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#72233403

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

Aliases

No aliases for this group.

Subgroups

3219 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 32 points:

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

Polycyclic presentation:

2^10|a^2=g,b^2=ghij,e^2=i,c^a=ce,c^b=cf,d^a=dghj,d^b=dij,d^c=dij,e^b=eh,e^c=ei,e^d=eij,f^a=fhj,f^b=fij,f^e=fj,g^c=gi,h^c=hj

Conjugacy classes & character table

70 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.7);;
gap> SetPower(coll, 2, F.7*F.8*F.9*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.9*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);