Finite Group Databasebeta

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#72306524

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

Aliases

No aliases for this group.

Subgroups

Only the 2857 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Presentation

Polycyclic presentation:

2^12|a^2=f,b^2=l,e^2=fhik,f^2=k,i^2=l,j^2=l,b^a=bk,d^c=dkl,e^a=ei,e^b=eh,e^c=el,e^d=eg,f^e=fj,g^c=gl,h^a=hl,i^a=ij,i^e=ijl,i^f=ikl,j^a=jk,j^e=jk,j^i=jl,k^e=kl

Conjugacy classes & character table

226 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", "k", "l");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.6);;
gap> SetPower(coll, 2, F.12);;
gap> SetPower(coll, 5, F.6*F.8*F.9*F.11);;
gap> SetPower(coll, 6, F.11);;
gap> SetPower(coll, 9, F.12);;
gap> SetPower(coll, 10, F.12);;
gap> SetConjugate(coll, 2, 1, F.2*F.11);;
gap> SetConjugate(coll, 4, 3, F.4*F.11*F.12);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.12);;
gap> SetConjugate(coll, 5, 4, F.5*F.7);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.12);;
gap> SetConjugate(coll, 8, 1, F.8*F.12);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 5, F.9*F.10*F.12);;
gap> SetConjugate(coll, 9, 6, F.9*F.11*F.12);;
gap> SetConjugate(coll, 10, 1, F.10*F.11);;
gap> SetConjugate(coll, 10, 5, F.10*F.11);;
gap> SetConjugate(coll, 10, 9, F.10*F.12);;
gap> SetConjugate(coll, 11, 5, F.11*F.12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);