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#72321899

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

Aliases

No aliases for this group.

Subgroups

2481 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 32 points:

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

Polycyclic presentation:

2^10|a^2=f,b^2=f,c^2=fhij,e^2=i,f^2=i,g^2=h,h^2=j,c^a=ch,c^b=cg,d^a=di,e^a=ei,f^c=fj,g^a=gj,g^b=gh,g^c=gh,h^b=hj,h^c=hj

Conjugacy classes & character table

124 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.6);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.6*F.8*F.9*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 7, F.8);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.8);;
gap> SetConjugate(coll, 7, 3, F.7*F.8);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);