Finite Group Databasebeta

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#72309573

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

Aliases

No aliases for this group.

Subgroups

1710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,b^2=j,c^2=e,d^2=ghj,f^2=h,g^2=i,i^2=j,b^a=bf,c^b=cfhj,d^a=dg,d^c=dhij,e^d=ej,f^a=fh,f^b=fh,f^c=fh,g^a=gi,g^c=gj,i^a=ij

Conjugacy classes & character table

79 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.5);;
gap> SetPower(coll, 2, F.10);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 4, F.7*F.8*F.10);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.8*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);