Finite Group Databasebeta

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#72307213

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

Aliases

No aliases for this group.

Subgroups

1401 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 40 points:

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

Polycyclic presentation:

2^10|a^2=ghj,c^2=f,d^2=h,e^2=i,f^2=i,i^2=j,c^a=ce,c^b=cd,d^a=dg,d^b=dh,e^a=ei,e^b=egj,e^d=ej,f^a=fi,f^b=fh,g^c=gj,i^a=ij

Conjugacy classes & character table

79 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.7*F.8*F.10);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.8);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.4);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
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);