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#72283530

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

Aliases

No aliases for this group.

Subgroups

4991 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=j,c^2=h,d^2=ej,f^2=ij,g^2=i,c^a=ch,c^b=cj,d^a=de,d^b=dg,d^c=df,e^b=ei,e^c=eij,f^a=fi,f^b=fh,f^c=fi,g^a=gi,g^b=gi,g^c=ghj,g^f=gj,h^d=hj

Conjugacy classes & character table

67 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, 2, F.10);;
gap> SetPower(coll, 3, F.8);;
gap> SetPower(coll, 4, F.5*F.10);;
gap> SetPower(coll, 6, F.9*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*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);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.8*F.10);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);