Finite Group Databasebeta

?

← Prev (#72233434) Next (#72233436) →

#72233435

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

Aliases

No aliases for this group.

Subgroups

13816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

(1,2)(3,5)(4,6)(7,8)(9,10)(11,12)(13,21)(14,16)(15,24)(17,20)(18,19)(22,23);(1,2)(3,5)(4,6)(7,8)(9,11)(10,12)(13,22,24,17)(14,19)(15,23,21,20)(16,18);(1,3)(2,5)(4,7)(6,8)(9,12)(10,11)(13,23,24,20)(14,18)(15,17,21,22)(16,19);(5,8)(9,13)(10,15)(11,17)(12,20)(14,24)(16,21)(18,23)(19,22);(9,10)(11,18)(12,19)(13,15)(14,16)(17,23)(20,22)(21,24)

Polycyclic presentation:

2^10|b^2=h,c^2=h,b^a=bh,c^b=ch,d^a=dg,d^b=dgj,d^c=df,e^b=ej,e^c=ehj,f^a=fi,f^b=fij,f^c=fj,f^e=fj,g^b=gj,g^c=gi,h^d=hj

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