/* Group 12960.bb downloaded from the LMFDB on 23 July 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< 12 | (1,2,3,4,5)(7,8)(9,10,11,12), (1,3)(5,6)(7,9,10,8)(11,12) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_12960_bb := 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, 9, G!(7,10)(9,11)>,< 2, 45, G!(2,5)(3,6)>,< 2, 405, G!(1,2)(5,6)(7,12)(9,11)>,< 3, 4, G!(8,11,9)>,< 3, 4, G!(7,10,12)(8,9,11)>,< 3, 40, G!(1,2,5)>,< 3, 40, G!(1,6,3)(2,5,4)>,< 3, 160, G!(3,4,5)(7,12,10)(8,11,9)>,< 3, 160, G!(1,4,5)(2,3,6)(7,12,10)>,< 3, 160, G!(2,6,4)(8,11,9)>,< 3, 160, G!(1,4,6)(2,3,5)(7,10,12)(8,11,9)>,< 4, 9, G!(7,11)(8,10,9,12)>,< 4, 9, G!(7,11)(8,12,9,10)>,< 4, 90, G!(1,6,5,4)(2,3)>,< 4, 405, G!(1,5)(3,4)(7,11,10,9)(8,12)>,< 4, 405, G!(1,5)(3,4)(7,9,10,11)(8,12)>,< 4, 810, G!(1,4)(2,6,5,3)(7,10)(8,11)>,< 4, 810, G!(1,6,2,5)(3,4)(7,9,12,11)(8,10)>,< 4, 810, G!(1,5,2,6)(3,4)(7,11,12,9)(8,10)>,< 5, 72, G!(1,5,3,6,2)>,< 5, 72, G!(1,3,2,5,6)>,< 6, 180, G!(1,5)(4,6)(7,10,12)>,< 6, 180, G!(1,5)(2,3)(7,12,10)(8,11,9)>,< 6, 360, G!(1,5,2)(7,12)(8,11)>,< 6, 360, G!(1,3,6)(2,4,5)(7,10)(8,9)>,< 10, 648, G!(1,6,3,5,4)(8,9)(10,12)>,< 10, 648, G!(1,5,6,4,3)(8,9)(10,12)>,< 12, 360, G!(1,4,5,6)(2,3)(7,12,10)>,< 12, 360, G!(1,3,5,2)(4,6)(7,10,12)(8,9,11)>,< 12, 360, G!(1,2,5)(7,11,12,8)(9,10)>,< 12, 360, G!(1,5,2)(7,8,12,11)(9,10)>,< 12, 360, G!(1,6,3)(2,5,4)(7,9,10,8)(11,12)>,< 12, 360, G!(1,3,6)(2,4,5)(7,8,10,9)(11,12)>,< 15, 288, G!(1,3,2,5,6)(8,9,11)>,< 15, 288, G!(1,2,6,3,5)(8,11,9)>,< 15, 288, G!(1,6,5,3,2)(7,10,12)(8,9,11)>,< 15, 288, G!(1,5,2,6,3)(7,12,10)(8,11,9)>,< 20, 648, G!(1,5,6,4,3)(7,11)(8,10,9,12)>,< 20, 648, G!(1,3,4,6,5)(7,11)(8,12,9,10)>,< 20, 648, G!(1,4,5,3,6)(7,11)(8,12,9,10)>,< 20, 648, G!(1,6,3,5,4)(7,11)(8,10,9,12)>]); 
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, 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, 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,-1*K.1,K.1,1,-1*K.1,K.1,-1,-1*K.1,K.1,1,1,1,1,-1,-1,-1,-1,1,1,-1*K.1,K.1,-1*K.1,K.1,1,1,1,1,-1*K.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,-1,1,1,1,1,1,1,1,1,K.1,-1*K.1,1,K.1,-1*K.1,-1,K.1,-1*K.1,1,1,1,1,-1,-1,-1,-1,1,1,K.1,-1*K.1,K.1,-1*K.1,1,1,1,1,K.1,-1*K.1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 0, 4, 0, -2, 1, 4, 4, 1, -2, -2, 1, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, -2, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 0, 4, 0, 1, -2, 4, 4, -2, 1, 1, -2, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 1, -2, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, 1, -2, -2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[5, 5, 1, 1, 5, 5, -1, 2, -1, 2, -1, 2, 5, 5, -1, 1, 1, -1, -1, -1, 0, 0, 1, 1, -1, 2, 0, 0, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[5, 5, 1, 1, 5, 5, 2, -1, 2, -1, 2, -1, 5, 5, -1, 1, 1, -1, -1, -1, 0, 0, 1, 1, 2, -1, 0, 0, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[5, 5, 1, 1, 5, 5, -1, 2, -1, 2, -1, 2, -5, -5, -1, -1, -1, -1, 1, 1, 0, 0, 1, 1, -1, 2, 0, 0, -1, -1, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[5, 5, 1, 1, 5, 5, 2, -1, 2, -1, 2, -1, -5, -5, -1, -1, -1, -1, 1, 1, 0, 0, 1, 1, 2, -1, 0, 0, -1, -1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |5,-5,1,-1,5,5,-1,2,-1,2,-1,2,-5*K.1,5*K.1,-1,-1*K.1,K.1,1,K.1,-1*K.1,0,0,1,1,1,-2,0,0,-1,-1,K.1,-1*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |5,-5,1,-1,5,5,-1,2,-1,2,-1,2,5*K.1,-5*K.1,-1,K.1,-1*K.1,1,-1*K.1,K.1,0,0,1,1,1,-2,0,0,-1,-1,-1*K.1,K.1,2*K.1,-2*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |5,-5,1,-1,5,5,2,-1,2,-1,2,-1,-5*K.1,5*K.1,-1,-1*K.1,K.1,1,K.1,-1*K.1,0,0,1,1,-2,1,0,0,-1,-1,-2*K.1,2*K.1,K.1,-1*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |5,-5,1,-1,5,5,2,-1,2,-1,2,-1,5*K.1,-5*K.1,-1,K.1,-1*K.1,1,-1*K.1,K.1,0,0,1,1,-2,1,0,0,-1,-1,2*K.1,-2*K.1,-1*K.1,K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,8,0,0,8,8,-1,-1,-1,-1,-1,-1,8,8,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,-1,-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,-1,-1,-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.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-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 |8,8,0,0,8,8,-1,-1,-1,-1,-1,-1,8,8,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,-1,-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,-1,-1,-1,-1,-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-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-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 |8,8,0,0,8,8,-1,-1,-1,-1,-1,-1,-8,-8,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,-1,-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,1,1,1,1,-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,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-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 |8,8,0,0,8,8,-1,-1,-1,-1,-1,-1,-8,-8,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,-1,-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,1,1,1,1,-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,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |8,-8,0,0,8,8,-1,-1,-1,-1,-1,-1,-8*K.1^5,8*K.1^5,0,0,0,0,0,0,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,0,0,1,1,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,0,0,K.1^5,-1*K.1^5,K.1^5,-1*K.1^5,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1*K.1^3-K.1^7,K.1^3+K.1^7,-1*K.1^3+K.1^5-K.1^7,K.1^3-K.1^5+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |8,-8,0,0,8,8,-1,-1,-1,-1,-1,-1,8*K.1^5,-8*K.1^5,0,0,0,0,0,0,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,0,0,1,1,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,0,0,-1*K.1^5,K.1^5,-1*K.1^5,K.1^5,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^3+K.1^7,-1*K.1^3-K.1^7,K.1^3-K.1^5+K.1^7,-1*K.1^3+K.1^5-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |8,-8,0,0,8,8,-1,-1,-1,-1,-1,-1,-8*K.1^5,8*K.1^5,0,0,0,0,0,0,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,0,0,1,1,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,0,0,K.1^5,-1*K.1^5,K.1^5,-1*K.1^5,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,K.1^3-K.1^5+K.1^7,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^7,-1*K.1^3-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |8,-8,0,0,8,8,-1,-1,-1,-1,-1,-1,8*K.1^5,-8*K.1^5,0,0,0,0,0,0,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,0,0,1,1,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,0,0,-1*K.1^5,K.1^5,-1*K.1^5,K.1^5,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^3+K.1^5-K.1^7,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^7,K.1^3+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[9, 9, 1, 1, 9, 9, 0, 0, 0, 0, 0, 0, 9, 9, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[9, 9, 1, 1, 9, 9, 0, 0, 0, 0, 0, 0, -9, -9, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |9,-9,1,-1,9,9,0,0,0,0,0,0,-9*K.1,9*K.1,1,-1*K.1,K.1,-1,-1*K.1,K.1,-1,-1,1,1,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,K.1,-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 |9,-9,1,-1,9,9,0,0,0,0,0,0,9*K.1,-9*K.1,1,K.1,-1*K.1,-1,K.1,-1*K.1,-1,-1,1,1,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1*K.1,K.1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[10, 10, -2, -2, 10, 10, 1, 1, 1, 1, 1, 1, 10, 10, 0, -2, -2, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[10, 10, -2, -2, 10, 10, 1, 1, 1, 1, 1, 1, -10, -10, 0, 2, 2, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |10,-10,-2,2,10,10,1,1,1,1,1,1,-10*K.1,10*K.1,0,2*K.1,-2*K.1,0,0,0,0,0,-2,-2,-1,-1,0,0,0,0,-1*K.1,K.1,-1*K.1,K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |10,-10,-2,2,10,10,1,1,1,1,1,1,10*K.1,-10*K.1,0,-2*K.1,2*K.1,0,0,0,0,0,-2,-2,-1,-1,0,0,0,0,K.1,-1*K.1,K.1,-1*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[20, 0, 4, 0, -10, 5, -4, 8, -1, -4, 2, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[20, 0, 4, 0, -10, 5, 8, -4, 2, 2, -4, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[20, 0, 4, 0, 5, -10, -4, 8, 2, 2, -1, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[20, 0, 4, 0, 5, -10, 8, -4, -4, -1, 2, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |32,0,0,0,-16,8,-4,-4,-1,2,2,-1,0,0,0,0,0,0,0,0,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*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 |32,0,0,0,-16,8,-4,-4,-1,2,2,-1,0,0,0,0,0,0,0,0,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+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 |32,0,0,0,8,-16,-4,-4,2,-1,-1,2,0,0,0,0,0,0,0,0,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+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 |32,0,0,0,8,-16,-4,-4,2,-1,-1,2,0,0,0,0,0,0,0,0,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[36, 0, 4, 0, -18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, -4, -2, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 2, 2, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[36, 0, 4, 0, 9, -18, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, -4, 1, -2, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -1, -1, 2, 2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[40, 0, -8, 0, -20, 10, 4, 4, 1, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 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!\[40, 0, -8, 0, 10, -20, 4, 4, -2, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_12960_bb:= KnownIrreducibles(CR);