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#72334347

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

Aliases

No aliases for this group.

Subgroups

66592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

(1,2)(3,4)(5,6,7,8)(11,15)(13,16)(17,18,20,22)(19,23,24,21);(1,2)(3,4)(5,6)(7,8)(9,10,12,14)(11,16,15,13)(19,24)(21,23);(1,2,3,4)(5,6,7,8)(9,11,12,15)(10,13,14,16)(17,18)(19,23)(20,22)(21,24);(2,4)(10,14)(13,16);(6,8)(9,11)(10,13)(12,15)(14,16)(17,19)(18,21)(20,24)(22,23);(1,2)(3,4)(5,6)(7,8)(9,10)(11,16)(12,14)(13,15)(17,18)(19,23)(20,22)(21,24)

Polycyclic presentation:

2^10|a^2=g,b^2=j,c^2=i,b^a=bh,c^a=cgi,c^b=ci,d^a=dhij,d^b=dhi,d^c=dhij,e^a=egj,e^b=egj,e^c=egj,f^a=fg,f^b=fj,f^c=fi,f^d=fhi,f^e=fgj

Conjugacy classes & character table

154 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.10);;
gap> SetPower(coll, 3, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.9);;
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.8*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.7*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.7*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.7);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.8*F.9);;
gap> SetConjugate(coll, 6, 5, F.6*F.7*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);