Finite Group Databasebeta

?

← Prev (#72239337) Next (#72239339) →

#72239338

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

Aliases

No aliases for this group.

Subgroups

2293 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 48 points:

(4,12)(7,14)(9,15)(10,16);(1,2)(3,9,11,15)(4,7)(5,8)(6,10,13,16)(12,14)(17,18)(19,28)(20,33)(21,35)(22,25)(23,27)(24,30)(26,37)(29,41)(31,45)(32,38)(34,40)(36,47)(39,46)(42,43)(44,48);(1,3)(2,6,8,13)(4,10)(5,11)(7,9,14,15)(12,16)(17,19,21,31,22,32,36,46,23,29,37,43,20,30,34,44)(18,24,26,39,25,28,40,42,27,38,35,48,33,41,47,45);(19,29)(24,38)(28,41)(30,32)(31,43)(39,48)(42,45)(44,46)

Polycyclic presentation:

2^10|b^2=f,c^2=g,e^2=hj,g^2=i,i^2=j,b^a=bf,c^b=ce,d^c=dj,e^a=eh,e^b=ej,f^c=fh,g^b=ghj

Conjugacy classes & character table

148 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.6);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 5, F.8*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 2, F.7*F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);