/* Group 3960.o downloaded from the LMFDB on 19 November 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< 14 | (1,2,3,5,4)(6,9,8,10,11)(12,13), (2,4,7)(3,6,9)(5,8,10)(13,14) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_3960_o := rec< RF |  
Agroup := true,
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, 3, G!(12,14)>,< 2, 55, G!(1,9)(3,6)(4,8)(7,10)>,< 2, 165, G!(1,4)(2,8)(3,7)(5,6)(13,14)>,< 3, 2, G!(12,13,14)>,< 3, 110, G!(2,5,3)(6,7,8)(9,10,11)>,< 3, 220, G!(1,6,7)(2,11,5)(3,10,9)(12,14,13)>,< 5, 132, G!(1,10,8,5,11)(2,4,6,7,3)>,< 5, 132, G!(1,8,11,10,5)(2,6,3,4,7)>,< 6, 110, G!(2,10)(3,8)(4,11)(7,9)(12,13,14)>,< 6, 110, G!(1,7,3,9,2,11)(4,5)(6,10,8)>,< 6, 220, G!(1,10,6,9,7,3)(2,5,11)(4,8)(12,13,14)>,< 6, 330, G!(1,4)(2,7,5,8,3,6)(9,11,10)(13,14)>,< 6, 330, G!(1,2,11)(4,8,9)(5,7,6)(12,14)>,< 10, 396, G!(1,2,7,9,10)(3,11,4,8,5)(12,14)>,< 10, 396, G!(1,9,2,10,7)(3,8,11,5,4)(12,14)>,< 11, 60, G!(1,2,3,11,6,10,5,8,9,4,7)>,< 11, 60, G!(1,7,4,9,8,5,10,6,11,3,2)>,< 15, 264, G!(1,8,11,10,5)(2,6,3,4,7)(12,14,13)>,< 15, 264, G!(1,11,5,8,10)(2,3,7,6,4)(12,13,14)>,< 22, 180, G!(1,5,2,8,3,9,11,4,6,7,10)(12,14)>,< 22, 180, G!(1,10,7,6,4,11,9,3,8,2,5)(12,14)>,< 33, 120, G!(1,5,3,10,4,6,8,2,7,9,11)(12,14,13)>,< 33, 120, G!(1,11,9,7,2,8,6,4,10,3,5)(12,13,14)>]); 
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!\[2, 0, 2, 0, -1, 2, -1, 2, 2, -1, 2, -1, 0, 0, 0, 0, 2, 2, -1, -1, 0, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |5,5,1,1,5,-1,-1,0,0,1,1,1,1,-1,0,0,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2,K.1+K.1^3+K.1^4+K.1^5+K.1^-2,0,0,K.1+K.1^3+K.1^4+K.1^5+K.1^-2,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2,K.1+K.1^3+K.1^4+K.1^5+K.1^-2,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |5,5,1,1,5,-1,-1,0,0,1,1,1,1,-1,0,0,K.1+K.1^3+K.1^4+K.1^5+K.1^-2,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2,0,0,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2,K.1+K.1^3+K.1^4+K.1^5+K.1^-2,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2,K.1+K.1^3+K.1^4+K.1^5+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |5,-5,1,-1,5,-1,-1,0,0,1,1,1,-1,1,0,0,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2,K.1+K.1^3+K.1^4+K.1^5+K.1^-2,0,0,-1*K.1-K.1^3-K.1^4-K.1^5-K.1^-2,1+K.1+K.1^3+K.1^4+K.1^5+K.1^-2,K.1+K.1^3+K.1^4+K.1^5+K.1^-2,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |5,-5,1,-1,5,-1,-1,0,0,1,1,1,-1,1,0,0,K.1+K.1^3+K.1^4+K.1^5+K.1^-2,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2,0,0,1+K.1+K.1^3+K.1^4+K.1^5+K.1^-2,-1*K.1-K.1^3-K.1^4-K.1^5-K.1^-2,-1-K.1-K.1^3-K.1^4-K.1^5-K.1^-2,K.1+K.1^3+K.1^4+K.1^5+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[10, 10, 2, 2, 10, 1, 1, 0, 0, 2, -1, -1, -1, 1, 0, 0, -1, -1, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[10, -10, 2, -2, 10, 1, 1, 0, 0, 2, -1, -1, 1, -1, 0, 0, -1, -1, 0, 0, 1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[10, 10, -2, -2, 10, 1, 1, 0, 0, -2, 1, 1, 1, 1, 0, 0, -1, -1, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[10, -10, -2, 2, 10, 1, 1, 0, 0, -2, 1, 1, -1, -1, 0, 0, -1, -1, 0, 0, 1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,2,0,-5,-2,1,0,0,-1,2,-1,0,0,0,0,-2-2*K.1-2*K.1^3-2*K.1^4-2*K.1^5-2*K.1^-2,2*K.1+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^-2,0,0,0,0,-1*K.1-K.1^3-K.1^4-K.1^5-K.1^-2,1+K.1+K.1^3+K.1^4+K.1^5+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,2,0,-5,-2,1,0,0,-1,2,-1,0,0,0,0,2*K.1+2*K.1^3+2*K.1^4+2*K.1^5+2*K.1^-2,-2-2*K.1-2*K.1^3-2*K.1^4-2*K.1^5-2*K.1^-2,0,0,0,0,1+K.1+K.1^3+K.1^4+K.1^5+K.1^-2,-1*K.1-K.1^3-K.1^4-K.1^5-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[11, 11, -1, -1, 11, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[11, -11, -1, 1, 11, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,12,0,0,12,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,1,1,K.1+K.1^-1,K.1^2+K.1^-2,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,12,0,0,12,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,1,1,K.1^2+K.1^-2,K.1+K.1^-1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,-12,0,0,12,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,1,1,K.1+K.1^-1,K.1^2+K.1^-2,-1,-1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,-12,0,0,12,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,1,1,K.1^2+K.1^-2,K.1+K.1^-1,-1,-1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[20, 0, 4, 0, -10, 2, -1, 0, 0, -2, -2, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[20, 0, -4, 0, -10, 2, -1, 0, 0, 2, 2, -1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[22, 0, -2, 0, -11, -2, 1, 2, 2, 1, -2, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |24,0,0,0,-12,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,2,2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |24,0,0,0,-12,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,2,2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_3960_o:= KnownIrreducibles(CR);