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#72266716

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

Aliases

No aliases for this group.

Subgroups

3679 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,c^2=g,b^a=be,c^a=cg,c^b=cf,d^a=dj,e^a=ei,e^c=eh,f^a=fhij,f^c=fi,f^e=fj,g^b=gi,h^b=hj

Conjugacy classes & character table

64 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, 3, F.7);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);