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#72343903

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

Aliases

No aliases for this group.

Subgroups

5378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^11|a^2=f,b^2=ik,f^2=i,h^2=jk,j^2=k,b^a=bj,c^b=cg,d^b=dh,d^c=dgik,e^b=egik,f^b=fk,h^a=hk,h^b=hj,h^d=hj,j^b=jk,j^d=jk

Conjugacy classes & character table

176 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", "k");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.6);;
gap> SetPower(coll, 2, F.9*F.11);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 8, F.10*F.11);;
gap> SetPower(coll, 10, F.11);;
gap> SetConjugate(coll, 2, 1, F.2*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.7*F.9*F.11);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.9*F.11);;
gap> SetConjugate(coll, 6, 2, F.6*F.11);;
gap> SetConjugate(coll, 8, 1, F.8*F.11);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 10, 2, F.10*F.11);;
gap> SetConjugate(coll, 10, 4, F.10*F.11);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);