/* Group 90720.g downloaded from the LMFDB on 29 December 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 | (1,3)(2,4,6,5,7,8)(10,12,14,11,13), (1,2,3,5,6,4)(8,9)(10,11,12) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_90720_g := 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, 15, G!(10,13)(12,14)>,< 2, 63, G!(2,9)(3,4)(5,8)(6,7)>,< 2, 945, G!(2,3)(4,9)(5,7)(6,8)(11,13)(12,14)>,< 3, 20, G!(11,14,12)>,< 3, 56, G!(1,9,4)(2,8,7)(3,5,6)>,< 3, 84, G!(2,7,4)(3,5,9)>,< 3, 84, G!(2,4,7)(3,9,5)>,< 3, 1120, G!(1,5,9)(2,4,6)(3,7,8)(10,12,11)>,< 3, 1680, G!(2,6,3)(4,9,7)(10,14,12)>,< 3, 1680, G!(2,3,6)(4,7,9)(10,12,14)>,< 5, 12, G!(10,12,14,13,11)>,< 5, 12, G!(10,14,11,12,13)>,< 6, 252, G!(1,3)(2,6,5,4,7,9)>,< 6, 252, G!(1,3)(2,9,7,4,5,6)>,< 6, 840, G!(1,7,9)(2,5,3)(4,6,8)(10,13)(12,14)>,< 6, 1260, G!(1,4)(2,5)(6,9)(7,8)(10,14,11)>,< 6, 1260, G!(2,8,5)(3,7,4)(10,14)(11,13)>,< 6, 1260, G!(2,5,8)(3,4,7)(10,14)(11,13)>,< 6, 3780, G!(2,9,7,3,4,5)(6,8)(11,13)(12,14)>,< 6, 3780, G!(2,5,4,3,7,9)(6,8)(11,13)(12,14)>,< 6, 5040, G!(2,4,6,9,3,7)(5,8)(10,12,14)>,< 6, 5040, G!(2,7,3,9,6,4)(5,8)(10,14,12)>,< 7, 216, G!(1,2,9,8,7,3,4)>,< 9, 168, G!(1,3,4,5,6,8,7,9,2)>,< 9, 168, G!(1,8,6,7,3,2,4,9,5)>,< 9, 168, G!(1,5,9,4,2,3,7,6,8)>,< 9, 3360, G!(1,5,7,8,9,6,4,2,3)(10,12,11)>,< 9, 3360, G!(1,3,7,9,5,2,4,6,8)(10,11,14)>,< 9, 3360, G!(1,8,6,4,2,5,9,7,3)(10,14,11)>,< 10, 756, G!(1,3)(2,4)(5,9)(6,7)(10,12,13,11,14)>,< 10, 756, G!(1,3)(2,4)(5,9)(6,7)(10,11,12,14,13)>,< 14, 3240, G!(1,4,7,5,3,2,8)(10,11)(13,14)>,< 15, 672, G!(1,7,5)(2,8,4)(3,9,6)(10,14,11,12,13)>,< 15, 672, G!(1,5,7)(2,4,8)(3,6,9)(10,11,13,14,12)>,< 15, 1008, G!(2,7,5)(4,6,9)(10,14,11,13,12)>,< 15, 1008, G!(2,5,7)(4,9,6)(10,12,13,11,14)>,< 15, 1008, G!(2,5,7)(4,9,6)(10,11,12,14,13)>,< 15, 1008, G!(2,7,5)(4,6,9)(10,13,14,12,11)>,< 18, 2520, G!(1,3,4,7,2,6,9,5,8)(10,13)(12,14)>,< 18, 2520, G!(1,7,3,6,5,9,4,8,2)(10,11)(12,14)>,< 18, 2520, G!(1,2,8,4,9,5,6,3,7)(10,11)(12,14)>,< 21, 4320, G!(1,7,6,4,2,5,8)(11,14,12)>,< 30, 3024, G!(1,3)(2,9,7,4,5,6)(10,13,14,12,11)>,< 30, 3024, G!(1,3)(2,6,5,4,7,9)(10,11,12,14,13)>,< 30, 3024, G!(1,3)(2,9,7,4,5,6)(10,14,11,13,12)>,< 30, 3024, G!(1,3)(2,6,5,4,7,9)(10,12,13,11,14)>,< 35, 2592, G!(1,8,4,9,3,2,7)(10,14,12,11,13)>,< 35, 2592, G!(1,4,3,7,8,9,2)(10,12,13,14,11)>,< 45, 2016, G!(1,4,6,7,2,3,5,8,9)(10,11,13,14,12)>,< 45, 2016, G!(1,6,2,5,9,4,7,3,8)(10,13,12,11,14)>,< 45, 2016, G!(1,6,3,4,5,8,7,2,9)(10,11,12,13,14)>,< 45, 2016, G!(1,9,2,7,8,5,4,3,6)(10,14,13,12,11)>,< 45, 2016, G!(1,3,5,7,9,6,4,8,2)(10,12,14,11,13)>,< 45, 2016, G!(1,2,8,4,6,9,7,5,3)(10,13,11,14,12)>]); 
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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,1,K.1^-1,K.1,1,K.1,K.1^-1,1,1,K.1,K.1^-1,1,1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,1,1,K.1,K.1^-1,1,K.1,K.1^-1,1,1,1,1,1,K.1^-1,K.1,K.1^-1,K.1,1,K.1^-1,K.1,1,K.1,K.1^-1,K.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(3: Sparse := true);
S := [ K |1,1,1,1,1,1,K.1,K.1^-1,1,K.1^-1,K.1,1,1,K.1^-1,K.1,1,1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,1,1,K.1^-1,K.1,1,K.1^-1,K.1,1,1,1,1,1,K.1,K.1^-1,K.1,K.1^-1,1,K.1,K.1^-1,1,K.1^-1,K.1,K.1^-1,K.1,1,1,1,1,K.1,K.1^-1,K.1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |3,-1,3,-1,0,3,3,3,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,3,3,-1,0,-1,-1,-1,-1,0,0,3,3,3,3,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1,-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,-1,-1,-1,0,-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-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-K.1^-1,-1*K.1^2-K.1^-2,-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 |3,-1,3,-1,0,3,3,3,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,3,3,-1,0,-1,-1,-1,-1,0,0,3,3,3,3,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-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,-1,-1,-1,0,-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.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-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(15: Sparse := true);
S := [ K |3,-1,3,-1,0,3,3*K.1^-5,3*K.1^5,0,0,0,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,3*K.1^5,3*K.1^-5,-1,0,-1*K.1^5,-1*K.1^-5,-1*K.1^5,-1*K.1^-5,0,0,3,3,3*K.1^5,3*K.1^-5,0,0,0,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,-1,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1*K.1-K.1^4,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1+K.1+K.1^4-K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1,-1*K.1^-5,-1*K.1^5,0,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1+K.1+K.1^4-K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1*K.1-K.1^4,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,-1+K.1+K.1^4-K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1*K.1-K.1^4,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,-1,3,-1,0,3,3*K.1^5,3*K.1^-5,0,0,0,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,3*K.1^-5,3*K.1^5,-1,0,-1*K.1^-5,-1*K.1^5,-1*K.1^-5,-1*K.1^5,0,0,3,3,3*K.1^-5,3*K.1^5,0,0,0,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,-1,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1+K.1+K.1^4-K.1^5,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1-K.1^4,-1,-1*K.1^5,-1*K.1^-5,0,-1+K.1+K.1^4-K.1^5,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1-K.1^4,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1-K.1^4,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1+K.1+K.1^4-K.1^5]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,-1,3,-1,0,3,3*K.1^-5,3*K.1^5,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,3*K.1^5,3*K.1^-5,-1,0,-1*K.1^5,-1*K.1^-5,-1*K.1^5,-1*K.1^-5,0,0,3,3,3*K.1^5,3*K.1^-5,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,-1+K.1+K.1^4-K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1*K.1-K.1^4,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1,-1*K.1^-5,-1*K.1^5,0,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1*K.1-K.1^4,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1+K.1+K.1^4-K.1^5,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1*K.1-K.1^4,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1+K.1+K.1^4-K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,-1,3,-1,0,3,3*K.1^5,3*K.1^-5,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,3*K.1^-5,3*K.1^5,-1,0,-1*K.1^-5,-1*K.1^5,-1*K.1^-5,-1*K.1^5,0,0,3,3,3*K.1^-5,3*K.1^5,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1-K.1^4,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1+K.1+K.1^4-K.1^5,-1,-1*K.1^5,-1*K.1^-5,0,-1*K.1-K.1^4,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1+K.1+K.1^4-K.1^5,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1+K.1+K.1^4-K.1^5,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1-K.1^4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 0, 4, 0, 1, 4, 4, 4, 1, 1, 1, -1, -1, 4, 4, 0, 1, 0, 0, 0, 0, 1, 1, 4, 4, 4, 4, 1, 1, 1, -1, -1, 0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,4,0,1,4,4*K.1^-1,4*K.1,1,K.1,K.1^-1,-1,-1,4*K.1,4*K.1^-1,0,1,0,0,0,0,K.1^-1,K.1,4,4,4*K.1,4*K.1^-1,1,K.1,K.1^-1,-1,-1,0,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,0,0,0,1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1,-1,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,0,4,0,1,4,4*K.1,4*K.1^-1,1,K.1^-1,K.1,-1,-1,4*K.1^-1,4*K.1,0,1,0,0,0,0,K.1,K.1^-1,4,4,4*K.1^-1,4*K.1,1,K.1^-1,K.1,-1,-1,0,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,0,0,0,1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1,-1,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[5, 1, 5, 1, -1, 5, 5, 5, -1, -1, -1, 0, 0, 5, 5, 1, -1, 1, 1, 1, 1, -1, -1, 5, 5, 5, 5, -1, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |5,1,5,1,-1,5,5*K.1^-1,5*K.1,-1,-1*K.1,-1*K.1^-1,0,0,5*K.1,5*K.1^-1,1,-1,K.1,K.1^-1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,5,5,5*K.1,5*K.1^-1,-1,-1*K.1,-1*K.1^-1,0,0,1,0,0,0,0,0,0,1,K.1^-1,K.1,-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |5,1,5,1,-1,5,5*K.1,5*K.1^-1,-1,-1*K.1^-1,-1*K.1,0,0,5*K.1^-1,5*K.1,1,-1,K.1^-1,K.1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,5,5,5*K.1^-1,5*K.1,-1,-1*K.1^-1,-1*K.1,0,0,1,0,0,0,0,0,0,1,K.1,K.1^-1,-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[7, 7, -1, -1, 7, -2, 1, 1, -2, 1, 1, 7, 7, -1, -1, -2, -1, 1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 1, 1, 1, -1, -1, 0, -2, -2, 1, 1, 1, 1, 1, 1, 1, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,7,-1,-1,7,-2,K.1^-1,K.1,-2,K.1,K.1^-1,7,7,-1*K.1,-1*K.1^-1,-2,-1,K.1,K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,0,1,K.1,K.1^-1,1,K.1,K.1^-1,-1,-1,0,-2,-2,K.1^-1,K.1,K.1^-1,K.1,1,K.1^-1,K.1,0,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,0,0,1,1,K.1^-1,K.1,K.1^-1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,7,-1,-1,7,-2,K.1,K.1^-1,-2,K.1^-1,K.1,7,7,-1*K.1^-1,-1*K.1,-2,-1,K.1^-1,K.1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,0,1,K.1^-1,K.1,1,K.1^-1,K.1,-1,-1,0,-2,-2,K.1,K.1^-1,K.1,K.1^-1,1,K.1,K.1^-1,0,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,0,0,1,1,K.1,K.1^-1,K.1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, 8, 0, 0, 8, -1, 2, 2, -1, 2, 2, 8, 8, 0, 0, -1, 0, 2, 2, 0, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, 0, 0, 1, -1, -1, 2, 2, 2, 2, -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(3: Sparse := true);
S := [ K |8,8,0,0,8,-1,2*K.1^-1,2*K.1,-1,2*K.1,2*K.1^-1,8,8,0,0,-1,0,2*K.1,2*K.1^-1,0,0,0,0,1,-1,-1*K.1,-1*K.1^-1,-1,-1*K.1,-1*K.1^-1,0,0,1,-1,-1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,-1,-1*K.1^-1,-1*K.1,1,0,0,0,0,1,1,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |8,8,0,0,8,-1,2*K.1,2*K.1^-1,-1,2*K.1^-1,2*K.1,8,8,0,0,-1,0,2*K.1^-1,2*K.1,0,0,0,0,1,-1,-1*K.1^-1,-1*K.1,-1,-1*K.1^-1,-1*K.1,0,0,1,-1,-1,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,-1,-1*K.1,-1*K.1^-1,1,0,0,0,0,1,1,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[21, 21, -3, -3, 21, 3, 0, 0, 3, 0, 0, 21, 21, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 3, 3, 0, 0, 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; 
K := CyclotomicField(5: Sparse := true);
S := [ K |21,-7,-3,1,0,-6,3,3,0,0,0,-7*K.1-7*K.1^-1,-7*K.1^2-7*K.1^-2,-3,-3,2,0,-1,-1,1,1,0,0,0,3,3,3,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,2*K.1^2+2*K.1^-2,2*K.1+2*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,-1,-1,0,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,0,0,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |21,-7,-3,1,0,-6,3,3,0,0,0,-7*K.1^2-7*K.1^-2,-7*K.1-7*K.1^-1,-3,-3,2,0,-1,-1,1,1,0,0,0,3,3,3,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,2*K.1+2*K.1^-1,2*K.1^2+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,-1,-1,-1,0,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,0,0,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |21,-7,-3,1,0,-6,3*K.1^-5,3*K.1^5,0,0,0,-7*K.1^3-7*K.1^-3,-7*K.1^6-7*K.1^-6,-3*K.1^5,-3*K.1^-5,2,0,-1*K.1^5,-1*K.1^-5,K.1^5,K.1^-5,0,0,0,3,3*K.1^5,3*K.1^-5,0,0,0,K.1^3+K.1^-3,K.1^6+K.1^-6,0,2*K.1^6+2*K.1^-6,2*K.1^3+2*K.1^-3,-1*K.1-K.1^4,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1+K.1+K.1^4-K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1,-1*K.1^-5,-1*K.1^5,0,-1+K.1+K.1^2-K.1^3+K.1^4-K.1^5+K.1^7,1-K.1-K.1^4+K.1^5,1-K.1-K.1^2+K.1^3-K.1^4-K.1^7,K.1+K.1^4,0,0,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,-1+K.1+K.1^4-K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1*K.1-K.1^4,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |21,-7,-3,1,0,-6,3*K.1^5,3*K.1^-5,0,0,0,-7*K.1^3-7*K.1^-3,-7*K.1^6-7*K.1^-6,-3*K.1^-5,-3*K.1^5,2,0,-1*K.1^-5,-1*K.1^5,K.1^-5,K.1^5,0,0,0,3,3*K.1^-5,3*K.1^5,0,0,0,K.1^3+K.1^-3,K.1^6+K.1^-6,0,2*K.1^6+2*K.1^-6,2*K.1^3+2*K.1^-3,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1+K.1+K.1^4-K.1^5,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1-K.1^4,-1,-1*K.1^5,-1*K.1^-5,0,1-K.1-K.1^4+K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4-K.1^5+K.1^7,K.1+K.1^4,1-K.1-K.1^2+K.1^3-K.1^4-K.1^7,0,0,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1-K.1^4,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1+K.1+K.1^4-K.1^5]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |21,-7,-3,1,0,-6,3*K.1^-5,3*K.1^5,0,0,0,-7*K.1^6-7*K.1^-6,-7*K.1^3-7*K.1^-3,-3*K.1^5,-3*K.1^-5,2,0,-1*K.1^5,-1*K.1^-5,K.1^5,K.1^-5,0,0,0,3,3*K.1^5,3*K.1^-5,0,0,0,K.1^6+K.1^-6,K.1^3+K.1^-3,0,2*K.1^3+2*K.1^-3,2*K.1^6+2*K.1^-6,-1+K.1+K.1^4-K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1*K.1-K.1^4,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1,-1*K.1^-5,-1*K.1^5,0,1-K.1-K.1^2+K.1^3-K.1^4-K.1^7,K.1+K.1^4,-1+K.1+K.1^2-K.1^3+K.1^4-K.1^5+K.1^7,1-K.1-K.1^4+K.1^5,0,0,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1*K.1-K.1^4,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1+K.1+K.1^4-K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |21,-7,-3,1,0,-6,3*K.1^5,3*K.1^-5,0,0,0,-7*K.1^6-7*K.1^-6,-7*K.1^3-7*K.1^-3,-3*K.1^-5,-3*K.1^5,2,0,-1*K.1^-5,-1*K.1^5,K.1^-5,K.1^5,0,0,0,3,3*K.1^-5,3*K.1^5,0,0,0,K.1^6+K.1^-6,K.1^3+K.1^-3,0,2*K.1^3+2*K.1^-3,2*K.1^6+2*K.1^-6,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1-K.1^4,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1+K.1+K.1^4-K.1^5,-1,-1*K.1^5,-1*K.1^-5,0,K.1+K.1^4,1-K.1-K.1^2+K.1^3-K.1^4-K.1^7,1-K.1-K.1^4+K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4-K.1^5+K.1^7,0,0,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,-1+K.1+K.1^2-K.1^3+K.1^4+K.1^7,-1+K.1+K.1^4-K.1^5,1-K.1-K.1^2+K.1^3-K.1^4+K.1^5-K.1^7,-1*K.1-K.1^4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |24,-8,0,0,0,-3,6,6,0,0,0,-8*K.1-8*K.1^-1,-8*K.1^2-8*K.1^-2,0,0,1,0,-2,-2,0,0,0,0,3,-3,-3,-3,0,0,0,0,0,-1,K.1^2+K.1^-2,K.1+K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,1,1,1,0,0,0,0,0,-1*K.1-K.1^-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,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 |24,-8,0,0,0,-3,6,6,0,0,0,-8*K.1^2-8*K.1^-2,-8*K.1-8*K.1^-1,0,0,1,0,-2,-2,0,0,0,0,3,-3,-3,-3,0,0,0,0,0,-1,K.1+K.1^-1,K.1^2+K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,1,1,1,0,0,0,0,0,-1*K.1^2-K.1^-2,-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+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 |24,-8,0,0,0,-3,6*K.1^-5,6*K.1^5,0,0,0,-8*K.1^3-8*K.1^-3,-8*K.1^6-8*K.1^-6,0,0,1,0,-2*K.1^5,-2*K.1^-5,0,0,0,0,3,-3,-3*K.1^5,-3*K.1^-5,0,0,0,0,0,-1,K.1^6+K.1^-6,K.1^3+K.1^-3,-2*K.1-2*K.1^4,2-2*K.1-2*K.1^2+2*K.1^3-2*K.1^4+2*K.1^5-2*K.1^7,-2+2*K.1+2*K.1^4-2*K.1^5,-2+2*K.1+2*K.1^2-2*K.1^3+2*K.1^4+2*K.1^7,1,K.1^-5,K.1^5,0,0,0,0,0,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,1-K.1-K.1^4+K.1^5,1-K.1-K.1^2+K.1^3-K.1^4-K.1^7,K.1+K.1^4,-1+K.1+K.1^2-K.1^3+K.1^4-K.1^5+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |24,-8,0,0,0,-3,6*K.1^5,6*K.1^-5,0,0,0,-8*K.1^3-8*K.1^-3,-8*K.1^6-8*K.1^-6,0,0,1,0,-2*K.1^-5,-2*K.1^5,0,0,0,0,3,-3,-3*K.1^-5,-3*K.1^5,0,0,0,0,0,-1,K.1^6+K.1^-6,K.1^3+K.1^-3,-2+2*K.1+2*K.1^2-2*K.1^3+2*K.1^4+2*K.1^7,-2+2*K.1+2*K.1^4-2*K.1^5,2-2*K.1-2*K.1^2+2*K.1^3-2*K.1^4+2*K.1^5-2*K.1^7,-2*K.1-2*K.1^4,1,K.1^5,K.1^-5,0,0,0,0,0,-1*K.1^3-K.1^-3,-1*K.1^6-K.1^-6,K.1^3+K.1^-3,K.1^6+K.1^-6,-1+K.1+K.1^2-K.1^3+K.1^4-K.1^5+K.1^7,K.1+K.1^4,1-K.1-K.1^2+K.1^3-K.1^4-K.1^7,1-K.1-K.1^4+K.1^5]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |24,-8,0,0,0,-3,6*K.1^-5,6*K.1^5,0,0,0,-8*K.1^6-8*K.1^-6,-8*K.1^3-8*K.1^-3,0,0,1,0,-2*K.1^5,-2*K.1^-5,0,0,0,0,3,-3,-3*K.1^5,-3*K.1^-5,0,0,0,0,0,-1,K.1^3+K.1^-3,K.1^6+K.1^-6,-2+2*K.1+2*K.1^4-2*K.1^5,-2+2*K.1+2*K.1^2-2*K.1^3+2*K.1^4+2*K.1^7,-2*K.1-2*K.1^4,2-2*K.1-2*K.1^2+2*K.1^3-2*K.1^4+2*K.1^5-2*K.1^7,1,K.1^-5,K.1^5,0,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,K.1+K.1^4,-1+K.1+K.1^2-K.1^3+K.1^4-K.1^5+K.1^7,1-K.1-K.1^4+K.1^5,1-K.1-K.1^2+K.1^3-K.1^4-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |24,-8,0,0,0,-3,6*K.1^5,6*K.1^-5,0,0,0,-8*K.1^6-8*K.1^-6,-8*K.1^3-8*K.1^-3,0,0,1,0,-2*K.1^-5,-2*K.1^5,0,0,0,0,3,-3,-3*K.1^-5,-3*K.1^5,0,0,0,0,0,-1,K.1^3+K.1^-3,K.1^6+K.1^-6,2-2*K.1-2*K.1^2+2*K.1^3-2*K.1^4+2*K.1^5-2*K.1^7,-2*K.1-2*K.1^4,-2+2*K.1+2*K.1^2-2*K.1^3+2*K.1^4+2*K.1^7,-2+2*K.1+2*K.1^4-2*K.1^5,1,K.1^5,K.1^-5,0,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^3-K.1^-3,K.1^6+K.1^-6,K.1^3+K.1^-3,1-K.1-K.1^2+K.1^3-K.1^4-K.1^7,1-K.1-K.1^4+K.1^5,-1+K.1+K.1^2-K.1^3+K.1^4-K.1^5+K.1^7,K.1+K.1^4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[27, 27, 3, 3, 27, 0, 0, 0, 0, 0, 0, 27, 27, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, 3, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[28, 0, -4, 0, 7, -8, 4, 4, -2, 1, 1, -7, -7, -4, -4, 0, -1, 0, 0, 0, 0, -1, -1, 0, 4, 4, 4, 1, 1, 1, 1, 1, 0, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |28,0,-4,0,7,-8,4*K.1^-1,4*K.1,-2,K.1,K.1^-1,-7,-7,-4*K.1,-4*K.1^-1,0,-1,0,0,0,0,-1*K.1^-1,-1*K.1,0,4,4*K.1,4*K.1^-1,1,K.1,K.1^-1,1,1,0,2,2,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,0,0,0,0,K.1,K.1^-1,K.1,K.1^-1,0,0,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |28,0,-4,0,7,-8,4*K.1,4*K.1^-1,-2,K.1^-1,K.1,-7,-7,-4*K.1^-1,-4*K.1,0,-1,0,0,0,0,-1*K.1,-1*K.1^-1,0,4,4*K.1^-1,4*K.1,1,K.1^-1,K.1,1,1,0,2,2,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,0,0,0,0,K.1^-1,K.1,K.1^-1,K.1,0,0,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[32, 0, 0, 0, 8, -4, 8, 8, -1, 2, 2, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, -1, -1, -1, 0, 0, 0, 1, 1, -2, -2, -2, -2, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |32,0,0,0,8,-4,8*K.1^-1,8*K.1,-1,2*K.1,2*K.1^-1,-8,-8,0,0,0,0,0,0,0,0,0,0,4,-4,-4*K.1,-4*K.1^-1,-1,-1*K.1,-1*K.1^-1,0,0,0,1,1,-2*K.1^-1,-2*K.1,-2*K.1^-1,-2*K.1,0,0,0,1,0,0,0,0,-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(3: Sparse := true);
S := [ K |32,0,0,0,8,-4,8*K.1,8*K.1^-1,-1,2*K.1^-1,2*K.1,-8,-8,0,0,0,0,0,0,0,0,0,0,4,-4,-4*K.1^-1,-4*K.1,-1,-1*K.1^-1,-1*K.1,0,0,0,1,1,-2*K.1,-2*K.1^-1,-2*K.1,-2*K.1^-1,0,0,0,1,0,0,0,0,-1,-1,1,1,K.1,K.1^-1,K.1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[35, 7, -5, -1, -7, -10, 5, 5, 2, -1, -1, 0, 0, -5, -5, -2, 1, 1, 1, -1, -1, 1, 1, 0, 5, 5, 5, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |35,7,-5,-1,-7,-10,5*K.1^-1,5*K.1,2,-1*K.1,-1*K.1^-1,0,0,-5*K.1,-5*K.1^-1,-2,1,K.1,K.1^-1,-1*K.1,-1*K.1^-1,K.1^-1,K.1,0,5,5*K.1,5*K.1^-1,-1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,0,1,K.1^-1,K.1,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |35,7,-5,-1,-7,-10,5*K.1,5*K.1^-1,2,-1*K.1^-1,-1*K.1,0,0,-5*K.1^-1,-5*K.1,-2,1,K.1^-1,K.1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,5,5*K.1^-1,5*K.1,-1,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0,0,1,K.1,K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[40, 8, 0, 0, -8, -5, 10, 10, 1, -2, -2, 0, 0, 0, 0, -1, 0, 2, 2, 0, 0, 0, 0, 5, -5, -5, -5, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |40,8,0,0,-8,-5,10*K.1^-1,10*K.1,1,-2*K.1,-2*K.1^-1,0,0,0,0,-1,0,2*K.1,2*K.1^-1,0,0,0,0,5,-5,-5*K.1,-5*K.1^-1,1,K.1,K.1^-1,0,0,1,0,0,0,0,0,0,-1,-1*K.1^-1,-1*K.1,-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |40,8,0,0,-8,-5,10*K.1,10*K.1^-1,1,-2*K.1^-1,-2*K.1,0,0,0,0,-1,0,2*K.1^-1,2*K.1,0,0,0,0,5,-5,-5*K.1^-1,-5*K.1,1,K.1^-1,K.1,0,0,1,0,0,0,0,0,0,-1,-1*K.1,-1*K.1^-1,-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |63,-21,-9,3,0,9,0,0,0,0,0,-21*K.1-21*K.1^-1,-21*K.1^2-21*K.1^-2,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |63,-21,-9,3,0,9,0,0,0,0,0,-21*K.1^2-21*K.1^-2,-21*K.1-21*K.1^-1,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |81,-27,9,-3,0,0,0,0,0,0,0,-27*K.1-27*K.1^-1,-27*K.1^2-27*K.1^-2,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |81,-27,9,-3,0,0,0,0,0,0,0,-27*K.1^2-27*K.1^-2,-27*K.1-27*K.1^-1,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[84, 0, -12, 0, 21, 12, 0, 0, 3, 0, 0, -21, -21, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, -3, -3, 0, 0, 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!\[105, 21, -15, -3, -21, 15, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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!\[108, 0, 12, 0, 27, 0, 0, 0, 0, 0, 0, -27, -27, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[135, 27, 15, 3, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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_90720_g:= KnownIrreducibles(CR);