Finite Group Databasebeta

?

← Prev (#72322491) Next (#72322493) →

#72322492

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

Aliases

No aliases for this group.

Subgroups

4722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|a^2=h,b^2=e,d^2=f,e^2=i,h^2=j,j^2=k,b^a=bhjk,c^a=ch,d^a=dg,d^c=di,e^a=ek,h^b=hj,h^c=hjk,j^b=jk,j^c=jk

Conjugacy classes & character table

200 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, 1, F.8);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 10, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.8*F.10*F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.11);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10*F.11);;
gap> SetConjugate(coll, 10, 2, F.10*F.11);;
gap> SetConjugate(coll, 10, 3, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);