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#72309642

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

Aliases

No aliases for this group.

Subgroups

3448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Polycyclic presentation:

2^10|a^2=f,b^2=g,c^2=fhij,e^2=hj,g^2=i,h^2=j,i^2=j,b^a=bg,c^b=ch,d^a=dhij,d^b=dhi,e^a=ehj,e^c=ej,f^b=fj,g^a=gi,g^c=gj,h^a=hj,i^a=ij

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