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#72308407

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

Aliases

No aliases for this group.

Subgroups

2929 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,c^2=f,d^2=fghi,e^2=ij,h^2=j,b^a=bg,c^a=ch,d^a=degij,d^b=dg,d^c=dj,e^b=ei,e^d=ej,f^a=fj,g^a=gi,h^a=hj

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