Finite Group Databasebeta

?

← Prev (#72225715) Next (#72225717) →

#72225716

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

Aliases

No aliases for this group.

Subgroups

9478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=f,c^2=h,c^a=cfg,c^b=cg,d^a=dgi,d^b=dgh,d^c=dhj,e^a=eghi,e^b=eghi,e^c=eghi,f^d=fj,g^c=gj,h^a=hj,h^b=hj,i^a=ij,i^b=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.6);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.6*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.8*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.8*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.8*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);