/* Group 144.120 downloaded from the LMFDB on 23 July 2026. */
 
/* 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, -3, 3, 12, 218, 50, 2884, 490, 496, 142, 581, 1739, 1025, 455]); a,b,c,d := Explode([GPC.1, GPC.3, GPC.5, GPC.6]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "d"]);
GPerm := PermutationGroup< 13 | (2,4,5,9)(3,7,8,6)(10,11)(12,13), (2,3,5,8)(4,6,9,7)(10,12,11,13), (2,5)(3,8)(4,9)(6,7), (10,11)(12,13), (1,2,5)(3,6,9)(4,7,8), (1,3,8)(2,6,4)(5,9,7) >;
GLFp := MatrixGroup< 4, GF(3) | [[0, 2, 2, 1, 0, 0, 0, 1, 1, 0, 1, 2, 0, 2, 0, 1], [1, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 1, 1], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2], [0, 0, 1, 1, 2, 2, 1, 2, 1, 1, 0, 0, 1, 2, 2, 2], [0, 1, 1, 2, 2, 0, 1, 0, 0, 2, 1, 2, 1, 2, 2, 2], [1, 0, 0, 0, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 1, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_144_120 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, a^2*b^2>,< 2, 9, b^2>,< 2, 9, a^2*c^2>,< 3, 8, d^2>,< 4, 18, b>,< 4, 18, a^2*b*c*d^2>,< 4, 18, a*b^3*d>,< 4, 18, a^3*b^3*c^2*d^2>,< 4, 18, a^3*c^2*d>,< 4, 18, a*c^2*d^2>,< 6, 8, a^2*b^2*d>]); 
CR := CharacterRing(G);
x := CR!\[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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,-1,1,-1,1,-1*K.1,-1,1,-1*K.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 |1,-1,1,-1,1,K.1,-1,1,K.1,-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*K.1,1,-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 |1,-1,1,-1,1,K.1,1,-1,-1*K.1,K.1,-1*K.1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 2]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[8, 8, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_144_120:= KnownIrreducibles(CR);