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#72225397

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

Aliases

No aliases for this group.

Subgroups

87 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 64 points:

(1,2,3,11,5,12,18,37,6,14,19,39,25,35,48,58,8,15,21,40,28,42,51,60,30,45,53,62,26,36,49,59,9,16,22,41,29,43,52,61,31,46,54,63,24,56,47,64,7,32,20,55,27,34,50,57,23,13,44,38,4,10,17,33);(2,10,13,34,32,56,46,43,16,36,45,42,15,35,14,12)(11,33,38,57,55,64,63,61,41,59,62,60,40,58,39,37)

Polycyclic presentation:

2^10|a^2=c,b^2=defgij,c^2=e,d^2=fh,e^2=g,f^2=hj,g^2=i,h^2=j,i^2=j,b^a=bd,d^a=df,f^a=fh,h^a=hj

Conjugacy classes & character table

304 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.3);;
gap> SetPower(coll, 2, F.4*F.5*F.6*F.7*F.9*F.10);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 4, F.6*F.8);;
gap> SetPower(coll, 5, F.7);;
gap> SetPower(coll, 6, 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.4);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);