/* Group 100.10 downloaded from the LMFDB on 16 June 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([4, -2, -2, -5, -5, 8, 98, 102, 1283]); a,b,c := Explode([GPC.1, GPC.3, GPC.4]); AssignNames(~GPC, ["a", "a2", "b", "c"]);
GPerm := PermutationGroup< 10 | (2,3,4,5)(7,8)(9,10), (2,4)(3,5), (6,7,9,10,8), (1,2,5,3,4) >;
GLFp := MatrixGroup< 3, GF(5) | [[4, 3, 4, 0, 0, 3, 2, 1, 0], [4, 1, 0, 1, 3, 0, 3, 1, 1], [4, 0, 3, 2, 3, 1, 4, 2, 4], [4, 3, 1, 1, 2, 2, 4, 0, 2]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_100_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, 5, a^2>,< 4, 25, a*b^4*c^4>,< 4, 25, a^3*b^3*c^4>,< 5, 2, c^2>,< 5, 2, c^4>,< 5, 4, b>,< 5, 4, b*c>,< 5, 4, b^2*c>,< 5, 4, b*c^3>,< 5, 4, b*c^2>,< 10, 10, a^2*c>,< 10, 10, a^2*c^2>]); 
CR := CharacterRing(G);
x := CR!\[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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,-1,-1*K.1,K.1,1,1,1,1,1,1,1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,-1,K.1,-1*K.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 |2,2,0,0,K.1^2+K.1^-2,K.1+K.1^-1,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,K.1^2+K.1^-2,K.1+K.1^-1,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, 0, 0, 0, 4, 4, -1, -1, -1, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1*K.1-K.1^2+K.1^-2,1+2*K.1+K.1^-2,-1,-1-2*K.1-K.1^2-2*K.1^-2,1+K.1+2*K.1^2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,1+K.1+2*K.1^2,-1-2*K.1-K.1^2-2*K.1^-2,-1,1+2*K.1+K.1^-2,-1*K.1-K.1^2+K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,-1*K.1-K.1^2+K.1^-2,-1,1+K.1+2*K.1^2,1+2*K.1+K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,1+2*K.1+K.1^-2,1+K.1+2*K.1^2,-1,-1*K.1-K.1^2+K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_100_10:= KnownIrreducibles(CR);