/* Group 960.10981 downloaded from the LMFDB on 17 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([8, -2, -2, -3, -2, 2, 2, -2, -5, 161, 41, 194, 23043, 4043, 1939, 1307, 30244, 14892, 7580, 14405, 4909, 741, 2141, 1093, 141, 24206, 166, 24591]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.4, GPC.5, GPC.6]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "e", "e2", "e4"]);
GPerm := PermutationGroup< 21 | (1,2)(3,6)(4,7)(5,8)(9,12)(10,14)(11,15)(13,16)(18,19)(20,21), (1,3)(2,6)(4,8)(5,7)(9,14)(10,12)(11,15)(13,16), (1,2,6,3)(4,7,12,9)(5,8,14,10)(11,15,13,16), (4,5,13)(7,8,16)(9,10,15)(11,12,14), (17,18,20,21,19), (1,4,6,12)(2,7,3,9)(5,13,14,11)(8,16,10,15), (1,5,6,14)(2,8,3,10)(4,11,12,13)(7,15,9,16), (1,6)(2,3)(4,12)(5,14)(7,9)(8,10)(11,13)(15,16) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_960_10981 := 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, e^10>,< 2, 6, d>,< 2, 10, b^3*c*d*e^6>,< 2, 10, b^3*e^4>,< 2, 12, a>,< 2, 12, a*d*e^5>,< 2, 60, a*b^3*c*e^17>,< 3, 8, b^4*c*e^15>,< 4, 2, c*d>,< 4, 6, c>,< 4, 30, b^3*e>,< 4, 30, b^3*d>,< 4, 60, a*b^3*c*d*e^18>,< 5, 2, e^8>,< 5, 2, e^16>,< 6, 8, b^2*c*e^10>,< 6, 80, b^5*c*d*e^11>,< 6, 80, b*e^4>,< 8, 12, a*e^15>,< 8, 12, a*d*e^10>,< 8, 30, a*b*e>,< 8, 30, a*b*e^3>,< 8, 60, a*b^3*d*e^2>,< 10, 2, e^14>,< 10, 2, e^2>,< 10, 12, d*e^4>,< 10, 12, d*e^2>,< 10, 24, a*e^4>,< 10, 24, a*e^2>,< 10, 24, a*d*e>,< 10, 24, a*d*e^3>,< 12, 16, b^4*d*e^15>,< 15, 16, b^2*c*e^16>,< 15, 16, b^4*c*e^7>,< 20, 4, c*d*e^12>,< 20, 4, c*d*e^6>,< 20, 12, c*e^7>,< 20, 12, c*e>,< 30, 16, b^4*c*e^13>,< 30, 16, b^4*c*e>,< 40, 24, a*e>,< 40, 24, a*e^3>,< 40, 24, a*d*e^4>,< 40, 24, a*d*e^2>,< 60, 16, b^2*d*e^4>,< 60, 16, b^2*d*e>,< 60, 16, b^2*d*e^12>,< 60, 16, b^2*d*e^2>]); 
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, 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, 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, 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, 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, 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, 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, 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, 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, 2, 2, 0, 0, 0, -1, 2, 2, 2, 2, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, 0, 0, 0, -1, -2, 2, 2, -2, 0, 2, 2, -1, 1, -1, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 1, -1, -1, -2, -2, 2, 2, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, -2, 0, 0, 0, -1, -2, 2, -2, 2, 0, 2, 2, -1, -1, 1, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 1, -1, -1, -2, -2, 2, 2, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, -2, -2, 0, 0, 0, -1, 2, 2, -2, -2, 0, 2, 2, -1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,0,0,2,2,0,2,2,2,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,2,0,0,2,2,0,0,0,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^-1,2,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.1^2+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.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,0,0,2,2,0,2,2,2,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,2,0,0,2,2,0,0,0,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^-2,2,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+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+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,0,0,-2,2,0,2,-2,2,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,2,0,0,-2,2,0,0,0,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.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-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+K.1^-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,-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,-2,0,0,-2,2,0,2,-2,2,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,2,0,0,-2,2,0,0,0,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+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-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+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-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 |2,2,-2,0,0,2,-2,0,2,-2,2,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,2,0,0,2,-2,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-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,-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-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,-2,0,0,2,-2,0,2,-2,2,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,2,0,0,2,-2,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-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,-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.1^2-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 |2,2,2,0,0,-2,-2,0,2,2,2,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,2,0,0,-2,-2,0,0,0,K.1+K.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-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-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,-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,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 |2,2,2,0,0,-2,-2,0,2,2,2,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,2,0,0,-2,-2,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,2,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,-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,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; 
x := CR!\[3, 3, -1, 3, 3, 1, 1, 1, 0, 3, -1, -1, -1, 1, 3, 3, 0, 0, 0, -1, -1, -1, -1, -1, 3, 3, -1, -1, 1, 1, 1, 1, 0, 0, 0, 3, 3, -1, -1, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, 3, 3, -1, -1, -1, 0, 3, -1, -1, -1, -1, 3, 3, 0, 0, 0, 1, 1, 1, 1, 1, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, 3, 3, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -3, -3, -1, -1, 1, 0, 3, -1, 1, 1, 1, 3, 3, 0, 0, 0, 1, 1, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, 3, 3, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -1, -3, -3, 1, 1, -1, 0, 3, -1, 1, 1, -1, 3, 3, 0, 0, 0, -1, -1, 1, 1, 1, 3, 3, -1, -1, 1, 1, 1, 1, 0, 0, 0, 3, 3, -1, -1, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 1, -3, 3, -1, 1, -1, 0, -3, -1, -1, 1, 1, 3, 3, 0, 0, 0, 1, -1, 1, 1, -1, 3, 3, 1, 1, 1, 1, -1, -1, 0, 0, 0, -3, -3, -1, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 1, -3, 3, 1, -1, 1, 0, -3, -1, -1, 1, -1, 3, 3, 0, 0, 0, -1, 1, -1, -1, 1, 3, 3, 1, 1, -1, -1, 1, 1, 0, 0, 0, -3, -3, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 1, 3, -3, -1, 1, 1, 0, -3, -1, 1, -1, -1, 3, 3, 0, 0, 0, 1, -1, -1, -1, 1, 3, 3, 1, 1, 1, 1, -1, -1, 0, 0, 0, -3, -3, -1, -1, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 1, 3, -3, 1, -1, -1, 0, -3, -1, 1, -1, 1, 3, 3, 0, 0, 0, -1, 1, 1, 1, -1, 3, 3, 1, 1, -1, -1, 1, 1, 0, 0, 0, -3, -3, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,4,0,0,0,0,0,-2,4,4,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,-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^-1,2*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^-1,0,0,0,0,-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 |4,4,4,0,0,0,0,0,-2,4,4,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,-2,-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^-2,2*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^-2,0,0,0,0,-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 |4,4,-4,0,0,0,0,0,-2,-4,4,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,2,-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^-1,2*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^-1,0,0,0,0,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 |4,4,-4,0,0,0,0,0,-2,-4,4,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,2,-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^-2,2*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^-2,0,0,0,0,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(8: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,-2,0,0,0,0,0,4,4,2,0,0,0,0,-2*K.1-2*K.1^3,2*K.1+2*K.1^3,0,-4,-4,0,0,0,0,0,0,0,-2,-2,0,0,0,0,2,2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,-2,0,0,0,0,0,4,4,2,0,0,0,0,2*K.1+2*K.1^3,-2*K.1-2*K.1^3,0,-4,-4,0,0,0,0,0,0,0,-2,-2,0,0,0,0,2,2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,-2,0,0,2,2,0,0,6,-2,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,-2,-2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1-K.1^-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^-1,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-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^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,-2,0,0,2,2,0,0,6,-2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,-2,-2,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1^2-K.1^-2,-1*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^-2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-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^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,-2,0,0,-2,-2,0,0,6,-2,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,2,2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-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^-1,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.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(5: Sparse := true);
S := [ K |6,6,-2,0,0,-2,-2,0,0,6,-2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,2,2,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-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^-2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*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+K.1^-1,K.1^2+K.1^-2,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 |6,6,2,0,0,-2,2,0,0,-6,-2,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,2,-2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*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^-1,0,0,0,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-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^-2,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,2,0,0,-2,2,0,0,-6,-2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,2,-2,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*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^-2,0,0,0,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-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^-1,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,2,0,0,2,-2,0,0,-6,-2,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,-2,2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-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(5: Sparse := true);
S := [ K |6,6,2,0,0,2,-2,0,0,-6,-2,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,-2,2,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,-3*K.1-3*K.1^-1,-3*K.1^2-3*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+K.1^-1,-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; 
x := CR!\[8, -8, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 8, -2, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,0,-4,0,0,0,0,0,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,4,0,0,0,0,0,0,0,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,0,-4,0,0,0,0,0,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,4,0,0,0,0,0,0,0,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,0,0,0,0,0,0,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(60: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,0,2,0,0,0,0,0,-4*K.1^6-4*K.1^-6,4*K.1^12+4*K.1^-12,-2,0,0,0,0,0,0,0,-4*K.1^12-4*K.1^-12,4*K.1^6+4*K.1^-6,0,0,0,0,0,0,0,K.1^12+K.1^-12,-1*K.1^6-K.1^-6,0,0,0,0,K.1^6+K.1^-6,-1*K.1^12-K.1^-12,0,0,0,0,K.1+2*K.1^3-2*K.1^7-K.1^9-K.1^11-2*K.1^13+K.1^15,-1*K.1-2*K.1^3+2*K.1^7+K.1^9+K.1^11+2*K.1^13-K.1^15,3*K.1-2*K.1^5-2*K.1^7-K.1^9+K.1^11+2*K.1^13+2*K.1^15,-3*K.1+2*K.1^5+2*K.1^7+K.1^9-K.1^11-2*K.1^13-2*K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(60: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,0,2,0,0,0,0,0,-4*K.1^6-4*K.1^-6,4*K.1^12+4*K.1^-12,-2,0,0,0,0,0,0,0,-4*K.1^12-4*K.1^-12,4*K.1^6+4*K.1^-6,0,0,0,0,0,0,0,K.1^12+K.1^-12,-1*K.1^6-K.1^-6,0,0,0,0,K.1^6+K.1^-6,-1*K.1^12-K.1^-12,0,0,0,0,-1*K.1-2*K.1^3+2*K.1^7+K.1^9+K.1^11+2*K.1^13-K.1^15,K.1+2*K.1^3-2*K.1^7-K.1^9-K.1^11-2*K.1^13+K.1^15,-3*K.1+2*K.1^5+2*K.1^7+K.1^9-K.1^11-2*K.1^13-2*K.1^15,3*K.1-2*K.1^5-2*K.1^7-K.1^9+K.1^11+2*K.1^13+2*K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(60: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,0,2,0,0,0,0,0,4*K.1^12+4*K.1^-12,-4*K.1^6-4*K.1^-6,-2,0,0,0,0,0,0,0,4*K.1^6+4*K.1^-6,-4*K.1^12-4*K.1^-12,0,0,0,0,0,0,0,-1*K.1^6-K.1^-6,K.1^12+K.1^-12,0,0,0,0,-1*K.1^12-K.1^-12,K.1^6+K.1^-6,0,0,0,0,-3*K.1+2*K.1^5+2*K.1^7+K.1^9-K.1^11-2*K.1^13-2*K.1^15,3*K.1-2*K.1^5-2*K.1^7-K.1^9+K.1^11+2*K.1^13+2*K.1^15,K.1+2*K.1^3-2*K.1^7-K.1^9-K.1^11-2*K.1^13+K.1^15,-1*K.1-2*K.1^3+2*K.1^7+K.1^9+K.1^11+2*K.1^13-K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(60: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,0,2,0,0,0,0,0,4*K.1^12+4*K.1^-12,-4*K.1^6-4*K.1^-6,-2,0,0,0,0,0,0,0,4*K.1^6+4*K.1^-6,-4*K.1^12-4*K.1^-12,0,0,0,0,0,0,0,-1*K.1^6-K.1^-6,K.1^12+K.1^-12,0,0,0,0,-1*K.1^12-K.1^-12,K.1^6+K.1^-6,0,0,0,0,3*K.1-2*K.1^5-2*K.1^7-K.1^9+K.1^11+2*K.1^13+2*K.1^15,-3*K.1+2*K.1^5+2*K.1^7+K.1^9-K.1^11-2*K.1^13-2*K.1^15,-1*K.1-2*K.1^3+2*K.1^7+K.1^9+K.1^11+2*K.1^13-K.1^15,K.1+2*K.1^3-2*K.1^7-K.1^9-K.1^11-2*K.1^13+K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_960_10981:= KnownIrreducibles(CR);