Finite Group Databasebeta

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#72239680

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

Aliases

No aliases for this group.

Subgroups

2063 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=f,d^2=e,e^2=h,g^2=i,h^2=j,i^2=j,d^a=dg,d^b=di,d^c=dfj,e^a=ei,e^b=ej,e^c=ej,f^d=fj,g^a=gi,g^b=gj,h^a=hj,i^a=ij

Conjugacy classes & character table

130 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.6);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);