/* Group 384.20080 downloaded from the LMFDB on 04 February 2026. */
 
/* 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, -3, -2, 2, 2, 2, 353, 41, 482, 66, 515, 2884, 972, 740, 268, 1741, 309, 461, 8070, 8078, 2710, 2046, 23047, 3087, 4631, 799]); a,b,c,d,e,f := Explode([GPC.1, GPC.2, GPC.5, GPC.6, GPC.7, GPC.8]); AssignNames(~GPC, ["a", "b", "b2", "b4", "c", "d", "e", "f"]);
GPerm := PermutationGroup< 12 | (3,4)(5,6)(7,8)(10,12), (5,7,8,6), (5,8)(6,7), (2,3,4)(10,11,12), (1,2)(3,4), (1,3)(2,4), (9,10)(11,12), (9,11)(10,12) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_384_20080 := 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, 1, G!(5,8)(6,7)>,< 2, 3, G!(5,8)(6,7)(9,10)(11,12)>,< 2, 3, G!(1,2)(3,4)(5,8)(6,7)>,< 2, 3, G!(1,2)(3,4)(5,8)(6,7)(9,11)(10,12)>,< 2, 3, G!(9,11)(10,12)>,< 2, 3, G!(1,3)(2,4)(9,12)(10,11)>,< 2, 3, G!(1,3)(2,4)>,< 2, 6, G!(1,2)(3,4)(9,10)(11,12)>,< 2, 6, G!(1,2)(3,4)(5,8)(6,7)(9,10)(11,12)>,< 2, 24, G!(3,4)(5,7)(6,8)(10,12)>,< 2, 24, G!(1,2)(6,7)(10,12)>,< 3, 32, G!(2,3,4)(9,11,10)>,< 4, 2, G!(5,6,8,7)>,< 4, 6, G!(5,6,8,7)(9,10)(11,12)>,< 4, 6, G!(1,2)(3,4)(5,6,8,7)>,< 4, 6, G!(1,2)(3,4)(5,6,8,7)(9,11)(10,12)>,< 4, 6, G!(1,2)(3,4)(5,6,8,7)(9,10)(11,12)>,< 4, 6, G!(1,2)(3,4)(5,6,8,7)(9,12)(10,11)>,< 4, 24, G!(3,4)(5,6)(7,8)(9,12,11,10)>,< 4, 24, G!(1,2,3,4)(5,6)(7,8)(9,10,12,11)>,< 4, 24, G!(1,2,3,4)(5,8)(9,10,12,11)>,< 4, 24, G!(2,4)(5,8)(9,11,12,10)>,< 4, 24, G!(1,2,3,4)(5,8)(9,12)>,< 4, 24, G!(1,4,3,2)(5,6)(7,8)(9,12)>,< 6, 32, G!(2,4,3)(5,8)(6,7)(9,10,11)>,< 12, 32, G!(2,3,4)(5,7,8,6)(9,11,10)>,< 12, 32, G!(2,4,3)(5,7,8,6)(9,10,11)>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,-2,-2,2,-2,2,2,2,-2,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1-K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,-2,-2,2,-2,2,2,2,-2,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,K.1+K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -1, 3, -1, 3, -1, -1, 1, 1, 0, 3, 3, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, 3, -1, -1, 3, -1, -1, -1, 1, 1, 0, 3, -1, 3, -1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, 3, -1, -1, -1, -1, -1, 1, 1, 0, 3, -1, -1, 3, -1, -1, 1, -1, -1, -1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -1, 3, -1, 3, -1, -1, -1, -1, 0, 3, 3, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, 3, -1, -1, 3, -1, -1, -1, -1, -1, 0, 3, -1, 3, -1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, 3, -1, -1, -1, -1, -1, -1, -1, 0, 3, -1, -1, 3, -1, -1, -1, 1, 1, 1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -1, 3, -1, 3, -1, -1, -1, 1, 0, -3, -3, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -1, -1, 3, -1, 3, -1, -1, 1, -1, 0, -3, -3, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, 3, -1, -1, 3, -1, -1, -1, -1, 1, 0, -3, 1, -3, 1, 1, 1, -1, -1, -1, 1, 1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, 3, -1, -1, 3, -1, -1, -1, 1, -1, 0, -3, 1, -3, 1, 1, 1, 1, 1, 1, -1, -1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, 3, -1, -1, -1, -1, -1, -1, 1, 0, -3, 1, 1, -3, 1, 1, 1, -1, 1, -1, -1, 1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, 3, -1, -1, -1, -1, -1, 1, -1, 0, -3, 1, 1, -3, 1, 1, -1, 1, -1, 1, 1, -1, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 6, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, -6, 2, 6, 2, -2, -2, -2, 2, 0, 0, 0, 0, 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, 2, -6, -2, 2, 6, -2, -2, 2, 0, 0, 0, 0, 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, 2, 2, -2, -6, -2, 6, -2, 2, 0, 0, 0, 0, 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, -2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, -6, 2, 2, 2, -2, -2, 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 |6,-6,2,2,-2,2,-2,-2,2,-2,0,0,0,0,0,0,0,-4*K.1,4*K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,-6,2,2,-2,2,-2,-2,2,-2,0,0,0,0,0,0,0,4*K.1,-4*K.1,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_384_20080:= KnownIrreducibles(CR);