/* Group 64.253 downloaded from the LMFDB on 14 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, -2, 332, 681, 69, 730, 88]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.3, GPC.4]); AssignNames(~GPC, ["a", "b", "c", "d", "d2", "d4"]);
GPerm := PermutationGroup< 18 | (1,2)(3,10)(4,8)(5,9)(6,13)(7,11)(12,15)(14,16)(17,18), (1,3)(2,7)(4,11)(5,12)(6,14)(8,15)(9,16)(10,13)(17,18), (1,4,5,6)(2,8,9,13)(3,11,12,14)(7,15,16,10)(17,18), (1,5)(2,9)(3,12)(4,6)(7,16)(8,13)(10,15)(11,14)(17,18), (1,6,5,4)(2,8,9,13)(3,11,12,14)(7,10,16,15), (1,5)(2,9)(3,12)(4,6)(7,16)(8,13)(10,15)(11,14) >;
GLZq := MatrixGroup< 2, Integers(16) | [[1, 2, 0, 1], [7, 0, 0, 7], [1, 4, 0, 1], [1, 0, 0, 9], [11, 1, 8, 13], [1, 8, 0, 1]] >;
F:=GF(9); al:=F.1; GLFq := MatrixGroup< 3, F | [[al^5, al^6, al^7], [0, al^1, al^7], [al^6, al^1, 1]],[[al^7, al^7, al^6], [al^5, al^7, al^1], [al^3, 1, al^1]],[[1, 1, 1], [al^5, al^7, al^1], [al^1, al^5, al^6]],[[al^4, al^7, al^7], [al^4, al^7, 1], [1, al^4, al^1]],[[al^4, 0, 0], [0, al^4, 0], [0, 0, al^4]],[[al^4, al^7, al^3], [al^4, al^7, al^4], [al^4, 1, al^5]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_64_253 := 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 := false,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GLZq;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Matrix(2, [1, 0, 0, 1])>,< 2, 1, Matrix(2, [7, 0, 0, 7])>,< 2, 1, Matrix(2, [7, 8, 0, 7])>,< 2, 1, Matrix(2, [1, 8, 0, 1])>,< 2, 2, Matrix(2, [7, 8, 0, 15])>,< 2, 2, Matrix(2, [1, 8, 0, 9])>,< 2, 4, Matrix(2, [11, 1, 8, 5])>,< 2, 4, Matrix(2, [11, 7, 8, 5])>,< 2, 4, Matrix(2, [13, 7, 8, 3])>,< 2, 4, Matrix(2, [13, 1, 8, 3])>,< 4, 1, Matrix(2, [7, 4, 0, 15])>,< 4, 1, Matrix(2, [7, 12, 0, 15])>,< 4, 1, Matrix(2, [1, 12, 0, 9])>,< 4, 1, Matrix(2, [1, 4, 0, 9])>,< 4, 2, Matrix(2, [7, 12, 0, 7])>,< 4, 2, Matrix(2, [1, 4, 0, 1])>,< 4, 4, Matrix(2, [13, 7, 8, 11])>,< 4, 4, Matrix(2, [13, 1, 8, 11])>,< 4, 4, Matrix(2, [11, 1, 8, 13])>,< 4, 4, Matrix(2, [11, 7, 8, 13])>,< 8, 2, Matrix(2, [1, 2, 0, 1])>,< 8, 2, Matrix(2, [1, 10, 0, 1])>,< 8, 2, Matrix(2, [7, 6, 0, 15])>,< 8, 2, Matrix(2, [7, 14, 0, 15])>,< 8, 2, Matrix(2, [7, 14, 0, 7])>,< 8, 2, Matrix(2, [7, 6, 0, 7])>,< 8, 2, Matrix(2, [1, 10, 0, 9])>,< 8, 2, Matrix(2, [1, 2, 0, 9])>]); 
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!\[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!\[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!\[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, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,0,0,-2*K.1^2,2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,-1*K.1-K.1^3,K.1+K.1^-1,-1*K.1-K.1^3,-1*K.1-K.1^-1,K.1+K.1^3,K.1+K.1^-1,K.1+K.1^3,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,0,0,2*K.1^2,-2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,K.1+K.1^3,K.1+K.1^-1,K.1+K.1^3,-1*K.1-K.1^-1,-1*K.1-K.1^3,K.1+K.1^-1,-1*K.1-K.1^3,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,0,0,-2*K.1^2,2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,K.1+K.1^3,-1*K.1-K.1^-1,K.1+K.1^3,K.1+K.1^-1,-1*K.1-K.1^3,-1*K.1-K.1^-1,-1*K.1-K.1^3,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,-2,2,0,0,0,0,0,0,2*K.1^2,-2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,-1*K.1-K.1^3,-1*K.1-K.1^-1,-1*K.1-K.1^3,K.1+K.1^-1,K.1+K.1^3,-1*K.1-K.1^-1,K.1+K.1^3,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,0,-2*K.1^2,2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,-1*K.1-K.1^3,K.1+K.1^-1,K.1+K.1^3,-1*K.1-K.1^-1,-1*K.1-K.1^3,-1*K.1-K.1^-1,K.1+K.1^3,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,0,2*K.1^2,-2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,K.1+K.1^3,K.1+K.1^-1,-1*K.1-K.1^3,-1*K.1-K.1^-1,K.1+K.1^3,-1*K.1-K.1^-1,-1*K.1-K.1^3,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,0,-2*K.1^2,2*K.1^2,-2*K.1^2,2*K.1^2,0,0,0,0,0,0,K.1+K.1^3,-1*K.1-K.1^-1,-1*K.1-K.1^3,K.1+K.1^-1,K.1+K.1^3,K.1+K.1^-1,-1*K.1-K.1^3,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,0,0,0,0,0,0,2*K.1^2,-2*K.1^2,2*K.1^2,-2*K.1^2,0,0,0,0,0,0,-1*K.1-K.1^3,-1*K.1-K.1^-1,K.1+K.1^3,K.1+K.1^-1,-1*K.1-K.1^3,K.1+K.1^-1,K.1+K.1^3,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_64_253:= KnownIrreducibles(CR);