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#72260803

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

Aliases

No aliases for this group.

Subgroups

4475 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=ij,c^2=g,d^2=j,e^2=j,b^a=bi,c^a=ce,d^a=df,d^b=di,d^c=dg,e^a=ej,e^c=ei,e^d=eh,f^c=fhi,f^e=fj,g^a=gij,h^a=hj

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