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#72310283

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

Aliases

No aliases for this group.

Subgroups

4129 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

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

Polycyclic presentation:

2^10|a^2=i,b^2=d,c^2=eg,b^a=bi,c^a=cf,c^b=cde,d^c=dh,e^a=ei,e^b=eh,f^a=fj,f^b=fi,f^c=fij,f^e=fj,g^a=gj,i^c=ij

Conjugacy classes & character table

82 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.9);;
gap> SetPower(coll, 2, F.4);;
gap> SetPower(coll, 3, F.5*F.7);;
gap> SetConjugate(coll, 2, 1, F.2*F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);