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#72297582

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

Aliases

No aliases for this group.

Subgroups

23527 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=j,c^2=h,b^a=bh,c^a=cg,c^b=ch,d^a=dgi,d^b=di,d^c=dh,e^a=eh,e^c=eh,e^d=eh,f^a=fgi,f^c=fgi,f^d=fgi,f^e=fi

Conjugacy classes & character table

202 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.10);;
gap> SetPower(coll, 3, F.8);;
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.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.7*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.7*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.7*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);