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#72304153

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

Aliases

No aliases for this group.

Subgroups

2694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 40 points:

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

Polycyclic presentation:

2^10|b^2=g,c^2=d,d^2=j,e^2=i,b^a=bhj,c^a=cf,c^b=ce,d^b=dh,e^a=eh,e^b=ej,e^c=ehi,e^d=ej,f^b=fh,f^e=fj,g^c=gij,h^c=hj

Conjugacy classes & character table

106 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.7);;
gap> SetPower(coll, 3, F.4);;
gap> SetPower(coll, 4, F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.8*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);