/* Group 384.5714 downloaded from the LMFDB on 30 October 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, -2, 1536, 3297, 41, 4898, 66, 6403, 795, 652, 3469, 325, 237, 8078, 1214, 382, 166]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.5, GPC.6, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "b4", "c", "d", "e", "e2"]); GPerm := PermutationGroup< 96 | (1,50,2,49)(3,52,4,51)(5,54,6,53)(7,56,8,55)(9,58,10,57)(11,60,12,59)(13,62,14,61)(15,64,16,63)(17,66,18,65)(19,68,20,67)(21,70,22,69)(23,72,24,71)(25,74,26,73)(27,76,28,75)(29,78,30,77)(31,80,32,79)(33,82,34,81)(35,84,36,83)(37,86,38,85)(39,88,40,87)(41,90,42,89)(43,92,44,91)(45,94,46,93)(47,96,48,95), (1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16)(17,19,18,20)(21,23,22,24)(25,31,26,32)(27,29,28,30)(33,39,34,40)(35,37,36,38)(41,47,42,48)(43,45,44,46)(49,79,50,80)(51,77,52,78)(53,76,54,75)(55,74,56,73)(57,87,58,88)(59,85,60,86)(61,84,62,83)(63,82,64,81)(65,95,66,96)(67,93,68,94)(69,92,70,91)(71,90,72,89), (1,30,6,26,2,29,5,25)(3,31,7,28,4,32,8,27)(9,38,14,34,10,37,13,33)(11,39,15,36,12,40,16,35)(17,46,22,42,18,45,21,41)(19,47,23,44,20,48,24,43)(49,73,53,77,50,74,54,78)(51,75,56,80,52,76,55,79)(57,81,61,85,58,82,62,86)(59,83,64,88,60,84,63,87)(65,89,69,93,66,90,70,94)(67,91,72,96,68,92,71,95), (1,5,2,6)(3,8,4,7)(9,13,10,14)(11,16,12,15)(17,21,18,22)(19,24,20,23)(25,29,26,30)(27,32,28,31)(33,37,34,38)(35,40,36,39)(41,45,42,46)(43,48,44,47)(49,54,50,53)(51,55,52,56)(57,62,58,61)(59,63,60,64)(65,70,66,69)(67,71,68,72)(73,78,74,77)(75,79,76,80)(81,86,82,85)(83,87,84,88)(89,94,90,93)(91,95,92,96), (1,17,9)(2,18,10)(3,19,11)(4,20,12)(5,21,13)(6,22,14)(7,23,15)(8,24,16)(25,41,33)(26,42,34)(27,43,35)(28,44,36)(29,45,37)(30,46,38)(31,47,39)(32,48,40)(49,57,65)(50,58,66)(51,59,67)(52,60,68)(53,61,69)(54,62,70)(55,63,71)(56,64,72)(73,81,89)(74,82,90)(75,83,91)(76,84,92)(77,85,93)(78,86,94)(79,87,95)(80,88,96), (1,6,2,5)(3,8,4,7)(9,12,10,11)(13,15,14,16)(17,23,18,24)(19,22,20,21)(25,30,26,29)(27,32,28,31)(33,36,34,35)(37,39,38,40)(41,47,42,48)(43,46,44,45)(49,51,50,52)(53,56,54,55)(57,64,58,63)(59,61,60,62)(65,69,66,70)(67,71,68,72)(73,75,74,76)(77,80,78,79)(81,88,82,87)(83,85,84,86)(89,93,90,94)(91,95,92,96), (1,4,2,3)(5,7,6,8)(9,15,10,16)(11,14,12,13)(17,22,18,21)(19,24,20,23)(25,28,26,27)(29,31,30,32)(33,39,34,40)(35,38,36,37)(41,46,42,45)(43,48,44,47)(49,53,50,54)(51,55,52,56)(57,59,58,60)(61,64,62,63)(65,72,66,71)(67,69,68,70)(73,77,74,78)(75,79,76,80)(81,83,82,84)(85,88,86,87)(89,96,90,95)(91,93,92,94), (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)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96) >; /* Booleans */ RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; booleans_384_5714 := rec< RF | Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false>; /* Character Table */ G:= GPC; C := SequenceToConjugacyClasses([car |< 1, 1, Id(G)>,< 2, 1, e^2>,< 2, 6, b^4*e>,< 2, 24, a*b^2*d*e^3>,< 3, 8, c^2>,< 4, 2, b^4*e^2>,< 4, 6, d*e>,< 4, 8, a*e^2>,< 4, 48, a*b^3*e^2>,< 6, 8, c*e^2>,< 8, 2, b^6>,< 8, 2, b^2>,< 8, 12, b^2*e>,< 8, 48, a*b^5*c^2*e>,< 12, 16, b^4*c^2>,< 12, 32, a*c>,< 12, 32, a*c^2*e^2>,< 16, 12, b*d>,< 16, 12, b*d*e^2>,< 16, 12, b^3*d>,< 16, 12, b^5*d>,< 16, 24, b*c*e^2>,< 16, 24, b^3*c*e^2>,< 24, 16, b^2*c>,< 24, 16, b^2*c*e^2>]); 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]; 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]; 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]; 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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 2, 2, 2, -1, 2, 2, 2, 0, -1, 2, 2, 2, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 2, 2, 0, 2, 2, 2, 0, 0, 2, -2, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 2, 2, -2, -1, 2, 2, -2, 0, -1, 2, 2, 2, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(8: Sparse := true); S := [ K |2,2,-2,0,2,-2,2,0,0,2,0,0,0,0,-2,0,0,-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,K.1+K.1^-1,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(8: Sparse := true); S := [ K |2,2,-2,0,2,-2,2,0,0,2,0,0,0,0,-2,0,0,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,-1*K.1-K.1^-1,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |2,2,2,0,-1,2,2,0,0,-1,-2,-2,-2,0,-1,-1-2*K.1,1+2*K.1,0,0,0,0,0,0,1,1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |2,2,2,0,-1,2,2,0,0,-1,-2,-2,-2,0,-1,1+2*K.1,-1-2*K.1,0,0,0,0,0,0,1,1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; x := CR!\[3, 3, -1, -1, 0, 3, -1, 3, 1, 0, 3, 3, -1, -1, 0, 0, 0, -1, -1, -1, -1, 1, 1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[3, 3, -1, -1, 0, 3, -1, 3, -1, 0, 3, 3, -1, 1, 0, 0, 0, 1, 1, 1, 1, -1, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[3, 3, -1, 1, 0, 3, -1, -3, -1, 0, 3, 3, -1, 1, 0, 0, 0, -1, -1, -1, -1, 1, 1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[3, 3, -1, 1, 0, 3, -1, -3, 1, 0, 3, 3, -1, -1, 0, 0, 0, 1, 1, 1, 1, -1, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[4, 4, -4, 0, -2, -4, 4, 0, 0, -2, 0, 0, 0, 0, 2, 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,-2,0,0,0,0,2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,0,0,-1*K.1-K.1^3-K.1^5-K.1^7,K.1+K.1^3+K.1^5+K.1^7,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,-1*K.1^2-K.1^-2,K.1^2+K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(16: Sparse := true); S := [ K |4,-4,0,0,-2,0,0,0,0,2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,0,0,K.1+K.1^3+K.1^5+K.1^7,-1*K.1-K.1^3-K.1^5-K.1^7,-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,-1*K.1^2-K.1^-2,K.1^2+K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(16: Sparse := true); S := [ K |4,-4,0,0,-2,0,0,0,0,2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,0,0,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,K.1^2+K.1^-2,-1*K.1^2-K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(16: Sparse := true); S := [ K |4,-4,0,0,-2,0,0,0,0,2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,0,0,-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,K.1^2+K.1^-2,-1*K.1^2-K.1^-2]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; x := CR!\[6, 6, -2, 0, 0, 6, -2, 0, 0, 0, -6, -6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(8: Sparse := true); S := [ K |6,6,2,0,0,-6,-2,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(8: Sparse := true); S := [ K |6,6,2,0,0,-6,-2,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(8: Sparse := true); S := [ K |8,-8,0,0,2,0,0,0,0,-2,-4*K.1-4*K.1^-1,4*K.1+4*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,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 |8,-8,0,0,2,0,0,0,0,-2,4*K.1+4*K.1^-1,-4*K.1-4*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1]; x := CR!S; x`IsCharacter := true; x`Schur := -1; x`IsIrreducible := true; _ := CharacterTable(G : Check := 0); chartbl_384_5714:= KnownIrreducibles(CR);