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#72309496

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

Aliases

No aliases for this group.

Subgroups

4311 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Polycyclic presentation:

2^10|a^2=h,b^2=f,c^2=j,e^2=fj,g^2=i,h^2=j,b^a=bh,c^b=cj,d^a=di,d^b=di,d^c=dg,e^a=ej,e^b=ej,e^d=ei,g^c=gi,g^d=gi,h^b=hj

Conjugacy classes & character table

124 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);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.10);;
gap> SetPower(coll, 5, F.6*F.10);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);