Finite Group Databasebeta

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#72308369

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

Aliases

No aliases for this group.

Subgroups

5811 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=f,d^2=ghij,e^2=h,i^2=j,b^a=bf,c^a=cf,c^b=cfg,d^a=dfij,d^b=dfgh,d^c=dhj,e^b=egj,e^c=ehj,e^d=ehj,i^a=ij

Conjugacy classes & character table

118 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.6);;
gap> SetPower(coll, 4, F.7*F.8*F.9*F.10);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.6*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.6*F.9*F.10);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.8*F.10);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.10);;
gap> SetConjugate(coll, 5, 3, F.5*F.8*F.10);;
gap> SetConjugate(coll, 5, 4, F.5*F.8*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);