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#72257168

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

Aliases

No aliases for this group.

Subgroups

2065 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=h,d^2=egh,e^2=ij,f^2=j,i^2=j,c^a=cij,c^b=cg,d^a=df,d^b=dghj,d^c=de,e^a=ej,e^c=ei,f^c=fj,g^d=gj,h^c=hj,h^d=hj,i^c=ij

Conjugacy classes & character table

100 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.8);;
gap> SetPower(coll, 4, F.5*F.7*F.8);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 6, F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8*F.10);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 7, 4, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*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);