Finite Group Databasebeta

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#72255255

• supersolvable
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

At least 22822 conjugacy classes of subgroups; only the 503 normal subgroups are shown.

Full subgroup data →

Presentation

Polycyclic presentation:

2^11,3|a^2=e,b^2=j,c^2=fg,d^2=ej,b^a=be,c^a=ch,c^b=cf,d^b=de,d^c=dgik,e^c=ei,f^a=fj,f^b=fk,f^c=fik,g^a=gij,g^b=gi,g^c=gik,g^d=gik,h^a=hi,h^b=hijk,h^c=hi,h^d=hijk,h^f=hk,h^g=hk,j^c=jk,l^d=l^2

Conjugacy classes & character table

174 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, 3]);;
gap> SetPower(coll, 1, F.5);;
gap> SetPower(coll, 2, F.10);;
gap> SetPower(coll, 3, F.6*F.7);;
gap> SetPower(coll, 4, F.5*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.7*F.9*F.11);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.11);;
gap> SetConjugate(coll, 6, 3, F.6*F.9*F.11);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.11);;
gap> SetConjugate(coll, 7, 4, F.7*F.9*F.11);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.9*F.10*F.11);;
gap> SetConjugate(coll, 8, 3, F.8*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.9*F.10*F.11);;
gap> SetConjugate(coll, 8, 6, F.8*F.11);;
gap> SetConjugate(coll, 8, 7, F.8*F.11);;
gap> SetConjugate(coll, 10, 3, F.10*F.11);;
gap> SetConjugate(coll, 12, 4, F.12^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);