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#72256396

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

Aliases

No aliases for this group.

Subgroups

4310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=hi,c^2=ij,d^2=h,b^a=bf,c^a=ce,c^b=cg,d^a=dij,d^b=dfj,d^c=degh,e^a=ej,e^b=eh,e^d=ehi,f^c=fij,g^a=ghi,g^d=ghi,g^e=gj,h^c=hj

Conjugacy classes & character table

58 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.8*F.9);;
gap> SetPower(coll, 3, F.9*F.10);;
gap> SetPower(coll, 4, F.8);;
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.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.7*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.8*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.8*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.8*F.9);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);