Finite Group Databasebeta

?

← Prev (#72287204) Next (#72287206) →

#72287205

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

Aliases

No aliases for this group.

Subgroups

1644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|b^2=e,c^2=eghi,d^2=gik,e^2=h,g^2=i,h^2=j,i^2=k,b^a=bf,c^b=cg,d^b=dgik,d^c=dik,e^c=ek,e^d=ek,g^b=gi,g^c=gk,i^b=ik

Conjugacy classes & character table

272 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", "k");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.5*F.7*F.8*F.9);;
gap> SetPower(coll, 4, F.7*F.9*F.11);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.9*F.11);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.11);;
gap> SetConjugate(coll, 5, 3, F.5*F.11);;
gap> SetConjugate(coll, 5, 4, F.5*F.11);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.11);;
gap> SetConjugate(coll, 9, 2, F.9*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);