Finite Group Databasebeta

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#72283142

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

Aliases

No aliases for this group.

Subgroups

At least 22842 conjugacy classes of subgroups; only the 980 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^11|b^2=jk,c^2=ik,d^2=jk,e^2=fgjk,g^2=jk,h^2=k,b^a=bjk,c^a=cik,d^b=dij,e^a=ef,e^b=eh,e^c=eg,e^d=efgjk,f^b=fi,f^c=fk,g^b=gik,g^c=gj,g^d=gjk,h^a=hik,h^b=hk,h^c=hi,h^f=hk,h^g=hk,i^e=ik

Conjugacy classes & character table

113 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.10*F.11);;
gap> SetPower(coll, 3, F.9*F.11);;
gap> SetPower(coll, 4, F.10*F.11);;
gap> SetPower(coll, 5, F.6*F.7*F.10*F.11);;
gap> SetPower(coll, 7, F.10*F.11);;
gap> SetPower(coll, 8, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.10*F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.9*F.11);;
gap> SetConjugate(coll, 4, 2, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.7);;
gap> SetConjugate(coll, 5, 4, F.5*F.6*F.7*F.10*F.11);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.11);;
gap> SetConjugate(coll, 7, 2, F.7*F.9*F.11);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10*F.11);;
gap> SetConjugate(coll, 8, 1, F.8*F.9*F.11);;
gap> SetConjugate(coll, 8, 2, F.8*F.11);;
gap> SetConjugate(coll, 8, 3, F.8*F.9);;
gap> SetConjugate(coll, 8, 6, F.8*F.11);;
gap> SetConjugate(coll, 8, 7, F.8*F.11);;
gap> SetConjugate(coll, 9, 5, F.9*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);