/* Group 1728.46903 downloaded from the LMFDB on 02 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([9, 2, 2, 2, 2, 3, 2, 3, 2, 3, 542, 389, 74, 1443, 102, 1444, 12983, 6188, 3605, 158, 3048, 107143, 9529, 11698, 1987, 214, 101096, 15578]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.3, GPC.6, GPC.8]); AssignNames(~GPC, ["a", "b", "c", "c2", "c4", "d", "d2", "e", "e2"]);
GPerm := PermutationGroup< 14 | (2,4)(6,7), (8,9)(10,11)(13,14), (9,11), (8,10)(9,11), (2,3,4), (5,6,7), (12,13,14), (1,2)(3,4), (1,3)(2,4) >;
GLZN := MatrixGroup< 2, Integers(84) | [[1, 42, 42, 1], [31, 27, 78, 11], [71, 49, 0, 1], [1, 28, 0, 1], [17, 60, 36, 53], [43, 0, 42, 43], [22, 63, 63, 1], [13, 48, 36, 49], [13, 0, 0, 13]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1728_46903 := 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:= GLZN;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Matrix(2, [1, 0, 0, 1])>,< 2, 1, Matrix(2, [13, 0, 0, 13])>,< 2, 2, Matrix(2, [17, 48, 36, 53])>,< 2, 3, Matrix(2, [43, 0, 42, 43])>,< 2, 3, Matrix(2, [55, 42, 0, 55])>,< 2, 6, Matrix(2, [59, 6, 36, 11])>,< 2, 6, Matrix(2, [49, 48, 48, 49])>,< 2, 18, Matrix(2, [71, 77, 0, 1])>,< 2, 18, Matrix(2, [20, 35, 63, 76])>,< 2, 18, Matrix(2, [13, 42, 78, 1])>,< 2, 36, Matrix(2, [31, 13, 36, 53])>,< 2, 108, Matrix(2, [56, 43, 15, 28])>,< 3, 2, Matrix(2, [13, 48, 36, 49])>,< 3, 2, Matrix(2, [1, 56, 0, 1])>,< 3, 4, Matrix(2, [49, 8, 48, 13])>,< 3, 8, Matrix(2, [43, 21, 63, 64])>,< 3, 8, Matrix(2, [43, 77, 63, 64])>,< 3, 8, Matrix(2, [1, 7, 63, 22])>,< 3, 16, Matrix(2, [28, 71, 69, 55])>,< 3, 16, Matrix(2, [34, 13, 57, 49])>,< 3, 16, Matrix(2, [76, 27, 57, 7])>,< 4, 6, Matrix(2, [41, 24, 60, 29])>,< 4, 18, Matrix(2, [71, 7, 42, 43])>,< 4, 18, Matrix(2, [53, 78, 18, 17])>,< 4, 18, Matrix(2, [62, 21, 21, 76])>,< 4, 36, Matrix(2, [31, 83, 78, 11])>,< 4, 108, Matrix(2, [1, 74, 3, 41])>,< 4, 108, Matrix(2, [67, 17, 48, 17])>,< 4, 108, Matrix(2, [14, 1, 57, 28])>,< 6, 2, Matrix(2, [49, 48, 36, 1])>,< 6, 2, Matrix(2, [13, 56, 0, 13])>,< 6, 2, Matrix(2, [29, 60, 24, 53])>,< 6, 2, Matrix(2, [17, 60, 24, 41])>,< 6, 4, Matrix(2, [1, 64, 48, 49])>,< 6, 4, Matrix(2, [17, 20, 36, 53])>,< 6, 4, Matrix(2, [17, 32, 24, 41])>,< 6, 4, Matrix(2, [29, 4, 24, 53])>,< 6, 6, Matrix(2, [43, 56, 42, 43])>,< 6, 6, Matrix(2, [43, 78, 48, 7])>,< 6, 6, Matrix(2, [55, 56, 42, 55])>,< 6, 6, Matrix(2, [55, 6, 36, 7])>,< 6, 6, Matrix(2, [59, 18, 24, 83])>,< 6, 6, Matrix(2, [71, 18, 24, 11])>,< 6, 8, Matrix(2, [55, 21, 63, 76])>,< 6, 8, Matrix(2, [55, 49, 63, 76])>,< 6, 8, Matrix(2, [13, 35, 63, 34])>,< 6, 12, Matrix(2, [49, 50, 6, 13])>,< 6, 12, Matrix(2, [49, 62, 78, 1])>,< 6, 12, Matrix(2, [59, 76, 78, 11])>,< 6, 12, Matrix(2, [49, 76, 48, 49])>,< 6, 12, Matrix(2, [29, 46, 66, 53])>,< 6, 12, Matrix(2, [17, 46, 66, 41])>,< 6, 16, Matrix(2, [43, 1, 27, 28])>,< 6, 16, Matrix(2, [49, 83, 15, 22])>,< 6, 16, Matrix(2, [7, 69, 15, 64])>,< 6, 16, Matrix(2, [80, 27, 57, 11])>,< 6, 16, Matrix(2, [80, 83, 57, 11])>,< 6, 16, Matrix(2, [38, 13, 57, 53])>,< 6, 16, Matrix(2, [80, 11, 45, 83])>,< 6, 16, Matrix(2, [29, 67, 3, 74])>,< 6, 16, Matrix(2, [50, 67, 3, 53])>,< 6, 16, Matrix(2, [59, 53, 3, 20])>,< 6, 16, Matrix(2, [8, 39, 45, 11])>,< 6, 16, Matrix(2, [80, 81, 3, 83])>,< 6, 36, Matrix(2, [83, 41, 36, 49])>,< 6, 36, Matrix(2, [8, 71, 27, 28])>,< 6, 36, Matrix(2, [13, 14, 78, 1])>,< 6, 36, Matrix(2, [31, 25, 24, 41])>,< 6, 36, Matrix(2, [43, 81, 24, 53])>,< 6, 48, Matrix(2, [76, 13, 63, 43])>,< 6, 48, Matrix(2, [1, 57, 21, 34])>,< 6, 48, Matrix(2, [7, 1, 15, 28])>,< 12, 12, Matrix(2, [29, 32, 24, 41])>,< 12, 36, Matrix(2, [77, 43, 6, 13])>,< 12, 36, Matrix(2, [17, 34, 66, 53])>,< 12, 36, Matrix(2, [8, 57, 69, 70])>,< 12, 36, Matrix(2, [1, 11, 66, 53])>,< 12, 36, Matrix(2, [73, 11, 66, 41])>,< 12, 48, Matrix(2, [80, 39, 57, 11])>,< 12, 48, Matrix(2, [32, 43, 81, 59])>,< 12, 48, Matrix(2, [50, 53, 45, 41])>]); 
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, 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, -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, -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, -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, -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, 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, 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, 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!\[2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, -1, 2, -1, 2, 2, 2, -1, -1, -1, 0, 2, 0, 2, 2, 0, 0, 0, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, 2, 2, -1, 2, -1, 0, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, 0, -1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0, -1, -1, 2, -1, 0, -1, 0, 0, 0, -1, 2, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 2, -1, -1, -1, 0, -1, 0, 0, 0, -1, -1, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 0, 0, 0, 0, -1, 2, -1, -1, 0, -1, 0, 0, 0, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, -1, -1, -1, 2, 0, 2, 0, 0, 0, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 2, -2, 0, 0, -2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 2, -2, 2, -2, 0, 0, -2, -2, -2, 2, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 2, -2, 0, 0, 2, 0, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 2, -2, 2, -2, 0, 0, -2, -2, -2, 2, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, -2, 0, -2, 0, 0, 0, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, 0, 2, 0, 0, 0, 0, 0, -2, -2, 2, -1, -1, 1, 1, 1, -1, 2, 2, -1, -2, -2, 2, -1, -1, -1, 1, -1, 1, 1, 1, 2, -2, -1, 1, 1, 1, -2, 1, 1, -2, 1, -1, 1, 0, 0, 0, 0, 1, 1, -2, -1, 0, -1, 0, 0, 0, -1, 2, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, -2, 0, -2, 0, 0, 0, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 0, 2, 0, 0, 0, 0, 0, -2, -2, 2, -1, -1, 1, 1, 1, -1, 2, 2, -1, -2, -2, -1, 2, -1, -1, 1, -1, 1, 1, 1, -1, 1, 2, 1, -2, -2, 1, 1, -2, 1, 1, -1, 1, 0, 0, 0, 0, -2, 1, 1, -1, 0, -1, 0, 0, 0, -1, -1, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, -2, 0, -2, 0, 0, 0, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 0, 2, 0, 0, 0, 0, 0, -2, -2, 2, -1, -1, 1, 1, 1, -1, 2, 2, -1, -2, -2, -1, -1, 2, -1, 1, -1, 1, 1, 1, -1, 1, -1, -2, 1, 1, 1, -2, 1, 1, -2, 2, 1, 0, 0, 0, 0, 1, -2, 1, -1, 0, -1, 0, 0, 0, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, -2, 0, -2, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 0, 2, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -1, -1, -1, 2, -2, 2, -2, -2, -2, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -2, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 0, 0, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 0, -2, 0, -2, 2, 0, -1, 2, -1, 2, 2, 2, -1, -1, -1, 0, -2, 0, -2, 2, 0, 0, 0, 1, 1, -1, 2, -1, -2, 1, 1, 2, -1, -1, 2, 1, 1, 2, 2, 2, -1, -2, -1, 0, 1, 1, -1, -2, -1, -2, -2, 1, 1, 1, 1, 1, 1, -1, 0, -1, 1, -1, 1, 0, 0, 0, 0, 1, 0, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 0, 2, 0, 2, -2, 0, -1, 2, -1, 2, 2, 2, -1, -1, -1, 0, 2, 0, 2, -2, 0, 0, 0, 1, 1, -1, 2, -1, -2, 1, 1, 2, -1, -1, 2, 1, 1, 2, 2, 2, -1, -2, -1, 0, 1, 1, -1, -2, -1, -2, -2, 1, 1, 1, 1, 1, 1, -1, 0, 1, -1, 1, -1, 0, 0, 0, 0, -1, 0, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 2, 0, 2, 0, 0, 0, 2, -1, -1, -1, -1, 2, 2, -1, -1, -2, 0, -2, 0, 0, 0, 0, 0, -2, -2, 2, -1, -1, 1, 1, 1, -1, 2, 2, -1, -2, -2, 2, -1, -1, -1, 1, -1, -1, 1, 1, 2, -2, -1, 1, 1, 1, -2, 1, 1, -2, 1, -1, -1, 0, 0, 0, 0, -1, -1, 2, 1, 0, 1, 0, 0, 0, 1, -2, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 2, 0, 2, 0, 0, 0, 2, -1, -1, -1, 2, -1, -1, 2, -1, -2, 0, -2, 0, 0, 0, 0, 0, -2, -2, 2, -1, -1, 1, 1, 1, -1, 2, 2, -1, -2, -2, -1, 2, -1, -1, 1, -1, -1, 1, 1, -1, 1, 2, 1, -2, -2, 1, 1, -2, 1, 1, -1, -1, 0, 0, 0, 0, 2, -1, -1, 1, 0, 1, 0, 0, 0, 1, 1, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 2, 0, 2, 0, 0, 0, 2, -1, -1, 2, -1, -1, -1, -1, 2, -2, 0, -2, 0, 0, 0, 0, 0, -2, -2, 2, -1, -1, 1, 1, 1, -1, 2, 2, -1, -2, -2, -1, -1, 2, -1, 1, -1, -1, 1, 1, -1, 1, -1, -2, 1, 1, 1, -2, 1, 1, -2, 2, -1, 0, 0, 0, 0, -1, 2, -1, 1, 0, 1, 0, 0, 0, -2, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 2, 0, 2, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, 0, -2, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -1, -1, -1, 2, -2, 2, 2, -2, -2, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 2, 0, 0, 0, 0, -1, -1, -1, -2, 0, -2, 0, 0, 0, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, -2, 0, -2, 0, 0, 0, 2, -1, -1, -1, -1, 2, 2, -1, -1, -2, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, 1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 1, 0, 0, 0, 0, 1, 1, -2, 1, 0, 1, 0, 0, 0, 1, -2, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, -2, 0, -2, 0, 0, 0, 2, -1, -1, -1, 2, -1, -1, 2, -1, -2, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, 1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, 1, 0, 0, 0, 0, -2, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, -2, 0, -2, 0, 0, 0, 2, -1, -1, 2, -1, -1, -1, -1, 2, -2, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, 1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, 1, 0, 0, 0, 0, 1, -2, 1, 1, 0, 1, 0, 0, 0, -2, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, -2, 0, -2, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, 0, 0, 0, 0, 1, 1, 1, -2, 0, -2, 0, 0, 0, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, -2, 0, -2, -2, 0, -1, 2, -1, 2, 2, 2, -1, -1, -1, 0, -2, 0, -2, -2, 0, 0, 0, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, 2, 2, -1, 2, -1, 0, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,-2,0,2,0,0,-1,2,-1,2,2,2,-1,-1,-1,0,2,0,-2,0,0,0,0,-1-2*K.1,1+2*K.1,1,-2,1,0,1+2*K.1,-1-2*K.1,2,1,-1,-2,-1-2*K.1,1+2*K.1,-2,-2,-2,-1,0,1,0,1+2*K.1,-1-2*K.1,1,0,1,0,0,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,1,0,-1-2*K.1,-1,1+2*K.1,1,0,0,0,0,-1,0,-1-2*K.1,1+2*K.1,1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,-2,0,2,0,0,-1,2,-1,2,2,2,-1,-1,-1,0,2,0,-2,0,0,0,0,1+2*K.1,-1-2*K.1,1,-2,1,0,-1-2*K.1,1+2*K.1,2,1,-1,-2,1+2*K.1,-1-2*K.1,-2,-2,-2,-1,0,1,0,-1-2*K.1,1+2*K.1,1,0,1,0,0,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,1,0,1+2*K.1,-1,-1-2*K.1,1,0,0,0,0,-1,0,1+2*K.1,-1-2*K.1,1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,2,0,-2,0,0,-1,2,-1,2,2,2,-1,-1,-1,0,-2,0,2,0,0,0,0,-1-2*K.1,1+2*K.1,1,-2,1,0,1+2*K.1,-1-2*K.1,2,1,-1,-2,-1-2*K.1,1+2*K.1,-2,-2,-2,-1,0,1,0,1+2*K.1,-1-2*K.1,1,0,1,0,0,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,1,0,1+2*K.1,1,-1-2*K.1,-1,0,0,0,0,1,0,1+2*K.1,-1-2*K.1,-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,0,2,0,-2,0,0,-1,2,-1,2,2,2,-1,-1,-1,0,-2,0,2,0,0,0,0,1+2*K.1,-1-2*K.1,1,-2,1,0,-1-2*K.1,1+2*K.1,2,1,-1,-2,1+2*K.1,-1-2*K.1,-2,-2,-2,-1,0,1,0,-1-2*K.1,1+2*K.1,1,0,1,0,0,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,1,0,-1-2*K.1,1,1+2*K.1,-1,0,0,0,0,1,0,-1-2*K.1,1+2*K.1,-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, 3, 1, -1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, -1, -1, -1, -1, -1, 1, -1, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 1, 1, 0, 0, 0, 3, -1, -1, -1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, 3, -1, -1, -1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 1, -1, 1, 1, 1, -1, 1, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 3, 1, -1, 1, 1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, -3, -1, 1, -1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 1, -1, 1, -1, 1, -1, -1, -3, -3, 3, 3, 3, -3, -3, -3, -1, -1, -1, -1, 1, 1, 0, 0, 0, -1, 1, -1, -3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1, 0, 0, 0, 3, 1, -1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, -3, 1, 1, 1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, -1, -1, -1, 1, -1, 1, 1, -3, -3, 3, 3, 3, -3, -3, -3, -1, -1, -1, -1, 1, 1, 0, 0, 0, -1, 1, -1, -3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, 0, 0, 0, 3, -1, -1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, 3, -1, -1, -1, 1, -1, 3, 3, 3, 0, 0, 0, 0, 0, 0, -3, 1, 1, 1, -1, -1, 1, 1, -3, -3, 3, 3, 3, -3, -3, -3, -1, -1, -1, -1, 1, 1, 0, 0, 0, -1, 1, -1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 0, 0, 0, -3, 1, 1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, 3, 1, -1, 1, -1, 1, 3, 3, 3, 0, 0, 0, 0, 0, 0, -3, -1, 1, -1, 1, 1, -1, -1, -3, -3, 3, 3, 3, -3, -3, -3, -1, -1, -1, -1, 1, 1, 0, 0, 0, -1, 1, -1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, -1, 1, 0, 0, 0, -3, -1, 1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, -3, -1, 1, -1, -1, 1, 3, 3, 3, 0, 0, 0, 0, 0, 0, -3, 1, 1, 1, 1, -1, 1, -1, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, -3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 0, 0, 0, -3, 1, 1, 1, 1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, -3, 1, 1, 1, 1, -1, 3, 3, 3, 0, 0, 0, 0, 0, 0, -3, -1, 1, -1, -1, 1, -1, 1, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, -3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, -3, -1, 1, -1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, 1, -2, -2, 4, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, -2, 1, 1, -2, -2, -2, -2, -2, -2, 4, -2, -2, 1, -2, 1, 0, 1, 1, -2, 4, 1, -2, -2, 1, -2, 1, 1, -2, 1, 1, 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!\[4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, 1, -2, 4, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, -2, 1, 1, -2, -2, -2, -2, -2, -2, -2, 4, -2, 1, -2, 1, 0, 1, 1, 1, -2, -2, -2, 4, -2, 1, 1, -2, 1, 1, 1, 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!\[4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, -2, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, 4, 1, -2, 1, 0, 1, 1, 1, -2, 1, 4, -2, 1, 1, -2, 1, 1, -2, -2, 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!\[4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 4, -2, 4, -2, -2, 4, -2, -2, 4, -2, -2, -2, -2, -2, -2, 4, -2, 0, -2, -2, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 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!\[4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, -2, -4, 4, 2, 0, 0, -4, 2, 2, -2, 0, 2, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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!\[4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, -2, -4, 4, 2, 0, 0, 2, -4, 2, -2, 0, 2, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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!\[4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 4, -2, -2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, -2, -4, 4, 2, 0, 0, 2, 2, -4, -2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 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!\[4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 4, -4, 4, -4, 0, 0, 2, 2, 2, 4, 0, -4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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!\[4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, -2, -2, 1, -2, -2, 4, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 1, 2, -1, -1, -2, -2, -2, -2, 2, 2, 4, -2, -2, 1, 2, 1, 0, -1, -1, -2, -4, 1, 2, 2, -1, 2, -1, -1, 2, -1, 1, 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!\[4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, -2, -2, 1, -2, 4, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 1, 2, -1, -1, -2, -2, -2, -2, 2, 2, -2, 4, -2, 1, 2, 1, 0, -1, -1, 1, 2, -2, 2, -4, 2, -1, -1, 2, -1, -1, 1, 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!\[4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 1, 2, -1, -1, -2, -2, -2, -2, 2, 2, -2, -2, 4, 1, 2, 1, 0, -1, -1, 1, 2, 1, -4, 2, -1, -1, 2, -1, -1, 2, -2, 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!\[4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 4, -2, -4, 2, 2, 4, -2, -2, 4, 2, 2, -2, -2, -2, -2, -4, -2, 0, 2, 2, 1, 2, 1, 2, 2, -1, -1, -1, -1, -1, -1, 1, 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(3: Sparse := true);
S := [ K |4,-4,0,4,-4,0,0,0,0,0,0,0,-2,-2,1,-2,-2,4,-2,1,1,0,0,0,0,0,0,0,0,-2-4*K.1,2+4*K.1,2,2,-1,0,-1-2*K.1,1+2*K.1,-2,2,-2,2,-2-4*K.1,2+4*K.1,-4,2,2,1,0,-1,0,-1-2*K.1,1+2*K.1,2,0,-1,0,0,-1-2*K.1,-2-4*K.1,-1-2*K.1,1+2*K.1,2+4*K.1,1+2*K.1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,4,-4,0,0,0,0,0,0,0,-2,-2,1,-2,-2,4,-2,1,1,0,0,0,0,0,0,0,0,2+4*K.1,-2-4*K.1,2,2,-1,0,1+2*K.1,-1-2*K.1,-2,2,-2,2,2+4*K.1,-2-4*K.1,-4,2,2,1,0,-1,0,1+2*K.1,-1-2*K.1,2,0,-1,0,0,1+2*K.1,2+4*K.1,1+2*K.1,-1-2*K.1,-2-4*K.1,-1-2*K.1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,4,-4,0,0,0,0,0,0,0,-2,-2,1,-2,4,-2,1,-2,1,0,0,0,0,0,0,0,0,-2-4*K.1,2+4*K.1,2,2,-1,0,-1-2*K.1,1+2*K.1,-2,2,-2,2,-2-4*K.1,2+4*K.1,2,-4,2,1,0,-1,0,-1-2*K.1,1+2*K.1,-1,0,2,0,0,2+4*K.1,1+2*K.1,-1-2*K.1,-2-4*K.1,-1-2*K.1,1+2*K.1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,4,-4,0,0,0,0,0,0,0,-2,-2,1,-2,4,-2,1,-2,1,0,0,0,0,0,0,0,0,2+4*K.1,-2-4*K.1,2,2,-1,0,1+2*K.1,-1-2*K.1,-2,2,-2,2,2+4*K.1,-2-4*K.1,2,-4,2,1,0,-1,0,1+2*K.1,-1-2*K.1,-1,0,2,0,0,-2-4*K.1,-1-2*K.1,1+2*K.1,2+4*K.1,1+2*K.1,-1-2*K.1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,4,-4,0,0,0,0,0,0,0,-2,-2,1,4,-2,-2,1,1,-2,0,0,0,0,0,0,0,0,-2-4*K.1,2+4*K.1,2,2,-1,0,-1-2*K.1,1+2*K.1,-2,2,-2,2,-2-4*K.1,2+4*K.1,2,2,-4,1,0,-1,0,-1-2*K.1,1+2*K.1,-1,0,-1,0,0,-1-2*K.1,1+2*K.1,2+4*K.1,1+2*K.1,-1-2*K.1,-2-4*K.1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,4,-4,0,0,0,0,0,0,0,-2,-2,1,4,-2,-2,1,1,-2,0,0,0,0,0,0,0,0,2+4*K.1,-2-4*K.1,2,2,-1,0,1+2*K.1,-1-2*K.1,-2,2,-2,2,2+4*K.1,-2-4*K.1,2,2,-4,1,0,-1,0,1+2*K.1,-1-2*K.1,-1,0,-1,0,0,1+2*K.1,-1-2*K.1,-2-4*K.1,-1-2*K.1,1+2*K.1,2+4*K.1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,4,-4,0,0,0,0,0,0,0,-2,4,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,0,-2-4*K.1,2+4*K.1,2,-4,2,0,2+4*K.1,-2-4*K.1,4,2,-2,-4,-2-4*K.1,2+4*K.1,2,2,2,-2,0,2,0,2+4*K.1,-2-4*K.1,-1,0,-1,0,0,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,4,-4,0,0,0,0,0,0,0,-2,4,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,0,2+4*K.1,-2-4*K.1,2,-4,2,0,-2-4*K.1,2+4*K.1,4,2,-2,-4,2+4*K.1,-2-4*K.1,2,2,2,-2,0,2,0,-2-4*K.1,2+4*K.1,-1,0,-1,0,0,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,1+2*K.1,-1-2*K.1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, -2, -2, -2, 6, 0, -2, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 6, 6, 6, -3, -3, -3, -3, -3, 1, -2, -2, 1, -2, -2, 0, 0, 0, 1, 1, 1, -3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, -2, -2, -2, 0, 2, 0, 2, 2, 0, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, -3, -3, -3, 6, -3, 6, -3, -3, -2, 1, 1, -2, 1, 1, 0, 0, 0, 1, -2, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, 0, -2, 2, 0, 0, -2, 0, 2, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -6, -6, -6, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, 0, -2, 2, 0, 0, 2, 0, -2, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -6, -6, -6, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -2, -2, 2, -6, 0, 2, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, -6, -6, 6, -3, -3, 3, 3, 3, 1, -2, -2, 1, 2, 2, 0, 0, 0, 1, -1, 1, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -2, -2, 2, 6, 0, -2, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, -6, -6, 6, -3, -3, 3, 3, 3, 1, -2, -2, 1, 2, 2, 0, 0, 0, 1, -1, 1, -3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, -2, -2, -2, -6, 0, 2, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 6, 6, 6, -3, -3, -3, -3, -3, 1, -2, -2, 1, -2, -2, 0, 0, 0, 1, 1, 1, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, -2, -2, -2, 0, -2, 0, -2, -2, 0, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, -3, -3, -3, 6, -3, 6, -3, -3, -2, 1, 1, -2, 1, 1, 0, 0, 0, 1, -2, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, 0, -1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -2, -2, 2, 0, -2, 0, -2, 2, 0, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, 3, 3, -3, 6, -3, -6, 3, 3, -2, 1, 1, -2, -1, -1, 0, 0, 0, 1, 2, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, -1, 0, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -2, -2, 2, 0, 2, 0, 2, -2, 0, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 0, 0, 3, 3, -3, 6, -3, -6, 3, 3, -2, 1, 1, -2, -1, -1, 0, 0, 0, 1, 2, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 1, 0, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,-6,0,-2,2,0,0,-2,0,2,0,0,-3,6,-3,0,0,0,0,0,0,0,-2,0,2,0,0,0,0,-3-6*K.1,3+6*K.1,3,-6,3,0,3+6*K.1,-3-6*K.1,-2,-1,1,2,1+2*K.1,-1-2*K.1,0,0,0,1,0,-1,0,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1-2*K.1,-1,1+2*K.1,1,0,0,0,0,1,0,1+2*K.1,-1-2*K.1,-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,-6,0,-2,2,0,0,-2,0,2,0,0,-3,6,-3,0,0,0,0,0,0,0,-2,0,2,0,0,0,0,3+6*K.1,-3-6*K.1,3,-6,3,0,-3-6*K.1,3+6*K.1,-2,-1,1,2,-1-2*K.1,1+2*K.1,0,0,0,1,0,-1,0,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,1+2*K.1,-1,-1-2*K.1,1,0,0,0,0,1,0,-1-2*K.1,1+2*K.1,-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,-6,0,-2,2,0,0,2,0,-2,0,0,-3,6,-3,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,-3-6*K.1,3+6*K.1,3,-6,3,0,3+6*K.1,-3-6*K.1,-2,-1,1,2,1+2*K.1,-1-2*K.1,0,0,0,1,0,-1,0,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,1+2*K.1,1,-1-2*K.1,-1,0,0,0,0,-1,0,-1-2*K.1,1+2*K.1,1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |6,-6,0,-2,2,0,0,2,0,-2,0,0,-3,6,-3,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,3+6*K.1,-3-6*K.1,3,-6,3,0,-3-6*K.1,3+6*K.1,-2,-1,1,2,-1-2*K.1,1+2*K.1,0,0,0,1,0,-1,0,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1-2*K.1,1,1+2*K.1,-1,0,0,0,0,-1,0,1+2*K.1,-1-2*K.1,1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[12, 12, 12, -4, -4, -4, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, 3, -6, 3, 3, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, 2, -1, 0, -1, -1, 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!\[12, -12, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 6, 6, 0, 0, 0, 2, 4, -4, -2, 0, 0, 0, 0, 0, 2, 0, -2, 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!\[12, 12, -12, -4, -4, 4, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -6, -6, 3, 6, -3, -3, 2, 2, 2, 2, -2, -2, 0, 0, 0, -1, -2, -1, 0, 1, 1, 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; 
K := CyclotomicField(3: Sparse := true);
S := [ K |12,-12,0,-4,4,0,0,0,0,0,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6-12*K.1,6+12*K.1,6,6,-3,0,-3-6*K.1,3+6*K.1,2,-2,2,-2,2+4*K.1,-2-4*K.1,0,0,0,-1,0,1,0,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |12,-12,0,-4,4,0,0,0,0,0,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6+12*K.1,-6-12*K.1,6,6,-3,0,3+6*K.1,-3-6*K.1,2,-2,2,-2,-2-4*K.1,2+4*K.1,0,0,0,-1,0,1,0,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_1728_46903:= KnownIrreducibles(CR);