Finite Group Databasebeta

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#72257378

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

Aliases

No aliases for this group.

Subgroups

2293 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

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

Polycyclic presentation:

2^10|b^2=g,c^2=h,d^2=eghj,e^2=ij,g^2=j,i^2=j,b^a=bf,d^a=dfghi,d^b=de,d^c=dij,e^b=ei,e^c=ej,e^d=ej,f^d=fj,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, 2, F.7);;
gap> SetPower(coll, 3, F.8);;
gap> SetPower(coll, 4, F.5*F.7*F.8*F.10);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.7*F.8*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
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);