/* Group 240.102 downloaded from the LMFDB on 16 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 */
GPC := PCGroup([6, -2, -3, -2, 2, -2, -5, 720, 49, 3350, 548, 374, 3171, 225, 543, 69, 88]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.3, GPC.4]); AssignNames(~GPC, ["a", "b", "c", "d", "d2", "d4"]);
GPerm := PermutationGroup< 21 | (1,2,5,8)(3,7,11,13)(4,6,9,15)(10,16,12,14), (17,18,19,20,21), (3,9,12)(4,10,11)(6,13,16)(7,14,15), (1,3,5,11)(2,6,8,15)(4,12,9,10)(7,16,13,14), (1,4,5,9)(2,7,8,13)(3,10,11,12)(6,14,15,16), (1,5)(2,8)(3,11)(4,9)(6,15)(7,13)(10,12)(14,16) >;
GLFp := MatrixGroup< 2, GF(31) | [[5, 19, 4, 3], [14, 4, 17, 16], [27, 0, 0, 27]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_240_102 := 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 := true,
supersolvable := false>; 

 
/* Character Table */
G:= GLFp;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Matrix(2, [1, 0, 0, 1])>,< 2, 1, Matrix(2, [30, 0, 0, 30])>,< 3, 8, Matrix(2, [0, 16, 29, 30])>,< 4, 6, Matrix(2, [14, 19, 19, 17])>,< 4, 12, Matrix(2, [4, 20, 10, 27])>,< 5, 1, Matrix(2, [4, 0, 0, 4])>,< 5, 1, Matrix(2, [8, 0, 0, 8])>,< 5, 1, Matrix(2, [16, 0, 0, 16])>,< 5, 1, Matrix(2, [2, 0, 0, 2])>,< 6, 8, Matrix(2, [1, 16, 29, 0])>,< 8, 6, Matrix(2, [29, 14, 14, 10])>,< 8, 6, Matrix(2, [21, 14, 14, 2])>,< 10, 1, Matrix(2, [29, 0, 0, 29])>,< 10, 1, Matrix(2, [15, 0, 0, 15])>,< 10, 1, Matrix(2, [23, 0, 0, 23])>,< 10, 1, Matrix(2, [27, 0, 0, 27])>,< 15, 8, Matrix(2, [23, 27, 16, 0])>,< 15, 8, Matrix(2, [0, 2, 23, 27])>,< 15, 8, Matrix(2, [0, 1, 27, 29])>,< 15, 8, Matrix(2, [15, 23, 1, 0])>,< 20, 6, Matrix(2, [19, 28, 28, 12])>,< 20, 6, Matrix(2, [6, 17, 17, 25])>,< 20, 6, Matrix(2, [24, 6, 6, 7])>,< 20, 6, Matrix(2, [28, 7, 7, 3])>,< 20, 12, Matrix(2, [1, 5, 18, 30])>,< 20, 12, Matrix(2, [3, 11, 9, 28])>,< 20, 12, Matrix(2, [1, 22, 1, 30])>,< 20, 12, Matrix(2, [4, 26, 4, 27])>,< 30, 8, Matrix(2, [0, 23, 1, 16])>,< 30, 8, Matrix(2, [0, 30, 4, 2])>,< 30, 8, Matrix(2, [0, 27, 16, 8])>,< 30, 8, Matrix(2, [0, 29, 8, 4])>,< 40, 6, Matrix(2, [1, 24, 24, 26])>,< 40, 6, Matrix(2, [4, 3, 3, 11])>,< 40, 6, Matrix(2, [4, 27, 7, 28])>,< 40, 6, Matrix(2, [8, 23, 14, 25])>,< 40, 6, Matrix(2, [6, 23, 14, 23])>,< 40, 6, Matrix(2, [3, 27, 7, 27])>,< 40, 6, Matrix(2, [5, 24, 24, 30])>,< 40, 6, Matrix(2, [2, 29, 19, 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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,1,K.1^-2,K.1,K.1^-1,K.1^2,1,1,1,K.1^2,K.1^-2,K.1^-1,K.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^-1,K.1,K.1^-2,K.1^2,K.1^-1,K.1,K.1^-2,K.1^2,K.1^-1,K.1^2,K.1,K.1,K.1^2,K.1^-2,K.1^-1,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,1,K.1^2,K.1^-1,K.1,K.1^-2,1,1,1,K.1^-2,K.1^2,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-1,K.1,K.1^-1,K.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,K.1^-2,K.1^-1,K.1^-1,K.1^-2,K.1^2,K.1,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,1,K.1^-1,K.1^-2,K.1^2,K.1,1,1,1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-1,K.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^-1,K.1,K.1^2,K.1^-2,K.1^-1,K.1,K.1^2,K.1,K.1^-2,K.1^-2,K.1,K.1^-1,K.1^2,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,1,K.1,K.1^2,K.1^-2,K.1^-1,1,1,1,K.1^-1,K.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^-1,K.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^-1,K.1^2,K.1^2,K.1^-1,K.1,K.1^-2,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,-1,K.1^-2,K.1,K.1^-1,K.1^2,1,-1,-1,K.1^2,K.1^-2,K.1^-1,K.1,K.1^-2,K.1^2,K.1,K.1^-1,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,-1,K.1^2,K.1^-1,K.1,K.1^-2,1,-1,-1,K.1^-2,K.1^2,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-1,K.1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,-1,K.1^-1,K.1^-2,K.1^2,K.1,1,-1,-1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-1,K.1,K.1^-2,K.1^2,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,-1,K.1,K.1^2,K.1^-2,K.1^-1,1,-1,-1,K.1^-1,K.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^-1,K.1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, -1, 2, 0, 2, 2, 2, 2, -1, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 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(8: Sparse := true);
S := [ K |2,-2,-1,0,0,2,2,2,2,1,-1*K.1-K.1^-1,K.1+K.1^-1,-2,-2,-2,-2,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-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(8: Sparse := true);
S := [ K |2,-2,-1,0,0,2,2,2,2,1,K.1+K.1^-1,-1*K.1-K.1^-1,-2,-2,-2,-2,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*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 |2,2,-1,2,0,2*K.1^-2,2*K.1,2*K.1^-1,2*K.1^2,-1,0,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,0,0,0,0,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-1,2,0,2*K.1^2,2*K.1^-1,2*K.1,2*K.1^-2,-1,0,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,0,0,0,0,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-1,2,0,2*K.1^-1,2*K.1^-2,2*K.1^2,2*K.1,-1,0,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,0,0,0,0,-1*K.1^2,-1*K.1^-2,-1*K.1^-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(5: Sparse := true);
S := [ K |2,2,-1,2,0,2*K.1,2*K.1^2,2*K.1^-2,2*K.1^-1,-1,0,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,0,0,0,0,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |2,-2,-1,0,0,-2*K.1^4,2*K.1^8,-2*K.1^12,2*K.1^16,1,-1*K.1^5-K.1^-5,K.1^5+K.1^-5,-2*K.1^16,2*K.1^4,2*K.1^12,-2*K.1^8,K.1^4,-1*K.1^16,-1*K.1^8,K.1^12,0,0,0,0,0,0,0,0,-1*K.1^12,K.1^8,-1*K.1^4,K.1^16,-1*K.1+K.1^5+K.1^7-K.1^9+K.1^13,K.1-K.1^11,K.1^3+K.1^13,-1*K.1^3-K.1^13,-1*K.1+K.1^11,-1*K.1^3+K.1^7-K.1^9-K.1^11+K.1^15,K.1-K.1^5-K.1^7+K.1^9-K.1^13,K.1^3-K.1^7+K.1^9+K.1^11-K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |2,-2,-1,0,0,2*K.1^16,-2*K.1^12,2*K.1^8,-2*K.1^4,1,-1*K.1^5-K.1^-5,K.1^5+K.1^-5,2*K.1^4,-2*K.1^16,-2*K.1^8,2*K.1^12,-1*K.1^16,K.1^4,K.1^12,-1*K.1^8,0,0,0,0,0,0,0,0,K.1^8,-1*K.1^12,K.1^16,-1*K.1^4,-1*K.1^3-K.1^13,K.1^3-K.1^7+K.1^9+K.1^11-K.1^15,K.1-K.1^5-K.1^7+K.1^9-K.1^13,-1*K.1+K.1^5+K.1^7-K.1^9+K.1^13,-1*K.1^3+K.1^7-K.1^9-K.1^11+K.1^15,-1*K.1+K.1^11,K.1^3+K.1^13,K.1-K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |2,-2,-1,0,0,-2*K.1^4,2*K.1^8,-2*K.1^12,2*K.1^16,1,K.1^5+K.1^-5,-1*K.1^5-K.1^-5,-2*K.1^16,2*K.1^4,2*K.1^12,-2*K.1^8,K.1^4,-1*K.1^16,-1*K.1^8,K.1^12,0,0,0,0,0,0,0,0,-1*K.1^12,K.1^8,-1*K.1^4,K.1^16,K.1-K.1^5-K.1^7+K.1^9-K.1^13,-1*K.1+K.1^11,-1*K.1^3-K.1^13,K.1^3+K.1^13,K.1-K.1^11,K.1^3-K.1^7+K.1^9+K.1^11-K.1^15,-1*K.1+K.1^5+K.1^7-K.1^9+K.1^13,-1*K.1^3+K.1^7-K.1^9-K.1^11+K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |2,-2,-1,0,0,2*K.1^16,-2*K.1^12,2*K.1^8,-2*K.1^4,1,K.1^5+K.1^-5,-1*K.1^5-K.1^-5,2*K.1^4,-2*K.1^16,-2*K.1^8,2*K.1^12,-1*K.1^16,K.1^4,K.1^12,-1*K.1^8,0,0,0,0,0,0,0,0,K.1^8,-1*K.1^12,K.1^16,-1*K.1^4,K.1^3+K.1^13,-1*K.1^3+K.1^7-K.1^9-K.1^11+K.1^15,-1*K.1+K.1^5+K.1^7-K.1^9+K.1^13,K.1-K.1^5-K.1^7+K.1^9-K.1^13,K.1^3-K.1^7+K.1^9+K.1^11-K.1^15,K.1-K.1^11,-1*K.1^3-K.1^13,-1*K.1+K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |2,-2,-1,0,0,-2*K.1^12,-2*K.1^4,2*K.1^16,2*K.1^8,1,-1*K.1^5-K.1^-5,K.1^5+K.1^-5,-2*K.1^8,2*K.1^12,-2*K.1^16,2*K.1^4,K.1^12,-1*K.1^8,K.1^4,-1*K.1^16,0,0,0,0,0,0,0,0,K.1^16,-1*K.1^4,-1*K.1^12,K.1^8,K.1-K.1^11,-1*K.1^3-K.1^13,-1*K.1^3+K.1^7-K.1^9-K.1^11+K.1^15,K.1^3-K.1^7+K.1^9+K.1^11-K.1^15,K.1^3+K.1^13,K.1-K.1^5-K.1^7+K.1^9-K.1^13,-1*K.1+K.1^11,-1*K.1+K.1^5+K.1^7-K.1^9+K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |2,-2,-1,0,0,2*K.1^8,2*K.1^16,-2*K.1^4,-2*K.1^12,1,-1*K.1^5-K.1^-5,K.1^5+K.1^-5,2*K.1^12,-2*K.1^8,2*K.1^4,-2*K.1^16,-1*K.1^8,K.1^12,-1*K.1^16,K.1^4,0,0,0,0,0,0,0,0,-1*K.1^4,K.1^16,K.1^8,-1*K.1^12,K.1^3-K.1^7+K.1^9+K.1^11-K.1^15,-1*K.1+K.1^5+K.1^7-K.1^9+K.1^13,-1*K.1+K.1^11,K.1-K.1^11,K.1-K.1^5-K.1^7+K.1^9-K.1^13,K.1^3+K.1^13,-1*K.1^3+K.1^7-K.1^9-K.1^11+K.1^15,-1*K.1^3-K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |2,-2,-1,0,0,-2*K.1^12,-2*K.1^4,2*K.1^16,2*K.1^8,1,K.1^5+K.1^-5,-1*K.1^5-K.1^-5,-2*K.1^8,2*K.1^12,-2*K.1^16,2*K.1^4,K.1^12,-1*K.1^8,K.1^4,-1*K.1^16,0,0,0,0,0,0,0,0,K.1^16,-1*K.1^4,-1*K.1^12,K.1^8,-1*K.1+K.1^11,K.1^3+K.1^13,K.1^3-K.1^7+K.1^9+K.1^11-K.1^15,-1*K.1^3+K.1^7-K.1^9-K.1^11+K.1^15,-1*K.1^3-K.1^13,-1*K.1+K.1^5+K.1^7-K.1^9+K.1^13,K.1-K.1^11,K.1-K.1^5-K.1^7+K.1^9-K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |2,-2,-1,0,0,2*K.1^8,2*K.1^16,-2*K.1^4,-2*K.1^12,1,K.1^5+K.1^-5,-1*K.1^5-K.1^-5,2*K.1^12,-2*K.1^8,2*K.1^4,-2*K.1^16,-1*K.1^8,K.1^12,-1*K.1^16,K.1^4,0,0,0,0,0,0,0,0,-1*K.1^4,K.1^16,K.1^8,-1*K.1^12,-1*K.1^3+K.1^7-K.1^9-K.1^11+K.1^15,K.1-K.1^5-K.1^7+K.1^9-K.1^13,K.1-K.1^11,-1*K.1+K.1^11,-1*K.1+K.1^5+K.1^7-K.1^9+K.1^13,-1*K.1^3-K.1^13,K.1^3-K.1^7+K.1^9+K.1^11-K.1^15,K.1^3+K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, 3, 0, -1, 1, 3, 3, 3, 3, 0, -1, -1, 3, 3, 3, 3, 0, 0, 0, 0, -1, -1, -1, -1, 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!\[3, 3, 0, -1, -1, 3, 3, 3, 3, 0, 1, 1, 3, 3, 3, 3, 0, 0, 0, 0, -1, -1, -1, -1, -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(5: Sparse := true);
S := [ K |3,3,0,-1,1,3*K.1^-2,3*K.1,3*K.1^-1,3*K.1^2,0,-1,-1,3*K.1^2,3*K.1^-2,3*K.1^-1,3*K.1,0,0,0,0,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,K.1^-1,K.1,K.1^-2,K.1^2,0,0,0,0,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |3,3,0,-1,1,3*K.1^2,3*K.1^-1,3*K.1,3*K.1^-2,0,-1,-1,3*K.1^-2,3*K.1^2,3*K.1,3*K.1^-1,0,0,0,0,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,K.1,K.1^-1,K.1^2,K.1^-2,0,0,0,0,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |3,3,0,-1,1,3*K.1^-1,3*K.1^-2,3*K.1^2,3*K.1,0,-1,-1,3*K.1,3*K.1^-1,3*K.1^2,3*K.1^-2,0,0,0,0,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,K.1^2,K.1^-2,K.1^-1,K.1,0,0,0,0,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |3,3,0,-1,1,3*K.1,3*K.1^2,3*K.1^-2,3*K.1^-1,0,-1,-1,3*K.1^-1,3*K.1,3*K.1^-2,3*K.1^2,0,0,0,0,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,K.1^-2,K.1^2,K.1,K.1^-1,0,0,0,0,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |3,3,0,-1,-1,3*K.1^-2,3*K.1,3*K.1^-1,3*K.1^2,0,1,1,3*K.1^2,3*K.1^-2,3*K.1^-1,3*K.1,0,0,0,0,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,0,0,0,0,K.1^-1,K.1^2,K.1,K.1,K.1^2,K.1^-2,K.1^-1,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |3,3,0,-1,-1,3*K.1^2,3*K.1^-1,3*K.1,3*K.1^-2,0,1,1,3*K.1^-2,3*K.1^2,3*K.1,3*K.1^-1,0,0,0,0,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,0,0,0,0,K.1,K.1^-2,K.1^-1,K.1^-1,K.1^-2,K.1^2,K.1,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |3,3,0,-1,-1,3*K.1^-1,3*K.1^-2,3*K.1^2,3*K.1,0,1,1,3*K.1,3*K.1^-1,3*K.1^2,3*K.1^-2,0,0,0,0,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,0,0,0,0,K.1^2,K.1,K.1^-2,K.1^-2,K.1,K.1^-1,K.1^2,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |3,3,0,-1,-1,3*K.1,3*K.1^2,3*K.1^-2,3*K.1^-1,0,1,1,3*K.1^-1,3*K.1,3*K.1^-2,3*K.1^2,0,0,0,0,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,0,0,0,0,K.1^-2,K.1^-1,K.1^2,K.1^2,K.1^-1,K.1,K.1^-2,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, 1, 0, 0, 4, 4, 4, 4, -1, 0, 0, -4, -4, -4, -4, 1, 1, 1, 1, 0, 0, 0, 0, 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(5: Sparse := true);
S := [ K |4,-4,1,0,0,4*K.1^-2,4*K.1,4*K.1^-1,4*K.1^2,-1,0,0,-4*K.1^2,-4*K.1^-2,-4*K.1^-1,-4*K.1,K.1^-2,K.1^2,K.1,K.1^-1,0,0,0,0,0,0,0,0,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,1,0,0,4*K.1^2,4*K.1^-1,4*K.1,4*K.1^-2,-1,0,0,-4*K.1^-2,-4*K.1^2,-4*K.1,-4*K.1^-1,K.1^2,K.1^-2,K.1^-1,K.1,0,0,0,0,0,0,0,0,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,1,0,0,4*K.1^-1,4*K.1^-2,4*K.1^2,4*K.1,-1,0,0,-4*K.1,-4*K.1^-1,-4*K.1^2,-4*K.1^-2,K.1^-1,K.1,K.1^-2,K.1^2,0,0,0,0,0,0,0,0,-1*K.1^2,-1*K.1^-2,-1*K.1^-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(5: Sparse := true);
S := [ K |4,-4,1,0,0,4*K.1,4*K.1^2,4*K.1^-2,4*K.1^-1,-1,0,0,-4*K.1^-1,-4*K.1,-4*K.1^-2,-4*K.1^2,K.1,K.1^-1,K.1^2,K.1^-2,0,0,0,0,0,0,0,0,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_240_102:= KnownIrreducibles(CR);