Finite Group Databasebeta

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#72250180

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

Aliases

No aliases for this group.

Subgroups

5761 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=f,d^2=gij,e^2=i,g^2=ij,i^2=j,c^a=cfh,c^b=cfh,d^a=de,d^b=degi,e^a=ei,e^b=ej,e^c=ej,f^d=fj,g^a=gij,g^b=gj,i^a=ij

Conjugacy classes & character table

106 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);;
gap> SetPower(coll, 4, F.7*F.9*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 7, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.7*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);