Finite Group Databasebeta

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#72318988

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

Aliases

No aliases for this group.

Subgroups

998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,b^2=f,c^2=eh,e^2=h,f^2=i,i^2=j,b^a=bi,c^b=cfij,d^a=dg,d^b=dh,d^c=dj,e^b=ej,f^a=fj,f^c=fi,i^c=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.5);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.5*F.8);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, 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.6*F.9*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);