Finite Group Databasebeta

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#72225224

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

Aliases

No aliases for this group.

Subgroups

1564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|a^2=e,c^2=fi,d^2=gj,e^2=h,f^2=ik,g^2=j,h^2=j,i^2=k,c^a=cik,c^b=cf,d^a=dj,d^b=dg,e^c=ek,f^a=fk,f^b=fi,g^b=gj,i^b=ik

Conjugacy classes & character table

176 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", "k");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.5);;
gap> SetPower(coll, 3, F.6*F.9);;
gap> SetPower(coll, 4, F.7*F.10);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, F.9*F.11);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.9*F.11);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 5, 3, F.5*F.11);;
gap> SetConjugate(coll, 6, 1, F.6*F.11);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);