Finite Group Databasebeta

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#72322902

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

Aliases

No aliases for this group.

Subgroups

4267 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

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

Polycyclic presentation:

2^10|a^2=h,b^2=f,d^2=g,e^2=i,f^2=j,h^2=i,i^2=j,b^a=bhij,c^a=cg,d^a=dfi,d^b=dg,d^c=dg,e^b=ei,f^a=fj,h^b=hi,h^d=hj,i^b=ij

Conjugacy classes & character table

112 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.8);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 6, 1, F.6*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);