Finite Group Databasebeta

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#72302172

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

Aliases

No aliases for this group.

Subgroups

4028 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=h,b^2=ij,c^2=e,d^2=i,g^2=j,b^a=bg,c^a=cj,c^b=cf,d^b=di,d^c=de,e^b=ei,f^c=fi,f^d=fi,g^b=gj,h^b=hj

Conjugacy classes & character table

112 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.8);;
gap> SetPower(coll, 2, F.9*F.10);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 4, F.9);;
gap> SetPower(coll, 7, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);