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#72302897

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

Aliases

No aliases for this group.

Subgroups

4446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=j,c^2=hj,e^2=j,d^a=df,d^b=dj,d^c=de,e^a=eh,e^d=ej,f^a=fi,f^c=fhj,f^e=fj,g^d=gi,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, 5, F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
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);;
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);