Finite Group Databasebeta

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#72306573

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

Aliases

No aliases for this group.

Subgroups

1523 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=f,c^2=gh,e^2=hi,g^2=ij,h^2=j,b^a=bi,c^b=ce,d^b=dj,d^c=di,e^b=eg,e^d=ej,f^a=fj,f^c=fgh,f^e=fhi,g^b=gh,g^f=gij,h^b=hi,h^f=hj,i^b=ij

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