/* Group 576.8300 downloaded from the LMFDB on 23 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([8, 2, 2, 2, 2, 2, 3, 2, 3, 97, 41, 290, 66, 19844, 11212, 4660, 428, 116, 19973, 10765, 3093, 413, 26886, 8974, 2262, 3390, 166, 24583, 2063, 3607, 3103]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.5, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "b4", "c", "c2", "d", "d2"]);
GPerm := PermutationGroup< 13 | (2,4,6,3,7,8,5,9)(10,11,12,13), (2,5)(3,9)(6,7)(11,13), (10,11)(12,13), (2,6,7,5)(3,8,9,4)(10,12)(11,13), (10,12)(11,13), (2,7)(3,9)(4,8)(5,6), (1,2,7)(3,8,6)(4,9,5), (1,3,9)(2,8,5)(4,7,6) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_576_8300 := 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:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, d^3>,< 2, 2, c^3>,< 2, 9, b^4*d>,< 2, 9, b^4*c^2*d^2>,< 2, 18, b^4*c>,< 2, 24, a*b^4*c^4*d>,< 3, 8, c^2>,< 4, 18, b^6*c^4*d^3>,< 4, 18, b^6*d^4>,< 4, 24, a*b^2*c*d^5>,< 4, 36, a*b^3*c*d^3>,< 4, 36, b^6*c^3*d>,< 4, 36, a*b*c*d^3>,< 4, 36, a*b^5*d>,< 4, 36, a*b*c^4>,< 6, 8, c^4*d^3>,< 6, 16, c>,< 6, 48, a*b^4*c^4*d^3>,< 8, 36, b^3*c^3*d>,< 8, 36, b^5*c^5>,< 8, 36, b^3*c^4*d^2>,< 8, 36, b^5*d^2>,< 12, 48, a*b^2*c^3*d^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; 
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; 
x := CR!\[2, -2, 0, -2, 2, 0, 0, 2, -2, 2, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, -2, 2, 0, 0, 2, -2, 2, 0, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, -2, 2, 0, 0, 2, 2, -2, 0, 0, 0, -2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, -2, 2, 0, 0, 2, 2, -2, 0, 0, 0, 2, -2, 0, -2, 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, 2, -2, -2, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 2, -2, -2, 0, 0, -2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,0,2,0,0,0,0,0,0,0,0,2,-2,0,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,0,2,0,0,0,0,0,0,0,0,2,-2,0,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,2,-2,-2,-2,0,2,0,0,0,0,0,0,0,0,2,2,0,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,2,-2,-2,-2,0,2,0,0,0,0,0,0,0,0,2,2,0,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[8, 8, 8, 0, 0, 0, 2, -1, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 8, 8, 0, 0, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 8, -8, 0, 0, 0, -2, -1, 0, 0, 2, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 8, -8, 0, 0, 0, 2, -1, 0, 0, -2, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[16, -16, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_576_8300:= KnownIrreducibles(CR);