Finite Group Databasebeta

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#72340735

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

Aliases

No aliases for this group.

Subgroups

At least 20881 conjugacy classes of subgroups; only the 835 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^12|a^2=h,d^2=jk,f^2=l,g^2=jkl,i^2=l,c^a=ch,d^a=dg,d^b=dl,d^c=df,e^a=eh,e^c=el,f^a=fi,f^c=fl,g^c=gij,g^d=gjkl,g^e=gjkl,g^f=gk,h^d=hjkl,h^f=hl,i^c=il,i^d=ik,i^e=il,i^f=il,k^c=kl

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

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