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#72310366

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

Aliases

No aliases for this group.

Subgroups

3853 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 20 points:

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

Polycyclic presentation:

2^10|a^2=e,b^2=degj,d^2=j,e^2=j,b^a=bd,c^b=cf,d^a=dh,d^b=dhj,d^c=di,e^b=ehj,f^a=fij,f^b=fi,f^d=fj,f^e=fj,h^c=hj,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.5);;
gap> SetPower(coll, 2, F.4*F.5*F.7*F.10);;
gap> SetPower(coll, 4, F.10);;
gap> SetPower(coll, 5, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.4);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);