/* Group 1024.dhr downloaded from the LMFDB on 22 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([10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20, 171, 24362, 432, 82, 24643, 11693, 7424, 32645, 2895, 78407, 36817, 15067, 7077, 847, 537, 237, 79928, 12978, 7948, 1848, 268, 57609]); a,b,c,d,e,f := Explode([GPC.1, GPC.3, GPC.5, GPC.6, GPC.7, GPC.8]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "d", "e", "f", "f2", "f4"]);
GPerm := PermutationGroup< 16 | (1,9,8,15,3,12,5,13)(2,10,7,16,4,11,6,14), (3,4)(5,6)(7,8)(13,16,14,15) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1024_dhr := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GPerm;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, G!(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)>,< 2, 2, G!(9,10)(11,12)(13,14)(15,16)>,< 2, 4, G!(5,6)(7,8)(13,14)(15,16)>,< 2, 4, G!(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)>,< 2, 4, G!(9,10)(11,12)>,< 2, 8, G!(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,16)(14,15)>,< 2, 8, G!(1,4)(2,3)(5,8)(6,7)(9,11)(10,12)(13,15)(14,16)>,< 2, 16, G!(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,15)(12,16)>,< 4, 8, G!(1,2)(7,8)(9,12,10,11)(13,16,14,15)>,< 4, 8, G!(1,2)(7,8)(9,11,10,12)(13,15,14,16)>,< 4, 16, G!(7,8)(9,11,10,12)>,< 4, 16, G!(7,8)(9,11,10,12)(13,14)(15,16)>,< 4, 16, G!(5,7,6,8)(9,10)(11,12)(15,16)>,< 4, 16, G!(3,4)(7,8)(9,11,10,12)(13,15,14,16)>,< 4, 16, G!(3,4)(5,6)(7,8)(9,10)(11,12)(13,15,14,16)>,< 4, 16, G!(1,6,2,5)(3,7,4,8)(9,16,10,15)(11,14,12,13)>,< 4, 32, G!(5,7)(6,8)(9,11,10,12)(15,16)>,< 4, 32, G!(3,4)(5,7,6,8)(9,10)(11,12)(13,15)(14,16)>,< 4, 32, G!(1,5)(2,6)(3,7)(4,8)(9,13,10,14)(11,16,12,15)>,< 4, 32, G!(3,4)(5,7)(6,8)(9,11,10,12)(13,15)(14,16)>,< 4, 32, G!(3,4)(5,7)(6,8)(9,12,10,11)(13,15)(14,16)>,< 4, 32, G!(1,6,4,7)(2,5,3,8)(9,15,11,13)(10,16,12,14)>,< 4, 32, G!(1,7,4,6)(2,8,3,5)(9,13,11,15)(10,14,12,16)>,< 4, 64, G!(1,15,6,11)(2,16,5,12)(3,13,8,10)(4,14,7,9)>,< 4, 64, G!(1,11,6,15)(2,12,5,16)(3,10,8,13)(4,9,7,14)>,< 8, 64, G!(1,8,2,7)(3,6)(4,5)(9,14,12,15,10,13,11,16)>,< 8, 64, G!(1,7,2,8)(3,6)(4,5)(9,16,11,13,10,15,12,14)>,< 8, 64, G!(1,9,6,16,2,10,5,15)(3,11,7,14,4,12,8,13)>,< 8, 64, G!(1,15,5,10,2,16,6,9)(3,13,8,12,4,14,7,11)>,< 8, 64, G!(1,11,6,13,4,9,7,15)(2,12,5,14,3,10,8,16)>,< 8, 64, G!(1,15,7,9,4,13,6,11)(2,16,8,10,3,14,5,12)>,< 8, 64, G!(1,13,7,11,4,15,6,9)(2,14,8,12,3,16,5,10)>,< 8, 64, G!(1,9,6,15,4,11,7,13)(2,10,5,16,3,12,8,14)>]); 
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, 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, -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, -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, 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,-1,1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1*K.1,K.1,K.1,1,1,-1*K.1,-1*K.1,K.1,K.1,-1*K.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,-1,1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,K.1,-1*K.1,-1*K.1,1,1,K.1,K.1,-1*K.1,-1*K.1,K.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,-1,1,1,1,1,1,1,-1,1,1,1,-1,-1,1,1,-1,-1*K.1,K.1,K.1,-1,-1,-1*K.1,K.1,-1*K.1,-1*K.1,K.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,-1,1,1,1,1,1,1,-1,1,1,1,-1,-1,1,1,-1,K.1,-1*K.1,-1*K.1,-1,-1,K.1,-1*K.1,K.1,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 2, 2, -2, -2, -2, 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, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, -2, -2, -2, -2, 2, 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,-2,-2,2,-2,2,-2,-2,0,0,2,0,2,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,-1*K.1-K.1^3,-1*K.1-K.1^3,K.1+K.1^3,K.1+K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,2,2,-2,-2,2,-2,2,-2,-2,0,0,2,0,2,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,K.1+K.1^3,K.1+K.1^3,-1*K.1-K.1^3,-1*K.1-K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,2,-2,-2,2,-2,0,2,2,0,0,-2,0,0,0,0,0,-2*K.1,2*K.1,0,0,0,-1+K.1,-1-K.1,1+K.1,0,0,1-K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,2,-2,-2,2,-2,0,2,2,0,0,-2,0,0,0,0,0,2*K.1,-2*K.1,0,0,0,-1-K.1,-1+K.1,1-K.1,0,0,1+K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,2,-2,-2,2,-2,0,2,2,0,0,-2,0,0,0,0,0,-2*K.1,2*K.1,0,0,0,1-K.1,1+K.1,-1-K.1,0,0,-1+K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,2,-2,-2,2,-2,0,2,2,0,0,-2,0,0,0,0,0,2*K.1,-2*K.1,0,0,0,1+K.1,1-K.1,-1+K.1,0,0,-1-K.1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,2,2,-2,-2,2,-2,-2,-2,-2,0,0,2,0,-2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,-1*K.1-K.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(8: Sparse := true);
S := [ K |2,2,2,2,-2,-2,2,-2,-2,-2,-2,0,0,2,0,-2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,K.1+K.1^-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; 
x := CR!\[4, 4, 4, 4, 4, 4, 4, 4, 0, -4, -4, 0, 0, -4, 0, 0, 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!\[4, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, -2, -2, 0, -2, 0, -2, 2, 2, 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!\[4, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 2, 2, 0, 2, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 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 |4,4,4,4,-4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,4,4,-4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, 8, 8, -8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 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!\[8, 8, 8, -8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 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!\[8, -8, 0, 0, -4, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, 0, -4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, -2, 0, 0, 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 |8,8,-8,0,0,0,0,0,0,-4*K.1,4*K.1,-2,2,0,2,0,-2,2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |8,8,-8,0,0,0,0,0,0,4*K.1,-4*K.1,-2,2,0,2,0,-2,-2*K.1,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |8,8,-8,0,0,0,0,0,0,-4*K.1,4*K.1,2,-2,0,-2,0,2,-2*K.1,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |8,8,-8,0,0,0,0,0,0,4*K.1,-4*K.1,2,-2,0,-2,0,2,2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[16, -16, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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; 
_ := CharacterTable(G : Check := 0); 
chartbl_1024_dhr:= KnownIrreducibles(CR);