Finite Group Databasebeta

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#72260743

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

Aliases

No aliases for this group.

Subgroups

4685 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=i,c^2=g,f^2=j,b^a=be,c^a=cf,d^b=dh,e^c=ei,e^d=ej,f^a=fj,f^b=fi,f^c=fi,g^a=gij,h^a=hj

Conjugacy classes & character table

100 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.9);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 6, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
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);