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#72233007

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

Aliases

No aliases for this group.

Subgroups

2507 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 32 points:

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

Polycyclic presentation:

2^10|a^2=f,b^2=eg,c^2=dgij,b^a=be,c^a=cd,c^b=cdefg,d^a=dh,d^b=dhi,e^a=ehj,e^c=eij,e^d=ej,f^b=fhj,f^c=fh,g^a=ghj,g^c=gj,i^a=ij,i^b=ij,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, 2, F.5*F.7);;
gap> SetPower(coll, 3, F.4*F.7*F.9*F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.4);;
gap> SetConjugate(coll, 3, 2, F.3*F.4*F.5*F.6*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.8*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.8*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.8*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);