Finite Group Databasebeta

?

← Prev (#72234412) Next (#72234414) →

#72234413

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

Aliases

No aliases for this group.

Subgroups

5162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=ij,c^2=hij,b^a=bij,c^a=ch,c^b=ch,d^a=dg,d^b=df,d^c=de,e^a=ei,e^b=eh,e^c=ej,f^b=fj,f^c=fh,g^b=gj,g^c=gij,g^e=gj,i^d=ij

Conjugacy classes & character table

67 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.9*F.10);;
gap> SetPower(coll, 3, F.8*F.9*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);