Finite Group Databasebeta

?

← Prev (#72257305) Next (#72257307) →

#72257306

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

Aliases

No aliases for this group.

Subgroups

2206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=i,c^2=h,d^2=ehi,e^2=i,i^2=j,b^a=bh,c^a=cf,d^a=dj,d^b=dg,d^c=de,e^c=ei,e^d=ej,f^a=fj,g^a=gj,h^d=hj,i^c=ij

Conjugacy classes & character table

94 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.9);;
gap> SetPower(coll, 3, F.8);;
gap> SetPower(coll, 4, F.5*F.8*F.9);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);