Finite Group Databasebeta

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#72262767

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

Aliases

No aliases for this group.

Subgroups

At least 10489 conjugacy classes of subgroups; only the 231 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^12|a^2=jkl,b^2=fjkl,c^2=efl,e^2=jl,f^2=jkl,g^2=l,b^a=bf,c^a=cfgl,c^b=ce,d^b=djkl,d^c=djkl,e^a=eh,e^b=ehi,e^c=ehijl,e^d=el,f^a=fjkl,f^c=fhij,f^e=fk,g^a=gjk,g^b=gijk,g^c=gikl,g^e=gjl,g^f=gjk,h^b=hj,h^e=hl,h^f=hl,h^g=hl,i^a=ijk,i^b=ijk,i^c=ikl,j^a=jl,j^b=jl,j^c=jl,k^a=kl,k^b=kl

Conjugacy classes & character table

91 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.10*F.11*F.12);;
gap> SetPower(coll, 2, F.6*F.10*F.11*F.12);;
gap> SetPower(coll, 3, F.5*F.6*F.12);;
gap> SetPower(coll, 5, F.10*F.12);;
gap> SetPower(coll, 6, F.10*F.11*F.12);;
gap> SetPower(coll, 7, F.12);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.6*F.7*F.12);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.10*F.11*F.12);;
gap> SetConjugate(coll, 4, 3, F.4*F.10*F.11*F.12);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.9*F.10*F.12);;
gap> SetConjugate(coll, 5, 4, F.5*F.12);;
gap> SetConjugate(coll, 6, 1, F.6*F.10*F.11*F.12);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.11);;
gap> SetConjugate(coll, 7, 1, F.7*F.10*F.11);;
gap> SetConjugate(coll, 7, 2, F.7*F.9*F.10*F.11);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.11*F.12);;
gap> SetConjugate(coll, 7, 5, F.7*F.10*F.12);;
gap> SetConjugate(coll, 7, 6, F.7*F.10*F.11);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 5, F.8*F.12);;
gap> SetConjugate(coll, 8, 6, F.8*F.12);;
gap> SetConjugate(coll, 8, 7, F.8*F.12);;
gap> SetConjugate(coll, 9, 1, F.9*F.10*F.11);;
gap> SetConjugate(coll, 9, 2, F.9*F.10*F.11);;
gap> SetConjugate(coll, 9, 3, F.9*F.11*F.12);;
gap> SetConjugate(coll, 10, 1, F.10*F.12);;
gap> SetConjugate(coll, 10, 2, F.10*F.12);;
gap> SetConjugate(coll, 10, 3, F.10*F.12);;
gap> SetConjugate(coll, 11, 1, F.11*F.12);;
gap> SetConjugate(coll, 11, 2, F.11*F.12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);