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#72227212

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

Aliases

No aliases for this group.

Subgroups

611 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 40 points:

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

Polycyclic presentation:

2^10|a^2=d,c^2=fi,d^2=g,e^2=hj,f^2=ij,g^2=j,i^2=j,b^a=be,c^a=cij,c^b=cf,d^b=dj,d^c=dj,e^a=eh,e^b=ehj,f^a=fj,f^b=fi,i^b=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.4);;
gap> SetPower(coll, 3, F.6*F.9);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8*F.10);;
gap> SetPower(coll, 6, F.9*F.10);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);