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#72263335

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

Aliases

No aliases for this group.

Subgroups

3813 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=g,d^2=j,f^2=i,c^a=cj,c^b=chi,d^a=df,d^c=de,e^a=eh,e^b=ej,e^c=ei,f^a=fi,f^c=fhj,f^d=fi,f^e=fj,g^d=gi,h^d=hj

Conjugacy classes & character table

82 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, 3, F.7);;
gap> SetPower(coll, 4, F.10);;
gap> SetPower(coll, 6, F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.8*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);