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#72233261

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

Aliases

No aliases for this group.

Subgroups

6583 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=e,b^a=bij,c^a=cg,c^b=cf,d^b=dj,d^c=dh,e^a=eh,e^b=ehi,f^a=fhi,f^c=fhi,f^e=fj,g^b=ghi,g^c=gh,g^f=gj,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, 2, 1, F.2*F.9*F.10);;
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.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
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.8*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.8*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.8);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);