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#72262712

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

Aliases

No aliases for this group.

Subgroups

3079 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=hj,c^2=i,b^a=be,c^a=cfg,c^b=ceh,d^b=dgi,e^a=eh,e^b=ej,e^c=ej,e^d=ei,f^b=fh,f^c=fi,f^e=fj,g^a=gi,g^c=gi,h^a=hj,h^c=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.6);;
gap> SetPower(coll, 2, F.8*F.10);;
gap> SetPower(coll, 3, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.6*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.5*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);