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#72259152

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

Aliases

No aliases for this group.

Subgroups

5002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=e,b^a=bg,c^a=cf,c^b=ce,d^a=dj,d^b=dj,d^c=de,e^a=eh,f^b=fi,f^c=fh,f^d=fhj,f^e=fj,g^c=ghij,h^c=hj,i^c=ij

Conjugacy classes & character table

64 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, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 6, 4, F.6*F.8*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);