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#72308481

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

Aliases

No aliases for this group.

Subgroups

1730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=ij,c^2=f,d^2=efgh,e^2=hij,i^2=j,b^a=bghij,c^b=cj,d^a=de,d^b=dgh,d^c=dij,e^a=ei,e^b=eh,e^c=ej,e^d=ehj,f^d=fj,g^d=gh,i^a=ij

Conjugacy classes & character table

88 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.7);;
gap> SetPower(coll, 2, F.9*F.10);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.5*F.6*F.7*F.8);;
gap> SetPower(coll, 5, F.8*F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.8*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.8);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);