Finite Group Databasebeta

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#72252587

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

Aliases

No aliases for this group.

Subgroups

At least 33858 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^12|d^2=f,f^2=l,d^a=dg,d^b=dgj,d^c=dh,e^a=egkl,e^b=egk,e^c=ehijl,e^d=efjkl,f^a=fi,f^b=fik,f^c=fj,f^e=fkl,g^d=gi,g^f=gl,h^d=hj,h^e=hkl,h^f=hk,i^d=il,i^e=il,j^d=jk,j^e=jk

Conjugacy classes & character table

166 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, 4, F.6);;
gap> SetPower(coll, 6, F.12);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.11*F.12);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.11);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.9*F.10*F.12);;
gap> SetConjugate(coll, 5, 4, F.5*F.6*F.10*F.11*F.12);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9*F.11);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.11*F.12);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 7, 6, F.7*F.12);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 8, 5, F.8*F.11*F.12);;
gap> SetConjugate(coll, 8, 6, F.8*F.11);;
gap> SetConjugate(coll, 9, 4, F.9*F.12);;
gap> SetConjugate(coll, 9, 5, F.9*F.12);;
gap> SetConjugate(coll, 10, 4, F.10*F.11);;
gap> SetConjugate(coll, 10, 5, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);