/* Group 972.802 downloaded from the LMFDB on 21 July 2026. */
 
/* 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([7, -2, -3, -2, -3, -3, -3, -3, 14, 632, 58, 675, 12604, 11981, 438, 9077, 3799, 1538, 5312]); a,b,c,d,e := Explode([GPC.1, GPC.3, GPC.5, GPC.6, GPC.7]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "d", "e"]);
GPerm := PermutationGroup< 27 | (4,7)(5,8)(6,9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27), (2,3)(5,6)(8,9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26), (10,11,12)(13,14,15)(16,17,18)(19,21,20)(22,24,23)(25,27,26), (4,5,6)(7,9,8)(13,14,15)(16,18,17)(22,23,24)(25,27,26), (1,19,10)(2,20,11)(3,21,12)(4,22,13)(5,23,14)(6,24,15)(7,25,16)(8,26,17)(9,27,18), (1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,25,22)(20,26,23)(21,27,24), (1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,27,26) >;
GLFp := MatrixGroup< 4, GF(3) | [[1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 1, 0, 1], [0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 2, 1], [2, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0], [2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 1, 2], [0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 1, 1, 1, 0], [1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_972_802 := 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 := true>; 

 
/* Character Table */
G:= GLFp;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Matrix(4, [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1])>,< 2, 9, Matrix(4, [0, 2, 2, 1, 0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2])>,< 2, 27, Matrix(4, [1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2])>,< 2, 27, Matrix(4, [0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2])>,< 3, 2, Matrix(4, [1, 1, 2, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2])>,< 3, 3, Matrix(4, [1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0, 1, 2, 0])>,< 3, 3, Matrix(4, [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 1, 2])>,< 3, 6, Matrix(4, [0, 1, 0, 2, 0, 1, 0, 0, 2, 1, 1, 2, 1, 2, 0, 2])>,< 3, 6, Matrix(4, [1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 1, 2, 0])>,< 3, 6, Matrix(4, [1, 2, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 1])>,< 3, 6, Matrix(4, [0, 1, 0, 2, 0, 2, 2, 2, 2, 1, 1, 2, 1, 0, 2, 1])>,< 3, 6, Matrix(4, [2, 2, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 0, 1, 1])>,< 3, 6, Matrix(4, [1, 0, 2, 2, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0])>,< 3, 6, Matrix(4, [1, 1, 0, 0, 0, 2, 2, 2, 0, 1, 1, 0, 0, 0, 2, 0])>,< 3, 6, Matrix(4, [1, 1, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 1, 2])>,< 3, 6, Matrix(4, [1, 2, 1, 1, 0, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0])>,< 3, 12, Matrix(4, [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0])>,< 3, 12, Matrix(4, [0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 1, 2, 1, 0, 0, 2])>,< 3, 12, Matrix(4, [0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 1, 1, 1, 1, 0])>,< 3, 12, Matrix(4, [0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0])>,< 3, 12, Matrix(4, [0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0])>,< 3, 12, Matrix(4, [1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 2, 0])>,< 3, 12, Matrix(4, [1, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1, 0, 1])>,< 3, 12, Matrix(4, [0, 0, 0, 2, 0, 0, 1, 1, 2, 2, 2, 0, 1, 0, 0, 2])>,< 3, 12, Matrix(4, [2, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 0, 0, 0])>,< 3, 12, Matrix(4, [0, 0, 0, 2, 0, 0, 1, 1, 2, 0, 1, 2, 1, 2, 1, 0])>,< 3, 12, Matrix(4, [2, 1, 2, 0, 0, 2, 2, 2, 1, 1, 0, 0, 2, 0, 0, 0])>,< 3, 12, Matrix(4, [0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 0, 1, 1, 0, 2, 1])>,< 3, 12, Matrix(4, [2, 2, 0, 1, 0, 2, 2, 2, 1, 0, 0, 0, 2, 1, 0, 0])>,< 3, 12, Matrix(4, [0, 0, 0, 2, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 2, 1])>,< 3, 12, Matrix(4, [0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 1, 2, 1, 0])>,< 6, 18, Matrix(4, [0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 1])>,< 6, 27, Matrix(4, [1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 1, 0, 1])>,< 6, 27, Matrix(4, [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 2, 2, 0])>,< 6, 27, Matrix(4, [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0])>,< 6, 27, Matrix(4, [2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 1, 0, 1])>,< 6, 27, Matrix(4, [0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 1, 0, 0])>,< 6, 27, Matrix(4, [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2])>,< 6, 54, Matrix(4, [2, 1, 0, 1, 0, 2, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0])>,< 6, 54, Matrix(4, [1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 1, 1, 0, 2])>,< 6, 54, Matrix(4, [2, 2, 1, 2, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1])>,< 6, 54, Matrix(4, [2, 2, 0, 1, 0, 0, 2, 2, 1, 1, 2, 2, 2, 0, 2, 2])>,< 6, 54, Matrix(4, [0, 1, 0, 2, 0, 1, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0])>,< 6, 54, Matrix(4, [0, 2, 0, 2, 0, 2, 2, 2, 1, 0, 1, 1, 2, 1, 2, 2])>,< 6, 54, Matrix(4, [0, 1, 2, 1, 0, 0, 1, 1, 1, 2, 0, 0, 2, 0, 2, 2])>,< 6, 54, Matrix(4, [2, 1, 0, 1, 0, 0, 2, 2, 0, 2, 1, 0, 0, 2, 0, 1])>,< 6, 54, Matrix(4, [2, 2, 2, 0, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 2])>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,K.1^-1,K.1,1,1,K.1^-1,K.1,K.1^-1,1,K.1,K.1,K.1^-1,K.1,K.1,1,1,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,K.1^-1,K.1^-1,K.1,K.1,K.1,1,K.1^-1,K.1^-1,1,K.1,K.1^-1,K.1,K.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,K.1,K.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^-1,1,1,K.1,K.1,K.1^-1,K.1,K.1^-1,1,K.1,1,K.1,K.1^-1,1,1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.1^-1,1,K.1,K.1,1,K.1^-1,K.1,K.1^-1,K.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,K.1^-1,K.1,1,1,K.1^-1,K.1,K.1^-1,1,K.1,K.1,K.1^-1,K.1,K.1,1,1,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*K.1^-1,-1*K.1^-1,K.1,-1*K.1,-1*K.1,1,K.1^-1,-1*K.1^-1,-1,-1*K.1,-1*K.1^-1,K.1,-1*K.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,K.1,K.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^-1,1,1,K.1,K.1,K.1^-1,K.1,K.1^-1,1,K.1,1,K.1,K.1^-1,1,-1,K.1,-1*K.1,-1*K.1,K.1^-1,-1*K.1^-1,-1*K.1^-1,1,K.1,-1*K.1,-1,-1*K.1^-1,-1*K.1,K.1^-1,-1*K.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,K.1^-1,K.1,1,1,K.1^-1,K.1,K.1^-1,1,K.1,K.1,K.1^-1,K.1,K.1,1,1,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,-1*K.1^-1,K.1^-1,-1*K.1^-1,-1*K.1,K.1,-1*K.1,-1,-1*K.1^-1,-1*K.1^-1,1,-1*K.1,K.1^-1,-1*K.1,K.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,K.1,K.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^-1,1,1,K.1,K.1,K.1^-1,K.1,K.1^-1,1,K.1,1,K.1,K.1^-1,1,-1,-1*K.1,K.1,-1*K.1,-1*K.1^-1,K.1^-1,-1*K.1^-1,-1,-1*K.1,-1*K.1,1,-1*K.1^-1,K.1,-1*K.1^-1,K.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,K.1^-1,K.1,1,1,K.1^-1,K.1,K.1^-1,1,K.1,K.1,K.1^-1,K.1,K.1,1,1,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,-1*K.1^-1,-1*K.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*K.1,-1*K.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,K.1,K.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^-1,1,1,K.1,K.1,K.1^-1,K.1,K.1^-1,1,K.1,1,K.1,K.1^-1,1,1,-1*K.1,-1*K.1,K.1,-1*K.1^-1,-1*K.1^-1,K.1^-1,-1,-1*K.1,K.1,-1,K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 0, 0, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 0, 2, 0, 0, 2, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 0, 2, 0, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, 2, 2, -1, 2, -1, 2, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, -1, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 0, 2, 2, 2, -1, 2, -1, 2, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -2, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 0, -2, 0, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 0, 0, -2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 0, -2, 0, 0, -2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,0,0,2,2,2*K.1^-1,2*K.1,2,2,2*K.1^-1,-1*K.1,-1*K.1^-1,-1,2*K.1,2*K.1,2*K.1^-1,-1*K.1,2*K.1,-1,-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,2*K.1^-1,-1*K.1,2,-1*K.1^-1,-1,-1*K.1^-1,-1*K.1,-1,0,2*K.1^-1,0,0,2*K.1,0,0,-1,-1*K.1^-1,0,0,0,0,-1*K.1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,0,0,2,2,2*K.1,2*K.1^-1,2,2,2*K.1,-1*K.1^-1,-1*K.1,-1,2*K.1^-1,2*K.1^-1,2*K.1,-1*K.1^-1,2*K.1^-1,-1,-1,-1*K.1,-1*K.1,-1*K.1^-1,2*K.1,-1*K.1^-1,2,-1*K.1,-1,-1*K.1,-1*K.1^-1,-1,0,2*K.1,0,0,2*K.1^-1,0,0,-1,-1*K.1,0,0,0,0,-1*K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,0,2,0,2,2*K.1^-1,2*K.1,2,-1,2*K.1^-1,2*K.1,2*K.1^-1,2,2*K.1,-1*K.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^-1,2*K.1,-1,2*K.1^-1,2,-1*K.1^-1,-1*K.1,-1,0,0,2*K.1^-1,0,0,2*K.1,0,0,0,0,-1,0,-1*K.1^-1,0,-1*K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,0,2,0,2,2*K.1,2*K.1^-1,2,-1,2*K.1,2*K.1^-1,2*K.1,2,2*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1,-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1,2*K.1^-1,-1,2*K.1,2,-1*K.1,-1*K.1^-1,-1,0,0,2*K.1,0,0,2*K.1^-1,0,0,0,0,-1,0,-1*K.1,0,-1*K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,0,0,2,2*K.1^-1,2*K.1,-1,2,-1*K.1^-1,2*K.1,2*K.1^-1,2,-1*K.1,2*K.1,2*K.1^-1,-1*K.1,-1*K.1,-1,2,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1,-1*K.1^-1,-1,2*K.1^-1,2*K.1,-1,2,0,0,2*K.1^-1,0,0,2*K.1,0,0,-1*K.1^-1,0,-1*K.1,0,0,0,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,0,0,2,2*K.1,2*K.1^-1,-1,2,-1*K.1,2*K.1^-1,2*K.1,2,-1*K.1^-1,2*K.1^-1,2*K.1,-1*K.1^-1,-1*K.1^-1,-1,2,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1,-1*K.1,-1,2*K.1,2*K.1^-1,-1,2,0,0,2*K.1,0,0,2*K.1^-1,0,0,-1*K.1,0,-1*K.1^-1,0,0,0,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,0,2,2*K.1^-1,2*K.1,-1,2,-1*K.1^-1,2*K.1,2*K.1^-1,2,-1*K.1,2*K.1,2*K.1^-1,-1*K.1,-1*K.1,-1,2,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1,-1*K.1^-1,-1,2*K.1^-1,2*K.1,-1,-2,0,0,-2*K.1^-1,0,0,-2*K.1,0,0,K.1^-1,0,K.1,0,0,0,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,0,2,2*K.1,2*K.1^-1,-1,2,-1*K.1,2*K.1^-1,2*K.1,2,-1*K.1^-1,2*K.1^-1,2*K.1,-1*K.1^-1,-1*K.1^-1,-1,2,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1,-1*K.1,-1,2*K.1,2*K.1^-1,-1,-2,0,0,-2*K.1,0,0,-2*K.1^-1,0,0,K.1,0,K.1^-1,0,0,0,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,0,-2,0,2,2*K.1^-1,2*K.1,2,-1,2*K.1^-1,2*K.1,2*K.1^-1,2,2*K.1,-1*K.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^-1,2*K.1,-1,2*K.1^-1,2,-1*K.1^-1,-1*K.1,-1,0,0,-2*K.1^-1,0,0,-2*K.1,0,0,0,0,1,0,K.1^-1,0,K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,0,-2,0,2,2*K.1,2*K.1^-1,2,-1,2*K.1,2*K.1^-1,2*K.1,2,2*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1,-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1,2*K.1^-1,-1,2*K.1,2,-1*K.1,-1*K.1^-1,-1,0,0,-2*K.1,0,0,-2*K.1^-1,0,0,0,0,1,0,K.1,0,K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,0,0,-2,2,2*K.1^-1,2*K.1,2,2,2*K.1^-1,-1*K.1,-1*K.1^-1,-1,2*K.1,2*K.1,2*K.1^-1,-1*K.1,2*K.1,-1,-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,2*K.1^-1,-1*K.1,2,-1*K.1^-1,-1,-1*K.1^-1,-1*K.1,-1,0,-2*K.1^-1,0,0,-2*K.1,0,0,1,K.1^-1,0,0,0,0,K.1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,0,0,-2,2,2*K.1,2*K.1^-1,2,2,2*K.1,-1*K.1^-1,-1*K.1,-1,2*K.1^-1,2*K.1^-1,2*K.1,-1*K.1^-1,2*K.1^-1,-1,-1,-1*K.1,-1*K.1,-1*K.1^-1,2*K.1,-1*K.1^-1,2,-1*K.1,-1,-1*K.1,-1*K.1^-1,-1,0,-2*K.1,0,0,-2*K.1^-1,0,0,1,K.1,0,0,0,0,K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 0, 0, 0, 4, 4, 4, -2, -2, -2, 4, 4, 4, -2, -2, -2, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, -2, -2, -2, -2, 1, 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!\[4, 0, 0, 0, 4, 4, 4, -2, 4, -2, -2, -2, -2, -2, 4, 4, 1, -2, 1, -2, 1, 1, 1, -2, 1, -2, 1, 1, -2, -2, 1, 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!\[4, 0, 0, 0, 4, 4, 4, 4, -2, 4, -2, -2, -2, 4, -2, -2, 1, -2, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, 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 |4,0,0,0,4,4*K.1^-1,4*K.1,-2,-2,-2*K.1^-1,4*K.1,4*K.1^-1,4,-2*K.1,-2*K.1,-2*K.1^-1,K.1,K.1,1,-2,K.1^-1,K.1^-1,K.1,K.1^-1,-2*K.1,1,-2*K.1^-1,-2,-2*K.1^-1,-2*K.1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4*K.1,4*K.1^-1,-2,-2,-2*K.1,4*K.1^-1,4*K.1,4,-2*K.1^-1,-2*K.1^-1,-2*K.1,K.1^-1,K.1^-1,1,-2,K.1,K.1,K.1^-1,K.1,-2*K.1^-1,1,-2*K.1,-2,-2*K.1,-2*K.1^-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4*K.1^-1,4*K.1,-2,4,-2*K.1^-1,-2*K.1,-2*K.1^-1,-2,-2*K.1,4*K.1,4*K.1^-1,K.1,-2*K.1,1,-2,K.1^-1,K.1^-1,K.1,-2*K.1^-1,K.1,-2,K.1^-1,1,-2*K.1^-1,-2*K.1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4*K.1,4*K.1^-1,-2,4,-2*K.1,-2*K.1^-1,-2*K.1,-2,-2*K.1^-1,4*K.1^-1,4*K.1,K.1^-1,-2*K.1^-1,1,-2,K.1,K.1,K.1^-1,-2*K.1,K.1^-1,-2,K.1,1,-2*K.1,-2*K.1^-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4*K.1^-1,4*K.1,4,-2,4*K.1^-1,-2*K.1,-2*K.1^-1,-2,4*K.1,-2*K.1,-2*K.1^-1,K.1,-2*K.1,1,1,K.1^-1,K.1^-1,K.1,-2*K.1^-1,-2*K.1,-2,-2*K.1^-1,-2,K.1^-1,K.1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4*K.1,4*K.1^-1,4,-2,4*K.1,-2*K.1^-1,-2*K.1,-2,4*K.1^-1,-2*K.1^-1,-2*K.1,K.1^-1,-2*K.1^-1,1,1,K.1,K.1,K.1^-1,-2*K.1,-2*K.1^-1,-2,-2*K.1,-2,K.1,K.1^-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4,4,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2-3*K.1,1,-2-3*K.1,1,1+3*K.1,-2-3*K.1,1+3*K.1,1,1,1,1,1,1,1,1+3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4,4,-2,-2,-2,-2,-2,-2,-2,-2,-2,1+3*K.1,1,1+3*K.1,1,-2-3*K.1,1+3*K.1,-2-3*K.1,1,1,1,1,1,1,1,-2-3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4*K.1^-1,4*K.1,-2,-2,-2*K.1^-1,-2*K.1,-2*K.1^-1,-2,-2*K.1,-2*K.1,-2*K.1^-1,-3-2*K.1,K.1,1+3*K.1,1,-1+2*K.1,2-K.1,3+K.1,K.1^-1,K.1,1,K.1^-1,1,K.1^-1,K.1,-2-3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4*K.1,4*K.1^-1,-2,-2,-2*K.1,-2*K.1^-1,-2*K.1,-2,-2*K.1^-1,-2*K.1^-1,-2*K.1,-1+2*K.1,K.1^-1,-2-3*K.1,1,-3-2*K.1,3+K.1,2-K.1,K.1,K.1^-1,1,K.1,1,K.1,K.1^-1,1+3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4*K.1^-1,4*K.1,-2,-2,-2*K.1^-1,-2*K.1,-2*K.1^-1,-2,-2*K.1,-2*K.1,-2*K.1^-1,3+K.1,K.1,-2-3*K.1,1,2-K.1,-1+2*K.1,-3-2*K.1,K.1^-1,K.1,1,K.1^-1,1,K.1^-1,K.1,1+3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,0,0,4,4*K.1,4*K.1^-1,-2,-2,-2*K.1,-2*K.1^-1,-2*K.1,-2,-2*K.1^-1,-2*K.1^-1,-2*K.1,2-K.1,K.1^-1,1+3*K.1,1,3+K.1,-3-2*K.1,-1+2*K.1,K.1,K.1^-1,1,K.1,1,K.1,K.1^-1,-2-3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[18, 6, 0, 0, -9, 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, -3, 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, 0, 0, -9, 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, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_972_802:= KnownIrreducibles(CR);