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#72337328

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

Aliases

No aliases for this group.

Subgroups

68417 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

Polycyclic presentation:

2^10|a^2=i,b^2=g,c^2=gh,e^2=gj,c^a=ci,c^b=ch,d^b=dhij,d^c=dhi,e^a=ei,e^b=ej,e^c=ehj,e^d=ehij,f^b=fij,f^c=fij,f^e=fij

Conjugacy classes & character table

208 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.9);;
gap> SetPower(coll, 2, F.7);;
gap> SetPower(coll, 3, F.7*F.8);;
gap> SetPower(coll, 5, F.7*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.9);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);