Finite Group Databasebeta

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#72238604

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

Aliases

No aliases for this group.

Subgroups

At least 11111 conjugacy classes of subgroups; only the 329 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^12|b^2=h,c^2=l,e^2=jkl,g^2=jl,b^a=bjl,c^a=cil,c^b=chkl,d^a=df,d^b=dfgjl,d^c=de,e^a=ej,e^b=ei,e^c=ejkl,e^d=ejkl,f^b=fjl,f^c=fjkl,g^a=gjl,g^b=gjl,g^c=gi,g^d=gjl,g^e=gk,h^c=hl,h^d=hjl,h^e=hl,i^b=il,i^d=ik,i^e=il,i^g=il,j^c=jl,k^b=kl,k^c=kl

Conjugacy classes & character table

103 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, 2, F.8);;
gap> SetPower(coll, 3, F.12);;
gap> SetPower(coll, 5, F.10*F.11*F.12);;
gap> SetPower(coll, 7, F.10*F.12);;
gap> SetConjugate(coll, 2, 1, F.2*F.10*F.12);;
gap> SetConjugate(coll, 3, 1, F.3*F.9*F.12);;
gap> SetConjugate(coll, 3, 2, F.3*F.8*F.11*F.12);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7*F.10*F.12);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.10*F.11*F.12);;
gap> SetConjugate(coll, 5, 4, F.5*F.10*F.11*F.12);;
gap> SetConjugate(coll, 6, 2, F.6*F.10*F.12);;
gap> SetConjugate(coll, 6, 3, F.6*F.10*F.11*F.12);;
gap> SetConjugate(coll, 7, 1, F.7*F.10*F.12);;
gap> SetConjugate(coll, 7, 2, F.7*F.10*F.12);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.10*F.12);;
gap> SetConjugate(coll, 7, 5, F.7*F.11);;
gap> SetConjugate(coll, 8, 3, F.8*F.12);;
gap> SetConjugate(coll, 8, 4, F.8*F.10*F.12);;
gap> SetConjugate(coll, 8, 5, F.8*F.12);;
gap> SetConjugate(coll, 9, 2, F.9*F.12);;
gap> SetConjugate(coll, 9, 4, F.9*F.11);;
gap> SetConjugate(coll, 9, 5, F.9*F.12);;
gap> SetConjugate(coll, 9, 7, F.9*F.12);;
gap> SetConjugate(coll, 10, 3, F.10*F.12);;
gap> SetConjugate(coll, 11, 2, F.11*F.12);;
gap> SetConjugate(coll, 11, 3, F.11*F.12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);