/* Group 1210.10 downloaded from the LMFDB on 18 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([4, -2, -5, -11, -11, 8, 842, 306, 14083, 7927]); a,b,c := Explode([GPC.1, GPC.3, GPC.4]); AssignNames(~GPC, ["a", "a2", "b", "c"]);
GPerm := PermutationGroup< 22 | (2,3)(4,6)(5,8)(7,11)(9,10)(13,14)(15,17)(16,18)(19,22)(20,21), (2,4,7,8,10)(3,6,11,5,9)(13,15,18,21,19)(14,17,16,20,22), (12,13,16,15,19,21,20,22,17,18,14), (1,2,5,10,4,7,11,6,9,8,3) >;
GLFp := MatrixGroup< 3, GF(11) | [[10, 0, 0, 1, 1, 0, 0, 0, 10], [9, 5, 0, 7, 4, 0, 2, 4, 1], [7, 1, 8, 4, 9, 7, 6, 1, 5], [1, 0, 0, 0, 1, 0, 5, 10, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1210_10 := rec< RF |  
Agroup := true,
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, 121, a^5*b^5*c^2>,< 5, 121, a^6*b^9*c^9>,< 5, 121, a^4*b^6*c^8>,< 5, 121, a^2*b*c^3>,< 5, 121, a^8*b^2*c^7>,< 10, 121, a^3*b^3*c^6>,< 10, 121, a^7*b^4*c^10>,< 10, 121, a^9*b^10*c^5>,< 10, 121, a*b^7*c^4>,< 11, 10, c>,< 11, 10, b>,< 11, 10, b*c>,< 11, 10, b^2*c^2>,< 11, 10, b^3*c^3>,< 11, 10, b*c^5>,< 11, 10, b*c^3>,< 11, 10, b*c^2>,< 11, 10, b^2*c^4>,< 11, 10, b*c^7>,< 11, 10, b^2*c^5>,< 11, 10, b^2*c^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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,K.1^-2,K.1^2,K.1,K.1^-1,K.1,K.1^-1,K.1^-2,K.1^2,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,K.1^2,K.1^-2,K.1^-1,K.1,K.1^-1,K.1,K.1^2,K.1^-2,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^-2,K.1^2,K.1^-1,K.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(5: Sparse := true);
S := [ K |1,1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1,K.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(5: Sparse := true);
S := [ K |1,-1,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,-1,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,-1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.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(5: Sparse := true);
S := [ K |1,-1,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.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!\[10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 10, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3,-1,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1,-1,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2,-1,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4,-1,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2,-1,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2,-1,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2,-1,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2,-1,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3,-1,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1,-1,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4,-1,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2,-1,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2,-1,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3,-1,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1,-1,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2,-1,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2,-1,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3,-1,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(11: Sparse := true);
S := [ K |10,0,0,0,0,0,0,0,0,0,2+2*K.1+2*K.1^3+2*K.1^-3+2*K.1^-1,-1,-1+K.1^2-K.1^3+K.1^4-K.1^5-K.1^-5+K.1^-4-K.1^-3+K.1^-2,2*K.1^3+K.1^4+2*K.1^5+2*K.1^-5+K.1^-4+2*K.1^-3,2+2*K.1+2*K.1^4+2*K.1^-4+2*K.1^-1,-2-2*K.1^2-K.1^3-2*K.1^4-2*K.1^-4-K.1^-3-2*K.1^-2,2+2*K.1^2+2*K.1^3+2*K.1^-3+2*K.1^-2,K.1^2+2*K.1^3+2*K.1^4+2*K.1^-4+2*K.1^-3+K.1^-2,-1,2+2*K.1^4+2*K.1^5+2*K.1^-5+2*K.1^-4,-2-2*K.1^3-2*K.1^4-K.1^5-K.1^-5-2*K.1^-4-2*K.1^-3,2+2*K.1^2+2*K.1^5+2*K.1^-5+2*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_1210_10:= KnownIrreducibles(CR);