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#72262518

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

Aliases

No aliases for this group.

Subgroups

3595 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=g,b^a=bghij,c^a=cf,c^b=ce,d^a=dg,d^b=dj,e^a=eh,e^b=ei,f^a=fi,f^b=fhi,f^d=fi,f^e=fj,g^c=gi,h^c=hj

Conjugacy classes & character table

58 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, 2, F.7);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 6, 2, F.6*F.8*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.9);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);