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#72334847

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

Aliases

No aliases for this group.

Subgroups

3037 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,c^2=f,b^a=bh,c^b=ci,d^a=dhij,d^b=df,d^c=dfi,e^a=egh,e^b=eg,e^c=ehi,e^d=ehij,f^e=fj,g^d=gj,h^c=hj,i^a=ij

Conjugacy classes & character table

82 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, 3, F.6);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.9);;
gap> SetConjugate(coll, 4, 1, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.7);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.8*F.9*F.10);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);