Finite Group Databasebeta

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#72315794

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

Aliases

No aliases for this group.

Subgroups

Only the 38852 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Presentation

Polycyclic presentation:

2^11|c^2=i,e^2=k,f^2=k,g^2=h,h^2=k,c^a=ci,c^b=ck,d^a=di,d^b=dk,d^c=di,e^c=ei,e^d=ei,g^a=gi,g^b=gj,g^e=gh,g^f=gk,h^e=hk

Conjugacy classes & character table

272 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, 3, F.9);;
gap> SetPower(coll, 5, F.11);;
gap> SetPower(coll, 6, F.11);;
gap> SetPower(coll, 7, F.8);;
gap> SetPower(coll, 8, F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.11);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.11);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 5, F.7*F.8);;
gap> SetConjugate(coll, 7, 6, F.7*F.11);;
gap> SetConjugate(coll, 8, 5, F.8*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);