Finite Group Databasebeta

?

← Prev (#72233481) Next (#72233483) →

#72233482

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

Aliases

No aliases for this group.

Subgroups

5013 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=h,b^2=ghi,e^2=j,b^a=bg,c^a=chj,c^b=chij,d^a=de,d^b=dej,d^c=df,e^b=ei,e^c=eh,e^d=ej,f^a=fh,f^b=fh,f^e=fj,g^d=gi,h^d=hj

Conjugacy classes & character table

64 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.8);;
gap> SetPower(coll, 2, F.7*F.8*F.9);;
gap> SetPower(coll, 5, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.8*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);