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#72282018

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

Aliases

No aliases for this group.

Subgroups

4383 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=g,d^2=eij,e^2=ij,f^2=i,b^a=bg,d^a=dj,d^b=df,d^c=de,e^b=ei,e^c=eij,f^a=fh,f^b=fhij,f^c=fi,g^d=ghj,g^f=gj,h^b=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.7);;
gap> SetPower(coll, 4, F.5*F.9*F.10);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 6, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
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.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.8*F.10);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);