/* Group 32.44 downloaded from the LMFDB on 11 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([5, -2, 2, 2, -2, -2, 86, 302, 97, 42, 248, 58]); a,b,c := Explode([GPC.1, GPC.2, GPC.3]); AssignNames(~GPC, ["a", "b", "c", "c2", "c4"]);
GPerm := PermutationGroup< 16 | (1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16), (1,6,2,5)(3,8,4,7)(9,16,10,15)(11,13,12,14), (9,10)(11,12)(13,14)(15,16), (1,4,2,3)(5,7,6,8)(9,11,10,12)(13,16,14,15), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16) >;
GLFp := MatrixGroup< 4, GF(3) | [[2, 1, 1, 0, 2, 2, 1, 2, 2, 2, 0, 1, 1, 0, 1, 2], [1, 1, 1, 0, 1, 0, 1, 2, 0, 2, 1, 1, 1, 1, 2, 1], [2, 0, 0, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 1], [0, 1, 2, 1, 1, 1, 2, 0, 1, 0, 1, 1, 2, 2, 2, 1], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_32_44 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := true,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, c^4>,< 2, 2, a>,< 2, 4, b*c>,< 4, 2, a*c^2>,< 4, 2, c^2>,< 4, 4, b>,< 4, 4, a*b>,< 4, 4, a*b*c>,< 8, 4, c>,< 8, 4, a*c>]); 
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!\[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, -2, 0, 2, -2, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 0, -2, -2, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_32_44:= KnownIrreducibles(CR);