Finite Group Databasebeta

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#72344184

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

Aliases

No aliases for this group.

Splittings

Subgroups

Only the 31 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3,2^11|d^2=j,e^2=j,f^2=j,g^2=j,h^2=m,i^2=mn,c^a=c^2,c^b=c^2,d^a=fj,d^b=fiklmn,d^c=e,e^a=fg,e^b=fghjklmn,e^c=dej,e^d=ej,f^a=dj,f^b=dik,f^c=g,g^a=de,g^b=dehjkn,g^c=fgj,g^f=gj,h^a=himn,h^b=him,h^c=im,h^d=hjk,h^e=hjkl,h^f=hjkl,h^g=hjk,i^a=imn,i^c=hi,i^d=ilm,i^e=ijkmn,i^f=ilm,i^g=ijklmn,j^b=jl,j^h=jm,j^i=jmn,k^a=kmn,k^b=klmn,k^c=kmn,k^d=km,k^e=kmn,k^f=kn,k^g=km,k^h=km,k^i=kmn,l^d=lmn,l^e=ln,l^f=lmn,l^g=ln,m^a=n,m^b=n,m^c=mn,n^a=m,n^b=m,n^c=m

Conjugacy classes & character table

90 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", "l", "m", "n");;
gap> coll := SingleCollector(F, [2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 4, F.10);;
gap> SetPower(coll, 5, F.10);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 8, F.13);;
gap> SetPower(coll, 9, F.13*F.14);;
gap> SetConjugate(coll, 3, 1, F.3^2);;
gap> SetConjugate(coll, 3, 2, F.3^2);;
gap> SetConjugate(coll, 4, 1, F.6*F.10);;
gap> SetConjugate(coll, 4, 2, F.6*F.9*F.11*F.12*F.13*F.14);;
gap> SetConjugate(coll, 4, 3, F.5);;
gap> SetConjugate(coll, 5, 1, F.6*F.7);;
gap> SetConjugate(coll, 5, 2, F.6*F.7*F.8*F.10*F.11*F.12*F.13*F.14);;
gap> SetConjugate(coll, 5, 3, F.4*F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.4*F.10);;
gap> SetConjugate(coll, 6, 2, F.4*F.9*F.11);;
gap> SetConjugate(coll, 6, 3, F.7);;
gap> SetConjugate(coll, 7, 1, F.4*F.5);;
gap> SetConjugate(coll, 7, 2, F.4*F.5*F.8*F.10*F.11*F.14);;
gap> SetConjugate(coll, 7, 3, F.6*F.7*F.10);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9*F.13*F.14);;
gap> SetConjugate(coll, 8, 2, F.8*F.9*F.13);;
gap> SetConjugate(coll, 8, 3, F.9*F.13);;
gap> SetConjugate(coll, 8, 4, F.8*F.10*F.11);;
gap> SetConjugate(coll, 8, 5, F.8*F.10*F.11*F.12);;
gap> SetConjugate(coll, 8, 6, F.8*F.10*F.11*F.12);;
gap> SetConjugate(coll, 8, 7, F.8*F.10*F.11);;
gap> SetConjugate(coll, 9, 1, F.9*F.13*F.14);;
gap> SetConjugate(coll, 9, 3, F.8*F.9);;
gap> SetConjugate(coll, 9, 4, F.9*F.12*F.13);;
gap> SetConjugate(coll, 9, 5, F.9*F.10*F.11*F.13*F.14);;
gap> SetConjugate(coll, 9, 6, F.9*F.12*F.13);;
gap> SetConjugate(coll, 9, 7, F.9*F.10*F.11*F.12*F.13*F.14);;
gap> SetConjugate(coll, 10, 2, F.10*F.12);;
gap> SetConjugate(coll, 10, 8, F.10*F.13);;
gap> SetConjugate(coll, 10, 9, F.10*F.13*F.14);;
gap> SetConjugate(coll, 11, 1, F.11*F.13*F.14);;
gap> SetConjugate(coll, 11, 2, F.11*F.12*F.13*F.14);;
gap> SetConjugate(coll, 11, 3, F.11*F.13*F.14);;
gap> SetConjugate(coll, 11, 4, F.11*F.13);;
gap> SetConjugate(coll, 11, 5, F.11*F.13*F.14);;
gap> SetConjugate(coll, 11, 6, F.11*F.14);;
gap> SetConjugate(coll, 11, 7, F.11*F.13);;
gap> SetConjugate(coll, 11, 8, F.11*F.13);;
gap> SetConjugate(coll, 11, 9, F.11*F.13*F.14);;
gap> SetConjugate(coll, 12, 4, F.12*F.13*F.14);;
gap> SetConjugate(coll, 12, 5, F.12*F.14);;
gap> SetConjugate(coll, 12, 6, F.12*F.13*F.14);;
gap> SetConjugate(coll, 12, 7, F.12*F.14);;
gap> SetConjugate(coll, 13, 1, F.14);;
gap> SetConjugate(coll, 13, 2, F.14);;
gap> SetConjugate(coll, 13, 3, F.13*F.14);;
gap> SetConjugate(coll, 14, 1, F.13);;
gap> SetConjugate(coll, 14, 2, F.13);;
gap> SetConjugate(coll, 14, 3, F.13);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);