Finite Group Databasebeta

?

← Prev (#72303462) Next (#72303464) →

#72303463

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

Aliases

No aliases for this group.

Subgroups

5652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

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

Polycyclic presentation:

2^10|b^2=hi,d^2=ef,e^2=j,b^a=bh,c^a=cg,c^b=cg,d^a=dgj,d^b=dgij,d^c=de,e^c=ej,e^d=ej,f^c=fj,f^d=fj,g^b=gi,h^c=hi,h^d=hi

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