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#72237467

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

Aliases

No aliases for this group.

Subgroups

4889 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 32 points:

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

Polycyclic presentation:

2^10|a^2=d,b^2=ef,c^2=hij,b^a=bde,c^a=cfg,c^b=cgi,d^c=dj,e^b=eh,e^c=ehi,f^a=fh,f^b=fh,f^c=fj,f^e=fj,g^a=ghj,g^b=ghi,h^b=hj,i^a=ij,i^b=ij

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