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#72303146

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

Aliases

No aliases for this group.

Subgroups

4466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=j,c^2=hj,d^2=i,e^2=j,f^2=j,d^a=df,d^c=de,e^a=eh,e^d=ej,f^a=fi,f^c=fhj,f^e=fj,g^d=gij,g^f=gj,h^d=hj,i^a=ij

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