/* Group 23.1 downloaded from the LMFDB on 18 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([1, -23]); a := Explode([GPC.1]); AssignNames(~GPC, ["a"]);
GPerm := PermutationGroup< 23 | (1,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2) >;
GLFp := MatrixGroup< 2, GF(23) | [[1, 1, 0, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_23_1 := rec< RF |  
Agroup := true,
Zgroup := true,
abelian := true,
almost_simple := false,
cyclic := true,
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)>,< 23, 1, a>,< 23, 1, a^22>,< 23, 1, a^2>,< 23, 1, a^21>,< 23, 1, a^3>,< 23, 1, a^20>,< 23, 1, a^4>,< 23, 1, a^19>,< 23, 1, a^5>,< 23, 1, a^18>,< 23, 1, a^6>,< 23, 1, a^17>,< 23, 1, a^7>,< 23, 1, a^16>,< 23, 1, a^8>,< 23, 1, a^15>,< 23, 1, a^9>,< 23, 1, a^14>,< 23, 1, a^10>,< 23, 1, a^13>,< 23, 1, a^11>,< 23, 1, a^12>]); 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-11,K.1^-5,K.1^7,K.1^-4,K.1^8,K.1^-3,K.1^9,K.1^-2,K.1^10,K.1^-1,K.1^11,K.1^6,K.1^5,K.1^-7,K.1^4,K.1^-8,K.1^3,K.1^-9,K.1^2,K.1^-10,K.1,K.1^-6]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^11,K.1^5,K.1^-7,K.1^4,K.1^-8,K.1^3,K.1^-9,K.1^2,K.1^-10,K.1,K.1^-11,K.1^-6,K.1^-5,K.1^7,K.1^-4,K.1^8,K.1^-3,K.1^9,K.1^-2,K.1^10,K.1^-1,K.1^6]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-10,K.1^8,K.1^-2,K.1^11,K.1,K.1^-9,K.1^4,K.1^-6,K.1^7,K.1^-3,K.1^10,K.1^-5,K.1^-8,K.1^2,K.1^-11,K.1^-1,K.1^9,K.1^-4,K.1^6,K.1^-7,K.1^3,K.1^5]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^10,K.1^-8,K.1^2,K.1^-11,K.1^-1,K.1^9,K.1^-4,K.1^6,K.1^-7,K.1^3,K.1^-10,K.1^5,K.1^8,K.1^-2,K.1^11,K.1,K.1^-9,K.1^4,K.1^-6,K.1^7,K.1^-3,K.1^-5]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-9,K.1^-2,K.1^-11,K.1^3,K.1^-6,K.1^8,K.1^-1,K.1^-10,K.1^4,K.1^-5,K.1^9,K.1^7,K.1^2,K.1^11,K.1^-3,K.1^6,K.1^-8,K.1,K.1^10,K.1^-4,K.1^5,K.1^-7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^9,K.1^2,K.1^11,K.1^-3,K.1^6,K.1^-8,K.1,K.1^10,K.1^-4,K.1^5,K.1^-9,K.1^-7,K.1^-2,K.1^-11,K.1^3,K.1^-6,K.1^8,K.1^-1,K.1^-10,K.1^4,K.1^-5,K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-8,K.1^11,K.1^3,K.1^-5,K.1^10,K.1^2,K.1^-6,K.1^9,K.1,K.1^-7,K.1^8,K.1^-4,K.1^-11,K.1^-3,K.1^5,K.1^-10,K.1^-2,K.1^6,K.1^-9,K.1^-1,K.1^7,K.1^4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^8,K.1^-11,K.1^-3,K.1^5,K.1^-10,K.1^-2,K.1^6,K.1^-9,K.1^-1,K.1^7,K.1^-8,K.1^4,K.1^11,K.1^3,K.1^-5,K.1^10,K.1^2,K.1^-6,K.1^9,K.1,K.1^-7,K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-7,K.1,K.1^-6,K.1^10,K.1^3,K.1^-4,K.1^-11,K.1^5,K.1^-2,K.1^-9,K.1^7,K.1^8,K.1^-1,K.1^6,K.1^-10,K.1^-3,K.1^4,K.1^11,K.1^-5,K.1^2,K.1^9,K.1^-8]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^7,K.1^-1,K.1^6,K.1^-10,K.1^-3,K.1^4,K.1^11,K.1^-5,K.1^2,K.1^9,K.1^-7,K.1^-8,K.1,K.1^-6,K.1^10,K.1^3,K.1^-4,K.1^-11,K.1^5,K.1^-2,K.1^-9,K.1^8]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-6,K.1^-9,K.1^8,K.1^2,K.1^-4,K.1^-10,K.1^7,K.1,K.1^-5,K.1^-11,K.1^6,K.1^-3,K.1^9,K.1^-8,K.1^-2,K.1^4,K.1^10,K.1^-7,K.1^-1,K.1^5,K.1^11,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^6,K.1^9,K.1^-8,K.1^-2,K.1^4,K.1^10,K.1^-7,K.1^-1,K.1^5,K.1^11,K.1^-6,K.1^3,K.1^-9,K.1^8,K.1^2,K.1^-4,K.1^-10,K.1^7,K.1,K.1^-5,K.1^-11,K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-5,K.1^4,K.1^-1,K.1^-6,K.1^-11,K.1^7,K.1^2,K.1^-3,K.1^-8,K.1^10,K.1^5,K.1^9,K.1^-4,K.1,K.1^6,K.1^11,K.1^-7,K.1^-2,K.1^3,K.1^8,K.1^-10,K.1^-9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^5,K.1^-4,K.1,K.1^6,K.1^11,K.1^-7,K.1^-2,K.1^3,K.1^8,K.1^-10,K.1^-5,K.1^-9,K.1^4,K.1^-1,K.1^-6,K.1^-11,K.1^7,K.1^2,K.1^-3,K.1^-8,K.1^10,K.1^9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-4,K.1^-6,K.1^-10,K.1^9,K.1^5,K.1,K.1^-3,K.1^-7,K.1^-11,K.1^8,K.1^4,K.1^-2,K.1^6,K.1^10,K.1^-9,K.1^-5,K.1^-1,K.1^3,K.1^7,K.1^11,K.1^-8,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^4,K.1^6,K.1^10,K.1^-9,K.1^-5,K.1^-1,K.1^3,K.1^7,K.1^11,K.1^-8,K.1^-4,K.1^2,K.1^-6,K.1^-10,K.1^9,K.1^5,K.1,K.1^-3,K.1^-7,K.1^-11,K.1^8,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-3,K.1^7,K.1^4,K.1,K.1^-2,K.1^-5,K.1^-8,K.1^-11,K.1^9,K.1^6,K.1^3,K.1^10,K.1^-7,K.1^-4,K.1^-1,K.1^2,K.1^5,K.1^8,K.1^11,K.1^-9,K.1^-6,K.1^-10]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^3,K.1^-7,K.1^-4,K.1^-1,K.1^2,K.1^5,K.1^8,K.1^11,K.1^-9,K.1^-6,K.1^-3,K.1^-10,K.1^7,K.1^4,K.1,K.1^-2,K.1^-5,K.1^-8,K.1^-11,K.1^9,K.1^6,K.1^10]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-2,K.1^-3,K.1^-5,K.1^-7,K.1^-9,K.1^-11,K.1^10,K.1^8,K.1^6,K.1^4,K.1^2,K.1^-1,K.1^3,K.1^5,K.1^7,K.1^9,K.1^11,K.1^-10,K.1^-8,K.1^-6,K.1^-4,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^2,K.1^3,K.1^5,K.1^7,K.1^9,K.1^11,K.1^-10,K.1^-8,K.1^-6,K.1^-4,K.1^-2,K.1,K.1^-3,K.1^-5,K.1^-7,K.1^-9,K.1^-11,K.1^10,K.1^8,K.1^6,K.1^4,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1^-1,K.1^10,K.1^9,K.1^8,K.1^7,K.1^6,K.1^5,K.1^4,K.1^3,K.1^2,K.1,K.1^11,K.1^-10,K.1^-9,K.1^-8,K.1^-7,K.1^-6,K.1^-5,K.1^-4,K.1^-3,K.1^-2,K.1^-11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(23: Sparse := true);
S := [ K |1,K.1,K.1^-10,K.1^-9,K.1^-8,K.1^-7,K.1^-6,K.1^-5,K.1^-4,K.1^-3,K.1^-2,K.1^-1,K.1^-11,K.1^10,K.1^9,K.1^8,K.1^7,K.1^6,K.1^5,K.1^4,K.1^3,K.1^2,K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_23_1:= KnownIrreducibles(CR);