Finite Group Databasebeta

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#72308804

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

Aliases

No aliases for this group.

Subgroups

2093 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=f,b^2=e,c^2=f,e^2=h,g^2=i,h^2=j,i^2=j,b^a=bg,c^b=cfi,d^b=dhij,e^a=eh,f^b=fj,g^a=gi,g^b=ghij,g^c=gj,h^a=hj,i^a=ij

Conjugacy classes & character table

100 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);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 6, 2, F.6*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.8*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);