Finite Group Databasebeta

?

← Prev (#72262852) Next (#72262854) →

#72262853

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

Aliases

No aliases for this group.

Subgroups

3300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=ej,b^a=bg,c^a=ce,c^b=cf,d^a=dghj,d^b=dghi,d^c=dghj,e^b=eh,e^d=ei,f^a=fhi,f^c=fh,f^d=fi,f^e=fj,g^c=gij,h^c=hj

Conjugacy classes & character table

58 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, 3, F.5*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.7*F.8*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.8*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 6, 4, F.6*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);