Finite Group Databasebeta

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#72250422

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

Aliases

No aliases for this group.

Subgroups

4107 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=g,d^2=ej,e^2=i,g^2=j,i^2=j,b^a=bh,c^b=ce,d^a=dghi,d^b=def,d^c=deij,e^b=ei,e^c=eij,g^c=gj,g^d=gj,h^d=hj,i^b=ij,i^c=ij

Conjugacy classes & character table

94 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, 4, F.5*F.10);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);