Finite Group Databasebeta

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#72340564

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

Aliases

No aliases for this group.

Subgroups

At least 8977 conjugacy classes of subgroups; only the 605 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^12|a^2=ik,c^2=k,d^2=l,f^2=k,h^2=l,c^a=cf,c^b=cg,d^a=dh,d^b=dgk,e^c=egkl,e^d=el,f^b=fi,f^c=fk,f^d=fj,f^e=fi,g^a=gik,g^f=gk,h^b=hikl,h^c=hj,h^d=hl,h^g=hl,i^c=ik,i^d=il,j^b=jkl,j^e=jl

Conjugacy classes & character table

106 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.9*F.11);;
gap> SetPower(coll, 3, F.11);;
gap> SetPower(coll, 4, F.12);;
gap> SetPower(coll, 6, F.11);;
gap> SetPower(coll, 8, F.12);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.11);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.11*F.12);;
gap> SetConjugate(coll, 5, 4, F.5*F.12);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.11);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.11);;
gap> SetConjugate(coll, 7, 6, F.7*F.11);;
gap> SetConjugate(coll, 8, 2, F.8*F.9*F.11*F.12);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.12);;
gap> SetConjugate(coll, 8, 7, F.8*F.12);;
gap> SetConjugate(coll, 9, 3, F.9*F.11);;
gap> SetConjugate(coll, 9, 4, F.9*F.12);;
gap> SetConjugate(coll, 10, 2, F.10*F.11*F.12);;
gap> SetConjugate(coll, 10, 5, F.10*F.12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);