Finite Group Databasebeta

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#72287668

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

Aliases

No aliases for this group.

Subgroups

2504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 40 points:

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

Polycyclic presentation:

2^10|b^2=e,c^2=ehj,d^2=ej,e^2=i,h^2=j,i^2=j,c^b=cj,d^a=df,d^b=dfg,d^c=dfhj,h^d=hj

Conjugacy classes & character table

208 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, 2, F.5);;
gap> SetPower(coll, 3, F.5*F.8*F.10);;
gap> SetPower(coll, 4, F.5*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.6*F.8*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);