Finite Group Databasebeta

?

← Prev (#72321184) Next (#72321186) →

#72321185

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

Aliases

No aliases for this group.

Subgroups

1722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=h,b^2=e,c^2=f,d^2=f,e^2=j,h^2=i,i^2=j,b^a=bhij,d^a=dfg,d^b=dfg,d^c=dei,e^a=ej,g^c=gj,h^b=hi,i^b=ij

Conjugacy classes & character table

112 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.8);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 5, F.10);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);