Finite Group Databasebeta

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#72321882

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

Aliases

No aliases for this group.

Subgroups

2809 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 40 points:

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

Polycyclic presentation:

2^10|b^2=g,e^2=fh,f^2=hj,g^2=i,h^2=j,b^a=bh,c^b=ci,d^b=dj,e^a=ef,e^b=ej,f^a=fh,g^a=gj,h^a=hj

Conjugacy classes & character table

172 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.7);;
gap> SetPower(coll, 5, F.6*F.8);;
gap> SetPower(coll, 6, F.8*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);