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#72256041

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

Aliases

No aliases for this group.

Subgroups

3185 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2)(3,11,13,7)(4,8)(5,10)(6,9)(12,20,29,28)(14,26,30,21)(15,32,31,22)(16,24)(17,27)(18,23)(19,25);(1,3)(2,7)(4,15,16,31)(5,14)(6,13)(8,22)(9,11)(10,26)(12,17,29,18)(19,30)(20,23)(21,25)(24,32)(27,28);(1,4)(2,8)(3,12)(5,18)(6,16)(7,20)(9,24)(10,27)(11,28)(13,29)(14,31)(15,30)(17,19)(21,32)(22,26)(23,25)

Polycyclic presentation:

2^10|a^2=e,b^2=f,g^2=j,b^a=bd,c^a=cdehij,c^b=cg,d^a=dj,d^b=di,d^c=dj,e^b=ej,f^a=fi,f^c=fh,g^a=gi,g^b=ghj,g^c=gj,g^d=gj,h^a=hj,i^c=ij

Conjugacy classes & character table

64 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.6);;
gap> SetPower(coll, 7, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.4);;
gap> SetConjugate(coll, 3, 1, F.3*F.4*F.5*F.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.8*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);