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#72280265

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

Aliases

No aliases for this group.

Subgroups

1679 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 36 points:

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

Polycyclic presentation:

2^10|a^2=e,b^2=g,c^2=h,d^2=i,e^2=ij,f^2=j,i^2=j,b^a=bf,c^a=cd,c^b=cgh,d^b=dj,d^c=di,e^b=eh,e^c=eij,f^a=fhj,f^b=fj,f^e=fj,h^a=hj,i^c=ij

Conjugacy classes & character table

76 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.5);;
gap> SetPower(coll, 2, F.7);;
gap> SetPower(coll, 3, F.8);;
gap> SetPower(coll, 4, F.9);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.4);;
gap> SetConjugate(coll, 3, 2, F.3*F.7*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);