Finite Group Databasebeta

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#72319016

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

Aliases

No aliases for this group.

Subgroups

5716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

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

Polycyclic presentation:

2^11|b^2=g,c^2=f,d^2=fi,f^2=i,g^2=j,j^2=k,c^b=cgjk,d^b=djk,e^a=eh,e^b=ei,e^c=ek,e^d=eik,f^b=fk,g^c=gj,g^d=gk,j^c=jk

Conjugacy classes & character table

170 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.7);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.6*F.9);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 10, F.11);;
gap> SetConjugate(coll, 3, 2, F.3*F.7*F.10*F.11);;
gap> SetConjugate(coll, 4, 2, F.4*F.10*F.11);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.11);;
gap> SetConjugate(coll, 5, 4, F.5*F.9*F.11);;
gap> SetConjugate(coll, 6, 2, F.6*F.11);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.11);;
gap> SetConjugate(coll, 10, 3, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);