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#72268225

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

Aliases

No aliases for this group.

Subgroups

3929 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=g,e^2=j,f^2=j,b^a=be,c^a=cgh,c^b=ci,d^a=dgh,d^b=dghi,e^a=eh,e^b=ei,e^d=ei,f^b=fhj,f^c=fi,f^d=fi,f^e=fj,g^a=gij,h^a=hj

Conjugacy classes & character table

70 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.6);;
gap> SetPower(coll, 2, F.7);;
gap> SetPower(coll, 5, F.10);;
gap> SetPower(coll, 6, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8*F.9);;
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.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.8*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);