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#72263343

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

Aliases

No aliases for this group.

Subgroups

3253 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=hij,d^2=ij,b^a=bhj,c^a=cghi,c^b=cghi,d^a=de,d^b=def,e^a=ei,e^b=eh,e^c=eij,f^a=fhi,f^b=fh,f^d=fj,f^e=fj,g^d=gi,h^d=hj

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