Finite Group Databasebeta

?

← Prev (#72225696) Next (#72225698) →

#72225697

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

Aliases

No aliases for this group.

Subgroups

13722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Polycyclic presentation:

2^10|a^2=f,c^2=j,b^a=bfg,c^a=cf,c^b=ch,d^a=dgi,d^b=dh,d^c=dh,e^a=eghij,e^c=eghij,f^d=fj,g^c=gj,h^a=hj,i^a=ij,i^c=ij

Conjugacy classes & character table

100 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, 3, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);