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#72233273

• p-group
• nilpotent
• supersolvable
• solvable
• monomial
• stem
• rational
• ambivalent

Aliases

No aliases for this group.

Subgroups

5465 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=hij,b^2=hij,e^2=ij,c^a=ce,c^b=cef,d^a=dg,d^b=dgij,e^a=ei,e^b=eh,e^c=eij,e^d=eij,f^a=fhij,f^b=fhij,f^c=fj,f^e=fj,g^c=gij,h^c=hj

Conjugacy classes & character table

64 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.8*F.9*F.10);;
gap> SetPower(coll, 2, F.8*F.9*F.10);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.5*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.9*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);