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#72258308

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

Aliases

No aliases for this group.

Subgroups

4308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=d,c^2=g,d^2=j,b^a=bf,c^a=cdg,c^b=ce,d^b=dh,e^a=ehi,e^c=eh,e^d=ej,f^a=fh,f^c=fhi,g^a=gj,g^b=gh,g^e=gj,h^c=hj,i^a=ij,i^c=ij

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