/* Group 384.5615 downloaded from the LMFDB on 06 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([8, -2, -2, -2, -2, -3, -2, 2, -2, 3617, 41, 5090, 66, 1283, 91, 8964, 516, 4613, 6925, 1749, 1757, 469, 237, 2694, 9422, 3382, 2382, 878, 382, 166]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.6, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "b4", "b8", "c", "d", "d2"]);
GPerm := PermutationGroup< 64 | (3,6)(4,5)(7,8)(11,14)(12,13)(15,16)(19,22)(20,21)(23,24)(27,30)(28,29)(31,32)(33,34)(35,37)(36,38)(41,42)(43,45)(44,46)(49,50)(51,53)(52,54)(57,58)(59,61)(60,62), (1,58,26,42,10,50,18,34,2,57,25,41,9,49,17,33)(3,60,28,44,12,52,20,36,4,59,27,43,11,51,19,35)(5,62,30,46,14,54,22,38,6,61,29,45,13,53,21,37)(7,64,32,48,16,56,24,40,8,63,31,47,15,55,23,39), (1,26,10,18,2,25,9,17)(3,28,12,20,4,27,11,19)(5,30,14,22,6,29,13,21)(7,32,16,24,8,31,15,23)(33,58,42,50,34,57,41,49)(35,60,44,52,36,59,43,51)(37,62,46,54,38,61,45,53)(39,64,48,56,40,63,47,55), (1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,26,18,25)(19,28,20,27)(21,30,22,29)(23,32,24,31)(33,42,34,41)(35,44,36,43)(37,46,38,45)(39,48,40,47)(49,58,50,57)(51,60,52,59)(53,62,54,61)(55,64,56,63), (3,8,5)(4,7,6)(11,16,13)(12,15,14)(19,24,21)(20,23,22)(27,32,29)(28,31,30)(35,40,37)(36,39,38)(43,48,45)(44,47,46)(51,56,53)(52,55,54)(59,64,61)(60,63,62), (1,6,2,5)(3,8,4,7)(9,14,10,13)(11,16,12,15)(17,22,18,21)(19,24,20,23)(25,30,26,29)(27,32,28,31)(33,38,34,37)(35,40,36,39)(41,46,42,45)(43,48,44,47)(49,54,50,53)(51,56,52,55)(57,62,58,61)(59,64,60,63), (1,4,2,3)(5,7,6,8)(9,12,10,11)(13,15,14,16)(17,20,18,19)(21,23,22,24)(25,28,26,27)(29,31,30,32)(33,36,34,35)(37,39,38,40)(41,44,42,43)(45,47,46,48)(49,52,50,51)(53,55,54,56)(57,60,58,59)(61,63,62,64), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_384_5615 := 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:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, d^2>,< 2, 6, b^12*c>,< 2, 12, a>,< 3, 8, b^16>,< 4, 1, b^12*d^2>,< 4, 1, b^12>,< 4, 6, c*d>,< 4, 12, a*b^4>,< 4, 12, a*b^2*d>,< 4, 12, a*b^6*d>,< 6, 8, b^8>,< 8, 1, b^18*d^2>,< 8, 1, b^6>,< 8, 1, b^6*d^2>,< 8, 1, b^18>,< 8, 6, b^18*d>,< 8, 6, b^6*d>,< 8, 12, a*d>,< 8, 12, a*b^4*c>,< 8, 12, a*b^2>,< 8, 12, a*b^6>,< 12, 8, b^4>,< 12, 8, b^20*d^2>,< 16, 2, b^3>,< 16, 2, b^21*d^2>,< 16, 2, b^9>,< 16, 2, b^15*d^2>,< 16, 6, b^9*d>,< 16, 6, b^15*d>,< 16, 6, b^3*d>,< 16, 6, b^21*d>,< 16, 12, a*b>,< 16, 12, a*b^7>,< 16, 12, a*b^3>,< 16, 12, a*b^5>,< 16, 12, a*b*c>,< 16, 12, a*b^7*c>,< 16, 12, a*b^3*d>,< 16, 12, a*b^5*d>,< 24, 8, b^2>,< 24, 8, b^22*d^2>,< 24, 8, b^10>,< 24, 8, b^14*d^2>,< 48, 8, b>,< 48, 8, b^7>,< 48, 8, b^5>,< 48, 8, b^11*d^2>,< 48, 8, b^11>,< 48, 8, b^5*d^2>,< 48, 8, b*d^2>,< 48, 8, b^7*d^2>]); 
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; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,-1,-1,-1,-1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,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,K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1,-1,-1,-1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-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*K.1,K.1,-1*K.1,K.1,-1,-1,-1,-1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,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,K.1,-1*K.1,K.1,-1*K.1,-1,-1,-1,-1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,1,-1,-1,1,-1,-1,1,-1*K.1^2,1,K.1^2,1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1,1,K.1^2,-1*K.1^2,-1,-1,-1*K.1,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,K.1^3,K.1,-1*K.1^3,-1*K.1,-1*K.1^3,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,K.1^3,K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1^3,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,1,-1,-1,1,-1,-1,1,K.1^2,1,-1*K.1^2,1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,-1,1,-1*K.1^2,K.1^2,-1,-1,K.1^3,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1^3,-1*K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1,-1*K.1^3,K.1,K.1^3,K.1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1,-1*K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,K.1,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,1,-1,-1,1,-1,-1,1,-1*K.1^2,1,K.1^2,1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1,1,K.1^2,-1*K.1^2,-1,-1,K.1,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1^3,-1*K.1,K.1^3,K.1,K.1^3,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^3,-1*K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,K.1^3,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,1,-1,-1,1,-1,-1,1,K.1^2,1,-1*K.1^2,1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,-1,1,-1*K.1^2,K.1^2,-1,-1,-1*K.1^3,K.1^3,K.1,-1*K.1,K.1,-1*K.1^3,K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,K.1,K.1^3,-1*K.1,-1*K.1^3,-1*K.1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1,K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,1,-1*K.1^2,-1,K.1^2,1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,1,-1,K.1^2,-1*K.1^2,-1,-1,K.1^3,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1^3,-1*K.1^3,K.1,-1*K.1^3,K.1^3,K.1,K.1,K.1^3,-1*K.1,-1*K.1^3,-1*K.1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1,-1*K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,K.1,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,1,K.1^2,-1,-1*K.1^2,1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,1,-1,-1*K.1^2,K.1^2,-1,-1,-1*K.1,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1,-1*K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1^3,-1*K.1,K.1^3,K.1,K.1^3,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,K.1^3,K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1^3,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,1,-1*K.1^2,-1,K.1^2,1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,1,-1,K.1^2,-1*K.1^2,-1,-1,-1*K.1^3,K.1^3,K.1,-1*K.1,K.1,-1*K.1^3,K.1^3,-1*K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1,-1*K.1^3,K.1,K.1^3,K.1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1,K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,1,K.1^2,-1,-1*K.1^2,1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,1,-1,-1*K.1^2,K.1^2,-1,-1,K.1,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1,K.1^3,-1*K.1,K.1,K.1^3,K.1^3,K.1,-1*K.1^3,-1*K.1,-1*K.1^3,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^3,-1*K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,K.1^3,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 0, -1, 2, 2, 2, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -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, 0, -1, 2, 2, 2, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,0,-1,2,2,2,0,0,0,-1,-2,-2,-2,-2,-2,-2,0,0,0,0,-1,-1,-2*K.1,-2*K.1,2*K.1,2*K.1,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,0,0,1,1,1,1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,0,-1,2,2,2,0,0,0,-1,-2,-2,-2,-2,-2,-2,0,0,0,0,-1,-1,2*K.1,2*K.1,-2*K.1,-2*K.1,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,0,0,1,1,1,1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,-1,-2,-2,2,0,0,0,-1,-2*K.1^2,2*K.1^2,2*K.1^2,-2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,1,1,-2*K.1,2*K.1,2*K.1^3,-2*K.1^3,2*K.1^3,-2*K.1,2*K.1,-2*K.1^3,0,0,0,0,0,0,0,0,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1^3,-1*K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,K.1^3,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,-1,-2,-2,2,0,0,0,-1,2*K.1^2,-2*K.1^2,-2*K.1^2,2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,1,1,2*K.1^3,-2*K.1^3,-2*K.1,2*K.1,-2*K.1,2*K.1^3,-2*K.1^3,2*K.1,0,0,0,0,0,0,0,0,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,K.1,K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,-1,-2,-2,2,0,0,0,-1,-2*K.1^2,2*K.1^2,2*K.1^2,-2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,1,1,2*K.1,-2*K.1,-2*K.1^3,2*K.1^3,-2*K.1^3,2*K.1,-2*K.1,2*K.1^3,0,0,0,0,0,0,0,0,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^3,K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1^3,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,0,-1,-2,-2,2,0,0,0,-1,2*K.1^2,-2*K.1^2,-2*K.1^2,2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,1,1,-2*K.1^3,2*K.1^3,2*K.1,-2*K.1,2*K.1,-2*K.1^3,2*K.1^3,-2*K.1,0,0,0,0,0,0,0,0,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1,-1*K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,K.1,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, 1, 0, 3, 3, -1, -1, 1, -1, 0, 3, 3, 3, 3, -1, -1, -1, -1, 1, 1, 0, 0, 3, 3, 3, 3, -1, -1, -1, -1, 1, -1, -1, 1, 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; 
x := CR!\[3, 3, -1, -1, 0, 3, 3, -1, 1, -1, 1, 0, 3, 3, 3, 3, -1, -1, 1, 1, -1, -1, 0, 0, 3, 3, 3, 3, -1, -1, -1, -1, -1, 1, 1, -1, -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; 
x := CR!\[3, 3, -1, -1, 0, 3, 3, -1, 1, -1, 1, 0, 3, 3, 3, 3, -1, -1, 1, 1, -1, -1, 0, 0, -3, -3, -3, -3, 1, 1, 1, 1, 1, -1, -1, 1, 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; 
x := CR!\[3, 3, -1, 1, 0, 3, 3, -1, -1, 1, -1, 0, 3, 3, 3, 3, -1, -1, -1, -1, 1, 1, 0, 0, -3, -3, -3, -3, 1, 1, 1, 1, -1, 1, 1, -1, -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(4: Sparse := true);
S := [ K |3,3,-1,-1,0,3,3,-1,-1,-1,-1,0,-3,-3,-3,-3,1,1,1,1,1,1,0,0,-3*K.1,-3*K.1,3*K.1,3*K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.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(4: Sparse := true);
S := [ K |3,3,-1,-1,0,3,3,-1,-1,-1,-1,0,-3,-3,-3,-3,1,1,1,1,1,1,0,0,3*K.1,3*K.1,-3*K.1,-3*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,K.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(4: Sparse := true);
S := [ K |3,3,-1,1,0,3,3,-1,1,1,1,0,-3,-3,-3,-3,1,1,-1,-1,-1,-1,0,0,-3*K.1,-3*K.1,3*K.1,3*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,K.1,K.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(4: Sparse := true);
S := [ K |3,3,-1,1,0,3,3,-1,1,1,1,0,-3,-3,-3,-3,1,1,-1,-1,-1,-1,0,0,3*K.1,3*K.1,-3*K.1,-3*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.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(8: Sparse := true);
S := [ K |3,3,1,-1,0,-3,-3,-1,-1*K.1^2,1,K.1^2,0,3*K.1^2,-3*K.1^2,-3*K.1^2,3*K.1^2,-1*K.1^2,K.1^2,1,-1,-1*K.1^2,K.1^2,0,0,3*K.1^3,-3*K.1^3,-3*K.1,3*K.1,K.1,-1*K.1^3,K.1^3,-1*K.1,K.1^3,K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1,-1*K.1^3,K.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(8: Sparse := true);
S := [ K |3,3,1,-1,0,-3,-3,-1,K.1^2,1,-1*K.1^2,0,-3*K.1^2,3*K.1^2,3*K.1^2,-3*K.1^2,K.1^2,-1*K.1^2,1,-1,K.1^2,-1*K.1^2,0,0,-3*K.1,3*K.1,3*K.1^3,-3*K.1^3,-1*K.1^3,K.1,-1*K.1,K.1^3,-1*K.1,-1*K.1,-1*K.1^3,K.1^3,K.1,K.1^3,K.1,-1*K.1^3,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |3,3,1,-1,0,-3,-3,-1,-1*K.1^2,1,K.1^2,0,3*K.1^2,-3*K.1^2,-3*K.1^2,3*K.1^2,-1*K.1^2,K.1^2,1,-1,-1*K.1^2,K.1^2,0,0,-3*K.1^3,3*K.1^3,3*K.1,-3*K.1,-1*K.1,K.1^3,-1*K.1^3,K.1,-1*K.1^3,-1*K.1^3,-1*K.1,K.1,K.1^3,K.1,K.1^3,-1*K.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(8: Sparse := true);
S := [ K |3,3,1,-1,0,-3,-3,-1,K.1^2,1,-1*K.1^2,0,-3*K.1^2,3*K.1^2,3*K.1^2,-3*K.1^2,K.1^2,-1*K.1^2,1,-1,K.1^2,-1*K.1^2,0,0,3*K.1,-3*K.1,-3*K.1^3,3*K.1^3,K.1^3,-1*K.1,K.1,-1*K.1^3,K.1,K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1^3,-1*K.1,K.1^3,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |3,3,1,1,0,-3,-3,-1,-1*K.1^2,-1,K.1^2,0,-3*K.1^2,3*K.1^2,3*K.1^2,-3*K.1^2,K.1^2,-1*K.1^2,-1,1,-1*K.1^2,K.1^2,0,0,-3*K.1,3*K.1,3*K.1^3,-3*K.1^3,-1*K.1^3,K.1,-1*K.1,K.1^3,K.1,K.1,K.1^3,-1*K.1^3,-1*K.1,-1*K.1^3,-1*K.1,K.1^3,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |3,3,1,1,0,-3,-3,-1,K.1^2,-1,-1*K.1^2,0,3*K.1^2,-3*K.1^2,-3*K.1^2,3*K.1^2,-1*K.1^2,K.1^2,-1,1,K.1^2,-1*K.1^2,0,0,3*K.1^3,-3*K.1^3,-3*K.1,3*K.1,K.1,-1*K.1^3,K.1^3,-1*K.1,-1*K.1^3,-1*K.1^3,-1*K.1,K.1,K.1^3,K.1,K.1^3,-1*K.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(8: Sparse := true);
S := [ K |3,3,1,1,0,-3,-3,-1,-1*K.1^2,-1,K.1^2,0,-3*K.1^2,3*K.1^2,3*K.1^2,-3*K.1^2,K.1^2,-1*K.1^2,-1,1,-1*K.1^2,K.1^2,0,0,3*K.1,-3*K.1,-3*K.1^3,3*K.1^3,K.1^3,-1*K.1,K.1,-1*K.1^3,-1*K.1,-1*K.1,-1*K.1^3,K.1^3,K.1,K.1^3,K.1,-1*K.1^3,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |3,3,1,1,0,-3,-3,-1,K.1^2,-1,-1*K.1^2,0,3*K.1^2,-3*K.1^2,-3*K.1^2,3*K.1^2,-1*K.1^2,K.1^2,-1,1,K.1^2,-1*K.1^2,0,0,-3*K.1^3,3*K.1^3,3*K.1,-3*K.1,-1*K.1,K.1^3,-1*K.1^3,K.1,K.1^3,K.1^3,K.1,-1*K.1,-1*K.1^3,-1*K.1,-1*K.1^3,K.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(8: Sparse := true);
S := [ K |4,-4,0,0,-2,-4*K.1^2,4*K.1^2,0,0,0,0,2,4*K.1^3,-4*K.1,4*K.1,-4*K.1^3,0,0,0,0,0,0,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1^3,-2*K.1,-2*K.1^3,2*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,0,0,-2,4*K.1^2,-4*K.1^2,0,0,0,0,2,-4*K.1,4*K.1^3,-4*K.1^3,4*K.1,0,0,0,0,0,0,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1^3,2*K.1,-2*K.1^3,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,0,0,-2,-4*K.1^2,4*K.1^2,0,0,0,0,2,-4*K.1^3,4*K.1,-4*K.1,4*K.1^3,0,0,0,0,0,0,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^3,2*K.1,2*K.1^3,-2*K.1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,0,0,-2,4*K.1^2,-4*K.1^2,0,0,0,0,2,4*K.1,-4*K.1^3,4*K.1^3,-4*K.1,0,0,0,0,0,0,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1^3,-2*K.1,2*K.1^3,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(48: Sparse := true);
S := [ K |4,-4,0,0,1,-4*K.1^12,4*K.1^12,0,0,0,0,-1,4*K.1^18,-4*K.1^6,4*K.1^6,-4*K.1^18,0,0,0,0,0,0,-1*K.1^12,K.1^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^18,K.1^6,K.1^18,-1*K.1^6,-1*K.1^5-K.1^13,-2*K.1^7+K.1^15,K.1^5+K.1^13,2*K.1^7-K.1^15,-1*K.1^3+2*K.1^11,-2*K.1+K.1^9,2*K.1-K.1^9,K.1^3-2*K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(48: Sparse := true);
S := [ K |4,-4,0,0,1,4*K.1^12,-4*K.1^12,0,0,0,0,-1,-4*K.1^6,4*K.1^18,-4*K.1^18,4*K.1^6,0,0,0,0,0,0,K.1^12,-1*K.1^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^6,-1*K.1^18,-1*K.1^6,K.1^18,-1*K.1^3+2*K.1^11,-2*K.1+K.1^9,K.1^3-2*K.1^11,2*K.1-K.1^9,-1*K.1^5-K.1^13,-2*K.1^7+K.1^15,2*K.1^7-K.1^15,K.1^5+K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(48: Sparse := true);
S := [ K |4,-4,0,0,1,-4*K.1^12,4*K.1^12,0,0,0,0,-1,4*K.1^18,-4*K.1^6,4*K.1^6,-4*K.1^18,0,0,0,0,0,0,-1*K.1^12,K.1^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^18,K.1^6,K.1^18,-1*K.1^6,K.1^5+K.1^13,2*K.1^7-K.1^15,-1*K.1^5-K.1^13,-2*K.1^7+K.1^15,K.1^3-2*K.1^11,2*K.1-K.1^9,-2*K.1+K.1^9,-1*K.1^3+2*K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(48: Sparse := true);
S := [ K |4,-4,0,0,1,4*K.1^12,-4*K.1^12,0,0,0,0,-1,-4*K.1^6,4*K.1^18,-4*K.1^18,4*K.1^6,0,0,0,0,0,0,K.1^12,-1*K.1^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^6,-1*K.1^18,-1*K.1^6,K.1^18,K.1^3-2*K.1^11,2*K.1-K.1^9,-1*K.1^3+2*K.1^11,-2*K.1+K.1^9,K.1^5+K.1^13,2*K.1^7-K.1^15,-2*K.1^7+K.1^15,-1*K.1^5-K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(48: Sparse := true);
S := [ K |4,-4,0,0,1,-4*K.1^12,4*K.1^12,0,0,0,0,-1,-4*K.1^18,4*K.1^6,-4*K.1^6,4*K.1^18,0,0,0,0,0,0,-1*K.1^12,K.1^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^18,-1*K.1^6,-1*K.1^18,K.1^6,-2*K.1+K.1^9,K.1^3-2*K.1^11,2*K.1-K.1^9,-1*K.1^3+2*K.1^11,-2*K.1^7+K.1^15,K.1^5+K.1^13,-1*K.1^5-K.1^13,2*K.1^7-K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(48: Sparse := true);
S := [ K |4,-4,0,0,1,4*K.1^12,-4*K.1^12,0,0,0,0,-1,4*K.1^6,-4*K.1^18,4*K.1^18,-4*K.1^6,0,0,0,0,0,0,K.1^12,-1*K.1^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^6,K.1^18,K.1^6,-1*K.1^18,-2*K.1^7+K.1^15,K.1^5+K.1^13,2*K.1^7-K.1^15,-1*K.1^5-K.1^13,-2*K.1+K.1^9,K.1^3-2*K.1^11,-1*K.1^3+2*K.1^11,2*K.1-K.1^9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(48: Sparse := true);
S := [ K |4,-4,0,0,1,-4*K.1^12,4*K.1^12,0,0,0,0,-1,-4*K.1^18,4*K.1^6,-4*K.1^6,4*K.1^18,0,0,0,0,0,0,-1*K.1^12,K.1^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^18,-1*K.1^6,-1*K.1^18,K.1^6,2*K.1-K.1^9,-1*K.1^3+2*K.1^11,-2*K.1+K.1^9,K.1^3-2*K.1^11,2*K.1^7-K.1^15,-1*K.1^5-K.1^13,K.1^5+K.1^13,-2*K.1^7+K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(48: Sparse := true);
S := [ K |4,-4,0,0,1,4*K.1^12,-4*K.1^12,0,0,0,0,-1,4*K.1^6,-4*K.1^18,4*K.1^18,-4*K.1^6,0,0,0,0,0,0,K.1^12,-1*K.1^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^6,K.1^18,K.1^6,-1*K.1^18,2*K.1^7-K.1^15,-1*K.1^5-K.1^13,-2*K.1^7+K.1^15,K.1^5+K.1^13,2*K.1-K.1^9,-1*K.1^3+2*K.1^11,K.1^3-2*K.1^11,-2*K.1+K.1^9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_384_5615:= KnownIrreducibles(CR);