/* Group 3888.by downloaded from the LMFDB on 07 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([9, 2, 2, 3, 2, 3, 2, 3, 3, 3, 8316, 44029, 46, 16742, 35436, 29289, 102, 1093, 68045, 65138, 45221, 9428, 158, 217734, 54447, 6828, 1545, 10384, 62233, 916, 81656, 23345, 40850, 20447, 2969]); a,b,c,d,e,f := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.8, GPC.9]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "d2", "e", "f"]);
GPerm := PermutationGroup< 12 | (1,3,6)(2,4,7,9)(5,8)(10,12,11), (1,2,3,5)(6,7)(8,9)(10,11) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_3888_by := 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:= GPerm;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 27, G!(4,8)(5,7)>,< 2, 27, G!(4,9)(11,12)>,< 2, 54, G!(1,8)(3,9)(4,6)(11,12)>,< 2, 54, G!(1,9)(2,7)(3,4)(6,8)>,< 2, 81, G!(2,5)(3,6)(4,9)(11,12)>,< 3, 2, G!(10,11,12)>,< 3, 6, G!(1,6,3)>,< 3, 8, G!(1,3,6)(2,5,7)(4,8,9)>,< 3, 12, G!(1,6,3)(2,5,7)>,< 3, 12, G!(2,5,7)(10,12,11)>,< 3, 16, G!(1,3,6)(2,5,7)(4,8,9)(10,11,12)>,< 3, 24, G!(1,6,3)(2,5,7)(10,11,12)>,< 3, 72, G!(1,8,7)(2,6,4)(3,9,5)>,< 3, 144, G!(1,2,8)(3,7,9)(4,6,5)(10,12,11)>,< 4, 54, G!(2,9)(4,5,8,7)>,< 4, 486, G!(2,4)(3,6)(5,8,7,9)(10,11)>,< 6, 54, G!(1,3,6)(4,8)(5,7)>,< 6, 54, G!(3,6)(4,9)(10,12,11)>,< 6, 108, G!(1,9)(2,7)(3,4)(6,8)(10,12,11)>,< 6, 108, G!(1,5)(2,3)(4,8,9)(6,7)(10,11)>,< 6, 108, G!(1,2,6,5,3,7)(4,8)>,< 6, 108, G!(1,6)(2,7,5)(4,8)(10,11,12)>,< 6, 108, G!(1,5,3,2,6,7)(11,12)>,< 6, 108, G!(1,3,6)(2,5,7)(4,9)(11,12)>,< 6, 108, G!(1,6)(2,7,5)(11,12)>,< 6, 216, G!(1,4,3,8,6,9)(2,7,5)(11,12)>,< 6, 216, G!(1,2,6,5,3,7)(4,8)(10,12,11)>,< 6, 648, G!(1,7,8)(2,9,6,5,4,3)(11,12)>,< 9, 144, G!(1,7,9,3,5,4,6,2,8)>,< 9, 144, G!(1,4,5,6,9,7,3,8,2)(10,12,11)>,< 9, 144, G!(1,2,8,3,7,9,6,5,4)(10,11,12)>,< 12, 108, G!(1,6,3)(2,9)(4,7,8,5)>,< 12, 108, G!(1,8)(3,4,6,9)(10,11,12)>,< 12, 108, G!(1,4,6,8)(2,5,7)(3,9)(10,12,11)>,< 12, 108, G!(1,8,6,4)(2,7,5)(3,9)(10,11,12)>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, 0, -1, 2, 2, 2, -1, -1, -1, 2, -1, 2, 0, 2, -1, -1, 0, 2, -1, 0, 0, 0, 0, -1, 0, 2, -1, -1, -1, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, 0, -2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 2, 2, 0, 0, 0, 2, -2, 0, -2, 0, 0, 1, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, -2, 0, -1, 2, 2, 2, -1, -1, -1, 2, -1, -2, 0, 2, -1, 1, 0, -2, -1, 0, 0, 0, 0, 1, 0, 2, -1, -1, 1, -2, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, 1, -1, 1, -3, 3, 3, 3, 3, 3, 3, 3, 0, 0, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, 1, 1, -1, -3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 0, 0, 0, 0, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 0, 0, 0, -2, 4, 4, 4, -2, -2, -2, -2, 1, 0, 0, 4, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 2, 4, 2, 0, 0, 6, 3, -3, 0, 3, -3, 0, 0, 0, 2, 0, -1, 2, 0, -1, 0, -1, 1, 2, -2, -1, 0, 0, 0, 0, 0, 2, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, 0, 0, 2, 0, -3, 6, 6, 6, -3, -3, -3, 0, 0, -2, 0, -2, 1, -1, 0, 2, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -2, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -2, 0, 0, -2, 0, -3, 6, 6, 6, -3, -3, -3, 0, 0, 2, 0, -2, 1, 1, 0, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 2, -4, -2, 0, 0, 6, 3, -3, 0, 3, -3, 0, 0, 0, 2, 0, -1, 2, 0, 1, 0, -1, -1, -2, 2, 1, 0, 0, 0, 0, 0, 2, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 2, -4, 2, 0, 0, 6, 3, -3, 0, 3, -3, 0, 0, 0, -2, 0, -1, 2, 0, -1, 0, -1, -1, 2, 2, -1, 0, 0, 0, 0, 0, -2, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 2, 4, -2, 0, 0, 6, 3, -3, 0, 3, -3, 0, 0, 0, -2, 0, -1, 2, 0, 1, 0, -1, 1, -2, -2, 1, 0, 0, 0, 0, 0, -2, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, 4, 0, 0, 8, -4, -1, 2, -4, -1, 2, 2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 0, 0, -4, 0, 0, 8, -4, -1, 2, -4, -1, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -1, 0, 0, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 0, 4, 2, 2, 0, 12, 0, 3, -3, 0, 3, -3, 0, 0, 0, 0, 0, 0, 2, 2, -1, 0, -2, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 4, 0, 0, 0, 0, -6, 6, -6, 0, -3, 3, 0, 0, 0, 4, 0, -2, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, -4, 0, 0, 0, 0, 12, 6, -6, 0, 6, -6, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 0, -4, 2, -2, 0, 12, 0, 3, -3, 0, 3, -3, 0, 0, 0, 0, 0, 0, -2, 2, 1, 0, 2, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 0, 4, -2, -2, 0, 12, 0, 3, -3, 0, 3, -3, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 0, -4, -2, 2, 0, 12, 0, 3, -3, 0, 3, -3, 0, 0, 0, 0, 0, 0, 2, -2, -1, 0, 2, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 4, 0, 0, 0, 0, -6, 6, -6, 0, -3, 3, 0, 0, 0, -4, 0, -2, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |12,-4,0,0,0,0,-6,6,-6,0,-3,3,0,0,0,0,0,2,2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-3*K.1,3*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |12,-4,0,0,0,0,-6,6,-6,0,-3,3,0,0,0,0,0,2,2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,3*K.1,-3*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[16, 0, 0, 0, 0, 0, 16, -8, -2, 4, -8, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[16, 0, 0, 0, 0, 0, -8, -8, -2, 4, 4, 1, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |16,0,0,0,0,0,-8,-8,-2,4,4,1,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-2-3*K.1,1+3*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |16,0,0,0,0,0,-8,-8,-2,4,4,1,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1+3*K.1,-2-3*K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[24, 0, 0, 0, 4, 0, -12, 0, 6, -6, 0, -3, 3, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[24, 0, 0, 0, -4, 0, -12, 0, 6, -6, 0, -3, 3, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_3888_by:= KnownIrreducibles(CR);