/* Group 126.7 downloaded from the LMFDB on 30 September 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([4, -2, -3, -3, -7, 8, 722, 582, 46, 867, 295]); a,b := Explode([GPC.1, GPC.3]); AssignNames(~GPC, ["a", "a2", "b", "b3"]);
GPerm := PermutationGroup< 10 | (2,3)(4,6)(5,7), (2,4,5)(3,6,7)(8,9,10), (8,10,9), (1,2,5,6,4,7,3) >;
GLFp := MatrixGroup< 2, GF(7) | [[1, 1, 0, 1], [1, 0, 0, 3], [2, 0, 0, 4]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_126_7 := rec< RF |  
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 7, a^3>,< 3, 1, b^14>,< 3, 1, b^7>,< 3, 7, a^2>,< 3, 7, a^4>,< 3, 7, a^2*b^11>,< 3, 7, a^4*b^19>,< 3, 7, a^2*b>,< 3, 7, a^4*b^17>,< 6, 7, a>,< 6, 7, a^5>,< 6, 7, a*b>,< 6, 7, a^5*b^2>,< 6, 7, a*b^2>,< 6, 7, a^5*b>,< 6, 7, a^3*b>,< 6, 7, a^3*b^2>,< 7, 6, b^3>,< 21, 6, b>,< 21, 6, b^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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,1,1,1,K.1,K.1^-1,K.1,K.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,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,1,1,1,K.1^-1,K.1,K.1^-1,K.1,1,K.1^-1,K.1,1,K.1^-1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1^-1,K.1,K.1,K.1^-1,1,1,K.1^-1,K.1,K.1,1,1,K.1,K.1,K.1^-1,K.1^-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,K.1,K.1^-1,K.1^-1,K.1,1,1,K.1,K.1^-1,K.1^-1,1,1,K.1^-1,K.1^-1,K.1,K.1,K.1,1,K.1^-1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1^-1,K.1,1,1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,1,K.1,1,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,K.1,K.1^-1,1,1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1,K.1^-1,K.1^-1,1,K.1^-1,1,K.1,1,K.1^-1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,K.1,1,K.1^-1,K.1^-1,K.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,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,1,K.1,K.1,K.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,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,1,1,-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,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,1,1,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,K.1^-1,K.1,K.1,K.1^-1,1,1,K.1^-1,K.1,-1*K.1,-1,-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-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,K.1,K.1^-1,K.1^-1,K.1,1,1,K.1,K.1^-1,-1*K.1^-1,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,K.1^-1,K.1,1,1,K.1^-1,K.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^-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,K.1,K.1^-1,1,1,K.1,K.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,-1,-1*K.1,1,K.1^-1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,-1,1,1,K.1^-1,K.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^-1,-1*K.1^-1,-1*K.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,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1,-1*K.1,-1*K.1,-1*K.1^-1,-1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,0,6*K.1^-1,6*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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 |6,0,6*K.1,6*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1*K.1^-1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_126_7:= KnownIrreducibles(CR);