/* Group 480.1201 downloaded from the LMFDB on 22 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, -3, -2, 2, 2, 2, -5, 57, 2592, 1011, 514, 221, 18401, 6186, 124, 18822]); a,b,c,d,e,f := Explode([GPC.1, GPC.2, GPC.3, GPC.4, GPC.5, GPC.6]); AssignNames(~GPC, ["a", "b", "c", "d", "e", "f", "f2"]);
GPerm := PermutationGroup< 13 | (1,2)(3,7)(4,6)(5,8)(10,11)(12,13), (3,4,5)(6,7,8), (9,10,12,13,11), (1,3)(2,6)(4,5)(7,8), (1,4)(2,7)(3,5)(6,8), (1,5)(2,6)(3,4)(7,8), (1,4)(2,8)(3,5)(6,7) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_480_1201 := 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:= GPerm;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 3, G!(1,3)(2,6)(4,5)(7,8)>,< 2, 3, G!(1,3)(2,7)(4,5)(6,8)>,< 2, 3, G!(1,3)(2,8)(4,5)(6,7)>,< 2, 6, G!(2,6)(7,8)>,< 2, 60, G!(1,7)(2,3)(4,8)(5,6)(9,12)(11,13)>,< 3, 32, G!(3,4,5)(6,7,8)>,< 4, 60, G!(1,2,5,8)(3,7,4,6)(9,12)(11,13)>,< 4, 60, G!(1,7,3,2)(4,8,5,6)(10,11)(12,13)>,< 4, 60, G!(1,6,3,7)(2,4,8,5)(10,11)(12,13)>,< 5, 2, G!(9,12,11,10,13)>,< 5, 2, G!(9,11,13,12,10)>,< 10, 6, G!(1,3)(2,6)(4,5)(7,8)(9,10,12,13,11)>,< 10, 6, G!(1,3)(2,6)(4,5)(7,8)(9,12,11,10,13)>,< 10, 6, G!(1,3)(2,7)(4,5)(6,8)(9,10,12,13,11)>,< 10, 6, G!(1,3)(2,7)(4,5)(6,8)(9,12,11,10,13)>,< 10, 6, G!(1,3)(2,8)(4,5)(6,7)(9,10,12,13,11)>,< 10, 6, G!(1,3)(2,8)(4,5)(6,7)(9,12,11,10,13)>,< 10, 6, G!(2,6)(7,8)(9,10,12,13,11)>,< 10, 6, G!(2,6)(7,8)(9,11,13,12,10)>,< 10, 6, G!(2,6)(7,8)(9,13,10,11,12)>,< 10, 6, G!(2,6)(7,8)(9,12,11,10,13)>,< 15, 32, G!(3,5,4)(6,8,7)(9,10,12,13,11)>,< 15, 32, G!(3,4,5)(6,7,8)(9,12,11,10,13)>,< 15, 32, G!(3,5,4)(6,8,7)(9,11,13,12,10)>,< 15, 32, G!(3,5,4)(6,8,7)(9,12,11,10,13)>]); 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 0, -1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,0,2,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.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 |2,2,2,2,2,0,2,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,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(15: Sparse := true);
S := [ K |2,2,2,2,2,0,-1,0,0,0,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^7+K.1^-7,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |2,2,2,2,2,0,-1,0,0,0,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^7+K.1^-7,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |2,2,2,2,2,0,-1,0,0,0,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^4+K.1^-4,K.1^7+K.1^-7,K.1+K.1^-1,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |2,2,2,2,2,0,-1,0,0,0,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^7+K.1^-7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, -1, 3, -1, 1, 0, -1, -1, 1, 3, 3, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, 3, -1, -1, 1, 0, -1, 1, -1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -1, 1, 0, 1, -1, -1, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, -1, 3, -1, -1, 0, 1, 1, -1, 3, 3, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, 3, -1, -1, -1, 0, 1, -1, 1, 3, 3, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -1, -1, 0, -1, 1, 1, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, -2, -2, 2, 0, 0, 0, 0, 0, 6, 6, -2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,-2,6,-2,0,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,-2,6,-2,0,0,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,6,-2,-2,0,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,6,-2,-2,0,0,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,-2,-2,-2,0,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,-2,-2,-2,0,0,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,-2,-2,2,0,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2+3*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,1+4*K.1+K.1^2+K.1^-2,-3-4*K.1-3*K.1^2-3*K.1^-2,3*K.1^2-K.1^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,-2,-2,2,0,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,3*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-3-4*K.1-3*K.1^2-3*K.1^-2,1+4*K.1+K.1^2+K.1^-2,-1*K.1^2+3*K.1^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,-2,-2,2,0,0,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-3-4*K.1-3*K.1^2-3*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2+3*K.1^-2,3*K.1^2-K.1^-2,1+4*K.1+K.1^2+K.1^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,-2,-2,2,0,0,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,1+4*K.1+K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,3*K.1^2-K.1^-2,-1*K.1^2+3*K.1^-2,-3-4*K.1-3*K.1^2-3*K.1^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_480_1201:= KnownIrreducibles(CR);