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#72250913

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

Aliases

No aliases for this group.

Subgroups

2495 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 36 points:

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

Polycyclic presentation:

2^10|a^2=j,b^2=g,c^2=hi,d^2=i,h^2=j,b^a=be,c^a=cf,c^b=cd,d^a=dh,d^b=dij,e^c=ehij,e^d=ei,g^c=gj,h^a=hj,h^b=hi,h^e=hj,i^a=ij

Conjugacy classes & character table

64 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.10);;
gap> SetPower(coll, 2, F.7);;
gap> SetPower(coll, 3, F.8*F.9);;
gap> SetPower(coll, 4, F.9);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.4);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.9);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.9);;
gap> SetConjugate(coll, 8, 5, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);