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#72263248

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

Aliases

No aliases for this group.

Subgroups

3925 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=ij,c^2=i,d^2=ij,f^2=i,b^a=bg,c^a=cgi,c^b=ci,d^a=de,d^b=df,e^b=eh,e^c=ei,f^a=fhij,f^b=fi,f^d=fi,f^e=fj,g^d=gi,h^d=hj

Conjugacy classes & character table

64 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.9*F.10);;
gap> SetPower(coll, 3, F.9);;
gap> SetPower(coll, 4, F.9*F.10);;
gap> SetPower(coll, 6, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
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);