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#72311403

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

Aliases

No aliases for this group.

Subgroups

5693 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=hj,c^2=i,e^2=f,g^2=j,h^2=j,b^a=bghj,c^a=cgj,c^b=cg,d^b=dj,e^a=ef,e^b=efghj,e^c=ei,f^b=fi,g^c=gj,h^c=hj,h^e=hi

Conjugacy classes & character table

100 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.10);;
gap> SetPower(coll, 3, F.9);;
gap> SetPower(coll, 5, F.6);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.8*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.6);;
gap> SetConjugate(coll, 5, 2, F.5*F.6*F.7*F.8*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 8, 5, F.8*F.9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);