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#72233166

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

Aliases

No aliases for this group.

Subgroups

4220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=j,b^2=gj,b^a=bg,c^a=cgh,c^b=cgj,d^a=de,d^b=dej,d^c=df,e^b=eh,e^c=ehi,f^a=fij,f^b=fij,f^e=fj,g^d=gh,i^d=ij

Conjugacy classes & character table

58 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.10);;
gap> SetPower(coll, 2, F.7*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.7*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.9*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, 4, F.7*F.8);;
gap> SetConjugate(coll, 9, 4, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);