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#72239249

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

Aliases

No aliases for this group.

Subgroups

2907 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

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

Polycyclic presentation:

2^10|b^2=f,c^2=g,d^2=h,g^2=i,i^2=j,b^a=bf,c^a=ce,c^b=ce,d^c=dij,e^b=ej,f^c=fj,g^d=gj,h^c=hj

Conjugacy classes & character table

160 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, 2, F.6);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 4, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);