Finite Group Databasebeta

?

← Prev (#72265227) Next (#72265229) →

#72265228

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

Aliases

No aliases for this group.

Subgroups

2207 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 40 points:

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

Polycyclic presentation:

2^10|b^2=h,c^2=hij,d^2=e,e^2=i,g^2=j,h^2=j,i^2=j,b^a=bf,c^b=cg,d^a=dfghj,d^b=de,d^c=dgj,e^b=ei,e^c=ej,f^d=fj,g^b=gj,h^d=hj,i^b=ij

Conjugacy classes & character table

100 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.8);;
gap> SetPower(coll, 3, F.8*F.9*F.10);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.7*F.8*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.7*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);