/* Group 4032.cm downloaded from the LMFDB on 29 December 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, -3, -3, -7, -2, 2, 2, 2, 2, 18, 22196, 11513, 101, 16203, 39216, 11362, 11363, 1544, 150828, 83364, 38391, 9294, 272167, 113416, 24217, 12634, 224540, 35738, 51056, 1169]); a,b,c,d,e,f,g := Explode([GPC.1, GPC.3, GPC.5, GPC.6, GPC.7, GPC.8, GPC.9]); AssignNames(~GPC, ["a", "a2", "b", "b3", "c", "d", "e", "f", "g"]);
GPerm := PermutationGroup< 12 | (1,3,5)(4,7,6)(9,10,11,12), (1,2)(3,4,6,5,7,8)(10,11) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_4032_cm := 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!(9,10)(11,12)>,< 2, 6, G!(9,10)>,< 2, 7, G!(1,2)(3,5)(4,7)(6,8)>,< 2, 21, G!(1,4)(2,7)(3,6)(5,8)(9,10)(11,12)>,< 2, 42, G!(1,5)(2,3)(4,8)(6,7)(9,12)>,< 3, 8, G!(10,12,11)>,< 3, 28, G!(3,6,7)(4,5,8)>,< 3, 28, G!(3,7,6)(4,8,5)>,< 3, 224, G!(2,8,3)(5,6,7)(10,11,12)>,< 3, 224, G!(2,3,8)(5,7,6)(10,12,11)>,< 4, 6, G!(9,11,10,12)>,< 4, 42, G!(1,8)(2,6)(3,7)(4,5)(9,10,11,12)>,< 6, 28, G!(1,2)(3,4,6,5,7,8)>,< 6, 28, G!(1,2)(3,8,7,5,6,4)>,< 6, 56, G!(1,2)(3,5)(4,7)(6,8)(10,11,12)>,< 6, 84, G!(1,4,6)(2,8,5)(9,11)(10,12)>,< 6, 84, G!(1,6,4)(2,5,8)(9,11)(10,12)>,< 6, 84, G!(1,3,5,4,6,8)(2,7)(9,10)(11,12)>,< 6, 84, G!(1,8,6,4,5,3)(2,7)(9,10)(11,12)>,< 6, 168, G!(1,7,8)(4,5,6)(9,10)>,< 6, 168, G!(1,8,7)(4,6,5)(9,10)>,< 6, 168, G!(1,5)(2,7,4,3,6,8)(9,12)>,< 6, 168, G!(1,5)(2,8,6,3,4,7)(9,12)>,< 6, 224, G!(1,4)(2,6,8,7,3,5)(10,12,11)>,< 6, 224, G!(1,4)(2,5,3,7,8,6)(10,11,12)>,< 7, 24, G!(1,3,8,6,2,7,5)>,< 7, 24, G!(1,5,7,2,6,8,3)>,< 12, 168, G!(1,2,4,8,6,5)(3,7)(9,12,11,10)>,< 12, 168, G!(1,5,6,8,4,2)(3,7)(9,10,11,12)>,< 12, 168, G!(2,5,7)(3,6,4)(9,11,10,12)>,< 12, 168, G!(2,7,5)(3,4,6)(9,12,10,11)>,< 14, 72, G!(1,2,3,7,8,5,6)(9,10)(11,12)>,< 14, 72, G!(1,6,5,8,7,3,2)(9,10)(11,12)>,< 14, 144, G!(1,7,2,5,4,8,6)(9,10)>,< 14, 144, G!(1,6,8,4,5,2,7)(9,10)>,< 21, 192, G!(1,6,5,8,7,3,2)(10,11,12)>,< 21, 192, G!(1,2,3,7,8,5,6)(10,12,11)>,< 28, 144, G!(1,8,2,5,3,6,7)(9,12,10,11)>,< 28, 144, G!(1,7,6,3,5,2,8)(9,11,10,12)>]); 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,1,1,K.1^-1,K.1,K.1,K.1^-1,1,1,K.1,K.1^-1,1,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,K.1^-1,K.1,K.1,K.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 |1,1,1,1,1,1,1,K.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,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,1,1,K.1,K.1^-1,K.1^-1,K.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,-1,1,1,-1,1,K.1^-1,K.1,K.1,K.1^-1,-1,-1,K.1,K.1^-1,1,K.1,K.1^-1,K.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*K.1^-1,-1*K.1,-1*K.1,-1*K.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,-1,1,1,-1,1,K.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*K.1^-1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,1,1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.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, 0, 2, 2, 0, -1, 2, 2, -1, -1, 0, 0, 2, 2, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,0,2,2,0,-1,2*K.1^-1,2*K.1,-1*K.1,-1*K.1^-1,0,0,2*K.1,2*K.1^-1,-1,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,0,0,0,0,-1*K.1^-1,-1*K.1,2,2,0,0,0,0,2,2,0,0,-1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,0,2,2,0,-1,2*K.1,2*K.1^-1,-1*K.1^-1,-1*K.1,0,0,2*K.1^-1,2*K.1,-1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,0,0,0,0,-1*K.1,-1*K.1^-1,2,2,0,0,0,0,2,2,0,0,-1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, -1, 1, 3, -1, 1, 0, 3, 3, 0, 0, -1, -1, 3, 3, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 3, 3, -1, -1, -1, -1, -1, -1, 1, 1, 0, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, -1, 3, -1, -1, 0, 3, 3, 0, 0, 1, 1, 3, 3, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 3, 3, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |3,3,3,3,3,3,3,0,0,0,0,3,3,0,0,3,0,0,0,0,0,0,0,0,0,0,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,0,0,0,0,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |3,3,3,3,3,3,3,0,0,0,0,3,3,0,0,3,0,0,0,0,0,0,0,0,0,0,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,0,0,0,0,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,-1,1,3,-1,1,0,3*K.1^-1,3*K.1,0,0,-1,-1,3*K.1,3*K.1^-1,0,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,K.1^-1,K.1,K.1,K.1^-1,0,0,3,3,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1,-1,1,1,0,0,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,-1,1,3,-1,1,0,3*K.1,3*K.1^-1,0,0,-1,-1,3*K.1^-1,3*K.1,0,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,K.1^-1,K.1,0,0,3,3,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1,-1,1,1,0,0,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |3,3,-3,3,3,-3,3,0,0,0,0,-3,-3,0,0,3,0,0,0,0,0,0,0,0,0,0,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,0,0,0,0,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,-1*K.1-K.1^2-K.1^-3,1+K.1+K.1^2+K.1^-3,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,1+K.1+K.1^2+K.1^-3,-1*K.1-K.1^2-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |3,3,-3,3,3,-3,3,0,0,0,0,-3,-3,0,0,3,0,0,0,0,0,0,0,0,0,0,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,0,0,0,0,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,1+K.1+K.1^2+K.1^-3,-1*K.1-K.1^2-K.1^-3,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,-1*K.1-K.1^2-K.1^-3,1+K.1+K.1^2+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,-1,-1,3,-1,-1,0,3*K.1^-1,3*K.1,0,0,1,1,3*K.1,3*K.1^-1,0,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,0,0,3,3,K.1^-1,K.1,K.1,K.1^-1,-1,-1,-1,-1,0,0,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,-1,-1,3,-1,-1,0,3*K.1,3*K.1^-1,0,0,1,1,3*K.1^-1,3*K.1,0,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,0,0,3,3,K.1,K.1^-1,K.1^-1,K.1,-1,-1,-1,-1,0,0,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |6,6,0,6,6,0,-3,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,0,0,0,-2-2*K.1-2*K.1^2-2*K.1^-3,2*K.1+2*K.1^2+2*K.1^-3,0,0,0,0,-2-2*K.1-2*K.1^2-2*K.1^-3,2*K.1+2*K.1^2+2*K.1^-3,0,0,-1*K.1-K.1^2-K.1^-3,1+K.1+K.1^2+K.1^-3,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |6,6,0,6,6,0,-3,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^2+2*K.1^-3,-2-2*K.1-2*K.1^2-2*K.1^-3,0,0,0,0,2*K.1+2*K.1^2+2*K.1^-3,-2-2*K.1-2*K.1^2-2*K.1^-3,0,0,1+K.1+K.1^2+K.1^-3,-1*K.1-K.1^2-K.1^-3,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[7, 7, 7, -1, -1, -1, 7, 1, 1, 1, 1, 7, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[7, 7, -7, -1, -1, 1, 7, 1, 1, 1, 1, -7, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,7,7,-1,-1,-1,7,K.1^-1,K.1,K.1,K.1^-1,7,-1,-1*K.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*K.1^-1,-1*K.1^-1,-1*K.1,0,0,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,7,7,-1,-1,-1,7,K.1,K.1^-1,K.1^-1,K.1,7,-1,-1*K.1^-1,-1*K.1,-1,K.1^-1,K.1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,0,0,-1*K.1,-1*K.1^-1,K.1^-1,K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,7,-7,-1,-1,1,7,K.1^-1,K.1,K.1,K.1^-1,-7,1,-1*K.1,-1*K.1^-1,-1,K.1,K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,0,0,K.1^-1,K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,7,-7,-1,-1,1,7,K.1,K.1^-1,K.1^-1,K.1,-7,1,-1*K.1^-1,-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^-1,K.1,-1*K.1,-1*K.1^-1,0,0,K.1,K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |9,-3,3,9,-3,3,0,0,0,0,0,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,-3-3*K.1-3*K.1^2-3*K.1^-3,3*K.1+3*K.1^2+3*K.1^-3,0,0,0,0,1+K.1+K.1^2+K.1^-3,-1*K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,0,0,1+K.1+K.1^2+K.1^-3,-1*K.1-K.1^2-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |9,-3,3,9,-3,3,0,0,0,0,0,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1+3*K.1^2+3*K.1^-3,-3-3*K.1-3*K.1^2-3*K.1^-3,0,0,0,0,-1*K.1-K.1^2-K.1^-3,1+K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3,0,0,-1*K.1-K.1^2-K.1^-3,1+K.1+K.1^2+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |9,-3,-3,9,-3,-3,0,0,0,0,0,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-3-3*K.1-3*K.1^2-3*K.1^-3,3*K.1+3*K.1^2+3*K.1^-3,0,0,0,0,1+K.1+K.1^2+K.1^-3,-1*K.1-K.1^2-K.1^-3,-1*K.1-K.1^2-K.1^-3,1+K.1+K.1^2+K.1^-3,0,0,-1-K.1-K.1^2-K.1^-3,K.1+K.1^2+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |9,-3,-3,9,-3,-3,0,0,0,0,0,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1+3*K.1^2+3*K.1^-3,-3-3*K.1-3*K.1^2-3*K.1^-3,0,0,0,0,-1*K.1-K.1^2-K.1^-3,1+K.1+K.1^2+K.1^-3,1+K.1+K.1^2+K.1^-3,-1*K.1-K.1^2-K.1^-3,0,0,K.1+K.1^2+K.1^-3,-1-K.1-K.1^2-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[14, 14, 0, -2, -2, 0, -7, 2, 2, -1, -1, 0, 0, -2, -2, 1, 2, 2, -2, -2, 0, 0, 0, 0, 1, 1, 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 |14,14,0,-2,-2,0,-7,2*K.1^-1,2*K.1,-1*K.1,-1*K.1^-1,0,0,-2*K.1,-2*K.1^-1,1,2*K.1,2*K.1^-1,-2*K.1,-2*K.1^-1,0,0,0,0,K.1^-1,K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |14,14,0,-2,-2,0,-7,2*K.1,2*K.1^-1,-1*K.1^-1,-1*K.1,0,0,-2*K.1^-1,-2*K.1,1,2*K.1^-1,2*K.1,-2*K.1^-1,-2*K.1,0,0,0,0,K.1,K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[21, -7, 7, -3, 1, -1, 0, 3, 3, 0, 0, -7, 1, -3, -3, 0, -1, -1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[21, -7, -7, -3, 1, 1, 0, 3, 3, 0, 0, 7, -1, -3, -3, 0, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |21,-7,7,-3,1,-1,0,3*K.1^-1,3*K.1,0,0,-7,1,-3*K.1,-3*K.1^-1,0,-1*K.1,-1*K.1^-1,K.1,K.1^-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,0,0,0,0,K.1^-1,K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |21,-7,7,-3,1,-1,0,3*K.1,3*K.1^-1,0,0,-7,1,-3*K.1^-1,-3*K.1,0,-1*K.1^-1,-1*K.1,K.1^-1,K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,K.1,K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |21,-7,-7,-3,1,1,0,3*K.1^-1,3*K.1,0,0,7,-1,-3*K.1,-3*K.1^-1,0,-1*K.1,-1*K.1^-1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,0,0,0,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |21,-7,-7,-3,1,1,0,3*K.1,3*K.1^-1,0,0,7,-1,-3*K.1^-1,-3*K.1,0,-1*K.1^-1,-1*K.1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,K.1^-1,K.1,0,0,0,0,-1*K.1,-1*K.1^-1,K.1^-1,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_4032_cm:= KnownIrreducibles(CR);