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#72262748

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

Aliases

No aliases for this group.

Subgroups

3686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=hi,e^2=i,b^a=bf,c^a=chij,c^b=ce,d^a=dg,d^c=dj,e^a=eh,e^b=ei,e^c=eij,f^c=fh,f^d=fij,f^e=fj,g^b=gij,h^b=hj

Conjugacy classes & character table

58 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, 3, F.8*F.9);;
gap> SetPower(coll, 5, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 6, 4, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);