Finite Group Databasebeta

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#72324348

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

Aliases

No aliases for this group.

Subgroups

Only the 490 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Presentation

Polycyclic presentation:

2^13|a^2=h,c^2=ik,b^a=be,c^a=cf,d^c=dg,e^c=ei,f^a=fk,f^b=fik,f^c=fk,f^d=fj,f^e=fk,g^a=gjm,g^c=glm,g^e=gl,g^f=gm,h^c=hk,h^g=hm,i^a=ik,i^d=il,j^a=jm,j^b=jlm,j^e=jm,k^d=km,l^a=lm

Conjugacy classes & character table

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