Finite Group Databasebeta

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#72256865

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

Aliases

No aliases for this group.

Subgroups

3979 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

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

Polycyclic presentation:

2^10|b^2=f,c^2=gij,d^2=g,e^2=i,i^2=j,b^a=bg,c^a=ch,d^c=di,e^a=eg,e^b=ef,e^c=eij,e^d=ej,g^c=gj,h^b=hj,h^e=hj,i^c=ij

Conjugacy classes & character table

112 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);;
gap> SetPower(coll, 3, F.7*F.9*F.10);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.7);;
gap> SetConjugate(coll, 5, 2, F.5*F.6);;
gap> SetConjugate(coll, 5, 3, F.5*F.9*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.10);;
gap> SetConjugate(coll, 8, 2, F.8*F.10);;
gap> SetConjugate(coll, 8, 5, F.8*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);