/* Group 2400.bp downloaded from the LMFDB on 14 November 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 */
GPerm := PermutationGroup< 29 | (1,2,4,7)(3,6,9,14)(5,8,11,16)(10,15,18,22)(12,13,17,20)(19,23,24,21)(25,26)(27,29), (1,3,2,6,4,9,7,14)(5,12,8,13,11,17,16,20)(10,19,15,23,18,24,22,21)(26,27,29,28), (25,27,29,26,28), (1,4)(2,7)(3,9)(5,11)(6,14)(8,16)(10,18)(12,17)(13,20)(15,22)(19,24)(21,23)(25,28,26,29,27), (1,5,13,19,9,18,2,8,17,23,14,22,4,11,20,24,3,10,7,16,12,21,6,15)(25,29,26,27) >;
GLFp := MatrixGroup< 4, GF(5) | [[2, 1, 2, 4, 1, 1, 1, 0, 0, 4, 1, 1, 3, 2, 0, 2], [0, 0, 1, 1, 4, 1, 1, 1, 0, 0, 1, 0, 4, 0, 1, 2], [3, 4, 3, 4, 3, 3, 4, 0, 1, 0, 3, 4, 1, 4, 1, 1], [1, 0, 1, 2, 0, 4, 2, 4, 4, 4, 4, 2, 3, 1, 1, 4], [0, 4, 4, 0, 1, 1, 1, 2, 2, 0, 0, 3, 2, 4, 0, 3]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_2400_bp := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := false,
supersolvable := false>; 

 
/* Character Table */
G:= GLFp;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Matrix(4, [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1])>,< 2, 1, Matrix(4, [2, 4, 4, 0, 2, 3, 0, 1, 1, 0, 3, 4, 0, 4, 2, 2])>,< 2, 150, Matrix(4, [3, 1, 1, 0, 4, 4, 1, 1, 3, 3, 1, 4, 4, 3, 1, 2])>,< 3, 20, Matrix(4, [4, 3, 0, 4, 0, 2, 3, 4, 4, 3, 3, 3, 4, 0, 3, 2])>,< 4, 5, Matrix(4, [4, 2, 0, 3, 2, 0, 4, 2, 4, 0, 4, 1, 4, 2, 2, 3])>,< 4, 5, Matrix(4, [2, 4, 2, 3, 3, 1, 4, 0, 2, 0, 0, 3, 4, 4, 3, 1])>,< 4, 30, Matrix(4, [0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 2, 3, 4, 4, 0, 3])>,< 4, 150, Matrix(4, [0, 3, 3, 0, 2, 3, 3, 3, 4, 4, 4, 2, 2, 4, 3, 2])>,< 4, 150, Matrix(4, [1, 1, 1, 0, 4, 2, 1, 1, 3, 3, 4, 4, 4, 3, 1, 0])>,< 4, 150, Matrix(4, [2, 3, 2, 3, 4, 0, 3, 4, 3, 2, 1, 0, 0, 1, 0, 2])>,< 4, 150, Matrix(4, [1, 0, 3, 1, 0, 3, 1, 4, 2, 4, 0, 4, 0, 1, 2, 1])>,< 5, 4, Matrix(4, [4, 0, 2, 2, 3, 1, 2, 2, 0, 0, 1, 0, 3, 0, 2, 3])>,< 5, 24, Matrix(4, [1, 0, 0, 0, 3, 3, 2, 0, 2, 3, 4, 0, 3, 2, 2, 1])>,< 5, 48, Matrix(4, [3, 1, 0, 2, 1, 0, 2, 0, 2, 4, 2, 4, 0, 2, 4, 4])>,< 5, 48, Matrix(4, [4, 3, 4, 4, 3, 4, 4, 4, 2, 1, 3, 2, 1, 2, 2, 3])>,< 6, 20, Matrix(4, [1, 1, 3, 4, 4, 1, 3, 1, 1, 3, 2, 1, 4, 3, 2, 4])>,< 8, 100, Matrix(4, [2, 1, 3, 0, 0, 4, 4, 4, 0, 2, 0, 3, 3, 4, 2, 1])>,< 8, 100, Matrix(4, [3, 4, 3, 0, 1, 0, 3, 1, 3, 4, 2, 3, 1, 0, 0, 1])>,< 10, 4, Matrix(4, [1, 4, 0, 1, 1, 3, 1, 2, 1, 0, 3, 4, 4, 4, 3, 3])>,< 10, 24, Matrix(4, [2, 4, 4, 0, 3, 2, 4, 1, 0, 1, 4, 4, 1, 3, 1, 2])>,< 10, 48, Matrix(4, [0, 1, 0, 0, 3, 1, 0, 2, 0, 3, 0, 2, 4, 3, 1, 4])>,< 10, 48, Matrix(4, [0, 0, 0, 1, 0, 4, 1, 2, 0, 2, 2, 3, 4, 3, 4, 4])>,< 12, 100, Matrix(4, [3, 0, 2, 1, 3, 3, 0, 3, 0, 1, 4, 4, 2, 4, 4, 3])>,< 12, 100, Matrix(4, [2, 1, 3, 1, 1, 1, 0, 2, 4, 1, 2, 0, 2, 0, 2, 2])>,< 15, 80, Matrix(4, [3, 2, 2, 1, 1, 4, 3, 1, 3, 3, 1, 4, 4, 4, 2, 3])>,< 20, 120, Matrix(4, [4, 1, 2, 1, 1, 2, 3, 3, 0, 2, 2, 3, 3, 4, 1, 4])>,< 20, 120, Matrix(4, [3, 2, 1, 4, 2, 4, 4, 3, 3, 1, 0, 1, 4, 1, 2, 4])>,< 20, 120, Matrix(4, [1, 4, 3, 4, 3, 0, 4, 1, 1, 1, 1, 3, 4, 3, 3, 2])>,< 24, 100, Matrix(4, [2, 1, 2, 4, 3, 3, 1, 1, 3, 2, 1, 0, 0, 4, 0, 3])>,< 24, 100, Matrix(4, [1, 0, 3, 2, 0, 2, 3, 1, 2, 1, 1, 2, 0, 4, 1, 4])>,< 24, 100, Matrix(4, [4, 2, 0, 2, 1, 3, 3, 4, 0, 1, 2, 4, 0, 1, 2, 2])>,< 24, 100, Matrix(4, [1, 2, 3, 4, 1, 1, 1, 0, 2, 2, 4, 1, 0, 0, 3, 2])>,< 30, 80, Matrix(4, [2, 0, 3, 4, 2, 3, 1, 1, 0, 3, 0, 2, 1, 2, 4, 3])>]); 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,-1,-1,1,-1*K.1,K.1,-1*K.1,K.1,1,1,1,1,1,K.1,-1*K.1,1,1,1,1,-1,-1,1,-1,-1,1,-1*K.1,K.1,K.1,-1*K.1,1]; 
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,K.1,-1*K.1,K.1,-1*K.1,1,1,1,1,1,-1*K.1,K.1,1,1,1,1,-1,-1,1,-1,-1,1,K.1,-1*K.1,-1*K.1,K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, -1, 4, -1, -1, 4, 0, 0, -1, 4, -1, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 1, 4, 4, 0, 0, 0, 0, 0, 4, -1, -1, -1, 1, 2, 2, 4, -1, -1, -1, 1, 1, 1, -1, -1, 0, -1, -1, -1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 0, 1, 4, 4, 0, 0, 0, 0, 0, 4, -1, -1, -1, 1, -2, -2, 4, -1, -1, -1, 1, 1, 1, -1, -1, 0, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,0,1,-4,-4,0,0,0,0,0,4,-1,-1,-1,1,-2*K.1,2*K.1,4,-1,-1,-1,-1,-1,1,1,1,0,-1*K.1,K.1,K.1,-1*K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,0,1,-4,-4,0,0,0,0,0,4,-1,-1,-1,1,2*K.1,-2*K.1,4,-1,-1,-1,-1,-1,1,1,1,0,K.1,-1*K.1,-1*K.1,K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,-4,0,-2,-4*K.1,4*K.1,0,0,0,0,0,4,-1,-1,-1,2,0,0,-4,1,1,1,-2*K.1,2*K.1,-2,K.1,-1*K.1,0,0,0,0,0,2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,-4,0,-2,4*K.1,-4*K.1,0,0,0,0,0,4,-1,-1,-1,2,0,0,-4,1,1,1,2*K.1,-2*K.1,-2,-1*K.1,K.1,0,0,0,0,0,2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |4,-4,0,1,-4*K.1^6,4*K.1^6,0,0,0,0,0,4,-1,-1,-1,-1,0,0,-4,1,1,1,K.1^6,-1*K.1^6,1,K.1^6,-1*K.1^6,0,-1*K.1^3+2*K.1^7,-1*K.1-K.1^5,K.1+K.1^5,K.1^3-2*K.1^7,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |4,-4,0,1,4*K.1^6,-4*K.1^6,0,0,0,0,0,4,-1,-1,-1,-1,0,0,-4,1,1,1,-1*K.1^6,K.1^6,1,-1*K.1^6,K.1^6,0,-1*K.1-K.1^5,-1*K.1^3+2*K.1^7,K.1^3-2*K.1^7,K.1+K.1^5,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |4,-4,0,1,-4*K.1^6,4*K.1^6,0,0,0,0,0,4,-1,-1,-1,-1,0,0,-4,1,1,1,K.1^6,-1*K.1^6,1,K.1^6,-1*K.1^6,0,K.1^3-2*K.1^7,K.1+K.1^5,-1*K.1-K.1^5,-1*K.1^3+2*K.1^7,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(24: Sparse := true);
S := [ K |4,-4,0,1,4*K.1^6,-4*K.1^6,0,0,0,0,0,4,-1,-1,-1,-1,0,0,-4,1,1,1,-1*K.1^6,K.1^6,1,-1*K.1^6,K.1^6,0,K.1+K.1^5,K.1^3-2*K.1^7,-1*K.1^3+2*K.1^7,-1*K.1-K.1^5,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[5, 5, 1, -1, 5, 5, 1, 1, 1, 1, 1, 5, 0, 0, 0, -1, -1, -1, 5, 0, 0, 0, -1, -1, -1, 0, 0, 1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[5, 5, 1, -1, 5, 5, 1, -1, -1, -1, -1, 5, 0, 0, 0, -1, 1, 1, 5, 0, 0, 0, -1, -1, -1, 0, 0, 1, 1, 1, 1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |5,5,-1,-1,-5,-5,1,-1*K.1,K.1,-1*K.1,K.1,5,0,0,0,-1,-1*K.1,K.1,5,0,0,0,1,1,-1,0,0,1,K.1,-1*K.1,-1*K.1,K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |5,5,-1,-1,-5,-5,1,K.1,-1*K.1,K.1,-1*K.1,5,0,0,0,-1,K.1,-1*K.1,5,0,0,0,1,1,-1,0,0,1,-1*K.1,K.1,K.1,-1*K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, 6, 2, 0, -6, -6, -2, 0, 0, 0, 0, 6, 1, 1, 1, 0, 0, 0, 6, 1, 1, 1, 0, 0, 0, -1, -1, -2, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -2, 0, 6, 6, -2, 0, 0, 0, 0, 6, 1, 1, 1, 0, 0, 0, 6, 1, 1, 1, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,-6,0,0,-6*K.1,6*K.1,0,-1+K.1,-1-K.1,1-K.1,1+K.1,6,1,1,1,0,0,0,-6,-1,-1,-1,0,0,0,-1*K.1,K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,-6,0,0,6*K.1,-6*K.1,0,-1-K.1,-1+K.1,1+K.1,1-K.1,6,1,1,1,0,0,0,-6,-1,-1,-1,0,0,0,K.1,-1*K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,-6,0,0,-6*K.1,6*K.1,0,1-K.1,1+K.1,-1+K.1,-1-K.1,6,1,1,1,0,0,0,-6,-1,-1,-1,0,0,0,-1*K.1,K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,-6,0,0,6*K.1,-6*K.1,0,1+K.1,1-K.1,-1-K.1,-1+K.1,6,1,1,1,0,0,0,-6,-1,-1,-1,0,0,0,K.1,-1*K.1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 3, 4, 0, 0, 2, 2, 2, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, 4, 0, 0, 2, 2, -3, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, 0, 0, 0, 0, -4, 0, 0, 0, 0, -3, 2, -3, 2, 0, 0, 0, -3, 2, -3, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, 0, 0, 0, 0, -4, 0, 0, 0, 0, -3, 2, 2, -3, 0, 0, 0, -3, 2, 2, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[16, 16, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, -4, 1, 1, 4, 0, 0, -4, -4, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[16, -16, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, -4, 1, 1, -4, 0, 0, 4, 4, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[20, 20, 0, -4, 0, 0, 4, 0, 0, 0, 0, -5, 0, 0, 0, -4, 0, 0, -5, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, -1, -1, 0, 0, 0, 6, -4, 1, 1, 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_2400_bp:= KnownIrreducibles(CR);