/* Group 288.928 downloaded from the LMFDB on 26 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, -2, -3, -2, 2, -3, 197, 36, 58, 2951, 1278, 760, 2532, 775, 1160, 124, 4717]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.5, GPC.6]); AssignNames(~GPC, ["a", "b", "b2", "b4", "c", "d", "d2"]);
GPerm := PermutationGroup< 11 | (1,2)(3,4)(6,7), (2,4), (9,11,10), (1,3)(2,4), (8,9)(10,11), (8,10)(9,11), (5,6,7) >;
GLZN := MatrixGroup< 2, Integers(28) | [[22, 25, 1, 5], [13, 0, 0, 13], [1, 14, 14, 1], [13, 24, 0, 1], [15, 0, 14, 15], [9, 10, 6, 19], [22, 7, 7, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_288_928 := rec< RF |  
Agroup := false,
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:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, b^6>,< 2, 2, a>,< 2, 3, d^3>,< 2, 3, b^6*d^3>,< 2, 6, a*d^3>,< 2, 6, a*b^3>,< 2, 18, a*b^3*c*d^4>,< 3, 2, d^4>,< 3, 4, b^8>,< 3, 4, b^4>,< 3, 8, b^4*d^4>,< 3, 8, b^8*d^2>,< 4, 6, b^3*d^4>,< 4, 18, b^9*c*d>,< 6, 2, b^6*d^2>,< 6, 2, a*d^2>,< 6, 2, a*d^4>,< 6, 4, b^2*d^3>,< 6, 4, b^10*c>,< 6, 6, d>,< 6, 6, b^6*d>,< 6, 6, a*d>,< 6, 6, a*c*d^2>,< 6, 8, b^2*d^2>,< 6, 8, b^10*d^2>,< 6, 8, a*b^4>,< 6, 8, a*b^2>,< 6, 8, a*b^4*d^2>,< 6, 8, a*b^2*d^2>,< 6, 8, a*b^4*d>,< 6, 8, a*b^2*d>,< 6, 24, a*b^7*c*d^3>,< 6, 24, a*b^11*c>,< 12, 24, b*c*d^4>,< 12, 24, b^11*d>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,K.1^-1,K.1,K.1,K.1^-1,1,1,1,1,1,K.1^-1,K.1,1,1,1,1,K.1^-1,K.1,K.1,K.1,K.1^-1,K.1,K.1^-1,K.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 |1,1,1,1,1,1,1,1,1,K.1,K.1^-1,K.1^-1,K.1,1,1,1,1,1,K.1,K.1^-1,1,1,1,1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,K.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,-1,1,1,-1,-1,-1,1,K.1^-1,K.1,K.1,K.1^-1,1,1,1,-1,-1,K.1^-1,K.1,1,-1,1,-1,K.1^-1,K.1,-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*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,-1,-1,-1,1,K.1,K.1^-1,K.1^-1,K.1,1,1,1,-1,-1,K.1,K.1^-1,1,-1,1,-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*K.1,-1*K.1^-1,-1*K.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,-1,1,1,-1,1,1,1,K.1^-1,K.1,K.1,K.1^-1,-1,-1,1,-1,-1,K.1^-1,K.1,1,-1,1,-1,K.1^-1,K.1,-1*K.1,-1*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,-1,1,1,-1,1,1,1,K.1,K.1^-1,K.1^-1,K.1,-1,-1,1,-1,-1,K.1,K.1^-1,1,-1,1,-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*K.1,K.1^-1,K.1,-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 |1,1,1,1,1,1,-1,-1,1,K.1^-1,K.1,K.1,K.1^-1,-1,-1,1,1,1,K.1^-1,K.1,1,1,1,1,K.1^-1,K.1,K.1,K.1,K.1^-1,K.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 |1,1,1,1,1,1,-1,-1,1,K.1,K.1^-1,K.1^-1,K.1,-1,-1,1,1,1,K.1,K.1^-1,1,1,1,1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, -1, -1, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 0, 0, -1, 2, 2, -1, -1, 0, 0, -1, 1, 1, 2, 2, -1, 1, -1, 1, -1, -1, -2, 1, 1, 1, 1, -2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,2,2,0,0,-1,2*K.1^-1,2*K.1,-1*K.1,-1*K.1^-1,0,0,-1,-1,-1,2*K.1^-1,2*K.1,-1,-1,-1,-1,-1*K.1^-1,-1*K.1,2*K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,2*K.1^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,2,2,0,0,-1,2*K.1,2*K.1^-1,-1*K.1^-1,-1*K.1,0,0,-1,-1,-1,2*K.1,2*K.1^-1,-1,-1,-1,-1,-1*K.1,-1*K.1^-1,2*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,2*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,0,-1,2,2,-1,-1,0,0,1,-1-2*K.1,1+2*K.1,-2,-2,1,1+2*K.1,-1,-1-2*K.1,1,1,0,1+2*K.1,-1-2*K.1,-1-2*K.1,1+2*K.1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,0,-1,2,2,-1,-1,0,0,1,1+2*K.1,-1-2*K.1,-2,-2,1,-1-2*K.1,-1,1+2*K.1,1,1,0,-1-2*K.1,1+2*K.1,1+2*K.1,-1-2*K.1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,0,2,2*K.1^-1,2*K.1,2*K.1,2*K.1^-1,0,0,-2,0,0,-2*K.1^-1,-2*K.1,-2,0,2,0,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,0,2,2*K.1,2*K.1^-1,2*K.1^-1,2*K.1,0,0,-2,0,0,-2*K.1,-2*K.1^-1,-2,0,2,0,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,2,2,-2,0,0,-1,2*K.1^-1,2*K.1,-1*K.1,-1*K.1^-1,0,0,-1,1,1,2*K.1^-1,2*K.1,-1,1,-1,1,-1*K.1^-1,-1*K.1,-2*K.1,K.1,K.1^-1,K.1,K.1^-1,-2*K.1^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,2,2,-2,0,0,-1,2*K.1,2*K.1^-1,-1*K.1^-1,-1*K.1,0,0,-1,1,1,2*K.1,2*K.1^-1,-1,1,-1,1,-1*K.1,-1*K.1^-1,-2*K.1^-1,K.1^-1,K.1,K.1^-1,K.1,-2*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,0,-1,2*K.1^-1,2*K.1,-1*K.1,-1*K.1^-1,0,0,1,-1-2*K.1,1+2*K.1,-2*K.1^-1,-2*K.1,1,1+2*K.1,-1,-1-2*K.1,K.1^-1,K.1,0,-2-K.1,-1+K.1,2+K.1,1-K.1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,0,-1,2*K.1,2*K.1^-1,-1*K.1^-1,-1*K.1,0,0,1,1+2*K.1,-1-2*K.1,-2*K.1,-2*K.1^-1,1,-1-2*K.1,-1,1+2*K.1,K.1,K.1^-1,0,-1+K.1,-2-K.1,1-K.1,2+K.1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,0,-1,2*K.1^-1,2*K.1,-1*K.1,-1*K.1^-1,0,0,1,1+2*K.1,-1-2*K.1,-2*K.1^-1,-2*K.1,1,-1-2*K.1,-1,1+2*K.1,K.1^-1,K.1,0,2+K.1,1-K.1,-2-K.1,-1+K.1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,0,-1,2*K.1,2*K.1^-1,-1*K.1^-1,-1*K.1,0,0,1,-1-2*K.1,1+2*K.1,-2*K.1,-2*K.1^-1,1,1+2*K.1,-1,-1-2*K.1,K.1,K.1^-1,0,1-K.1,2+K.1,-1+K.1,-2-K.1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, 3, -1, 3, 0, 0, 0, 0, 3, -1, 3, 3, 3, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, -3, 1, 3, 0, 0, 0, 0, 3, -1, 3, -3, -3, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, 3, -1, 3, 0, 0, 0, 0, -3, 1, 3, -3, -3, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, -3, 1, 3, 0, 0, 0, 0, -3, 1, 3, 3, 3, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, -2, -2, -2, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, -3, -3, 0, 0, 1, 1, 1, 1, 0, 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, -2, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -2, -2, 2, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 3, 3, 0, 0, 1, -1, 1, -1, 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 |6,-6,0,-2,2,0,0,0,-3,0,0,0,0,0,0,3,-3-6*K.1,3+6*K.1,0,0,-1,-1-2*K.1,1,1+2*K.1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,-6,0,-2,2,0,0,0,-3,0,0,0,0,0,0,3,3+6*K.1,-3-6*K.1,0,0,-1,1+2*K.1,1,-1-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_288_928:= KnownIrreducibles(CR);