/* Group 480.973 downloaded from the LMFDB on 16 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([7, -2, -2, -3, -2, 2, -2, -5, 1680, 3501, 36, 170, 10083, 1690, 941, 584, 5464, 4001, 3483, 795, 102, 9084, 124, 9421]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.4, GPC.5]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "d2", "d4"]);
GPerm := PermutationGroup< 21 | (2,6)(7,13)(8,14)(15,16)(18,19)(20,21), (1,2,5,6)(3,8,11,14)(4,7,9,13)(10,16,12,15), (3,9,12)(4,10,11)(7,14,16)(8,15,13), (17,18,20,21,19), (1,3,5,11)(2,7,6,13)(4,12,9,10)(8,16,14,15), (1,4,5,9)(2,8,6,14)(3,10,11,12)(7,15,13,16), (1,5)(2,6)(3,11)(4,9)(7,13)(8,14)(10,12)(15,16) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_480_973 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
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, d^10>,< 2, 10, b^3*d^18>,< 2, 60, a*b>,< 3, 8, b^2>,< 4, 6, c*d^5>,< 4, 12, a>,< 4, 30, b^3*c*d^13>,< 5, 2, d^12>,< 5, 2, d^4>,< 6, 8, b^4*d^10>,< 6, 40, b*d^18>,< 6, 40, b^5*d^18>,< 8, 12, a*d^15>,< 8, 60, a*b^3*d^13>,< 10, 2, d^6>,< 10, 2, d^18>,< 15, 16, b^4*d^4>,< 15, 16, b^2*d^8>,< 20, 12, c*d^17>,< 20, 12, c*d^11>,< 20, 24, a*d^12>,< 20, 24, a*d^6>,< 30, 16, b^2*d^2>,< 30, 16, b^2*d>,< 40, 12, a*d>,< 40, 12, a*b^2*d>,< 40, 12, a*d^3>,< 40, 12, a*d^13>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 0, -1, 2, 0, 2, 2, 2, -1, -1, -1, 0, 0, 2, 2, -1, -1, 2, 2, 0, 0, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, -1, 2, 0, -2, 2, 2, -1, 1, 1, 0, 0, 2, 2, -1, -1, 2, 2, 0, 0, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,0,0,2,2,2,0,K.1^2+K.1^-2,K.1+K.1^-1,2,0,0,2,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,0,0,2,2,2,0,K.1+K.1^-1,K.1^2+K.1^-2,2,0,0,2,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,0,0,2,2,-2,0,K.1^2+K.1^-2,K.1+K.1^-1,2,0,0,-2,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,0,0,2,2,-2,0,K.1+K.1^-1,K.1^2+K.1^-2,2,0,0,-2,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-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!\[3, 3, 3, 1, 0, -1, 1, -1, 3, 3, 0, 0, 0, -1, -1, 3, 3, 0, 0, -1, -1, 1, 1, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, 0, -1, -1, -1, 3, 3, 0, 0, 0, 1, 1, 3, 3, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, 0, -1, 1, 1, 3, 3, 0, 0, 0, -1, 1, 3, 3, 0, 0, -1, -1, 1, 1, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, 1, 0, -1, -1, 1, 3, 3, 0, 0, 0, 1, -1, 3, 3, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 0, -2, 0, 0, 0, 4, 4, 2, 0, 0, 0, 0, -4, -4, -2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,0,0,-2,4,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,0,0,-2,4,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,0,1,0,0,0,4,4,-1,-1-2*K.1,1+2*K.1,0,0,-4,-4,1,1,0,0,0,0,-1,-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,0,1,0,0,0,4,4,-1,1+2*K.1,-1-2*K.1,0,0,-4,-4,1,1,0,0,0,0,-1,-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,0,0,-2,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,2,0,0,0,0,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,0,0,0,0,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,0,0,-2,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,2,0,0,0,0,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,0,0,0,0,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,0,0,-2,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2,0,0,0,0,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,0,0,0,0,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,0,0,-2,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2,0,0,0,0,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,0,0,0,0,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,0,0,0,-2,2,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,-2,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,0,0,0,-2,2,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,-2,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,0,0,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,0,0,0,-2,-2,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,2,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,0,0,0,-2,-2,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,2,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,-8,0,0,2,0,0,0,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,-2,0,0,0,0,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,-8,0,0,2,0,0,0,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,-2,0,0,0,0,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_480_973:= KnownIrreducibles(CR);