Finite Group Databasebeta

?

← Prev (#72281980) Next (#72281982) →

#72281981

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

Aliases

No aliases for this group.

Subgroups

4613 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=g,d^2=ehij,e^2=i,f^2=ij,b^a=bg,d^a=de,d^b=df,d^c=dh,e^a=ei,e^b=ei,f^a=fh,f^b=fh,f^c=fj,g^d=ghij,g^f=gj,h^b=hj

Conjugacy classes & character table

76 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, 2, F.7);;
gap> SetPower(coll, 4, F.5*F.8*F.9*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 6, F.9*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);