Finite Group Databasebeta

?

← Prev (#72258168) Next (#72258170) →

#72258169

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

Aliases

No aliases for this group.

Subgroups

1062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|b^2=d,c^2=e,d^2=g,e^2=h,f^2=i,h^2=j,i^2=k,b^a=bf,c^a=cf,c^b=cfhk,d^a=dk,d^c=dj,e^a=ei,e^b=eij,f^a=fik,f^b=fi,h^a=hk,h^b=hk,i^a=ik,i^b=ik

Conjugacy classes & character table

212 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", "k");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.4);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.8*F.11);;
gap> SetConjugate(coll, 4, 1, F.4*F.11);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.9*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.9*F.11);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 8, 1, F.8*F.11);;
gap> SetConjugate(coll, 8, 2, F.8*F.11);;
gap> SetConjugate(coll, 9, 1, F.9*F.11);;
gap> SetConjugate(coll, 9, 2, F.9*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);