/* Group 96.16 downloaded from the LMFDB on 15 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([6, -2, -2, -2, -2, -2, -3, 313, 31, 2115, 681, 69, 2404, 88, 2309]); a,b,c := Explode([GPC.1, GPC.2, GPC.4]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "c4"]);
GPerm := PermutationGroup< 15 | (1,2)(3,4)(6,7)(9,12)(11,14)(13,15), (1,3,4,2)(8,9,10,13)(11,15,14,12), (1,4)(2,3)(8,10)(9,13)(11,14)(12,15), (1,4)(2,3)(8,11,10,14)(9,12,13,15), (8,10)(9,13)(11,14)(12,15), (5,6,7) >;
GLZ := MatrixGroup< 6, Integers() | [[-1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [-1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 1, 1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0]] >;
GLZN := MatrixGroup< 2, Integers(15) | [[9, 14, 2, 1], [13, 3, 9, 1], [13, 10, 10, 8], [4, 0, 0, 4], [11, 0, 0, 11], [1, 5, 5, 11]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_96_16 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
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, b^2*c^6>,< 2, 1, c^6>,< 2, 1, b^2>,< 2, 12, a*c^11>,< 2, 12, a*b^2*c^11>,< 3, 2, c^4>,< 4, 2, b^2*c^9>,< 4, 2, c^3>,< 4, 4, b^3>,< 4, 4, b>,< 6, 2, b^2*c^2>,< 6, 2, c^2>,< 6, 2, b^2*c^8>,< 8, 6, a*b>,< 8, 6, a*b^3>,< 8, 6, a*b^3*c^2>,< 8, 6, a*b*c^2>,< 12, 4, c>,< 12, 4, b^2*c>,< 12, 4, b*c^4>,< 12, 4, b^3*c^2>,< 12, 4, b*c^2>,< 12, 4, b^3*c^4>]); 
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; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,-1,-1,1,-1,1,1,-1,1,-1*K.1,K.1,-1,-1,1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,-1,K.1,K.1,-1*K.1,1]; 
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,K.1,-1*K.1,-1,-1,1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1,-1*K.1,-1*K.1,K.1,1]; 
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*K.1,K.1,-1,-1,1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1,K.1,K.1,-1*K.1,1]; 
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,K.1,-1*K.1,-1,-1,1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1,-1*K.1,-1*K.1,K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, -1, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, 0, 0, 2, 2, -2, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 2, -2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, -1, 2, 2, -2, -2, -1, -1, -1, 0, 0, 0, 0, 1, -1, 1, 1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,0,0,2,0,0,0,0,2,-2,-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,0,0,2,0,0,0,0,2,-2,-2,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,0,2,0,0,0,0,-2,2,-2,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,0,2,0,0,0,0,-2,2,-2,K.1+K.1^3,-1*K.1-K.1^3,K.1+K.1^3,-1*K.1-K.1^3,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,-2,2,0,0,-1,-2,2,-2*K.1,2*K.1,1,1,-1,0,0,0,0,K.1,1,-1*K.1,-1*K.1,K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,-2,2,0,0,-1,-2,2,2*K.1,-2*K.1,1,1,-1,0,0,0,0,-1*K.1,1,K.1,K.1,-1*K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,-2,2,0,0,-1,2,-2,0,0,1,1,-1,0,0,0,0,-1*K.1-K.1^-1,-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,-2,2,0,0,-1,2,-2,0,0,1,1,-1,0,0,0,0,K.1+K.1^-1,-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,0,0,-1,-2,-2,0,0,-1,-1,-1,0,0,0,0,-1-2*K.1,1,-1-2*K.1,1+2*K.1,1+2*K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,2,0,0,-1,-2,-2,0,0,-1,-1,-1,0,0,0,0,1+2*K.1,1,1+2*K.1,-1-2*K.1,-1-2*K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 0, 0, -2, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, -4, 0, 0, -2, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_96_16:= KnownIrreducibles(CR);