Finite Group Databasebeta

?

← Prev (#72239384) Next (#72239386) →

#72239385

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

Aliases

No aliases for this group.

Subgroups

4780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,6)(4,8,7,5)(10,14,17,20)(11,18,19,21);(9,10,15,14,13,17,12,20)(11,16,18,22,19,23,21,24);(2,5,6,8)(9,11)(10,16)(12,21)(13,19)(14,22)(15,18)(17,23)(20,24);(2,6)(5,8)(10,17)(14,20)(16,23)(22,24)

Polycyclic presentation:

2^10|a^2=f,b^2=fgij,c^2=e,g^2=i,h^2=j,b^a=bg,c^a=cghj,d^a=dj,d^b=di,e^a=ej,f^b=fi,f^c=fi,g^b=gi,g^c=gi,h^a=hj

Conjugacy classes & character table

196 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.6);;
gap> SetPower(coll, 2, F.6*F.7*F.9*F.10);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);