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#72343673

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

Aliases

No aliases for this group.

Subgroups

5295 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|a^2=f,f^2=i,h^2=j,j^2=k,b^a=bjk,c^a=cg,d^a=dghjk,d^b=dhijk,e^c=egi,f^d=fk,h^a=hj,h^b=hjk,h^d=hjk,j^a=jk,j^b=jk,j^d=jk

Conjugacy classes & character table

158 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", "k");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.6);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 10, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.10*F.11);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8*F.10*F.11);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.9*F.10*F.11);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.11);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10*F.11);;
gap> SetConjugate(coll, 8, 4, F.8*F.10*F.11);;
gap> SetConjugate(coll, 10, 1, F.10*F.11);;
gap> SetConjugate(coll, 10, 2, F.10*F.11);;
gap> SetConjugate(coll, 10, 4, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);