Finite Group Databasebeta

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#72240605

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

Aliases

No aliases for this group.

Subgroups

At least 7290 conjugacy classes of subgroups; only the 888 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^11|b^2=e,e^2=jk,f^2=j,h^2=k,b^a=bijk,c^b=cefj,d^b=dehk,d^c=dg,e^a=ek,e^c=ei,e^d=ej,f^a=fk,f^b=fi,f^c=fi,f^d=fj,f^e=fk,h^a=hk,h^c=hi,h^f=hk,i^b=ik

Conjugacy classes & character table

152 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 5, F.10*F.11);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 8, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.9*F.10*F.11);;
gap> SetConjugate(coll, 3, 2, F.3*F.5*F.6*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.8*F.11);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.11);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.11);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.11);;
gap> SetConjugate(coll, 8, 1, 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, 9, 2, F.9*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);