Finite Group Databasebeta

?

← Prev (#72284500) Next (#72284502) →

#72284501

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

Aliases

No aliases for this group.

Subgroups

3693 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=g,d^2=e,e^2=j,f^2=i,b^a=bg,d^a=dhj,d^b=df,d^c=dj,e^b=ei,f^a=fh,f^b=fhi,g^d=gh,g^f=gj,h^b=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, 4, F.5);;
gap> SetPower(coll, 5, F.10);;
gap> SetPower(coll, 6, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.8*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.8*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.8);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);