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#72233489

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

Aliases

No aliases for this group.

Subgroups

3236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=g,c^2=hi,e^2=i,c^a=cghi,c^b=cj,d^a=de,d^b=dei,d^c=def,e^c=eh,e^d=ei,f^a=fhi,f^b=fhj,f^c=fhi,f^d=fj,f^e=fj,g^d=gi,h^d=hj

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