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#72285098

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

Aliases

No aliases for this group.

Subgroups

4105 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=e,h^2=j,b^a=bg,c^a=cf,c^b=cd,d^a=dj,d^b=dj,e^a=eh,e^c=ej,f^b=fj,g^b=ghj,g^e=gij,h^a=hj,h^b=hi,h^e=hj,h^g=hj,i^a=ij,i^b=ij

Conjugacy classes & character table

64 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.5);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.4);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.8*F.10);;
gap> SetConjugate(coll, 7, 5, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> SetConjugate(coll, 8, 5, F.8*F.10);;
gap> SetConjugate(coll, 8, 7, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);