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#72231481

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

Aliases

No aliases for this group.

Subgroups

At least 10801 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 16 points:

(5,8);(9,10)(11,15,16,14)(12,13);(1,2)(3,5,7,8)(4,6)(11,14,16,15);(1,3)(2,5,6,8)(4,7)(9,11)(10,14)(12,15)(13,16)

Polycyclic presentation:

2^11|b^2=ijk,c^2=gijk,d^2=e,f^2=k,c^a=cg,d^a=de,d^b=dh,d^c=df,e^c=ei,f^b=fij,f^c=fi,f^d=fik,g^d=gi,h^b=hk,h^c=hijk,h^f=hk,j^d=jk

Conjugacy classes & character table

122 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.9*F.10*F.11);;
gap> SetPower(coll, 3, F.7*F.9*F.10*F.11);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 6, F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.6);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.9*F.11);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.11);;
gap> SetConjugate(coll, 8, 3, F.8*F.9*F.10*F.11);;
gap> SetConjugate(coll, 8, 6, F.8*F.11);;
gap> SetConjugate(coll, 10, 4, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);