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#72260807

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

Aliases

No aliases for this group.

Subgroups

3962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 32 points:

(1,2,7,11)(3,14,21,9)(4,8,22,23)(5,12,6,13)(10,18,25,20)(15,29,17,26)(16,24,32,27)(19,28,31,30);(3,15)(4,18)(8,23)(9,26)(10,25)(14,29)(17,21)(20,22)(24,30)(27,28);(2,8,11,23)(4,18)(9,27,14,24)(10,12,25,13)(16,19)(20,22)(26,30,29,28)(31,32);(1,3,6,17)(2,9,13,29)(4,19,20,32)(5,15,7,21)(8,24,10,30)(11,14,12,26)(16,22,31,18)(23,27,25,28)

Polycyclic presentation:

2^10|a^2=ij,c^2=g,d^2=j,e^2=j,b^a=bf,c^a=ce,c^b=cg,d^a=dfij,d^b=di,d^c=dg,e^a=ej,e^b=eh,e^c=ei,e^d=eh,f^c=fhi,f^e=fj,g^a=gij,h^a=hj

Conjugacy classes & character table

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