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#72309552

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

Aliases

No aliases for this group.

Subgroups

4097 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

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

Polycyclic presentation:

2^10|a^2=g,b^2=e,c^2=i,d^2=j,b^a=bd,c^a=cf,c^b=ci,d^a=dj,d^b=dh,d^c=di,e^a=ehj,f^a=fj,f^b=fi,f^c=fj,f^d=fj,g^c=gj,i^a=ij

Conjugacy classes & character table

82 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.7);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.9);;
gap> SetPower(coll, 4, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.4);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.8*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);