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#72256372

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

Aliases

No aliases for this group.

Subgroups

3657 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=f,d^2=hi,b^a=bij,c^a=cg,c^b=ce,d^a=dh,d^b=dfj,d^c=degh,e^a=eh,e^b=ei,e^d=eh,f^c=fi,g^b=ghj,g^d=gh,g^e=gj,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, 2, F.6);;
gap> SetPower(coll, 4, F.8*F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.9*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.7*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.8*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.8);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);