Finite Group Databasebeta

?

← Prev (#72279259) Next (#72279261) →

#72279260

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

Aliases

No aliases for this group.

Subgroups

2989 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=d,c^2=e,d^2=i,g^2=j,h^2=j,c^a=cg,c^b=cf,d^c=dh,e^a=ej,f^a=fj,g^a=gh,g^b=gj,g^d=gij,h^a=hi,h^c=hj,h^g=hj,i^c=ij

Conjugacy classes & character table

82 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.4);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 4, F.9);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.8);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 8, 7, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);