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#72233249

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

Aliases

No aliases for this group.

Subgroups

8045 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=e,c^a=cg,c^b=cf,d^b=dhij,e^a=eh,e^b=ehi,f^a=fj,f^c=fhi,f^d=fj,f^e=fj,g^b=gj,g^c=gh,i^c=ij

Conjugacy classes & character table

79 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, 3, F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.8);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);