Finite Group Databasebeta

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#72250394

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

Aliases

No aliases for this group.

Subgroups

4569 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=e,c^2=j,d^2=eghi,e^2=ij,f^2=j,i^2=j,b^a=bh,c^a=ch,c^b=cej,d^a=dg,d^b=df,d^c=dej,e^c=ei,e^d=ej,f^c=fj,g^b=gj,g^c=gj,h^d=hj,i^c=ij

Conjugacy classes & character table

88 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);;
gap> SetPower(coll, 3, F.10);;
gap> SetPower(coll, 4, F.5*F.7*F.8*F.9);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.5*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);