Finite Group Databasebeta

?

← Prev (#72257247) Next (#72257249) →

#72257248

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

Aliases

No aliases for this group.

Subgroups

3038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=h,d^2=fghj,e^2=i,h^2=j,i^2=j,b^a=bg,c^a=ce,d^a=dgij,d^b=dhij,d^c=df,e^a=ei,e^c=eij,e^d=ej,f^d=fj,g^d=gj,h^c=hj,i^a=ij,i^c=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.6*F.7*F.8*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 8, 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.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.6);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, 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.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);