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#72338796

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

Aliases

No aliases for this group.

Subgroups

4809 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|a^2=f,f^2=h,b^a=bh,c^a=ce,d^a=dh,d^c=dij,e^a=eg,e^b=ejk,f^c=fg,f^e=fi,g^a=gi,g^d=gk,g^f=gj,h^c=hj,h^e=hk,i^a=ij,i^f=ik,j^a=jk

Conjugacy classes & character table

74 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.8);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.7);;
gap> SetConjugate(coll, 5, 2, F.5*F.10*F.11);;
gap> SetConjugate(coll, 6, 3, F.6*F.7);;
gap> SetConjugate(coll, 6, 5, F.6*F.9);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.11);;
gap> SetConjugate(coll, 7, 6, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 8, 5, F.8*F.11);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 6, F.9*F.11);;
gap> SetConjugate(coll, 10, 1, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);