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#72337662

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

Aliases

No aliases for this group.

Subgroups

3787 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 32 points:

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

Polycyclic presentation:

2^10|b^2=f,e^2=j,b^a=bij,c^a=cf,d^b=dg,d^c=dh,e^a=egj,e^b=ehj,e^c=ej,e^d=ej,f^d=fi,f^e=fj,g^b=gi,g^c=gj,h^a=hi,h^b=hj

Conjugacy classes & character table

64 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.6);;
gap> SetPower(coll, 5, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);