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#72257448

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

Aliases

No aliases for this group.

Subgroups

2074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=fi,c^2=h,d^2=e,e^2=i,i^2=j,b^a=bf,c^b=cfg,d^a=dghj,d^b=dgh,d^c=de,e^c=ei,f^d=fj,g^b=gj,g^d=gj,h^d=hj,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.6*F.9);;
gap> SetPower(coll, 3, F.8);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.7*F.8*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.7*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.5);;
gap> SetConjugate(coll, 5, 3, F.5*F.9);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, 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, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);