Finite Group Databasebeta

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#72320492

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

Aliases

No aliases for this group.

Subgroups

658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=e,c^2=j,d^2=fh,e^2=g,f^2=hj,g^2=i,h^2=j,b^a=bf,c^b=cj,d^a=df,d^b=dh,e^a=eh,e^d=ej,f^a=fh,f^b=fj,g^a=gj,h^a=hj

Conjugacy classes & character table

184 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.5);;
gap> SetPower(coll, 3, F.10);;
gap> SetPower(coll, 4, F.6*F.8);;
gap> SetPower(coll, 5, F.7);;
gap> SetPower(coll, 6, F.8*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, 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.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);