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#72277909

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

Aliases

No aliases for this group.

Subgroups

3217 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=hij,c^2=j,e^2=i,c^a=ce,c^b=cef,d^b=dhij,d^c=di,e^a=ej,e^b=eh,e^c=ei,f^a=fh,f^b=fhi,f^c=fj,f^d=fj,f^e=fj,g^c=gij,h^c=hj

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