Finite Group Databasebeta

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#72263642

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

Aliases

No aliases for this group.

Subgroups

Only the 4795 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Presentation

Polycyclic presentation:

2^12|b^2=j,c^2=kl,d^2=i,e^2=fkl,g^2=l,b^a=bj,c^a=ck,d^a=djl,d^c=dg,e^a=ejk,e^c=ef,e^d=eh,f^d=fj,g^a=gl,g^e=gjk,h^a=hl,h^c=hkl,h^d=hjl,h^e=hjl,h^g=hl,i^c=il,i^e=ijl,k^d=kl

Conjugacy classes & character table

238 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, 2, F.10);;
gap> SetPower(coll, 3, F.11*F.12);;
gap> SetPower(coll, 4, F.9);;
gap> SetPower(coll, 5, F.6*F.11*F.12);;
gap> SetPower(coll, 7, F.12);;
gap> SetConjugate(coll, 2, 1, F.2*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.11);;
gap> SetConjugate(coll, 4, 1, F.4*F.10*F.12);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.10*F.11);;
gap> SetConjugate(coll, 5, 3, F.5*F.6);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.12);;
gap> SetConjugate(coll, 7, 5, F.7*F.10*F.11);;
gap> SetConjugate(coll, 8, 1, F.8*F.12);;
gap> SetConjugate(coll, 8, 3, F.8*F.11*F.12);;
gap> SetConjugate(coll, 8, 4, F.8*F.10*F.12);;
gap> SetConjugate(coll, 8, 5, F.8*F.10*F.12);;
gap> SetConjugate(coll, 8, 7, F.8*F.12);;
gap> SetConjugate(coll, 9, 3, F.9*F.12);;
gap> SetConjugate(coll, 9, 5, F.9*F.10*F.12);;
gap> SetConjugate(coll, 11, 4, F.11*F.12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);