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#72225784

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

Aliases

No aliases for this group.

Subgroups

At least 7042 conjugacy classes of subgroups; only the 4388 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

(6,10)(18,20);(1,2)(3,4)(5,6,8,12,9,10,15,17)(7,11,13,18,14,16,19,20);(6,10)(11,16);(2,4);(5,7)(6,11)(8,13)(9,14)(10,16)(12,18)(15,19)(17,20)

Polycyclic presentation:

2^11|b^2=f,f^2=k,b^a=bg,c^b=ch,d^b=di,e^a=ej,f^a=fj,f^c=fj,g^b=gj,g^e=gk,g^f=gk,h^b=hj,h^f=hk,j^b=jk

Conjugacy classes & character table

200 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.6);;
gap> SetPower(coll, 6, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 5, F.7*F.11);;
gap> SetConjugate(coll, 7, 6, F.7*F.11);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 6, F.8*F.11);;
gap> SetConjugate(coll, 10, 2, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);