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#72238384

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

Aliases

No aliases for this group.

Subgroups

At least 10493 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^12|a^2=f,c^2=k,d^2=jl,e^2=l,f^2=jl,g^2=l,b^a=bfjl,c^a=ce,c^b=cg,d^a=djl,d^b=djl,d^c=dh,e^a=eh,e^b=ehi,e^d=ekl,f^b=fjl,f^c=fhl,f^e=fk,g^a=gijl,g^b=gl,g^d=gj,g^e=gkl,g^f=gj,h^a=hk,h^b=hj,h^d=hl,h^f=hl,h^g=hl,i^a=ij,i^b=ij,i^c=ik,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.6);;
gap> SetPower(coll, 3, F.11);;
gap> SetPower(coll, 4, F.10*F.12);;
gap> SetPower(coll, 5, F.12);;
gap> SetPower(coll, 6, F.10*F.12);;
gap> SetPower(coll, 7, F.12);;
gap> SetConjugate(coll, 2, 1, F.2*F.6*F.10*F.12);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.10*F.12);;
gap> SetConjugate(coll, 4, 2, F.4*F.10*F.12);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.11*F.12);;
gap> SetConjugate(coll, 6, 2, F.6*F.10*F.12);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.12);;
gap> SetConjugate(coll, 6, 5, F.6*F.11);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.10*F.12);;
gap> SetConjugate(coll, 7, 2, F.7*F.12);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 7, 5, F.7*F.11*F.12);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.11);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 4, 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);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.11);;
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);