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#72257138

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

Aliases

No aliases for this group.

Subgroups

4290 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)(7,12,18,27,17,23,31,34)(8,19,20,29,16,13,28,30)(15,25,32,35,21,26,33,36);(12,23)(25,26)(27,34)(35,36);(2,4)(6,11)(7,15)(8,20)(9,22)(12,25)(13,29)(16,28)(17,21)(18,33)(19,30)(23,26)(27,36)(31,32)(34,35);(2,4)(5,7,16,15,22,31,20,33,10,17,8,21,9,18,28,32)(6,12,13,25,24,34,29,36,11,23,19,26,14,27,30,35)

Polycyclic presentation:

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

Conjugacy classes & character table

88 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, 4, F.5*F.7*F.10);;
gap> SetPower(coll, 5, F.9*F.10);;
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.6*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
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, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, 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);