/* Group 648.300 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, 2, 3, 3, 2, 3, 3, 141, 36, 170, 12771, 6394, 3125, 3371, 438, 102, 8076, 1027, 166, 10597]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.4, GPC.5]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "d2", "d6"]);
GPerm := PermutationGroup< 29 | (3,10)(7,17)(8,19)(11,23)(12,24)(14,25)(16,20)(18,26)(21,27), (2,5)(3,11)(4,13)(6,9)(7,14)(8,20)(10,23)(12,24)(15,22)(16,19)(17,25)(18,21)(26,27)(28,29), (28,29), (1,2,6,13,22,15,4,9,5)(3,8,16,23,17,26,12,21,14)(7,18,24,27,25,10,19,20,11), (2,7,17)(3,12,23)(5,14,25)(6,16,20)(8,9,19)(10,11,24)(15,26,18)(21,22,27), (1,3,11)(2,8,7)(4,12,10)(5,14,20)(6,16,18)(9,21,19)(13,23,24)(15,26,25)(17,27,22), (1,4,13)(2,9,22)(3,12,23)(5,15,6)(7,19,27)(8,21,17)(10,24,11)(14,26,16)(18,20,25) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_648_300 := 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 := true>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, d^9>,< 2, 9, a>,< 2, 9, a*d^9>,< 2, 27, b^3*c*d^5>,< 2, 27, b^3*c^2*d^16>,< 2, 27, a*b^3*d^17>,< 2, 27, a*b^3*d^6>,< 3, 2, d^6>,< 3, 6, c^2*d^6>,< 3, 18, b^4*d^6>,< 6, 2, d^3>,< 6, 6, c*d^3>,< 6, 18, b^2*d^3>,< 6, 18, a*d^6>,< 6, 18, a*d^3>,< 6, 54, b^5*c^2*d^11>,< 6, 54, b^5*c*d^10>,< 6, 54, a*b^3*c*d^11>,< 6, 54, a*b^3*c>,< 9, 6, d^2>,< 9, 6, d^4>,< 9, 6, d^8>,< 9, 36, b^2*c^2*d^2>,< 18, 6, d>,< 18, 6, d^13>,< 18, 6, d^7>,< 18, 18, a*d^2>,< 18, 18, a*d^8>,< 18, 18, a*d^4>,< 18, 18, a*d>,< 18, 18, a*d^13>,< 18, 18, a*d^7>,< 18, 36, b^4*d^13>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, 2, 2, -1, 0, 0, -1, -1, 0, 0, 2, 2, 2, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -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, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, -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, 0, 0, 0, 0, -2, 2, 2, 2, -1, -2, -2, 1, 0, 0, -1, 1, 0, 0, 2, 2, 2, -1, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 0, 0, 0, 2, -2, 2, 2, -1, -2, -2, 1, 0, 0, 1, -1, 0, 0, 2, 2, 2, -1, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, -2, 0, 0, 0, 0, -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, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, -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, 0, 0, 0, 0, -2, -2, 2, 2, -1, 2, 2, -1, 0, 0, 1, 1, 0, 0, 2, 2, 2, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 0, 0, 0, 0, 4, 4, -2, 4, 4, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, -2, -2, -2, 0, 0, 0, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 0, 0, 0, 0, 0, 4, 4, -2, -4, -4, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 0, 0, 2, 2, 0, 0, 6, -3, 0, 6, -3, 0, 0, 0, 0, 0, -1, -1, 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!\[6, 6, 0, 0, -2, -2, 0, 0, 6, -3, 0, 6, -3, 0, 0, 0, 0, 0, 1, 1, 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!\[6, -6, 0, 0, -2, 2, 0, 0, 6, -3, 0, -6, 3, 0, 0, 0, 0, 0, -1, 1, 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!\[6, -6, 0, 0, 2, -2, 0, 0, 6, -3, 0, -6, 3, 0, 0, 0, 0, 0, 1, -1, 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(9: Sparse := true);
S := [ K |6,6,2,2,0,0,0,0,-3,0,0,-3,0,0,-1,-1,0,0,0,0,-1*K.1+K.1^2+K.1^4+2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,0,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,6,2,2,0,0,0,0,-3,0,0,-3,0,0,-1,-1,0,0,0,0,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,0,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,6,2,2,0,0,0,0,-3,0,0,-3,0,0,-1,-1,0,0,0,0,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,0,-1*K.1+K.1^2-2*K.1^4-K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,-3,0,0,3,0,0,1,-1,0,0,0,0,-1*K.1+K.1^2+K.1^4+2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,0,K.1-K.1^2-K.1^4-2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,-3,0,0,3,0,0,1,-1,0,0,0,0,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,0,-2*K.1+2*K.1^2-K.1^4+K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-6,-2,2,0,0,0,0,-3,0,0,3,0,0,1,-1,0,0,0,0,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,0,K.1-K.1^2+2*K.1^4+K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-6,2,-2,0,0,0,0,-3,0,0,3,0,0,-1,1,0,0,0,0,-1*K.1+K.1^2+K.1^4+2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,0,K.1-K.1^2-K.1^4-2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,K.1+K.1^-1,K.1^4+K.1^-4,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-6,2,-2,0,0,0,0,-3,0,0,3,0,0,-1,1,0,0,0,0,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,0,-2*K.1+2*K.1^2-K.1^4+K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,K.1-K.1^2+2*K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,K.1^4+K.1^-4,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,-6,2,-2,0,0,0,0,-3,0,0,3,0,0,-1,1,0,0,0,0,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,0,K.1-K.1^2+2*K.1^4+K.1^-4,-2*K.1+2*K.1^2-K.1^4+K.1^-4,K.1-K.1^2-K.1^4-2*K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,6,-2,-2,0,0,0,0,-3,0,0,-3,0,0,1,1,0,0,0,0,-1*K.1+K.1^2+K.1^4+2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,0,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,6,-2,-2,0,0,0,0,-3,0,0,-3,0,0,1,1,0,0,0,0,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,0,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(9: Sparse := true);
S := [ K |6,6,-2,-2,0,0,0,0,-3,0,0,-3,0,0,1,1,0,0,0,0,-1*K.1+K.1^2-2*K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,0,-1*K.1+K.1^2-2*K.1^4-K.1^-4,2*K.1-2*K.1^2+K.1^4-K.1^-4,-1*K.1+K.1^2+K.1^4+2*K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^4-K.1^-4,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_648_300:= KnownIrreducibles(CR);