Finite Group Databasebeta

?

← Prev (#72321364) Next (#72321366) →

#72321365

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

Aliases

No aliases for this group.

Subgroups

2317 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,c^2=eij,d^2=f,h^2=i,i^2=j,b^a=bh,c^a=ci,c^b=cf,d^b=dg,d^c=defj,e^b=ej,g^c=gj,h^a=hi,h^b=hij,h^c=hj,i^a=ij,i^b=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, 1, F.5);;
gap> SetPower(coll, 3, F.5*F.9*F.10);;
gap> SetPower(coll, 4, F.6);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.6*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.9*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);