/* Group 648.276 downloaded from the LMFDB on 23 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([7, 2, 3, 3, 2, 3, 2, 3, 57, 884, 11595, 5554, 80, 2524, 22685, 3666, 1279, 124, 21174, 6334, 2078]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.3, GPC.4, GPC.6]); AssignNames(~GPC, ["a", "b", "c", "d", "d2", "e", "e2"]);
GPerm := PermutationGroup< 13 | (2,4)(3,6)(5,8)(7,9)(11,12), (1,2,4)(3,7,5)(6,8,9)(11,12,13), (1,3,6)(2,5,9)(4,7,8), (1,4,2)(3,5,7), (1,4,2)(3,7,5)(6,8,9), (10,11)(12,13), (10,12)(11,13) >;
GLZN := MatrixGroup< 2, Integers(36) | [[1, 12, 0, 1], [19, 0, 18, 19], [22, 15, 15, 25], [31, 5, 6, 23], [13, 16, 24, 13], [1, 18, 18, 1], [1, 33, 21, 10]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_648_276 := 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:= GLZN;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Matrix(2, [1, 0, 0, 1])>,< 2, 3, Matrix(2, [19, 0, 18, 19])>,< 2, 54, Matrix(2, [28, 13, 9, 8])>,< 3, 2, Matrix(2, [1, 24, 0, 1])>,< 3, 3, Matrix(2, [13, 24, 0, 25])>,< 3, 3, Matrix(2, [25, 12, 0, 13])>,< 3, 18, Matrix(2, [13, 20, 12, 13])>,< 3, 24, Matrix(2, [4, 33, 15, 7])>,< 3, 24, Matrix(2, [4, 21, 15, 7])>,< 3, 24, Matrix(2, [22, 27, 15, 25])>,< 4, 54, Matrix(2, [34, 23, 3, 20])>,< 6, 6, Matrix(2, [19, 12, 18, 19])>,< 6, 9, Matrix(2, [25, 30, 18, 13])>,< 6, 9, Matrix(2, [13, 6, 18, 25])>,< 6, 18, Matrix(2, [31, 34, 24, 31])>,< 6, 18, Matrix(2, [31, 32, 30, 31])>,< 6, 18, Matrix(2, [31, 28, 6, 31])>,< 6, 54, Matrix(2, [4, 13, 9, 20])>,< 6, 54, Matrix(2, [16, 13, 9, 32])>,< 9, 72, Matrix(2, [4, 31, 21, 19])>,< 9, 72, Matrix(2, [16, 35, 9, 31])>,< 12, 54, Matrix(2, [28, 23, 3, 14])>,< 12, 54, Matrix(2, [22, 23, 3, 8])>]); 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 2, 2, 2, -1, -1, -1, -1, 0, 2, 2, 2, -1, -1, -1, 0, 0, -1, 2, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 2, 2, 2, -1, -1, -1, -1, 0, 2, 2, 2, -1, -1, -1, 0, 0, 2, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 2, 2, 2, -1, 2, 2, 2, 0, 2, 2, 2, -1, -1, -1, 0, 0, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 2, 2, 2, 2, -1, -1, -1, 0, 2, 2, 2, 2, 2, 2, 0, 0, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, 1, 3, 3, 3, 3, 0, 0, 0, -1, -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, 3, 3, 3, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,1,3,3*K.1^-1,3*K.1,0,0,0,0,1,3,3*K.1,3*K.1^-1,0,0,0,K.1^-1,K.1,0,0,K.1^-1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,1,3,3*K.1,3*K.1^-1,0,0,0,0,1,3,3*K.1^-1,3*K.1,0,0,0,K.1,K.1^-1,0,0,K.1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,-1,3,3*K.1^-1,3*K.1,0,0,0,0,-1,3,3*K.1,3*K.1^-1,0,0,0,-1*K.1^-1,-1*K.1,0,0,-1*K.1^-1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3,-1,3,3*K.1,3*K.1^-1,0,0,0,0,-1,3,3*K.1^-1,3*K.1,0,0,0,-1*K.1,-1*K.1^-1,0,0,-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 |3,-1,-1,3,3*K.1^-1,3*K.1,0,0,0,0,1,-1,-1*K.1,-1*K.1^-1,2,2*K.1^-1,2*K.1,-1*K.1^-1,-1*K.1,0,0,K.1^-1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,-1,-1,3,3*K.1,3*K.1^-1,0,0,0,0,1,-1,-1*K.1^-1,-1*K.1,2,2*K.1,2*K.1^-1,-1*K.1,-1*K.1^-1,0,0,K.1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,-1,1,3,3*K.1^-1,3*K.1,0,0,0,0,-1,-1,-1*K.1,-1*K.1^-1,2,2*K.1^-1,2*K.1,K.1^-1,K.1,0,0,-1*K.1^-1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,-1,1,3,3*K.1,3*K.1^-1,0,0,0,0,-1,-1,-1*K.1^-1,-1*K.1,2,2*K.1,2*K.1^-1,K.1,K.1^-1,0,0,-1*K.1,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, 6, 0, -3, 0, 0, 0, -3, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 0, -3, 0, 0, 0, 0, 3, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 0, -3, 0, 0, 0, 3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, 0, 6, 6, 6, -3, 0, 0, 0, 0, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,-2,0,6,6*K.1^-1,6*K.1,0,0,0,0,0,-2,-2*K.1,-2*K.1^-1,-2,-2*K.1^-1,-2*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 |6,-2,0,6,6*K.1,6*K.1^-1,0,0,0,0,0,-2,-2*K.1^-1,-2*K.1,-2,-2*K.1,-2*K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[18, -6, 0, -9, 0, 0, 0, 0, 0, 0, 0, 3, 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_648_276:= KnownIrreducibles(CR);