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#72319467

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

Aliases

No aliases for this group.

Subgroups

5999 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|b^2=g,c^2=f,d^2=f,f^2=i,g^2=j,j^2=k,c^a=ch,c^b=cgj,d^b=djk,e^c=eik,f^b=fk,g^c=gj,g^d=gk,j^c=jk

Conjugacy classes & character table

224 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);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 10, F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.7*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.10*F.11);;
gap> SetConjugate(coll, 5, 3, 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);