Finite Group Databasebeta

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#72340403

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Subgroups

5452 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 40 points:

(3,7)(5,8)(9,10)(11,19)(12,17)(13,27)(14,16)(15,22)(18,20)(21,35)(23,34)(24,38)(25,40)(26,31)(28,29)(30,37)(32,39)(33,36);(2,5,6,8)(9,11,20,22,14,23,13,28)(10,15,18,34,16,29,27,19)(12,24,25,37,26,21,36,39)(17,32,40,38,31,30,33,35);(10,16)(15,29)(17,31)(18,27)(19,34)(30,32)(33,40)(35,38);(1,2)(3,8)(4,6)(5,7)(11,21)(15,30)(19,35)(22,37)(23,24)(28,39)(29,32)(34,38)

Polycyclic presentation:

2^10|b^2=fg,e^2=h,f^2=j,b^a=bf,c^a=cj,d^b=de,e^a=eh,e^b=ei,e^d=eh,f^a=fj,f^b=fj,f^d=fh,g^a=gj,g^b=gj,g^d=gi,g^e=gj,i^b=ij

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i", "j");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.6*F.7);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);