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#72306359

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

Aliases

No aliases for this group.

Subgroups

2809 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,d^2=egj,e^2=i,g^2=j,h^2=j,c^b=cij,d^a=dg,d^b=dj,d^c=df,e^d=eh,f^b=fj,g^a=gh,g^d=gh,g^e=gij,h^a=hi,h^d=hi,h^g=hj,i^d=ij

Conjugacy classes & character table

76 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.5);;
gap> SetPower(coll, 4, F.5*F.7*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.6);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.8);;
gap> SetConjugate(coll, 7, 4, F.7*F.8);;
gap> SetConjugate(coll, 7, 5, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.9);;
gap> SetConjugate(coll, 8, 7, F.8*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);