/* Group 3024.r downloaded from the LMFDB on 29 December 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 */
GPerm := PermutationGroup< 11 | (1,2)(4,5,6,7,9,8)(10,11), (1,3,2,4,6,8)(7,9) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_3024_r := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := false,
supersolvable := false>; 

 
/* Character Table */
G:= GPerm;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, G!(10,11)>,< 2, 63, G!(2,5)(3,4)(6,8)(7,9)>,< 2, 63, G!(1,2)(3,9)(4,5)(7,8)(10,11)>,< 3, 56, G!(1,4,9)(2,5,7)(3,8,6)>,< 3, 84, G!(2,3,8)(4,6,5)>,< 3, 84, G!(2,8,3)(4,5,6)>,< 6, 56, G!(1,9,4)(2,7,5)(3,6,8)(10,11)>,< 6, 84, G!(1,8,5)(2,9,7)(10,11)>,< 6, 84, G!(1,5,8)(2,7,9)(10,11)>,< 6, 252, G!(2,6,3,5,8,4)(7,9)>,< 6, 252, G!(2,4,8,5,3,6)(7,9)>,< 6, 252, G!(1,4,7,2,5,8)(3,9)(10,11)>,< 6, 252, G!(1,8,5,2,7,4)(3,9)(10,11)>,< 7, 216, G!(1,8,5,4,2,3,7)>,< 9, 168, G!(1,3,2,4,8,5,9,6,7)>,< 9, 168, G!(1,8,3,4,7,9,6,2,5)>,< 9, 168, G!(1,5,2,6,9,7,4,3,8)>,< 14, 216, G!(1,2,8,3,5,7,4)(10,11)>,< 18, 168, G!(1,5,3,9,2,6,4,7,8)(10,11)>,< 18, 168, G!(1,9,8,6,3,2,4,5,7)(10,11)>,< 18, 168, G!(1,7,5,4,2,3,6,8,9)(10,11)>]); 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,K.1^-1,K.1,1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.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 |1,1,1,1,1,K.1,K.1^-1,1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,1,1,K.1,K.1^-1,1,1,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,-1,1,K.1^-1,K.1,-1,-1*K.1^-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,-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,K.1,K.1^-1,-1,-1*K.1,-1*K.1^-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,1,1,K.1,K.1^-1,-1,-1,-1*K.1^-1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[7, -7, -1, 1, -2, 1, 1, 2, -1, -1, -1, -1, 1, 1, 0, 1, 1, 1, 0, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[7, 7, -1, -1, -2, 1, 1, -2, 1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 0, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,-7,-1,1,-2,K.1^-1,K.1,2,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,K.1^-1,K.1,0,1,K.1^-1,K.1,0,-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 |7,-7,-1,1,-2,K.1,K.1^-1,2,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,1,K.1,K.1^-1,0,-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 |7,7,-1,-1,-2,K.1^-1,K.1,-2,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,0,1,K.1^-1,K.1,0,1,K.1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,7,-1,-1,-2,K.1,K.1^-1,-2,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,0,1,K.1,K.1^-1,0,1,K.1^-1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, 8, 0, 0, -1, 2, 2, -1, 2, 2, 0, 0, 0, 0, 1, -1, -1, -1, 1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, 0, -1, 2, 2, 1, -2, -2, 0, 0, 0, 0, 1, -1, -1, -1, -1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |8,8,0,0,-1,2*K.1^-1,2*K.1,-1,2*K.1^-1,2*K.1,0,0,0,0,1,-1,-1*K.1^-1,-1*K.1,1,-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 |8,8,0,0,-1,2*K.1,2*K.1^-1,-1,2*K.1,2*K.1^-1,0,0,0,0,1,-1,-1*K.1,-1*K.1^-1,1,-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 |8,-8,0,0,-1,2*K.1^-1,2*K.1,1,-2*K.1^-1,-2*K.1,0,0,0,0,1,-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 |8,-8,0,0,-1,2*K.1,2*K.1^-1,1,-2*K.1,-2*K.1^-1,0,0,0,0,1,-1,-1*K.1,-1*K.1^-1,-1,1,K.1^-1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[21, -21, -3, 3, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[21, 21, -3, -3, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[27, 27, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[27, -27, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_3024_r:= KnownIrreducibles(CR);