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#72250022

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

Aliases

No aliases for this group.

Subgroups

3772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|b^2=j,c^2=fj,d^2=efj,e^2=ij,g^2=ij,i^2=j,b^a=bh,c^a=ch,c^b=cf,d^a=dh,d^b=de,d^c=defg,e^b=ei,e^c=ej,e^d=ej,f^d=fj,g^b=gij,g^c=gj,i^b=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, 2, F.10);;
gap> SetPower(coll, 3, F.6*F.10);;
gap> SetPower(coll, 4, F.5*F.6*F.10);;
gap> SetPower(coll, 5, F.9*F.10);;
gap> SetPower(coll, 7, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.8);;
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.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.5);;
gap> SetConjugate(coll, 4, 3, F.4*F.5*F.6*F.7);;
gap> SetConjugate(coll, 5, 2, F.5*F.9);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 4, F.6*F.10);;
gap> SetConjugate(coll, 7, 2, F.7*F.9*F.10);;
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);