Finite Group Databasebeta

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#72287006

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

Aliases

No aliases for this group.

Subgroups

2556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 32 points:

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

Polycyclic presentation:

2^10|b^2=f,c^2=h,e^2=ghj,f^2=h,g^2=i,i^2=j,c^b=ci,d^b=dh,d^c=dh,e^a=ej,e^b=eg,e^c=eghij,e^d=ej,f^e=fj,g^b=gi,g^c=gij,i^b=ij,i^c=ij

Conjugacy classes & character table

136 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.8);;
gap> SetPower(coll, 5, F.7*F.8*F.10);;
gap> SetPower(coll, 6, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.8);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.7);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);