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#72283413

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

Aliases

No aliases for this group.

Subgroups

4788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=i,b^2=h,d^2=e,f^2=ij,g^2=i,c^a=ci,d^a=dg,d^b=df,d^c=dij,e^a=ei,e^b=eij,f^a=fh,f^b=fi,g^a=gi,g^b=ghj,g^f=gj,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, 1, F.9);;
gap> SetPower(coll, 2, F.8);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 6, F.9*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
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.9*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.8*F.10);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);