Finite Group Databasebeta

?

← Prev (#72240009) Next (#72240011) →

#72240010

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

Aliases

No aliases for this group.

Subgroups

2281 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=ghj,c^2=e,e^2=i,f^2=j,i^2=j,b^a=bgh,c^a=cf,c^b=ci,d^c=dhj,e^a=ej,e^b=ej,f^b=fj,g^c=gj

Conjugacy classes & character table

136 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, 1, F.7);;
gap> SetPower(coll, 2, F.7*F.8*F.10);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);