/* Group 128.927 downloaded from the LMFDB on 25 September 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, 2, 2, 2, 2, 2, 232, 1598, 1227, 58, 675, 570, 80, 1684, 102, 4710, 2365]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.3, GPC.7]); AssignNames(~GPC, ["a", "b", "c", "c2", "c4", "c8", "d"]);
GPerm := PermutationGroup< 64 | (1,34,2,33)(3,36,4,35)(5,38,6,37)(7,40,8,39)(9,42,10,41)(11,44,12,43)(13,46,14,45)(15,48,16,47)(17,50,18,49)(19,52,20,51)(21,54,22,53)(23,56,24,55)(25,58,26,57)(27,60,28,59)(29,62,30,61)(31,64,32,63), (1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(33,53)(34,54)(35,55)(36,56)(37,52)(38,51)(39,49)(40,50)(41,61)(42,62)(43,63)(44,64)(45,60)(46,59)(47,57)(48,58), (1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,26,18,25)(19,28,20,27)(21,30,22,29)(23,32,24,31)(33,43,34,44)(35,42,36,41)(37,47,38,48)(39,46,40,45)(49,59,50,60)(51,58,52,57)(53,63,54,64)(55,62,56,61), (1,7,3,6,2,8,4,5)(9,15,11,14,10,16,12,13)(17,21,20,24,18,22,19,23)(25,29,28,32,26,30,27,31)(33,37,36,40,34,38,35,39)(41,45,44,48,42,46,43,47)(49,55,51,54,50,56,52,53)(57,63,59,62,58,64,60,61), (1,3,2,4)(5,7,6,8)(9,12,10,11)(13,16,14,15)(17,19,18,20)(21,23,22,24)(25,28,26,27)(29,32,30,31)(33,36,34,35)(37,40,38,39)(41,43,42,44)(45,47,46,48)(49,52,50,51)(53,56,54,55)(57,59,58,60)(61,63,62,64), (1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15)(17,19,18,20)(21,23,22,24)(25,27,26,28)(29,31,30,32)(33,35,34,36)(37,39,38,40)(41,43,42,44)(45,47,46,48)(49,52,50,51)(53,56,54,55)(57,60,58,59)(61,64,62,63), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_128_927 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
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, 1, c^8>,< 2, 2, d>,< 2, 4, b*d>,< 2, 8, a>,< 4, 2, c^4>,< 4, 2, c^12*d>,< 4, 4, b>,< 4, 8, a*d>,< 4, 8, a*b>,< 4, 8, a*b*d>,< 4, 16, a*b*c^13*d>,< 8, 2, c^6*d>,< 8, 2, c^2*d>,< 8, 4, c^2>,< 8, 8, b*c^2>,< 8, 16, a*c^15>,< 16, 4, c>,< 16, 4, c^3>,< 16, 4, c*d>,< 16, 4, c^9>,< 16, 8, b*c>,< 16, 8, b*c*d>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, -2, 2, -2, 0, 2, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, 0, 2, -2, 0, 0, -2, 2, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, 0, 2, -2, 0, 0, 2, -2, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, 0, 2, 2, -2, 0, -2, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, -2, 0, 2, 2, -2, 0, 0, 0, 0, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,0,-2,2,2,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*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 |2,2,-2,-2,0,-2,2,2,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-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(8: Sparse := true);
S := [ K |2,2,-2,2,0,-2,2,-2,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-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(8: Sparse := true);
S := [ K |2,2,-2,2,0,-2,2,-2,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,0,0,0,0,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,-1*K.1-K.1^3+K.1^5+K.1^7,K.1-K.1^3+K.1^5-K.1^7,-1*K.1+K.1^3-K.1^5+K.1^7,K.1+K.1^3-K.1^5-K.1^7,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,0,0,0,0,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,K.1+K.1^3-K.1^5-K.1^7,-1*K.1+K.1^3-K.1^5+K.1^7,K.1-K.1^3+K.1^5-K.1^7,-1*K.1-K.1^3+K.1^5+K.1^7,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,-1*K.1+K.1^3-K.1^5+K.1^7,-1*K.1-K.1^3+K.1^5+K.1^7,K.1+K.1^3-K.1^5-K.1^7,K.1-K.1^3+K.1^5-K.1^7,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(16: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,K.1-K.1^3+K.1^5-K.1^7,K.1+K.1^3-K.1^5-K.1^7,-1*K.1-K.1^3+K.1^5+K.1^7,-1*K.1+K.1^3-K.1^5+K.1^7,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_128_927:= KnownIrreducibles(CR);