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#72265070

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

Aliases

No aliases for this group.

Subgroups

2566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=f,c^2=fgi,e^2=h,g^2=i,h^2=j,i^2=j,c^a=cg,c^b=ce,d^c=dhij,e^a=eh,e^b=eh,e^c=ej,f^c=fj,g^a=gi,g^b=gh,g^c=gj,h^a=hj,h^b=hj,i^a=ij,i^b=ij

Conjugacy classes & character table

106 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.6);;
gap> SetPower(coll, 3, F.6*F.7*F.9);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.8);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);