Finite Group Databasebeta

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#72286271

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

Aliases

No aliases for this group.

Subgroups

1983 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=d,h^2=j,b^a=bi,c^a=cf,c^b=ce,e^a=ej,f^a=fh,g^b=gj,g^c=ghj,g^f=gij,h^a=hi,h^c=hj,h^f=hj,h^g=hj,i^a=ij,i^c=ij

Conjugacy classes & character table

76 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.7);;
gap> SetPower(coll, 2, F.4);;
gap> SetPower(coll, 8, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.9);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.5);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 6, 1, F.6*F.8);;
gap> SetConjugate(coll, 7, 2, F.7*F.10);;
gap> SetConjugate(coll, 7, 3, F.7*F.8*F.10);;
gap> SetConjugate(coll, 7, 6, F.7*F.9*F.10);;
gap> SetConjugate(coll, 8, 1, F.8*F.9);;
gap> SetConjugate(coll, 8, 3, F.8*F.10);;
gap> SetConjugate(coll, 8, 6, F.8*F.10);;
gap> SetConjugate(coll, 8, 7, F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> SetConjugate(coll, 9, 3, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);