Finite Group Databasebeta

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#72224826

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

Aliases

No aliases for this group.

Subgroups

4669 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=h,b^2=f,c^2=g,d^2=g,h^2=i,i^2=j,c^a=chij,c^b=cf,d^a=dij,e^a=ej,e^b=ej,g^a=gj,h^c=hi,h^d=hj,i^c=ij

Conjugacy classes & character table

130 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.8);;
gap> SetPower(coll, 2, F.6);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.8*F.9*F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 1, F.4*F.9*F.10);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.10);;
gap> SetConjugate(coll, 7, 1, F.7*F.10);;
gap> SetConjugate(coll, 8, 3, F.8*F.9);;
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);