Finite Group Databasebeta

?

← Prev (#72309670) Next (#72309672) →

#72309671

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

Aliases

No aliases for this group.

Subgroups

2527 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=h,c^2=f,d^2=g,e^2=h,g^2=i,i^2=j,b^a=bj,d^a=dg,d^c=di,e^b=eh,f^d=fj,g^a=gi,g^c=gj,i^a=ij

Conjugacy classes & character table

115 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, 1, F.6);;
gap> SetPower(coll, 2, F.8);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);