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#72337330

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

Aliases

No aliases for this group.

Subgroups

67619 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

Polycyclic presentation:

2^10|a^2=i,d^2=g,f^2=ghij,b^a=bi,d^a=di,d^b=dh,d^c=di,e^d=ehj,f^a=fi,f^b=fh,f^c=fij,f^d=fhij,f^e=fhj

Conjugacy classes & character table

202 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, 4, F.7);;
gap> SetPower(coll, 6, F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.8*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);