 3, 3, 3, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -3, -3, 1, 1, 1, -1, 1, 1, 1, -1, -1, 0, 0, 0, 3, 3, 0, 0, -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 |3,3,3,1,1,1,3,3*K.1^-1,3*K.1,0,0,0,3,3,0,3*K.1^-1,3*K.1,0,0,0,0,3,1,3,3*K.1^-1,3*K.1,3,0,0,0,3*K.1,3*K.1^-1,K.1^-1,K.1,0,0,0,0,K.1^-1,K.1,0,K.1^-1,K.1,K.1^-1,1,K.1,0,0,0,0,3,3*K.1,3*K.1^-1,0,0,0,0,K.1,K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,3,1,1,1,3,3*K.1,3*K.1^-1,0,0,0,3,3,0,3*K.1,3*K.1^-1,0,0,0,0,3,1,3,3*K.1,3*K.1^-1,3,0,0,0,3*K.1^-1,3*K.1,K.1,K.1^-1,0,0,0,0,K.1,K.1^-1,0,K.1,K.1^-1,K.1,1,K.1^-1,0,0,0,0,3,3*K.1^-1,3*K.1,0,0,0,0,K.1^-1,K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,3,-1,-1,-1,3,3*K.1^-1,3*K.1,0,0,0,3,3,0,3*K.1^-1,3*K.1,0,0,0,0,3,-1,3,3*K.1^-1,3*K.1,3,0,0,0,3*K.1,3*K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,-1*K.1^-1,-1*K.1,0,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1,-1*K.1,0,0,0,0,3,3*K.1,3*K.1^-1,0,0,0,0,-1*K.1,-1*K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,3,-1,-1,-1,3,3*K.1,3*K.1^-1,0,0,0,3,3,0,3*K.1,3*K.1^-1,0,0,0,0,3,-1,3,3*K.1,3*K.1^-1,3,0,0,0,3*K.1^-1,3*K.1,-1*K.1,-1*K.1^-1,0,0,0,0,-1*K.1,-1*K.1^-1,0,-1*K.1,-1*K.1^-1,-1*K.1,-1,-1*K.1^-1,0,0,0,0,3,3*K.1^-1,3*K.1,0,0,0,0,-1*K.1^-1,-1*K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,-3,-1,-1,1,3,3*K.1^-1,3*K.1,0,0,0,3,3,0,3*K.1^-1,3*K.1,0,0,0,0,-3,1,3,3*K.1^-1,3*K.1,-3,0,0,0,-3*K.1,-3*K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,-1*K.1^-1,-1*K.1,0,K.1^-1,K.1,-1*K.1^-1,-1,-1*K.1,0,0,0,0,-3,-3*K.1,-3*K.1^-1,0,0,0,0,K.1,K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,-3,-1,-1,1,3,3*K.1,3*K.1^-1,0,0,0,3,3,0,3*K.1,3*K.1^-1,0,0,0,0,-3,1,3,3*K.1,3*K.1^-1,-3,0,0,0,-3*K.1^-1,-3*K.1,-1*K.1,-1*K.1^-1,0,0,0,0,-1*K.1,-1*K.1^-1,0,K.1,K.1^-1,-1*K.1,-1,-1*K.1^-1,0,0,0,0,-3,-3*K.1^-1,-3*K.1,0,0,0,0,K.1^-1,K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,-3,1,1,-1,3,3*K.1^-1,3*K.1,0,0,0,3,3,0,3*K.1^-1,3*K.1,0,0,0,0,-3,-1,3,3*K.1^-1,3*K.1,-3,0,0,0,-3*K.1,-3*K.1^-1,K.1^-1,K.1,0,0,0,0,K.1^-1,K.1,0,-1*K.1^-1,-1*K.1,K.1^-1,1,K.1,0,0,0,0,-3,-3*K.1,-3*K.1^-1,0,0,0,0,-1*K.1,-1*K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,-3,1,1,-1,3,3*K.1,3*K.1^-1,0,0,0,3,3,0,3*K.1,3*K.1^-1,0,0,0,0,-3,-1,3,3*K.1,3*K.1^-1,-3,0,0,0,-3*K.1^-1,-3*K.1,K.1,K.1^-1,0,0,0,0,K.1,K.1^-1,0,-1*K.1,-1*K.1^-1,K.1,1,K.1^-1,0,0,0,0,-3,-3*K.1^-1,-3*K.1,0,0,0,0,-1*K.1^-1,-1*K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 4, 4, 4, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 4, 4, 4, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, 4, -2, -2, 1, 1, 1, -2, 0, 0, 4, 4, 4, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 1, 0, 0, 4, 4, 4, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 0, 0, 0, -3, 0, 0, -3, 3, 0, 6, -3, 0, 0, 0, 3, 0, -3, 0, 6, 0, -3, 0, 0, -3, 0, -3, 3, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 0, 0, 0, -3, 0, 0, 0, -3, 3, 6, -3, 0, 0, 0, -3, 3, 0, 0, 6, 0, -3, 0, 0, -3, 3, 0, -3, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 0, 0, 0, -3, 0, 0, 3, 0, -3, 6, -3, 0, 0, 0, 0, -3, 3, 0, 6, 0, -3, 0, 0, -3, -3, 3, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, 2, 0, 0, 0, 6, 6, 6, -3, -3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, -2, 2, 1, 1, 1, 2, 2, 0, 0, -1, -1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, -3, 6, 0, 0, -2, -2, -2, 1, 1, 1, 1, 0, 0, 1, -2, -1, 2, 1, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, 2, 0, 0, 0, 6, 6, 6, -3, -3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, -2, 2, 1, 1, 1, 2, 2, 0, 0, -1, -1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 6, -3, 0, 0, -2, -2, -2, 1, 1, 1, 1, 0, 0, -2, 1, 2, -1, -2, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, 2, 0, 0, 0, 6, 6, 6, -3, -3, -3, 0, 0, 6, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, -2, 2, 1, 1, 1, 2, 2, 0, 0, -1, -1, -1, -2, 0, 0, 2, 0, 0, 0, 0, 0, -3, -3, 0, 0, -2, -2, -2, 1, 1, 1, -2, 0, 0, 1, 1, -1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, 2, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, -2, 2, -2, -2, -2, 2, 2, 0, 0, 2, 2, 2, 1, 0, 0, -1, 0, 0, 0, 0, 0, -3, -3, 0, 0, -2, -2, -2, -2, -2, -2, 1, 0, 0, 1, 1, -1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, -2, 0, 0, 0, 6, 6, 6, -3, -3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, -2, -2, 1, 1, 1, -2, -2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, -3, 6, 0, 0, 2, 2, 2, -1, -1, -1, -1, 0, 0, 1, -2, 1, -2, -1, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, -2, 0, 0, 0, 6, 6, 6, -3, -3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, -2, -2, 1, 1, 1, -2, -2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 6, -3, 0, 0, 2, 2, 2, -1, -1, -1, -1, 0, 0, -2, 1, -2, 1, 2, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, -2, 0, 0, 0, 6, 6, 6, -3, -3, -3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, -2, -2, 1, 1, 1, -2, -2, 0, 0, 1, 1, 1, -2, 0, 0, -2, 0, 0, 0, 0, 0, -3, -3, 0, 0, 2, 2, 2, -1, -1, -1, 2, 0, 0, 1, 1, 1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, -2, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, -3, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, -2, -2, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0, -3, -3, 0, 0, 2, 2, 2, 2, 2, 2, -1, 0, 0, 1, 1, 1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, 0, 0, 0, -3, 0, 0, -3, 3, 0, 6, -3, 0, 0, 0, 3, 0, -3, 0, -6, 0, -3, 0, 0, 3, 0, -3, 3, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, 0, 0, 0, -3, 0, 0, 0, -3, 3, 6, -3, 0, 0, 0, -3, 3, 0, 0, -6, 0, -3, 0, 0, 3, 3, 0, -3, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, 0, 0, 0, -3, 0, 0, 3, 0, -3, 6, -3, 0, 0, 0, 0, -3, 3, 0, -6, 0, -3, 0, 0, 3, -3, 3, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, -3, 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 |6,6,0,2,2,0,6,6*K.1^-1,6*K.1,0,0,0,-3,-3,0,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,6,6*K.1^-1,6*K.1,0,0,0,0,0,0,2*K.1^-1,2*K.1,0,0,0,0,2*K.1^-1,2*K.1,0,0,0,-1*K.1^-1,-1,-1*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,6,0,2,2,0,6,6*K.1,6*K.1^-1,0,0,0,-3,-3,0,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,6,6*K.1,6*K.1^-1,0,0,0,0,0,0,2*K.1,2*K.1^-1,0,0,0,0,2*K.1,2*K.1^-1,0,0,0,-1*K.1,-1,-1*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,6,0,-2,-2,0,6,6*K.1^-1,6*K.1,0,0,0,-3,-3,0,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,6,6*K.1^-1,6*K.1,0,0,0,0,0,0,-2*K.1^-1,-2*K.1,0,0,0,0,-2*K.1^-1,-2*K.1,0,0,0,K.1^-1,1,K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,6,0,-2,-2,0,6,6*K.1,6*K.1^-1,0,0,0,-3,-3,0,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,6,6*K.1,6*K.1^-1,0,0,0,0,0,0,-2*K.1,-2*K.1^-1,0,0,0,0,-2*K.1,-2*K.1^-1,0,0,0,K.1,1,K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-3,3,3,-1,1,9,9*K.1^-1,9*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-3,-1,-3,-3*K.1^-1,-3*K.1,3,0,0,0,3*K.1,3*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,-1*K.1^-1,-1*K.1,0,K.1^-1,K.1,0,0,0,0,0,0,0,-3,-3*K.1,-3*K.1^-1,0,0,0,0,-1*K.1,-1*K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-3,3,3,-1,1,9,9*K.1,9*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,-3,-1,-3,-3*K.1,-3*K.1^-1,3,0,0,0,3*K.1^-1,3*K.1,3*K.1,3*K.1^-1,0,0,0,0,-1*K.1,-1*K.1^-1,0,K.1,K.1^-1,0,0,0,0,0,0,0,-3,-3*K.1^-1,-3*K.1,0,0,0,0,-1*K.1^-1,-1*K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-3,-3,-3,1,1,9,9*K.1^-1,9*K.1,0,0,0,0,0,0,0,0,0,0,0,0,3,-1,-3,-3*K.1^-1,-3*K.1,-3,0,0,0,-3*K.1,-3*K.1^-1,-3*K.1^-1,-3*K.1,0,0,0,0,K.1^-1,K.1,0,K.1^-1,K.1,0,0,0,0,0,0,0,3,3*K.1,3*K.1^-1,0,0,0,0,-1*K.1,-1*K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-3,-3,-3,1,1,9,9*K.1,9*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,3,-1,-3,-3*K.1,-3*K.1^-1,-3,0,0,0,-3*K.1^-1,-3*K.1,-3*K.1,-3*K.1^-1,0,0,0,0,K.1,K.1^-1,0,K.1,K.1^-1,0,0,0,0,0,0,0,3,3*K.1^-1,3*K.1,0,0,0,0,-1*K.1^-1,-1*K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-3,-3,3,-1,-1,9,9*K.1^-1,9*K.1,0,0,0,0,0,0,0,0,0,0,0,0,3,1,-3,-3*K.1^-1,-3*K.1,-3,0,0,0,-3*K.1,-3*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,-1*K.1^-1,-1*K.1,0,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,3,3*K.1,3*K.1^-1,0,0,0,0,K.1,K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-3,-3,3,-1,-1,9,9*K.1,9*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,3,1,-3,-3*K.1,-3*K.1^-1,-3,0,0,0,-3*K.1^-1,-3*K.1,3*K.1,3*K.1^-1,0,0,0,0,-1*K.1,-1*K.1^-1,0,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,3,3*K.1^-1,3*K.1,0,0,0,0,K.1^-1,K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-3,3,-3,1,-1,9,9*K.1^-1,9*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-3,1,-3,-3*K.1^-1,-3*K.1,3,0,0,0,3*K.1,3*K.1^-1,-3*K.1^-1,-3*K.1,0,0,0,0,K.1^-1,K.1,0,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,-3,-3*K.1,-3*K.1^-1,0,0,0,0,K.1,K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-3,3,-3,1,-1,9,9*K.1,9*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,-3,1,-3,-3*K.1,-3*K.1^-1,3,0,0,0,3*K.1^-1,3*K.1,-3*K.1,-3*K.1^-1,0,0,0,0,K.1,K.1^-1,0,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,-3,-3*K.1^-1,-3*K.1,0,0,0,0,K.1^-1,K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[12, 12, 0, 0, 0, 0, -6, 0, 0, -6, 6, 0, -6, 3, 0, 0, 0, -3, 0, 3, 0, 0, 0, -6, 0, 0, 0, 0, -6, 6, 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, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, 0, 0, 0, 0, -6, 0, 0, 0, -6, 6, -6, 3, 0, 0, 0, 3, -3, 0, 0, 0, 0, -6, 0, 0, 0, 6, 0, -6, 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, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, 0, 0, 0, 0, -6, 0, 0, 6, 0, -6, -6, 3, 0, 0, 0, 0, 3, -3, 0, 0, 0, -6, 0, 0, 0, -6, 6, 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, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[18, -6, 6, 0, 0, 0, -9, 0, 0, -9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, -3, 0, 3, -3, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[18, -6, 6, 0, 0, 0, -9, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, -3, -3, 0, 3, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[18, -6, 6, 0, 0, 0, -9, 0, 0, 9, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, -3, 3, -3, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[18, -6, -6, 0, 0, 0, -9, 0, 0, -9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0, 0, 3, 0, 3, -3, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[18, -6, -6, 0, 0, 0, -9, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0, 0, 3, -3, 0, 3, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[18, -6, -6, 0, 0, 0, -9, 0, 0, 9, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0, 0, 3, 3, -3, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_3888_jh:= KnownIrreducibles(CR);