/* Group 288.874 downloaded from the LMFDB on 15 September 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, -2, -2, -2, -3, 3, 336, 85, 36, 1094, 268, 7843, 3930, 297, 80, 6164, 3091, 718, 102, 10757, 5388, 691, 3933, 2372]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.4, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "c4", "d"]);
GPerm := PermutationGroup< 22 | (1,2)(3,5)(4,6)(7,8)(9,16)(10,14)(11,20)(12,15)(13,18)(17,21)(19,22), (4,5)(7,9,12,19)(8,13,15,21)(10,18,11,17)(14,22,20,16), (7,10,12,11)(8,14,15,20)(9,17,19,18)(13,16,21,22), (3,6)(4,5)(7,11,12,10)(8,14,15,20)(9,18,19,17)(13,16,21,22), (7,12)(8,15)(9,19)(10,11)(13,21)(14,20)(16,22)(17,18), (1,3,6)(2,4,5), (1,3,6)(2,5,4) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_288_874 := 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:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, c^6>,< 2, 12, a*b*c^8>,< 2, 18, b^2*c^5*d^2>,< 3, 4, c^8*d^2>,< 3, 4, c^4*d^2>,< 4, 2, c^3>,< 4, 12, a*b*c^3>,< 4, 12, a*c^4*d^2>,< 4, 12, a*c^5*d>,< 4, 18, b^2*c^4>,< 6, 4, c^2>,< 6, 4, c^2*d>,< 6, 12, a*b*d>,< 6, 12, a*b*d^2>,< 8, 36, b*c^10*d^2>,< 8, 36, b^3*c^5*d^2>,< 12, 4, c>,< 12, 4, c*d>,< 12, 8, c*d^2>,< 12, 12, a*b*c*d>,< 12, 12, a*b*c*d^2>,< 12, 24, a*c^10*d>,< 12, 24, a*c^11*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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, -2, 2, 2, 2, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 2, 2, 2, -2, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, -2, 1, 4, 0, 2, 2, 0, -2, 1, 0, 0, 0, 0, -2, -2, 1, 0, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 2, 0, 1, -2, 4, 2, 0, 0, 0, 1, -2, -1, -1, 0, 0, 1, 1, -2, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -2, 0, 1, -2, 4, -2, 0, 0, 0, 1, -2, 1, 1, 0, 0, 1, 1, -2, 1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, -2, 1, 4, 0, -2, -2, 0, -2, 1, 0, 0, 0, 0, -2, -2, 1, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -2, 0, 1, -2, -4, 2, 0, 0, 0, 1, -2, 1, 1, 0, 0, -1, -1, 2, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, -2, 1, -4, 0, -2, 2, 0, -2, 1, 0, 0, 0, 0, 2, 2, -1, 0, 0, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, -2, 1, -4, 0, 2, -2, 0, -2, 1, 0, 0, 0, 0, 2, 2, -1, 0, 0, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 2, 0, 1, -2, -4, -2, 0, 0, 0, 1, -2, -1, -1, 0, 0, -1, -1, 2, 1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 0, 4, 4, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,0,0,1,-2,0,0,0,0,0,-1,2,1-2*K.1^2,-1+2*K.1^2,0,0,-3*K.1^3,3*K.1^3,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,0,0,1,-2,0,0,0,0,0,-1,2,-1+2*K.1^2,1-2*K.1^2,0,0,3*K.1^3,-3*K.1^3,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,0,0,1,-2,0,0,0,0,0,-1,2,1-2*K.1^2,-1+2*K.1^2,0,0,3*K.1^3,-3*K.1^3,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,0,0,1,-2,0,0,0,0,0,-1,2,-1+2*K.1^2,1-2*K.1^2,0,0,-3*K.1^3,3*K.1^3,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, 0, -4, 2, 0, 0, 0, 0, 0, 4, -2, 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_288_874:= KnownIrreducibles(CR);