Finite Group Databasebeta

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#72256444

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

Aliases

No aliases for this group.

Subgroups

At least 17060 conjugacy classes of subgroups; only the 691 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^12|a^2=h,b^2=e,c^2=ik,d^2=k,i^2=l,b^a=bg,c^a=cf,c^b=cd,d^a=di,d^b=dl,e^a=ej,e^c=ekl,f^a=fl,f^c=fl,g^a=gj,g^b=gj,g^c=gik,g^d=gkl,h^b=hj,h^c=hl,h^d=hl,i^b=ik,i^g=il,j^c=jl,k^a=kl

Conjugacy classes & character table

148 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.8);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.9*F.11);;
gap> SetPower(coll, 4, F.11);;
gap> SetPower(coll, 9, F.12);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.4);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.12);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.11*F.12);;
gap> SetConjugate(coll, 6, 1, F.6*F.12);;
gap> SetConjugate(coll, 6, 3, F.6*F.12);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.11);;
gap> SetConjugate(coll, 7, 4, F.7*F.11*F.12);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.12);;
gap> SetConjugate(coll, 8, 4, F.8*F.12);;
gap> SetConjugate(coll, 9, 2, F.9*F.11);;
gap> SetConjugate(coll, 9, 7, F.9*F.12);;
gap> SetConjugate(coll, 10, 3, F.10*F.12);;
gap> SetConjugate(coll, 11, 1, F.11*F.12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);