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#72240519

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

Aliases

No aliases for this group.

Subgroups

4575 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 32 points:

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

Polycyclic presentation:

2^10|a^2=i,c^2=dej,e^2=j,b^a=bf,c^a=cd,c^b=cfg,d^a=dj,d^b=dh,d^c=dj,e^c=ej,f^c=fhi,f^d=fj,g^a=gij,g^c=gi,g^d=gj,h^a=hj,i^c=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.9);;
gap> SetPower(coll, 3, F.4*F.5*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.4);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);