/* Group 2160.ck downloaded from the LMFDB on 12 June 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 */
GPerm := PermutationGroup< 13 | (1,2,3,5,6,8,9,10)(11,12), (1,2,4,7,9,10,5,8,3,6)(11,13) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_2160_ck := 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, 45, G!(1,9)(2,7)(3,5)(6,10)>,< 2, 108, G!(1,6)(2,9)(3,10)(4,5)(7,8)(11,13)>,< 3, 2, G!(11,13,12)>,< 3, 80, G!(1,2,6)(3,8,9)(4,5,7)>,< 3, 80, G!(2,5,4)(3,9,6)(7,8,10)(11,12,13)>,< 3, 80, G!(2,4,5)(3,6,9)(7,10,8)(11,13,12)>,< 4, 90, G!(1,7,9,2)(3,10,5,6)>,< 5, 72, G!(1,6,2,4,8)(3,7,9,5,10)>,< 5, 72, G!(1,2,8,6,4)(3,9,10,7,5)>,< 6, 90, G!(1,9)(2,7)(3,5)(6,10)(11,12,13)>,< 8, 270, G!(1,10,9,7,3,5,6,4)(11,12)>,< 8, 270, G!(1,7,6,10,3,4,9,5)(11,12)>,< 10, 216, G!(1,9,7,5,10,6,2,8,4,3)(11,13)>,< 10, 216, G!(1,5,2,3,7,6,4,9,10,8)(11,13)>,< 12, 180, G!(1,2,9,7)(3,6,5,10)(11,13,12)>,< 15, 144, G!(1,2,8,6,4)(3,9,10,7,5)(11,12,13)>,< 15, 144, G!(1,8,4,2,6)(3,10,5,9,7)(11,13,12)>]); 
CR := CharacterRing(G);
x := CR!\[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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, -1, 2, -1, -1, 2, 2, 2, -1, 0, 0, 0, 0, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,2,8,-1,-1,-1,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,2,8,-1,-1,-1,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,-2,8,-1,-1,-1,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,-2,8,-1,-1,-1,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[9, 1, -1, 9, 0, 0, 0, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[9, 1, 1, 9, 0, 0, 0, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[10, 2, 0, 10, 1, 1, 1, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |10,2,0,-5,1,-2-3*K.1,1+3*K.1,-2,0,0,-1,0,0,0,0,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |10,2,0,-5,1,1+3*K.1,-2-3*K.1,-2,0,0,-1,0,0,0,0,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |10,-2,0,10,1,1,1,0,0,0,-2,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |10,-2,0,10,1,1,1,0,0,0,-2,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |16,0,0,-8,-2,1,1,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |16,0,0,-8,-2,1,1,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[18, 2, 0, -9, 0, 0, 0, 2, -2, -2, -1, 0, 0, 0, 0, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[20, -4, 0, -10, 2, -1, -1, 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_2160_ck:= KnownIrreducibles(CR);