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#72237489

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

Aliases

No aliases for this group.

Subgroups

4325 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=f,b^a=be,c^a=cgh,d^a=di,d^b=dgh,e^a=ei,e^b=eh,e^c=eij,f^a=fh,f^d=fij,f^e=fj,g^b=gi,h^b=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.6);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 6, 4, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);