Finite Group Databasebeta

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#72308630

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

Aliases

No aliases for this group.

Subgroups

5742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^10|a^2=g,b^2=g,c^2=g,d^2=g,e^2=hi,i^2=j,c^b=cj,d^a=df,d^b=dfgh,d^c=dg,e^a=ei,e^b=egh,e^d=egj,i^a=ij

Conjugacy classes & character table

106 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.7);;
gap> SetPower(coll, 3, F.7);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8*F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 3, 2, F.3*F.10);;
gap> SetConjugate(coll, 4, 1, F.4*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.6*F.7*F.8);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 5, 1, F.5*F.9);;
gap> SetConjugate(coll, 5, 2, F.5*F.7*F.8);;
gap> SetConjugate(coll, 5, 4, F.5*F.7*F.10);;
gap> SetConjugate(coll, 9, 1, F.9*F.10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);