/* Group 672.313 downloaded from the LMFDB on 31 October 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([7, -2, -3, -2, -2, -7, -2, -2, 14, 380, 576, 58, 1011, 1522, 80, 2524, 851, 3547, 124]); a,b,c := Explode([GPC.1, GPC.3, GPC.6]); AssignNames(~GPC, ["a", "a2", "b", "b2", "b4", "c", "c2"]);
GPerm := PermutationGroup< 15 | (2,3)(4,6)(5,7)(10,11)(12,13)(14,15), (8,9)(10,11)(12,14,13,15), (8,10,9,11)(12,14)(13,15), (2,4,5)(3,6,7), (8,9)(10,11), (12,13)(14,15), (1,2,5,6,4,7,3) >;
GLZN := MatrixGroup< 2, Integers(56) | [[25, 0, 0, 9], [1, 28, 0, 1], [29, 0, 0, 29], [13, 42, 0, 13], [13, 44, 28, 1], [27, 17, 0, 29], [1, 8, 0, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_672_313 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, b^14*c^2>,< 2, 1, c^2>,< 2, 1, b^14>,< 2, 14, a^3>,< 2, 14, a^3*c^2>,< 2, 28, a^3*b^11>,< 2, 28, a^3*b^21*c^3>,< 3, 7, a^4*b^20>,< 3, 7, a^2*b^16>,< 4, 2, c^3>,< 4, 2, b^14*c^3>,< 4, 4, b^7>,< 4, 4, b^7*c>,< 4, 14, a^3*c^3>,< 4, 14, a^3*c>,< 6, 7, a^2*b^2*c^2>,< 6, 7, a^4*b^2*c^2>,< 6, 7, a^4*c^2>,< 6, 7, a^2*c^2>,< 6, 7, a^4*b^26>,< 6, 7, a^2*b^18>,< 6, 14, a>,< 6, 14, a^5>,< 6, 14, a*c^2>,< 6, 14, a^5*c^2>,< 6, 28, a*b^3>,< 6, 28, a^5*b^27>,< 6, 28, a*b^21*c^3>,< 6, 28, a^5*b^21*c^3>,< 7, 6, b^4>,< 12, 14, a^2*c>,< 12, 14, a^4*c>,< 12, 14, a^2*b^2*c>,< 12, 14, a^4*b^2*c>,< 12, 14, a*c>,< 12, 14, a^5*c^3>,< 12, 14, a^5*c>,< 12, 14, a*c^3>,< 12, 28, a^2*b^25*c^3>,< 12, 28, a^4*b^19*c^3>,< 12, 28, a^4*b^5>,< 12, 28, a^2*b^11>,< 14, 6, b^2*c^2>,< 14, 6, b^8*c^2>,< 14, 6, b^2>,< 28, 12, b^4*c>,< 28, 12, b^2*c>,< 28, 12, b>,< 28, 12, b^5>,< 28, 12, b*c>,< 28, 12, b^5*c>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,K.1^-1,K.1,1,1,1,1,1,1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,1,K.1^-1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,K.1,K.1^-1,1,1,1,1,1,1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,1,1,1,1,1,1,1,1,1]; 
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,-1,-1,K.1^-1,K.1,1,1,1,1,-1,-1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,1,K.1^-1,-1*K.1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,1,1,1,1,1,1,1,1,1]; 
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,-1,-1,K.1,K.1^-1,1,1,1,1,-1,-1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,1,K.1,-1*K.1^-1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,1,1,1,1,1,1,1,1,1]; 
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,-1,1,K.1^-1,K.1,-1,-1,1,-1,1,1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,K.1,K.1^-1,1,-1*K.1^-1,K.1,-1*K.1,K.1,K.1^-1,K.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]; 
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,-1,1,K.1,K.1^-1,-1,-1,1,-1,1,1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,K.1^-1,K.1,1,-1*K.1,K.1^-1,-1*K.1^-1,K.1^-1,K.1,K.1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,1,1,1,-1,-1,1,1,-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,-1,1,-1,K.1^-1,K.1,-1,-1,-1,1,1,1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,K.1,K.1^-1,-1*K.1,-1*K.1^-1,1,-1*K.1^-1,K.1,-1*K.1,K.1,K.1^-1,K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,1,1,1,-1,1,-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,-1,1,-1,K.1,K.1^-1,-1,-1,-1,1,1,1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,K.1^-1,K.1,-1*K.1^-1,-1*K.1,1,-1*K.1,K.1^-1,-1*K.1^-1,K.1^-1,K.1,K.1,-1*K.1^-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,-1,-1,1,1,K.1^-1,K.1,1,1,-1,-1,-1,-1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,K.1,K.1^-1,K.1,K.1^-1,1,K.1^-1,-1*K.1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,1,1,1,1,-1,-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,-1,1,1,K.1,K.1^-1,1,1,-1,-1,-1,-1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,K.1^-1,K.1,K.1^-1,K.1,1,K.1,-1*K.1^-1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,1,1,1,1,-1,-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,-1,-1,K.1^-1,K.1,1,1,-1,-1,1,1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.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,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,1,1,1,1,-1,-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,-1,-1,K.1,K.1^-1,1,1,-1,-1,1,1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,K.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^-1,K.1^-1,K.1,K.1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,1,1,1,1,-1,-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,-1,1,K.1^-1,K.1,-1,-1,-1,1,-1,-1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,K.1,K.1^-1,-1*K.1,-1*K.1^-1,K.1,K.1^-1,1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,1,1,1,-1,1,-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,-1,1,K.1,K.1^-1,-1,-1,-1,1,-1,-1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,-1*K.1^-1,-1*K.1,K.1^-1,K.1,1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,1,1,-1,K.1^-1,K.1,-1,-1,1,-1,-1,-1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,-1*K.1,-1*K.1^-1,1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,1,1,1,-1,K.1,K.1^-1,-1,-1,1,-1,-1,-1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,-1*K.1^-1,-1*K.1,1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,1,1,1,-1,-1,1,1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, 0, 0, 0, 0, 2, 2, -2, 2, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, 2, -2, -2, 0, 0, 0, 0, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, -2, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, -2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,2,2,0,0,0,0,-2*K.1,2*K.1,2,-2,-2,-2,2,-2,0,0,0,0,0,0,0,0,2,0,-2*K.1,0,2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,2,-2,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,2,2,0,0,0,0,2*K.1,-2*K.1,2,-2,-2,-2,2,-2,0,0,0,0,0,0,0,0,2,0,2*K.1,0,-2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,2,-2,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,2*K.1^-1,2*K.1,-2,2,0,0,0,0,-2*K.1,-2*K.1^-1,2*K.1,2*K.1^-1,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,2,2*K.1^-1,0,2*K.1,0,0,0,-2*K.1,-2*K.1^-1,0,0,0,0,-2,2,-2,-2,0,0,0,0,2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,2*K.1,2*K.1^-1,-2,2,0,0,0,0,-2*K.1^-1,-2*K.1,2*K.1^-1,2*K.1,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,2,2*K.1,0,2*K.1^-1,0,0,0,-2*K.1^-1,-2*K.1,0,0,0,0,-2,2,-2,-2,0,0,0,0,2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,2*K.1^-1,2*K.1,2,-2,0,0,0,0,-2*K.1,-2*K.1^-1,2*K.1,2*K.1^-1,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,2,-2*K.1^-1,0,-2*K.1,0,0,0,2*K.1,2*K.1^-1,0,0,0,0,-2,2,-2,2,0,0,0,0,-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,2*K.1,2*K.1^-1,2,-2,0,0,0,0,-2*K.1^-1,-2*K.1,2*K.1^-1,2*K.1,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,2,-2*K.1,0,-2*K.1^-1,0,0,0,2*K.1^-1,2*K.1,0,0,0,0,-2,2,-2,2,0,0,0,0,-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,0,0,2*K.1^-1,2*K.1,0,0,0,0,0,0,-2*K.1,2*K.1^-1,-2*K.1,-2*K.1^-1,-2*K.1^-1,2*K.1,-2*K.1,-2*K.1^-1,2*K.1,2*K.1^-1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,0,0,2*K.1,2*K.1^-1,0,0,0,0,0,0,-2*K.1^-1,2*K.1,-2*K.1^-1,-2*K.1,-2*K.1,2*K.1^-1,-2*K.1^-1,-2*K.1,2*K.1^-1,2*K.1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,2,-2,0,0,2*K.1^-1,2*K.1,0,0,0,0,0,0,-2*K.1,2*K.1^-1,-2*K.1,-2*K.1^-1,-2*K.1^-1,2*K.1,2*K.1,2*K.1^-1,-2*K.1,-2*K.1^-1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,-2,-2,2,-2,0,0,2*K.1,2*K.1^-1,0,0,0,0,0,0,-2*K.1^-1,2*K.1,-2*K.1^-1,-2*K.1,-2*K.1,2*K.1^-1,2*K.1^-1,2*K.1,-2*K.1^-1,-2*K.1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,-2*K.1^2,2*K.1^4,0,0,0,0,-2*K.1^3,2*K.1^3,2*K.1^4,2*K.1^2,-2*K.1^4,2*K.1^2,-2*K.1^2,-2*K.1^4,0,0,0,0,0,0,0,0,2,0,2*K.1,0,-2*K.1,-2*K.1^5,2*K.1^5,0,0,0,0,0,0,2,-2,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,2*K.1^4,-2*K.1^2,0,0,0,0,2*K.1^3,-2*K.1^3,-2*K.1^2,-2*K.1^4,2*K.1^2,-2*K.1^4,2*K.1^4,2*K.1^2,0,0,0,0,0,0,0,0,2,0,-2*K.1^5,0,2*K.1^5,2*K.1,-2*K.1,0,0,0,0,0,0,2,-2,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,-2*K.1^2,2*K.1^4,0,0,0,0,2*K.1^3,-2*K.1^3,2*K.1^4,2*K.1^2,-2*K.1^4,2*K.1^2,-2*K.1^2,-2*K.1^4,0,0,0,0,0,0,0,0,2,0,-2*K.1,0,2*K.1,2*K.1^5,-2*K.1^5,0,0,0,0,0,0,2,-2,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,2*K.1^4,-2*K.1^2,0,0,0,0,-2*K.1^3,2*K.1^3,-2*K.1^2,-2*K.1^4,2*K.1^2,-2*K.1^4,2*K.1^4,2*K.1^2,0,0,0,0,0,0,0,0,2,0,2*K.1^5,0,-2*K.1^5,-2*K.1,2*K.1,0,0,0,0,0,0,2,-2,-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 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, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 0, 0, 0, 0, 0, 0, -6, -6, -6, 6, 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, 0, 0, 0, -1, -1, -1, 1, -1, 1, 1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 0, 0, 0, 0, 0, 0, -6, -6, 6, -6, 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, 0, 0, 0, -1, -1, -1, 1, 1, -1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, -6, -6, 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, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |6,-6,-6,6,0,0,0,0,0,0,-6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,1,-2*K.1+K.1^7-2*K.1^9+2*K.1^11,2*K.1-K.1^7+2*K.1^9-2*K.1^11,-2*K.1+K.1^7-2*K.1^9+2*K.1^11,2*K.1-K.1^7+2*K.1^9-2*K.1^11,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |6,-6,-6,6,0,0,0,0,0,0,-6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,1,2*K.1-K.1^7+2*K.1^9-2*K.1^11,-2*K.1+K.1^7-2*K.1^9+2*K.1^11,2*K.1-K.1^7+2*K.1^9-2*K.1^11,-2*K.1+K.1^7-2*K.1^9+2*K.1^11,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |6,-6,-6,6,0,0,0,0,0,0,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,-2*K.1+K.1^7-2*K.1^9+2*K.1^11,-2*K.1+K.1^7-2*K.1^9+2*K.1^11,2*K.1-K.1^7+2*K.1^9-2*K.1^11,2*K.1-K.1^7+2*K.1^9-2*K.1^11,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |6,-6,-6,6,0,0,0,0,0,0,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,2*K.1-K.1^7+2*K.1^9-2*K.1^11,2*K.1-K.1^7+2*K.1^9-2*K.1^11,-2*K.1+K.1^7-2*K.1^9+2*K.1^11,-2*K.1+K.1^7-2*K.1^9+2*K.1^11,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, -12, -12, 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, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, -12, 12, -12, 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, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_672_313:= KnownIrreducibles(CR);