/* Group 648.717 downloaded from the LMFDB on 20 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, 2, 3, 2, 3, 3, 3, 14, 590, 93, 1907, 850, 80, 1824, 851, 21173, 3036, 530, 28230, 10597, 1791]); a,b,c,d,e := Explode([GPC.1, GPC.3, GPC.4, GPC.6, GPC.7]); AssignNames(~GPC, ["a", "a2", "b", "c", "c2", "d", "e"]);
GPerm := PermutationGroup< 12 | (1,7)(2,9,3,8)(4,10)(5,12,6,11), (1,4)(2,5)(3,6)(7,10)(8,11)(9,12), (2,3)(5,6)(8,9)(11,12), (7,8,9)(10,12,11), (1,2,3)(4,6,5)(7,8,9)(10,12,11), (7,9,8)(10,12,11), (1,3,2)(4,6,5)(7,9,8)(10,12,11) >;
GLFp := MatrixGroup< 4, GF(3) | [[1, 0, 0, 0, 2, 0, 1, 0, 2, 2, 2, 0, 2, 2, 1, 1], [1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 1], [1, 0, 0, 0, 1, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 1, 2], [1, 0, 0, 0, 2, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 1], [2, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 0, 1, 1, 1], [1, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 0, 2, 2, 1, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_648_717 := rec< RF |  
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>; 

 
/* 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, [1, 0, 0, 0, 2, 0, 1, 0, 1, 1, 0, 0, 2, 2, 1, 1])>,< 2, 9, Matrix(4, [1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2])>,< 2, 81, Matrix(4, [1, 0, 0, 0, 2, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2])>,< 3, 4, Matrix(4, [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1])>,< 3, 4, Matrix(4, [1, 0, 0, 0, 2, 0, 1, 0, 2, 2, 2, 0, 1, 1, 2, 1])>,< 3, 4, Matrix(4, [1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1])>,< 3, 4, Matrix(4, [1, 0, 0, 0, 2, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 1])>,< 3, 8, Matrix(4, [1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 1])>,< 3, 8, Matrix(4, [1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 0, 1])>,< 3, 8, Matrix(4, [1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 1])>,< 3, 8, Matrix(4, [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1])>,< 3, 8, Matrix(4, [1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 1, 2, 1])>,< 3, 8, Matrix(4, [1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 2, 1, 1])>,< 3, 8, Matrix(4, [1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 1, 2, 1])>,< 3, 8, Matrix(4, [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 1])>,< 4, 81, Matrix(4, [2, 0, 0, 0, 0, 1, 1, 2, 1, 0, 2, 2, 2, 0, 2, 1])>,< 4, 81, Matrix(4, [2, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1, 1, 2, 0, 1, 2])>,< 4, 81, Matrix(4, [2, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 0, 0, 2, 1])>,< 4, 81, Matrix(4, [2, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 1, 0, 2, 2, 2])>,< 6, 36, Matrix(4, [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 1, 1])>,< 6, 36, Matrix(4, [1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 1, 2, 2])>,< 6, 36, Matrix(4, [1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1])>,< 6, 36, Matrix(4, [1, 0, 0, 0, 2, 1, 1, 0, 1, 2, 0, 0, 1, 0, 0, 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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
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*K.1,K.1,K.1,-1*K.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,K.1,-1*K.1,-1*K.1,K.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*K.1,K.1,-1*K.1,K.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,K.1,-1*K.1,K.1,-1*K.1,1,-1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 0, 4, 0, 4, -2, 4, 1, -2, -2, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 1, -2, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 0, 4, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 1, -2, -2, 0, 0, 0, 0, 0, -2, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, -2, 4, 1, 4, -2, 1, -2, 1, -2, 1, -2, 1, 0, 0, 0, 0, -2, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 1, 4, -2, 4, 1, -2, 1, -2, 1, -2, 1, -2, 0, 0, 0, 0, 1, 0, 0, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 0, -2, 4, 1, 4, -2, 1, -2, 1, -2, 1, -2, 1, 0, 0, 0, 0, 2, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 0, 1, 4, -2, 4, 1, -2, 1, -2, 1, -2, 1, -2, 0, 0, 0, 0, -1, 0, 0, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 0, -4, 0, 4, -2, 4, 1, -2, -2, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, -1, 2, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 0, -4, 0, 4, 1, 4, -2, 1, 1, 1, -2, -2, 1, -2, -2, 0, 0, 0, 0, 0, 2, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, 0, -4, -4, 2, 2, 2, -1, 2, -4, -1, -1, -1, 5, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, 0, -4, -4, 2, 2, 2, -1, 2, 5, -1, -1, -1, -4, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, 0, -4, 2, 2, -4, -1, -4, -1, -1, 2, 5, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, 0, -4, 2, 2, -4, -1, 5, -1, -1, 2, -4, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, 0, 2, -4, -4, 2, -1, 2, -1, -1, -4, 2, 5, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, 0, 2, -4, -4, 2, -1, 2, -1, -1, 5, 2, -4, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, 0, 2, 2, -4, -4, -4, -1, 5, 2, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, 0, 2, 2, -4, -4, 5, -1, -4, 2, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_648_717:= KnownIrreducibles(CR);