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#72308512

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

Aliases

No aliases for this group.

Subgroups

4953 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 40 points:

(1,2)(3,7)(4,6)(5,8)(9,10,12,18,15,16,14,29)(11,20,21,36,23,35,24,37)(13,26,25,31,28,40,27,19)(17,32,33,22,30,38,34,39);(1,3)(2,5)(4,8)(6,7);(2,6)(5,7);(10,16)(17,30)(18,29)(19,31)(20,35)(26,40)(33,34)(36,37);(3,8)(5,7)(9,11,13,22,14,21,27,38,15,23,28,39,12,24,25,32)(10,17,19,20,18,34,26,37,16,30,31,35,29,33,40,36)

Polycyclic presentation:

2^10|a^2=f,e^2=h,f^2=j,h^2=i,i^2=j,b^a=bg,c^a=cg,d^a=dj,e^a=eh,e^b=eg,f^e=fj,h^a=hi,i^a=ij

Conjugacy classes & character table

160 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, 5, F.8);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.7);;
gap> SetConjugate(coll, 6, 5, F.6*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);