Finite Group Databasebeta

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#72252511

• solvable
• monolithic
• monomial
• stem
• rational
• ambivalent

Aliases

No aliases for this group.

Splittings

Subgroups

Only the 236 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,3,2^5|a^2=f,b^2=f,e^2=l,h^2=l,i^2=l,c^a=ce,c^b=ce,d^a=df,d^b=df,e^c=el,e^d=el,f^c=fl,g^b=g^2,h^b=hi,h^g=i,i^b=il,i^g=hil,i^h=il,j^b=k,j^g=k,j^h=jl,j^i=jl,k^b=j,k^g=jk,k^i=kl

Conjugacy classes & character table

146 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, 3, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.6);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 5, F.12);;
gap> SetPower(coll, 8, F.12);;
gap> SetPower(coll, 9, F.12);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 5, 3, F.5*F.12);;
gap> SetConjugate(coll, 5, 4, F.5*F.12);;
gap> SetConjugate(coll, 6, 3, F.6*F.12);;
gap> SetConjugate(coll, 7, 2, F.7^2);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> SetConjugate(coll, 8, 7, F.9);;
gap> SetConjugate(coll, 9, 2, F.9*F.12);;
gap> SetConjugate(coll, 9, 7, F.8*F.9*F.12);;
gap> SetConjugate(coll, 9, 8, F.9*F.12);;
gap> SetConjugate(coll, 10, 2, F.11);;
gap> SetConjugate(coll, 10, 7, F.11);;
gap> SetConjugate(coll, 10, 8, F.10*F.12);;
gap> SetConjugate(coll, 10, 9, F.10*F.12);;
gap> SetConjugate(coll, 11, 2, F.10);;
gap> SetConjugate(coll, 11, 7, F.10*F.11);;
gap> SetConjugate(coll, 11, 9, F.11*F.12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);