Finite Group Databasebeta

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#72265488

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

Aliases

No aliases for this group.

Subgroups

2985 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=f,d^2=g,g^2=i,i^2=j,d^a=dh,d^b=dg,d^c=dhj,e^a=eh,e^c=ej,f^d=fj,g^b=gi,i^b=ij

Conjugacy classes & character table

130 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.6);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);