Finite Group Databasebeta

?

← Prev (#72320101) Next (#72320103) →

#72320102

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

Aliases

No aliases for this group.

Subgroups

3760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=h,b^2=f,d^2=f,g^2=i,i^2=j,c^b=cg,d^a=dh,d^c=dij,e^c=ej,e^d=ej,f^c=fj,g^b=gi,g^c=gij,g^d=gj,i^b=ij,i^c=ij

Conjugacy classes & character table

124 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.8);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);