/* Group 32.18 downloaded from the LMFDB on 22 September 2026. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation, GPerm is permutation group 
	 GLZ, GLFp, GLZN, 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([5, -2, 2, -2, -2, -2, 301, 26, 422, 42, 483, 58]); a,b := Explode([GPC.1, GPC.2]); AssignNames(~GPC, ["a", "b", "b2", "b4", "b8"]);
GPerm := PermutationGroup< 16 | (1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16), (3,4)(5,7)(6,8)(9,15)(10,16)(11,13)(12,14), (1,7,3,6,2,8,4,5)(9,13,12,16,10,14,11,15), (1,4,2,3)(5,8,6,7)(9,11,10,12)(13,15,14,16), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16) >;
GLFp := MatrixGroup< 2, GF(17) | [[0, 1, 1, 0], [3, 0, 0, 6]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; 
booleans_32_18 := rec< RF | 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := true,
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^8>,< 2, 8, a*b^3>,< 2, 8, a*b^8>,< 4, 2, b^4>,< 8, 2, b^2>,< 8, 2, b^6>,< 16, 2, b>,< 16, 2, b^3>,< 16, 2, b^5>,< 16, 2, b^9>]); 
CR := CharacterRing(G);
x := CR!\[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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 0, 2, -2, -2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,0,0,-2,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,0,0,-2,0,0,K.1+K.1^-1,-1*K.1-K.1^-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(16: Sparse := true);
S := [ K |2,-2,0,0,0,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1^3-K.1^-3,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^3+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |2,-2,0,0,0,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^3-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |2,-2,0,0,0,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |2,-2,0,0,0,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_32_18:= KnownIrreducibles(CR);