Finite Group Databasebeta

?

← Prev (#72321712) Next (#72321714) →

#72321713

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

Aliases

No aliases for this group.

Subgroups

2311 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=h,d^2=egi,h^2=ij,i^2=j,b^a=bg,c^a=ch,c^b=cf,d^a=dgh,d^b=de,d^c=dfgj,e^a=ej,e^c=ej,f^d=fj,g^d=gj,h^c=hi,h^d=hi,i^c=ij,i^d=ij

Conjugacy classes & character table

88 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, 4, F.5*F.7*F.9);;
gap> SetPower(coll, 8, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.7*F.10);;
gap> SetConjugate(coll, 5, 1, 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, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.9);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);