Finite Group Databasebeta

?

← Prev (#72249938) Next (#72249940) →

#72249939

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

Aliases

No aliases for this group.

Subgroups

3159 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=fh,c^2=fh,d^2=egij,g^2=i,i^2=j,b^a=bf,d^a=de,d^b=dfgij,d^c=dij,e^b=ej,f^d=fj,g^b=gi,g^c=gj,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, 2, F.6*F.8);;
gap> SetPower(coll, 3, F.6*F.8);;
gap> SetPower(coll, 4, F.5*F.7*F.9*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);