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#72285519

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

Aliases

No aliases for this group.

Subgroups

4005 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=j,b^2=hj,e^2=j,b^a=bh,d^a=df,d^b=de,d^c=deg,e^a=eh,e^d=ej,f^b=fh,f^c=fhi,f^e=fj,g^a=gij,g^c=gj,h^d=hj

Conjugacy classes & character table

67 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.10);;
gap> SetPower(coll, 2, F.8*F.10);;
gap> SetPower(coll, 5, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);