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#72303960

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

Aliases

No aliases for this group.

Subgroups

3276 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=i,c^2=hij,e^2=j,c^a=cghij,c^b=cgh,d^a=df,d^b=di,d^c=de,e^a=eh,e^b=ei,e^d=ej,f^a=fij,f^c=fhij,f^e=fj,g^d=gij,h^d=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, 2, F.9);;
gap> SetPower(coll, 3, F.8*F.9*F.10);;
gap> SetPower(coll, 5, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.7*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.9*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);