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#72340336

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

Aliases

No aliases for this group.

Subgroups

4442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 32 points:

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

Polycyclic presentation:

2^10|b^2=f,c^2=fghi,b^a=bg,c^a=cgh,c^b=cfg,d^a=di,d^b=di,e^b=eh,e^c=egj,f^a=fi,f^c=fi,f^e=fj,g^b=gi,g^c=gj,h^b=hj,h^c=hij

Conjugacy classes & character table

61 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, 2, F.6);;
gap> SetPower(coll, 3, F.6*F.7*F.8*F.9);;
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.6*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);