/* Group 387072.a 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< 18 | (1,12)(2,11)(3,14,4,13)(5,17,6,18)(7,16,8,15)(9,10), (1,15,9,8,4,12,2,16,10,7,3,11)(13,17,14,18) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_387072_a := 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!(1,2)(3,4)(5,6)(7,8)(9,10)(13,14)(15,16)(17,18)>,< 2, 36, G!(1,2)(11,12)>,< 2, 84, G!(3,4)(5,6)(9,10)(11,12)(13,14)(17,18)>,< 2, 126, G!(3,4)(9,10)(11,12)(13,14)>,< 2, 1008, G!(1,7)(2,8)(3,11)(4,12)(5,15)(6,16)(9,14)(10,13)>,< 3, 1344, G!(3,13,17)(4,14,18)(5,10,16)(6,9,15)>,< 3, 1344, G!(3,17,13)(4,18,14)(5,16,10)(6,15,9)>,< 3, 3584, G!(1,4,12)(2,3,11)(5,8,18)(6,7,17)(9,13,15)(10,14,16)>,< 4, 1008, G!(1,18,2,17)(3,14,4,13)(5,9,6,10)(11,16,12,15)>,< 4, 4032, G!(1,12,2,11)(3,5)(4,6)(7,8)(9,14)(10,13)(15,18)(16,17)>,< 4, 4032, G!(1,8)(2,7)(3,13,4,14)(5,12,6,11)(9,18,10,17)(15,16)>,< 4, 6048, G!(1,6)(2,5)(3,9,4,10)(7,15)(8,16)(11,14,12,13)>,< 6, 1344, G!(3,6,17,4,5,18)(9,14,12,10,13,11)>,< 6, 1344, G!(3,18,5,4,17,6)(9,11,13,10,12,14)>,< 6, 2688, G!(1,13,16,2,14,15)(3,17,9)(4,18,10)(5,6)(7,8)(11,12)>,< 6, 2688, G!(1,15,14,2,16,13)(3,9,17)(4,10,18)(5,6)(7,8)(11,12)>,< 6, 4032, G!(1,2)(3,17,13)(4,18,14)(5,16,10)(6,15,9)(11,12)>,< 6, 4032, G!(1,2)(3,13,17)(4,14,18)(5,10,16)(6,9,15)(11,12)>,< 6, 4032, G!(1,2)(3,10,15,4,9,16)(5,11,13,6,12,14)(17,18)>,< 6, 4032, G!(1,2)(3,16,9,4,15,10)(5,14,12,6,13,11)(17,18)>,< 6, 8064, G!(1,16,8)(2,15,7)(9,11,14,10,12,13)(17,18)>,< 6, 8064, G!(1,8,16)(2,7,15)(9,13,12,10,14,11)(17,18)>,< 6, 10752, G!(1,9,4,2,10,3)(5,17,13)(6,18,14)(7,16,12,8,15,11)>,< 6, 16128, G!(1,4,5,7,12,15)(2,3,6,8,11,16)(9,14)(10,13)>,< 6, 16128, G!(1,15,12,7,5,4)(2,16,11,8,6,3)(9,14)(10,13)>,< 7, 13824, G!(1,14,8,6,15,10,3)(2,13,7,5,16,9,4)>,< 9, 43008, G!(1,10,12,7,4,17,5,14,15)(2,9,11,8,3,18,6,13,16)>,< 9, 43008, G!(1,18,14,4,5,16,12,8,10)(2,17,13,3,6,15,11,7,9)>,< 9, 43008, G!(1,10,8,12,16,5,4,14,18)(2,9,7,11,15,6,3,13,17)>,< 12, 16128, G!(1,11,2,12)(3,10,17,5,13,16)(4,9,18,6,14,15)(7,8)>,< 12, 16128, G!(1,12,2,11)(3,16,13,5,17,10)(4,15,14,6,18,9)(7,8)>,< 12, 16128, G!(1,8)(2,7)(3,10,6,13,17,11,4,9,5,14,18,12)(15,16)>,< 12, 16128, G!(1,8)(2,7)(3,12,18,14,5,9,4,11,17,13,6,10)(15,16)>,< 12, 16128, G!(1,17,2,18)(3,12,10,14,15,5,4,11,9,13,16,6)>,< 12, 16128, G!(1,18,2,17)(3,6,16,13,9,11,4,5,15,14,10,12)>,< 14, 13824, G!(1,13,9,6,7,15,11)(2,14,10,5,8,16,12)(3,4)(17,18)>,< 14, 13824, G!(1,16,14,9,8,4,6,2,15,13,10,7,3,5)(17,18)>,< 14, 13824, G!(1,5,3,7,10,13,15,2,6,4,8,9,14,16)(17,18)>]); 
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]; 
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.1,1,1,1,1,1,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,1,K.1,K.1^-1,1,K.1,1,K.1^-1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1,1,1,1]; 
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^-1,1,1,1,1,1,K.1^-1,K.1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,1,K.1^-1,K.1,1,K.1^-1,1,K.1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.1^-1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[7, 7, 7, 7, 7, -1, 1, 1, -2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -1, -1, 0, 1, 1, 1, -1, -1, -1, -1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,7,7,7,7,-1,K.1^-1,K.1,-2,-1,-1,-1,-1,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,-2,-1*K.1,-1*K.1^-1,0,K.1,1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |7,7,7,7,7,-1,K.1,K.1^-1,-2,-1,-1,-1,-1,K.1^-1,K.1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,-2,-1*K.1^-1,-1*K.1,0,K.1^-1,1,K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, 8, 8, 8, 8, 0, 2, 2, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |8,8,8,8,8,0,2*K.1^-1,2*K.1,-1,0,0,0,0,2*K.1,2*K.1^-1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,2*K.1,2*K.1^-1,-1,0,0,1,-1*K.1,-1,-1*K.1^-1,0,0,0,0,0,0,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |8,8,8,8,8,0,2*K.1,2*K.1^-1,-1,0,0,0,0,2*K.1^-1,2*K.1,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1,2*K.1^-1,2*K.1^-1,2*K.1,-1,0,0,1,-1*K.1^-1,-1,-1*K.1,0,0,0,0,0,0,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[9, -7, 5, -3, 1, 1, 3, 3, 0, 1, -1, -1, 1, 3, 3, -3, -3, -1, -1, -1, -1, 1, 1, 0, 1, 1, 2, 0, 0, 0, -1, 1, -1, -1, -1, 1, 0, 0, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-7,5,-3,1,1,3*K.1^-1,3*K.1,0,1,-1,-1,1,3*K.1,3*K.1^-1,-3*K.1^-1,-3*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,K.1,K.1^-1,2,0,0,0,-1*K.1^-1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,K.1,0,0,-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |9,-7,5,-3,1,1,3*K.1,3*K.1^-1,0,1,-1,-1,1,3*K.1^-1,3*K.1,-3*K.1,-3*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,K.1^-1,K.1,0,K.1^-1,K.1,2,0,0,0,-1*K.1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,K.1^-1,0,0,-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[21, 21, 21, 21, 21, -3, 0, 0, 3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 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!\[27, 27, 27, 27, 27, 3, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |27,-21,15,-9,3,3,0,0,0,3,-3,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1-2*K.1-2*K.1^2-2*K.1^-3,1+2*K.1+2*K.1^2+2*K.1^-3,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |27,-21,15,-9,3,3,0,0,0,3,-3,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1+2*K.1+2*K.1^2+2*K.1^-3,-1-2*K.1-2*K.1^2-2*K.1^-3,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[36, 20, 8, 0, -4, -4, 3, 3, 0, 4, -2, 2, 0, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, -1, -1, 1, 0, 0, 0, -1, 1, 1, -1, 1, 1, -1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[36, 20, 8, 0, -4, 4, 3, 3, 0, -4, 2, -2, 0, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, 1, 1, 1, 0, 0, 0, 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 |36,20,8,0,-4,-4,3*K.1^-1,3*K.1,0,4,-2,2,0,3*K.1,3*K.1^-1,3*K.1^-1,3*K.1,-1*K.1^-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^-1,1,0,0,0,-1*K.1^-1,K.1^-1,K.1^-1,-1*K.1,K.1,K.1,-1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |36,20,8,0,-4,-4,3*K.1,3*K.1^-1,0,4,-2,2,0,3*K.1^-1,3*K.1,3*K.1,3*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,0,-1*K.1^-1,-1*K.1,1,0,0,0,-1*K.1,K.1,K.1,-1*K.1^-1,K.1^-1,K.1^-1,-1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |36,20,8,0,-4,4,3*K.1^-1,3*K.1,0,-4,2,-2,0,3*K.1,3*K.1^-1,3*K.1^-1,3*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,0,K.1,K.1^-1,1,0,0,0,K.1^-1,-1*K.1^-1,-1*K.1^-1,K.1,-1*K.1,-1*K.1,-1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |36,20,8,0,-4,4,3*K.1,3*K.1^-1,0,-4,2,-2,0,3*K.1^-1,3*K.1,3*K.1,3*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,0,K.1^-1,K.1,1,0,0,0,K.1,-1*K.1,-1*K.1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[63, -49, 35, -21, 7, -1, 3, 3, 0, -1, 1, 1, -1, 3, 3, -3, -3, -1, -1, -1, -1, 1, 1, 0, -1, -1, 0, 0, 0, 0, 1, -1, 1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |63,-49,35,-21,7,-1,3*K.1^-1,3*K.1,0,-1,1,1,-1,3*K.1,3*K.1^-1,-3*K.1^-1,-3*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,-1*K.1,-1*K.1^-1,0,0,0,0,K.1^-1,-1*K.1^-1,K.1^-1,K.1,K.1,-1*K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |63,-49,35,-21,7,-1,3*K.1,3*K.1^-1,0,-1,1,1,-1,3*K.1^-1,3*K.1,-3*K.1,-3*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,K.1^-1,K.1,0,-1*K.1^-1,-1*K.1,0,0,0,0,K.1,-1*K.1,K.1,K.1^-1,K.1^-1,-1*K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[84, -28, 0, 8, -4, 4, 3, 3, 3, -4, -2, 2, 0, -1, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, 1, 1, 0, 0, 0, 0, -1, -1, 1, -1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[84, -28, 0, 8, -4, -4, 3, 3, 3, 4, 2, -2, 0, -1, -1, -1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, -1, 1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |84,-28,0,8,-4,4,3*K.1^-1,3*K.1,3,-4,-2,2,0,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,3*K.1^-1,3*K.1,-1*K.1,-1*K.1^-1,-1,K.1,K.1^-1,0,0,0,0,-1*K.1^-1,-1*K.1^-1,K.1^-1,-1*K.1,K.1,-1*K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |84,-28,0,8,-4,4,3*K.1,3*K.1^-1,3,-4,-2,2,0,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,3*K.1,3*K.1^-1,-1*K.1^-1,-1*K.1,-1,K.1^-1,K.1,0,0,0,0,-1*K.1,-1*K.1,K.1,-1*K.1^-1,K.1^-1,-1*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 |84,-28,0,8,-4,-4,3*K.1^-1,3*K.1,3,4,2,-2,0,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,3*K.1^-1,3*K.1,-1*K.1,-1*K.1^-1,-1,-1*K.1,-1*K.1^-1,0,0,0,0,K.1^-1,K.1^-1,-1*K.1^-1,K.1,-1*K.1,K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |84,-28,0,8,-4,-4,3*K.1,3*K.1^-1,3,4,2,-2,0,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,3*K.1,3*K.1^-1,-1*K.1^-1,-1*K.1,-1,-1*K.1^-1,-1*K.1,0,0,0,0,K.1,K.1,-1*K.1,K.1^-1,-1*K.1^-1,K.1^-1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[126, 14, -14, -6, 6, 6, 6, 6, 0, 6, 0, 0, -2, -6, -6, 0, 0, 2, 2, -2, -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; 
K := CyclotomicField(3: Sparse := true);
S := [ K |126,14,-14,-6,6,6,6*K.1^-1,6*K.1,0,6,0,0,-2,-6*K.1,-6*K.1^-1,0,0,2*K.1^-1,2*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |126,14,-14,-6,6,6,6*K.1,6*K.1^-1,0,6,0,0,-2,-6*K.1^-1,-6*K.1,0,0,2*K.1,2*K.1^-1,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[168, -56, 0, 16, -8, 0, 0, 0, -3, 0, 0, 0, 0, 4, 4, -2, -2, 4, 4, 0, 0, -2, -2, 1, 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 |168,-56,0,16,-8,0,0,0,-3,0,0,0,0,4*K.1^-1,4*K.1,-2*K.1,-2*K.1^-1,4*K.1,4*K.1^-1,0,0,-2*K.1^-1,-2*K.1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |168,-56,0,16,-8,0,0,0,-3,0,0,0,0,4*K.1,4*K.1^-1,-2*K.1^-1,-2*K.1,4*K.1^-1,4*K.1,0,0,-2*K.1,-2*K.1^-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[216, 120, 48, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[378, 42, -42, -18, 18, -6, 0, 0, 0, -6, 0, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_387072_a:= KnownIrreducibles(CR);