Finite Group Databasebeta

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#72284889

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

Aliases

No aliases for this group.

Subgroups

5665 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=fg,d^2=i,e^2=j,b^a=bi,c^a=cf,c^b=ch,d^a=di,d^c=dgj,e^b=egj,e^d=efgj,f^b=fj,f^d=fj,g^d=gj,h^c=hj,i^c=ij

Conjugacy classes & character table

94 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, 3, F.6*F.7);;
gap> SetPower(coll, 4, F.9);;
gap> SetPower(coll, 5, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.7*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.6*F.7*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);