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#72344008

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

Aliases

No aliases for this group.

Subgroups

5070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|a^2=f,f^2=i,h^2=j,j^2=k,b^a=bj,c^b=cg,d^c=dgi,e^a=eh,e^b=eh,e^c=eg,e^d=ei,f^e=fk,h^a=hj,h^b=hjk,h^e=hjk,j^a=jk,j^b=jk,j^e=jk

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

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