Finite Group Databasebeta

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#72227185

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

Aliases

No aliases for this group.

Subgroups

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,5,4,6,7,8)(9,10,13,16,12,15,21,23,14,17,22,11,18,20,24,19)(26,30)(27,31,33,38)(28,35)(32,37)(34,40,39,36);(9,11,13,15,12,19,21,17,14,16,22,20,18,23,24,10)(25,26,28,30,29,32,35,37)(27,31,34,36,33,38,39,40);(9,12,14,18)(10,15,17,20)(11,19,16,23)(13,21,22,24)(25,27,26,31,28,34,30,36,29,33,32,38,35,39,37,40)

Polycyclic presentation:

2^11|a^2=d,b^2=e,c^2=fj,d^2=g,e^2=h,f^2=i,g^2=j,h^2=j,i^2=k,b^a=bhijk,c^a=cf,d^b=dj,d^c=dk,e^a=ejk,f^a=fi,i^a=ik

Conjugacy classes & character table

272 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, 1, F.4);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.6*F.10);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.8*F.9*F.10*F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.11);;
gap> SetConjugate(coll, 5, 1, F.5*F.10*F.11);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 9, 1, F.9*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);