/* Group 240.124 downloaded from the LMFDB on 13 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 */
GPC := PCGroup([6, -2, -2, -2, 2, -3, -5, 12, 3363, 1833, 69, 964, 970, 118, 3461, 3467]); a,b,c := Explode([GPC.1, GPC.3, GPC.4]); AssignNames(~GPC, ["a", "a2", "b", "c", "c2", "c6"]);
GPerm := PermutationGroup< 12 | (1,2)(3,4)(6,7)(9,10,11,12), (2,4), (9,11)(10,12), (1,3)(2,4), (5,6,7), (8,9,12,10,11) >;
GLZN := MatrixGroup< 2, Integers(20) | [[11, 10, 10, 1], [1, 9, 0, 3], [1, 10, 10, 11], [1, 4, 0, 1], [1, 0, 0, 9], [11, 15, 5, 16]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_240_124 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, b>,< 2, 2, c^15>,< 2, 5, a^2*c^12>,< 2, 5, a^2*b*c^12>,< 2, 10, a^2*c^21>,< 3, 2, c^10>,< 4, 30, a^3*c^22>,< 4, 30, a*c^16>,< 4, 30, a*c^17>,< 4, 30, a^3*b*c^29>,< 5, 4, c^12>,< 6, 2, b*c^10>,< 6, 2, c^5>,< 6, 2, c^25>,< 6, 10, a^2*c^2>,< 6, 10, a^2*b*c^2>,< 6, 10, a^2*c>,< 6, 10, a^2*b*c>,< 10, 4, b*c^6>,< 10, 4, c^3>,< 10, 4, c^9>,< 15, 4, c^4>,< 15, 4, c^26>,< 30, 4, b*c^2>,< 30, 4, b*c^14>,< 30, 4, c>,< 30, 4, b*c^7>,< 30, 4, c^7>,< 30, 4, b*c>]); 
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]; 
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]; 
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]; 
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]; 
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,-1,1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-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,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-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,-1*K.1,K.1,K.1,-1*K.1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1]; 
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,-1*K.1,K.1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 2, 0, 0, -2, 2, 2, 0, -2, 0, 0, -2, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 2, -2, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, -2, 0, 0, -2, 2, 2, 0, -2, 0, 0, -2, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, -1, 0, 0, 0, 0, 2, 1, -1, 1, 1, 1, -1, -1, -2, -2, 2, -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, -1, 0, 0, 0, 0, 2, 1, -1, 1, -1, -1, 1, 1, -2, -2, 2, -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, -1, 0, 0, 0, 0, 2, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,-2,2,0,-1,0,0,0,0,2,-1-2*K.1,1,1+2*K.1,1+2*K.1,-1-2*K.1,1,-1,0,0,-2,-1,-1,1+2*K.1,1,-1-2*K.1,-1-2*K.1,1,1+2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,-2,2,0,-1,0,0,0,0,2,1+2*K.1,1,-1-2*K.1,-1-2*K.1,1+2*K.1,1,-1,0,0,-2,-1,-1,-1-2*K.1,1,1+2*K.1,1+2*K.1,1,-1-2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,-1,0,0,0,0,2,-1-2*K.1,1,1+2*K.1,-1-2*K.1,1+2*K.1,-1,1,0,0,-2,-1,-1,1+2*K.1,1,-1-2*K.1,-1-2*K.1,1,1+2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,0,2,-2,0,-1,0,0,0,0,2,1+2*K.1,1,-1-2*K.1,1+2*K.1,-1-2*K.1,-1,1,0,0,-2,-1,-1,-1-2*K.1,1,1+2*K.1,1+2*K.1,1,-1-2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, -1, 4, 4, 4, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, 0, 0, 0, 4, 0, 0, 0, 0, -1, -4, 4, -4, 0, 0, 0, 0, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |4,4,4,0,0,0,-2,0,0,0,0,-1,-2,-2,-2,0,0,0,0,-1,-1,-1,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |4,4,4,0,0,0,-2,0,0,0,0,-1,-2,-2,-2,0,0,0,0,-1,-1,-1,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,0,0,0,0,4,0,0,0,0,-1,0,-4,0,0,0,0,0,1+2*K.1^2+2*K.1^-2,-1-2*K.1^2-2*K.1^-2,1,-1,-1,-1-2*K.1^2-2*K.1^-2,1,-1-2*K.1^2-2*K.1^-2,1+2*K.1^2+2*K.1^-2,1,1+2*K.1^2+2*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,0,0,0,0,4,0,0,0,0,-1,0,-4,0,0,0,0,0,-1-2*K.1^2-2*K.1^-2,1+2*K.1^2+2*K.1^-2,1,-1,-1,1+2*K.1^2+2*K.1^-2,1,1+2*K.1^2+2*K.1^-2,-1-2*K.1^2-2*K.1^-2,1,-1-2*K.1^2-2*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |4,4,-4,0,0,0,-2,0,0,0,0,-1,2,-2,2,0,0,0,0,1,1,-1,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,1-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,-2+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,1-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-2+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |4,4,-4,0,0,0,-2,0,0,0,0,-1,2,-2,2,0,0,0,0,1,1,-1,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-2+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,1-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-2+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,1-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |4,-4,0,0,0,0,-2,0,0,0,0,-1,-2-4*K.1^5,2,2+4*K.1^5,0,0,0,0,-1+2*K.1^2-2*K.1^3+2*K.1^7,1-2*K.1^2+2*K.1^3-2*K.1^7,1,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,-1+K.1^2-K.1^3-K.1^5+K.1^7,1-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,K.1^2-K.1^3+K.1^5+K.1^7,1-K.1^2+K.1^3+K.1^5-K.1^7,-2+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,-1*K.1^2+K.1^3-K.1^5-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |4,-4,0,0,0,0,-2,0,0,0,0,-1,2+4*K.1^5,2,-2-4*K.1^5,0,0,0,0,-1+2*K.1^2-2*K.1^3+2*K.1^7,1-2*K.1^2+2*K.1^3-2*K.1^7,1,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,K.1^2-K.1^3+K.1^5+K.1^7,-2+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,-1+K.1^2-K.1^3-K.1^5+K.1^7,-1*K.1^2+K.1^3-K.1^5-K.1^7,1-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,1-K.1^2+K.1^3+K.1^5-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |4,-4,0,0,0,0,-2,0,0,0,0,-1,-2-4*K.1^5,2,2+4*K.1^5,0,0,0,0,1-2*K.1^2+2*K.1^3-2*K.1^7,-1+2*K.1^2-2*K.1^3+2*K.1^7,1,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1*K.1^2+K.1^3-K.1^5-K.1^7,-2+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,1-K.1^2+K.1^3+K.1^5-K.1^7,K.1^2-K.1^3+K.1^5+K.1^7,1-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1+K.1^2-K.1^3-K.1^5+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |4,-4,0,0,0,0,-2,0,0,0,0,-1,2+4*K.1^5,2,-2-4*K.1^5,0,0,0,0,1-2*K.1^2+2*K.1^3-2*K.1^7,-1+2*K.1^2-2*K.1^3+2*K.1^7,1,2-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,1-K.1^2+K.1^3+K.1^5-K.1^7,1-2*K.1-K.1^2+K.1^3-2*K.1^4+K.1^5-K.1^7,-1*K.1^2+K.1^3-K.1^5-K.1^7,-1+K.1^2-K.1^3-K.1^5+K.1^7,-2+2*K.1+K.1^2-K.1^3+2*K.1^4-K.1^5+K.1^7,K.1^2-K.1^3+K.1^5+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_240_124:= KnownIrreducibles(CR);