Finite Group Databasebeta

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#72321792

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

Aliases

No aliases for this group.

Subgroups

2580 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

148 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.9);;
gap> SetPower(coll, 3, 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, 3, 1, F.3*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, 3, 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);