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#72321897

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

Aliases

No aliases for this group.

Subgroups

3796 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=fj,c^2=g,d^2=g,e^2=ij,f^2=j,i^2=j,c^a=cg,c^b=cg,d^a=dh,d^b=dg,d^c=dfij,e^a=eij,e^b=ej,h^c=hj,i^a=ij

Conjugacy classes & character table

112 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.6);;
gap> SetPower(coll, 2, F.6*F.10);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);