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#72250353

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

Aliases

No aliases for this group.

Subgroups

2098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=h,c^2=h,d^2=e,e^2=i,i^2=j,b^a=bg,d^a=df,d^b=de,d^c=di,e^a=eh,e^b=ei,e^c=ej,f^b=fhj,f^d=fh,f^e=fj,h^d=hj,i^b=ij

Conjugacy classes & character table

70 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.8);;
gap> SetPower(coll, 3, F.8);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
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.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.8*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.8);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);