/* Group 768.1090131 downloaded from the LMFDB on 04 February 2026. */
 
/* 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([9, 2, 2, 3, 2, 2, 2, 2, 2, 2, 181, 46, 218, 1299, 444, 345, 823, 157, 36941, 18158, 3263, 1976, 365, 158, 30246, 12111, 7584, 12967, 12112, 7801, 1762, 2059, 214, 19457, 1970]); a,b,c,d,e,f := Explode([GPC.1, GPC.2, GPC.4, GPC.5, GPC.6, GPC.8]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "e", "e2", "f", "f2"]);
GPerm := PermutationGroup< 18 | (2,6)(4,11)(7,14)(8,13)(9,16)(12,15)(17,18), (17,18), (2,3,6)(4,5,11)(7,10,14)(8,16,12)(9,13,15), (1,2)(3,6)(5,10)(8,13)(11,14)(15,16), (1,3)(2,6)(4,7)(9,12)(11,14)(15,16), (1,4)(2,7)(3,9)(5,11)(6,12)(8,15)(10,16)(13,14), (1,5)(2,8)(3,10)(4,11)(6,13)(7,15)(9,16)(12,14), (1,2)(3,6)(4,7)(5,8)(9,12)(10,13)(11,15)(14,16), (1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,16)(14,15) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_768_1090131 := 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:= GPerm;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, G!(17,18)>,< 2, 3, G!(1,2)(3,6)(4,7)(5,8)(9,12)(10,13)(11,15)(14,16)(17,18)>,< 2, 3, G!(1,2)(3,6)(4,7)(5,8)(9,12)(10,13)(11,15)(14,16)>,< 2, 12, G!(4,7)(5,13)(8,10)(9,12)(11,16)(14,15)(17,18)>,< 2, 12, G!(1,4)(2,7)(3,9)(5,11)(6,12)(8,15)(10,16)(13,14)(17,18)>,< 2, 12, G!(4,12)(5,10)(7,9)(8,13)(11,15)(14,16)>,< 2, 12, G!(1,7)(2,4)(3,12)(5,15)(6,9)(8,11)(10,14)(13,16)>,< 2, 24, G!(3,6)(5,11)(8,15)(9,12)(10,14)(13,16)>,< 2, 24, G!(3,6)(5,11)(8,15)(9,12)(10,14)(13,16)(17,18)>,< 3, 128, G!(1,5,4)(2,10,12)(3,13,7)(6,8,9)(14,15,16)>,< 4, 12, G!(1,4,2,7)(3,9,6,12)(5,14,8,16)(10,15,13,11)(17,18)>,< 4, 12, G!(1,16,6,15)(2,14,3,11)(4,5,12,13)(7,8,9,10)>,< 4, 24, G!(1,2,3,6)(4,11,9,16)(5,13,10,8)(7,14,12,15)>,< 4, 24, G!(1,2,3,6)(4,11,9,16)(5,13,10,8)(7,14,12,15)(17,18)>,< 4, 24, G!(1,4,3,9)(2,7,6,12)(5,15,10,14)(8,11,13,16)>,< 4, 24, G!(1,4,3,9)(2,7,6,12)(5,15,10,14)(8,11,13,16)(17,18)>,< 4, 48, G!(2,6)(4,14,12,16)(5,8,10,13)(7,11,9,15)(17,18)>,< 4, 48, G!(1,2,6,3)(4,10,7,5)(8,9,13,12)(11,14)>,< 4, 48, G!(1,10,7,14)(2,13,4,16)(3,8,12,11)(5,9,15,6)(17,18)>,< 4, 48, G!(1,13,16,7)(2,8,14,12)(3,10,11,4)(5,15,9,6)>,< 6, 128, G!(1,4,5)(2,12,10)(3,7,13)(6,9,8)(14,16,15)(17,18)>,< 8, 48, G!(1,8,16,9,6,10,15,7)(2,13,14,4,3,5,11,12)(17,18)>,< 8, 48, G!(1,14,12,10,2,16,9,13)(3,11,7,8,6,15,4,5)>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, -2, -2, 2, 2, 0, 0, -1, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -1, -1, -1, -1, 1, 1, 0, 3, 3, 1, 1, -1, -1, -1, -1, -1, -1, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -1, 3, -1, 3, 1, 1, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, -1, 3, -1, 1, 1, 0, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, 3, 3, -1, -1, -1, -1, 1, 1, 1, 1, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, -1, 3, -1, 3, -1, -1, 0, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, -1, 3, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -3, -3, 3, -3, 1, 3, -1, -1, 1, 0, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 0, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -3, -3, 3, -3, 1, 3, -1, 1, -1, 0, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 0, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -3, -3, 3, 1, -3, -1, 3, -1, 1, 0, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 0, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -3, -3, 3, 1, -3, -1, 3, 1, -1, 0, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 0, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -3, -3, 3, 1, 1, -1, -1, -1, 1, 0, -3, 3, -1, 1, -1, 1, -1, 1, -1, 1, 0, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -3, -3, 3, 1, 1, -1, -1, 1, -1, 0, -3, 3, 1, -1, -1, 1, 1, -1, 1, -1, 0, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, -2, -2, -2, -2, 0, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, -6, -6, 6, 2, 2, -2, -2, 0, 0, 0, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, -4, -4, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, -4, -4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, -12, 4, -4, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, -12, 4, -4, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_768_1090131:= KnownIrreducibles(CR);