Finite Group Databasebeta

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#72250656

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

Aliases

No aliases for this group.

Subgroups

2451 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,c^2=hj,d^2=fi,e^2=j,f^2=ij,i^2=j,c^a=ch,d^a=de,d^b=df,d^c=di,e^a=ej,e^c=ej,e^d=ej,f^b=fi,f^c=fj,h^d=hj,i^b=ij

Conjugacy classes & character table

94 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, 3, F.8*F.10);;
gap> SetPower(coll, 4, F.6*F.9);;
gap> SetPower(coll, 5, F.10);;
gap> SetPower(coll, 6, F.9*F.10);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 4, 2, F.4*F.6);;
gap> SetConjugate(coll, 4, 3, F.4*F.9);;
gap> SetConjugate(coll, 5, 1, F.5*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.10);;
gap> SetConjugate(coll, 6, 2, F.6*F.9);;
gap> SetConjugate(coll, 6, 3, F.6*F.10);;
gap> SetConjugate(coll, 8, 4, F.8*F.10);;
gap> SetConjugate(coll, 9, 2, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);