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#72286901

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

Aliases

No aliases for this group.

Subgroups

2437 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=efj,c^2=g,d^2=hij,f^2=j,h^2=ij,i^2=j,b^a=be,c^b=ci,d^b=dh,d^c=dj,g^b=gj,h^b=hi,i^b=ij

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