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#72226935

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

Aliases

No aliases for this group.

Subgroups

1860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|a^2=f,c^2=e,d^2=gi,f^2=hj,g^2=ik,h^2=j,i^2=k,b^a=bfgi,c^a=cj,c^b=cjk,d^a=dg,d^b=dg,d^c=dk,f^b=fh,g^a=gi,g^b=gi,h^b=hj,i^a=ik,i^b=ik

Conjugacy classes & character table

176 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, 1, F.6);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 4, F.7*F.9);;
gap> SetPower(coll, 6, F.8*F.10);;
gap> SetPower(coll, 7, F.9*F.11);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.6*F.7*F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.10*F.11);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.11);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.11);;
gap> SetConjugate(coll, 9, 2, F.9*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);