Finite Group Databasebeta

?

← Prev (#72338682) Next (#72338684) →

#72338683

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

Aliases

No aliases for this group.

Subgroups

3992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 32 points:

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

Polycyclic presentation:

2^10|c^2=h,e^2=gj,c^a=cf,d^a=dfg,d^b=di,d^c=dj,e^a=egj,e^c=efgj,e^d=eh,f^c=fi,f^d=fj,f^e=fij,g^c=gij,g^d=gj,h^a=hi,h^e=hj

Conjugacy classes & character table

73 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.8);;
gap> SetPower(coll, 5, F.7*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.6*F.7*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 5, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);