/* Group 576.8355 downloaded from the LMFDB on 02 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, -2, -2, -3, -2, 2, -3, 417, 1058, 346, 66, 1283, 91, 1284, 16133, 4053, 1757, 1045, 3382, 1038, 1550, 166, 6167]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.3, GPC.6, GPC.7]); AssignNames(~GPC, ["a", "b", "c", "c2", "c4", "d", "e", "e2"]);
GPerm := PermutationGroup< 11 | (2,4)(6,7), (2,4)(9,10), (1,2)(3,4), (1,3)(2,4), (9,10,11), (5,6,7), (8,9)(10,11), (8,10)(9,11) >;
GLZN := MatrixGroup< 2, Integers(60) | [[1, 30, 30, 1], [31, 0, 30, 31], [1, 20, 0, 1], [49, 0, 0, 49], [19, 51, 0, 1], [16, 15, 45, 31], [53, 12, 36, 17], [46, 45, 45, 26]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_576_8355 := 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 := true,
solvable := true,
supersolvable := false>; 

 
/* Character Table */
G:= GLZN;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Matrix(2, [1, 0, 0, 1])>,< 2, 1, Matrix(2, [49, 0, 0, 49])>,< 2, 2, Matrix(2, [53, 12, 36, 17])>,< 2, 3, Matrix(2, [31, 0, 30, 31])>,< 2, 3, Matrix(2, [19, 30, 0, 19])>,< 2, 6, Matrix(2, [23, 42, 36, 47])>,< 2, 6, Matrix(2, [1, 44, 0, 29])>,< 2, 12, Matrix(2, [19, 51, 0, 1])>,< 2, 18, Matrix(2, [19, 0, 15, 29])>,< 2, 18, Matrix(2, [19, 46, 0, 11])>,< 2, 18, Matrix(2, [31, 15, 0, 41])>,< 2, 36, Matrix(2, [23, 47, 36, 37])>,< 3, 2, Matrix(2, [1, 40, 0, 1])>,< 3, 8, Matrix(2, [1, 45, 45, 46])>,< 3, 16, Matrix(2, [46, 55, 15, 1])>,< 4, 6, Matrix(2, [17, 0, 24, 13])>,< 4, 12, Matrix(2, [19, 21, 30, 31])>,< 4, 12, Matrix(2, [47, 15, 24, 53])>,< 4, 12, Matrix(2, [47, 45, 54, 23])>,< 4, 18, Matrix(2, [47, 50, 24, 43])>,< 4, 18, Matrix(2, [49, 10, 45, 29])>,< 4, 18, Matrix(2, [1, 45, 30, 41])>,< 4, 36, Matrix(2, [2, 23, 39, 28])>,< 6, 2, Matrix(2, [49, 40, 0, 49])>,< 6, 4, Matrix(2, [53, 52, 36, 17])>,< 6, 6, Matrix(2, [31, 10, 0, 31])>,< 6, 6, Matrix(2, [19, 10, 0, 19])>,< 6, 8, Matrix(2, [19, 15, 45, 4])>,< 6, 12, Matrix(2, [23, 2, 36, 47])>,< 6, 16, Matrix(2, [49, 5, 45, 34])>,< 6, 16, Matrix(2, [38, 27, 51, 17])>,< 6, 16, Matrix(2, [38, 7, 51, 17])>,< 6, 16, Matrix(2, [38, 17, 21, 17])>,< 6, 24, Matrix(2, [19, 11, 0, 1])>,< 6, 48, Matrix(2, [46, 59, 15, 29])>,< 12, 24, Matrix(2, [49, 41, 30, 1])>,< 12, 24, Matrix(2, [23, 55, 36, 17])>,< 12, 24, Matrix(2, [53, 25, 6, 17])>,< 12, 48, Matrix(2, [8, 45, 51, 7])>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, -1, 2, -1, 0, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 0, -1, -1, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, -1, -1, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, 0, -1, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 2, -2, 0, 0, 0, -2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, -2, 2, 0, -2, 0, 2, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 0, 2, -2, 0, 0, 0, 2, 0, -2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 2, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, -2, 0, 0, -2, 0, 0, 2, -1, -1, 2, 0, 0, 0, 2, 0, 0, 0, 2, -2, 2, 2, -1, -2, 1, 1, -1, 1, 0, 1, 0, 0, 0, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 0, -2, 0, 0, 0, 0, -1, 2, -1, 0, 2, 2, -2, 0, 0, 0, 0, -1, 1, -1, -1, 2, 1, 1, 1, -1, -2, 1, 0, 1, -1, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 0, 2, 0, 0, 0, 0, -1, 2, -1, 0, -2, -2, 2, 0, 0, 0, 0, -1, 1, -1, -1, 2, 1, 1, 1, -1, -2, -1, 0, -1, 1, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 2, 2, -2, 2, 0, 0, 2, 0, 0, 2, -1, -1, -2, 0, 0, 0, -2, 0, 0, 0, 2, -2, 2, 2, -1, -2, 1, 1, -1, 1, 0, -1, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, -2, 0, 0, -2, 0, 0, 2, -1, -1, -2, 0, 0, 0, -2, 0, 0, 0, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, 0, 1, 0, 0, 0, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, -2, 0, 0, 0, 0, -1, 2, -1, 0, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 1, 0, 1, 1, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, 3, 1, 1, -1, 1, 1, 3, 0, 0, 3, 1, -1, -1, -1, -1, -1, -1, 3, 3, -1, -1, 0, -1, 0, 0, 0, 0, 1, 0, -1, 1, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, 3, -1, -1, -1, -1, -1, 3, 0, 0, 3, -1, 1, 1, -1, 1, 1, 1, 3, 3, -1, -1, 0, -1, 0, 0, 0, 0, -1, 0, 1, -1, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, -3, -1, 1, 1, 1, -1, 3, 0, 0, 3, 1, -1, 1, -1, -1, -1, 1, 3, -3, -1, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 1, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, -3, 1, -1, 1, -1, 1, 3, 0, 0, 3, -1, 1, -1, -1, 1, 1, -1, 3, -3, -1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, -1, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, 3, -1, -1, -1, -1, 1, 3, 0, 0, -3, 1, -1, 1, 1, 1, 1, -1, 3, -3, -1, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 1, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, -3, -1, -1, 1, 3, 1, 1, -1, 1, -1, 3, 0, 0, -3, -1, 1, -1, 1, -1, -1, 1, 3, -3, -1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, -1, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, -3, -1, 1, 1, 1, 1, 3, 0, 0, -3, -1, 1, 1, 1, -1, -1, -1, 3, 3, -1, -1, 0, -1, 0, 0, 0, 0, -1, 0, 1, -1, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, -1, -1, -1, -3, 1, -1, 1, -1, -1, 3, 0, 0, -3, 1, -1, -1, 1, 1, 1, 1, 3, 3, -1, -1, 0, -1, 0, 0, 0, 0, 1, 0, -1, 1, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 2, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, -4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, 2, -1, -1, 1, 2, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 2, 2, 0, -3, 3, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 2, 2, 0, 3, -3, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, -2, -2, -2, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, -3, -3, 1, 1, 0, 1, 0, 0, 0, 0, -1, 0, 1, -1, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, 0, -2, 2, 0, 0, 0, -2, 0, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -6, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, 0, -2, 2, 0, 0, 0, 2, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -6, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, -2, -2, -2, 0, -2, 0, 0, 0, 0, -3, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, -3, -3, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -2, -2, 2, 0, -2, 0, 0, 0, 0, -3, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, -3, 3, 1, 1, 0, -1, 0, 0, 0, 0, 1, 0, -1, -1, 1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -2, -2, 2, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, -3, 3, 1, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 1, -1, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, -12, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_576_8355:= KnownIrreducibles(CR);