Finite Group Databasebeta

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#72224944

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

Aliases

No aliases for this group.

Subgroups

991 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=e,b^2=eghi,d^2=gi,e^2=h,g^2=i,h^2=j,i^2=j,b^a=bg,c^a=cf,d^a=dgi,d^b=dij,d^c=dj,e^b=ej,e^d=ej,g^a=gi,g^b=gj,i^a=ij

Conjugacy classes & character table

136 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.5);;
gap> SetPower(coll, 2, F.5*F.7*F.8*F.9);;
gap> SetPower(coll, 4, F.7*F.9);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 7, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.9);;
gap> SetConjugate(coll, 4, 2, F.4*F.9*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);