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#72252618

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

Aliases

No aliases for this group.

Subgroups

2724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,h^2=i,i^2=j,b^a=bi,c^b=cg,d^a=dh,d^b=dhj,d^c=de,e^b=ej,f^d=fj,g^d=gj,h^a=hi,h^b=hij,h^d=hij,i^a=ij,i^b=ij,i^d=ij

Conjugacy classes & character table

100 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, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9);;
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.8*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.9*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.9*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);