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#72262288

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

Aliases

No aliases for this group.

Subgroups

4924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|d^2=hij,e^2=j,c^a=cf,c^b=cg,d^a=dij,d^b=dh,d^c=de,e^a=ej,e^b=eh,e^c=ej,f^b=fi,f^d=fj,g^a=gi,g^d=gh,g^e=gj,h^c=hj

Conjugacy classes & character table

67 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, 4, F.8*F.9*F.10);;
gap> SetPower(coll, 5, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.8);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);