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#72262570

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

Aliases

No aliases for this group.

Subgroups

3600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=g,b^a=bhj,c^a=cf,c^b=ce,d^a=dg,d^b=dj,e^a=eh,e^b=ei,f^a=fi,f^b=fh,f^d=fi,f^e=fj,g^c=gi,h^c=hj

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