/* Group 480.217 downloaded from the LMFDB on 22 September 2026. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation, GPerm is permutation group 
	 GLZ, GLFp, GLZN, 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 | (2,5,4)(6,8,7,9)(10,12,11,13), (1,5,2,3)(6,13,9,11,7,12,8,10) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; 
booleans_480_217 := 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!(6,7)(8,9)(10,11)(12,13)>,< 2, 15, G!(2,3)(4,5)>,< 2, 15, G!(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)>,< 3, 20, G!(3,5,4)>,< 4, 1, G!(6,9,7,8)(10,13,11,12)>,< 4, 1, G!(6,8,7,9)(10,12,11,13)>,< 4, 15, G!(1,4)(2,3)(6,9,7,8)(10,13,11,12)>,< 4, 15, G!(1,4)(2,3)(6,8,7,9)(10,12,11,13)>,< 5, 24, G!(1,2,5,3,4)>,< 6, 20, G!(3,4,5)(6,7)(8,9)(10,11)(12,13)>,< 8, 10, G!(1,2)(6,12,9,10,7,13,8,11)>,< 8, 10, G!(1,2)(6,11,8,13,7,10,9,12)>,< 8, 10, G!(1,2)(6,10,8,12,7,11,9,13)>,< 8, 10, G!(1,2)(6,13,9,11,7,12,8,10)>,< 8, 30, G!(1,3,4,2)(6,12,9,10,7,13,8,11)>,< 8, 30, G!(1,2,4,3)(6,11,8,13,7,10,9,12)>,< 8, 30, G!(1,2,4,3)(6,10,8,12,7,11,9,13)>,< 8, 30, G!(1,3,4,2)(6,13,9,11,7,12,8,10)>,< 10, 24, G!(1,3,2,4,5)(6,7)(8,9)(10,11)(12,13)>,< 12, 20, G!(3,5,4)(6,8,7,9)(10,12,11,13)>,< 12, 20, G!(3,4,5)(6,9,7,8)(10,13,11,12)>,< 20, 24, G!(1,4,3,5,2)(6,8,7,9)(10,12,11,13)>,< 20, 24, G!(1,2,5,3,4)(6,9,7,8)(10,13,11,12)>,< 24, 20, G!(1,2)(3,4,5)(6,10,8,12,7,11,9,13)>,< 24, 20, G!(1,2)(3,4,5)(6,13,9,11,7,12,8,10)>,< 24, 20, G!(1,2)(3,4,5)(6,11,8,13,7,10,9,12)>,< 24, 20, G!(1,2)(3,4,5)(6,12,9,10,7,13,8,11)>]); 
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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,-1,-1,-1,-1,1,1,-1*K.1,K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,1,-1,-1,-1,-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(4: Sparse := true);
S := [ K |1,1,1,1,1,-1,-1,-1,-1,1,1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,1,-1,-1,-1,-1,-1*K.1,K.1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,1,-1,K.1^3,-1*K.1,K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^3,-1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1,K.1^3,K.1,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,1,-1,-1*K.1,K.1^3,-1*K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,K.1,-1,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,K.1^3,-1*K.1,-1*K.1^3,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,1,-1,-1*K.1^3,K.1,-1*K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^3,-1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1,-1*K.1^3,-1*K.1,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,1,-1,K.1,-1*K.1^3,K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,-1*K.1,-1,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^3,K.1,K.1^3,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 1, 4, 4, 0, 0, -1, 1, 2, 2, 2, 2, 0, 0, 0, 0, -1, 1, 1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 1, 4, 4, 0, 0, -1, 1, -2, -2, -2, -2, 0, 0, 0, 0, -1, 1, 1, -1, -1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,0,0,1,-4,-4,0,0,-1,1,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,0,0,-1,-1,-1,1,1,-1*K.1,K.1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,0,0,1,-4,-4,0,0,-1,1,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,0,0,-1,-1,-1,1,1,K.1,-1*K.1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,0,0,1,-4*K.1^2,4*K.1^2,0,0,-1,-1,2*K.1^3,-2*K.1,2*K.1,-2*K.1^3,0,0,0,0,1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,K.1,-1*K.1^3,-1*K.1,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,0,0,1,4*K.1^2,-4*K.1^2,0,0,-1,-1,-2*K.1,2*K.1^3,-2*K.1^3,2*K.1,0,0,0,0,1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,-1*K.1^3,K.1,K.1^3,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,0,0,1,-4*K.1^2,4*K.1^2,0,0,-1,-1,-2*K.1^3,2*K.1,-2*K.1,2*K.1^3,0,0,0,0,1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1,K.1^3,K.1,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,0,0,1,4*K.1^2,-4*K.1^2,0,0,-1,-1,2*K.1,-2*K.1^3,2*K.1^3,-2*K.1,0,0,0,0,1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^3,-1*K.1,-1*K.1^3,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[5, 5, 1, 1, -1, 5, 5, 1, 1, 0, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, -1, -1, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[5, 5, 1, 1, -1, 5, 5, 1, 1, 0, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0, -1, -1, 0, 0, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |5,5,1,1,-1,-5,-5,-1,-1,0,-1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,0,1,1,0,0,K.1,-1*K.1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |5,5,1,1,-1,-5,-5,-1,-1,0,-1,K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,0,1,1,0,0,-1*K.1,K.1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |5,-5,1,-1,-1,-5*K.1^2,5*K.1^2,-1*K.1^2,K.1^2,0,1,K.1^3,-1*K.1,K.1,-1*K.1^3,K.1,-1*K.1,-1*K.1^3,K.1^3,0,-1*K.1^2,K.1^2,0,0,-1*K.1,K.1^3,K.1,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |5,-5,1,-1,-1,5*K.1^2,-5*K.1^2,K.1^2,-1*K.1^2,0,1,-1*K.1,K.1^3,-1*K.1^3,K.1,-1*K.1^3,K.1^3,K.1,-1*K.1,0,K.1^2,-1*K.1^2,0,0,K.1^3,-1*K.1,-1*K.1^3,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |5,-5,1,-1,-1,-5*K.1^2,5*K.1^2,-1*K.1^2,K.1^2,0,1,-1*K.1^3,K.1,-1*K.1,K.1^3,-1*K.1,K.1,K.1^3,-1*K.1^3,0,-1*K.1^2,K.1^2,0,0,K.1,-1*K.1^3,-1*K.1,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |5,-5,1,-1,-1,5*K.1^2,-5*K.1^2,K.1^2,-1*K.1^2,0,1,K.1,-1*K.1^3,K.1^3,-1*K.1,K.1^3,-1*K.1^3,-1*K.1,K.1,0,K.1^2,-1*K.1^2,0,0,-1*K.1^3,K.1,K.1^3,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 0, -6, -6, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, 0, 6, 6, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,-6,-2,2,0,-6*K.1,6*K.1,2*K.1,-2*K.1,1,0,0,0,0,0,0,0,0,0,-1,0,0,K.1,-1*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,-6,-2,2,0,6*K.1,-6*K.1,-2*K.1,2*K.1,1,0,0,0,0,0,0,0,0,0,-1,0,0,-1*K.1,K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_480_217:= KnownIrreducibles(CR);