Finite Group Databasebeta

?

← Prev (#72250009) Next (#72250011) →

#72250010

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

Aliases

No aliases for this group.

Subgroups

2367 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=f,c^2=g,d^2=h,g^2=i,i^2=j,c^a=cg,c^b=ci,d^a=df,d^c=de,e^a=ej,f^c=fj,g^a=gi,g^b=gj,i^a=ij

Conjugacy classes & character table

112 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.6);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 4, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);