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#72251876

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

Aliases

No aliases for this group.

Subgroups

4055 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,c^2=g,g^2=j,b^a=bfhij,c^a=ce,c^b=chj,d^a=di,d^c=dgj,e^a=eh,e^b=ehj,e^c=ei,e^d=ei,f^c=fh,g^a=gi,g^d=gj,g^e=gj,i^c=ij

Conjugacy classes & character table

64 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.6);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 7, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6*F.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.8*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.7*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 7, 5, F.7*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);