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#72257151

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

Aliases

No aliases for this group.

Subgroups

2817 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|c^2=f,d^2=egj,g^2=ij,i^2=j,b^a=bf,c^a=ch,c^b=cf,d^a=de,d^b=dfgi,d^c=dehij,e^b=ej,f^d=fj,g^b=gi,g^c=gj,i^b=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, 3, F.6);;
gap> SetPower(coll, 4, F.5*F.7*F.10);;
gap> SetPower(coll, 7, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7*F.9);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);